A national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

National Renewable Energy Laboratory 

Innovation for Our Energy Future 

Modeling and Testing of 

Unbalanced Loading and 

Voltage Regulation 

Final Report 

M.W. Davis 

DTE Energy 

Detroit, Michigan 

R. Broadwater 

Electrical Distribution Design Inc. 

Blacksburg, Virginia 

J. Hambrick 

Virginia Polytechnic Institute and State University 

Blacksburg, Virginia 

Subcontract Report 

NREL/SR-581-41805 

July 2007 

NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 
National Renewable Energy Laboratory

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Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337

Subcontract Report 

NREL/SR-581-41805 

July 2007 

Modeling and Testing of 

Unbalanced Loading and 

Voltage Regulation 

Final Report 

M.W. Davis 

DTE Energy 

Detroit, Michigan 

R. Broadwater 

Electrical Distribution Design Inc. 

Blacksburg, Virginia 

J. Hambrick 

Virginia Polytechnic Institute and State University 

Blacksburg, Virginia 

NREL Technical Monitor: Thomas Basso 

Prepared under Subcontract No. ZAT-5-32616-06 
The National Renewable Energy Laboratory is a national laboratory of the U.S. Department of Energy (DOE) managed by 

Midwest Research Institute for the U.S. Department of Energy under Contract Number DE-AC36-99GO10337. This report 

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List of Acronyms
 

ANSI American National Standards Institute 

BL beginning location 

CAP capacitor 

CC constant current 

CP constant power 

CT current transformer 

DG distributed generation/distributed generator 

DR distributed resource(s) 

EL end location 

GMD geometric mean distance 

HL heavy load 

HV high voltage 

LL light load 

LTC load tap changer/load tap-changing 

LV low voltage 

ML midlocation 

PF power factor 

VDC voltage-dependent current 

VR voltage regulator 

VRR voltage regulating relay 

VT voltage transformer 

iii 
Executive Summary 

Introduction 

A distributed generation (DG) penetration limit study (Davis 2003) indicated a range of DG 

sizes can be interconnected with a distribution circuit. The DG size limit is dependent on 

system voltage, the location of the DG on the circuit, and system protection, voltage 

regulation, and other issues related to DG and circuit characteristics. The study showed that 

the DG could be larger if it was allowed to actively regulate voltage, rather than operate at a 

fixed unity power factor. 

Fixed power factor operation of the DG has a minimum effect on the existing traditional 

voltage regulation controls of the circuit because, as the system voltage changes, the field 

current of the DG synchronous generator is adjusted to bring the kilovar output typically back 

to zero and maintain the desired kilowatt setpoint. Therefore, the only effect on the system 

voltage is the kilowatt injection at that point on the distribution circuit. However, if the DG 

synchronous machine is allowed to absorb or export volt-amperes reactive, the voltage can be 

decreased or increased at that point on the circuit, and much larger kilowatt injections—and 

thus, larger DG—can be installed on the circuit. 

A number of problems are associated with interconnecting DG with a distribution circuit. 

Some are related to circuit design and operation, and others are related to the analytical tools 

used to evaluate DG operation. Distribution circuits are primarily designed for radial, oneway power flow, and distribution line voltage regulators are typically designed to regulate 

voltage based on a unidirectional flow of power. When DG is interconnected with the circuit, 

two-way flows can result. In addition, most of the load served on a distribution circuit is 

single-phase, yet most of the analytical tools used to evaluate circuit performance are based 

on balanced three-phase loads and balanced three-phase line circuit impedances. When 

balanced three-phase power flow programs are used to calculate the voltage profile on a 

distribution circuit and determine if voltage limits are being violated by DG, the accuracy of 

the service voltages at the individual single-phase loads on the single-phase laterals is a 

concern because only the three-phase portion of the circuit is modeled. American National 

Standards Institute Standard C84.1 voltage limits may be satisfied based on three-phase 

balanced load/impedance analysis, but the voltages at single-phase loads may be violated 

when the DG operates or shuts down. 

This is a significant concern for utilities because liability issues arise when customer 

equipment is damaged because of HV or LV on a circuit. Therefore, it is critical to evaluate the 

effects of DG on the distribution circuit voltage profile to ensure customers do not receive 

service voltages (at the customer billing meter) outside Range A or Range B of American 

National Standards Institute C84.1. This can be accomplished by using modeling and 

simulation tools that recognize single-phase loads, unsymmetrical distribution transformer 

connections, and unbalanced line impedances. 

iv 
Purpose

The purpose of the project is to: 

•	 Explain how voltage regulation reduces voltage spread 

•	 Define the effects of unbalanced loading and voltage on system protection and DG 

output ratings 

•	 Develop models for an actual distribution circuit, its voltage regulation equipment, 

and all the DG generator types, recognizing unbalanced loading and unbalanced 

circuit impedances 

•	 Validate these models by comparing power flow simulations and voltage profiles with 

actual measured circuit data 

•	 Determine the optimum generator operating conditions (i.e., P and Q) to provide the 

greatest improvement in released capacity, reduced energy losses, and voltage regulation 

•	 Determine the maximum DG penetration limits with synchronous generator real and 

reactive power injections. 

Project Objectives 

The project objectives are five-fold: 

•	 To develop a load model for an actual 13.2-kV distribution circuit that represents how 

the real and reactive load on the circuit changes when the voltage is raised or lowered 

with capacitor switching, distribution line voltage regulator step changes, and load tap 

changer and DG voltage regulation 

•	 To develop models for distribution overhead and underground circuit line elements, 

transformers, shunt capacitors, step voltage regulators, and synchronous, induction, 

and inverter DG generators 

•	 To verify the models by comparing the power flow simulated data with actual circuit 

measured data 

•	 To determine the maximum DG size that can be interconnected with the circuit 

•	 To determine the optimum generator operating conditions for maximum released
 

capacity savings, reduced energy losses, and voltage regulation improvement. 

Project Results 

•	 The circuit load was modeled using constant current, constant power, and a voltagedependent current. The voltage-dependent current model best represented the load 

characteristics of the circuit, with a variance of only 2%. The constant current model 

had a variance of 3.9%, and the constant power model, which is typically used, had a 

variance of 12.5%. 

v 
The voltage-dependent current model that best represents how the load changes with 

changes in source voltage is: 

%ΔP

 = 1.26

%ΔV
 

%ΔQ = 4.66.

%ΔV 

•	 During heavy load conditions when all voltage regulation equipment was turned on, 

the circuit tag end voltage improvement was 14.87 V over only the load-tap changing 

transformer voltage. When the first step regulator was turned on, the tag end voltage 

improved 4.11 V. With the second, the voltage increased another 11.34 V. With the 

first capacitor turned on, the voltage increased only 0.97 V. When the second was 

turned on, the total voltage gain was 1.75 V. When the third was turned on, another 

1.66-V rise occurred at the tag end. It may be necessary to operate DG to absorb voltamperes reactive to prevent high voltage during light-load conditions. 

•	 The highest unbalanced voltage of 1.52% occurred during heavy load conditions with 

load tap changer regulation and one step regulator turned on. Because most 

synchronous generators trip when the unbalanced voltage is more than 3%, 

unbalanced three-phase power flow studies should always be conducted on the circuit 

to ensure unbalance does not exceed 3% at the point of interconnection (not the point 

of common coupling). Adding load tap changer regulation during heavy load 

conditions lowered the maximum unbalanced voltage to 1.44%; adding step regulators 

worsened the unbalanced voltage. This was to be expected because an increase in 

voltage causes an increase in load and unbalance. When all three capacitors were 

turned on, the maximum unbalanced voltage was reduced to 1.31%. Turning all 

regulation on lowered the maximum unbalanced voltage to 1.31%. The 13-utility 

unbalanced voltage survey showed a maximum measured voltage unbalance of 5.94%. 

The high imbalances occurred on open delta transformer connections. 

•	 The highest voltage unbalance during light-load conditions was 1.26%. 

•	 At many locations on the circuit, the current imbalance exceeded 20%. Most 

synchronous machines trip at 10%–20% current imbalance; therefore, studies must 

determine the current imbalance at the location where the DG is to be sited. 

Otherwise, it may never operate without tripping. The load imbalance at the substation 

reached 4% at heavy load and 6% at light load. 

•	 The causes of unbalanced voltage and current and how unbalanced conditions affect 

protective relaying are described. The neutral relay is set to trip for ground faults, and 

the trip value may have to be increased to account for increased neutral current 

because of unbalance. 

•	 Significant unbalanced loading can occur even though voltages are balanced at the 

source. Reclosers and the substation breaker with ground fault-sensing circuits are 

affected by load imbalance. Unequal single-phase load connected line-to-line does not 

produce neutral current in the ground relay. 

vi 
•	 Fuse preload because of unbalanced loading can cause fuses to become unselective 

with other protective devices such as reclosers and lead to misoperation. 

•	 Reducing unbalanced loading reduces the losses created by the neutral current in the 

neutral conductor. 

•	 Unbalanced three-phase voltages have a significant effect on the heating of induction 

and synchronous generators. For example, a 5.5% voltage unbalance can cause an 

approximate 25% increase in temperature. The phase currents with unbalanced 

voltages are greatly unbalanced, on the order of four to five times the voltage 

unbalance. If overload relay protection settings are raised because of unbalance, the 

generator may not be protected against overload and open phases. 

•	 Heating of induction generators because of voltage unbalance is affected by phase 

rotation because it affects which phase has the highest line currents. This means that 

negative sequence current protection must be used to protect the induction generator 

from failure because of voltage unbalance. The negative sequence losses are 

proportional to the square of the negative sequence voltage. The generator may have 

to reduce output below nameplate rating to avoid overheating with voltage unbalance. 

An equation was developed to determine machine rating under unbalanced voltages if 

one knows the unbalanced voltage and the ratio of the positive-to-negative sequence 

impedances of the induction generator. A 5% voltage unbalance causes a 3.2%–10.7% 

power output derate, depending on the positive-to-negative sequence impedance ratio. 

•	 Models were developed for: 

o	 Line impedance 

o	 Line voltage drop 

o	 Line loss (which was validated using unbalanced and balanced line 

configurations and unbalanced and balanced load conditions) 

o	 Transformers for three-phase and single-phase and different loading 

combinations 

o	 Secondary and service impedances 

o	 Shunt capacitors and step regulators 

o	 Synchronous, induction, and inverter generation. 

The models were validated by measuring power quantities throughout the circuit on the 

peak day and comparing these data with simulation data. The percent variance between 

field-measured data and simulation data for phase currents at eight nodes throughout 

the circuit were within 6%. The highest phase voltage variance was only 1.5%. 

vii 
•	 The voltage spread, measured as the difference between the highest three-phase 

voltage and the lowest single-phase voltage for the heavy-load condition, was 25.2 V 

with no regulation at the substation and on the distribution circuit. When all regulation 

was implemented, the voltage spread was reduced to only 10.4 V, and there were no 

voltage criteria violations. For the light-load condition, the voltage spread was 16.65 V 

for no regulation. With all regulation operating, the spread was only 2.91 V. 

•	 The load imbalance at the substation was 4% for heavy load and 5.45% for light load. 

Adding step regulators always worsened the voltage unbalance because of the effect of 

the voltage-dependent current model. 

•	 Three voltage control strategies were tested for the 400-kW induction generator at low 

and high substation primary voltage, for a total of six simulations. Three voltage 

control strategies were tested for the 400-kW inverter-based generation at low and 

high substation primary voltage, for a total of six simulations. Thirteen voltage control 

strategies were tested for high voltage, and 13 were tested for low voltage, for the 

synchronous generator at the beginning, mid-, and end locations of the circuit, for a 

total of 78 simulations. The maximum released capacity of 10.44% was achieved with 

the 1,000-kW synchronous generator with P = 100% and Q = 100%. The voltage 

improvement was 0.82%, and the loss reduction was 0.56% out of a 5.4% base. 

•	 The optimum location for the DG with the highest released capacity of 10.44% is at 

the source of the circuit because it directly offsets the load current and load losses of 

the circuit. The optimum DG location for loss reduction is at the end of the circuit. 

Adding generation here reduces, on a prorata basis, the load and the length of the 

circuit. To improve voltage regulation, there is little difference between locating the 

DG at the midpoint or end of the circuit. However, there is a slightly better 

improvement at the midpoint for circuits on which the conductor size of the entire 

three-phase backbone is the same. 

•	 The DG penetration study showed synchronous DG had a real power limit of 13,980 

kW at the tag end of the circuit. The optimum location was at the midpoint, with the 

lowest single-phase voltage improvement of 1.7% and a real power loss savings of 

2.04%. The base case real power losses were 5.4%. The DG penetration study found 

that the maximum real and reactive power output limit was 14,490 kW and 2,007 

kVAr, which allows a larger DG to be installed than when only real power is injected. 

Again, the optimum location was at the midpoint of the circuit. However, in this case, 

the lowest single-phase voltage was improved 4.55% versus only 1.7% in the real 

power limit case. The real power loss savings were marginally better, with a 2.3% 

savings versus 2.04%. 

Conclusions 

•	 The voltage-dependent current model best represents how the real and reactive 

components of the load change with changes in voltage. This model, which had an 

error of only 2%, should always be used in lieu of the constant power model, which 

had an error of 12.5%. 

viii 
•	 Heavy-load conditions produce the highest voltage unbalance, and adding a load tap 

changer and one step voltage regulator caused the maximum percent voltage 

unbalance to be 1.52%. The typical limit for voltage unbalance is 3%. It is 

recommended that a three-phase unbalanced power flow study be conducted on a 

circuit before a synchronous generator is installed because the unit may be installed at 

a location where the voltage unbalance causes the unit to trip. In this case, it will never 

operate at that location. Furthermore, the current imbalance cannot exceed 10%–20%, 

or the synchronous DG will trip. There were many locations on the distribution circuit 

at which the current imbalance exceeded 20%. Inverter-based generation was not 

sensitive to voltage or current unbalance and operated up to 100% current imbalance. 

•	 The models developed for the line elements, distribution equipment, and generation 

and the simulations conducted during peak load conditions compared favorably with 

the actual phase currents, phase voltages, and power factors measured at eight 

locations throughout the circuit. However, it is essential to know the phasing of the 

loads on the circuit to obtain this high degree of accuracy. The variance between 

simulated and measured data was less than 6% for phase currents and did not exceed 

1.5% for phase voltages. These low variances indicate the models are accurate enough 

to represent actual circuit operation under unbalanced load conditions. The only 

measured circuit data needed to perform accurate simulations are the phase voltages 

and currents at the source of the circuit and the regulator, capacitor, and DG locations. 

•	 Unbalanced load can cause neutral relaying trip settings to be increased and
 

preloading on fuses, which results in inselectivity with other protective devices. 

•	 Unbalanced voltage can derate the output of synchronous and induction generators up 

to 10.7%. 

•	 The optimum location of DG on a circuit for the highest released capacity of 10.44% is 

at the source of the circuit. The greatest loss reduction of 0.56% occurs when the DG is 

located at the tag end of the circuit. There is little difference between locating the DG at 

the midpoint or the tag end for the greatest improvement in voltage regulation. 

•	 The maximum DG real and reactive output was 14,490 kW and 2,007 kVAr, and 

the optimum location was at the midpoint of the circuit. The real power loss savings 

were 2.3% versus the base case of 5.4%. The lowest single-phase voltage was 

improved 4.55%. 

Recommendations 

•	 Always model distribution circuit loads with a voltage-dependent current, and use a 

validated unbalanced three-phase power flow to determine the percent unbalanced 

load and voltage during the peak load and at the locations where DG is planned. Using 

a balanced three-phase power flow or simplified single-phase power flow will not 

indicate the unbalanced load and voltage at locations where DG is planned. A location 

may be selected where a synchronous or induction generator may never operate 

because of circuit unbalance conditions. 

ix 
Successful modeling of a distribution circuit using an unbalanced three-phase power 

flow requires knowledge of which phases the loads are connected to. Otherwise, 

incorrect unbalanced load and voltage data will result. The use of three-phase metering 

is not warranted because the highest load imbalance occurs during light load and the 

highest unbalanced voltage occurs during heavy load. It is not practical to install 

metering at various locations throughout the circuit to capture light and heavy load 

unbalanced power quantities over a long period of time (such as a year) when 

simulations can produce similar information with nearly the same accuracy in 

considerably less time. 

•	 The optimum voltage regulation method for the least voltage spread used the 

substation transformer load tap changer, step regulators, capacitors, and DG. The 

maximum released capacity is achieved when the DG is located at the beginning of the 

circuit, the maximum loss reduction is achieved at the end, and the best voltage 

regulation occurs at the middle. It is recommended that the DG be located at the 

midpoint of the circuit to produce the best overall improvements in voltage regulation, 

loss reduction, and released capacity. 

•	 The circuit selected had voltage unbalance conditions that closely agreed with the 

average voltage unbalance measurements taken at 13 major utilities. Therefore, the 

results should be representative of the average distribution circuit. 

It was shown that single-phase DG connected to the appropriate phases can improve 

the phase unbalanced conditions. Simulation studies can be used to determine to which 

phases to connect single-phase DG. 

•	 Voltage regulation and system protection issues are the most difficult for 

interconnecting DG with a distribution circuit. It is recommended that inverter-based 

generation be considered as the preferred DG type where the level of unbalanced 

voltage and current may prevent synchronous and induction generators from operating 

on the circuit. 

•	 It is recommended that future research develop an optimal control algorithm to control 

the substation transformer load tap changer, the bidirectional step regulators, the 

switched capacitors, and the DG. This could be accomplished for less than $500,000 

because the equipment is already installed on the Milford Circuit 8103. 

Benefits to California 

Test data indicate the models developed for this project accurately represent the operation of a 

distribution circuit. Applying these models results in DG siting that ensures the DG will 

perform its intended function and produce the highest released capacity savings, lowest 

energy losses, and improved voltage regulation. 

x 
Table of Contents 

1 Introduction........................................................................................................................................... 1
 

2 Project Approach ................................................................................................................................. 2
 

3 Project Results: Traditional Voltage Regulation Methods............................................................... 3 

3.1 Introduction................................................................................................................... 3 

3.2 Distributed Generation Installed at Substation ............................................................. 3 

3.3 Substation Voltage-Regulating Equipment................................................................... 4 

3.4 Balancing Loads............................................................................................................ 4 

3.5 Increased Primary System Voltage ............................................................................... 4 

3.6 Increased Conductor Size or Reduced Conductor Spacing........................................... 4 

3.7 Conversion of Single-Phase Sections to Three-Phase .................................................. 4 

3.8 Voltage-Regulating Equipment..................................................................................... 9 

3.9 Shunt Capacitors ......................................................................................................... 11 

3.10 Load Tap-Changing Transformers.............................................................................. 11 

3.11 Voltage Regulator Theory of Operation ..................................................................... 12 

3.12 Bridging Reactor or Preventive Autotransformer....................................................... 16 

3.13 Equalizer Windings..................................................................................................... 17 

3.14 Types of Step Regulators ............................................................................................ 19 

3.15 Bidirectional Voltage Regulator ................................................................................. 22 

3.16 Step Voltage Regulator Control System ..................................................................... 25 

3.17 Voltage and Current Equations ................................................................................... 26 

3.18 Equivalent Circuits...................................................................................................... 30 

3.19 Line Drop Compensator.............................................................................................. 30 

3.20 Regulator Ratings........................................................................................................ 32 

3.21 Closed Delta – Leading Current and Lagging Current Connections .......................... 37 

3.22 Compensator Settings ................................................................................................. 41 

3.23 Other Compensator Settings and Corrections............................................................. 44 

3.24 Step Regulators in Series ............................................................................................ 44 

3.25 Fixed Capacitors on Circuits with Regulators ............................................................ 45 

3.26 Switched Capacitors on Circuits with Regulators....................................................... 46 

3.27 Switched Capacitors Downstream from Regulators ................................................... 48 

3.28 Capacitor Application ................................................................................................. 48 

3.29 Capacitor Controls ...................................................................................................... 50 

3.30 Capacitor Connections ................................................................................................ 52 

4 Project Results – Effects of Unbalanced Loading and Voltage on System Protection and
 

Distributed Generation ...................................................................................................................... 54 

4.1 Introduction................................................................................................................. 54 

4.2 System Protection Design Philosophy for Grounded and Ungrounded Systems ....... 54 

4.2.1 Four-Wire Grounded Wye Systems................................................................ 58 

4.2.2 Three-Wire Ungrounded Delta Systems ......................................................... 58 

4.3 Unbalanced Voltage Effects on Protective Relaying.................................................. 59 

xi 
4.4 Unbalanced Current Effects on Protective Relaying .................................................. 60 

4.4.1 Single-Phase Operation of Protective Devices ............................................... 60 

4.4.2 Operation of Circuit Protective Devices for Ground Faults ........................... 61 

4.4.3 Single-Phase Operation of Disconnect and Isolation Devices........................ 62 

4.4.4 Unbalanced Load Connected Line-to-Line..................................................... 62 

4.4.5 Fuse Preload Because of Unbalanced Loading or Unbalanced Voltages ....... 64 

4.5 Unbalanced Voltage Conditions ................................................................................. 67 

4.5.1 Induction Machines Operating on Unbalanced Voltages................................ 68 

4.5.2 Synchronous Generators Operating on Unbalanced Voltages........................ 88
 

5 Project Results – Development of Models....................................................................................... 92 

5.1 Introduction................................................................................................................. 92 

5.2 Three-Phase Substation Transformer Models............................................................. 92 

5.3 Three-Phase and Single-Phase Distribution Transformer Connections for 

Distribution Circuit ..................................................................................................... 94 

5.4 Distribution Transformer Impedance.......................................................................... 97 

5.5 Distribution Transformer Voltage Drop...................................................................... 98 

5.6 Distribution Transformer Losses............................................................................... 100 

5.6.1 Load Losses................................................................................................... 100 

5.6.2 No-Load Losses ............................................................................................ 101 

5.6.3 Total Losses .................................................................................................. 101 

5.7 Line Impedance Model ............................................................................................. 102 

5.8 Line Voltage Drop Model ......................................................................................... 105 

5.9 Line Losses Model and Validation ........................................................................... 106 

5.10 Secondary and Service Impedances and Voltage Drops........................................... 124 

5.11 Secondary and Service Real Losses.......................................................................... 125 

5.12 Shunt Capacitor Models............................................................................................ 127 

5.13 Step Voltage Regulator Models ................................................................................ 130 

5.14 Synchronous Generator Model ................................................................................. 131 

5.15 Self-Excited Induction Generator Model .................................................................. 132 

5.15.1 Resistive Load............................................................................................... 133 

5.15.2 RLC Load...................................................................................................... 135 

5.16 Inverter-Based Generator Model............................................................................... 136
 

6 Project Results – Circuit Voltage Profiles Under Different Loading Conditions ....................... 139 

6.1 Introduction............................................................................................................... 139 

6.2 Circuit Simulations and Voltage Profiles.................................................................. 144 

6.2.1 Heavy Load Circuit Voltage Profiles (First Set 95% and 105% 

Primary Voltage)........................................................................................... 174 

6.2.2 Heavy Load Comparison Circuit Voltage Profiles (Second Set 95% 

Primary Voltage)........................................................................................... 182 

6.2.3 Voltage Profile Data as a Function of Distance from Substation to 

Tag End ......................................................................................................... 189 

6.2.4 Light Load Circuit Voltage Profiles (Third Set 95% and 105% 

Primary Voltage)........................................................................................... 189 

6.2.5 Light Load Comparison Circuit Voltage Profiles (Fourth Set 95% 

Primary Voltage)........................................................................................... 200 

xii 
6.3 Distribution Circuit Simulation Summary Data for Tests 1– 8................................. 206 

6.3.1 Unbalanced Voltage ...................................................................................... 206 

6.3.2 Unbalanced Loading ..................................................................................... 208 

6.4 Significant Results and Conclusions......................................................................... 208
 

7 Project Results – Design of Field Voltage Regulation and Metering Equipment ...................... 211 

7.1 Introduction............................................................................................................... 211 

7.2 Voltage Regulation Equipment................................................................................. 211 

7.3 Major System Protection Equipment ........................................................................ 213 

7.4 Metering Equipment and Accuracy of Measurements.............................................. 214 

7.4.1 Substation Metering ...................................................................................... 214 

7.4.2 Synchronous Generator Metering ................................................................. 214 

7.4.3 Capacitor Location Metering ........................................................................ 215 

7.4.4 Voltage Regulator Locations......................................................................... 215 

7.4.5 Single-Phase Voltage Customer Metering.................................................... 215
 

8 Project Results – Distributed Generation Control Strategies for Field Verification.................. 216 

8.1 Introduction............................................................................................................... 216 

8.2 1,000-kW Synchronous Generator............................................................................ 216 

8.3 400-kW High-Speed Generator and Inverter ............................................................ 216 

8.4 400-kW Self-Excited Induction Generator ............................................................... 216 

8.5 Voltage Regulation Simulations and Field Verification Strategy 17........................ 216
 

9 Project Results – Field Verification of Models .............................................................................. 223 

9.1 Introduction............................................................................................................... 223 

9.2 Circuit and Generation Measured Data..................................................................... 223 

9.3 Bidirectional Voltage Regulator Measured Data ...................................................... 225 

9.4 Circuit Equipment (Capacitors) and Customer-Measured Data ............................... 225 

9.5 Percent Variance Between Simulated and Field-Measured Data ............................. 225 

9.6 Summary of Variance Results................................................................................... 231
 

10	 Project Results – Distributed Generation Penetration Limits Using Maximum Real Power
 

and Maximum Real and Reactive Power Methods of Voltage Control ....................................... 232 

10.1 Introduction............................................................................................................... 232 

10.2 Real Power Distributed Generation Size Limitation................................................. 232 

10.3 Real and Reactive Distributed Generation Size Limitation ...................................... 234 

10.4 Findings..................................................................................................................... 234
 

11	 Project Results – Distributed Generation Voltage Regulation and Optimum Generator 

Conditions for Maximum Improvement of Voltage Regulation, Loss Reduction, and 

Released Capacity............................................................................................................................ 235 

11.1 Introduction............................................................................................................... 235 

11.2 Factors to Consider for Test Result Evaluation ........................................................ 235 

11.2.1 Regulator Dead Band .................................................................................... 235 

11.2.2 Voltage-Dependent Current Source .............................................................. 236 

xiii 
11.3 Interpreting the Distributed Generation Voltage Regulation Application Results .. 236 

11.3.1 Induction Generator Voltage Regulation Application (High Voltage) – 

Heavy Load, Table 44................................................................................... 236 

11.3.2 Inverter Generator Voltage Regulation Application (High Voltage) – 

Heavy Load, Table 45.................................................................................. 238 

11.3.3 Synchronous Generator Voltage Regulation Application (Beginning
 

Location, High Voltage) – Heavy Load, Table 46........................................ 239 

11.3.4 Synchronous Generator Voltage Regulation Application (End Location, 

High Voltage) – Heavy Load, Table 47........................................................ 239 

11.3.5 Synchronous Generator Voltage Regulation Application (Midlocation, 

High Voltage) – Heavy Load, Table 48........................................................ 240 

11.3.6 Synchronous Generator Voltage Regulation Application (Beginning
 

Location, Low Voltage) Heavy Load, Table 49 ........................................... 240 

11.3.7 Synchronous Generator Voltage Regulation Application (End Location, 

Low Voltage) – Heavy Load, Table 50......................................................... 240 

11.3.8 Synchronous Generator Voltage Regulation Application (Midlocation, 

Low Voltage) – Heavy Load, Table 51......................................................... 240 

11.4 Plotted Performance Data ......................................................................................... 249 

11.5 Findings and Conclusions ......................................................................................... 266 

11.5.1 Synchronous Generator (Low Voltage on Primary of Substation) – Heavy
 

Load Condition ............................................................................................. 266 

11.5.2 Synchronous Generator (High Voltage on Primary of Generator 

Substation) – Heavy Load Condition............................................................ 267 

11.5.3 Induction Generator for Heavy Load Condition ........................................... 268 

11.5.4 Inverter Generator for Heavy Load Condition.............................................. 269 

11.6 Optimum Generator Conditions for Maximum Improvements – Heavy
 

Load Conditions........................................................................................................ 269 

11.7 Optimum Generator Conditions for Maximum Improvements – Light 

Load Conditions........................................................................................................ 269
 

12 Conclusions and Recommendations ............................................................................................. 280 

12.1 Conclusions............................................................................................................... 280 

12.2 Recommendations..................................................................................................... 283 

12.3 Benefits to California ................................................................................................ 284
 

13 References ........................................................................................................................................ 285
 

Appendix A .............................................................................................................................................. 287 

Appendix B .............................................................................................................................................. 295 

xiv 
List of Figures
 

Figure 1. Single-phase equivalent circuit .......................................................................... 6 

Figure 2. Single-phase phasor diagram ............................................................................. 6 

Figure 3. Two-phase lateral – voltage drop for load connected from A and B to neutral. 7 

Figure 4. Two-phase lateral – voltage drop for load connected from A and C to neutral. 8 

Figure 5. VRs in series .................................................................................................... 10

Figure 6. Step-up transformer.......................................................................................... 12 

Figure 7. Step-down transformer..................................................................................... 12 

Figure 8. Step regulator ................................................................................................... 13 

Figure 9. Step VR sequence of operation........................................................................ 15 

Figure 10. Step VR with reversing switch......................................................................... 16 

Figure 11. Non-bridging no load ....................................................................................... 17 

Figure 12. Bridging position no load................................................................................. 17 

Figure 13. Non-bridging load... ........................................................................................ 17 

Figure 14. Bridging position load...................................................................................... 17 

Figure 15. Application of equalizer windings ................................................................... 18 

Figure 16. Case A – without equalizer windings............................................................... 18 

Figure 17. Case B – without equalizer windings............................................................... 18 

Figure 18. Case C – with equalizer windings bridging position ....................................... 18 

Figure 19. Case D – with equalizer windings non-bridging position................................ 19 

Figure 20. ANSI Type A – series winding located on load side ....................................... 19 

Figure 21. ANSI Type B – series winding located on source side.................................... 20 

Figure 22. DR sources create bidirectional flows through a step VR ............................... 21 

Figure 23. Reverse power flow – additional VT required VT1 ......................................... 21 

Figure 24. Reverse power flow – differential transformer ................................................ 21 

Figure 25. Examples of unidirectional VRs and DR......................................................... 23 

Figure 26. Examples of bidirectional VRs and DR........................................................... 24 

Figure 27. Control circuit of step VR................................................................................ 25 

Figure 28. Type A step regulator – raise position ............................................................. 26 

Figure 29. Type A step regulator – lower position............................................................ 26 

Figure 30. Type B regulator – raise position..................................................................... 27 

Figure 31. Type B regulator – lower position ................................................................... 29 

Figure 32. Control system and line drop compensator...................................................... 31 

Figure 33. Phasor diagram for line drop compensator ...................................................... 31 

Figure 34. Three single-phase VRs connected wye on a four-wire, three-phase circuit... 33 

Figure 35. Voltage phasor diagram of wye-connected, three single-phase VRs............... 34 

Figure 36. Two single-phase VRs connected open delta on a three-wire, 

three-phase circuit ............................................................................................ 35 

Figure 37. Voltage phasor diagram of open delta-connected two single-phase VRs....... 36 

Figure 38. Voltage diagram of closed delta-connected three single-phase VRs.............. 38 

Figure 39. Closed delta-connected three single-phase VRs – leading connection............ 39 

Figure 40. Closed delta-connected three single-phase VRs – lagging connection............ 40 

Figure 41. Current at the regulator is not equal to current in the last section before the 

regulation point ................................................................................................ 42 

xv 
Figure 42. Phasor diagram of the effect of capacitors on the line drop compensator 

and regulator output voltages before and after relay settings are revised........ 46 

Figure 43. Control system and line drop compensator with use of a shunt capacitor 

at the location of the regulator ......................................................................... 47 

Figure 44. Voltage across impedance Z in relay circuit is equal to voltage rise 

because of capacitor current Ic ......................................................................... 48 

Figure 45. Application of shunt capacitors........................................................................ 49 

Figure 46. Phasor diagram of the reduction in the sending-end voltage with a 

shunt capacitor ................................................................................................. 51 

Figure 47. Voltage and current control of capacitor switching ......................................... 51 

Figure 48. Wye-connected capacitor bank ........................................................................ 52 

Figure 49. Delta-connected capacitor bank ....................................................................... 52 

Figure 50. Series resonance condition with open phases .................................................. 53 

Figure 51. Radial distribution circuit with typical system protection devices .................. 54 

Figure 52. Radial distribution circuit showing load .......................................................... 55 

Figure 53. Radial distribution circuit showing protection zones....................................... 55 

Figure 54. Relative tripping times for protective devices ................................................. 56 

Figure 55. Relative time-current curves for protective devices......................................... 57 

Figure 56. Three-phase diagram of a four-wire grounded system .................................... 58 

Figure 57. Three-phase diagram of a three-wire ungrounded system ............................... 59 

Figure 58. Single-phase operation of protective devices on a four-wire wye circuit of 

resistive loads................................................................................................... 60 

Figure 59. Diagram of substation breaker and relays with ground-sensing circuit........... 61 

Figure 60. Current flow in phase-to-phase-connected load............................................... 63 

Figure 61. Reduced melt time because of preloading of universal K link fuses ............... 64 

Figure 62. Fuse preloading causes inselectivity ................................................................ 65 

Figure 63. Coordination of 50K and 80K fuses ................................................................ 66 

Figure 64. Inselectivity of 80K and 50K fuses for unbalanced loading of 20% ............... 67 

Figure 65. Positive and negative sequence system of voltages ......................................... 71 

Figure 66. Positive sequence equivalent circuit for induction motor/generator................ 73 

Figure 67. Positive sequence induction motor/generator equivalent circuit for 

copper losses and shaft power.......................................................................... 73 

Figure 68. Simplified positive sequence induction motor/generator equivalent circuit.... 73 

Figure 69. Slip of rotor with respect to negative sequence field and positive 

sequence field................................................................................................... 74 

Figure 70. Negative sequence equivalent circuit for induction motor/generator .............. 76 

Figure 71. Negative sequence induction motor/generator equivalent circuit for copper 

losses and shaft power...................................................................................... 76 

Figure 72. Simplified negative sequence induction motor/generator equivalent circuit 

operating at small values of slip....................................................................... 76 

Figure 73. Phasor diagram for minimum heating in Phase A, θ = 180°............................ 87 

Figure 74. Phasor diagram for maximum heating in Phase A, θ = 0° ............................... 87 

Figure 75. Round rotor synchronous machine showing negative sequence current paths 

in the rotor surface ........................................................................................... 89 

Figure 76. Typical time-current curves for the Type SGC relay....................................... 91 

Figure 77. Delta-wye-grounded three-phase transformer.................................................. 92 

xvi 
Figure 78. Four-wire, wye-grounded, overhead distribution line with multi-grounded 

neutral............................................................................................................. 103 

Figure 79. Flat line spacing configuration....................................................................... 104 

Figure 80. Configuration, Phase, and Neutral Spacings; Phase and Neutral Sizes; and 

Conductor Types ............................................................................................ 107 

Figure 81. Line transposition and load ............................................................................ 108 

Figure 82. Total line losses versus load imbalance for each line configuration.............. 118 

Figure 83. Percent losses versus load imbalance for each line configuration ................. 118 

Figure 84. Voltage imbalance versus load imbalance for each line configuration.......... 119 

Figure 85. Sequence currents versus load imbalance for each line configuration .......... 119 

Figure 86. Voltage imbalance versus current imbalance equilateral spacing line........... 120 

Figure 87. Voltage imbalance versus current imbalance non-transposed line ................ 120 

Figure 88. Voltage imbalance versus current imbalance transposed line........................ 121 

Figure 89. Sequence currents versus current imbalance equilateral-spaced line ............ 121 

Figure 90. Sequence currents versus current imbalance for non-transposed line ........... 122 

Figure 91. Sequence currents versus current substance for transposed line.................... 122 

Figure 92. Distribution transformer servicing secondaries and services......................... 124 

Figure 93. Distribution service drop................................................................................ 124 

Figure 94. Steady-state synchronous machine model ..................................................... 131 

Figure 95. Two-phase primitive machine to be interconnected with an RLC load......... 132 

Figure 96. Stator direct axis with an R load added.......................................................... 133 

Figure 97. RLC load RL, LL, and CL connected to the self-excited capacitor CS ............ 135 

Figure 98. One-line diagram of 400-kW inverter-based generator and prime mover..... 136 

Figure 99. Voltage pullback curves................................................................................. 137 

Figure 100. Inverse time-current characteristic................................................................. 138 

Figure 101. Milford Substation one-line diagram ............................................................. 140 

Figure 102. Milford Circuit DC 8103................................................................................ 142 

Figure 103. HL circuit voltage profiles for all tests 

(first set – 95% and 105% substation primary voltage) ................................. 174 

Figure 104. Test 1 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (no LTC)............................................................................................ 175 

Figure 105. Test 2 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC)................................................................................................. 176 

Figure 106. Test 3 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC and VR 1) ................................................................................ 177 

Figure 107. Test 4 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC, VR 1, and VR 2)..................................................................... 178 

Figure 108. Test 5 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC and CAP 1) .............................................................................. 179 

Figure 109. Test 6 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC, CAP 1, and CAP 2) ................................................................ 180 

Figure 110. Test 7 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC, CAP 1, CAP 2, and CAP 3).................................................... 181 

Figure 111. Test 8 HL circuit voltage profiles for 95% and 105% substation primary
 

voltage (LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3)............................... 182 

xvii 
Figure 112. Comparison A: Test 2 and Test 3 HL circuit voltage profiles for 95% 

substation primary voltage (LTC versus LTC and VR 1).............................. 183 

Figure 113. Comparison B: Test 3 and Test 4 HL circuit voltage profiles for 95% 

Figure 114. Comparison C: Test 2 and Test 5 HL circuit voltage profiles for 95% 

Figure 115. Comparison D: Test 5 and Test 6 HL circuit voltage profiles for 95% 

substation primary voltage (LTC and CAP 1 versus LTC, CAP 1, 

Figure 116. Comparison E: Test 6 and Test 7 HL circuit voltage profiles for 95% 

substation primary voltage (LTC, CAP 1, and CAP 2 versus LTC, CAP 1, 

Figure 117. Comparison F: Test 2 and Test 8 HL circuit voltage profiles for 95% 

substation primary voltage (LTC vs. LTC, VR 1, VR 2, CAP 1, CAP 2, 

Figure 118. Comparison G: Test 7 and Test 8 HL circuit voltage profiles for 95% 

substation primary voltage (LTC, CAP 1, CAP 2, and CAP 3 versus LTC, 

Figure 119. LL circuit voltage profiles for all tests 

Figure 120. Test 1 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 121. Test 2 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 122. Test 3 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 123. Test 4 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 124. Test 5 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 125. Test 6 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 126. Test 7 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 127. Test 8 LL circuit voltage profiles for 95% and 105% substation primary
 

Figure 128. Comparison A: Test 2 and Test 3 LL circuit voltage profiles for 95% 

Figure 129. Comparison B: Test 3 and Test 4 LL circuit voltage profiles for 95% 

Figure 130. Comparison C: Test 2 and Test 5 LL circuit voltage profiles for 95% 

Figure 131. Comparison D: Test 5 and Test 6 LL circuit voltage profiles for 95% 

substation primary voltage (LTC and CAP 1 versus LTC, CAP 1, 

substation primary voltage (LTC and VR 1 versus LTC, VR 1, and VR 2).. 184 

substation primary voltage (LTC versus LTC and CAP 1)............................ 185 

and CAP 2)..................................................................................................... 186 

CAP 2, and CAP 3) ........................................................................................ 187 

and CAP 3)..................................................................................................... 188 

VR 1, VR 2, CAP 1, CAP 2, and CAP 3) ...................................................... 189 

(third set – 95% and 105% substation primary voltage)................................ 191 

voltage (no LTC)............................................................................................ 192 

voltage (LTC)................................................................................................. 193 

voltage (LTC and VR 1) ................................................................................ 194 

voltage (LTC, VR 1, and VR 2)..................................................................... 195 

voltage (LTC and CAP 1) .............................................................................. 196 

voltage (LTC, CAP 1, and CAP 2) ................................................................ 197 

voltage (LTC, CAP 1, CAP 2, and CAP 3).................................................... 198 

voltage (LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3)............................... 199 

substation primary voltage (LTC versus LTC and VR 1).............................. 200 

substation primary voltage (LTC versus LTC, VR 1, and VR 2) .................. 201 

substation primary voltage (LTC versus LTC and CAP 1)............................ 202 

and CAP 2)..................................................................................................... 203 

xviii 
Figure 132. Comparison E: Test 6 and Test 7 LL circuit voltage profiles for 95% 

substation primary voltage (LTC, CAP 1, and CAP 2 versus LTC, CAP 1, 

CAP 2, and CAP 3) ........................................................................................ 204 

Figure 133. Comparison F: Test 2 and Test 8 LL circuit voltage profiles for 95% 

substation primary voltage (LTC versus LTC, VR 1, VR 2, CAP 1, CAP 2, 

and CAP 3)..................................................................................................... 205 

Figure 134. Comparison G: Test 7 and Test 8 LL circuit voltage profiles for 95% 

substation primary voltage (LTC, CAP 1, CAP 2, and CAP 3 versus LTC, 

VR 1, VR 2, CAP 1, CAP 2, and CAP 3) ...................................................... 206 

Figure 135. Milford Circuit DC 8103................................................................................ 212 

Figure 136. Milford substation one-line diagram.............................................................. 213 

Figure 137. DR control strategies for a 1,000-kW synchronous machine ........................ 217 

Figure 138. DR control strategies for a 400-kW high-speed generator and inverter – 

current mode................................................................................................... 218 

Figure 139. DR control strategies for a 400-kW self-excited induction generator ........... 219 

Figure 140. Daily circuit load profile and time stamps ..................................................... 224 

Figure 141. HL condition – voltage rise or drop (in volts on a 120-V base) as a function 

of induction generator +/- reactive power with a constant real power 

output of 400 kW ........................................................................................... 254 

Figure 142. HL condition – reduction or increase in voltage (in percent on a 120-V 

base) as a function of induction generator +/- reactive power with a 

constant real power output of 400 kW ........................................................... 254 

Figure 143. HL condition – reduction or increase of real power (in percent of total 

circuit kilowatts) as a function of induction generator +/- reactive power 

with a constant real power output of 400 kW ................................................ 255 

Figure 144. HL load condition – reduction or increase of capacity (in percent of total 

circuit kilovolt-amperes) as a function of induction generator +/- reactive 

power with a CP output of 400 kW................................................................ 255 

Figure 145. HL condition – voltage rise or drop (in volts on a 120-V base) as a 

function of inverter generator +/- reactive power with a constant real 

power output of 400 kW ................................................................................ 256 

Figure 146. HL condition – reduction or increase in voltage (in percent on a 120-V 

base) as a function of inverter generator +/- reactive power with a 

constant real power output of 320 kW or 400 kW......................................... 256 

Figure 147. HL condition – reduction or increase of real power (in percent of total 

circuit kilowatts) as a function of induction generator +/- reactive power 

with a constant real power output of 320 kW or 400 kW .............................. 257 

Figure 148. HL condition – reduction or increase of capacity (in percent of total 

circuit kilovolt-amperes) as a function of induction generator +/- reactive 

power with a CP output of 320 kW or 400 kW.............................................. 257 

Figure 149. High substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 984 kW. 258 

Figure 150. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 984 kW.. 258 

xix 
Figure 151. High substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 246 kW.. 259 

Figure 152. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 246 kW.. 259 

Figure 153. High substation primary voltage, HL condition – reduction or increase in 

voltage (in volts on a 120-V base) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 984 kW ........................................................................................... 260 

Figure 154. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 984 kW.. 260 

Figure 155. High substation primary voltage, HL condition – reduction or increase in 

voltage (in volts on 120-V base) as a function of location and synchronous 

generator +/- reactive power with a constant real power output of 246 kW.. 261 

Figure 156. Low substation primary voltage, HL condition – reduction or increase in 

voltage (in volts on a 120-V base) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 246 kW ........................................................................................... 261 

Figure 157. High substation primary voltage, HL condition – reduction or increase of 

real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power 

output of 984 kW ........................................................................................... 262 

Figure 158. Low substation primary voltage, HL condition – reduction or increase of 

real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power 

output of 984 kW ........................................................................................... 262 

Figure 159. High substation primary voltage, HL condition – reduction or increase of 

real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power 

output of 246 kW ........................................................................................... 263 

Figure 160. Low substation primary voltage, HLcondition – reduction or increase of 

real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power 

output of 246 kW ........................................................................................... 263 

Figure 161. High substation primary voltage, HL condition – reduction or increase of 

capacity (in percent total circuit kilowatts) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 984 kW ........................................................................................... 264 

Figure 162. Low substation primary voltage, HL condition – reduction or increase of 

capacity (in percent total circuit kilowatts) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 984 kW ........................................................................................... 264 

xx 
Figure 163. High substation primary voltage, HL condition – reduction or increase of 

capacity (in percent total circuit kilowatts) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 246 kW ........................................................................................... 265 

Figure 164. Low substation primary voltage, HL condition – reduction or increase of
 

capacity (in percent total circuit kilowatts) as a function of location and 

synchronous generator +/- reactive power with a constant real power 

output of 246 kW ........................................................................................... 265
 

Figure A-1. Normal leakage currents to ground because of distributed capacitance ........ 287 

Figure A-2. Normal leakage currents to ground because of distributed capacitance – 

phasor diagram............................................................................................... 288 

Figure A-3. Increased leakage current on the unfaulted phases and resultant ground 

current IG and resultant zero sequence voltage 3 VO ..................................... 288 

Figure A-4. Increased leakage current on the unfaulted phases and resultant ground 

current IG and resultant zero sequence voltage 3 VO – phasor diagram......... 289
 

Figure B-1. Percent change in kilovolt-amperes or current from percent change 

in P and Q....................................................................................................... 296 

Figure B-2. Percent change in kilovolt-amperes or current............................................... 296 

Figure B-3. Zero sequence current on load side becomes negative sequence current
 

to the generator............................................................................................... 299 

Figure B-4. Determining IAG1............................................................................................ 300 

Figure B-5. Determining IAG2............................................................................................ 301 

Figure B-6. Determining IAG0............................................................................................ 301 

xxi 
List of Tables
 

Table 1. Comparison of National Electrical Manufacturers Association Standard 

Method with Correct Voltage Unbalance Calculations Using 

Symmetrical Components ................................................................................ 70 

Table 2. Per-Unit Line Currents for Percent Negative Sequence Voltage 

Single-Cage Induction Motor........................................................................... 79 

Table 3. Per-Unit Line Currents for Percent Negative Sequence Voltage 

Double-Cage Induction Motor ......................................................................... 79 

Table 4. Double- and Single-Cage Characteristics for 10-hp, Four-Pole, 220-V, 

Three-Phase, Wye-Connected Ungrounded Motors ........................................ 80 

Table 5. Single-Cage Induction Motor – 10 hp, 220 V, Four Pole, 

Wye-Connected Ungrounded........................................................................... 81 

Table 6. Double-Cage Induction Motor – 10 hp, 220 V, Four Pole, 

Wye-Connected Ungrounded........................................................................... 81 

Table 7. Maximum Allowable Power Output in Percent of Rated While Operating
 

at Unbalanced Voltages.................................................................................... 86 

Table 8. Comparison of Gafford, Duesterohoeft, and Mosher (1959) and Tracey
 

(1954) Motor Derate Data Operating at Unbalance Voltage ........................... 86 

Table 9. Unbalance Voltage Survey Results of Closed and Open Delta 

Transformer Connections................................................................................. 88 

Table 10. Distribution Transformer No Load (Core Losses) and Load 

(Copper Losses) ............................................................................................... 99 

Table 11. Equilateral Spacing Kilowatt Loss Evaluation .............................................. 112 

Table 12. Non-Transposed Kilowatt Loss Evaluation ................................................... 114 

Table 13. Transposed Kilowatt Loss Evaluation ........................................................... 116 

Table 14. The Effects of Circuit Spacing and Unbalanced Load on Percent 

Kilowatt Losses.............................................................................................. 123 

Table 15. Voltage Drop Summary – Transformer, Secondary, and Service Drop ........ 125 

Table 16. Peak Day Real Losses Comparison................................................................ 127 

Table 17. Circuit Customer Load Characteristics .......................................................... 140 

Table 18. Measurement Locations and Data Collection ................................................ 144 

Table 19. Matrix of Voltage Regulation Simulations .................................................... 145 

Table 20. Voltage Profile Data for HL Tests 1 Through 8 at 95% and 105% 

Substation Primary Voltage ........................................................................... 149 

Table 21. Voltage Profile Data for Light Load Tests 1 Through 8 at 95% and 105% 

Substation Primary Voltage ........................................................................... 158 

Table 22. Simulation Summary Data for Tests 1 Through 8 ......................................... 167 

Table 23. Simulation Summary Data for Unbalanced Loading (Tests 1 Through 8) .... 172 

Table 24. HL Circuit Voltage Profiles (First Set) .......................................................... 175 

Table 25. Voltage Profile Comparison for HL and 95% Primary Voltage .................... 183 

Table 26. LL Circuit Voltage Profiles (Third Set)......................................................... 190 

Table 27. Highest Unbalanced Voltages ........................................................................ 207 

Table 28. Voltage Regulation Equipment...................................................................... 211 

xxii 
Table 29. Major System Protection Equipment ............................................................. 213 

Table 30. Measurement Locations and Data Collection ................................................ 214 

Table 31. Accuracy of 3720 ACM................................................................................. 214 

Table 32. Matrix of Voltage Regulation Simulations and Control Strategy 17 

for Field Verification...................................................................................... 220 

Table 33. Test Dates and Data Collection Periods......................................................... 223 

Table 34. Circuit and Generation Measured Data.......................................................... 226 

Table 35. Bidirectional VR Measured Data ................................................................... 227 

Table 36. Circuit Equipment and Customer-Measured Data ......................................... 228 

Table 37. Field Verification Data – July 17, 2006 – DR Generation On....................... 229 

Table 38. Field Verification Data – July 29, 2006 – DR Generation On....................... 229 

Table 39. Field Verification Data – July 31, 2006 – DR Generation Off ...................... 230 

Table 40. Percent Variance Between Actual and Simulated Currents, Voltages, 

and Power Factors .......................................................................................... 231 

Table 41. Maximum Limit for Real Power Injection..................................................... 233 

Table 42. Maximum Limit for Real and Reactive Power Injection............................... 233 

Table 43. Explaining the Meaning of Positive and Negative Improvements for 

DG Applications ............................................................................................ 238 

Table 44. Induction Generator Voltage Regulation Application (LV, HV) – HL ......... 241 

Table 45. Inverter Generator Voltage Regulation Application (LV, HV) – HL............ 242 

Table 46. Synchronous Generator Voltage Regulation Application (BL, HV) – HL.... 243 

Table 47. Synchronous Generator Voltage Regulation Application (EL, HV) – HL .... 244 

Table 48. Synchronous Generator Voltage Regulation Application (ML, HV) – HL... 245 

Table 49. Synchronous Generator Voltage Regulation Application (BL, LV) – HL .... 246 

Table 50. Synchronous Generator Voltage Regulation Application (EL, LV) – HL..... 247 

Table 51. Synchronous Generator Voltage Regulation Application (ML, LV) – HL ... 248 

Table 52. Distributed Generator Voltage Regulation Application Summary – HL....... 250 

Table 53. Distributed Generator Voltage Regulation Application Summary – LL ....... 252 

Table 54. Optimum Generator Conditions for Maximum Improvements – HL............ 270 

Table 55. Optimum Generator Conditions for Maximum Improvement – LL .............. 271 

Table 56. Induction Generator Voltage Regulation Application (LV, HV) – LL.......... 272 

Table 57. Inverter Generator Voltage Regulation Application (LV, HV) – LL ............ 273 

Table 58. Synchronous Generator Voltage Regulation Application (BL, HV) – LL .... 274 

Table 59. Synchronous Generator Voltage Regulation Application (EL, HV) – LL..... 275 

Table 60. Synchronous Generator Voltage Regulation Application (ML, HV) – LL ... 276 

Table 61. Synchronous Generator Voltage Regulation Application (BL, LV) – LL..... 277 

Table 62. Synchronous Generator Voltage Regulation Application (EL, LV) – LL..... 278 

Table 63. Synchronous Generator Voltage Regulation Application (ML, LV) – LL.... 279
 

Table B-1. Simulation Summary Data for Tests 7 and 8 at 95% Voltage and HL 

Conditions and a Comparison of Modeling Results for CC, CP, and VDC .. 303 

Table B-2. Comparison of Line Currents for Simulated and Actual Measurements 

for Each Load Model and Each Test 7 and 8 ................................................. 304 

Table B-3. Sequence Currents for Each Test ................................................................... 305 

Table B-4. Simulation Data by Node for Test 8 at 95% HL with LTC, VR 1, VR 2, 

and Capacitors 1, 2, and 3 Regulation Methods Implemented (CC Model).. 306 

xxiii 
xxiv
 
1 Introduction 

An earlier study (Davis 2003) reported that the maximum-sized distributed generation (DG) 

that can be installed on a distribution circuit depends on: 

•	 Circuit system voltage 

•	 The location of DG on the circuit 

•	 Circuit configuration and characteristics 

•	 System protection issues 

•	 Voltage regulation issues 

•	 DG characteristics. 

The study also found that larger DG units can be installed on higher-system-voltage 

circuits and at the substation with fewer effects on system protection and voltage regulation. 

If the DG actively regulates voltage, larger units can be interconnected because high-voltage 

(HV) conditions during light-load (LL) conditions can be curtailed if the DG absorbs voltamperes reactive. 

These findings were the results of tests that used (3Φ) balanced power flows on distribution 

circuits with balanced loads. However, most distribution circuits have unbalanced loading 

conditions, unbalanced line impedances, and unbalanced voltage conditions. Therefore, there 

is no assurance that these results represent what happens on the single-phase (SΦ) laterals of a 

three-phase circuit. 

The single-phase portion of the circuit may serve more than 90% of the load. Just because the 

voltage limits are satisfied on the three-phase portion of the circuit does not mean there are no 

voltage limit violations on the single-phase loads. Installing DG on the circuit adds another 

level of complexity to the analysis of the distribution system, but it can also contribute added 

benefits of released capacity, lower energy losses, and improved voltage regulation. 

The objectives of this project are to: 

1.	 Select a distribution circuit and install DG to reduce an overload and improve 

voltage regulation 

2.	 Develop models and run simulations to calculate voltage profiles on the distribution 

circuit with the load tap changer (LTC), step regulators, capacitors, and DG regulating 

the voltage 

3.	 Install metering on the circuit and DG installations and compare actual measured data 

with simulations to verify the models 

4.	 Determine the maximum-sized DG and the optimum DG operating conditions that 

will provide the greatest released capacity, lowest energy losses, and most improved 

voltage regulation. 

1
 
2 Project Approach 

The approach of the project is to: 

1.	 Develop a load model of a distribution circuit to represent how circuit load changes 

with changes in voltage 

2.	 Develop circuit line elements and circuit equipment models 

3.	 Develop DG models for synchronous, induction, and inverter generation 

4.	 Model an entire 13.2-kV distribution circuit with all three-phase and single-phase 

loads connected to the correct phases of the distribution circuit 

5.	 Install a 1,000-kW synchronous generator on the circuit and install the appropriate 

metering equipment to measure the power quantities of the circuit, including 

single-phase loads 

6.	 Validate the models by conducting a multitude of power flow simulations and 

comparing the simulations with circuit-measured data on the circuit peak day (with 

DG on and off) 

7.	 Report the variance between simulated and measured power quantities 

8.	 Determine the largest DG that can be installed on the circuit without violating voltage, 

thermal, and reverse power criteria 

9.	 Determine the optimum DG operating conditions to give maximum released capacity, 

reduced energy losses, and improved voltage regulation. 

2
 
3 Project Results: Traditional Voltage Regulation Methods 

3.1 Introduction 

A number of methods can improve voltage regulation. Some use voltage regulation equipment 

to raise or lower voltage at the substation or on the distribution circuit to reduce the voltage 

difference between LL and heavy-load conditions. Others reduce the impedance of the circuit 

to reduce the voltage difference or spread, and still others reduce the load current (i.e., 

improve the power factor) to reduce the voltage drop and, thus, the voltage spread. 

Methods that can be applied at the substation include: 

•	 Use DG voltage regulators (VRs). 

•	 Apply capacitors at the distribution substation. 

•	 Apply voltage-regulating equipment, such as LTC transformers and bus or circuit 

voltage-regulating equipment, at the substation. 

•	 Balance the loads on the circuits. 

•	 Transfer loads to other substations. 

•	 Install new substations and circuits. 

•	 Install substation transformers with reduced reactance. 

Methods that can be used on the distribution circuit include: 

•	 Increase the primary system voltage of the circuit. 

•	 Increase the conductor size of the circuit or reduce conductor spacing and, 

consequently, reduce reactance. 

•	 Change circuit sections from single-phase to three-phase. 

•	 Transfer loads to other circuits. 

•	 Apply voltage-regulating equipment on the circuit. 

•	 Install DG on the circuit. 

•	 Apply shunt (or series) capacitors on the circuit. 

•	 Balance loads. 

•	 Increase the distribution transformer size. 

•	 Increase the conductor size of secondaries and services. 

3.2 Distributed Generation Installed at Substation 

The generator bus voltage can be regulated to maintain a fixed voltage for changes in load and 

reactive requirements. The generator field current can be varied to match the changes in load 

current. The voltage can be increased or decreased as the load increases or decreases. 

3
 
3.3 Substation Voltage-Regulating Equipment

One of the most common types of substation voltage-regulating equipment is the load tap 

changing (LTC) transformer. Step- or induction-type VRs may be installed between the 

secondary of the transformer and the secondary bus or on the secondary bus. Also, step- or 

induction-type regulators may be installed on individual circuits. Because circuit voltage is a 

function of voltage spread at the secondary of the substation bus, voltage-regulating 

equipment allows for a greater voltage drop in the circuit. 

3.4 Balancing Loads

If a circuit has poor voltage regulation, it could be due to a significant difference in phase 

loading. A 20% or more load imbalance on the primary of a circuit, especially during HL 

conditions, is not uncommon. In addition, a high load imbalance can cause substation 

transformers and VRs to overload, based on the highest phase load. Balanced loading should 

be achieved throughout the circuit, not just at the substation. 

3.5 Increased Primary System Voltage 

Increasing the system voltage reduces the load by the inverse ratio of the voltage change, but 

the voltage regulation changes as the square of the voltage change. Changing from a threewire ungrounded delta to a four-wire grounded wye increases the voltage by the √3 but 

reduces the voltage drop to 1/3 of the drop in the three-wire delta. However, it is common to 

increase the allowable load when this conversion is made to a higher system voltage; 

therefore, the voltage drop improvement is less than 2/3. This method is more expensive than 

using supplemental voltage regulation because it involves re-insulating the line and changing 

out electric transformation (i.e., transformers) and other equipment. 

3.6 Increased Conductor Size or Reduced Conductor Spacing 

Increasing conductor size is another expensive method to achieve improved voltage 

regulation. Increasing the size of the conductor reduces the resistance and, thus, the voltage 

drop and real losses. However, it may necessitate a rebuilding of the line because of the larger 

and heavier conductor. An alternative is to reduce the spacing between the phase conductors, 

which reduces the reactance and lowers the voltage drop. 

3.7 Conversion of Single-Phase Sections to Three-Phase 

Most general-purpose circuits are single-phase. For single-phase circuits, voltage drop occurs 

in both the phase conductor and the neutral for the wye systems and in both the phase 

conductors for the delta systems. Adding two conductors to a single-phase wye system, and 

assuming the existing load is evenly distributed among the three phases, results in 1/6 of the 

voltage drop that occurs on the single-phase wye lateral. This is demonstrated below. 

∆VsΦ = 2 IsΦ Z and Equation 3.1 

% ∆VsΦ = 2 IsΦ Z/VLN x 100 Equation 3.2 

4
 
where 

∆VsΦ = Voltage drop per unit length 

IsΦ = Line current 

Z = Impedance per unit length 

VLN = Line-to-neutral voltage. 

For the three-phase case, 

∆V3Φ = I3Φ Z Equation 3.3 

%∆V3Φ = (I3Φ Z)/VLN x 100 Equation 3.4 

where 

I3Φ = ISΦ/3. Equation 3.5 

Using equations 3.2, 3.4, and 3.5, the ratio of percent voltage drops is thus: 

% ∆VSΦ / % ∆V3Φ = [(2 ISΦ Z)/VLN]/[(I3Φ Z)/VLN]

 = (2 ISΦ)/I3Φ

 = [(2) (3) (I3Φ)]/I3Φ = 6. Equation 3.6 

Therefore, the voltage drop is six times less for the three-phase circuit than for the singlephase circuit for the same load. Of course, undoubtedly, the load will increase over time after 

the single-phase lateral is converted to three-phase. However, this does illustrate the concerns 

when single-phase DGs and three-phase DGs are added to the circuit. 

If only one phase conductor, rather than two, is added to a single-phase wye system, the 

problem becomes more complicated because the voltage drop depends on the two phases 

selected, the R/X ratio of the conductor, and the load power factor (PF). 

To describe the differences between the single-phase case and the two two-phase cases, 

circuit diagrams and phasor diagrams are used. Figure 1 and Figure 2 show the single-phase 

case, in which IA is the phase current that is equal to the neutral current IN. 

5
 
R X
 

I

A 

VS Load VR 

R X 

I

N 

Figure 1. Single-phase equivalent circuit 

VS 

VR 

I

A R 

I

AX + INX 

I

A or 

θ

 + I 

N R 

I

N 

Figure 2. Single-phase phasor diagram 

The approximate voltage drop consists of four components: 

∆V = |IA|R Cos θ + |IN|R Cos θ + |IA|X Sin θ + |IN|X Sin θ. Equation 3.7 

In each of the two-phase cases, the single-phase load is divided equally among the two phases; 

therefore, IA of the single-phase case is twice the magnitude of IA in the two-phase cases. 

In Figure 3 and Figure 4, it should be noted that the sending-end voltage VSA for Phase A with 

loads connected to phases A and C to neutral, as in Figure 4, is less than the sending-end 

voltage VSA for Phase A with loads connected to phases A and B to neutral, as shown in 

Figure 3. The primary reason is because the INX term is in phase with VRA in Figure 3, 

whereas it is rotated counterclockwise in Figure 4. Also, the load power factors and the R/X 

ratios must be taken into account when calculating the voltage drop. 

6
 
I

A 

A 

V VRA SA 

Rotation ABC 

B 

VSB 

I

B 

R 

X 

Loa

I d

N 

VSA 

VRB 

I

A

A

V VRA SA

R X R X Load 

2 

2 

Rotation ABC

B

VSB

I

B

R

X

Loa

I d

N

VSA

VRB

IA 

θ

120o 

VRA 

IAR 

IAX 

INR INX 

VSA 

VSA 

IN 

IB 

=30o 

Phase A 

(A and C to 

Neutral Loads) 

See Figure 3.3 

IA

θ

120o

VRA

IAR

IAX

INR INX

VSA

VSA

IN

IB

=30o

Phase A

(A and C to

Neutral Loads)

See Figure 3.3

Phase A

(A and B to

Neutral Loads)

VSA

Phase A

(A and B to

Neutral Loads)

VRB

Figure 3. Two-phase lateral – voltage drop for load connected from A and B to neutral 

7
 
C
 

A 

VSC 

R X R X Load 

2 

Rotation ABC 

VSA 

R 

X 

Loa

2 

d

VRA 

VRC 

Ph ase A

(A and C(A toand C to VSA

VRC 

IA 

IC 

30o 

θ

120o 

VRA 

IAR 

IAX 

INR 

INX 

IN 

Neutral Loads) VRC

IA

IC

30o

θ

120o

VRA

IAR

IAX

INR

INX

IN

Neutral Loads)

Figure 4. Two-phase lateral – voltage drop for load connected from A and C to neutral 

8
 
3.8 Voltage-Regulating Equipment 

VRs may be installed at the substation secondary voltage bus, at the circuit position of the 

substation, or out on the circuit. Their primary purpose is to reduce voltage spread so voltage 

is maintained within American National Standards Institute (ANSI) C84.1 Range A for 

normal conditions and Range B for infrequent operating conditions. Regulators may be used 

to “boost” the voltage for heavily loaded circuits or “buck” the voltage for lightly loaded 

circuits or circuits that have fixed shunt capacitors. For this reason, it may be necessary to use 

switched shunt capacitors to prevent (LV, switched on) during heavily loaded conditions and 

HV (switched off) during lightly loaded conditions. 

VRs may be applied in series, as shown in Figure 5. Where two or more are needed, fixed 

boost regulators may solve the LV problem if HV is not experienced during LL conditions. 

Fixed boost can be achieved by adding taps on the distribution transformers. In the upper 

portion of Figure 5, the voltage profile is given with the LTC VR installed at the substation. 

The voltage profile drops below the minimum voltage at the second and third loads. When the 

first (1) bus VR is added, the voltage at load (2) is within limits, but the voltage at load (3) is 

still below the minimum level. Adding the second (2) line regulator puts the voltage spread 

within limits for all three loads. 

9
 
Substation 

1 

Voltage Regulators 

2 

Load Load Load 

1 2 

1 

3 

2 

Minimum Voltage 

Minimum Voltage 

Maximum Voltage 

Maximum Voltage 

Substation 

Regulator 

Voltage 

Spread 

ΔV 

ΔV 

Variable 

Primary 

Voltage 

Variable 

Primary 

Voltage 

Substation 

Regulator 

Voltage 

Spread 

Figure 5. VRs in series 

10
 
3.9 Shunt Capacitors

Installing shunt capacitors causes a voltage rise or a reduced voltage drop. The capacitor 

current is leading and, when multiplied by the series circuit (inductive) reactance, causes a 

voltage rise. This rise is not dependent on load current and is highest at the capacitor location. 

The percentage of voltage rise is calculated as 

% ∆V rise = [(3ΦkVAr) (l) (X)] / [kV2 (10)] Equation 3.8 

where 

3Φ kVAr = The three-phase capacitor kVAr or kVA because, for the capacitor, kVAr 

= kVA 

X = Inductive line reactance in Ω per unit length 

kV = Line-to-line voltage 

l = Distance in unit length from the substation source to the capacitor. 

When the capacitor installed is single-phase, SΦ kVAr is used in Equation 3.8. However, the 

X is multiplied by two because there are two conductors, and kV is the line-to-line voltage 

between these two conductors. As an example, if a 600-kVAr, three-phase capacitor is 

installed on a 13.2-kV wye system at 3 miles and the line reactance of a 636-k cmil, allaluminum conductor is 0.536 Ω/mile/conductor, then 

% ∆V rise = [(600) (3) (0.536)]/[(13.2)2

 (10)] = 0.554%. Equation 3.9 

For single-phase, 

% ∆V rise = [(200) (3) (0.536) (2)]/[(7.62)2 (10)] = 1.108%, Equation 3.10 

or twice the percent voltage rise. As noted earlier, the voltage rise will be the same for LL and 

HL conditions. Therefore, it may be necessary to install capacitor switches. The amount of 

capacitors needed to correct an LV problem is dependent on the conductor size, load power 

factor, and how the load is distributed on the circuit. 

3.10 Load Tap-Changing Transformers

LTC transformers are often referred to as tap-changing under load. Load tap changers are 

applied to power transformers at the substation. They are used to control the voltage on the 

LV or secondary side to a fixed value with a variable primary voltage input, as shown in 

Figure 5. Also, LTCs may be used to control reactive power flow by shifting the phase angle 

of the transformer secondary voltages. The regulation range is typically 8, 16, and 32 steps 

with ±10% of rated voltage. The 32-step LTC is the most common for LTC transformers in 

substations. The 32 steps are divided into 16 steps raise and 16 steps lower, or a 5/8% change 

per step based on ±10% voltage range. The change in steps is made without interrupting the 

circuit by using a mid-tapped autotransformer, called a preventive autotransformer. The steptype VR theory of operation is similar to the LTC transformer. 

11
 
• • 

3.11 Voltage Regulator Theory of Operation

In general, the VR is a transformer. If two windings are wound on a common magnetic core 

and the numbers of turns is different, then the voltages across these windings will be different. 

The alternating voltage applied to the first coil will induce a voltage in the second coil, and 

the magnitude of voltage induced will be dependent on the turn ratio between these two 

windings. In the case of a regulator, the first coil is referred to as the primary, or exciting, 

winding and the second as the regulating, or series, winding. 

The step regulator is an autotransformer, the windings of which are connected in series and 

wound on the same magnetic core. There are two types of autotransformers: step-up and stepdown. Figure 6 shows a step-up transformer with a turn ratio of 10. For example, if N1 = 100 

and N2 = 10, then a = N1/N2 = 10. If the series winding is connected in series with the exciting 

or shunt winding that has the polarity, as shown in Figure 6, then 120 V applied to the 

exciting winding will result in 12 V on the series winding, which, when added to the primary 

voltage, results in a 132-V output. When the polarity of the series winding is reversed, as 

shown in Figure 7, then the 12 V on the series winding is subtracted from the 120 V primary 

voltage, and the output is 108 V. This is called a step-down transformer. To obtain a smaller 

change in voltage, the series winding is divided into eight equal parts, called taps, as shown in 

Figure 8. 

+

• •

+

V 1 = 120V12 + 120 = 132V 12 + 120 = 12 + 120 = 132V

primary or V 2 primar or V =132V 2 primary or V =132V 2 y or

exciting excitin exciting regulating or

winding winding w inding series winding series wind series winding - - a = 10:1a = 10:1a = 10:1

Figure 6. Step-up transformer 

Figure 7. Step-down transformer 

• 

• 

• 

• + 

+ 

- -

V 1 = 120 

V 2= 108 

120 - 12 = 108V 

V 2 =108V 

•

•

•

+

+

- -

V 1 = 120

V 2= 108

•

•

•

+

+

- -

V 1 = 120

V 2= 108

120 - 12 = 108V

V 2 =108V

•

•

•

• +

+

- -

V 1 = 120

V 2= 108

120 - 12 = 108V

V 2 =108V

•

•

•

+

+

- -

V 1 = 120

V 2= 108

•

•

•

+

+

- -

V 1 = 120

V 2= 108

120 - 12 = 108V

V 2 =108V

 12
 
• •

• + 

-

-

+ 

N 

V 1 

• •

• +

-

-

+

• •

• +

-

-

+

N

V 1

• •

• +

-

-

+

N

V 1

• •

• +

-

-

+

• •

• +

-

-

+

N

V 1

10% x 120 = 12V 10% x 120 = 12V % x 120 = 12V

12V/8 steps = 1.5V per step 12V/8 steps = 1.5V per st 12V/8 st12V/8 steps = 1.5V per step

10%/8 steps = 1 10%/8 steps = 1 10%/8 steps = 1 1⁄4% per step % per step

Figure 8. Step regulator 

The output voltage can be varied from 120 V if tapped at the neutral position, N, up to 132 V, 

with steps of 12 V divided by 8 or 1.5 V per step, or 1 1/4% changes in voltage per tap setting. 

The problem with this arrangement is the interruption of the circuit each time the tap changes. 

To avoid this, the moving tap can be broken into two fingers such that, as the moving tap 

changes from one tap position to the next, one finger is always in contact with a tap. This is 

shown in Figure 9. To prevent shorting out the turns of the series winding, as shown in Figure 

9b, when one finger is on one tap and the other finger is on the next tap, a preventive 

autotransformer is midtapped and connected to each finger. The center tap of this 

autotransformer is connected to the load bushing (L). In Figure 9a, when both fingers are on 

the neutral tap “0,” they are at the same voltage, and the center tap of the preventive auto is at 

the same voltage. When 120 V is applied to the primary, the voltage from the preventive auto, 

sometimes referred to as a bridging reactor, is at 120 V. When the moving fingers move toward 

Tap 1, the top finger is on Tap 1, while the bottom finger is on Tap 0. As shown in Figure 9b, 

there is a 1 1/4% voltage difference between Tap 0 and Tap 1 and the two fingers. But when 

the bridging reactor is connected between these two fingers and its center tap is connected to 

the load, the load will see one half of the 1 1/4%, or 5/8%, as shown in (2) of Figure 9b. This is 

called the bridging position 5/8%. When the top finger moves farther up and is resting on Tap 

1, and the bottom finger is resting on Tap 1, then the center tap is at the same voltage as the 

two fingers and Tap 1. Now the voltage at the load is up 1 1/4% voltage (see Figure 9c). For 

higher-voltage outputs, this process repeats where the fingers are in non-bridging and bridging 

positions until the top tap is reached and a full 10% voltage increase is attained. 

13
 
14 

b. Bridging position 5/8% 

+ 

-

• 

• 0 

bridging

reactor 

1 

0% 

1 

+

-

•

•

0

bridging

reactor

1

0%

1

+

-

•

•

0

bridging

reactor

1

0%

1

+

-

•

•

0

bridging

reactor

1

0%

1

a. Non-bridging position 0% 

1.25% 

0 

1 2 

5/8% 

1.25%

0

1 2

5/8%

1.25%

01 2

5/8%
8 

7 

6 

5 

3 

4 

2 

1 

0 1 1/4% 

8

7

6

5

3

4

2

1

0

8

7

6

5

3

4

2

1

0 1 1/4%

8

7

6

5

3

4

2

1

0

8

7

6

5

3

4210 1 1/4%

876534210876534

2

1

0 1 1/4%

c. Non-bridging position 1 1/4% 

Figure 9. Step VR sequence of operation 

For decreases in voltage, the process is reversed until both fingers are resting on Tap 0. This 

process has addressed only increases in voltage above the primary voltage. To lower the 

voltage below the primary voltage, it is necessary to reverse the polarity, which is similar to 

the step-down transformer of Figure 7. This is accomplished by adding the reversing switch 

of Figure 10, which changes the polarity of the series winding. Now, the regulator can raise 

or lower the voltage by ±10%. 

15
 
• 

• 

-

8 

7 

6 

5 

3 

4 

2 

1 

0 

• 

Reversing 

Switch 

• • 

• 

• 

•

•

+ 

-

8

7

6

5

3

4

2

1

0

8

7

6

5

3

4

2

1

0

•

Reversing 

Switch

• •

•

•

•

•

+

-

8

7

6

5

3

4

2

1

0

876534210

•

Reversing 

Switch

• •

•

•

•

•

+

-

8765342108765

3

4

2

1

0

•

Reversing 

Switch

• •

•

•

Figure 10. Step VR with reversing switch 

3.12 Bridging Reactor or Preventive Autotransformer 

Before, the bridging reactor was introduced to achieve one-half of a voltage step between 

taps and eliminate shorted turns when the moving fingers were on different taps. The current 

in these fingers is not the same when moving from non-bridging and bridging positions. 

Four conditions are examined: (1) non-bridging no-load, (2) bridging no-load, (3) non-bridging 

load, and (4) bridging load. Figure 11 illustrates the non-bridging no-load condition. When both 

fingers are on the same tap (1) and no load, there is no voltage difference across the bridging 

reactor and the load current IL = 0. When the top finger moves to Tap 2, and the bottom finger 

remains on Tap 1 (bridging position), a voltage appears across the reactor. A circulating current 

(IC) flows from the higher voltage of Tap 2 to the lower voltage of Tap 1. See Figure 12. The 

current through the top finger is the same as the bottom-finger current because there is no load. 

With no load, there is a current in the reactor for every bridging position. This explains why 

current is flowing even though there is no load current on the circuit. 

When load (IL) is applied and the top and bottom fingers are on the same tap (Figure 13), the 

current is equal in the two fingers because since the ampere turns in the reactor are balanced 

and Ia = 1/2 IL and Ib = 1/2 IL. When the fingers are on different taps, such as the bridging 

position of Figure 14, a circulatory current flows. Now, the top-finger current Ia = 1/2 IL + IC, 

and the bottom-finger current Ib = 1/2 IL – IC. The circulatory current is approaching 50% of 

the value of the load current and flows from the higher voltage on Tap 2 to the lower voltage 

on Tap 1. 

16
 
F

F

F

U 

F1 

F2

F1
 

F

F

FFF FFF

The current in the top finger is higher than the current in the bottom finger because of this 

circulating current. This difference can be reduced with equalizer windings. 

Series Winding Ser es Windin Seri ges Winding

Stationary Contacts S ationary Contac Stationary Contacts F3

I a I L = 0 3 2

I C U

No Load 2 I F a= 0 F1

I L = 0 F1No Load No Load I B

I a = I CI b= 0 I b = I C

Figure 11. Non-bridging no load Figure 12. Bridging position no load 

3 3 I a I L 2 Ia 2

I U

LI I C Load

F1 Load F1 I b

I b

I a = 1⁄2 I L Ia = 1⁄2 I L I + I a = 1⁄2 I L c

I b = 1⁄2 I L I I b = 1⁄2 L - I b = 1⁄2 c

Figure 13. Non-bridging load Figure 14. Bridging position load 

3.13 Equalizer Windings 

Equalizer windings are wound on the same central core as the primary and series windings 

and equal about 1/2 the number of turns between each tap on the series winding. These 

windings reduce the voltage during switching and thus prolong the life of the tap changer and 

equalize the current on the fingers because the net circulating current reverses for odd- and 

even-numbered taps. Figure 15 shows the application of the equalizer windings. 

Four cases are studied: one set without equalizer windings and one set with equalizer 

windings. Case A, Figure 16, shows what happens when the lower finger moves from Tap 2 

to Tap 1. When the lower finger, b, moves off Tap 2, the voltage between b and 2 is V, which 

causes an arc on b and contact erosion. But when the lower finger, b, moves from Tap 2 of 

Case B to Tap 3 (Figure 17), there is no arc because there is no voltage difference. 

When equalizer windings are present in Case C (Figure 18) and finger b moves to Tap 1, the 

voltage difference between b and 2 is 1/2 V. Therefore, the contact erosion is reduced. Case 

D (Figure 19) shows the non-bridging case, in which finger b moves from 2 to 3. Here, 

when b moves off of 2, a voltage difference of 1/2 V appears between 2 and b, so that the 

arcing is the same as in Case C. The contact wear is thus equalized between bridging and 

non-bridging positions. 

17
 
Equalizer Winding 

Preventive 

Auto 

Equalizer Winding 

F2

F3

Load 

Equalizer Winding

Preventive

Auto

Equalizer Winding

F2

F3

Load

Equalizer Winding

Preventive

Auto

Equalizer Winding

F2

F3

Load

Equalizer Winding

Preventive

Auto

Equalizer Winding

F2

F3

Load

Figure 15. Application of equalizer windings 

Series Winding

V 

a 

b 

Load 

1 

2 

1⁄2V 

1⁄2V 

Series Winding

V

a

b

Load

1

2

1⁄2 V

1⁄2 V

Series Winding

V

a

b

Load

1

2

1⁄2 V

1⁄2 V V

a

b

Load

1

2

1⁄2 V

1⁄2 V

Figure 16. Case A – without equalizer windings 

a v

2 b Load

3 

2 b

3

Figure 17. Case B – without equalizer windings 

V 

a 

Load 

1 

2 b 

1⁄4V 

1⁄4V 

1⁄4V 

1⁄4V Preventive 

Auto 

V

a

Load

1

2 b

1⁄4 V

1⁄4 V

1⁄4 V

1⁄4 V Preventive

Auto

V

a

Load

1

2 b

1⁄4 V

1⁄4 V

1⁄4 V

1⁄4 V Preventive

Auto

V

a

Load

1

2 b

1⁄4 V

1⁄4 V

1⁄4 V

1⁄4 V Preventive

Auto

Figure 18. Case C – with equalizer windings bridging position 

18
 
V 

a 

2 Load

3 

b 

Preventive 

Auto 

V

a

2 Load

3

b

Preventive 

Auto

V

a

2 Load

3

b

Preventive 

Auto

V

a

2 Load

3

b

Preventive 

Auto

Figure 19. Case D – with equalizer windings non-bridging position 

3.14 Types of Step Regulators 

There are three types of VRs: Type A, Type B, and bi-directional (or cogeneration). For Type 

A, the primary is connected to the exciting winding or the shunt winding. See Figure 20. The 

series winding is connected to the shunt winding via the reversing switch, as shown in Figure 

10. Therefore, the series winding is connected to the load side. Type B, shown in Figure 21, 

is more common. Its series winding is connected to the source side. 

power flow 

Substation 

Source 

V2 Load 

V1 N1 

power flow

Substation

Source

V2 Load

V1 N1

power flow

Substation

Source

Series Winding CT 

N 

VT 

Control 

System 

N2 

Exciting 

Winding 

(Shunt) 

V2 Load

V1 N1

V V 1= 2

1 NN2

Figure 20. ANSI Type A – series winding located on load side 

19
 
Series Winding

V2 Load 

V1 

N 

Substation 

Source Exciting 

Winding 

(Shunt) 

CT 

VT 

V2 Load

V1

N

Substation

Source Exciting

Winding

(Shunt)

Control 

System 

CT

VT

Figure 21. ANSI Type B – series winding located on source side 

When applying Type A and B regulators, there is only one source of power (e.g., the 

substation source). However, there are applications in which power may flow from either 

direction through the regulator, as shown in Figure 22. In this figure, the regulator is located 

between two power sources: the substation and a distributed resource (DR). In Figure 23, 

assume the power flows from left to right. The voltage transformer (VT) VT2 is connected 

across the load side. When the VT2 senses LV and the regulator voltage is adjusted up, the 

voltage at the output is increased. Now, suppose the power flows in the reverse direction 

because of the operation of the DR in Figure 22. Because VT2 is now connected across the 

source side, it will measure the V2 voltage. When the V2 voltage is low, the control system 

will cause the voltage to rise and thus insert more series winding, N2. The voltage turns ratio 

equation, 

V1 V2 = , Equation 3.11 N1 N2 

shows that increasing N2 will cause V1/N1 to change. Because N1 is the turns on the exciting 

winding, which is a constant, V1 voltage will drop even further, thus lowering voltage V1 

rather than raising the voltage. This will cause the regulator to go to the maximum raised 

position. If the voltage V2 changes, then the regulator will chase up and down continuously 

between all raise and all lower. 

Changes must correct this problem. First, the regulator must recognize the power flow has 

reversed. This can be accomplished using the current transformer (CT) input to the control 

system. Second, the VT must sense the voltage on the V1 side or the load side for the reversepower use. Third, there must be a change in the line drop compensator settings because the 

regulation point has now changed to a different location with different circuit R and X values 

and voltage settings. Another solution is shown in Figure 24, in which the change in power 

flow is sensed, but a differential transformer reads the difference between V1 and V2. Here, 

the control system will compensate for the voltage difference between V1 and V2 and correct 

for the LV or HV problem, which is independent of the power flow. This is called a 

bidirectional VR. 

20
 
Substation

Sour ce

DR Source

Regulator 

Load Load 

Load Load 

Regulator

power flow power flow power flow

Figure 22. DR sources create bidirectional flows through a step VR 

Reverse

Power Flow

V2 

V1 

VT1 

VT2 

CT 

Forward 

Power Flow 

V2

V1

VT1

Control 

System 

VT2

CT

Forward

Power Flow

Notes: (1) Reverse flow - use VT1 voltage

(2) Logic controls motor rotation direction (2) Logic controls motor rotation direction

Figure 23. Reverse power flow – additional VT required VT1 

V2 

V 1 

Reverse 

Power Flow 

V2 - V1 = V CT Δ 

V2

V1

Reverse

Power Flow

V2 - V1 = V CT

V2

V1

Reverse

Power Flow

Δ

Control 

System 

V2 - V1 = V CT Δ

Figure 24. Reverse power flow – differential transformer 

21
 
3.15 Bidirectional Voltage Regulator 

The bidirectional VR may use either of the methods outlined in Figure 23 or Figure 24, but a 

VT must be added for the method shown in Figure 23. Therefore, it is common to have the 

logic, based on the direction of current flow, calculate the voltage on either the source or load 

side based on one VT voltage measurement. Also, the logic in the control system knows the 

position of the reversing switch and the tap position number by counting the number of tap 

positions from neutral, either raise or lower. This results in a lower-cost regulator for DR 

applications. In addition, the RL and XL settings are usually different when the current 

reverses direction; therefore, this regulator must have a set of forward settings and a set of 

reverse settings. 

Figure 25 shows four application cases—a, b, c, and d—for the unidirectional step VR. The 

first case (a) is a simple application of an LTC transformer (1) at the substation. The voltage 

drop in the feeder to the feed point is compensated using the R1 and X1 values of the circuit 

to provide a fixed voltage VR1 at the regulation point as the load current and load power 

factor change and as the primary voltage on the LTC transformer changes. The second case 

(b) shows the LTC transformer regulation device (1) regulating to VR1 and a DR (2) 

regulating voltage at VR2. The third case (c) uses an LTC transformer (1) regulating to VR1 

and a unidirectional step regulator (2) regulating to voltage VR2. It is not necessary to know 

the R2 and X2 values for this case, but they must be known for cases e, f, and g, which follow 

in Figure 26. For consistency, these values are shown in all the latter application cases. The 

fourth case (d) has three methods of voltage regulation: the LTC (1), the unidirectional 

regulator (2), and a capacitor (3). All of these cases are used in the modeling and circuit 

simulation studies to determine resultant voltage profiles. 

Figure 26 consists of three additional cases—e, f, and g—in which bidirectional VRs and DR 

are applied to regulate the voltage on the circuit. The fifth case, e, shows LTC regulation (1), 

bidirectional voltage regulation (2), DR regulation (3), and a reactive compensation capacitor 

(4). If the DR is an induction generator, a capacitor is often used to provide the voltage if it 

becomes isolated from the circuit because an induction generator does not create voltage. 

But, the kilowatt injection at 3 will improve the voltage because less load current flows 

through the circuit elements. The sixth case, f, adds an additional bidirectional regulator (3). 

The final case, g, involves the addition of a second DR, which does not regulate voltage. 

However, the DR at 4 does provide Var production and Var absorption to regulate voltage. It 

should be remembered the loads in Figure 25 and Figure 26 are shown as lumped loads. In 

actual applications, the loads are distributed throughout the circuit. All these cases will be 

analyzed in detail to show the effects of DR generation, DR voltage regulation on a normal 

voltage- regulated circuit that contains an LTC, step regulators, and capacitors. 

22
 
LTC 

Power Flow 

VR1 

LTC

Pow

R1 X1 

Load 

Load 1 Load 

er Flow

VR1

(a)

Forward Forward Reverse

LTC Power Flow 

VR1 VR2 

DR 

LTC Power Flow

R1 X1 

Power Flow

VR1

Load 

Load 1 Load 

VR2

2 

DR

Power Flow

(b)

LTC Power Flow 

VR1 VR2 V3 

LTC Power Flow

VR1 VR2

R1 X1 

1 Load 

R2 X2 

2 

R3 X3 R4 X4 

Load Load 

V3

(c)

τ < τ 

Figure 25. Examples of unidirectional VRs and DR 

LTC Power Flow 

VR1 VR2 

LTC

R1 X1 

Power Flow

VR1

1 Load 

VR2

R2 X2 

2 

R3 X3 R4 X4 

Load Load 

V3 

(d) 

21 

3 

23
 
Forward Reverse 

Power Flow Power Flow 

LTC 

VR1 VR2 VR3 

(e) 

DR 

LTC

R1 X1 

VR1 VR2

R2 X2 R3 X3 R4 

Load 1 2 

X4 

Load 3 

4 

Load 

VR3

(e)

DR

Forward Forward Reverse

LTC 

Power Flow 

VR2 

VR3 

(f) 

DR 

VR1 

Power Flow 

LTC

X1 

Power Flow

VR2

R2 X2 R3 X3 R4 

Load Load 

R1 

1 2 

X4 

4 

5 

3 

VR3

(f)

DR

VR1

Load 

R5 X5 

Power Flow

Forward Reverse 

LTC 

R1 X1 

Power Flow 

1 

VR2 

R2 X2 

2 

R3 X3 R4 X4 

Load 

Load 

VR3 

4 

DR 

VR1 

Load 

R5 X5 

Power Flow 

No Regulation 

3 

5 

DR 

(g) 

Figure 26. Examples of bidirectional VRs and DR 

24
 
3.16 Step Voltage Regulator Control System 

Four settings are required to control voltage: 

•	 Set point voltage – The voltage required at the load on a 120-V base 

•	 Voltage bandwidth – The voltage variation from the set point voltage at the load. If 

the set point voltage is 125 V and the bandwidth is 2 V, the regulator will control the 

voltage within 126 V and 124 V 

1V 

Set point = 125V Bandwidth 

1V 

•	 Time delay – The time between when a change in voltage is sensed and when the 

change in voltage occurs. The time delay allows for the short-term surge currents, 

such as motor-starting currents, to occur so that tap changing does not occur during 

these temporary periods of voltage drop 

•	 Line drop compensator – The compensator for the voltage drop in the circuit between 

the regulator and the load. The R and X values of the line are set to determine the 

voltage drop in the line. 

VT 

VL 

VS 

VT

Line Drop 

Compensator 

Voltage 

Relay 

Reactor 

Circuit Time Delay 

VL

VS

Figure 27. Control circuit of step VR 

The components of the control circuit are illustrated in Figure 27. The kilovolt-ampere rating 

of the regulator is determined using the same approach as that used for the autotransformer 

because since the shunt and series windings form an autotransformer. The kilovolt-ampere 

rating is usually 10% of the rated current flowing through the series winding. 

25
 
3.17 Voltage and Current Equations

As previously noted, there are three types of VRs: Type A, Type B, and bidirectional. The 

most common is Type B. Figure 28 shows Type A. Here, the preventive autotransformer 

winding is connected to the load terminal (L). The regulator is in the raise, r, position; the I2 

current is “up”; and the excitation current of the shunt winding, I1, is “down.” The exciting 

current varies because it is connected to the source, S. When the reversing switch is 

connected to the lower terminal (l), the I2 current is reversed (“down”), as in Figure 29, and 

the I1 current is “up.” This is because the polarity of the series winding has changed because 

of the reversing switch changing its polarity. 

Substation 

Source 

VLLoad 

CT 

VS 

N 

VT 

N2 

I 

s 

I

L Series Winding 

N2 

I

2 

E2 

E1 

N1 

I

1 

Substation

Source

VLLoad

CT

VS

N

VT

Control 

System 

N2

I

s

I

L Series Winding

S 

L 

SL 

r 

l 

N2

I

2

E2

E1

N1

I

1

Figure 28. Type A step regulator – raise position 

Substation 

Source 

CT 

VS 

N 

VT 

N2 

I

s 

I Series Winding L

N2 

I

2 

E2 

E1 

N1 

I

1 

Substation

Source

CT

VS

N

VT

Control 

System 

N2

I

s

I Series Winding L

S 

L 

SL 

r 

l 

N2

I

2

E2

E1

N1

I

1

Figure 29. Type A step regulator – lower position 

For the Type B regulator, the preventive auto is connected to the source terminal (S). Figure 

30 shows the Type B regulator in the raise position (r). 

26
 
Series Winding 

VLLoad 

VS 

N 

Substation 

Source Exciting 

Winding 

(Shunt) 

I

L 

E1 

E2 

I s 

N2 

I

2 

I N 1

1 

CT 

VT 

Series Winding

VLLoad

VS

N

Substation

Source Exciting

Winding

(Shunt)

Control 

System 

S 

L 

SL 

r 

l 

I

L

E1

E2

I

s

N2

I

2

I N 1

1

CT

VT

Figure 30. Type B regulator – raise position 

Here, the excitation current is constant because the shunt winding is connected to the load 

side (L) or the regulated circuit side. 

For the Type B regulator in the raise position of Figure 30, the voltage and current equations 

may be written as: 

Raise Position Equations 

N1I1 = N2I2 Equation 3.12 

2 

2 

1 

1 

N 

E 

N 

E = Equation 3.13 

IL = IS – I1 Equation 3.14 

VS = E1 – E2 Equation 3.15 

IL = IS – I1 Equation 3.16 

E1 = VL Equation 3.17 

IS = I2 Equation 3.18 

From equations 3.13 and 3.17, 

E2 = (N2/N1) E1 = (N2/N1) VL. Equation 3.19 

27
 
From Equations 3.12 and 3.18, 

I1 = (N2/N1) I2 = (N2/N1) IS. Equation 3.20 

From Equations 3.15, 3.17, and 3.19, 

VS = E1 – E2 = E1 – (N2/N1) VL = VL – (N2/N1) VL 

VS = (1 – (N2/N1) VL. Equation 3.21 

From Equations 3.16 and 3.20, 

IL = IS – I1 = IS – (N2/N1) IS 

IL = (1 – N2/N1) IS. Equation 3.22 

Defining the raise turns ratio term as 

ar = (1- N2/N1) Equation 3.23 

and substituting into equations 3.21 and 3.22, 

VS = ar V Equation 3.24 

IL = ar IS. Equation 3.25 

Using Figure 31, the voltage and current equations for the lower regulator position may be 

defined as: 

Lower Position Equations 

N1 I1 = N2 I2 Equation 3.26 

E1 E2 = Equation 3.27 N1 N2 

IL = IS + I1 Equation 3.28 

VS = E1 + E2 Equation 3.29 

E1 = VL Equation 3.30 

IS = I2. Equation 3.31 

28
 
Series Winding 

VLLoad 

VS 

N 

Substation 

Source Exciting 

Winding 

(Shunt) 

E1 

E2 

I 

s 

N2 

I

2 

N1 

I

1 

I

L 

CT 

VT 

Series Winding

VLLoad

VS

N

Substation

Source Exciting

Winding

(Shunt)

Control 

System 

L 

SL 

r 

l 

S 

E1

E2

I

s

N2

I

2

N1

I

1

I

L

CT

VT

Figure 31. Type B regulator – lower position 

From equations 3.27 and 3.30, 

E2 = (N2/N1) E1 = (N2/N1) VL. Equation 3.32 

From equations 3.26 and 3.31, 

I1 = (N2/N1) I2 = (N2/N1) IS. Equation 3.33 

From equations 3.29, 3.30, and 3.32, 

VS = E1 + (N2/N1) E1 = VL + (N2/N1) VL 

VS = (1 + N2/N1) VL. Equation 3.34 

From equations 3.28 and 3.33, 

IL = IS + I1 = IS + (N2/N1) I2 

IL = IS (1 + N2/N1). Equation 3.35 

Defining the lower position turns ratio term as 

al = (l + N2/N1), then Equation 3.36 

VS = al VL Equation 3.37 

IL = al IS. Equation 3.38 

29
 
Notice that the only difference between voltage and current raise equations 3.21 and 3.22 and 

voltage and current lower equations 3.34 and 3.35 is the sign of the turns ratio N2/N1. The 

sign of the raise position is negative, and the sign of lower position is positive. It is not 

necessary to know the turns ratio of equations 3.21, 3.22, 3.34, and 3.35 because each tap 

represents a voltage change of 5/8% or 0.00625 p.u. Therefore, ar and al can be described as 

ar, al = 1 -, + (0.00625) tap position for a Type B regulator. Equation 3.39 

For the Type A regulator, the ar and al are

 ar, al = 1 +, - (0.00625) tap position. Equation 3.40 

3.18 Equivalent Circuits 

Because the series impedance and shunt admittance of a step VR are negligible, their effects 

can be ignored. But if desired, this effect can be included in the same manner as the 

equivalent circuit for an autotransformer. 

3.19 Line Drop Compensator 

For VRs to operate properly, when applied at a substation or on a circuit, and maintain voltage 

at the regulation point, line drop compensators are required. The voltage at the regulation point 

is to be constant even through the load power factor and the load change. This is achieved by 

setting the resistance and reactance controls on the control panel of the regulator. 

The voltage-regulating relay of Figure 32 causes the regulator to return to the preset voltage, 

VR, when a change in voltage occurs. For the VR to compensate for the voltage drop in the 

circuit to the regulation point, an additional voltage must be added between the VT output 

and the voltage-regulating relay (VRR) so that the VRR sees a reduced voltage proportional 

to the load current and load power factor. The current from the VT is almost in phase with 

the voltage because the resistance of its secondary circuit is high compared with the 

reactance of this circuit. The current from the CT adds current through the RL and XL that has 

the same phase angle as the load current and is proportional to the load current. The VRR is 

adjusted so that, with no load current, the regulator output is equal to the set point voltage at 

the regulation point. The compensator RL and XL elements are adjusted so they are 

proportional to the RL and XL of the circuit between the regulator and regulation point. The 

phasor diagram of Figure 33 shows how the regulation point voltage, VR, or the voltage 

across the VRR is determined from the output voltage of the regulator, VO (from the VT), 

and the RL and XL values of the circuit. IL is the load current, and θ is the power factor angle 

of the load current from the CT. The ILRL voltage drop is the voltage drop across the RL of 

the compensator, and ILXL is the voltage drop across the XL of the compensator. 

30
 
Voltage CT 

Regulation 

Point 

to 

load 

Source 

Regulator I

L 

Line Drop 

Compensator shown dotted 

VO VRR VR 

CT

Regulati

X RL L

RLset XLset 

on

Point

to

load

Source

Regulator I

L

Line Drop

Compensator shown dotted

VO VRR VR

RL = Line resistance L

VO = Regulator output voltage	 XL VO = Regulator output voltage X = Line reactance L = Line reactance

VR= Relay Voltage	 θ = Load Power Factor

I

L = Load Current	 RLset IL = Load Current R = Compensator resistance Lset= Compensator resistance

XLset = Compensator reactance Lset

Figure 32. Control system and line drop compensator 

I

L

VO 

VR 

I

L XL 

I

L RL 

θ

VO

VR

I

L XL

I

L RL

θ

Figure 33. Phasor diagram for line drop compensator 

The values RL and XL are calibrated in volts on the dials of the compensator panel. When the 

dial is set at a voltage value, this is the voltage compensation at rated current in the secondary 

of the CT. The regulator rating must be determined before the RL and XL settings can be 

defined. 

31
 
3.20 Regulator Ratings

If VO is the output voltage and Vi is the input voltage for a single-phase regulator, then the 

percent regulation range is 

% R = [(|Vo| – |Vi|)/|Vi|] x 100 Equation 3.41 

in either the buck or boost direction. The regulation kilovolt-amperes is defined as 

kVARegulation = [(|Vo| – |Vi|)/|Vo|] kVA SΦ circuit, Equation 3.42 

and the regulator kilovolt-amperes rating is 

{[(|Vo| – |Vi|)/| Vi|][100 x kVA SΦ circuit]}/100 Equation 3.43 

kVA SΦ Rating = [% R (kVA SΦ circuit)]/100 = (% R |kVLL| |IL|)/100,

 Equation 3.44 

where kVLL is line-to-line voltage, and IL is the load current. For the three-phase, four-wire 

wye system of Figure 34, Equation 3.44 is used, but the kilovolt-amperes of the circuit are 

now three-phase. 

kVA 3Φ Rating = [% R (kVA 3Φ circuit)]/100 or 

kVA 3Φ Rating = [% R √3|kVLL| |IL|]/100. Equation 3.45 

Figure 35 shows the phasor diagram for the wye connection. Notice that the regulated 

voltages are in phase with the input voltages. For a 13.2-kV three-phase, four-wire wye 

system and an 8,000-kVA circuit load, IL = 350 A. With ±10% regulation, the rating is 

kVA 3Φ Rating = [(10) (√ 3) (13.2 kV) (350 amps)]/100 = 800 kVA. 

Equation 3.46 

32
 
A'

Regulator 1 

Regulator 2 

B' 

A 

Regulator 3 

I

A 

B 

I

B 

C 

C' 

N 

I

C 

Regulator 1

Regulator 2

B'

A

Regulator 3

I

A

B

I

B

C

C'

N

I

C

Figure 34. Three single-phase VRs connected wye 

on a four-wire, three-phase circuit 

Load

33
 
B B'

VNB 

VNB' 

N 

VNA' 

VNA 

A' 

A 

VNC' 

VNC 

C 

C' 

B B'

VNB

VNB'

N

VNA'

VNA

A'

A

VNC'

VNC

C

C'

Figure 35. Voltage phasor diagram of wye-connected, three single-phase VRs 

Notice, from Equation 3.46, that the kilovolt-ampere three-phase rating of the ±10% 

regulator is just 10% times the three-phase circuit load. For a three-phase, three-wire circuit, 

Equation 3.46 applies because the regulator is connected in wye, but there is no connection to
 

the neutral of the regulator.
 

Sometimes, two single-phase regulators are connected open delta or “vee” to obtain voltage
 

regulation on a delta three-wire system. This connection is shown in Figure 36. For its phasor 

diagram, see Figure 37. The same percentage increase in voltage on VCB to VC’B and VBA to 

VBA’ causes the same percentage increase on VAC to VA’C’. The input to the regulator is the 

line voltage, not the line-to-neutral voltage, as in Figure 34. From Equation 3.44, the singlephase rating can be used because the voltage is line-to-line. The-three phase circuit kVA = √
 

3 kVLL IL, and each single-phase regulator kilovolt-ampere rating is 

kVA SΦ Rating = [(%R √ 3 | kVLL | | IL | )]/[(100) (√ 3 )]. Equation 3.47 

34
 
IA

B 

C 

A 

IB 

IC 

Regulator 1 

Regulator 2 

B

C

A

IB

IC

Regulator 1

Regulator 2

Figure 36. Two single-phase VRs connected open delta 

on a three-wire, three-phase circuit 

35
 
A’

B 

A 

C 

VBA 

VCB 

VA’C’ VAC B

A

C

VBA

VCB

VA’C’ VAC

C’

Regulator Input Voltages V Regulator Input Voltages VBAVCBVAC

Regulator Output Voltages V Regulator Output Voltages VBA’VC’BVA’C’

Figure 37. Voltage phasor diagram of open delta-connected 

two single-phase VRs 

The √ 3 is needed in the denominator to obtain the phase current. When a ±10% regulation is 

substituted for %R in Equation 3.47., the kilovolt-ampere rating is 

kVA SΦ Rating = [(10) (kVA 3Φ circuit)]/[(100√3)]

 = (kVA 3Φ circuit)/(17.32). Equation 3.48 

For a 4.8-kV, three-phase, three-wire delta system and a 2,000-kVA, three-phase circuit load, 

the load current is 241 A. Applying Equation 3.48 and using ±10% regulation, each singlephase unit connected in open delta is 

kVA SΦ Rating = [(10) (2,000)]/[(100) (17.32)] = 115 kVA. Equation 3.49 

In this case, the rating is 6% of the three-phase circuit load, not the 10% calculated for the 

four-wire wye system above. 

36
 
Three-phase regulation can be achieved for a closed delta. Closing the delta with the third 

regulator does not allow more circuit load, but it does increase the percentage regulation 

from ±10% to ±15%. This is shown in the phasor diagram of Figure 38. Each regulator of the 

closed delta carries the phase load current, as was the case for the open delta, and the 

regulator rating is determined from equations 3.47 and 3.48, which is identical to the 

regulator rating obtained in the open delta configuration. There are two possible connections 

for the closed delta: the load current leading the line-to-line voltage across the shunt winding 

by 30° and current lagging the line-to-line voltage by 30°. Each of these will be explained. 

3.21 Closed Delta – Leading Current and Lagging Current Connections 

The leading current connection and its phasor diagram are shown in Figure 39, and the 

lagging current connection and its phasor diagram are shown in Figure 40. A phase shift 

results between the input and output voltages, as shown in Figure 38, and different phase 

shifts occur depending on the tap and boost or buck positions. The smaller phase shifts occur 

for the lower tap positions. Although there are no advantages to either 30° leading or lagging 

connections, it may be necessary to go beyond the range of the compensator settings for one 

versus the other connection. Therefore, one of these connections may be chosen to solve this 

problem. It is generally not recommended to use wye-connected, single-phase regulators for 

the delta system because the neutral will shift for unbalanced loads. Because there are 

separate controls for each regulator, this may cause a different response and result in a 

neutral shift. 

37
 
C'

10%

115 %

A 

10% 

115% 

115% 

10% 

C 

A 

B 

100% 

100% 

100% 

A

10%

115%

115%

10%

C

A

B

100%

100%

100%

A'

B'

Figure 38. Voltage diagram of closed delta-connected 

three single-phase VRs 

38
 
C'

Regulator 1 

Regulator

Regulator 3 

2

IC 

B 

A 

A' 

C 

C 

B 

A 

B' 

IA 

A' 

B' 

VA' C' IB 

VB' A' 

C' 

VC' B' 

Regulator 1

Regulator

Regulator 3

2

IC

B

A

A'

C

C

B

A

B'

I

Regulator 1

Regu

A

A'

B'

VA' C' IB

VB' A'

C'

lator

Regulator 3

2

IC

B

A

A'

C

C

B

A

B'

IA

A'

B'

VA' C' IB

VB' A'

C'

VC' B'

Regulator 3

VC’B’

30o 

30o 

30o 

IA 

VB’A’ 

IB VA’C’ 

Current leads 

the voltage 

IC 

30o

30o

30o

IA

VB’A’

IB VA’C’

Current leads

the voltage 

IC

Regulator 2 Regulator 1

Figure 39. Closed delta-connected three single-phase VRs – leading connection 

39
 
Regulator 1 

Regulator 2 C 

C'

I

C

IC

C'

A C

A'VB'C'

VC'A'

I

B

IB

B'

Regulator 3 Re atorgul 3atorgul 3ator

B

VA 'B' 

B' B

AA'

I

A

IA

Regulator 1 Regulator 1 Regulator 2

IC VC’A’ VA’B’

30o

Current lags 30o the voltage IA

30o

IB

VB’C’

Regulator 3

Figure 40. Closed delta-connected three single-phase VRs – lagging connection 

40
 
3.22 Compensator Settings 

If no load is connected between the regulator and the regulation point, it is easy to determine 

the settings of RL and XL. This is the case for a typical substation step regulator, as in Figure 

32 and Figure 33. The RL setting and XL settings are determined from equations 3.50 and 

3.51 as 

RLset = [(CTP/NVT)] (RL) (l) Equation 3.50 

XLset = [(CTP/NVT)] (XL) (l) Equation 3.51 

where 

RLset = Dial setting for the resistance in the feeder portion of the circuit given in volts 

XLset = Dial setting for the reactance in the feeder portion of the circuit given in volts 

NVT = VT ratio of primary voltage/secondary voltage 

CTP = Primary rating of the CT given in amperes 

RL = Resistance per conductor in unit length from the LTC to regulation point, 

normally given in ohms per mile 

XL = Reactance per conductor in unit length from the LTC to regulation point, 

normally given in ohms per mile 

l = Unit length in miles to the regulation point. 

The settings for RLset and XLset can now be determined. But first, the regulator rating must 

be calculated. 

From Equation 3.46, the rated amperes for three single-phase regulators connected wye and 

rated 13.8 kV, 1,000 kVA, and ±10 regulation is 418 A. The CT ratio is 500:5, and the VT 

ratio is 13.8 kV/√3 = 7,960:120. The regulator is located 3 miles from the regulation point, and 

the conductor size is 636 kcmil all aluminum. From the resistance and reactance values of 

X = 0.536 Ω/mile/conductor (see Equation 3.9) 

R = 0.164 Ω/mile/conductor, 

and using equations 3.50 and 3.51, 

XLset = [(500)/(7960/120)] [(0.536) (3)] = 12.12 V Equation 3.50 

RLset = [(500)/(66.3)] [(0.164) (3)] = 3.71 V. Equation 3.51 

41
 
The control panel dial settings are based on the rated current of 500 A for the CT primary, 

not the load current or the rated current for the regulator. For step regulators installed on the 

circuit, the primary rating of the CT is the same as the regulator current rating. Hence, the 

regulator current rating can be substituted for the CT primary current rating in equations 3.50 

and 3.51. Load may be connected between the regulator and the voltage regulation point; 

therefore, the magnitude of the current flowing through the CT of the regulator does not 

equal the magnitude of the current flowing through the balance of the RL and XL of the 

circuit to the regulation point. This is especially true for regulators installed beyond the feed 

point voltage VR. Equations 3.50 and 3.51 can be corrected with the aid of Figure 41. 

1 mile1 mile1 mile

Section (1) Section (1) Section (2) Section (3) Section (2) Section (3)

I1 = 400A I

2 = 350A I I1 = 400A I2 = 350A I3 = 300AVR

ΔV1 ΔV2 ΔV

Load1 Load2 

3 

Other 

Loads 

ΔV1 ΔV2 ΔV3

Feed Point or IL= 400 A = 400 A

50A Regulation Regulator Regulator 50A

Poin t

Figure 41. Current at the regulator is not equal to current 

in the last section before the regulation point 

The RL set and XL set can be changed to consider the effect of load being served before the 

regulation point. 

RLset = (CTP/NVT) / (RLE), Equation 3.52 

where the effective resistance RLE when multiplied by IL gives the same voltage drop as the 

sum of the drops through the various sections of line (e.g., Section 1, Section 2, and Section 3 

in Figure 41). Thus, RLE can be written as 

n 

RLE = ( ∑ | ΔViR | )/IL Equation 3.53 

i = 1 

n 

∑ |ΔViR| = | I1 | RL1 l1 + | I2 | RL2 l2 + | I3 | RL3 l3 ... | In | RLn ln. 

i = 1 Equation 3.54 

n 

∑ | ΔViR| = The total voltage drop from regulator to the regulation point. 

i = 1 

42
 
RLE = Effective resistance 

| IL | = Load current flowing through the regulator 

| I1 |, | I2 |, | I3 |, ... | In | = The load current in each line section to the regulation point 

RL1, RL2, RL3 ... RLn = The resistance in ohms per mile of each section from regulator 

to the regulation point 

l1, l2, l3, ... ln = The length of conductor in miles for each section from regulator to 

the regulation point 

n = number of line sections. 

The 

XLset = CTp/NVT (XLE), Equation 3.55 

where XLE takes on the same form as equations 3.53 and 3.54 for RLE. Based on Figure 41, 

and Equation 3.54, the RLE is found as follows: 

3 

∑ |ΔViR | = (400) (0.164) (1) + (350) (0.164) (1) + (300) (0.164) (1) 

i = 1 

 = 65.6 + 57.4 + 49.2 = 172.2 V. Equation 3.56 

From Equation 3.53, 

RLE = 172.2/400 = 0.4305 Ω Equation 3.57 

RLset = (500/66.3) 0.4305 = 3.25 V. Equation 3.58 

In reference to the RLset values of equations 3.53 and 3.58, the value of Equation 3.58 is 

lower because the load current has stepped down after having served loads 1 and 2. Thus, the 

total voltage drop is less and the compensation is less. 

Equation 3.54 has considered the power factor angle to be the same for each section. 

However, in fact, this angle may not be the same for each section. A more practical approach 

is to measure the load current at the regulator, the load power factor, and the voltages at the 

regulation point and the regulator output at the same time. From these data and the X/R ratio 

out to the regulation point, and by applying the voltage drop equation, the effective values of 

RLE and XLE can now be calculated. 

ΔV = IL RLE Cos θ + IL XLE Sin θ Equation 3.59 

43
 
3.23 Other Compensator Settings and Corrections 

Settings for three-phase regulators connected wye and three single-phase regulators 

connected wye are determined using the same approach as that outlined above. However, 

when single-phase regulators are connected in open delta, the control voltage and current in 

the compensator do have the same phase relationship as the wye-connected regulators. For 

example, the open delta connection described in Figure 36 and Figure 37 show the control 

voltage and current as VBA and IA for Regulator 1 and as VCB and IC for Regulator 2, which 

are 30° out of phase with the wye connection shown dashed in Figure 37. The current of one 

regulator lags the voltage by 30° plus the power factor angle, and the current of the other 

regulator leads the voltage by 30° minus the power factor angle. Therefore, phase-shifting 

networks are used, or corrections are made to the settings. On the control panel of substation 

regulators, a 30° shift forward or 30° shift back is selected to correct this problem. 

For single-phase connected open delta regulators applied to the circuit, corrections are made 

to the settings by using a 30° phase shift in the voltage on the compensator circuit. For the 

lead unit regulator in an open delta connection, the corrected settings are determined by 

multiplying the original settings obtained earlier by the quantity cos 30° – j sin 30°, or 

RLC + jXLC = (0.866 – j0.5) (RL + jXL), Equation 3.60 

where RLC + jXLC are the corrected values. 

For the lag unit regulator in an open delta connection, the corrected settings are found by 

multiplying the original settings by the quantity cos 30° + j sin 30°, or 

RLC + jXLC = (0.866 – j0.5) (RL + jXL). Equation 3.61 

Because these new, corrected settings require the phase angle to be moved back 30° or 

forward 30°, negative RL values result when increasing the phase angle, and negative XL 

values result when decreasing the phase angle. 

3.24 Step Regulators in Series 

Often, to obtain the needed voltage profile on a circuit and not subject customers to LV or 

HV, two or more regulators are installed. This was illustrated in Figure 5. The solutions to 

the problems associated with these installations are dependent on the time delay settings, the 

bandwidth settings, and the voltage magnitude of the tap position steps. Other factors include 

changes in voltage at the primary side of the substation transformer, size of loads, location of 

loads, and the rate of change of load current and the resultant voltage. 

Generally, the best solution is a short first regulator time delay, so the voltage is changed 

before the second regulator begins to make a change. The second regulator then completes its 

change before the third regulator begins to make a change, and so on. However, the time 

delay on the last regulator should not be long enough to subject customers to a long period of 

LV or HV. 

44
 
However, there are exceptions to this rule if large loads are installed on the tag end of a 

circuit. In this case, the preferred solution is to have the last regulator respond first to the 

voltage correction and then readjust after the regulators upstream have operated. The 

optimum solution is the least number of regulator voltage adjustments for all the regulators 

on the circuit. The application of capacitors complicates the problem because, when 

capacitors are switched “on,” the input voltage to the nearby regulators goes up, and the 

regulators may operate to control the voltage within limits. 

3.25 Fixed Capacitors on Circuits with Regulators 

When a fixed capacitor is installed at the regulation point or downstream on the circuit, no 

changes to the compensator settings of equations 3.50 and 3.51 are needed. This is because 

the capacitor current IC is included with the IL current, and the current in the CT of the 

compensator includes both IL and IC. This assumes no load is connected between the 

regulator at the substation and the regulation point or between the regulator on the circuit and 

the regulation point. When load is connected between the regulator and the regulation point, 

then equations 3.52 and 3.55 for the RLset and XLset are not correct. This is because the ICRE 

and ICXE are not equal to the ICRa and ICXa, where the actual line resistance is Ra and the 

actual line reactance is Xa. This is shown in Figure 42. This phasor diagram shows the 

received voltage difference before and after the fixed capacitor is installed is 

| V’RC | - | VRC | = | IC | (Xa – XE). Equation 3.62 

This equation applies when the capacitor is located at the regulation point or downstream. 

This effect can be taken into account by changing the compensator settings or the VRR 

setting. The easiest and most common solution is to change the VRR setting. However, if the 

compensator settings are to be revised, then equations 3.53, 3.54, and 3.55 must be modified 

to include IC, or 

n

 RLE = [ ∑ | ΔVir |]/( | IL+ IC | ) Equation 3.63 

 i=1

 n

 XLE =[ ∑ | ΔVix |]/( | IL+ IC | ). Equation 3.64 

 i=1 

45
 
- XE I ) C (Xa 

I

C 

I

C Ra 

I

C RE 

V'RC 

VRC 

VR 

I

L RE IL XE 

I

CXa 

I

CXE 

θ

I

C

I

C Ra

I

C RE

V'RC

VRC

VR

I

L RE IL XE

I

CXa

I

CXE

θ

I

L

Figure 42. Phasor diagram of the effect of capacitors on the line drop compensator 

and regulator output voltages before and after relay settings are revised 

VR = Relay setting and regulation point voltage without capacitors 

Ra = Actual resistance from regulator to regulation point 

RE = Effective line resistance from the regulator to regulation point or the resistive 

voltage drop to regulation point. 

IL = Load current at regulator 

Xa = Actual reactance from regulator to regulation point 

XE = Effective line reactance from the regulator to the regulation point 

VRC = Regulator output voltage (relay R and X settings) after capacitors are “on” 

VR’C = Regulator output voltage to have VR at regulation point after capacitors are 

“on” or VR – IC (XL – XE) 

V = Voltage at regulation point with adjusted relay settings because of capacitors 

If a fixed capacitor is installed between the regulator and the regulation point, the IC current 

flows only to the capacitor and is not in the IL current at the regulation point. Again, the best 

method to correct this problem is to change the VRR setting. 

3.26 Switched Capacitors on Circuits with Regulators

When a switched capacitor is switched “on,” the effect on the regulator settings is the same 

as that of a fixed capacitor. If a switched capacitor is installed at the same location as the 

regulator, then the regulator can be operated properly when the capacitor is turned “on” or 

“off.” If the switched capacitor is installed on the source side of the regulator, regulator 

operation is not affected by the capacitor because the IC current does not flow through the 

regulator. However, it is common practice to locate the capacitor on the load side because the 

capacitive current will lower the IL current through the regulator. In this case, regulator 

operation is affected by the capacitor current, and the compensating circuit must be modified. 

This is explained in Figure 43. If the switched capacitor is voltage-controlled and the 

46
 
capacitor is located on the load side of the regulator, the VT of the capacitor control should 

be located on the source side because the regulator operation will not affect the capacitor 

operation. Notice in Figure 43, with a CT in the capacitor circuit connected to the CT of the 

regulator control, that there is no IC current in the compensator RL and XL. 

Another method of control is shown in Figure 44, in which an impedance has been added in 

series with the RL and XL of the compensator circuit that has a voltage drop equal to the 

voltage rise because of the capacitor. When the capacitor is switched “on,” the auxiliary 

contact is open, which adds a voltage drop in the compensator circuit. When the capacitor is 

switched “off,” the contact shorts out the impedance Z, and the regulator operation reverts 

back to normal, as though the capacitor were not there. 

A third method of control is to change the VRR setting or the compensator settings as 

described earlier. The VRR setting is determined with the capacitor on, but a full setting 

increase should not be used because too low of a voltage will now occur at LL when the 

capacitor is off. 

CT 

to 

load 

Source 

Voltage 

Regulator 

VO VRR VR 

I

L 

I

C 

I

C 

SW 

Capacitor 

Bank 

I

C 

I

C 

I

L 

(IL + IC) CT

to

load

Source

Voltage

Regulator

RL XL

RLset XLset 

I

L 

VO VRR VR

I

L

I

C

I

C

SW

Capacitor

Bank

I

C

I

C

I

L

(IL + IC)

VO= Regulator output voltage = Regulator output voltage RL = Line resistance L = Line resistance

VR= Relay Voltage = Relay Voltage XL = Line reactance L = Line reactance

I

L= Load Current = Load Current θ = Load Power Factor

Figure 43. Control system and line drop compensator with use 

of a shunt capacitor at the location of regulator 

47
 
Voltage Regulator

Aux. contact 

Source 

(IL + IC) 

VT 

RL XL 

VRR 

I

C 

I

L 

I

C 

I

L 

SW 

Aux. contact

Source

(IL + IC)

VT

RL XL

VRR

I

C

I

L

I

C

Z 

I

L

SW

Figure 44. Voltage across impedance Z in relay circuit 

is equal to voltage rise because of capacitor current Ic 

3.27 Switched Capacitors Downstream from Regulators 

When switched capacitors are installed downstream from the regulators, the compensator 

settings or the voltage setting on the VRR can be changed. The easiest approach is to change 

the VRR setting. Coordination of regulators and switched capacitors on the same circuit is 

generally not a problem because the bandwidth on the capacitor voltage control relay is 

greater than the regulator bandwidth and the time delay for the capacitor control is more than 

the regulator time delay (which is similar to regulators installed in series, in which the 

downstream regulators have a greater time delay than the upstream regulators). Also, the 

voltage change at the capacitor when it switches on is high compared with what the upstream 

regulators see. 

3.28 Capacitor Application 

As noted earlier, capacitors can be added to distribution circuits to improve voltage 

regulation. Equation 3.8 showed that voltage rise (a reduction in load current IL) can be 

calculated if one knows the single-phase kilovolt-amperes reactive or three-phase kilovoltamperes reactive, the distance from the source to the capacitor, the inductive line reactance, 

and the line-to-line voltage. The voltage rise is independent of the load magnitude. Therefore, 

it is common to install switches to turn them on and off to not subject customers to HV 

during LL conditions, when the voltage drop in the circuit is low. 

Capacitors are rated in kilovars, the value of which is derived from the capacitance C in 

microfarads, the rms voltage V, and the frequency, or 

kVAr = (V2

 2πƒ C x 10 –6)/1,000. Equation 3.65 

Notice the kilovar value is proportional to the square of the voltage. As voltage drops on a 

circuit, the kilovar value decreases, and the voltage rise decreases. 

48
 
kVA

0 

There are two types of capacitors: series and shunt. Series capacitors are not discussed here 

because their application can cause a sub-synchronous resonance condition. Often, additional 

resistance must be added to correct this problem. Shunt capacitors supply a source of kilovars 

similar to an overexcited synchronous generator. They are often applied to induction 

generators to supply a source of voltage. Shunt capacitors lower or counteract the lagging 

component of circuit current and, thus, increase the voltage at their location. This improves 

the voltage regulation. Because the lagging component of current is reduced, capacitors 

reduce the I2RL real losses and the I2XL reactive losses. They are a low-cost solution to 

improving the power factor of load because synchronous generator volt-amperes reactive are 

about four times the cost of static capacitors. This reduces the kilovolt-ampere loading on 

synchronous generators, which in turn, allows more kilowatt generation (if this is not limited 

by the prime mover kilowatt output). When capacitors are added to a circuit, they reduce the 

load current, release capacity to serve future load, and reduce the cost to serve kilowatts. 

Correction to unity power factor where no reactive current exists in the load current is 

generally not economical. Power factors ranging from about 0.975 up to 0.980 are normally 

the most economic, as seen by the generation source. The diminishing return effect is 

illustrated in Figure 45. 

Shunt Capacitors 

Load kW 

high P.F. 

low P.F. 

Shunt Capacitors

Load kW

high P.F.

low P.F.

A 

Tota l

Load

kVAr

B A

Change in kVA

Figure 45. Application of shunt capacitors 

Applying enough kilovar shunt capacitance to offset just half the load kilovars results in a 

large kilovolt-ampere reduction of “A.” If an additional equal amount of kilovars is added, it 

results in only a small kilovolt-ampere reduction of “B.” Thus, the lower the power factor, 

the more benefit that is derived from installing shunt capacitors. 

49
 
The voltage drop ∆V in a circuit can be approximated by 

∆V = IrR + IxX, or Equation 3.66 

∆V = I (R Cos θ + X Sin θ), Equation 3.67 

where: 

I = Load current
 

Ir = Real component of current 

Ix = Reactive component of current 

θ = Load power factor angle. 

When a capacitor is added, Equation 3.66 becomes 

∆V = IrR + IxX – IcX, Equation 3.68 

where: 

Ic = Capacitive reactive components of current. 

If too many volt-amperes reactive are added to the circuit during LL conditions, the circuit 

can become overcompensated because IC is proportional to V, not the load. 

Figure 46 shows the phasor diagram when a shunt capacitor is added at the load. The 

sending-end voltage with the capacitor applied (VSC) is less than the sending-end voltage 

without the capacitor (VS). 

3.29 Capacitor Controls

Capacitor control can be accomplished through the: 

• Time clock 

• Voltage 

• Current 

• Temperature 

• Time clock with voltage override 

• Time clock with different VRR settings 

• Current with voltage override 

• Radio or other communication medium 

• Power factor. 

The most common and simplest control is time clock control because the load profile on 

most circuits is predictable. As such, the time clock turns the capacitor on at a set time in the 

morning and off at a set time at night. 

Figure 47 shows a voltage-current control in which the voltage can be measured at the 

capacitor or another location on the circuit and the VRR signals the capacitor switch to close. 

50
 
VSVR

Source 

Shunt 

Capacitor 

I 

VSC 

ICR 

Ir IX 

I 

ICX 

IXX 

IrR 

VR 

IXR 

VS 

IrX 

R X 

Source

Shunt

Capacitor

I

VSC

ICR

Ir IX

I

ICX

IXX

IrR

VR

IXR

VS

IrX

Source

Shunt

Capacitor

I

Load 

VSC

ICR

Ir IX

I

ICX

IXX

IrR

VR

IXR

VS

IrX

R X

The IxX Component is parallel to and opposite to the I The I X Component is parallel to and opposite to the IcX component. X component.

VR= voltage at the load or receiving end voltage. = voltage at the load or receiving end voltage.

VS= sending end voltage = sending end voltage

VSC = sending end voltage with capacitor SC = sending end voltage with capacitor

Figure 46. Phasor diagram of the reduction in the sending-end voltage with a shunt capacitor 

The resistor R is chosen so that its voltage drop represents the drop in voltage to the 

regulation point. If the power factor varies, it may be necessary to add a reactance with the 

resistance. 

CTTo Load

Source 

VT 

Capacitor 

Bank Source

T

Capacitor

R 

VRR 

Figure 47. Voltage and current control of capacitor switching 

51
 
3.30 Capacitor Connections 

Three-phase capacitor banks are normally connected delta or wye with the neutral grounded 

as in Figure 48 or wye with the neutral ungrounded as in Figure 49. Delta-connected 

capacitors or ungrounded wye-connected capacitors may result in a resonant condition when 

one or more of the phase conductors on the source is open, as shown in Figure 50. The 

capacitor bank can provide voltage to the loads when an open phase (or phases) occurs. 

A 

C 

I

C 

I

C 

B VCN BB 

neutral 

BA VAN 

VBN 

A 

C 

N 

I

C

B 

BC 

A

C

I

C

I

C

B VCN BB

neutral

BA VAN

VBN

A

C

N

I

C

B

BC

Figure 48. Wye-connected capacitor bank 

ICA A

I

CC 

C B 

I

C 

VAB 

VCA 

VBC 

BC 

I

C 

AB 

I

C 

CA 

ICA A

I

CC

C B

I

C

VAB

VCA

VBC

BC

I

C

AB

I

C

CA

Figure 49. Delta-connected capacitor bank 

52
 
C 

A
 

B
 

Source Load 

Figure 50. Series resonance condition with open phases 

Putting capacitors in series with transformers feeding load may create a series resonant 

circuit. For this reason, it is not recommended that capacitor banks be put on the load side of 

single-phase fuses, sectionalizers, or reclosers. Grounded wye capacitors are used on fourwire wye systems. Grounded wye capacitors applied to ungrounded wye or ungrounded delta 

systems cause ground currents and overvoltages during ground faults. Therefore, grounded 

wye banks are not used on delta systems or ungrounded wye systems. Delta-connected banks 

are used on delta systems and ungrounded wye systems. 

53
 
4 Project Results – Effects of Unbalanced Loading and 

Voltage on System Protection and Distributed Generation 

4.1	 Introduction 

This section describes the effects of unbalanced voltage and load on system protection. The 

effects of unbalanced voltage and load on sensitive ground relaying were studied for a 

selected circuit, and adequate protective relaying limits were determined for different levels 

of unbalance and different energy conversion devices. 

This section includes an overview of system protection philosophy, focused on the issues 

associated with unbalanced loading. Descriptions of the operation of protective devices under 

unbalanced conditions are also provided. For a detailed discussion of protective relay theory 

and operation, consult Elmore (1994), Electrical Distribution (2005), and Mason. 

4.2	 System Protection Design Philosophy for Grounded and 

Ungrounded Systems 

Substation Substation 3 Phase 3-Single Phase
 

Transformer Breaker Recloser Reclosers
 

3-Single Phase 

Reclosers 

3 Single Phase 

Lateral Fuses 

Figure 51. Radial distribution circuit with typical system protection devices 

Figure 51 shows overcurrent relaying application for the entire circuit. The protective 

devices must be capable of carrying the intended load (loadability), sensing and clearing 

faults (sensitivity), and selectively de-energizing the minimum amount of load to isolate 

faults (selectivity). 

Typical loads, as seen by major protective devices, are shown in Figure 52. Devices at the 

substation must carry the load of the entire circuit; devices downstream carry less load. The 

amount of unbalance in the phase currents may or may not be greatest at the substation breaker. 

54
 
Substation Substation 3 Phase 3-Single Phase 

Transformer Breaker Recloser Reclosers 

3-Single Phase 

Reclosers 

3 Single Phase 

Lateral Fuses 

LOAD LOAD LOAD 

LOAD 

LOAD 

Figure 52. Radial distribution circuit showing load 

Figure 53 shows the portions of the circuit where the protective device must sense faults. 

Note that, for full circuit protection, the zone of protection for the upstream device must 

extend beyond (overlap) the beginning of the next downstream device. 

Substation 3 Phase 3-Single Phase 

Breaker Recloser Reclosers 

3-Single Phase 

Reclosers 

3 Single Phase 

Lateral Fuses 

Figure 53. Radial distribution circuit showing protection zones 

Figure 54 shows the relative tripping times for the substation breaker, the three-phase 

recloser, and the single-phase recloser. As the distance between a protective device and a 

fault increases, tripping time increases. For a fault downstream at point A, the single-phase 

recloser will trip in about 0.5 seconds. The three-phase recloser will trip in about 0.8 seconds. 

If the single-phase recloser operates correctly, the three-phase recloser should not operate, 

and only load beyond B will be interrupted. 

55
 
(B) 3-Single Phase 

Reclosers 

0.7 

0.6 

0.5 

Substation
 

Breaker
 

3 Phase 

Recloser 

3-Single Phase 

Reclosers 

3 Single Phase 

Lateral Fuses 

Fault "A" 

Figure 54. Relative tripping times for protective devices 

Figure 55 shows the time-current characteristics for a typical breaker and reclosers. For any 

specific value of current, the device closest to the substation operates last, and the device 

furthest from the substation operates first. 

56
 
Figure 55. Relative time-current curves for protective devices 

57
 
4.2.1 Four-Wire Grounded Wye Systems 

Four-wire grounded wye systems have a substation transformer with a grounded wye 

winding sourcing the circuit bus. The primary of the transformer is typically connected in a 

delta. The neutral point of the transformer secondary is grounded and taken out on the circuit 

as the neutral with the three-phase conductors. The three-phase diagram in Figure 56 shows 

details of the connections at the substation and load on the circuit. A single-phase load 

connected line-to-ground will cause current to flow in the neutral of the system unless it is 

balanced by equal amounts of other single-phase loads connected to the alternate phases. 

SUBSTATION
 

TRANSFORMER
 

CURRENT 

TRANSFORMERS SUBSTATION AND RELAYS BREAKER LINE TO GROUND LOAD 

A 

B 

C 

A 

B C N 

NEUTRAL 

Figure 56. Three-phase diagram of a four-wire grounded system 

4.2.2 Three-Wire Ungrounded Delta Systems 

Three-wire ungrounded delta systems have a substation transformer with an ungrounded 

delta winding sourcing the circuit bus. The primary of the transformer may be configured in 

an ungrounded wye, grounded wye, or delta. Figure 57 shows details of the connections at 

the substation and load connected on the circuit. The ungrounded delta system differs from 

the grounded wye system because the load is always connected phase-to-phase. Typically, 

there is no neutral or ground relay connected to detect ground faults, as is the case for the 

four-wire grounded wye system. A small amount of current will flow if a phase conductor 

makes solid contact with ground. Some systems may use a ground current relay to detect this. 

A ground detector system is typically installed to alarm for unintentional grounds caused by 

downed conductors or foreign objects making contact with a phase conductor. Ground 

detector systems and why ground currents will flow on ungrounded systems are explained in 

Appendix A. 

58
 
A 

B 

C 

A 

B C 

Ground 

Detector 

VTs 

Ungrounded 

Wye-Delta 

Substation 

Transformer 

L 

L 

L 

Figure 57. Three-phase diagram of a three-wire ungrounded system 

4.3 Unbalanced Voltage Effects on Protective Relaying 

Unbalanced voltages can cause an addition to current already in the neutral conductor and 

relay because of unbalanced load. For the case in which balanced loads are served from a 

distribution circuit with balanced voltages, no current is in the neutrals of a four-wire system. 

For the case in which the voltage is unbalanced and the load is primarily resistive and 

connected line-to-ground, the load will decrease on the lowest voltage phase and increase on 

the highest voltage phase. The current imbalance will result in a current flow in the neutral 

conductor and ground (earth). For the case in which the motor load consists primarily of 

single-phase loads connected line-to-ground, lowering the voltage on one phase will cause 

the current to increase on that phase. This is due to the essentially constant power (CP) 

characteristic of the motor. This current imbalance will cause additional neutral current. 

Additional unbalance can result from failed capacitor cans (units) within a capacitor bank. 

The volt-amperes reactive from the capacitor bank are directly proportional to the voltage 

squared. (See Equation 3.65 in Section 3.) Unbalancing the voltage causes an unequal supply 

of volt-amperes reactive and an unbalanced loading effect with increased neutral current. 

The ultimate effect of unbalanced voltage on the neutral current of the distribution circuit can 

depend on a number of factors, including: 

•	 The mix of single-phase resistances and single-phase motor load 

•	 Capacitor size, location, and unbalance because of unit failures 

•	 Current unbalance and significant increased losses from unbalanced voltages applied 

to three-phase induction and synchronous machines 

•	 Unsymmetrical transformer connections (e.g., open-delta, open-wye, and 

unequal impedances) 

•	 Untransposed lines 

•	 Open phases because of single-phase fuse blowing and single-phase 

protective devices 

•	 Malfunctioning single-phase VR within a three-phase or open-delta or 

open-wye configuration 

59
 
•	 Single-phase VRs connected in a bank and operating to correct a voltage
 

unbalance condition 

•	 Single-phase VRs operating on a long single-phase portion of a three-phase circuit. 

Additional neutral current caused by unbalanced voltage on the circuit will flow in the 

neutral relay (51N) at the substation if neutral current flows through any three-phase 

protective device downstream from the substation. However, circuit unbalance can occur on 

a portion of the circuit but be balanced with other connected load such that no neutral current 

reaches the neutral relay element of that protective device. This relay must be set to trip for 

ground faults. The setting may have to be increased to take into account the increased neutral 

current because of the unbalanced condition. 

4.4 Unbalanced Current Effects on Protective Relaying 

Unbalanced loading can occur even though voltages are balanced at the source. The factors 

that affect unbalanced loading are similar to those factors that affect unbalanced voltage. 

4.4.1 Single-Phase Operation of Protective Devices 

Substation 

Breaker 

(1) 3 Phase 

Recloser (4) 3-Fuses 

(3) 3-Single 

Phase 

Reclosers 

3 Single Phase 

Substation 

Transformer 

(2) 3 Phase 

Recloser 

Fault "C" 

I

A=600 A 

I

B=600 A 

I

C=600 A I

A=200 A 

I

B=200 A 

I

C=200 A 

I

A=400 A 

I

B=400 A 

I

C=400 A 

I

A=100 A 

I

B=100 A 

I

C=100 A 

I

A=150 A 

I

B=150 A 

I

C=150 A 

I

B=150 A 

I

A=150 A 

I

C

Single 

Phase 

Single 

Phase 

B 

A 

C 

Fault "D" 

=150 A 

Single 

Phase 

Lateral Fuses 

Figure 58. Single-phase operation of protective devices 

on a four-wire wye circuit of resistive loads 

Figure 58 shows that protective devices may be three-phase devices, a set of three singlephase devices, or single-phase devices that protect single-phase laterals. Operation of one of 

these single-phase devices on a previously balanced loaded circuit will cause unbalanced 

loading and neutral current. When the circuit is in a normal state with the loads given in 

Figure 58, the three-phase recloser (1) has no current in the neutral relay element. When the 

single-phase recloser (3) on Phase C opens because of the fault at C, load of 150 A is lost on 

Phase C downstream of the recloser. The phase currents on the substation breaker change to: 

60
 
I	 = 600 A ∠0°, I = 600 A ∠ -120°, I = 600 A -150 A ∠120° = 450 A ∠120°. A B	 C 

Current in the neutral element is determined by vectorally adding the three-phase currents. 

I = I ∠0° + I ∠ -120° + I ∠120° N A B C Equation 4.1

I N	 = 600 A ∠0° + 600 A ∠ -120° + 450 A ∠120°
 

=150 A ∠ - 60°
 

4.4.2 Operation of Circuit Protective Devices for Ground Faults 

B 

C 

A 

600 A 

450 A 

5 A 5 A 3.75 A

600 A 600:5 

1.25 A A B C N 150 A 

Figure 59. Diagram of substation breaker and relays with ground-sensing circuit 

The equipment arrangement shown in Figure 59 is typical for a four-wire grounded system. 

The substation transformer, CTs, protective relay current coils, and circuit breaker are 

represented. For simplicity, it is assumed that all load is resistive and connected line-toground and that the phase currents are in phase with their respective voltages. Unbalanced 

currents resulting from phase-to-phase-connected load may not show up in the ground or 

neutral relay sensing circuits. 

Unbalanced current flowing to the load on the circuit will result in current in the neutral relay 

coil (N). The example shows loads of 600 A, 600 A, and 450 A, respectively, on A, B, and C 

phases. Taking into account the CT ratio of 120, the neutral current in the relay element is 

150/120 = 1.25 A. The setting is based on two times the minimum load, which is 1.8 MVA 

or 157 A. 

1,800 kVA 2 Imin = 2 = 2 x 78.73 =157 amperes	 Equation 4.2 3	 x 13.2 kV 

Because the setting is 157/120 = 1.31 A and neutral current is 1.25 A, the breaker will not 

open for the unbalance caused by clearing Fault C, but the single-phase recloser (3) will open 

and lock out for the permanent fault. (See Figure 58.) 

61
 
Reclosers with ground fault-sensing circuits will be affected similarly by load unbalance. The 

same equations can be used for the recloser and the circuit breaker. 

Another case to consider is the opening of a fuse (4) in Figure 58 for a fault at D. The 

unbalance current is 100 A, which results in IN = 100 A ∠ − 60° and a relay element current 

of 0.833 A. Because this is below the setting of 1.31 A, the breaker will not trip, and the fuse 

(4) will isolate the fault. 

The fault current that occurred at D and caused the 150-A fuse (4) to blow was significantly 

higher than the resultant unbalanced current (neutral current) after the fault cleared. For 

example, the fault current magnitude could range from 1,500 to 7,000 A. In this case, the 

neutral relay would see from 12.5 A to 58.3 A for approximately 0.1–0.06 seconds (fuseclearing time). See Figure 63. 

4.4.3 Single-Phase Operation of Disconnect and Isolation Devices 

Opening the fused disconnect (5) of Figure 58 has the same effect as the cleared fault D on 

the neutral current. Disconnects are often opened to allow maintenance and repair of 

downstream equipment. 

4.4.4 Unbalanced Load Connected Line-to-Line 

Load that is connected line-to-line will not produce current in the neutral relay element. Even 

unequal single-phase load connected line-to-line will not produce neutral current in the 

ground relay. For example, unequal load connected line-to-line will result in negative 

sequence current but no zero-sequence neutral current because 

IA + IB + IC = 0. Equation 4.3 

The equations for the substation breaker also apply in this case. However, caution must be 

exercised to use the correct phase angle of the current in each phase. Figure 60 shows 

resistive load connected between B and C phases. Current flowing in the load equals the 

voltage across the load divided by the resistance. 

62
 
B 

C 

A 

 Resistive LOAD 

I

A 

I

B 

I

C 

I

R 

A B C N

VA 

VB 

Vc 

VB - VC 

Figure 60. Current flow in phase-to-phase-connected load 

For this circuit, assume: 

V = 7,620�Ú0° A Equation 4.4 

VB = 7,620�Ú-120° 

VC = 7,620�Ú120° 
 

�ËV = V - V = 13,200�Ú- 90 BC B C 

PL = 100kW �ËIL = 100,000 Watts ÷13,200volts = 7.56 amperes 

For this circuit, current in Phase B returns on Phase C. Or IB = -IC. 

Voltage across the load equals the difference between the voltages VB and VC or VB – VC. 

Current in the load equals the voltage across the load divided by the resistance or (VBVC)/RL. If no other load is on the circuit, then IB = IR = -IC and IA= 0.
 

Using the equations for the substation breaker: 

I = I + I + I N A B C 

Equation 4.5 I = 0�Ú = 7.56�Ú 0° I - 90° I = 7.56�Ú- 90° A B C 

(Current in amperes)
 

I N = 0�Ú + 7.56�Ú 7.56�Ú- 90° = 0 0° - 90° Equation 4.6

63
 
Even though the load is unbalanced, it is important to consider how the load is connected, 

which has an effect on the phase angle of the currents flowing, as seen at the substation 

breaker and the respective relays. 

4.4.5 Fuse Preload Because of Unbalanced Loading or Unbalanced Voltages 

Load unbalance can cause fuses to become unselective with other protective devices (such as 

reclosers). This inselectivity is due to load-unbalanced currents heating the fuse element and 

causing a shift in the time-current characteristic. In Figure 61, the melting time as a 

percentage of the published time-current characteristic for a fuse is shown as a function of 

the load current in percentage of the fuse ampere rating. Notice that the melt time is reduced 

to 52% when the load current on one of the phases of the three-phase circuit is 150% of the 

fuse ampere rating. 

Figure 61. Reduced melt time because of preloading of universal K link fuses 

(S&C Electric Co. 2000) 

To illustrate this coordination issue, Figure 62 shows a distribution circuit with an 

unbalanced three-phase lateral that serves a number of single-phase loads. For simplicity, 

each single-phase load is fused with a 50K fuse. The three-phase load, as seen by the 80K 

fuses, is unbalanced by 20%. 

64
 
Substation 

Fault "B" Load 

(Temporary) 

50K 

50K 

Substation 

Breaker 

3 Phase 

Recloser 

3-Single Phase 

Reclosers 

80K Fuses 

Transformer 

LOAD 

LOAD 

#1 

50K 

LOAD 

#2 

LOAD 

#3 

LOAD 

I

L = 2 MVA 

Fault "A" 

20% Unbalanced 

3 Phase 

Notes: 

Loading of 13.2-kV three-phase lateral: 

ILavg = 87.50 A 

ILhigh phase = 105 A 

Figure 62. Fuse preloading causes inselectivity 

The average current is 87.5 A, and the high-load phase current is 120% of average, or 105 A. 

Figure 63 shows the fuse time-current for the 80K fuse (Curve 1) and the 50K fuses (Curve 2) 

with no preloading on any phase. Notice that these curves do not intersect until a fault greater 

than 2,000 A occurs on this lateral. If a fault, A, of 600 A or greater occurs on this lateral with 

a 150% preload, then the 80K fuse and the 50K fuses would blow near simultaneously, thus 

causing the unnecessary loss of loads 1, 2, and 3, rather than only Load 1. 

65
 
Figure 63. Coordination of 50K and 80K fuses (S&C Electric Co.) 

66
 
Figure 64. Inselectivity of 80K and 50K fuses for unbalanced loading of 20% (S&C Electric Co.) 

Another example of this inselectivity may occur when the 80K fuse is preloaded because of 

unbalance and a temporary fault is placed at B of Figure 62. The fault would cause the 

recloser to open on the fast curve, the 80k fuse would blow because of preload, and all of the 

load on the lateral would be lost before the recloser restores power to the then-unfaulted 

lateral. Without the preloading because of the unbalance, the 80K fuse would not have 

blown, and the recloser would have restored power after the temporary fault cleared. 

Because unbalanced voltages create unbalanced currents, similar effects of inselectivity can 

occur between protective devices. 

4.5 Unbalanced Voltage Conditions

Unbalanced voltages may exist on distribution primaries and secondaries because: 

67
 
•	 The loads on a distribution circuit are not all three-phase but predominately
 

single-phase 

•	 The distribution phases are not fully transposed to balance the line impedances 

•	 The phase conductors are different and thus have different impedances 

•	 The transformer banks serving the three-phase loads are not identical single-phase 

units of the same size and impedance 

•	 The transformer connections are either open delta or open wye 

•	 One of the phase conductors is open upstream from the load because of a blown 

single-phase fuse or other open single-phase protective device 

•	 The phase conductor is broken 

•	 Individual units of capacitors within a capacitor bank fail and cause
 

unbalanced conditions. 

It is important to keep the three-phase circuits as closely balanced as possible to prevent 

overloading the equipment on the highest loaded phase. Also, it is recommended that the 

unbalanced loading be kept to no more than 10%–20% because it permits more sensitivity in 

setting the ground fault relay. 

Reducing the unbalanced loading reduces the losses created by the neutral current in the 

neutral conductor. Unbalance tends to be greater during off-peak conditions and at points at 

which the single-phase laterals are tapped to the three-phase primary. Unbalanced threephase voltages have a significant effect on the design and operation of transformers and 

induction and synchronous machines. Unbalance causes a voltage with a rotation that is 

opposite to the voltage of a balanced supply. These opposite rotating voltages, called 

“negative sequence voltages,” produce a flux in the air gap of these machines that counters 

the rotor rotation and causes high line currents in the phases that feed the machines. These 

higher line currents cause additional losses in the motors, generators, and distribution system. 

4.5.1 Induction Machines Operating on Unbalanced Voltages 

The National Electrical Manufacturers Association Standard MG1-14.34 (National Electrical 

Manufacturers Association 1978) specifies the voltage unbalance at the terminals of the 

polyphase induction motor is not to exceed 1%. The voltage unbalance, in percentage, is 

defined as 

maximum voltage deviation from avg. voltage Percent voltage unbalance = 100 x average voltage 

 Equation 4.7 

The standard goes on to say that: 

68
 
“A relatively small unbalance in voltage will cause a considerable increase in 

temperature rise. In the phase with the highest current, the percentage increase 

in temperature rise will be approximately two times the square of the percent 

voltage unbalance. The increase in losses and consequently the increase in 

average heating of the whole winding will be slightly lower than the winding 

with the highest current. 

“To illustrate the severity of this condition, an approximate 3.5 percent 

voltage unbalance will cause an approximate 25 percent increase in 

temperature rise.” 

The breakdown torque and locked rotor torque are decreased for unbalanced voltages. The 

phase currents with unbalanced voltages are greatly unbalanced, on the order of four to five 

times the voltage unbalance. This creates a problem of choosing the correct overload 

protection because the proper setting for one unbalanced condition may not be adequate for 

another unbalanced condition. If the setting is raised, the motor may not be protected against 

overload and open phases. 

The load or generation may have to be reduced below the nameplate output rating to avoid 

overheating. For example a 5% voltage unbalance might result in a 25% reduction in the 

nameplate rating. If lowering the load is not possible, the size of the motor would have to be 

increased if the unbalanced abnormal condition prevails and cannot be corrected. 

Equation 4.7 is usually accurate enough to predict the percent voltage unbalance for 

unbalanced conditions less than 3%, but at 5% or greater, the method of symmetrical 

components should be used. The example below (Table 1) compares the percent voltage 

imbalance determined from Equation 4.7 with the correct percent voltage unbalance 

calculated using symmetrical components. The correct voltage unbalance is calculated by 

first determining the positive sequence voltage V1 from the measured line-to-line voltages, 

VA, VB, and VC. The Law of Cosines is used to calculate the angles once the magnitudes are 

measured. The positive sequence voltage V1 is 

V1 = 1/3 (VA + a VB + a2

 VC). Equation 4.8 

The negative sequence voltage, V2, 

V2 = 1/3 (VA + a2

 VB + a VC), Equation 4.9 

is then determined. Next the negative sequence voltage is divided by the positive sequence 

voltage. The percent voltage unbalance %Vu is found from 

V2 %Vu = x 100 . Equation 4.10 V1 

The zero sequence voltage is 

V0 = 1/3 (VA + VB + VC), Equation 4.11 

69
 
which is zero for VA + VB + VC = 0. All bolded symbols are vector quantities. 

Table 1. Comparison of National Electrical Manufacturers Association Standard Method 

with Correct Voltage Unbalance Calculations Using Symmetrical Components 

Case I Case II 

Rev. Rotation Case III Case IV 

Rev. Rotation 

VA 232 225 233 226 

VB 230 230 228 228 

VC 225 232 226 233 

Vavg 229 229 229 229 

VA1 

229.0 59.7° 228.9 60.7° 228.9 59.3° 229.0 60.3° 

VA2 

3.56 105.2° 4.13 -103.0° 4.30 76.5° 4.00 -76.5° 

Equation 4.7 1.75% 1.75% 1.75% 1.75% 

Equation 4.10 1.55% 1.80% 1.88% 1.75% 

In the above comparison, little difference exists between the percent unbalance using 

Equation 4.7 and Equation 4.10. Equation 4.10 will be used for all calculations of percent 

unbalanced voltage beginning at 3%. 

The effects of unbalanced voltages are greater unbalanced line currents, significantly 

increased losses, decreased torques, and increased slip. 

4.5.1.1 Positive and Negative Sequence Equivalent Circuits 

The positive and negative sequence voltages (Wagner and Evans 1933) are defined in equations 

4.8 and 4.9. They each form symmetrical three-phase systems, as shown in Figure 65. 

The positive sequence system consists of three equal voltages with an angle of 120° between 

them. When applied to the stator winding, the rotating field revolves in the positive direction. 

When the negative sequence system is applied to the stator winding, the field rotates in the 

opposite direction of the field produced by the positive sequence voltages. The results can be 

superimposed because they act independently. 

70
 
V rot.rot. A1 VA2

120o 120o 

120o 

120o 120o

120o

120o 120 o

120 o

V 0 C1 V VB2 B1VC2

Positive Sequence Positive Sequence Negative Sequence

Note: Notice the negative sequence system of vectors rotates in the opposite direction to positive Note: Notice the negative sequence system of vectors rotates in the opposite direction to positive

sequence. But when vectorally adding positive and negative sequence vectors, both sequence. But when vectorally adding positive and negative sequence vectors, both

systems must rotate in the counterclockwise direction with V systems must rotate in the counterclockwise direction with VA1, VB1, and VC1 A1, VB1, and VC1 for positive and for positive and

VA2, VC2, and VB2 V for negative. A2, VC2, and VB2 for negative.

Figure 65. Positive and negative sequence system of voltages 

4.5.1.1.1 Positive Sequence Equivalent Circuit 

The equivalent circuit is shown in Figure 66 for the positive sequence system. The symbols 

are: 

Rs = Resistance per phase for the stator 

Rr1 = Resistance per phase for the rotor referred to the stator 

Xs = Leakage reactance per phase for the stator 

Xr1 = Leakage reactance per phase for the rotor referred to the stator 

Xm = magnetizing reactance 

s = Slip 

Is1 = Stator current per phase for the positive sequence
 

Ir1 = Rotor current per phase referred to the stator for the positive sequence.
 

Rr

1 (1- s) = R r + R r Equation 4.12 

s 1 1 s 

Multiplying by Ir1

2

 results in 

2 Rr1 2 2 (1- s) Ir = Ir Rr + Ir Rr . Equation 4.13 1 s 1 1 1 1 s 

71
 
Now, 

2 Rr1

Ir = Power input to the rotor per phase, Equation 4.14 1 s 

Ir

2 Rr = Copper losses in the rotor per phase, Equation 4.15 1 1 

2 (1- s) Ir Rr = Loss in a fictitious resistance that is equal to the gross mechanical 1 1 s 

power developed by the rotor per phase without including the loss for friction and 

windage, Equation 4.16 

and 

(1- s) Rr1 = Fictitious resistance. Equation 4.17 

s 

The equivalent circuit of Figure 66 can now be changed to that of Figure 67 using equations 

4.15 and 4.16. The gross mechanical power output for three phases without the friction and 

windage losses subtracted is from Equation 4.16. 

2 (1- s) P1(3 Φ output) = 3 Ir Rr , watts Equation 4.18 1 1 s 

The gross mechanical power may be represented in terms of torque, T, or, 

(T) (2 π rpm) (h.p.) P1(3 Φ output) = . Equation 4.19 33,000 

Because the actual revolutions per minute of the rotor are equal to the synchronous 

revolutions per minute times (1-s) and T is the torque in pound-feet, then 

T 2 π rpm sync.(1- s) 3 Ir1

2 Rr1 (1- s)

= . Equation 4.20 33,000 746 s 

72
 
Rs jXsjXr1

VS1 

jXm 

IS1 

Ir1 

s 

Rr 1

Z+ 

VS1

jXm

IS1

Ir1

s

Rr1

Z+

Figure 66. Positive sequence equivalent circuit for induction motor/generator 

Rs jXsjXr1 jXs jXr1

VS1 

jXm 

(Shaft Power) 

per phase 

IS1 

Ir1 

(Copper Loss) 

per phase 

I Rr1 r1 

2 Rr1 

Rr1 s 

s-1

r1 

2 

r1 R 

s 

s-1 I 

VS1

jXm

(Shaft Power)

per phase

IS1

Ir1

(Copper Loss)

per phase

I Rr1 r1

2 Rr1

Rr1 s

s-1

r1

2

r1 R

s

s-1 I

Figure 67. Positive sequence induction motor/generator equivalent circuit 

for copper losses and shaft power 

R + Rr1 j(X + Xr1) s s

VS1 

jXm 

I

S1 

I

r1 

Rr1 s 

s-1 VS1

jXm

I

S1

I

r1

Rr1 s

s-1

Figure 68. Simplified positive sequence induction motor/generator equivalent circuit 

73
 
The 

120 f 120 x frequency rpm sync. = = , Equation 4.21 p no.of poles 

and 

33,000 p 3 Ir1

2 Rr

1

T lb-ft = , Equation 4.22 2π x 746 120 f s 

I 2

p r r R

T lb ft = 0.1765 1 1 

. Equation 4.23 f s 

The equivalent circuit of Figure 68 is an approximation of that in Figure 67, with the jXm 

term moved out to the terminals. Because the magnitude of Xm is large compared with those 

of the other terms in the equivalent circuit, this approximation is acceptable. 

4.5.1.1.2 Negative Sequence Equivalent Circuit 

The rotor is rotating in the direction of the positive sequence field with slip (s). The negative 

sequence field is rotating in the opposite direction at synchronous speed. 

s' = Slip of Rotor 

With Respect to 

Negative 

Sequence Field 

2.0 

1.0 

0 s= .033 1.0 2.0

s' = Slip of Rotor

With Respect to

Negative

Sequence Field

2.0

1.0

0 s= .033 1.0 2.0

s = Sli s = Slip of Rotor with Res of Rotor with Respect to Positive Se ect to Positive Sequence Field uence Field

Figure 69. Slip of rotor with respect to negative sequence field and positive sequence field 

If the speed of the field in the negative direction is ω and the speed of the rotor in the positive 

direction is ω (l-s), then the slip, with respect to the negative sequence field, is 

ω +ω (l - s) s'= = 2 - s. Equation 4.24

ω

74
 
Also, this could be obtained from Figure 69. When s = 0, then s' = 2. When the rotor is at 

standstill or s = 1, then s' = 1. When s = 2, then s' = 0. The negative sequence equivalent 

circuit of Figure 71 will be similar to the positive sequence of Figure 67, but the term 

s 

s)(l ­ Rr1 of the positive sequence will be replaced with s' s')(l ­ Rr2. 

Because s' = 2 – s, from Equation 4.24, then 

s' 

(l - s') Rr2 = 

s2 ­

1- (2 - s) Rr2 

(1- s) Rr2 = − . Equation 4.25 2 - s 

Because the slip (s) is small, typically 2%–3%, 

(1- s) R - Rr2 ≅ − r2 , Equation 4.26 2 - s 2 

which is shown in the simplified equivalent circuit of Figure 72. The negative sequence 

mechanical power P2 for all three phases is from Equation 4.25 and equal to 

⎛ 1- s ⎜

⎝

⎞

⎟

⎠

2 P Equation 4.27 2 (3φ output) = -3
 R I
 , watts r r2 2 ­s 2 

where Ir2

2

 is the negative sequence rotor current referred to the stator. The gross mechanical 

power output because of both positive and negative sequence voltages is 

P1 (3φ output) - P2 (3 =
 φ output) 

1- s 

The gross torque T is 

⎛ l ­ ⎜

⎝

⎞

⎟

⎠

2 s 2 3 I
 R
 - 3
 R I
 , watts . Equation 4.28 r1 r1 r2 r 2 - s 2 s 

⎡ ⎤ 2 2 ⎛

⎜

⎜

⎝

⎢

⎢⎣

⎛

⎜

⎜

⎞

⎟

⎟

⎞

⎟

⎟

I
 Ir2 

2 ­

T = 0.1765
 

p R

f

r1 

s 

⎥ lb - ft. Equation 4.29 

⎥⎦

- r2

s ⎠ ⎝ ⎠

75
 
Rs jXsjXr2 jXs jXr2

VS1 jXm 

IS1 Ir2 

s-2 

Rr 2

ZVS1 jXm

IS1 Ir2

s-2

Rr 2

ZFigure 70. Negative sequence equivalent circuit for induction motor/generator 

Rs jXsjXr1 jXs jXr1

VS2 

jXm 

(Shaft Power) 

IS2 

Ir2 

(Copper Loss) 

I Rr2 r2 

2 Rr2 

s-2 

s-1

r2 

2 

r2 R s-2 

s-1 IVS2

jXm

(Shaft Power)

IS2

Ir2

(Copper Loss)

I Rr2 r2

2 Rr2

s-2

s-1

r2

2

r2 R s-2

s-1 IFigure 71. Negative sequence induction motor/generator equivalent circuit 

for copper losses and shaft power 

Rr2

VS2 

I

S2 

j(Xs + Xr2) 

2 

Rr 2

Rs + Rr2 

VS2

I

S2

j(Xs + Xr2)

2

Rr 2

Rs + Rr2

Figure 72. Simplified negative sequence induction motor/generator equivalent circuit 

operating at small values of slip 

76
 
Because the negative sequence power output is negative (see Equation 4.27), the power 

output is reduced with negative sequence voltages, which reduces the nameplate capability of 

the machine. An example demonstrates the significance of this. 

4.5.1.1.2.1 Negative Sequence Voltages Increase Losses 

The example uses test data from Williams (1954). Table 2 and Table 3 show the line currents 

for various percent unbalanced voltages, as measured for single-cage and double-cage 

induction motors with similar performance characteristics. These motors are 10-hp, fourpole, 220-V, three-phase, and wye-connected ungrounded. The process of determining the 

effects of unbalanced voltages is detailed below. 

1.	 From the percent unbalanced voltages or the negative sequence divided by the 

positive sequence voltage, measure the line currents IA, IB, and IC for both ABC and 

ACB rotation. 

2.	 Calculate the negative sequence currents for 3%, 5%, 8%, 10%, and 11% negative 

sequence voltages. Repeat this step for the single-cage and double-cage induction 

machines for both ABC and ACB rotation. See Table 2 and Table 3. Two major 

conclusions should be noted from the test data of these tables: 

A. Phase rotation affects which of the phases has the highest line current. This 

presents a real problem for protecting the motor/generator from overcurrent 

failure. At a 3% negative sequence voltage, for the single cage-motor, Phase C 

has the highest phase current IC of 1.12 p.u. for ABC rotation. The Phase A 

motor has the highest phase current IA of 1.145 p.u. for ACB rotation. When 

V2/V1% is increased to 5%, IC increases to 1.19 p.u. for ABC rotation, and IA 

is 1.245 p.u. for ACB rotation. 

Overcurrent motor/generator protection is typically installed on two of the 

three phases. If the protection is installed on phases A and B for the singlecage motor with ABC rotation and set to trip at 115%, then the motor 

protection will not trip to protect the motor because IA is 1.09 p.u. and IB is 

only 0.760 p.u. However, phase IC current is 1.19 p.u. Similarly, if this same 

motor is operated at 5% negative sequence voltage with ACB rotation and the 

protection is installed on phases B and C, then the IA current is 1.245 p.u., and 

the IB and IC currents are only 0.980 p.u. and 0.825 p.u., respectively. Again, 

the protection will not trip to protect the motor because the currents IB and IC 

are below 0.980 p.u., yet IA current is at 1.245 p.u., or 24.5% over rated 

current. Following this same case, even with V2/V1% = 11%, the IB and IC 

currents are only 1.040 p.u. and 0.695 p.u., respectively, yet the IA current is 

1.535 p.u., or 53.5% over rated current. The overcurrent protection still has 

not operated to trip and protect the motor. This conclusion indicates that 

negative sequence current protection must be used to protect the motor or 

generator to prevent failure because of unbalanced voltages. This condition is 

not the same for ABC rotation. In fact, at V2/V1% = 8%, IA = 1.165 p.u., IB = 

0.620 p.u., and IC = 1.31 p.u. Therefore, the overcurrent motor protection 

under worst-case conditions would trip the motor at IC = 1.31 p.u. if the 

protection was installed on phases A and B. 

77
 
 

 

Although the problem is less severe for the double-cage motor, the phase 

current IA for rotation ACB reaches 1.48 p.u., or 48% over rated current at 

V2/V1% = 11%. Yet overcurrent tripping would occur for ABC rotation at 

V2/V1% = 8%. 

B. The percent negative sequence current is independent of phase rotation. For 

example, referring to the single-cage motor at V2/V1% = 5%, the I2/I1% = 

25.08% for ABC rotation and I2/I1% = 25.68% for ACB rotation. The same is 

true for the double-cage motor. The phase rotation does not affect the result, 

but the percent negative sequence current is somewhat less at 21.6%. This 

confirms the need for negative sequence current protection because a safe 

level of overcurrent can be selected to protect the motor/generator that is 

independent of phases selected for protection and the phase rotation applied to 

the terminals of the motor or generator. 

3.	 From the motor characteristics of Table 4, determine the positive and negative 

sequence equivalent circuits and the positive Z+

 and negative sequence Zimpedances. The positive sequence impedance Z+

 is shown in Figure 66 and is given 

as Equation 4.30; the negative sequence impedance Z-

 is shown in Figure 70 and is 

given as Equation 4.31. 

2 ⎡ R ⎤ ⎡ ⎤ r1 

s 

Rr1 

s 

⎛

⎜

⎝

⎛

⎜

⎝

⎞

⎟

⎠

⎞

⎟

⎠

2 X
 X
 X X (X
 Xm ⎢ )

⎢

⎢

⎢

⎥

⎥

⎥

⎥

+ j 

⎢

⎢

⎢

⎢

+ + ⎥

⎥

⎥

⎥

m m r1 m r1

+ Z
 =
 R
 + X + , s 2 s 2

Rr1 

s 

Rr1 

s 

⎛

⎜

⎝

⎞

⎟

⎠

⎛

⎜

⎝

⎞

⎟

⎠ Xm )

2 2 (X + (Xr1 + Xm + + ) r1 ⎣ ⎦ ⎣ ⎦

 Equation 4.30 

2 ⎡ R ⎤ ⎡ ⎤ r2 

2 ­

Rr2 

2 ­

⎛

⎜

⎝

⎛

⎜

⎝

⎞

⎟

⎠

⎞

⎟

⎠

2 X
 X
 X X (X
 Xm ⎢ )

⎢

⎢

⎢

⎥

⎥

⎥

⎥

+ j 

⎢

⎢

⎢

⎢

+ + ⎥

⎥

⎥

⎥

m m r2 m r2

− s s Z
 =
 R
 + X + . s 2 s 2

Rr2 

2 ­

Rr2 

2 ­

⎛

⎜

⎝

⎞

⎟

⎠

⎛

⎜

⎝

⎞

⎟

⎠

2 2 + (X
 Xm ) + (Xr2 + Xm + ) r2 ⎣ ⎦ ⎣ ⎦ s s 

 Equation 4.31 

78
 
V2/V1%

3.000

5.000

8.000

10.000

11.000

3.000

5.000

8.000

10.000

11.000

V2/V1%

3.000

5.000

8.000

10.000

11.000 

3.000

5.000

8.000

10.000 

11.000 

Table 2. Per-Unit Line Currents for Percent Negative Sequence Voltage 

Single-Cage Induction Motor 

Ref

Angle = Angle = 

IA0IBangle I angle I angle I angle I angle I angle I angle ICangle I1I2I2/I1%

Single Cage ABC Rotation Single Cage ABC Rotation Single Cage ABC Rotation e Cage ABC Rotation

1.045 0.000 0.855 -108.556 1.120 133.638 1.045 0.000 0.855 -108.556 1.120 133.638 1.045 0.000 0.855 -108.556 1.120 133.638 45 0.000 0.855 -108.556 1.120 133.638 1.001 0.155 15.437 1.001 0.155 15.437 1.001 0.155 15.437 1 0.155 15.437

1.090 0.000 0.760 -102.181 1.190 141.371 1.090 0.000 0.760 -102.181 1.190 141.371 1.090 0.000 0.760 -102.181 1.190 141.371 90 0.000 0.760 -102.181 1.190 141.371 0.999 0.251 25.086 0.999 0.251 25.086 0.999 0.251 25.086 9 0.251 25.086

1.165 0.000 0.620 -91.012 1.310 151.757 1.165 0.000 0.620 -91.012 1.310 151.757 1.165 0.000 0.620 -91.012 1.310 151.757 65 0.000 0.620 -91.012 1.310 151.757 0.997 0.399 40.052 0.997 0.399 40.052 0.997 0.399 40.052 7 0.399 40.052

1.230 0.000 0.520 -80.787 1.410 158.652 1.230 0.000 0.520 -80.787 1.410 158.652 1.230 0.000 0.520 -80.787 1.410 158.652 30 0.000 0.520 -80.787 1.410 158.652 0.997 0.514 51.565 0.997 0.514 51.565 0.997 0.514 51.565 7 0.514 51.565

1.262 0.000 0.486 -78.353 1.441 160.712 1.262 0.000 0.486 -78.353 1.441 160.712 1.262 0.000 0.486 -78.353 1.441 160.712 62 0.000 0.486 -78.353 1.441 160.712 0.999 0.551 55.206 0.999 0.551 55.206 0.999 0.551 55.206 9 0.551 55.206

Single Cage ACB Rotation Single Cage ACB Rotation Single Cage ACB Rotation Cage ACB Rotation

1.145 0.000 0.975 131.161 0.890 -124.435 1.145 0.000 0.975 131.161 0.890 -124.435 1.145 0.000 0.975 131.161 0.890 -124.435 45 0.000 0.975 131.161 0.890 -124.435 0.154 0.997 647.554 0.154 0.997 647.554 0.154 0.997 647.554 4 0.997 647.554

1.245 0.000 0.980 138.578 0.825 -128.196 1.245 0.000 0.980 138.578 0.825 -128.196 1.245 0.000 0.980 138.578 0.825 -128.196 45 0.000 0.980 138.578 0.825 -128.196 0.257 0.999 389.448 0.257 0.999 389.448 0.257 0.999 389.448 7 0.999 389.448

1.385 0.000 1.000 148.378 0.748 -135.496 1.385 0.000 1.000 148.378 0.748 -135.496 1.385 0.000 1.000 148.378 0.748 -135.496 85 0.000 1.000 148.378 0.748 -135.496 0.400 0.999 249.577 0.400 0.999 249.577 0.400 0.999 249.577 0 0.999 249.577

1.485 0.000 1.030 154.850 0.705 -141.618 1.485 0.000 1.030 154.850 0.705 -141.618 1.485 0.000 1.030 154.850 0.705 -141.618 85 0.000 1.030 154.850 0.705 -141.618 0.502 1.001 199.494 0.502 1.001 199.494 0.502 1.001 199.494 2 1.001 199.494

1.535 0.000 1.040 157.737 0.695 -145.465 1.535 0.000 1.040 157.737 0.695 -145.465 1.535 0.000 1.040 157.737 0.695 -145.465 35 0.000 1.040 157.737 0.695 -145.465 0.552 1.001 181.522 0.552 1.001 181.522 0.552 1.001 181.522 2 1.001 181.522

Table 3. Per-Unit Line Currents for Percent Negative Sequence Voltage 

Double-Cage Induction Motor 

Ref

Angle = Angle = 

IA0IBangle I angle I angle I angle I angle I angle I angle ICangle I1I2I2/I1%

Double Cage ABC Rotation Double Cage ABC Rotation Double Cage ABC Rotation ouble Cage ABC Rotation

1.065 0.000 0.870 -113.022 1.080 132.150 1.065 0.000 0.870 -113.022 1.080 132.150 1.065 0.000 0.870 -113.022 1.080 132.150 65 0.000 0.870 -113.022 1.080 132.150 1.001 0.131 13.121 1.001 0.131 13.121 1.001 0.131 13.121 1 0.131 13.121

1.112 0.000 0.785 -108.867 1.135 139.120 1.112 0.000 0.785 -108.867 1.135 139.120 1.112 0.000 0.785 -108.867 1.135 139.120 12 0.000 0.785 -108.867 1.135 139.120 1.000 0.216 21.582 1.000 0.216 21.582 1.000 0.216 21.582 0 0.216 21.582

1.190 0.000 0.660 -102.456 1.230 148.402 1.190 0.000 0.660 -102.456 1.230 148.402 1.190 0.000 0.660 -102.456 1.230 148.402 90 0.000 0.660 -102.456 1.230 148.402 1.002 0.343 34.289 1.002 0.343 34.289 1.002 0.343 34.289 2 0.343 34.289

1.250 0.000 0.572 -98.027 1.300 154.171 1.250 0.000 0.572 -98.027 1.300 154.171 1.250 0.000 0.572 -98.027 1.300 154.171 50 0.000 0.572 -98.027 1.300 154.171 1.003 0.433 43.226 1.003 0.433 1.00 0.433 43.226 1.003 0.433 43.226 3 0.433 43.226

1.281 0.000 0.522 -95.401 1.337 157.127 1.281 0.000 0.522 -95.401 1.337 157.1 1.281 0.000 0.522 -95.401 1.337 157.127 1.001 0.482 48.188 1.001 0.482 48.1 1.001 0.482 48.188

Double Cage ACB Rotation Double Cage ACB Rotatio Double Cage ACB Rotation

1.127 0.000 0.960 128.256 0.923 -125.241 1.127 0.000 0.960 128.256 0.923 -125.2 1.127 0.000 0.960 128.256 0.923 -125.241 0.130 0.999 771.314 0.130 0.999 771. 0.130 0.999 771.314

1.215 0.000 0.943 134.158 0.877 -129.519 1.215 0.000 0.943 134.158 0.877 -129.5 1.215 0.000 0.943 134.158 0.877 -129.519 0.219 0.999 456.403 0.219 0.999 456. 0.219 0.999 456.403

1.340 0.000 0.926 142.637 0.825 -137.066 1.340 0.000 0.926 142.637 0.825 -137.0 1.340 0.000 0.926 142.637 0.825 -137.066 0.348 0.995 286.260 0.348 0.995 286. 0.348 0.995 286.260

1.428 0.000 0.930 148.146 0.805 -142.432 1.428 0.000 0.930 148.146 0.805 -142.4 1.428 0.000 0.930 148.146 0.805 -142.432 0.433 0.998 230.641 0.433 0.998 230. 0.433 0.998 230.641

1.480 0.000 0.940 151.019 0.800 -145.298 1.480 0.000 0.940 151.019 0.800 -145.2 1.480 0.000 0.940 151.019 0.800 -145.298 0.479 1.004 209.439 0.479 1.004 209. 0.479 1.004 209.439

79
 
4.	 From the negative sequence voltage V2 and the negative sequence impedance Z-

, the 

negative sequence amperes are calculated and displayed in Table 5. Calculate the 

negative sequence stator losses from 3 Is2

2

 R1, where Is2 is the negative sequence stator 

current of Table 5 and Rs is the stator resistance of 0.153 Ω/Φ, shown in Table 4. 

5.	 The negative sequence rotor losses are calculated from (2 – s) 3I2

r2 (R- – Rs), where 

the negative sequence rotor current Ir2 can be approximated with the negative 

sequence stator current Is2 

[4], R-

 is the resistance portion of the negative sequence 

impedance Z-

 of Table 4, and Rs is the stator resistance. The total negative sequence 

losses are found by adding the negative sequence stator and rotor losses. 

Table 4. Double- and Single-Cage Characteristics for 10-hp, Four-Pole, 220-V, 

Three-Phase, Wye-Connected Ungrounded Motors 

Double-Cage Motor Single-Cage Motor 

Rs = 0.153 Ω/Φ Rs = 0.153 Ω/Φ

Xs = 0.500 Ω/Φ

Xm = 14.3 Ω/Φ

Xs = 0.500 Ω/Φ

Xm = 14.3 Ω/Φ

Rr1 = 0.188 Ω/Φ @ 

 s = 0.033 (2 Hz) 

Rr1 = 0.188 Ω/Φ @ 

 s = 0.033 (2 Hz) 

Rr2 = 0.507 Ω/Φ @ 

 s = 1.967 (118 Hz) 

Rr2 = 0.205 Ω/Φ @ 

 s = 1.967 (118 Hz) 

Xr1 = 0.760 Ω/Φ @ 

 s = 0.033 (2 Hz) 

Xr1 = 0.420 Ω/Φ @ 

 s = 0.033 (2 Hz) 

Xr2 = 0.482 Ω/Φ @ 

 s = 1.967 (118 Hz) 

Xr2 = 0.415 Ω/Φ @ 

 s = 1.967 (118 Hz)

 Z+

 = 4.01 + j 2.43 = 4.70 31.2° Z+ = 4.02 + j 2.13 = 4.55 28.0° 

Z­ = 0.395 + j 0.970 = 1.05 67.8° Z­ = 0.252 + j 0.903 = .938 74.4° 

@ 10% 

1 

2 

V 

V

 @ 10% 

1 

2 

V 

V 

V2 = 

3 

220 

x 0.10 = 12.7 volts 

I2 = 12.1amperes 1.05 

12.7 

Z 

V 

-

2 

==

V2 = 

3 

220 

x 0.10 = 12.7 volts 

I2 = 13.54 amperes .938 

12.7 

Z 

V 

-

2 

 ==

4.48

1.05 

4.70 

Z 

Z 

- ==

+ 

4.85 

0.938 

4.55 

Z 

Z 

- ==

+

80
 
g que

g que

Table 5. Single-Cage Induction Motor – 10 hp, 220 V, Four Pole, Wye-Connected Ungrounded 

Z­- V2/V1 % V2 I2 I V2/V1 % V 2 I2 I2angle

3.0 3.81 0.938 4.06 -74.4 3.0 3.81 0.938 4.06 -74.4 3.81 0.938 4.06 -74.4

5.0 6.35 0.938 6.77 -74.4 5.0 6.35 0.938 6.77 -74.4 6.35 0.938 6.77 -74.4

8.0 10.16 0.938 10.83 -74.4 8.0 10.16 0.938 10.83 -74.4 10.16 0.938 10.83 -74.4

10.0 12.70 0.938 13.54 -74.4 10.0 12.70 0.938 13.54 -74.4 0 12.70 0.938 13.54 -74.4

11.0 13.97 0.938 14.89 -74.4 11.0 13.97 0.938 14.89 -74.4 0 13.97 0.938 14.89 -74.4

RS =0.153 ohms/phase 0.153 ohms/phase

s = 0.033 s = 0.033

Ne ative Se nce Losses Negative Sequence Losses egative Sequence Losses

StatorRotor

3IS22

RS (2-s)3Ir2

2

(R2

- 3I -RS) Total S22

RS (2-s)3Ir2

2

(R2

-

-RS) Total S22RS (2-s)3Ir2

2

(R2

-

-RS) Total

% Increased% Increased

Losses Due to

NegativeNegative

SequenceSequence

Current

7.57 9.64 17.21 2.10

21.04 26.77 47.81 5.83

53.85 68.54 122.39 14.93

84.14 107.09 191.24 23.32

101.81 129.58 231.40 28.22

R-

= 0.252 Negative sequence equivalent circuit resistance, ohms/phase = 0.252 Negative sequence equivalent circuit resistance, ohms/phase

2-s = 1.967 2-s = 1.967 = 1.967

R-

-RS =0.099 ohms/phase 0.099 ohms/phase

Full LoadFull Load

Losses = 820 Watts Losses = 820 Watts osses = 820 Watts

V1 = 127 Volts = 127 Volts

I rated = 27 amperes I rated = 27 amperes ated = 27 amperes

Z-

= 0.938 ohms/phase = 0.938 ohms/phase

Zangle = 74.4 Degrees angle = 74.4 Degrees

Table 6. Double-Cage Induction Motor – 10 hp, 220 V, Four Pole, Wye-Connected Ungrounded 

Z­- V2/V1 % V2 I2 I V2/V1 % V 2 I2 I2angle

3.000 3.81 1.05 3.63 -67.8 3.000 3.81 1.05 3.63 -67.8 00 3.81 1.05 3.63 -67.8

5.000 6.35 1.05 6.05 -67.8 5.000 6.35 1.05 6.05 -67.8 00 6.35 1.05 6.05 -67.8

Ne ative Se nce Losses Negative Sequence Losses egative Sequence Losses

StatorRotor

3IS2

2

RS (2-s)3Ir2

2

(R2

-

-RS 3I ) Total S2

2

RS (2-s)3Ir2

2

(R2

-

-RS) Total S2

2

RS (2-s)3Ir2

2

(R2

-

-RS) Total

% Increased% Increased

Losses Due to

NegativeNegative

SequenceSequence

Current

6.043438 6.043438 18.80 24.85 18.80 24.85 3.03

16.78733 16.78733 52.23 69.02 52.23 69.02 8.42

8.000 10.16 1.05 9.68 -67.8 8.000 10.16 1.05 9.68 -67.8 00 10.16 1.05 9.68 -67.8 42.97556 133.71 176.68 42.97556 133.71 176.68 21.55

10.000 12.70 1.05 12.10 -67.8 10.000 12.70 1.05 12.10 -67.8 000 12.70 1.05 12.10 -67.8 67.14931 208.92 276.06 67.14931 208.92 276.06 33.67

11.000 13.97 1.05 13.30 -67.8 11.000 13.97 1.05 13.30 -67.8 000 13.97 1.05 13.30 -67.8 81.25066 252.79 334.04 81.25066 252.79 334.04 40.74

RS =0.153 ohms/phase 0.153 ohms/phase

s = 0.033 s = 0.033

R-

= 0.395 Negative sequence equivalent circuit resistance, ohms/phase = 0.395 Negative sequence equivalent circuit resistance, ohms/phase

2-s = 1.967 2-s = 1.967

R-

-RS =0.242 ohms/phase 0.242 ohms/phase

Full LoadFull Load

Losses = 820 Watts Losses = 820 Watts

V1 = 127 Volts = 127 Volts

I rated = 27 amperes I rated = 27 amperes

Z-

= 1.05 ohms/phase = 1.05 ohms/phase

Zangle = 67.8 Degrees angle = 67.8 Degrees

81
 
6.	 The percent increased losses because of the negative sequence currents are 

determined by dividing the total negative sequence losses of Step 5 by the full load 

losses. 

An example using the double-cage induction motor applied to a 10% negative 

sequence supply voltage illustrates steps 3–5. From Table 6: 

The negative sequence stator losses are 

3 Is2

2

 Rs = (3) (12.10)2 (0.153) = 67.2 W.	 Equation 4.32 

The negative sequence rotor losses are 

(2 – s) 3 Ir2

2

 (R- - Rs) = (2 - 0.033) (3) (12.10)2 (0.395 – 0.153) = 209.1 W.

 Equation 4.33 

The total negative sequence losses = 276.3 W.	 Equation 4.34 

The full load losses are equal to 820 W. Therefore, the percent increased losses 

because of a 10% negative sequence voltage is 

% ∆ losses (@ V2/V1 = 10%) = 276.3/820 x 100 = 33.7%. Equation 4.35 

This value is shown in Table 6 for V2/V1% = 10%. The negative sequence losses are 

proportional to the square of the negative sequence voltage. Or, at 11% negative 

sequence voltage, the increased losses are, from Equation 4.35, equal to 

⎛

⎜

⎝

11% ⎞

⎟

⎠

2 

33.7% = 40.7% . Equation 4.36 10%
 

Notice that the percent increased losses are much higher for the double-cage 

motor/generator than for the single-cage motor/generator at the same percent negative 

sequence voltage. This is primarily because the negative sequence resistance of the 

rotor (0.507 Ω/Φ) for the double-cage motor is much higher than the positive 

sequence resistance of the rotor (0.188 Ω/Φ). By comparison, the negative sequence 

resistance of the rotor (0.205 Ω/Φ) for the single-cage motor is only slightly higher 

than the positive sequence resistance (0.188 Ω/Φ). For example, at V2/V1% = 10%, 

the increased losses are 23.3% for the single cage but 33.7% for the double cage. This 

is a significant problem because the double-cage machines are typically the larger 

motor and generator units. 

82
 
4.5.1.1.2.2 Negative Sequence Voltage Affects Shaft Output Power and Reduces Capacity 

The next series of questions involves how negative sequence voltage affects the shaft output 

power and increased losses reduce the nameplate capacity. The gross mechanical power of 

the machine because of the positive and negative sequence voltage will be calculated. Again, 

using the test data, two examples—one for the single-cage motor and one for the double-cage 

motor—are considered. 

For a negative sequence voltage of 10%, applied to a single-cage motor, 

V1 127 I1 = + = = 27.9 amperes, and Z 4.55
 

V 12.7 I = 2 = =13.54 amperes. 2 Z- .938 

Because Rr1 = 0.188 Ω/Φ and Rr2 = 0.205 Ω/Φ, applying equations 4.23 and 4.27 results in 

1- s 2 1- s P1(3 Φ output) – P2(3Φ output) = 3 Ir1

2

 Rr1 - 3 Ir2 Rr2

s 2 - s 

 Equation 4.37 

(1-.033) (1-.033) P3 Φ output = (3) (27.9)2 (0.188) - (3) (13.54)2 (0.205) .033 2 -.033 

 = (439.02) (29.30) – (112.75) (0.4916) 

P3 Φ output = 12,863.3 watts – 55.43 watts. Equation 4.38 

 Positive Sequence Negative Sequence

 Power Output Power Output 

Notice that, at 10% negative sequence voltage, the power because of the negative sequence 

voltage is only 0.43% of the positive sequence power, or

55.43

 Decreased power = = - 0.43%. 12,863.3 

Therefore, voltage imbalance does not materially affect the power output of the rotor, but the 

rotor and stator copper losses increased 23.3% because of the negative sequence currents, as 

shown in Table 4. It is the increased losses, not the reduction in power because of the 

negative sequence voltage, that derate the motor. 

83
 
When a 10% negative sequence voltage is applied to a double-cage motor, the negative 

sequence reverse power as a percentage of positive sequence power is 0.91%, or more than 

twice that for the single-cage motor. The percentage increase in rotor and stator copper losses 

is 33.7%, for 44.6% higher losses than for the single-cage motor. 

The additional copper losses cause an increase in temperature above ambient temperature and 

reduce the power output capability of the motor or generator. The effect of this increase in 

temperature or the derating of the induction machine is illustrated inTable 7 Table 7. The higher 

the ratio of the positive-to-negative sequence impedances, the greater the capacity reduction. The 

negative sequence rotor values (Rr2, Xr2) are not readily known, but Tracey (1954) found the 

ratio Z+

/Z- can be approximated by dividing the locked rotor current by the rated full load 

current. 

If one knows the ratio of Z+

/Z- and the unbalanced voltage applied, an equation can be 

developed for derating the motor capacity. The equation is based on the assumptions that the 

total copper loss for the stator and rotor that corresponds to any stator current is proportional 

to that current squared and the change in rotor resistance with frequency is negligible. 

Because the positive sequence current will result in the same total copper losses as balanced 

conditions and rated load, 

Is

2 rated = Is12

 + Is2

2

, Equation 4.39 

where Is rated is the rated stator current, and Is1 and Is2 are the positive and negative 

sequence currents. 

From Equation 4.39, 

Is1 = 

2 

s2rated 

2 

s −II . Equation 4.40 

Defining

V2 V1 Is2 = − , and I = + , then s rated Z Z 

⎛ V Z+ ⎞ Is2 = ⎜

⎜

V

2 

Z ⎟

⎟ Is rated. Equation 4.41 

⎝ 1 

−

⎠

Substituting Equation 4.41 into Equation 4.40, 

⎛ V2 Z+ ⎞ Is1 = Is rated 1− ⎜

⎜ − ⎟

⎟ . Equation 4.42 

⎝ V1 Z ⎠

To prevent the motor from overheating, the positive sequence stator current cannot be greater 

than the value given in Equation 4.42. Remember that the negative sequence torque is very 

small. Therefore, the rating under unbalance conditions is 

84
 
1 ⎜

Machine Rating

under unbalanced voltages⎥

⎦

⎛ ⎡Machine ⎤ ⎜

⎝ ⎟

⎞

⎟

⎠

+ ⎡ ⎤ V2 Z 2

= − x . Equation 4.43 ⎢ -

⎣ V1 Z ⎢

⎣N.P. Rating⎥⎦

V2 (Note: is given in p.u. in Equation 4.43, not in percent.) V1 

It will be shown (see Equation 4.75) that when a phase conductor is opened on a three-phase 

supply to the induction machine, at standstill, the motor will not start. For example, when 

Z+

/Z- = 5 and V2/V1% = 20%, from Equation 4.43, the machine rating is zero! When 

Equation 4.43 is applied to a ratio of Z+

/Z- = 7, the zero rating occurs at V2/V1% = 15%; 

when it is applied to a ratio of 9, the zero rating occurs at V2/V1 = 11%. These zero rating 

values correspond with the value of the V2/V1% unbalance voltage, which occurs when an 

open phase conductor condition is applied to each of these machines. This result also applies 

to other Z+

/Z- ratio machines. 

From Table 4, the Z+

/Z- ratio for the single-cage motor is 4.85, and the ratio for the doublecage is 4.48. Using the approximate ratio value of 5 and applying the results of Table 7, for a 

V2/V1% = 5%, the motor must be derated to 97% of rated power. Obviously, this is a 

generalized result, and temperature rise and service factor data must be used from the actual 

design to obtain realistic and specific results. However, the test results of Gafford, 

Duesterohoeft, and Mosher (1959) and Tracey (1954), shown in Table 8, have comparable 

deratings for the same unbalanced voltages. 

No single-phase current or percent negative sequence current is indicative of the actual 

temperature rise. The losses in the stator are unevenly distributed because the line currents 

are not equal, and this causes hot spots, unbalanced temperatures, and resistances. Doublecage motors have to dissipate more losses than single-cage motors for the same negative 

sequence voltage. An unbalanced voltage condition not to exceed 3% to 5% is the 

recommended limit based on the line current not to exceed 120% (i.e., IC = 119%) to 125% 

(i.e., IA = 124.5%) of rated current, as shown in Table 2. This results in percent negative 

currents of about 25%–22% and increased losses of 5.85%–8.45% for single- and doublecage machines, respectively. 

85
 
Table 7. Maximum Allowable Power Output in Percent of Rated
 

While Operating at Unbalanced Voltages
 

V2 Z+ Z+ Z+ 

= 5 = 7 = 9 V1 Z- Z- Z3% 99.8 97.8 96.3 

5% 96.8 93.7 89.3 

8% 91.7 82.8 69.4 

10% 86.6 71.4 43.6 

11% 83.5 63.8 0 

13% 76.0 41.5 0 

14% 71.4 19.9 0 

15% 66.1 0 0 

20% 0 0 0 

Notes: 

From Tracey (1954)
 

(1) Z+

 = Motor impedance to V1 (positive sequence voltages) at rated 

(2) Z-

 = Motor impedance to V2 (negative sequence voltages) at rated load 

(3) Z+

/Z-≈ Locked rotor current/rated current 

Table 8. Comparison of Gafford, Duesterohoeft, and Mosher (1959) and Tracey (1954) 

Motor Derate Data Operating at Unbalance Voltage

 % Power Derate 

%

V 

V 

1 

2 P.u. Negative 

(Gafford, 

Duesterohoeft, 

and Mosher) 

Sequence I2 

P Output 

(Gafford, 

Duesterohoeft, 

and Mosher) 

p.u. @ Rated 

Temp. Rise 

∆ P% 

(Gafford, 

Duesterohoeft, 

and Mosher) 

= 5 

+ 

- Z 

Z 

∆ P % 

(Tracey) 

0 0 1.22 0 0 

3 0.160 1.20 1.64 1.0 

5 0.265 1.17 4.10 3.0 

8 0.420 1.10 9.84 8.0 

10 0.515 1.03 15.6 13.0 

11 0.570 0.98 19.7 16.5 

13 0.660 0.85 30.3 23.5 

15 0.750 0.66 45.9 34.0 

86
 
Note: The phasor diagram of Figure 73 was used as the voltage source by Gafford, 

Duesterohoeft, and Mosher (1959) to determine the heating condition of phases A, B, and C. 

VA1

VB2 

VC1 

VA1 

VA2 

VB1 

VC2 

VB1 VC1 

θ = 

180o 

VC2 VB2

VA2 

VB2

VC1

VA1

VA2

VB1

VC2

VB1 VC1

θ =

180o

VC2 VB2

VA2

Figure 73. Phasor diagram for minimum heating in Phase A, θ = 180° 

Figure 74. Phasor diagram for maximum heating in Phase A, θ = 0° 

4.5.1.2 Unbalance Voltage Survey 

The survey results of 13 utility systems are shown in Table 9. The data show the majority of 

unbalanced conditions occur with open delta transformer connections. But even then, the 

average unbalance is only 1.98%, with the highest being 10%. 

VC2 VB2 

VA2 

o θ = 0

VB1 VC1 

VA1 

VB1 

VC2 

VA2 

VA1 

VB2 

VC1 

VC2 VB2

VA2

o θ = 0

VB1 VC1

VA1

VB1

VC2

VA2

VA1

VB2

VC1

87
 
Table 9. Unbalance Voltage Survey Results of Closed 

and Open Delta Transformer Connections 

Wye and 

Closed Delta Open Delta Total 

Total N of Tests 919 290 1209 

Max. % Unbal. 5.94 10 10 

Min. % Unbal. 0.0 0.0 0.0 

Avg. % Unbal. 0.83 1.98 1.10 

N of tests @ 0% Unbal. 142 9 151 

% of Tests 

V2 % NEMA

V1 

0–0.5 25.5 7.9 21.2 

0.51–1 47.2 15.5 39.6 

1.01–1.5 14.7 21.7 16.4 

1.51–2 5.3 12.8 7.1 

2.01–2.5 2.7 10.3 4.6 

2.51–3 2.2 13.8 5.0 

3.01–3.5 0.9 5.9 2.1 

3.51–4 0.8 4.8 1.7 

4.01–4.5 0.1 2.8 0.7 

4.51–5 0.3 1.4 0.6 

>5 0.3 3.1 1.0 

Notes: 

(1) 1209 test (13-utility survey) 

(2) Average unbalanced = 1.1% 

(3) 12.5% of tests = 0% unbalance 

60% of tests <1% unbalance 

85% of tests <2% unbalance 

(4) Average unbalance = 0.83% for closed banks 

(5) Average unbalance = 1.98% for open delta 

4.5.2 Synchronous Generators Operating on Unbalanced Voltages

Unbalanced three-phase stator currents applied to synchronous generators cause negative 

sequence phase currents that, in turn, cause a double frequency current in the surface of the 

rotor. These currents flow through the retaining rings, slot wedges, and field winding and 

cause high temperatures and possibly failure. 

88
 
NegativeNegative

Retaining Rings Sequence Currents 

Rotor Shaft Field Winding Rotor Iron

Retaining Rings Sequence Currents

Field Winding Rotor Shaft

Figure 75. Round rotor synchronous machine
 

showing negative sequence current paths in the rotor surface
 

Typically, the unbalance comes from single-phase main unit transformers with different 

impedances, unbalanced loads, open phases, and faults. Phase-to-phase faults create the 

highest negative sequence currents. A line-to-ground fault on the wye side of a delta-wye 

step-up transformer creates a line-to-line fault, as seen by the generator. The fault current 

from a line-to-ground fault on the generator is less than the line-to-line fault, and the openphase condition produces less negative sequence current than the phase-to-phase or phase-toground fault. 

Because the negative sequence current components rotate in the opposite direction of the 

rotation of the rotor, the flux produced by these currents has a frequency twice the 

synchronous speed. The skin effect causes these double frequency currents to be 

concentrated on the surface of the poles and the teeth of the rotor. These currents flow along 

the axial length of the rotor until they contact the retaining rings, which are shrunk onto the 

ends of the rotor iron, as in Figure 75. A small portion of these negative sequence currents 

flows in the field winding. The negative sequence current beating of the rotor and retaining 

rings causes these rings to expand and become loose on the rotor iron. 

4.5.2.1 Negative Sequence Heating 

As was the case with induction machines, most of the increased losses for the synchronous 

generator because of negative sequence currents occur in the rotor. The temperature rise over 

time is proportional to the Is2

2

t, where the Is2 is the stator negative sequence current, and t is 

in seconds. The safe limit is established based on 

K = Is2

2

t, Equation 4.44 

where 

K = Constant based or a specific design and size of generator 

Is2 = The negative sequence stator current (rms) 

t = Time in seconds. 

89
 
The safe limit value of K is determined by measuring the temperature of the rotor with 

negative sequence current from the stator according to ANSI C50.13 and establishing the 

safe operating continuous unbalanced current capability of the generator. The safe limit is 

based on rated kilovolt-amperes and maximum current not to exceed 105% of rated current in 

any phase. Typically, the maximum permissible stator negative sequence IS2 current is 10% 

of the rated stator current, but the specific value recommended by the manufacturer should be 

used to set the value for the negative sequence relay. 

4.5.2.2 Negative Sequence Relay 

The negative sequence relays may be of definite-time-delay type or inverse-time type. The 

device 46 function is an inverse time overcurrent. Figure 76 shows typical time-negative 

sequence current curves for the Type SGC relay. Values for K can be calculated (G.E. 

Multilin 1998) using the p.u. locked rotor current ILR for a motor. If the p.u. ILR = 5, 

175 K = = 7 . Equation 4.45 I

2

LR 

Values ranging up 40 have been used. Also, synchronous generator values for K vary from 

about 4 to 8. A negative sequence pickup current setting of about 15% of full load current 

results in about 300 seconds. As shown in Table 2, a 15.44% negative sequence current 

results in a 3% voltage imbalance for the single-cage induction motor. 

90
 
Figure 76. Typical time-current curves for the Type SGC relay 

91
 
5 Project Results – Development of Models 

5.1 Introduction 

This section focuses on the development of models for DG and the distribution circuit 

voltage regulation equipment for unbalanced power systems. The voltage regulation models 

were developed for the substation LTC transformer, bidirectional step regulator, capacitors, 

and each of the distribution circuit transformer connections. In addition, line impedance, 

voltage drop, and losses were modeled, as were secondary and service drop impedance, 

voltage drop, and losses. Finally, a shunt capacitor model for a wye-grounded connection and 

models for synchronous, induction, and inverter-based generators were created. 

5.2 Three-Phase Substation Transformer Models 

Three-phase transformers are used at the distribution substation to transform voltage from the 

sub-transmission or, in some cases, transmission system down to distribution circuit levels. 

These three-phase transformers may have HV fixed taps or LV fixed taps or can be LTC or 

under LTC transformers. The typical distribution circuit is a four-wire wye multi-grounded 

system fed from a delta-wye-grounded, three-phase substation transformer. However, there 

are three-wire, ungrounded delta distribution circuits, and they are normally fed from deltadelta three-phase substation transformers. Three-phase and single-phase transformers on the 

circuit feed three-phase customer load or combinations of single-phase and three-phase loads. 

Also, single-phase transformers on the circuit feed single-phase loads. 

The delta-wye grounded transformer connection is shown in Figure 77. 

g 

VBC 

VAB 

VCA 

+ 

+ 

+ 

-

-

-

Vtc 

Vtb 

Vta 

+ 

+ 

+ 

-

-

-

zt 

zt 

zt 

+ 

-

+ 

-

+ 

-

Vbc 

Vab 

Vca 

+ 

Figure 77. Delta-wye grounded three-phase transformer 

From this figure, the primary-side line-to-line voltages can be written as a function of the 

ideal secondary-side voltages. 

92
 
⎡VAB 
 ⎤ ⎡ 0 - n 0 t ⎤ ⎡vta ⎤

VBC 
 0 0 - n t vt , Equation 5.1 b 

⎢

⎢

⎢

⎣VCA 

⎢

⎢

⎢

⎣

=⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦ vtc 

⎥

⎥

⎥

⎦ - n 0 0 t 

where the turns ratio nt is defined as 

VLLHS 

nt =
 . VLNLS 

Equation 5.2 

The ideal secondary voltage can be written as a function of the secondary-side line-to-neutral 

voltage as: 

Vtabc = VLGabc + Ztabc Iabc 

Equation 5.3 

where 

Z t 0 0 

0 Z t 0 

0 0 Z t

⎡ ⎤
 ⎢ Equation 5.4

⎢

⎢

⎣

⎥

⎥

⎥

⎦

Zt =
 .
 

The primary line-to-line voltage as a function of the secondary line-to-ground voltage and the 

secondary current Iabc is 

⎡

⎢

⎢

⎢

⎣

V V 

V V 

V V 

⎡

⎢

⎢

⎢

⎣

To make the transformer model consistent with other system models and therefore easier to 

calculate, the secondary-side line-to-ground voltage should be expressed as a function of the 

primary-side line-to-neutral voltage. This can be done using the theory of symmetrical 

components and algebraic manipulation. The resulting expression is 

⎛

⎜

⎜

⎜

I ⎞

⎟

⎟

⎟

AB ⎤ ⎡ 0 − nt 0
 ⎤ a ⎤ ⎡zt 0 0 ⎤ ⎡ a ⎤ ⎢

⎢

⎢

⎣

=⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

+⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

0 0 − n ⋅ 0 0 I Equation 5.5 t z . BC b t b

− n 0 0
 0 0 I t z CA ⎝ c t c ⎠

⎡

⎢

⎢

⎢

⎣

⎡

V
 

V
 

⎡

⎢

⎢

⎢

⎣

⎡⎤

V 

V 

V 

AB ⎤ ⎡ 1 −1 0 ⎤ A ⎤ ⎢

⎢

⎢

⎣

=⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

1 ⎥

⎥

⎥

⎦

0 1 − ⋅ BC B 

VCA −
 

⎡

⎢

⎢

⎢

⎣

1 0 1 

V 

V 

V 

C 

⎛

⎜

⎜

⎜

⎡

⎢

⎢

⎢

⎣

V 

Vb
 

V
 

I ⎞

⎟

⎟

⎟

1 −1 0
 ⎤ A 0 − nt 0
 ⎤ a ⎤ ⎡zt 0 0 ⎤ ⎡ a ⎤ ⎢

⎢

⎢

⎣

⎥

⎥

⎥

⎦

1 ⎢

⎢

⎢

⎣

=⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

+⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

0 1 − ⋅ 0 0 − n ⋅ 0 0 I t z B t b

−1 0 1 − n 0 0
 0 0 I t z C ⎝ c t c ⎠

93
 
⎡ 0 0 − ⎡ 1 −1 0
 ⎤ A ⎤ a ⎤ ⎡z t 0 0 ⎤ ⎡I a ⎤

1 

nt 

−1 0 0
 0 1 − ⋅ =
 0 z 0 I B b t b

V V 

V V 

V V 

z 0 0 

⎡

⎢

⎢

⎢

⎣

⎡

⎢

⎢

⎢

⎣

1 

⎢

⎢

⎢

⎣

⋅

⎤

⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

1

⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

+⎥

⎥

⎥

⎦ t 

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦ I c 

⎥

⎥

⎥

⎦ 0 −1 0 −1 0 1
 0 0 z C c 

V 

Vb
 

V
 

⎡

⎢

⎢

⎢

⎣

V 

V 

VC 

⎡

⎢

⎢

⎢

⎣

1 0 −1⎤ I

⎥

⎥

⎥

⎦

a ⎤ ⎡ A ⎤ ⎡ t ⎤ ⎡ a ⎤ ⎥

⎥

⎥

⎦

=
 

1 

nt 

⎢

⎢

⎢

⎣

⎢

⎢

⎢

⎣

−⎥

⎥

⎥

⎦

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦

⎥

⎥

⎥

⎦

−1 1 0 ⋅ 0 0 z 
 I . Equation 5.6 B t b

0 −1 1
 0 0 z I c t c 

5.3 Three-Phase and Single-Phase Distribution Transformer Connections for 

Distribution Circuit 

The following equations determine the voltage drop on the wye-grounded primary system 

feeding different transformer connections and three-phase and single-phase loading. The 

factor 0.9 IL in some of the equations represents the portion of the neutral current in the 

neutral conductor, the remainder of which is current in the earth. 

Wye-Grounded Primary System Transformer Connections and Voltage Regulation 

Case I. 

C 

SΦ SΦ

R X IL A

N 

RN XN IL 

R X IL 

a 

c 

b 

Equal Single-Phase

Loads 

B 

V = IL [R Cos θ + X Sin θ] + 0.9 IL [RN Cos (θ – 60°) + XN Sin (θ – 60°)] R NA 

Equation 5.7 

V = IL [R Cos θ + X Sin θ] + 0.9 IL [RN Cos (θ + 60°) + XN (θ +60°)] R CN

Equation 5.8 

Case II. 

a 

R X I

L A 

R 3 N XN I

L 

R X I

L 

b 3Φ

c N 

C B 

94
 
VR NA = IL [R Cos (θ – 30°) + X Sin (θ – 30°)] + 0.9 √3 IL [RN Cos (θ – 60°) + XN Sin (θ – 

60°)] Equation 5.9 

VR CN = IL [R Cos (θ + 30°) + X Sin (θ + 30°)] + 0.9 √3 IL [RN Cos (θ + 60°) + XN Sin (θ + 

60°)] Equation 5.10 

Case III. 

SΦ

a 

c 

N 

b 

R X I

L A 

C 

B 

R X 2 IL 

R X I

L 

VR NA = IL [R Cos (θ – 60°) + X Sin θ – 60°)] Equation 5.11 

VR BN = 2 IL (R Cos θ + X Sin θ) Equation 5.12 

VR CN = IL [R Cos (θ + 60°) + X Sin (θ + 60°)] Equation 5.13 

Case IV. 

R X I

L A 

3Φ R X I L 

B 

C 

R X IL 

N 

a 

c 

b 

VR AN = IL (R Cos θ + X Sin θ) on L-N Base Voltage Equation 5.14 

VR BN = IL (R Cos θ + X Sin θ) on L-N Base Voltage Equation 5.15 

VR CN = IL (R Cos θ + X Sin θ) on L-N Base Voltage Equation 5.16 

95
 
Case V. 

R X I

L A 

C R X I

L 

R X I

L 

a 

3Φ b 

B 

c 

VR NA = IL (R Cos θ + X Sin θ) Equation 5.17 

V = IL (R Cos θ + X Sin θ) Equation 5.18 R NB

V = IL (R Cos θ + X Sin θ) Equation 5.19 R NC

 Case VI. 

RN 

XN I

L N

R X I

L A a 

SΦ

N C B 

V = IL [R + RN) Cos θ + (X + XN) Sin θ] Equation 5.20 R NA

Case VII. 

R X I

L A 

a 

L-L Voltage SΦ Base 

b 

B 

RN XN 

R X 

C 

R X I

L 

N 

VR BA

 = 2 IL (R Cos θ + X Sin θ) Equation 5.21 

VR NA

 = IL [R Cos (θ – 30°) + X Sin (θ – 30°)] Equation 5.22 

VR BN

 = IL [R Cos (θ + 30°) + X Sin (θ + 30°)] Equation 5.23 

96
 
Case VIII. 

R X 2 IL A 

SΦ

c 

a 

b L-L Voltage 

Base RN XN 

R X I

L 

c 

R X I

L B 

N 

VR NA

 = 2 IL (R Cos θ + X Sin θ) Equation 5.24 

VR BN

 = IL [R Cos (θ + 60°) + X Sin (θ + 60°)] Equation 5.25 

VR CN = IL [R Cos (θ – 60°) + X Sin (θ – 60°)] Equation 5.26 

Case IX. 

3 Φ Φ

NA 3Φ

VR + NA SΦ = IL 3Φ [R Cos (θ3Φ – 30°) + X Sin (θ3Φ – 30°)] + 0.9 √3 IL 3Φ [RN Cos (θ3Φ – 

60°) + XN Sin (θ3Φ – 60°)] + IL SΦ [R Cos θ SΦ + X Sin θ SΦ] + 0.9 IL SΦ [RN Cos (θSΦ – 60°) + 

XN Sin (θSΦ – 60°)] Equation 5.27 

V = IL 3Φ [R Cos (θ3Φ + 30°) + X Sin (θ3Φ + 30°)] + 0.9 √3 IL 3Φ [RN Cos (θ3Φ + 60°) R CN 3Φ

+ XN Sin (θ3Φ + 60°)] Equation 5.28 

V + CA SΦ = IL 3Φ [R Cos (θ + 60°) + X Sin (θ + 60°) + IL 3Φ [R Cos (θ – 60°) + X Sin RCA 3Φ

(θ – 60°)] + IL SΦ [R Cos (θ – 30°) + X Sin (θ – 30°)] Equation 5.29 

5.4 Distribution Transformer Impedance

The percent resistance and percent reactance of transformers can be determined from load 

losses and percent impedance. 

97
 
X%R%Z% 2 2 +=

The percent Z is defined as 

, Equation 5.30 

and percent R is determined from 

Load Losses (watts) % R = . Equation 5.31 10 kVA 

Using the 25-kVA transformer load losses from Table 10, then 

397 watts % R = =1.59 . (10) (25) 

From Equation 5.30, the %R of Equation 5.31, and the %Z of Table 10, %X is determined as 

,R%Z%X% 2 2 −=

2.03)59.1((2.58)X% 2 2 = =− . 

5.5 Distribution Transformer Voltage Drop 

In one knows the R and X values, the load current, and the power factor, the voltage drop can 

be determined. The actual R and X values in ohms are found from the %R and %X values as 

follows: 

Voltage Drop for 25-kVA Transformer 

Base voltage = 240 V 

Base kVA = 25 kVA 

25,000 Base current = =104.17 amperes 240
 

240 Base Z = = 2.30 Ω

104.17 

98
 
Table 10. Distribution Transformer No Load (Core Losses) and Load (Copper Losses) 

NoLoad Load Tot 

Losses Losses Losses 

Type kVA Phase Sec. Volt Pri. Volt Watts Watts Watts %Z %Ie 

OH

OH

OH

OH

OH

 15 

25 

50 

100 

167 

S 

S 

S 

S 

S 

120/240 

120/240 

120/240 

120/240 

120/240 

4800/7620 

4800/7620 

4800/7620 

4800/7620 

4800/7620 

34 

43 

103 

165 

267 

280 

397 

564 

1150 

1749 

314 

440 

667 

1315 

2016 

2.58 

2.58 

1.97 

2.10 

2.37 

0.51 

0.27 

0.76 

0.21 

0.33 

PAD 

PAD 

PAD 

PAD 

PAD 

PAD 

PAD 

75 

150 

300 

500 

1000 

1500 

2000 

3 

3 

3 

3 

3 

3 

3 

120/208 

120/208 

120/208 

120/208 

480Y/277 

480Y/277 

480Y/277 

4800x13200/7620 

13200/7620 

13200/7620 

4800x13200/7620 

4160 

4800x13200 

4800x13200 

283 

328 

639 

1140 

1160 

1516 

1894 

836 

2026 

3198 

4085 

7601 

10294 

12933 

1119 

2354 

3837 

5225 

8761 

11810 

14827 

2.43 

2.37 

2.50 

3.45 

5.51 

6.04 

5.75 

0.78 

0.34 

0.55 

0.46 

0.23 

0.17 

0.15 

ISO 333 S 4800/8320 7620/13200 416 2937 3353 3.43 0.35 

PAD 

PAD 

PAD 

50 

100 

167 

S 

S 

S 

120/240 

120/240 

120/240 

7620 

7620 

4800x13200/7620 

107 

173 

231 

675 

1074 

1466 

782 

1247 

1697 

1.92 

2.34 

2.72 

0.30 

0.26 

0.20 

Actual R ohms = 1.59% x 2.30 Ω
 

= 0.0366 Ω
 

Actual X ohms = 2.0% x 2.30 Ω
 

= 0.0460 Ω
 

Actual Z ohms = 2.58% x 2.30 Ω
 

= 0.0593 Ω
 

Assuming a power factor of 0.90 (25.84°), a load current of 1.40 times rated kilovoltamperes, and a voltage of 105% of rated voltage, the current would be 

(104.17 amperes) I = x 1.40 =138.9 amperes. 1.05 

The approximate voltage drop is then 

∆ V = IR Cos θ + I X Sin θ, Equation 5.32 

 = (138.9) [(0.0366) (0.90) + (0.0460) (0.4358)]

 = (138.9) [0.03294 + 0.0200] 

99
 
∆ V = 7.36 V @ 240 V 

 Equation 5.33 

∆ V @ 120 V = 3.68 V . 

The voltage drop can be reduced if a 50-kVA transformer is substituted for the 25-kVA 

transformer. 

Voltage Drop for 50-kVA Transformer 

Base current = 208.34 A
 

240 Base Z = =1.15 Ω

208.34
 

Actual R ohms = 1.13% x 1.15 Ω
 

= 0.0130 Ω
 

Actual X ohms = 1.62% x 1.15 Ω

 = 0.0187 Ω
 

Actual Z ohms = 1.97% x 1.15 Ω
 

= 0.0227 Ω

Using a 0.90 power factor, 1.4 times rated current, and 105% voltage, the current is 

208.34 I = x 1.40 = 277.8 amperes 1.05 

and 

∆ V = IR Cos θ + I X Sin θ

 = (277.8) [(0.0130) (0.90) + (0.0187) (0.4358)]

 = (277.8) [0.0117 + 0.00815]
 

∆ V = 5.51 V @ 240 V 

∆ V @ 120 V = 2.75 V . Equation 5.34 

5.6 Distribution Transformer Losses 

Distribution transformer losses consist of load losses and no-load losses. 

5.6.1 Load Losses 

The load losses are proportional to the square of the load current. The test data in Table 10 

are given at rated load current. The load loss at loads other than rated load is 

100
 
⎛ I ⎞

2 

l oad Load loss = ⎜

⎜ ⎟⎟ (load loss at rated load), Equation 5.35 I ⎝ rated ⎠

⎛ kV kVA ⎞

2 

rated actual = ⎜

⎜ ⎟

⎟ (load loss at rated load). Equation 5.36 

⎝ kV actual kVArated ⎠

For the 25-kVA transformer, the load loss at rated load is 397 W. But at peak load, the load 

may be as high as 140%–200% of rated load. The load losses at 105% of rated voltage and 

140% of rated load are from Equation 5.36. 

⎛ 7620 (25) (1.40) ⎞

2 

Load losses = ⎜

⎜ x ⎟⎟ (397)

⎝(7620) (1.05) 25 ⎠

 = (1.78) (397) 

= 706 W 

Load Loss (watts) Load Loss (watts) Percent load loss = x100 = (1.4) (VA ) (Cos θ) (1.4) (10 kVA ) (Cos θ) rated rated 

 Equation 5.37 

For the 25-kVA transformer, the percent load loss is 

706 Percent load loss = = 2.24% . (1.4) (10) (25) (.90) 

5.6.2 No-Load Losses 

The no-load losses are the core losses, dielectric losses, and copper losses caused by the 

excitation current. However, the core losses because of the hysteresis and eddy current losses 

are the most significant. From Table 10, the no-load losses for the 25-kVA transformer are 

43 W. For operation above rated voltage, the no-load losses must be corrected. The 

correction factors are 1.15 at 105% of rated voltage and 1.30 at 110% of rated voltage. At 

105% voltage, 

No-load losses = (rated no-load losses) (voltage correction) Equation 5.38 

No-load losses = (43 W) (1.15) = 49.5 W. 

5.6.3 Total Losses 

Adding the no-load losses corrected for voltage and load losses corrected for voltage and 

current gives 2.4% total losses for the 25-kVA transformer. 

101
 
706 + 49.5 Total percent losses = = 2.40% Equation 5.39 (1.4) (10) (25) (0.90) 

For the 50-kVA transformer, the percent load losses are 

⎛ 7620 (50) (1.40) ⎞

2 

Load losses = ⎜

⎜ x ⎟⎟ (564)

⎝(7620) (1.05) 50 ⎠

= 1,003 W
 

1003 Percent load losses = = 1.59% . 

(1.4) (10) (50) (0.90) 

The percent no-load losses are 

No-load losses = (103) (1.15) = 118.5 W, 

and the total percent losses are 

1003 +118.5 Total percent losses = = 1.78% . Equation 5.40 (1.4) (10) (50) (0.90) 

5.7 Line Impedance Model 

A four-wire, wye-grounded, overhead line distribution circuit that consists of three-phase 

conductors and one neutral can be represented as a four-by-four matrix. With the aid of 

Figure 78, the resultant matrix, using Kirckhoff’s voltage law, is shown below. 

VA S VA L 

VB S VB L 

= VC S 

VC L 

VN S VN L 

+
 

ZA ZAB ZAC ZAN 

ZBA ZB ZBC ZBN

ZCA ZCB ZC ZCN

ZNA ZNB ZNC ZN 

I

A 

I

B 

I Equation 5.41 C 

I

N 

102
 
ZA 

S VA

S VB

S VC

S VN

ZB 

ZC 

ZN 

L VA

L VB

L VC

L VN

ZBA 

ZCB 

ZNC 

ZCA 

ZNB ZNA 

Figure 78. Four-wire, wye-grounded, overhead distribution line with multi-grounded neutral 

For a three-conductor cable with one neutral, the impedance matrix is: 

⎡ Z Z Z Z A AB AC AN 

Z Z Z Z BA B BC BN 

⎤
 ⎢

⎢

⎢

⎢

⎥

⎥

⎥

⎥

Z =
 

Z Z Z Z CA CB C CN 

Z Z Z Z NA NB NC N 

.
 

⎣ ⎦

103
 
For the flat-line configuration used in the Milford circuit, the line spacing is: 

2.42’ 

7.33’ 

4.00’ 

5.25’ 

B A C 

N 

Figure 79. Flat line spacing configuration 

The characteristics of the phase and neutral conductors are shown below. 

A B C N 

Conductor 636 Al 636 Al 636 Al 1/0 ACSR 

GMR (ft) 0.0294 0.0294 0.0294 0.006 

Resistance (Ω/mi) 0.146 0.146 0.146 1.153 

The diagonal and off-diagonal elements of the impedance matrix (Kersting 2004) are 

calculated using: 

zii = ri + 0.09530 + j0.12134 [ln(1/GMRi) + 7.93402] Ω/mi Equation 5.42 

zij = 0.09530 + j0.12134 [ln(1/Dij) + 7.93402] Ω/mi, Equation 5.43 

where 

ri = Resistance of conductor in Ω/mi 

Dij = Distance in feet from conductor i to conductor j 

GMRi = Geometric mean radius of the conductor in feet 

0.09530 = Equivalent resistance of earth (100 Ω-m) 

7.93402 = Equivalent mutual inductive reactance between a conductor and earth @ 60 Hz. 

It should be noted that the diagonal terms account for the self-inductance and resistance of 

the line and also contain expressions that take into account the effects of the earth return 

path. The off-diagonal elements account for the mutual inductance of the lines and again take 

into account the effects of the earth return path. 

For the flat-line model of Figure 79, the impedance matrix is: 

104
 
⎡.2413 + j1.3907 .0953 + j.85548 .0953 + j.72101 .0953 + j.70949 ⎤ ⎢ ⎥ .0953 + j.8554 .2413 + j1.3907 .0953 + j.76963 .0953 + j.78573 Z = ⎢ ⎥ . ⎢.0953 + j.72101 .0953 + j.76963 .2413 + j1.3907 .0953 + j.76267 ⎥ ⎢ ⎥ ⎣.0953 + j.70949 .0953 + j.78573 .0953 + j.76267 1.2483 + j1.3907⎦

 Equation 5.44 

The Kron reduction technique allows this four-by-four matrix to be reduced to a moreapplicable three-by-three matrix ZABC. 

⎡ ZA ZAB ZAC⎤ ⎡.2413 + j1.3907 .0953 + j.85548 .0953 + j.72101⎤ ⎢ ⎥ ⎢ ⎥ Zij = ZBA ZB ZBC = .0953 + j.8554 .2413 + j1.3907 .0953 + j.76963 ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ZCA ZCB ZC ⎦ ⎣.0953 + j.72101 .0953 + j.76963 .2413 + j1.3907⎦

 Equation 5.45 

⎡z AN ⎤ ⎡.0953 + j.70949⎤ ⎢ ⎥ ⎢ ⎥ Zin = zBN = .0953 + j.78573 Equation 5.46 ⎢ ⎥ ⎢ ⎥ ⎢z ⎥ ⎢.0953 + j.76267⎥ ⎣ CN ⎦ ⎣ ⎦

Znj = [Z NA Z Z NB NC ] = [.0953 + j.70949 .0953 + j.78573 .0953 + j.76267]

 Equation 5.47 

ZN = zN = 1.2483 + j1.5835 Equation 5.48 

⎡.3404 + j1.1566 .0953 + j.85548 .0953 + j.7210 ⎤ -1 ⎢ ⎥ ZABC = Zij - ZinZ N Znj = .0953 + j.85548 .2413 + j1.3907 .0953 + j.76963 ⎢ ⎥ ⎢ .0953 + j.7210 .0953 + j.76963 .2413 + j1.3907⎥ ⎣ ⎦

 Equation 5.49 

For a non-transposed line of 6.25 mi (33,000 ft), the impedance matrix becomes 

⎡2.1275 + j7.2289 1.3100 + j3.7384 1.2750 + j2.9420⎤ ⎢ ⎥ ZABC = 1.3100 + j3.7384 2.3108 + j6.9235 1.3689 + j3.0904 . Equation 5.50 ⎢ ⎥ ⎢1.2750 + j2.9420 1.3689 + j3.0904 2.2530 + j7.0188⎥ ⎣ ⎦

5.8 Line Voltage Drop Model 

The voltage drop for a given four-wire line segment is calculated using the impedance and 

matrix for that line segment. 

VS - VL = ZABC IABC Equation 5.51 

ΔV = ZABC IABC Equation 5.52 

105
⎡ΔV ⎤ ⎡ IA A z z z A AB AC ⎤ ⎡ ⎤

ΔVB 
 z z z IB

⎢

⎢

⎢

⎣ΔVC 

⎢

⎢

⎢

⎣

=⎥

⎥

⎥

⎦

BA B BC 

⎢

⎢

⎢

⎣

⋅ ⎥

⎥

⎥

⎦ IC 

⎥

⎥

⎥

⎦

 Equation 5.53 

z z z CA CB C 

The effects of the admittance matrix have been neglected because of the relatively short line 

length (6.25 mi). 

5.9 Line Losses Model and Validation 

To validate the line loss model, three line configurations and balanced and unbalanced load 

conditions are considered. These line configurations are shown in Figure 80. Figure 80a is a 

balanced impedance triangular or equilateral configuration with a high B phase. The 

geometric mean distance (GMD) of the phase spacings shown in Figure 80a is 53 in. (4.42 

ft), which is the same as the GMD of the flat configuration in Figure 79. Figure 80b is the flat 

non-transposed line, and Figure 80c is the flat transposed line. The dimensions between 

phases, neutral, and ground are identical in Figure 80b and Figure 80c, but the flat transposed 

line of Figure 80c has two transpositions. 

Figure 81 shows the flat transposed line, which consists of three line segments of 11,000 ft 

each, for a total length of 33,000 ft. The source is at Node 0, and the two transpositions are 

shown at Node 1 and Node 2. The lump load of 9,000 kVA at unity power factor is located at 

the end of the line at Node 3. 

106
 
35

" 

53" 

53 53 " ” B

N = 1/0 ACSR N = 1/0 ACN SR = 1/0 ACSR 53"

A C Φ = 636Al

63"

GMD = 53” N

(a) Equilateral Spacing (a) Equilateral Sp (a) Equilateral Spacing

88"

29"59"

A Φ B Φ C Φ

63" 96"

22' N = 1/0 ACSR N = 1/0 ACN SR = 1/0 ACSR

X-arm NΦ = 636Al

GMD = 53”GMD = 53”

Earth

(b) Flat Non-transposed (b) Flat N(b) Flat(b) Flat on-transposed Non-transposed

Note: Neutral to ground distance = 22' - 63" = 201" (16.75') Note: Neutral to ground distance = 22' - 63" = 201" (16.75' Note: Neutral to ground distance = 22' - 63" = 201" (16.75')

88"

29"59"

AΦ B Φ CΦ

63" 96"

22' N = 1/0 ACSR N = 1/0 ACSR

X-arm NΦ = 636Al

GMD = 53”GMD = 53”

Earth

(c) Flat Transposed (c) Flat Transp (c) Flat Transposed

Note: Neutral to ground distance = 22' - 63" = 201" (16.75') Note: Neutral to ground distance = 22' - 63" = 201" (16.75') ote: Neutral to ground distance = 22' - 63" = 201" (16.75')

Figure 80. Configuration, phase, and neutral spacings; 

phase and neutral sizes; and conductor types 

107
 
Transpositions 

A 

C 

B 

Segment #1 Segment #2 Segment #3 

Node 0 Node 1 Node 2 Node 3 

C 

B 

A 

B 

A 

C 

11,000 ft. 11,000 ft. 11,000 ft. 

Bus Line 

Load 

9000 kVA

θ = 0o 

33,000 ft. 

P.F. = 1.0 

Flat Transposed Line and Load Characteristics 

Figure 81. Line transposition and load 

The purpose of this validation is to show that with balanced line impedance and balanced 

load the kilowatt losses are equal in each phase and total kilowatt losses are lowest. In 

addition, even though the kilowatt losses per phase may not be correct because of the Kron 

reduction process (which reduces a four-by-four matrix to a three-by-three matrix) the total 

losses are, in fact, correct. Table 11, Table 12, and Table 13 and the associated graphs 

provide a summary of balanced and unbalanced loading for the equilateral line spacing, nontransposed flat line spacing, and transposed flat line spacing configurations. 

A balanced load of 3,000 kW per phase, modeled using constant impedance and computed 

using a nominal voltage of 7.62 kV, is attached at the end of the non-transposed line at Node 

3. The load impedance matrix is 

⎡

⎢

⎢

⎢

⎣

19.35 

0 19.35 0 

0 0 ⎤

⎥

⎥

⎥

⎦ 19.35 

Zload = Equation 5.54 

0 0
 

where 

2 (7.62kV) Zloadii = =
 19.35 . Equation 5.55 3MVA 

Attaching the load to the end of the above non-transposed line yields 

108 
VS = (Zload + ZABC) IABC . Equation 5.56 

For a 13.2-kV line, the above load, and the 6.25-mi non-transposed line, solving for IABC 

gives 

)

-1 IABC = (Zload + ZABC VS Equation 5.57 

⎡ 358.4∠ -10.2 ⎤
 ⎢

⎢

⎢

⎣

⎥

⎥

⎥

⎦

IABC 377.8 -130.2 

371.3 ∠108.4

=
 ∠ ,A . Equation 5.58 

Notice from the non-transposed spreadsheet of Table 12, at Node 3, the magnitudes of 

phase currents are IA = 356.2, IB = 375.9, and IC = 372.0. These data are based on the 

voltage-dependent current (VDC) source model rather than the constant-impedance model 

data in the matrix above. 

The load end voltage V load is therefore 

Vload = V - Z S ABC IABC

⎡ 6.94∠-10.2 ⎤
 ⎢

⎢

⎢

⎣

⎥

⎥

⎥

⎦

Vload 7.31 

7.19 

-130.2 

∠108.4

=
 ∠ ,kV . Equation 5.59 

The magnitudes of the phase voltages in kilovolts from Table 12 at Node 3 are VA = 6.96, VB 

= 7.31, and VC = 7.24. The power loss in the line is 

200.5 

71.6 

102.8 

⎡

⎢

⎢

⎢

⎣

⎤

⎥

⎥

⎥

⎦

Ploss = Re[Sin] - Re[Sout] =
 ,kW . Equation 5.60 

The total loss for the line is 374.9 kW. This compares to ΦA = 194.35 kW, ΦB = 72.47 kW, 

and ΦC = 84.29 kW, for a total of 351.11 kW for the VDC model. If the balanced load 

impedance matrix is replaced with an unbalanced load impedance matrix, the loss results 

may appear incorrect. 

12.90 

0 25.81 0 

⎡ 0 0

⎢

⎢

⎢

⎣

⎤

⎥

⎥

⎥

⎦ 25.81 

Zload = Equation 5.61 

0 0
 

109
 
The above impedance matrix corresponds to a heavily loaded A phase (4,500 kW) relative to 

the B and C phases (2,250 kW). The last line of Table 12 at Node 0 shows the voltage 

magnitudes in kilovolts of VA = 7.620, VB = 7.620, and VC = 7.620. Applying these balanced 

voltages and unbalanced loads for each phase, 

(7620) 2 

ZA = 3 = 12.90, 2250 x 10
 

(7620) 2
 

ZB = 3 = 25.81, and 4500 x 10
 

(7620) 2
 

ZC = 3 = 25.81. 

2250 x 10 

Repeating the above procedure to find the line losses yields 

⎡ 516.0 ⎤ ⎢ ⎥ Ploss = Re[Sin] - Re[Sout] = -164.4 ,kW . Equation 5.62 ⎢ ⎥ ⎢ 57.0 ⎥ ⎣ ⎦

The total loss for the line is 408.6 kW. The phase losses from the spreadsheet for the nontransposed case are 131.8, 390.5, and -117.4, corresponding to a heavily loaded B phase 

(4,500 kW) in the simulation case, or a total of 404.96 kW. It is obvious in this unbalanced 

case that the phase loss calculations do not represent the actual losses in each phase; 

however, the total line loss is correct. The inclusion of the effects of the earth and neutral in 

the three-by-three impedance matrix is the reason for the dubious phase loss numbers. To 

obtain correct losses for the individual phases, the I2

R losses should be calculated. First, the 

earth and neutral currents should be found. 

IN = ZNt IABC = 60.6∠157.5,A Equation 5.63 

where 

-1 ZNt IABC = -ZN Znj . Equation 5.64 

The earth current is 

IE = -(IA + IB + IC + IN) =127.9∠126.4,A . Equation 5.65 

Next, the I2

R losses for each phase, earth, and neutral are calculated. 

PlossA = IA 

2 RA = 209.1, kW Equation 5.66 

PlossB = IB 

2 RB = 88.4, kW Equation 5.67 

PlossC = IC 

2 RC = 75.0,kW Equation 5.68 

110
 
PlossE = IE 

2 RE = 9.7,kW Equation 5.69 

PlossN = IN 

2 RN = 26.4, kW Equation 5.70 

When the losses are summed from the I2

R calculations, the result is 408.6. This exactly 

matches the previously calculated total line loss. The reason for the slight difference between 

the total losses from the Table 12 spreadsheet data of 404.96 kW and the total losses of 408.6 

kW above is the spreadsheet data are for a VDC model. The total losses above are based on a 

constant-impedance model. 

Note: The PF in Table 11, Table 12, and Table 13 is the percent power flow imbalance 

(in kilovolt-amperes). 

111
 
Table 11. Equilateral Spacing Kilowatt Loss Evaluation 

Spot Load (kW) kW Losses Total kW kVar Losses Total kVar kW Flow 

ΦA ΦB ΦC ΦA ΦB ΦC Losses ΦA ΦB ΦC Losses ΦA ΦB ΦC Total kW Flow 

3000.00 3000.00 3000.00 117.17 117.02 116.89 351.08 515.76 515.74 515.68 1547.18 2758.79 2759.06 2759.28 8277.13 

3150.00 2925.00 2925.00 143.85 94.42 113.39 351.66 568.41 507.63 472.37 1548.41 2856.88 2713.97 2703.31 8274.16 

3300.00 2850.00 2850.00 171.35 72.44 109.62 353.41 622.80 498.63 430.76 1552.19 2951.53 2666.94 2646.96 8265.43 

3450.00 2775.00 2775.00 199.93 51.43 104.92 356.28 677.99 489.86 390.41 1558.26 3041.81 2619.49 2589.48 8250.78 

3600.00 2700.00 2700.00 228.92 31.27 100.01 360.20 734.23 480.24 351.94 1566.41 3128.22 2570.23 2531.83 8230.28 

3750.00 2625.00 2625.00 258.85 11.66 94.75 365.26 792.19 470.22 314.54 1576.95 3211.81 2519.64 2472.90 8204.35 

3900.00 2550.00 2550.00 289.23 -6.96 89.03 371.30 850.71 459.93 278.75 1589.39 3291.28 2468.02 2413.32 8172.62 

4050.00 2475.00 2475.00 320.05 -24.56 82.79 378.28 909.51 449.56 244.49 1603.56 3366.43 2415.58 2352.90 8134.91 

4200.00 2400.00 2400.00 351.17 -41.40 76.48 386.25 969.41 438.57 211.70 1619.68 3438.52 2361.61 2291.72 8091.85 

4350.00 2325.00 2325.00 382.50 -57.46 70.17 395.21 1030.43 426.96 180.38 1637.77 3507.79 2306.09 2229.77 8043.65 

4500.00 2250.00 2250.00 414.10 -72.43 63.39 405.06 1091.39 415.48 150.55 1657.42 3572.73 2249.97 2166.85 7989.55 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 368.22 368.25 368.28 0.02 368.24 0.01 0.0% 0.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 382.16 362.23 360.04 6.44 368.12 8.39 2.3% 4.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 395.74 355.95 351.85 12.85 367.78 16.63 4.5% 8.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 408.87 349.61 343.58 19.24 367.2 24.7 6.7% 11.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 421.56 343.04 335.36 25.53 366.38 32.61 8.9% 15.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 433.99 336.27 327.06 31.87 365.35 40.37 11.0% 19.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 445.97 329.36 318.74 38.14 364.09 47.97 13.2% 22.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 457.5 322.35 310.36 44.35 362.59 55.41 15.3% 26.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 468.72 315.12 301.96 50.54 360.88 62.69 17.4% 30.0% 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 479.63 307.68 293.51 56.72 358.97 69.83 19.5% 0.33 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 490.12 300.16 284.99 62.84 356.83 76.81 21.5% 0.37 

7.44 7.44 7.44 0.1 7444.34 0.08 0.0% 368.22 368.25 368.28 0.02 368.24 0.01 0.0% 0.0% 

7.42 7.46 7.45 27.28 7444.34 10.95 0.1% 382.16 362.23 360.04 6.44 368.12 8.39 2.3% 4.0% 

7.39 7.48 7.46 54.31 7444.22 21.65 0.3% 395.74 355.95 351.85 12.85 367.78 16.63 4.5% 8.0% 

7.36 7.5 7.47 81.21 7444.01 32.15 0.4% 408.87 349.61 343.58 19.24 367.2 24.7 6.7% 11.0% 

7.33 7.52 7.48 107.71 7443.74 42.43 0.6% 421.56 343.04 335.36 25.53 366.38 32.61 8.9% 15.0% 

7.3 7.54 7.49 134.43 7443.41 52.52 0.7% 433.99 336.27 327.06 31.87 365.35 40.37 11.0% 19.0% 

7.27 7.56 7.5 160.86 7443.01 62.4 0.8% 445.97 329.36 318.74 38.14 364.09 47.97 13.2% 22.0% 

7.25 7.58 7.51 187.04 7442.55 72.06 1.0% 457.5 322.35 310.36 44.35 362.59 55.41 15.3% 26.0% 

7.22 7.59 7.52 213.13 7442.05 81.53 1.1% 468.72 315.12 301.96 50.54 360.88 62.69 17.4% 30.0% 

7.19 7.61 7.53 239.13 7441.52 90.81 1.2% 479.63 307.68 293.51 56.72 358.97 69.83 19.5% 0.33 

7.16 7.63 7.54 264.96 7440.9 99.88 1.3% 490.12 300.16 284.99 62.84 356.83 76.81 21.5% 0.37 

7.29 7.29 7.3 0.19 7294.81 0.15 0.0% 368.23 368.27 368.29 0.02 368.26 0.01 0.0% 0.0% 

7.24 7.33 7.31 54.55 7294.79 21.95 0.3% 382.18 362.24 360.05 6.44 368.13 8.39 2.3% 3.0% 

7.19 7.37 7.33 108.61 7294.48 43.37 0.6% 395.76 355.97 351.86 12.85 367.79 16.63 4.5% 7.0% 

7.13 7.41 7.34 162.42 7293.96 64.36 0.9% 408.89 349.63 343.59 19.24 367.21 24.7 6.7% 10.0% 

7.08 7.45 7.36 215.42 7293.28 84.91 1.2% 421.58 343.05 335.37 25.52 366.39 32.61 8.9% 13.0% 

7.03 7.48 7.37 268.87 7292.42 105.1 1.4% 434.01 336.28 327.07 31.87 365.37 40.37 11.0% 17.0% 

6.98 7.52 7.39 321.72 7291.4 124.86 1.7% 445.99 329.38 318.74 38.14 364.11 47.97 13.2% 20.0% 

6.92 7.56 7.41 374.07 7290.21 144.19 2.0% 457.52 322.36 310.37 44.35 362.61 55.41 15.3% 23.0% 

6.87 7.6 7.42 426.25 7288.9 163.12 2.2% 468.74 315.14 301.96 50.54 360.9 62.69 17.4% 26.0% 

6.82 7.63 7.44 478.26 7287.49 181.69 2.5% 479.65 307.7 293.52 56.71 358.99 69.83 19.5% 0.29 

6.77 7.67 7.46 529.91 7285.88 199.83 2.7% 490.14 300.18 284.99 62.84 356.84 76.81 21.5% 0.32 

7.17 7.17 7.17 0.29 7174.03 0.24 0.0% 368.24 368.27 368.3 0.02 368.26 0.01 0.0% 0.0% 

7.1 7.23 7.19 81.83 7173.95 32.96 0.5% 382.19 362.25 360.06 6.44 368.14 8.39 2.3% 3.0% 

7.02 7.29 7.21 162.92 7173.39 65.08 0.9% 395.77 355.97 351.86 12.85 367.8 16.63 4.5% 6.0% 

6.95 7.35 7.23 243.63 7172.45 96.57 1.3% 408.9 349.63 343.59 19.24 367.22 24.7 6.7% 9.0% 

6.88 7.4 7.25 323.12 7171.2 127.4 1.8% 421.59 343.06 335.38 25.52 366.4 32.61 8.9% 12.0% 

6.8 7.46 7.27 403.29 7169.63 157.69 2.2% 434.02 336.29 327.07 31.87 365.37 40.37 11.0% 15.0% 

6.73 7.51 7.29 482.57 7167.75 187.32 2.6% 446 329.38 318.75 38.14 364.11 47.97 13.2% 17.0% 

6.66 7.57 7.31 561.09 7165.55 216.31 3.0% 457.53 322.37 310.37 44.35 362.62 55.4 15.3% 20.0% 

6.59 7.63 7.34 639.36 7163.11 244.72 3.4% 468.75 315.14 301.96 50.54 360.91 62.69 17.4% 23.0% 

6.52 7.68 7.36 717.38 7160.47 272.57 3.8% 479.67 307.7 293.52 56.71 358.99 69.83 19.5% 0.26 

6.44 7.74 7.38 794.85 7157.47 299.78 4.2% 490.16 300.18 284.99 62.84 356.85 76.81 21.5% 0.28 

Node 0 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 1 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 2 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 3 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

112
 
kVar Flow Total kVar kW Native Load Total kW kVar Native Load Total kVar 

ΦA ΦB ΦC Flow ΦA ΦB ΦC Load ΦA ΦB ΦC Load 

513.61 513.62 513.49 1540.72 2641.63 2642.04 2642.39 7926.06 -2.15 -2.12 -2.20 -6.47 

566.39 505.01 469.93 1541.33 2713.03 2619.55 2589.92 7922.50 -2.03 -2.62 -2.44 -7.09 

620.16 496.25 428.61 1545.02 2780.18 2594.50 2537.33 7912.01 -2.64 -2.38 -2.15 -7.17 

675.99 487.17 388.05 1551.21 2841.88 2568.05 2484.56 7894.49 -2.00 -2.70 -2.36 -7.06 

732.12 478.01 349.25 1559.38 2899.30 2538.95 2431.82 7870.07 -2.11 -2.23 -2.69 -7.03 

789.55 467.89 312.28 1569.72 2952.96 2507.99 2378.15 7839.10 -2.65 -2.33 -2.26 -7.24 

847.92 457.62 276.52 1582.06 3002.05 2474.98 2324.28 7801.31 -2.78 -2.31 -2.23 -7.32 

907.62 447.15 241.84 1596.61 3046.38 2440.15 2270.11 7756.64 -1.89 -2.41 -2.65 -6.95 

967.68 436.16 208.98 1612.82 3087.35 2403.01 2215.24 7705.60 -1.73 -2.42 -2.72 -6.87 

1027.84 424.65 177.97 1630.46 3125.30 2363.54 2159.60 7648.44 -2.58 -2.31 -2.41 -7.30 

1089.67 412.92 147.93 1650.52 3158.63 2322.40 2103.46 7584.49 -1.73 -2.56 -2.61 -6.90 

Plot Information: 

kW 

Node 0 Total kW Losses / Node 1 Node 2 Node 3 

I2/I1 Losses kW Flow V1/V2 V1/V2 V1/V2 I0 I1 I2 

0.0% 351.08 4.2% 0.0% 0.0% 0.0% 0.02 368.24 0.01 

2.3% 351.66 4.3% 0.1% 0.3% 0.5% 6.44 368.12 8.39 

4.5% 353.41 4.3% 0.3% 0.6% 0.9% 12.85 367.78 16.63 

6.7% 356.28 4.3% 0.4% 0.9% 1.3% 19.24 367.20 24.70 

8.9% 360.20 4.4% 0.6% 1.2% 1.8% 25.53 366.38 32.61 

11.0% 365.26 4.5% 0.7% 1.4% 2.2% 31.87 365.35 40.37 

13.2% 371.30 4.5% 0.8% 1.7% 2.6% 38.14 364.09 47.97 

15.3% 378.28 4.7% 1.0% 2.0% 3.0% 44.35 362.59 55.41 

17.4% 386.25 4.8% 1.1% 2.2% 3.4% 50.54 360.88 62.69 

19.5% 395.21 4.9% 1.2% 2.5% 3.8% 56.72 358.97 69.83 

21.5% 405.06 5.1% 1.3% 2.7% 4.2% 62.84 356.83 76.81 

113
 
Table 12. Non-Transposed Kilowatt Loss Evaluation 

Spot Load (kW) kW Losses Total kW kVar Losses Total kVar kW Flow 

ΦA ΦB ΦC ΦA ΦB ΦC Losses ΦA ΦB ΦC Losses ΦA ΦB ΦC Total kW Flow 

3000.00 3000.00 3000.00 194.35 72.47 84.29 351.11 468.69 504.08 571.12 1543.89 2673.63 2820.78 2777.24 8271.65 

2925.00 3150.00 2925.00 191.64 101.18 59.82 352.64 421.45 558.63 560.65 1540.73 2617.99 2918.11 2734.33 8270.43 

2850.00 3300.00 2850.00 187.85 130.92 36.35 355.12 376.15 614.45 549.88 1540.48 2561.96 3010.91 2690.10 8262.97 

2775.00 3450.00 2775.00 183.15 161.60 13.77 358.52 332.63 671.65 538.71 1542.99 2505.32 3099.54 2644.44 8249.30 

2700.00 3600.00 2700.00 177.65 193.08 -7.92 362.81 290.90 730.13 527.13 1548.16 2448.06 3184.09 2597.33 8229.48 

2625.00 3750.00 2625.00 171.40 225.19 -28.66 367.93 250.97 789.76 515.15 1555.88 2390.15 3264.58 2548.82 8203.55 

2550.00 3900.00 2550.00 164.51 257.80 -48.44 373.87 212.83 850.44 502.77 1566.04 2331.59 3341.09 2498.88 8171.56 

2475.00 4050.00 2475.00 157.03 290.77 -67.24 380.56 176.49 912.05 490.01 1578.55 2272.37 3413.67 2447.55 8133.59 

2400.00 4200.00 2400.00 149.06 323.97 -85.02 388.01 141.95 974.51 476.88 1593.34 2212.46 3482.4 2394.83 8089.69 

2325.00 4350.00 2325.00 140.67 357.27 -101.76 396.18 109.20 1037.72 463.38 1610.30 2151.87 3547.33 2340.72 8039.92 

2250.00 4500.00 2250.00 131.84 390.48 -117.36 404.96 78.33 1101.20 449.63 1629.16 2090.66 3608.08 2285.35 7984.09 

7.6200 7.6200 7.6200 0 7620.91 0.11 0.0% 356.11 375.94 371.99 3.24 367.98 9.3 2.5% 0.03 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 347.9 389.79 366.19 9.06 367.9 15.93 4.3% 0.06 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 339.73 403.15 360.22 15.38 367.57 23.48 6.4% 0.1 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 331.58 416.08 354.06 21.72 367.01 31.17 8.5% 0.13 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 323.45 428.57 347.7 28.05 366.2 38.8 10.6% 0.17 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 315.32 440.64 341.15 34.34 365.14 46.31 12.7% 0.2 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 307.19 452.3 334.41 40.59 363.85 53.68 14.8% 0.24 

7.62 7.62 7.6200 0 7620.91 0.11 0.0% 299.04 463.56 327.47 46.8 362.32 60.9 16.8% 0.28 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 290.89 474.41 320.35 52.97 360.56 67.97 18.9% 0.31 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 282.71 484.88 313.04 59.1 358.57 74.88 20.9% 0.35 

7.6200 7.62 7.62 0 7620.91 0.11 0.0% 274.51 494.92 305.56 65.15 356.34 81.62 22.9% 0.38 

7.38 7.49 7.46 17.54 7442.93 56.3 0.8% 356.11 375.94 371.99 3.24 367.98 9.3 2.5% 0.03 

7.39 7.46 7.48 42.54 7442.11 46.62 0.6% 347.9 389.79 366.19 9.06 367.9 15.93 4.3% 0.06 

7.39 7.43 7.5 71.6 7441.23 37.83 0.5% 339.73 403.15 360.22 15.38 367.57 23.48 6.4% 0.1 

7.4 7.4 7.52 101.14 7440.28 30.53 0.4% 331.58 416.08 354.06 21.72 367.01 31.17 8.5% 0.13 

7.41 7.37 7.54 130.7 7439.27 25.77 0.3% 323.45 428.57 347.7 28.05 366.2 38.8 10.6% 0.17 

7.42 7.34 7.57 160.16 7438.22 24.81 0.3% 315.32 440.64 341.15 34.34 365.14 46.31 12.7% 0.2 

7.43 7.3 7.59 189.47 7437.11 27.84 0.4% 307.19 452.3 334.41 40.59 363.85 53.68 14.8% 0.24 

7.43 7.27 7.61 218.59 7435.97 33.64 0.5% 299.04 463.56 327.47 46.8 362.32 60.9 16.8% 0.28 

7.44 7.24 7.63 247.53 7434.78 40.92 0.6% 290.89 474.41 320.35 52.97 360.56 67.97 18.9% 0.31 

7.45 7.21 7.65 276.27 7433.56 48.93 0.7% 282.71 484.88 313.04 59.1 358.57 74.88 20.9% 0.35 

7.46 7.18 7.67 304.7 7432.31 57.25 0.8% 274.51 494.92 305.56 65.15 356.34 81.62 22.9% 0.38 

7.16 7.39 7.33 35.08 7291.9 112.7 1.5% 356.14 375.94 372 3.24 367.99 9.29 2.5% 0.04 

7.17 7.33 7.38 85.08 7290.1 93.32 1.3% 347.93 389.8 366.2 9.06 367.91 15.91 4.3% 0.06 

7.18 7.27 7.42 143.2 7288.13 75.74 1.0% 339.76 403.16 360.23 15.37 367.59 23.47 6.4% 0.09 

7.19 7.21 7.46 202.27 7285.99 61.12 0.8% 331.61 416.08 354.07 21.72 367.02 31.16 8.5% 0.13 

7.21 7.15 7.5 261.4 7283.7 51.56 0.7% 323.47 428.58 347.71 28.04 366.21 38.79 10.6% 0.16 

7.22 7.09 7.54 320.31 7281.26 49.59 0.7% 315.34 440.65 341.16 34.34 365.16 46.3 12.7% 0.19 

7.24 7.03 7.59 378.92 7278.69 55.61 0.8% 307.21 452.31 334.41 40.59 363.87 53.67 14.7% 0.22 

7.25 6.98 7.63 437.17 7276 67.19 0.9% 299.07 463.57 327.48 46.8 362.34 60.89 16.8% 0.25 

7.27 6.92 7.67 495.05 7273.19 81.75 1.1% 290.91 474.43 320.36 52.97 360.58 67.96 18.8% 0.28 

7.28 6.86 7.71 552.53 7270.27 97.75 1.3% 282.73 484.9 313.05 59.09 358.59 74.87 20.9% 0.31 

7.3 6.8 7.75 609.38 7267.27 114.39 1.6% 274.52 494.94 305.57 65.15 356.36 81.61 22.9% 0.34 

6.96 7.31 7.24 52.62 7169.53 169.1 2.4% 356.17 375.94 372 3.24 368 9.27 2.5% 0.05 

6.97 7.23 7.3 127.61 7166.6 140.03 2.0% 347.95 389.79 366.2 9.05 367.92 15.9 4.3% 0.07 

6.99 7.14 7.37 214.79 7163.34 113.65 1.6% 339.78 403.16 360.23 15.37 367.6 23.47 6.4% 0.09 

7 7.06 7.43 303.4 7159.76 91.71 1.3% 331.63 416.08 354.07 21.71 367.03 31.15 8.5% 0.12 

7.02 6.98 7.49 392.08 7155.89 77.36 1.1% 323.49 428.58 347.71 28.04 366.22 38.78 10.6% 0.15 

7.04 6.9 7.55 480.44 7151.74 74.38 1.0% 315.36 440.65 341.16 34.33 365.17 46.29 12.7% 0.18 

7.05 6.82 7.62 568.36 7147.34 83.38 1.2% 307.23 452.32 334.41 40.58 363.88 53.66 14.7% 0.2 

7.07 6.74 7.68 655.73 7142.68 100.74 1.4% 299.08 463.57 327.48 46.8 362.35 60.89 16.8% 0.23 

7.09 6.66 7.74 742.55 7137.8 122.56 1.7% 290.92 474.43 320.36 52.96 360.59 67.95 18.8% 0.25 

7.11 6.58 7.8 828.77 7132.71 146.57 2.1% 282.74 484.9 313.05 59.09 358.6 74.86 20.9% 0.28 

7.14 6.5 7.86 914.04 7127.42 171.52 2.4% 274.54 494.94 305.57 65.14 356.37 81.6 22.9% 0.31 

Node 0 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 1 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 2 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 3 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

114
 
kVar Flow Total kVar kW Native Load Total kW kVar Native Load Total kVar 

ΦA ΦB ΦC Flow ΦA ΦB ΦC Load ΦA ΦB ΦC Load 

465.92 501.64 569.08 1536.64 2479.28 2748.31 2692.95 7920.54 -2.78 -2.43 -2.04 -7.25 

419.06 555.98 558.44 1533.48 2426.36 2816.93 2674.51 7917.80 -2.39 -2.66 -2.21 -7.26 

373.75 611.81 547.65 1533.21 2374.11 2879.99 2653.75 7907.85 -2.40 -2.63 -2.23 -7.26 

330.22 669.05 536.47 1535.74 2322.17 2937.94 2630.67 7890.78 -2.41 -2.60 -2.24 -7.25 

288.48 727.55 524.87 1540.90 2270.41 2991.02 2605.25 7866.68 -2.42 -2.58 -2.26 -7.26 

248.53 787.22 512.87 1548.62 2218.75 3039.39 2577.47 7835.61 -2.44 -2.54 -2.28 -7.26 

210.38 847.92 500.48 1558.78 2167.09 3083.29 2547.33 7797.71 -2.45 -2.52 -2.30 -7.27 

174.03 909.56 487.70 1571.29 2115.34 3122.90 2514.79 7753.03 -2.46 -2.48 -2.31 -7.25 

139.48 972.05 474.55 1586.08 2063.40 3158.43 2479.85 7701.68 -2.47 -2.47 -2.33 -7.27 

106.72 1035.28 461.04 1603.04 2011.20 3190.07 2442.48 7643.75 -2.48 -2.44 -2.35 -7.27 

75.60 1099.26 447.30 1622.16 1958.82 3217.60 2402.71 7579.13 -2.73 -1.94 -2.32 -6.99 

Plot Information: 

kW 

Node 0 Total kW Losses / Node 1 Node 2 Node 3 

I2/I1 Losses kW Flow V1/V2 V1/V2 V2/V1 I0 I1 I2 

2.5% 351.11 4.2% 0.8% 1.5% 2.4% 3.24 367.98 9.30 

4.3% 352.64 4.3% 0.6% 1.3% 2.0% 9.06 367.90 15.93 

6.4% 355.12 4.3% 0.5% 1.0% 1.6% 15.38 367.57 23.48 

8.5% 358.52 4.3% 0.4% 0.8% 1.3% 21.72 367.01 31.17 

10.6% 362.81 4.4% 0.3% 0.7% 1.1% 28.05 366.20 38.80 

12.7% 367.93 4.5% 0.3% 0.7% 1.0% 34.34 365.14 46.31 

14.8% 373.87 4.6% 0.4% 0.8% 1.2% 40.59 363.85 53.68 

16.8% 380.56 4.7% 0.5% 0.9% 1.4% 46.80 362.32 60.90 

18.9% 388.01 4.8% 0.6% 1.1% 1.7% 52.97 360.56 67.97 

20.9% 396.18 4.9% 0.7% 1.3% 2.1% 59.10 358.57 74.88 

22.9% 404.96 5.1% 0.8% 1.6% 2.4% 65.15 356.34 81.62 

115
 
Table 13. Transposed Kilowatt Loss Evaluation 

Spot Load (MW) kW Losses Total kW kVar Losses Total kVar kW Flow 

ΦA ΦB ΦC ΦA ΦB ΦC Losses ΦA ΦB ΦC Losses ΦA ΦB ΦC Total kW Flow 

3000.00 3000.00 3000.00 117.05 117.04 117.06 351.15 515.80 515.77 515.79 1547.36 2758.93 2758.99 2759.00 8276.92 

3150.00 2925.00 2925.00 144.46 91.77 115.41 351.64 570.85 508.10 469.82 1548.77 2854.89 2716.82 2702.11 8273.82 

3300.00 2850.00 2850.00 172.80 67.30 112.99 353.09 627.40 500.00 425.46 1552.86 2946.78 2673.22 2644.53 8264.53 

3450.00 2775.00 2775.00 201.93 43.65 109.86 355.44 685.35 491.46 382.72 1559.53 3034.65 2628.21 2586.23 8249.09 

3600.00 2700.00 2700.00 231.72 20.86 106.09 358.67 744.55 482.47 341.61 1568.63 3118.54 2581.78 2527.21 8227.53 

3750.00 2625.00 2625.00 262.04 -1.04 101.75 362.75 804.88 473.04 302.13 1580.05 3198.50 2533.96 2467.46 8199.92 

3900.00 2550.00 2550.00 292.76 -22.01 96.92 367.67 866.23 463.17 264.30 1593.70 3274.59 2484.74 2406.97 8166.30 

4050.00 2475.00 2475.00 323.76 -42.03 91.64 373.37 928.50 452.87 228.11 1609.48 3346.87 2434.14 2345.73 8126.74 

4200.00 2400.00 2400.00 354.91 -61.08 85.99 379.82 991.58 442.13 193.57 1627.28 3415.40 2382.16 2283.73 8081.29 

4350.00 2325.00 2325.00 386.12 -79.12 80.03 387.03 1055.39 430.97 160.70 1647.06 3480.26 2328.81 2220.98 8030.05 

4500.00 2250.00 2250.00 417.26 -96.12 73.83 394.97 1119.83 419.41 129.49 1668.73 3541.49 2274.10 2157.48 7973.07 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 368.23 368.24 368.24 0 368.23 0 0.0% 0 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 381.96 362.61 359.83 6.43 368.11 8.38 2.3% 0.04 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 395.27 356.79 351.42 12.82 367.74 16.59 4.5% 0.07 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 408.16 350.78 343 19.18 367.13 24.63 6.7% 0.11 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 420.63 344.57 334.58 25.5 366.28 32.5 8.9% 0.15 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 432.71 338.18 326.15 31.78 365.19 40.21 11.0% 0.18 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 444.38 331.59 317.7 38.03 363.86 47.74 13.1% 0.22 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 455.67 324.82 309.22 44.25 362.29 55.12 15.2% 0.25 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 466.58 317.85 300.71 50.42 360.49 62.33 17.3% 0.29 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 477.12 310.7 292.17 56.55 358.47 69.38 19.4% 0.33 

7.62 7.62 7.62 0 7620.91 0.11 0.0% 487.29 303.37 283.59 62.65 356.22 76.27 21.4% 0.36 

7.36 7.5 7.47 25.23 7444.34 60.26 0.8% 368.23 368.24 368.24 0 368.23 0 0.0% 0 

7.33 7.53 7.48 53.13 7445.92 64.24 0.9% 381.96 362.61 359.83 6.43 368.11 8.38 2.3% 0.04 

7.31 7.55 7.49 81.93 7447.38 69.72 0.9% 395.27 356.79 351.42 12.82 367.74 16.59 4.5% 0.07 

7.28 7.57 7.5 110.8 7448.72 76.26 1.0% 408.16 350.78 343 19.18 367.13 24.63 6.7% 0.11 

7.25 7.6 7.5 139.58 7449.95 83.52 1.1% 420.63 344.57 334.58 25.5 366.28 32.5 8.9% 0.15 

7.22 7.62 7.51 168.23 7451.06 91.24 1.2% 432.71 338.18 326.15 31.78 365.19 40.21 11.0% 0.18 

7.19 7.64 7.52 196.72 7452.07 99.22 1.3% 444.38 331.59 317.7 38.03 363.86 47.74 13.1% 0.22 

7.17 7.67 7.53 225.04 7452.99 107.34 1.4% 455.67 324.82 309.22 44.25 362.29 55.12 15.2% 0.25 

7.14 7.69 7.54 253.18 7453.81 115.52 1.5% 466.58 317.85 300.71 50.42 360.49 62.33 17.3% 0.29 

7.11 7.71 7.55 281.14 7454.54 123.67 1.7% 477.12 310.7 292.17 56.55 358.47 69.38 19.4% 0.33 

7.08 7.73 7.56 308.91 7455.2 131.77 1.8% 487.29 303.37 283.59 62.65 356.22 76.27 21.4% 0.36 

7.27 7.38 7.24 25.24 7294.81 60.31 0.8% 368.26 368.24 368.25 0 368.24 0.02 0.0% 0.01 

7.21 7.42 7.25 81.75 7295.27 47.15 0.6% 381.99 362.62 359.83 6.43 368.12 8.39 2.3% 0.02 

7.16 7.47 7.26 140.47 7295.49 42.66 0.6% 395.3 356.8 351.42 12.82 367.76 16.6 4.5% 0.05 

7.1 7.51 7.28 199.18 7295.5 48.7 0.7% 408.19 350.79 343.01 19.18 367.15 24.64 6.7% 0.09 

7.05 7.55 7.29 257.64 7295.3 61.82 0.8% 420.67 344.58 334.59 25.5 366.29 32.52 8.9% 0.12 

6.99 7.6 7.31 315.82 7294.91 78.2 1.1% 432.74 338.18 326.15 31.79 365.2 40.22 11.0% 0.15 

6.93 7.64 7.32 373.65 7294.34 95.91 1.3% 444.42 331.6 317.7 38.03 363.87 47.76 13.1% 0.18 

6.88 7.68 7.34 431.15 7293.6 114.1 1.6% 455.71 324.82 309.22 44.25 362.31 55.13 15.2% 0.21 

6.82 7.73 7.35 488.3 7292.7 132.4 1.8% 466.62 317.86 300.71 50.42 360.51 62.34 17.3% 0.24 

6.77 7.77 7.37 545.08 7291.65 150.59 2.1% 477.16 310.71 292.16 56.55 358.48 69.39 19.4% 0.27 

6.72 7.81 7.38 601.49 7290.47 168.59 2.3% 487.34 303.37 283.58 62.65 356.24 76.29 21.4% 0.3 

7.17 7.17 7.17 0.02 7174.03 0.06 0.0% 368.26 368.24 368.27 0 368.25 0.02 0.0% 0.01 

7.1 7.24 7.19 88.72 7173.81 32.68 0.5% 381.99 362.62 359.85 6.42 368.13 8.39 2.3% 0.03 

7.02 7.3 7.2 176.95 7173.18 64.7 0.9% 395.3 356.8 351.44 12.81 367.76 16.6 4.5% 0.05 

6.94 7.37 7.22 264.74 7172.14 96.06 1.3% 408.19 350.79 343.03 19.17 367.15 24.64 6.7% 0.08 

6.86 7.43 7.24 352.03 7170.74 126.76 1.8% 420.67 344.58 334.61 25.49 366.3 32.51 8.9% 0.11 

6.79 7.5 7.25 438.83 7168.98 156.81 2.2% 432.75 338.18 326.17 31.78 365.21 40.21 11.0% 0.14 

6.71 7.56 7.27 525.1 7166.88 186.21 2.6% 444.42 331.6 317.71 38.03 363.88 47.75 13.1% 0.16 

6.63 7.62 7.29 610.86 7164.47 214.97 3.0% 455.72 324.82 309.23 44.24 362.31 55.13 15.2% 0.19 

6.56 7.69 7.31 696.09 7161.77 243.1 3.4% 466.63 317.86 300.72 50.41 360.52 62.34 17.3% 0.22 

6.48 7.75 7.33 780.78 7158.78 270.59 3.8% 477.17 310.71 292.18 56.55 358.49 69.39 19.4% 0.24 

6.41 7.81 7.35 864.92 7155.53 297.47 4.2% 487.34 303.37 283.59 62.64 356.24 76.28 21.4% 0.27 

Node 0 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 1 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 2 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

Node 3 

Voltage Sequence Voltages (V) 

V2/V1 

Current Sequence Currents Imbalance 

ΦA ΦB ΦC V0 V1 V2 ΦA ΦB ΦC I0 I1 I2 I2/I1 PF 

116
 
kVar Flow Total kVar kW Native Load Total kW kVar Native Load Total kVar 

ΦA ΦB ΦC Flow ΦA ΦB ΦC Load ΦA ΦB ΦC Load

513.41 513.32 513.39 1540.12 2641.88 2641.94 2641.95 7925.77 -2.40 -2.45 -2.40 -7.25 

568.47 505.63 467.41 1541.51 2710.43 2625.05 2586.70 7922.18 -2.37 -2.47 -2.41 -7.25 

625.05 497.51 423.04 1545.60 2773.98 2605.92 2531.54 7911.44 -2.35 -2.48 -2.43 -7.26 

683.03 488.95 380.29 1552.27 2832.72 2584.56 2476.37 7893.65 -2.32 -2.51 -2.43 -7.26 

742.25 479.94 339.17 1561.36 2886.82 2560.92 2421.12 7868.86 -2.30 -2.52 -2.44 -7.26 

802.62 470.50 299.68 1572.80 2936.46 2534.99 2365.71 7837.16 -2.27 -2.55 -2.45 -7.27 

863.99 460.61 261.83 1586.43 2981.83 2506.75 2310.05 7798.63 -2.24 -2.56 -2.47 -7.27 

926.29 450.29 225.63 1602.21 3023.12 2476.17 2254.09 7753.38 -2.22 -2.58 -2.47 -7.27 

989.39 439.53 191.09 1620.01 3060.49 2443.24 2197.74 7701.47 -2.19 -2.60 -2.49 -7.28 

1053.22 428.35 158.21 1639.78 3094.14 2407.93 2140.95 7643.02 -2.17 -2.62 -2.49 -7.28 

1117.68 416.77 126.99 1661.44 3124.24 2370.22 2083.65 7578.11 -2.15 -2.64 -2.50 -7.29 

Plot Information: 

kW 

Node 0 Total kW Losses / Node 1 Node 2 Node 3 

I2/I1 Losses kW Flow V1/V2 V1/V2 V1/V2 I0 I1 I2 

0.0% 351.15 4.2% 0.8% 0.8% 0.0% 0.00 368.23 0.00 

2.3% 351.64 4.3% 0.9% 0.6% 0.5% 6.43 368.11 8.38 

4.5% 353.09 4.3% 0.9% 0.6% 0.9% 12.82 367.74 16.59 

6.7% 355.44 4.3% 1.0% 0.7% 1.3% 19.18 367.13 24.63 

8.9% 358.67 4.4% 1.1% 0.8% 1.8% 25.50 366.28 32.50 

11.0% 362.75 4.4% 1.2% 1.1% 2.2% 31.78 365.19 40.21 

13.1% 367.67 4.5% 1.3% 1.3% 2.6% 38.03 363.86 47.74 

15.2% 373.37 4.6% 1.4% 1.6% 3.0% 44.25 362.29 55.12 

17.3% 379.82 4.7% 1.5% 1.8% 3.4% 50.42 360.49 62.33 

19.4% 387.03 4.8% 1.7% 2.1% 3.8% 56.55 358.47 69.38 

21.4% 394.97 5.0% 1.8% 2.3% 4.2% 62.65 356.22 76.27 

117
 
Total kW Loss 

kW Loss / kW Flow kW Loss 

410.00 

400.00 

390.00 

380.00 

370.00 

360.00 

350.00 

340.00 

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 

Node 0 I2/I1 

Transposed Total kW Loss Nontransposed Total kW Loss Equal Spacing Total kW Loss 

Figure 82. Total line losses versus load imbalance for each line configuration 

Total kW Loss / kW Flow 

5.2% 

5.1% 

5.0% 

4.9% 

4.8% 

4.7% 

4.6% 

4.5% 

4.4% 

4.3% 

4.2% 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

Transposed % kW Loss Nontransposed % kW Loss Equal Spacing % kW Loss 

Figure 83. Percent losses versus load imbalance for each line configuration 

118
 
Voltage Imbalance vs Current Imbalance 

Amps 

0.0% 

1.0% 

2.0% 

3.0% 

4.0% 

5.0% 

6.0% 

V2/V1 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

Node 1 V. Imbalance, NT 

Node 1 V. Imbalance, T 

Node 1 V. Imbalance, ES 

Node 2 V. Imbalance, NT 

Node 2 V. Imbalance, T 

Node 2 V. Imbalance, ES 

Node 3 V. Imbalance, NT 

Node 3 V. Imbalance, T 

Node 3 V. Imbalance, ES 

Figure 84. Voltage imbalance versus load imbalance for each line configuration 

Sequence Currents vs Current Imbalance 

50.00 

100.00 

150.00 

200.00 

250.00 

300.00 

350.00 

400.00 

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 

Node 0 I2/I1 

I0, NT I1, NT I2, NT 

I0, T I1, T I2, T 

I0, ES I1, ES I2, ES 

Figure 85. Sequence currents versus load imbalance for each line configuration 

119
 

0.00 
Voltage Imbalance vs Current Imbalance
 

Equilateral Spacing Line
 

V2/V1 V2/V1 

4.5% 

4.0% 

3.5% 

3.0% 

2.5% 

2.0% 

1.5% 

1.0% 

0.5% 

0.0% 

0.0% 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 16.0% 18.0% 20.0% 

Node 0 I2/I1 

Node 1 Voltage Imbalance Node 2 Voltage Imbalance Node 3 Voltage Imbalance 

Figure 86. Voltage imbalance versus current imbalance equilateral spacing line 

Voltage Imbalance vs Current Imbalance
 

Nontransposed Line
 

3.0% 

2.5% 

2.0% 

1.5% 

1.0% 

0.5% 

0.0% 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

Node 1 Voltage Imbalance Node 2 Voltage Imbalance Node 3 Voltage Imbalance 

Figure 87. Voltage imbalance versus current imbalance non-transposed line 

120
 
Sequence Currents vs Current Imbalance
 

Transposed Line
 

0.00 

50.00 

100.00 

150.00 

200.00 

250.00 

300.00 

350.00 

400.00 

Amps 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

I0 I1 I2 

Figure 88. Voltage imbalance versus current imbalance transposed line 

Sequence Currents vs Current Imbalance 

Equilateral Spaced Line 

0.00 

50.00 

100.00 

150.00 

200.00 

250.00 

300.00 

350.00 

400.00 

Amps 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

I0 I1 I2 

Figure 89. Sequence currents versus current imbalance equilateral-spaced line 

121
 
Sequence Currents vs Current Imbalance
 

Nontransposed Line
 

0.00 

50.00 

100.00 

150.00 

200.00 

250.00 

300.00 

350.00 

400.00 

Amps 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

I0 I1 I2 

Figure 90. Sequence currents versus current imbalance for non-transposed line 

Sequence Currents vs Current Imbalance
 

Transposed Line
 

0.00 

50.00 

100.00 

150.00 

200.00 

250.00 

300.00 

350.00 

400.00 

Amps 

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 

Node 0 I2/I1 

I0 I1 I2 

Figure 91. Sequence currents versus current substance for transposed line 

122
 
Table 14. The Effects of Circuit Spacing and Unbalanced Load on Percent Kilowatt Losses 

Equilateral Spacing 

Balanced Load Total Unbalanced Load Total 

I2/I1 = 0% I2/I1 = 21.5% 

ΦA ΦB ΦC ΦA ΦB ΦC 

ΦI's 368.22 368.25 368.28 490.12 300.16 284.99 

kW 

Losses 117.17 117.02 116.89 351.08 414.10 -72.43 63.39 405.06 

% Losses 4.2% 5.10% 

Native 

Load kW 7926 7584 

Flat Non-Transposed 

Balanced Load Unbalanced Load 

I2/I1 = 2.5% I2/I1 = 22.9% 

ΦI's 356.11 375.94 371.99 274.51 494.92 305.56 

kW 

Losses 194.35 72.47 84.29 351.11 131.84 390.48 -117.36 404.96 

% Losses 4.2% 5.10% 

Native 

Load kW 7920 7579 

Flat Transposed 

Balanced Load Unbalanced Load 

I2/I1 = 0% I2/I1 = 21.4% 

ΦI's 368.23 368.24 368.24 487.29 303.37 283.59 

kW 

Losses 117.05 117.04 117.06 351.15 417.26 -96.12 73.83 394.97 

% Losses 4.2% 5.0% 

Native 

Load kW 7925 7578 

Notes: 

A. Balanced loads result in less loss. 

B. Kilowatt losses are greater for the non-transposed line than for the transposed line because %l2/l1 

is more for the non-transposed line. 

C. Unbalanced load is 4,500 kW on Phase A, 2,250 kW on Phase B, and 2,250 kW on Phase C. 

Balanced load is 3,000 kW on each of the three phases. 

Table 14 shows a summary of the effects of circuit spacing and unbalanced load on percent 

losses. For the balanced load of 3,000 kW on each phase (total load of 9,000 kW), the 4.2% 

real losses are the same for the equilateral spacing, flat non-transposed, and flat transposed. 

For the unbalanced load of 4,500 kW on Phase A, 2,250 kW on Phase B, and 2,250 kW on 

Phase C, the percent losses are 5.1% for the equilateral and flat non-transposed 

configurations and 5% for the flat transposed configuration. 

123
 
5.10 Secondary and Service Impedances and Voltage Drops 

11.66 kVA 11.66 kVA 11.66 kVA 

#1 #2 #3 

#4 #5 #6 

#0 #0 #0

100' 

100' 

100' 

100' 

100' 

100' 

C C C 

C C C 

B 150' #0 

150' 

#0 150' B

150' 

48.63A 

48.63A 

97.25A I

sec = 97.25A 

Load = 

70 kVA 

50 kVA 

transf. 

#0 

150' 

#0 #0 

11.66 kVA 11.66 kVA 11.66 kVA 

Figure 92. Distribution transformer servicing secondaries and services 

Transformer size = 50 kVA 

Dm = Maximum coincident total demand on the transformer 

Dm = 70 kVA of load and losses 

Cos θ = 0.90 

⎡70 kVA − 2 (11.66 kVA)⎤ ⎡46.68 kVA ⎤ Isec. = 1 97.25 A 2 ⎢

⎣ 240V ⎥⎦

= 1

2 ⎢

⎣ 240V ⎥⎦

=

Iservice = 1⁄2 (97.25A) = 48.63 A 

R 

R 

I

R = 43.76A 

I

R = 43.76A 

Load = 

48.63A 25.84o 

Figure 93. Distribution service drop 

124
 
The R and X values for the #0 triplex secondary and service are 

R = 0.211 Ω/1000' 

X = 0.031 Ω/1000'. 

The voltage drop in secondaries B is 

∆ V = 2 (I R Cos θ + I X Sin θ) Equation 5.71 

= 2 [97.25 (0.211 Ω/1000' x 150') 0.90 + 97.25 (0.031 Ω/1000' x 150') .436] 

= 2 (2.770 + 0.197) 

∆ V = 5.93 volts @ 240 V or 2.97 volts @ 120V base. Equation 5.72 

The drop in the services C is 

∆ V = 2 [48.63 (0.211 Ω/1000' x 100') .90 + 48.63 (0.031 Ω/1000' x 100') .436]

 = 2 (0.920 + 0.067) 

∆ V = 1.97 volts @ 240 V or 0.99 volts @ 120V base. Equation 5.73 

The voltage drop for customers 2 and 5 is only 0.99 V, but for customers 1, 3, 4, and 6, it is 

3.96 V (2.97 + 0.99). 

Table 15. Voltage Drop Summary – Transformer, Secondary, and Service Drop 

25 kVA 50 kVA 

N = 3 N = 2 N = 4 

No Secondary No Secondary Secondary 

Transformer 3.68 2.75 2.75 

Secondary -­ -­ 2.97 

Service 0.99 0.99 0.99 

Total 4.67 3.74 6.71 

5.11 Secondary and Service Real Losses 

Service Drop Real Losses: 

The resistance of #0 aluminum service drops for 100' is 

R service = 2 (0.211 Ω/1000' x 100') = 0.0422 Ω. Equation 5.74 

125
 
The resistance is doubled because of the forward and return path of the current. 

I

2

service R service = (48.63)2

 (0.0422) = 99.80 watts per service drop 

Equation 5.75 

Service drop total real losses = (6) (99.80 watts) = 598.8 watts Equation 5.76 

Secondary Real Losses: 

R secondary = 2 (0.211 Ω/1000' x 150') = 0.0633 Ω Equation 5.77 

I

2

sec. R secondary = (97.25)2

 (0.0633) = 598.7 watts per secondary 

Equation 5.78 

Secondary total real losses = 2 (598.7 watts) = 1197.3 watts Equation 5.79 

Total service and secondary real losses = 598.8 + 1197.3 Equation 5.80 

= 1796.1 watts 

1.796 kW Percent real losses = x 100 = 2.9% Equation 5.81 (1.4) (50 kVA) (0.90) 

Note: Add kilowatt losses for each circuit element and divide by the total kilowatt flow to 

obtain total circuit percent losses. Percent losses cannot be added for each element. 

A summary of the peak day (July 17, 2006) real power losses for the Milford substation 

transformer, the DC8103 primary, overhead and padmount transformers, secondary, and 

services is given in Table 16. 

The percent real losses shown in the first column are for the 4.8-kV Hickory Distribution 

Circuit, the reference of which is given in Note A. These are actual measured losses that total 

5.2%, excluding the substation transformer. The next two columns represent the percent real 

losses for the Milford 8103 circuit. The second column depicts the calculated losses based on 

the average peak loading of the transformers and services and a lumped load representing the 

peak circuit load placed at the midpoint to calculate the primary losses. The third column 

shows the calculated losses determined from the simulation of the circuit for the peak load 

hour on July 17, 2006. 

126
 
Table 16. Peak Day Real Losses Comparison

 Percent Losses 

Transmission -- 3.5 --

Sub-transmission -- 4.5 --

Hickory Milford 8103 Milford 8103 

Substation transformer 0.70 0.729 0.702 

Primary 

Overhead and underground transformers 

Secondary and services 

3.1A 

1.3A 

0.8A 

3.82B 

1.22B 

0.95D 

3.59C 

1.50C 

0.89D 

0.31E 

Total circuit losses 5.2 5.99 5.98D 5.4E 

Total system losses 13.9 14.72 14.68 14.10 

Notes: 

A.	 Data from Davis, Krupa, and Diedzic (1983) 

B.	 Approximate based on average loading of transformers and services and lump 

load placed at midpoint for the primary losses 

C. Distribution Engineering Workstation 

D. #4 MXAT Services used 

E.	 #0 MXAT Services used 

5.12 Shunt Capacitor Models

When capacitors are connected in parallel, kVAr = kVAr1 + kVAr2 + kVAr3 + ..., 

and when connected in series, 

1 kVAr =	 . 1 1 1

+ + + • • •

kVAr kVAr kVAr 1 2 3 

The capacitive reactance in ohms is 

1 XC = , Equation 5.82 2 π f C x 10-6 

where 1 μf is 2,653 Ω at 60 Hz, or 

2653 XC = , where C is 1 μf. C 

From Equation 5.82, C is then 

106 

 C = .	 Equation 5.83 2 π	 f XC 

127
 
Now, XC can be defined in terms of voltage and vars. 

V kVAr = kV IX, where IX = . XC
 

V Because kV = , then 1000 

kV2 1000 kVAr = , and XC 

kV2 1000 XC = . Equation 5.84 kVAr 

The capacitance C in microfarads can be determined in terms of voltage and Vars by 

substituting Equation 5.82 into Equation 5.84 and solving for C. 

1000 kVAr C = Equation 5.85 kV2 2 πf 

If the capacitance C and voltage are known, then KVAr can be found from Equation 5.85. 

kV2 2 π f C kVAr = Equation 5.86 1000 

Equations 5.84, 5.85, and 5.86 are the most commonly used. Two examples follow. 

The ohms per phase for a 300-kVAr, three-phase, 4.8-kV, delta-connected capacitor bank is 

300 kVAr kVAr/Φ = = 100 kVAr. 

3 

The line-to-line voltage applied across each capacitor is 4.8 kV. Applying Equation 5.84, 

4.82 (1000) XC = = 230.4 Ω. 100
 

The capacitance from Equation 5.85 is 

(1000) (100) C = = 11.51μf . (4.8) 2 (377) 

128
 
The ohms per phase for a 600-kVAr, three-phase, 13.2-kV, wye-connected capacitor bank is 

600 kVAr/Φ = = 200 kVAr. 

3
 

13.2kV The voltage across each capacitor is , . Therefore, using Equation 5.84 results in 3 

(7.620)2 1000 XC = = 290.3 Ω, 200 

and the capacitance is 

(1000) (200) C = = 9.14 μf . (7.620) 2 (377) 

Capacitor models can be developed using Equation 5.84, which is repeated below. 

kV2 1000 XC = kVAr . 

The susceptance BC is the reciprocal of XC; therefore, BC from Equation 5.84 becomes 

1 kVAr BC = = 2 , Equation 5.87 XC kV 1000 

where kVAr is the kilovars per phase and kV is the applied voltage across the capacitor. For 

a wye-connected capacitor bank 

1 kVAr BC = = 2 . Equation 5.88 XC kVLN 1000 

For a delta-connected capacitor bank 

1 kVAr BC = = . Equation 5.89 XC kVLL 

2 1000 

The line currents for the wye-connected bank are written from Equation 5.88. 

VAN = IC A j XA 

IC A = VAN = VAN j BA, Equation 5.90 j XA 

129
 
IC B = VBN j BB Equation 5.91 

IC C = VCN j BC Equation 5.92 

For the delta-connected bank, the phase currents are: 

I = VAB j BAB Equation 5.93 C AB 

I = VBC j BBC Equation 5.94 C BC 

I = VCA j BCA. Equation 5.95 C CA 

The line currents are: 

I = I − I C A C AB C CA Equation 5.96 

I = I − I C B C BC C AB Equation 5.97 

I = I − I C C C CA C BC . Equation 5.98 

In matrix form, equations 5.96, 5.97, and 5.98 can be written as: 

IC A 

1 0 -1 IC AB 

IC B = -1 1 0 IC BC . Equation 5.99 

IC C 

0 -1 1 IC CA 

5.13 Step Voltage Regulator Models 

Both Type A and Type B step VRs are modeled. The relationship between the source voltage 

VS and load voltage VL for the single-phase step VR is: 

VS = arVL, Equation 5.100 

where ar is defined as 

Total % Range a = 1m × Tap Equation 5.101 r #of Steps 

130
 
with the following sign convention. 

 Type A Type B 

Raise + -

Lower - +
 

The relationship between source current and load current for the single-phase step VR is 

1

IS = arIL . Equation 5.102 

5.14 Synchronous Generator Model 

The Distribution Engineering Workstation uses two models to represent the synchronous 

machine: one for power flow and one for transient analysis. Because this study does not 

involve transient analysis, only the power flow model is considered. Figure 94 is a graphical 

representation of the power flow synchronous machine model. 

P,Q Source 

Controller 

Z 

Figure 94. Steady-state synchronous machine model 

The synchronous machine model used for power flow consists of a real and reactive power 

source, along with the impedance Z (in this case, the synchronous impedance). The controller 

takes measurements (specifically, voltage magnitude and power factor) from machine 

terminals and allows the machine to operate in two modes: constant P with power factor 

control or constant P and constant Q. 

The model takes into account the minimum and maximum generation limits of the machine, 

and the controller adjusts the P, Q Source based on the control mode. For example, if the 

machine is in the constant P with power factor control mode, the controller will maintain real 

rated power while varying the reactive power within the machine limits in an attempt to hold 

the power factor at the point of measurement constant. 

131
 
5.15 Self-Excited Induction Generator Model 

A 

q 

C 

d 

B 

C 

ω

Rotor 

iqr iqs C

idr 

ids 

Figure 95. Two-phase primitive machine to be interconnected with an RLC load 

A self-excited induction generator can be represented as a two-phase primitive machine with 

stator windings fixed and rotor windings rotating. The currents ids and iqs are the stator 

currents, and idr and iqr are the rotor currents in the direct and quadrature axes, respectively. 

Figure 95 shows the mechanical angular speed of the rotor as ω = dθ/dt. A self-excited 

induction generator with capacitor added is represented in Equation 5.103. The voltage drop 

across the capacitor for the direct axis is vCd and for the quadrature axis is vCq. The term 1/pC 

represents this voltage drop because 

1 

v = �çidt, C
 

p = d/dt and 

1 t
 = �çdt 

p 

132
 
vds 

vqs 

vdr

vqr 

= 

R1 + L1 p + pC 

1 

0 

Mp 

0 

R1 + L1 p + pC 

1 

ωM 

Mp 

0 

R2 + L2 p 

0 

Mp 

ωL2

-ω M Mp -ω L2 R2 + L2 p 

ids 

iqs 

idr 

iqr

 Equation 5.103 

This equation represents the no-load condition, and the turns ratio is assumed to be unity. 

Therefore, if needed, the ratio must be included when referring the rotor parameters to 

the stator. 

The mutual inductance M varies with the relative position between the stator and rotor. R1 

and R2 are the stator and rotor resistances, and L1 and L2 are their inductances. The additional 

voltage drop because of the mutual flux is 

φm = Mi, and 

d φ di i dM 

v = m = M + . dt dt dt 

= Mpi + i pM Equation 5.104 

There is a nonlinear relationship between the magnetizing reactance and the magnetizing 

current. Therefore, the mutual inductance M varies continuously. The term Mpi represents the 

current variation because of the stator, and the term ipM is because of the rotation of the rotor. 

5.15.1 Resistive Load 

When a resistive load R is added in parallel with the self-excitation capacitor C, the voltage 

across this R load is the same as the voltage across the capacitor. In the direct axis stator of 

Figure 95, the addition of the load resistor changes the equivalent circuit to Figure 96. 

Figure 96. Stator direct axis with an R load added 

133
 
Because v load d = vCd = R i load d Equation 5.105 

d v and iCd = C Cd =C pvCd, then dt 

iCd = C p Ri load d. 

Because 

ids = iCd + i load d, 

ids = R Cp i load d + i load d and 

 = i load d (R Cpi + 1). Equation 5.106 

From Equation 5.105, 

ids i load d = . Equation 5.107 R C p +1 

Substituting Equation 5.107 into 5.105, results in 

R ids v load d = . Equation 5.108 R C p +1 

The quadrature load voltage is obtained in a similar manner. 

R iqs

v load q = Equation 5.109 R C p +1 

Now Equation 5.103 can be rewritten with the addition of the resistive load R from equations 

5.108 and 5.109. 

vds 

vqs

vdr

vqr

= 

R1 + L1 p + 1R Cp 

R 

+

0 

Mp 

0 

R1 + L1 p + 1R Cp 

R 

+

ωM 

Mp 

0 

R2 + L2 p 

0 

Mp 

ωL2

 ­ωM Mp -ωL2 R2 + L2 p 

ids 

iqs 

idr 

iqr

 Equation 5.110 

134
 
5.15.2 RLC Load 

When an RL load RL and LL is added in parallel with the self-excitation capacitor Cs, or a 

combination of this excitation capacitor and other capacitors CL on the circuit in parallel, C 

in the following equations considers this combination of capacitors. See Figure 97. 

Figure 97. RLC load RL, LL, and CL connected to the self-excited capacitor CS 

Because v load d = R i load d from Equation 5.105, v load d with load inductance added is 

v load d = R i load d + L pi load d, Equation 5.111 

and 

iCd = Cpv load d = (R C p + L C p2

) i load d. Equation 5.112 

Now from Equation 5.112, 

i = i + i load d = (R C p + L C p2

) i load d + i load d Equation 5.113 d s Cd 

and 

i ds i load d = 2 . Equation 5.114 R C p + L C p +1 

From Equation 5.111, 

v load d = R i load d + L pi load d, and 

v load d = (R + L p) i load d. Equation 5.115 

Substituting i load d from Equation 5.114 into Equation 5.115 results in

R + L p v load d = 2 i ds . Equation 5.116 R C p + L C p +1 

135
 
The quadrature load voltage becomes 

R + L p v load q = 2 i qs . Equation 5.117 R C p + L C p +1 

Equation 5.103 can be rewritten with the addition of resistance load R, inductive load L, and 

capacitive load C using Equation 5.117. 

Equation 5.118 is the impedance matrix for a single self-excited induction generator serving 

an RLC load. It must be remembered that the variation in the magnetizing reactance because 

of the magnetizing current must be included and corrected as in the development of 

Equation 5.104. 

vds R + L p R1 + L1 p + 2 0 Mp 0 

R Cp + L C p + 1 

vqs Mp R + L p 0 R1 + L1 p + 0

= 2 R Cp + L C p + 1 

vdr Mp ω M R2 + L2 p ωL2

vqr -ωM Mp -ωL2 R2 + L2 p

ids 

iqs 

idr 

iqr 

Equation 5.118 

5.16 Inverter-Based Generator Model 

The 400-kW, 500-kVA inverter-based generator consists of a high-speed AC generator 

driven by a 440-kW twin-spool gas turbine engine. Figure 98 is a simplified one-line diagram 

of the 400-kW, 60-Hz generator and inverter. 

Engine Controller 

Gas 

Turbine 

High Speed 

Generator Generator 

Step up Transformer 

( optional ) 

Load 

Bus Main Circuit 

Breaker Rectifier CT Inverter 

= 

Bus 

Figure 98. One-line diagram of 400-kW inverter-based generator and prime mover 

136
 
The unit has seamless transfer capability so it can operate in a current-source mode parallel 

to the electric power system with only 10% load and switch without outage to deliver power 

in the voltage-source mode to an islanded load. This generating unit has a continuous 

overload capability of 110% of rated load at any power factor from -0.8 to 0.8, and it can 

follow load steps of 25% up or down while maintaining frequency to less than +/-0.1 Hz. The 

voltage distortion is less than 2%, and it can handle 100% load imbalance. During short 

circuits, it can deliver 200% of rated current for about 8 seconds. 

The inverter model is represented by the voltage pullback curves in Figure 99. The unit can 

deliver 1.10 p.u. current (602 A rms) at 1.0 p.u. rated voltage (277 V rms) and 2.0 p.u. 

current at 0.56 p.u. voltage. The inverse time-current characteristic is given in Figure 100. Voltage (P.U.), 277 Vrms = 1.0 P.U. 

1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 

y = -0.0477x3 + 0.5556x2 - 1.8574x + 2.4336 

R2

 = 0.9998 

Current Limit 

kVA Limit = 550 kVA 

P.F. < 0.8 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 

Current (P.U.), 602 Arms = 1.0 P.U. 

Fi 5 22 V lt P llb k C 

Figure 99. Voltage pullback curves 

137
 
log(Time (secs))

Time (secs) 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

10000 

log(y)=175.265*x6

-1715.528*x5+6957.537*x4-

14963.291*x3

+17999.078*x2-11485.441*x+3041.135 

1000 

100 

Data 

Curve Fit 

10 

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 

Current (P.U.) 

Figure 100. Inverse time-current characteristic 

138
 

2 
6 Project Results – Circuit Voltage Profiles Under Different 

Loading Conditions 

6.1 Introduction 

This section summarizes work to perform simulations to determine the circuit voltage 

profiles of Milford Circuit DC 8103. The two-transformer Milford substation, shown in 

Figure 101, is fed from two 41.57-kV tie lines and one 41.57-kV trunk line. The Milford DC 

8103 circuit is fed by a delta-wye-connected 10-MVA LTC transformer with ±10% tap 

positions and 0 to ±5% fixed taps. The primary voltage is 41.57 kV, and the secondary 

voltage is 13.8 kV. The circuit is a 13.8-kV, multi-grounded, three-phase wye system, and it 

serves approximately 76.2% residential, 4% commercial, and 19.8% light industrial loads. 

See Table 17. The circuit summer peak maximum load is 15.3 MVA, and the summer peak 

minimum load is 5.91 MVA. The annual load factor for the circuit is 0.42. 

The circuit is about 31,000 ft, or 5.9 mi. The voltage profiles are determined for the peak 

load day, referred to as the heavy load (HL) condition, and the minimum load day, referred to 

as the LL condition, using eight traditional methods of voltage regulation. The voltage 

profiles are shown for the following voltage regulation cases: 

•	 No circuit voltage regulation, with variable transformer primary voltages (41.57 kV) 

ranging from 87%, 95%, 100%, and 105% voltage levels on a 120-V base (The 87% 

voltage level represents the lowest voltage for emergency operation, and the 100% 

voltage level represents the base case for determining the release capacity. The 

balance of the simulations represents normal operating conditions for HL and LL 

conditions with 95% and 105% primary substation voltages.) 

•	 The addition of LTC transformer regulation at the substation 

•	 The addition of step VR 1 

•	 The addition of step VR 1 and VR 2 

•	 The addition of capacitor CAP 1 

•	 The addition of capacitors CAP 1 and CAP 2 

•	 The addition of capacitors CAP 1, CAP 2, and CAP 3 

•	 The addition of all traditional voltage regulation methods (i.e., LTC, VR 1, VR 2, 

CAP 1, CAP 2, and CAP 3). 

139
 
Table 17. Circuit Customer Load Characteristics 

Customer 

Type 

Number of 

Customers 

Annual 

MWH 

MW 

Avg. 

Annual 

Load 

Factor 

Typ. 

MW 

Peak P.F. 

MVA 

Peak 

% on an 

MVA 

Basis 

Residential 

Commercial 

Industrial 

3178 

120 

3 

32,610 

2,667 

15,529 

3.72 

0.304 

1.77 

0.35 

0.57 

0.66 

10.6 

0.54 

2.67 

0.91 

0.89 

0.88 

11.7 

0.60 

3.04 

76.3 

3.9 

19.8 

Totals 3301 50,806 5.79 0.42 13.8 .90 15.3 100.0 

Tie Line Trunk Line Tie Line 

8623 3107 2819 

Proud Page Cody - Proud 

CAP 2 

12 MVAr 

N.O. 

41.57 kV 

Tie Line 

6117 

Placid Tie Line 

6147 

Placid 

Section 

Breaker 

Tie Line 

5831 

"A" Cable "B" Cable 

DC 8103 DC 8066 

13.8 kV 13.2 kV 

PTS 43283 

#1 #2

0% Fixed 

10 MVA 

+10% 

+5% Fixed 

41.57/13.2 kV 

N.O. 

5% Fixed 

10 MVA 

+10% 

0% Fixed 41.57/13.8 kV 

Figure 101. Milford Substation one-line diagram 

140
 
The Milford Circuit DC 8103 and substation are shown in Figure 102. It consists of a 

substation, shown as a cross-hatched square and denoted as Node 0; three-phase sections, 

represented as heavy-weight solid lines; and single-phase sections, represented as lightweight solid lines. The dotted lines represent two phases. The 10-MVA LTC transformer at 

the substation has an impedance of 7.02%, with 0, ±2.5%, and ±5% fixed taps with highside and low-side settings of 0 and ±5%. The LTC transformer is ±10% with ±16 steps. 

The voltage was regulated at 126.0 V on the secondary bus of the transformer. The circuit 

has three single-phase step bidirectional VRs (1) and three single-phase step bidirectional 

VRs (2). These single-phase regulators are each rated 167 kVA and connected wye. The 

second VR (2) is for study purposes. There are three capacitor banks. CAP 1 is a threephase, 900-kVAr capacity; CAP 2 is a 900-kVAr capacity; and CAP 3 is three-phase, 

1200-kVAr capacity. All capacitors are pole-mounted, switched capacitors with wyegrounded connections. 

141
 
. F.

E. 

osercl

G. 

MT3Φ

Φ

M

M 

2 

1 

M Φ

1

M Φ

2 

Φ

M Φ

6 

28 

26
 

M Φ 3	 

M Φ

K. J.24

MTS

19 Φ19

L.

MTSΦ 18

Phas e B MTSΦ

Ph ase C h 111V

Phase A I.

MT3Φ

17

80K20 125K 16 80K 40K 65K

21 100K22 15 40KFar End Far End

65K DR

40K 3 - SΦ	 (Study) H. 23 400 kW Inverter 400 kW Inverter 0 kW Inverter RegulatorsRegulatorsegulators GeneratorGenerator 400 kW Induction 400 kW Induction kW Induction (Study)

MT3Φ 3 43199 17

1200 kVAr 43199 1200 kVAr (Study) 14 (Study) 2 Generator (Study) Generator (Study) nerator (Study) 13 B. E.

Y, Z P1 P5	 MTSΦ 14 900 kVAr 900 kVAr Regulation P6 M3Φ 2 Path 43244 80K 12 10 8 11 43090 7 9

43052 C.43052 C. Midpoint DR Midpoint DRidpoint DR 43095 100K G. M3Φ 65K (actual site) (actual site)actual site) MT3Φ PTS

3 - SΦ 1000 kW

2Φ Regulators	 Regulators egulators Sync. Generator Sync. Generator

M3Φ D. ync. Generator

1

65K	 8 11

A. M3Φ 43283 P

3Φ 3Φ 3Φ

Near EndNear End R F..

DR (Study)DR (Study) R-1 125K R-1 125K 

5 40K65KR-3MT3Φ 65K 0 1 4 3Φ

2 recloser recloser 3-SΦ re scloser 65K 80K 140K

3 mov e 6 1 2Φ

25 L ZX

65K 2Φ 900 kVAr 900 kVAr900 kVAr ZX

80K 65K S 3

80K 2Φ 2Φ 40K

80K

L4

26

Note (1):	 Note (2): 2Φ

65K PCC VA, VB, VC 

PCC VA, VB, VC Metering ROC M 3Φ I

A, IB, IC IA, IB, IC MPermanent (SOC) 25K P, Q Installations

28 40K

40K 40K 65K DTECH MeteringMetering 3Φ M

25K(SOC) MTTemporary

Installations 27 1000 kW 1000 kW

Synchronous Machine Synchronous Machine ynchronous Machine

Note (3): Nodes where low voltage, high voltage, highest unbalance voltage, highest unbalanced load and nodes where Note (3): Nodes where low voltage, high voltage, highest unbalance voltage, highest unbalanced load and nodes where

actual values exceed pre-set values (criteria violations) may be different than the nodes indicated above. actual values exceed pre-set values (criteria violations) may be different than the nodes indicated above.

Note (4): The LTC voltage regulator is gang operated using the C phase as reference. Note (4): The LTC voltage regulator is gang operated using the C phase as reference.

Note (5): The "P" reclosure data is sent to midpoint DR consisting of I , IB, IC, VCN, VBN, VCN, kWA, kWB, kW C Note (5): The "P" reclosure data is sent to midpoint DR consisting of I , I , B, IC, VCN, VBN, VCN, kWA, kWB, kWC, A

kVArA, kVArB, kVArC kVArA, kVArB, kVArC

Figure 102. Milford Circuit DC 8103 

142
 
A number of circuit protection devices are shown on the circuit. These include a three-phase 

recloser ( ), three single-phase reclosers ( ), manual switches ( ), automatic controlled 

switches ( , in which a filled-in symbol represents the normally open mode), and threephase and single-phase fuses ( ), which are identified with a number size and Type K. 

Finally, there are three DR generators, a 1,000-kW synchronous generator at the midpoint 

denoted as Node [10], a 400-kW induction generator at Node [17] for study purposes, and, at 

the tag end of the circuit, and a 400-kW inverter-based generator at Node [23] for study 

purposes. The generation simulations and their resultant voltage profiles with and without 

traditional voltage regulation methods are provided in Section 10. 

As noted earlier, nodes are placed throughout the circuit. These are points at which the real 

and reactive power phase quantities, phase power factors, phase currents, and phase voltages 

are calculated. Nodes are placed on each side of the step VRs to provide calculated values of 

voltage before and after regulation and at each capacitor location to provide the calculated 

values of voltage. 

Table 18 provides the permanent metering points and quantities measured and the temporary 

metering points and quantities measured. All metering points are designated by a letter (e.g., 

A, B, and C) that corresponds to the circuit one-line diagram of Figure 102. Those shown 

with the letter T are temporarily installed for this project. Also, the metering may be threephase (3Φ) or single-phase (SΦ). The single-phase metering points J, K, and L are at the tag 

ends of the circuit. These measured quantities and the three-phase quantities were compared 

to the calculated values determined from the simulations, and adjustments were made to the 

circuit models and loads to ensure the simulations agree with field measurements. 

143
 
Table 18. Measurement Locations and Data Collection 

Permanent Metering Locations 

A. Substation M3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

B. 3 SΦ Bidirectional regulators M3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

C. 3 SΦ reclosures	 M3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

D. 1,000-kW Synchronous DR M3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

Temporary Metering Locations 

Customer E. MTSΦ VAN IA P, Q, P.F. (LV unbalanced voltage) 

F. 900-kVAr capacitor MT3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

G. 900-kVAr capacitor MT3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

H. 1,200-kVAr capacitor MT3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. 

3Φ circuit tag end I. MT3Φ VAN, VBN, VCN IA, IB, IC P, Q, P.F. (LV unbalanced voltage) 

J.K.L. Single-phase tag ends MTSΦ VCN VBN VAN 

6.2 Circuit Simulations and Voltage Profiles 

The simulations were extensive. To simplify the explanation of how they were conducted, 

Table 19 describes the tests run. These tests were organized into four groups. The first group 

consisted of tests 1–8, to which traditional voltage regulation (i.e., LTCs) was applied. The 

second group consisted of tests 9–11, to which DG voltage regulation strategy tests were 

applied. The third group consisted of tests 12–17, to which the combined traditional LTC and 

circuit regulation tests as well as DG regulation strategy tests were applied. The fourth group 

consisted of all traditional voltage regulation and all generation voltage regulation strategies 

(see tests 18–19). 

144
 
Table 19. Matrix of Voltage Regulation Simulations 

Test NumbersReference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourly quantities Light Load Day 24 Hourlyquantities LTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (Synchronous Machine) 

Locations (1) 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P variable 

(c) + P.F. Constant, Variable P & 

Q 

(d) + Q (Vars Volt reg) P Min 

(e) P+ jQ (Optimizing) 

(f) Fixed P.F. Anti-island 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 I.A. (a) (d) (f) x x 

2 I.B. (d) (f) x x x 

3 I.C. (d) (f) x x x x 

4 I.C '. (d) (f) x x x x x 

5 I.D (d) (f) x x x x 

6 I.D ' (d) (f) x x x x x 

7 I.D." (d) (f) x x x x x x 

8 I.E. (d) (f) x x x x x x x x 

9 II.A. x x x (b) (d) (e) 

10 II.B. x x x (b) (d) (e) 

11 II.C. x x x (b) (d) (e) 

12 II.D. Repeat IIA., IIB., IIC. turn on LTC 

13 II.E. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) 

14 II.F. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) 

15 II.G. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1) 

16 II.H. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1), (2) 

17 II.I. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1), (2), (3) 

18 

19 

20 

21 

22 

23 

24 

25 

Note (1): DR Control Strategies 

(a.) The DR is operated at fixed real power output and normally Is scheduled to run during peak periods when 

the cost of DR generation is lower than host utility cost. The Q is zero at the PCC. 984 kW rated 

(b.) The DR is operated at unity P.F. with variable power output. 492 kW (50%) to 1050 kW max. 

(c.) DR is operated at a fixed power factor either lead or lag (for example + 0.8 P.F.) with variable P and Q to 

not violate voltage criteria. 

(d.) The DR is operated as a synchronous condenser with minimum watts and variable VArs to regulate 

voltage. 246 kW (25% of rated) 

(e.) DR is operated with variable P and Q and is used to optimize to a specific set of criteria such as minimize 

real losses, minimize reactive losses, regulate voltage and maximize released capacity. 

145
 
Test Numbers

Reference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourly quantities Light Load Day 24 HourlyquantitiesLTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (H.S. Generator and Inverter) 

Locations 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P variable 

(c) + P.F. Constant, Variable P 

(d) + Q (Vars Volt Reg) P = 0 

(e) P+ jQ (Optimizing) 

(f) Frequency Dithering Anti-Island 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 (a) (d) (f) 

2 (d) (f) 

3 (d) (f) 

4 (d) (f) 

5 (d) (f) 

6 (d) (f) 

7 (d) (f) 

8 (d) (f) 

9 II.A. x x x (b) (d) (e) 

10 II.B. x x x (b) (d) (e) 

11 II.C. x x x (b) (d) (e) 

12 II.D. Repeat II.A., II.B., II.C. turn on LTC 

13 II.E. Repeat II.A., II.B., II.C. turn on LTC and Regulator (1) 

14 II.F. Repeat II.A., II.B., II.C. turn on LTC and Regulator (1) and (2) 

15 II.G. Repeat II.A., II.B., II.C. turn on LTC and Regulator (1) and (2) and Cap. (1) 

16 II.H. Repeat II.A., II.B., II.C. turn on LTC and Regulator (1) and (2) and Cap. (1) and (2) 

17 II.I. Repeat II.A., II.B., II.C. turn on LTC and Regulator (1) and (2) and Cap. (1), (2) and (3) 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

146
 
Test Numbers

Reference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourly quantities Light Load Day 24 HourlyquantitiesLTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (Induction Generator) 

Locations 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P fixed 

(c) + P.F. Constant, P fixed 

(d) + Q fixed, P fixed 

same as (c) 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 (a) (d) (f) 

2 (d) (f) 

3 (d) (f) 

4 (d) (f) 

5 (d) (f) 

6 (d) (f) 

7 (d) (f) 

8 (d) (f) 

9 II.A. x x x (b) (d) 

10 II.B. x x x (b) (d) 

11 II.C. x x x (b) (d) 

12 II.D. Repeat II.A., II.B., II.C. turn on LTC 

13 II.E. Repeat II.A., II.B., II.C. turn on LTC and Regualator (1) 

14 II.F. Repeat II.A., II.B., II.C. turn on LTC and Regulators (1) & (2) 

15 II.G. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) 

16 II.H. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) and (2) 

17 II.I. Repeat II.A., II.B., II.C. turn on LTC, Reg (1) & (2) and Cap (1), (2) & (3) 

18 III. Repeat synchronous and inverter generation 

19 IV. Repeat synchronous, inverter and induction generation 

20 

21 

22 

23 

24 

25 

26 

27 

28 

The first step of properly setting up the simulations was to ensure the simulated data matched 

the actual circuit conditions. Two conditions were modeled: the peak load day and the light 

load day. The Milford Circuit DC 8103 had a maximum load of 15.3 MVA on the peak day 

and a minimum load of 5.91 MVA on the peak day. 

147
 
To verify the accuracy of the model, simulation results for a given time were compared 

with recorded data. The modeled circuit was placed in a state closely resembling the 

conditions of the actual system when the measurement was made; specifically, the LTC, 

VR 1, and capacitor banks at nodes 6 and 12 (900 kVAr each) were enabled while at 100% 

primary voltage. The simulation HL base case feeder currents were 578 A, 654 A, and 637 

A for phases A, B, and C, respectively, compared with actual recorded currents of 565 A, 

651 A, and 637 A. The simulated megavolt-amperes of the circuit were 14.89, compared to 

a calculated 15.3 derived from the measured feeder currents and voltages. This was an error 

of 2.42%. 

The program employed to perform the modeling was the Distribution Engineering 

Workstation. With it, load can be modeled as a constant current (CC), CP (P + j Q), or VDC. 

At first, CC was selected to best represent the load characteristics of Milford DC 8103. But, as 

discussed later (see Appendix B.1), all three models were tested by comparing the actual phase 

currents at Node 0 with the simulated phase currents at Node 0. The VDC model yielded the 

most accurate results, with only 2% error for Test 8. The CC model had an error of 5.3%, 

compared with 12.3% error for the CP model. The circuit regulation path shown in Figure 102 

illustrates the nodes on this path from the first circuit (Node 1) to the major junction (Node 3) 

to the first step regulator (VR 1) to the next major junction (Node 8) and then through the 

second step regulator (VR 2) to the next major junction node (Node 11) and the following 

major junction (Node 14) and, finally, to the circuit tag end (Node 17). Voltage profiles are 

shown through each of these major nodes. Base case simulations were conducted for 100% 

voltage on the primary of the substation using only the LTC transformer regulation for both HL 

and LL conditions. This case was used to determine the released capacity and the real loss 

reduction when the 2/3s rule and 2/5s rule was applied for capacitive compensation and when 

the optimized size and locations were determined by the Distribution Engineering Workstation. 

The following circuit voltage profiles are shown for each test (i.e., tests 1–8 with the primary 

substation voltage set at 95% and 105%). The first set of profiles is for HL conditions at 95% 

and 105% primary voltage with different traditional voltage regulation methods applied. 

Simulated voltage data as a function of circuit distance in thousands of meters are given in 

Table 20 for the HL conditions. Simulated voltage data versus circuit length are given in 

Table 21 for LL. 

148
 
Table 20. Voltage Profile Data for HL Tests 1 Through 8 

at 95% and 105% Substation Primary Voltage 

Distance 

Test 8 105 

HL 

Test 8 95 

HL 

Test 7 105 

HL 

Test 7 95 

HL 

Test 6 105 

HL 

Test 6 95 

HL 

0.1034 123.4557 111.3062 123.6329 111.5378 123.2305 111.1696 

0.2378 125.708 123.0442 126.1231 123.5816 125.9826 122.6563 

0.3218 125.6375 122.9755 126.0558 123.5167 125.9165 122.5933 

0.3218 125.6375 122.9755 126.0558 123.5167 125.9165 122.5933 

0.5288 125.5127 122.8549 125.9412 123.4071 125.784 122.4678 

0.7648 125.3684 122.7151 125.8093 123.2809 125.6336 122.3253 

1.3788 124.9925 122.3509 125.4657 122.9521 125.2414 121.9537 

2.583 124.2592 121.6403 124.7952 122.3106 124.4755 121.228 

2.666 124.2088 121.5915 124.7492 122.2665 124.4228 121.1781 

3.206 123.896 121.2882 124.4645 121.9942 124.095 120.8676 

3.429 123.7671 121.1633 124.3472 121.8821 123.9599 120.7396 

3.716 123.6015 121.0028 124.1965 121.7379 123.7862 120.5751 

5.754 122.4322 119.8693 123.1323 120.72 122.5577 119.4114 

6.798 121.8696 119.3236 122.6233 120.2335 121.9637 118.8488 

6.9262 121.8012 119.2573 122.5615 120.1744 121.8913 118.7803 

7.0603 121.7295 119.1876 122.4967 120.1123 121.8155 118.7084 

7.2034 121.6533 119.1135 122.4279 120.0464 121.7349 118.6319 

7.3784 121.5602 119.023 122.3438 119.9659 121.6365 118.5384 

7.7094 121.3851 118.8527 122.1858 119.8145 121.4511 118.3625 

7.9064 121.2815 118.7519 122.0923 119.7249 121.3413 118.2582 

7.9064 121.2815 118.7519 122.0923 119.7249 121.3413 118.2582 

8.2464 121.1003 118.5758 121.9286 119.5681 121.1495 118.0761 

8.4174 121.0092 118.4872 121.8462 119.4892 121.053 117.9845 

8.8571 120.7771 118.2615 121.6366 119.2883 120.8069 117.7508 

9.4411 120.4697 117.9625 121.3589 119.0223 120.4807 117.4411 

9.6082 120.3851 117.8803 121.2829 118.9495 120.3907 117.3557 

10.0174 120.1793 117.68 121.098 118.7724 120.1715 117.1476 

10.3374 120.0189 117.5239 120.9538 118.6343 120.0005 116.9853 

10.5075 119.9332 117.4406 120.8768 118.5605 119.9092 116.8986 

10.8129 119.78 117.2915 120.739 118.4286 119.7458 116.7434 

10.9501 119.7113 117.2247 120.6773 118.3695 119.6725 116.6739 

11.0961 119.6384 117.1537 120.6118 118.3067 119.5947 116.6 

11.6971 119.3406 116.8639 120.3442 118.0505 119.2764 116.2978 

12.0081 119.1878 116.7151 120.2071 117.9191 119.113 116.1427 

12.0291 119.1799 116.7074 120.2002 117.9126 119.1063 116.1363 

12.0292 119.1799 116.7074 120.2002 117.9126 119.1063 116.1363 

12.2671 119.0908 116.6202 120.123 117.8384 119.0306 116.0647 

12.3884 119.0454 116.5758 120.0836 117.8006 118.992 116.0282 

12.5244 118.9949 116.5264 120.0398 117.7586 118.9492 115.9876 

12.6619 123.5833 121.719 119.6677 117.4023 118.5847 115.6436 

12.7589 123.5494 121.6858 119.6369 117.3728 118.5546 115.6152 

12.9495 123.4828 121.6208 119.5766 117.3149 118.4955 115.5593 

13.0549 123.4461 121.5849 119.5434 117.283 118.4629 115.5284 

149
 
Distance 

Test 8 105 

HL 

Test 8 95 

HL 

Test 7 105 

HL 

Test 7 95 

HL 

Test 6 105 

HL 

Test 6 95 

HL 

13.3859 123.3272 121.4686 119.4355 117.1794 118.3572 115.4284 

13.6541 123.2372 121.3807 119.3541 117.1013 118.2775 115.3529 

13.9121 123.1493 121.2948 119.2746 117.025 118.1997 115.2793 

14.1148 123.0811 121.2281 119.2129 116.9659 118.1393 115.2221 

14.5219 122.9253 121.0757 119.0711 116.8297 118.0004 115.0905 

15.0699 122.7163 120.8712 118.8808 116.647 117.814 114.9139 

15.2599 122.644 120.8006 118.8151 116.5839 117.7496 114.8529 

15.4019 122.5915 120.7492 118.7674 116.538 117.7029 114.8087 

15.5403 122.5407 120.6994 118.7212 116.4937 117.6576 114.7658 

15.8453 122.4272 120.5885 118.618 116.3947 117.5566 114.6701 

16.1153 122.3263 120.4897 118.5262 116.3065 117.4666 114.5849 

17.4453 121.8485 120.0221 118.0925 115.8901 117.0417 114.1825 

17.6035 121.7941 119.9687 118.0429 115.8424 116.9931 114.1362 

17.8465 121.7104 119.8865 117.9665 115.7688 116.9182 114.0649 

18.2915 121.5581 119.737 117.8278 115.6351 116.782 113.9354 

18.4488 121.5041 119.684 117.7785 115.5877 116.7337 113.8895 

18.6148 121.4471 119.628 117.7265 115.5376 116.6827 113.8409 

18.7818 121.3896 119.5716 117.6742 115.4872 116.6313 113.7921 

19.1128 121.2759 119.46 117.5705 115.3873 116.5296 113.6953 

19.4183 121.1659 119.352 117.47 115.2905 116.431 113.6015 

20.0144 120.9738 119.1627 117.2951 115.1221 116.2595 113.4383 

20.3923 120.8534 119.0441 117.1854 115.0165 116.152 113.3361 

20.7652 120.7479 118.94 117.09 114.9246 116.0583 113.2471 

20.9525 120.6938 118.8866 117.0408 114.8773 116.0102 113.2013 

21.4666 120.5452 118.74 116.9062 114.7477 115.8781 113.0758 

21.7311 120.4684 118.6642 116.8365 114.6806 115.8098 113.0109 

21.9173 120.4176 118.614 116.7906 114.6364 115.7648 112.9681 

22.0473 120.3945 118.591 116.77 114.6166 115.7445 112.9487 

22.1883 120.3691 118.5657 116.7473 114.5946 115.7222 112.9274 

22.3543 120.3392 118.5358 116.7206 114.5688 115.6959 112.9022 

22.4763 120.3188 118.5153 116.7024 114.5512 115.6779 112.8851 

22.8133 120.2615 118.458 116.6513 114.5019 115.6277 112.8371 

22.9733 120.2611 118.457 116.6524 114.5029 115.6288 112.8381 

23.1957 120.2593 118.4543 116.6526 114.5031 115.6289 112.8383 

23.3361 120.2518 118.4463 116.6469 114.4976 115.6234 112.833 

23.3575 120.2507 118.4451 116.6461 114.4968 115.6225 112.8321 

23.5515 120.2404 118.4341 116.6383 114.4892 115.6149 112.8248 

23.7088 120.2324 118.4255 116.6323 114.4834 115.6089 112.8191 

24.0118 120.2169 118.4089 116.6207 114.4722 115.5975 112.8082 

24.1251 120.2111 118.4026 116.6163 114.4679 115.5932 112.8041 

24.3851 120.1984 118.3889 116.6069 114.4588 115.5839 112.7952 

150
 
Distance 

Test 8 105 

HL 

Test 8 95 

HL 

Test 7 105 

HL 

Test 7 95 

HL 

Test 6 105 

HL 

Test 6 95 

HL 

24.6292 120.1855 118.3751 116.5971 114.4493 115.5743 112.786 

24.8032 120.1775 118.3664 116.5912 114.4437 115.5685 112.7805 

25.0212 120.1669 118.3549 116.5833 114.4361 115.5608 112.7731 

25.1302 120.1616 118.3492 116.5794 114.4323 115.5569 112.7694 

25.3432 120.1602 118.3468 116.5803 114.4331 115.5578 112.7702 

26.3495 120.1169 118.2991 116.5492 114.403 115.5272 112.741 

26.5235 120.1087 118.2901 116.5431 114.3971 115.5212 112.7352 

26.9295 120.0867 118.2664 116.5263 114.3809 115.5047 112.7195 

27.0567 120.0802 118.2593 116.5213 114.3761 115.4998 112.7148 

27.3222 120.0613 118.2394 116.506 114.3613 115.4848 112.7004 

27.3813 120.0555 118.2334 116.5011 114.3566 115.48 112.6959 

27.6828 120.0258 118.2027 116.4759 114.3322 115.4553 112.6722 

27.8391 124.8328 125.3121 116.46 114.3168 115.4396 112.6572 

27.9641 124.8208 125.3 116.4494 114.3066 115.4292 112.6473 

28.1491 124.8031 125.2822 116.4338 114.2915 115.4138 112.6326 

28.4312 124.7764 125.2551 116.4102 114.2687 115.3906 112.6105 

28.6137 124.7643 125.2429 116.3995 114.2584 115.3802 112.6004 

28.983 124.7407 125.2191 116.3787 114.2383 115.3598 112.581 

29.633 124.7009 125.1789 116.3436 114.2044 115.3253 112.548 

29.925 124.6853 125.1632 116.3299 114.1911 115.3118 112.5351 

30.264 124.6764 125.1541 116.322 114.1834 115.3041 112.5277 

30.904 124.6626 125.14 116.3098 114.1716 115.2922 112.5163 

31.183 124.66 125.1373 116.3076 114.1695 115.29 112.5143 

31.4215 124.6582 125.1354 116.3061 114.1681 115.2885 112.5128 

31.6365 124.6578 125.1349 116.3059 114.1679 115.2883 112.5126 

31.7505 124.6579 125.1349 116.306 114.168 115.2884 112.5127 

31.8455 124.6567 125.1337 116.305 114.167 115.2874 112.5117 

32.0297 124.6513 125.1283 116.3002 114.1624 115.2827 112.5073 

151
 
Distance 

Test 5 105 

HL 

Test 5 95 

HL 

Test 4 105 

HL 

Test 4 95 

HL 

Test 3 105 

HL 

Test 3 95 

HL 

0.1034 122.938 110.9229 122.3679 110.3743 122.402 110.4374 

0.2378 126.1191 122.0339 125.6008 120.704 125.6804 120.8505 

0.3218 126.054 121.9726 125.5325 120.6399 125.6127 120.7874 

0.3218 126.054 121.9726 125.5325 120.6399 125.6127 120.7874 

0.5288 125.9091 121.8367 125.3614 120.4788 125.444 120.6303 

0.7648 125.7461 121.6837 125.1687 120.2971 125.254 120.4534 

1.3788 125.3209 121.2847 124.6664 119.8238 124.759 119.9924 

2.583 124.4898 120.5049 123.6842 118.898 123.7909 119.0909 

2.666 124.4327 120.4512 123.6166 118.8343 123.7243 119.0289 

3.206 124.0755 120.1161 123.1915 118.4334 123.3056 118.6389 

3.429 123.9283 119.978 123.0162 118.2681 123.1329 118.4781 

3.716 123.739 119.8004 122.7908 118.0555 122.9109 118.2713 

5.754 122.3989 118.5429 121.1944 116.55 121.3383 116.8066 

6.798 121.7472 117.9315 120.4109 115.8106 120.5671 116.0882 

6.9262 121.6678 117.857 120.3152 115.7203 120.473 116.0005 

7.0603 121.5846 117.7787 120.2245 115.6346 120.3839 115.9175 

7.2034 121.496 117.6954 120.128 115.5434 120.2891 115.8292 

7.3784 121.3878 117.5936 120.01 115.4319 120.1732 115.7213 

7.7094 121.1841 117.4019 119.7878 115.2219 119.955 115.5181 

7.9064 121.0633 117.2882 119.656 115.0973 119.8256 115.3976 

7.9064 121.0633 117.2882 119.656 115.0973 119.8256 115.3976 

8.2464 120.8525 117.0899 119.4264 114.8803 119.6 115.1876 

8.4174 120.7464 116.9901 119.3108 114.7711 119.4865 115.0818 

8.8571 120.4757 116.7354 119.0157 114.4921 119.1966 114.8119 

9.4411 120.1168 116.3976 118.6245 114.1223 118.8124 114.454 

9.6082 120.0174 116.3041 118.5158 114.0195 118.7057 114.3547 

10.0174 119.7751 116.0761 118.2508 113.7688 118.4456 114.1124 

10.3374 119.586 115.8982 118.044 113.5732 118.2426 113.9233 

10.5075 119.4851 115.8032 117.9336 113.4688 118.1343 113.8224 

10.8129 119.3044 115.6332 117.736 113.2819 117.9403 113.6417 

10.9501 119.2234 115.5569 117.6474 113.198 117.8533 113.5607 

11.0961 119.1373 115.4759 117.5532 113.109 117.7609 113.4746 

11.6971 118.7849 115.1443 117.1676 112.7441 117.3825 113.1221 

12.0081 118.6037 114.9737 116.9693 112.5565 117.1878 112.9408 

12.0291 118.5958 114.9664 116.9603 112.5479 117.1791 112.9326 

12.0292 118.5958 114.9664 116.9603 112.5479 117.1791 112.9326 

12.2671 118.507 114.8829 116.8581 112.4503 117.0798 112.8402 

12.3884 118.4617 114.8403 116.806 112.4006 117.0292 112.7931 

12.5244 118.4113 114.7929 116.7479 112.3453 116.9729 112.7407 

12.6619 117.9452 114.355 121.8413 117.2531 122.089 117.6882 

12.7589 117.9097 114.3217 121.8023 117.2159 122.0512 117.653 

12.9495 117.84 114.2562 121.7257 117.1428 121.9769 117.5838 

13.0549 117.8016 114.22 121.6834 117.1024 121.9359 117.5456 

152
 
Distance 

Test 5 105 

HL 

Test 5 95 

HL 

Test 4 105 

HL 

Test 4 95 

HL 

Test 3 105 

HL 

Test 3 95 

HL 

13.3859 117.6775 114.1034 121.5472 116.9724 121.8035 117.4223 

13.6541 117.5828 114.0144 121.443 116.8729 121.7026 117.3283 

13.9121 117.4906 113.9277 121.3415 116.776 121.6042 117.2367 

14.1148 117.4189 113.8603 121.2625 116.7006 121.5277 117.1654 

14.5219 117.2574 113.7085 121.0856 116.5319 121.3555 117.005 

15.0699 117.0407 113.5047 120.8479 116.3053 121.1244 116.7897 

15.2599 116.9658 113.4342 120.7657 116.227 121.0445 116.7153 

15.4019 116.9111 113.3828 120.7058 116.1698 120.9862 116.661 

15.5403 116.8582 113.3331 120.6477 116.1144 120.9298 116.6084 

15.8453 116.7402 113.2221 120.5182 115.9909 120.8039 116.4911 

16.1153 116.6352 113.1234 120.403 115.8811 120.692 116.3868 

17.4453 116.1359 112.6539 119.8544 115.3575 120.1593 115.8906 

17.6035 116.0783 112.5995 119.7913 115.2969 120.0982 115.8334 

17.8465 115.9897 112.5157 119.6943 115.2037 120.0041 115.7453 

18.2915 115.8284 112.3633 119.5176 115.034 119.8329 115.5849 

18.4488 115.7711 112.3092 119.455 114.9738 119.7722 115.528 

18.6148 115.7107 112.2521 119.3889 114.9103 119.7081 115.468 

18.7818 115.6499 112.1947 119.3223 114.8464 119.6435 115.4076 

19.1128 115.5294 112.0808 119.1904 114.7197 119.5157 115.2878 

19.4183 115.4136 111.9713 119.0638 114.5982 119.3928 115.1727 

20.0144 115.2081 111.7771 118.8381 114.381 119.1747 114.9684 

20.3923 115.0791 111.6552 118.6963 114.2444 119.0377 114.8401 

20.7652 114.964 111.5464 118.5694 114.1218 118.9155 114.7257 

20.9525 114.9051 111.4907 118.5045 114.0591 118.853 114.6671 

21.4666 114.7434 111.338 118.3264 113.887 118.6815 114.5064 

21.7311 114.6599 111.259 118.2343 113.7982 118.5928 114.4234 

21.9173 114.604 111.2063 118.1726 113.7385 118.5335 114.3678 

22.0473 114.5842 111.1875 118.1498 113.7158 118.5124 114.348 

22.1883 114.5622 111.1667 118.1246 113.6908 118.489 114.3261 

22.3543 114.5363 111.1422 118.095 113.6614 118.4615 114.3004 

22.4763 114.5187 111.1256 118.0747 113.6412 118.4427 114.2828 

22.8133 114.4693 111.0789 118.0178 113.5846 118.3902 114.2337 

22.9733 114.4702 111.0798 118.0168 113.5821 118.3913 114.2347 

23.1957 114.4703 111.0799 118.0142 113.5775 118.3914 114.2348 

23.3361 114.4648 111.0747 118.0063 113.5684 118.3856 114.2294 

23.3575 114.464 111.0739 118.0051 113.567 118.3847 114.2285 

23.5515 114.4564 111.0668 117.9942 113.5546 118.3767 114.221 

23.7088 114.4505 111.0612 117.9856 113.5447 118.3705 114.2152 

24.0118 114.4392 111.0505 117.9692 113.5258 118.3586 114.204 

24.1251 114.435 111.0465 117.963 113.5187 118.3541 114.1998 

24.3851 114.4258 111.0378 117.9494 113.5029 118.3444 114.1907 

24.6292 114.4163 111.0288 117.9357 113.4872 118.3343 114.1813 

24.8032 114.4106 111.0235 117.9271 113.4771 118.3283 114.1757 

153
 
Distance 

Test 5 105 

HL 

Test 5 95 

HL 

Test 4 105 

HL 

Test 4 95 

HL 

Test 3 105 

HL 

Test 3 95 

HL 

25.0212 114.403 111.0162 117.9158 113.4639 118.3202 114.1681 

25.1302 114.3992 111.0126 117.9102 113.4573 118.3162 114.1643 

25.3432 114.3999 111.0133 117.9078 113.4526 118.3171 114.1651 

26.3495 114.3698 110.9849 117.8608 113.3966 118.2853 114.1353 

26.5235 114.3639 110.9793 117.8519 113.3862 118.279 114.1294 

26.9295 114.3477 110.9639 117.8286 113.3595 118.2618 114.1133 

27.0567 114.3429 110.9594 117.8217 113.3515 118.2568 114.1086 

27.3222 114.3281 110.9454 117.802 113.3299 118.2411 114.0939 

27.3813 114.3234 110.941 117.7961 113.3237 118.2361 114.0893 

27.6828 114.2992 110.9181 117.7659 113.2918 118.2104 114.0651 

27.8391 114.2838 110.9035 124.8491 125.4185 118.194 114.0498 

27.9641 114.2736 110.8939 124.8371 125.4064 118.1832 114.0397 

28.1491 114.2585 110.8796 124.8195 125.3886 118.1672 114.0247 

28.4312 114.2358 110.8582 124.7928 125.3617 118.1431 114.0021 

28.6137 114.2255 110.8484 124.7807 125.3496 118.1322 113.9919 

28.983 114.2055 110.8296 124.7573 125.3259 118.111 113.972 

29.633 114.1717 110.7976 124.7177 125.286 118.0752 113.9385 

29.925 114.1585 110.7851 124.7022 125.2703 118.0612 113.9253 

30.264 114.1509 110.7779 124.6933 125.2614 118.0532 113.9178 

30.904 114.1393 110.7669 124.6796 125.2476 118.0409 113.9063 

31.183 114.1371 110.7649 124.677 125.2448 118.0386 113.9042 

31.4215 114.1357 110.7635 124.6751 125.2429 118.0371 113.9027 

31.6365 114.1354 110.7632 124.6747 125.2425 118.0368 113.9025 

31.7505 114.1355 110.7633 124.6747 125.2425 118.0369 113.9025 

31.8455 114.1345 110.7624 124.6735 125.2413 118.0358 113.9016 

32.0297 114.1299 110.7581 124.6682 125.2358 118.031 113.897 

154
 
Distance 

Test 2 105 

HL 

Test 2 95 

HL 

Test 1 105 

HL 

Test 1 95 

HL 

0.1034 122.5967 110.633 122.9494 111.4887 

0.2378 126.1397 121.3093 121.7467 110.7418 

0.3218 126.075 121.2491 121.6862 110.6914 

0.3218 126.075 121.2491 121.6862 110.6914 

0.5288 125.9154 121.1006 121.5367 110.5674 

0.7648 125.7367 120.9344 121.3694 110.4285 

1.3788 125.271 120.5011 120.9332 110.0664 

2.583 124.3601 119.6537 120.0801 109.3582 

2.666 124.2974 119.5954 120.0214 109.3095 

3.206 123.9043 119.2297 119.6533 109.0039 

3.429 123.7422 119.0789 119.5015 108.8779 

3.716 123.5337 118.885 119.3062 108.7158 

5.754 122.0572 117.5112 117.9233 107.5674 

6.798 121.3351 116.8394 117.247 107.0059 

6.9262 121.247 116.7574 117.1644 106.9374 

7.0603 121.1643 116.6805 117.0871 106.8733 

7.2034 121.0764 116.5988 117.0048 106.8051 

7.3784 120.9689 116.4988 116.9042 106.7217 

7.7094 120.7665 116.3106 116.7147 106.5647 

7.9064 120.6465 116.1991 116.6024 106.4716 

7.9064 120.6465 116.1991 116.6024 106.4716 

8.2464 120.4372 116.0044 116.4064 106.3092 

8.4174 120.3318 115.9064 116.3078 106.2274 

8.8571 120.0629 115.6563 116.056 106.0187 

9.4411 119.7063 115.3247 115.7222 105.7419 

9.6082 119.6076 115.2329 115.6298 105.6653 

10.0174 119.367 115.0091 115.4045 105.4786 

10.3374 119.1791 114.8344 115.2287 105.3328 

10.5075 119.0789 114.7412 115.1349 105.255 

10.8129 118.8994 114.5743 114.9668 105.1156 

10.9501 118.8189 114.4994 114.8914 105.0532 

11.0961 118.7334 114.4199 114.8114 104.9868 

11.6971 118.3833 114.0942 114.4836 104.7149 

12.0081 118.2033 113.9268 114.3151 104.5752 

12.0291 118.1955 113.9196 114.3078 104.5692 

12.0292 118.1955 113.9196 114.3078 104.5692 

12.2671 118.1073 113.8377 114.2253 104.5011 

12.3884 118.0623 113.7959 114.1832 104.4664 

12.5244 118.0123 113.7494 114.1365 104.4278 

12.6619 117.5493 113.3197 113.7037 104.0708 

12.7589 117.514 113.2869 113.6707 104.0436 

12.9495 117.4448 113.2227 113.606 103.9902 

13.0549 117.4066 113.1872 113.5703 103.9607 

155
 
Distance 

Test 2 105 

HL 

Test 2 95 

HL 

Test 1 105 

HL 

Test 1 95 

HL 

13.3859 117.2834 113.0727 113.4551 103.8655 

13.6541 117.1894 112.9854 113.3672 103.793 

13.9121 117.0978 112.9003 113.2815 103.7223 

14.1148 117.0265 112.8342 113.2149 103.6673 

14.5219 116.8662 112.6852 113.0649 103.5433 

15.0699 116.6509 112.4851 112.8635 103.3767 

15.2599 116.5765 112.416 112.7939 103.3191 

15.4019 116.5222 112.3656 112.7431 103.2771 

15.5403 116.4697 112.3167 112.6939 103.2365 

15.8453 116.3525 112.2078 112.5843 103.1458 

16.1153 116.2482 112.1109 112.4867 103.0652 

17.4453 115.7523 111.6502 112.0228 102.6819 

17.6035 115.695 111.5967 111.969 102.6366 

17.8465 115.6069 111.5143 111.8861 102.5668 

18.2915 115.4466 111.3645 111.7353 102.4398 

18.4488 115.3898 111.3113 111.6818 102.3947 

18.6148 115.3298 111.2552 111.6254 102.3472 

18.7818 115.2693 111.1987 111.5685 102.2993 

19.1128 115.1496 111.0868 111.4559 102.2045 

19.4183 115.0345 110.9792 111.3476 102.1133 

20.0144 114.8303 110.7883 111.1555 101.9515 

20.3923 114.7021 110.6684 111.0349 101.8499 

20.7652 114.5877 110.5615 110.9273 101.7593 

20.9525 114.5292 110.5068 110.8722 101.7128 

21.4666 114.3686 110.3566 110.7211 101.5855 

21.7311 114.2856 110.279 110.643 101.5198 

21.9173 114.2301 110.2271 110.5908 101.4758 

22.0473 114.2103 110.2087 110.5722 101.4602 

22.1883 114.1885 110.1882 110.5517 101.4429 

22.3543 114.1627 110.1642 110.5275 101.4226 

22.4763 114.1452 110.1478 110.511 101.4088 

22.8133 114.0961 110.102 110.4649 101.37 

22.9733 114.097 110.1028 110.4658 101.3708 

23.1957 114.0971 110.1029 110.4659 101.3709 

23.3361 114.0917 110.0978 110.4607 101.3666 

23.3575 114.0908 110.097 110.46 101.3659 

23.5515 114.0833 110.09 110.4529 101.36 

23.7088 114.0775 110.0845 110.4474 101.3554 

24.0118 114.0662 110.074 110.4369 101.3465 

24.1251 114.062 110.0701 110.4329 101.3432 

24.3851 114.0529 110.0615 110.4243 101.336 

24.6292 114.0434 110.0527 110.4154 101.3285 

156
 
Distance 

Test 2 105 

HL 

Test 2 95 

HL 

Test 1 105 

HL 

Test 1 95 

HL 

24.8032 114.0378 110.0474 110.4101 101.324 

25.0212 114.0302 110.0403 110.403 101.318 

25.1302 114.0264 110.0367 110.3994 101.315 

25.3432 114.0271 110.0374 110.4001 101.3156 

26.3495 113.9972 110.0094 110.372 101.2919 

26.5235 113.9913 110.0039 110.3664 101.2872 

26.9295 113.9752 109.9888 110.3513 101.2744 

27.0567 113.9705 109.9844 110.3468 101.2706 

27.3222 113.9558 109.9707 110.333 101.259 

27.3813 113.9511 109.9663 110.3286 101.2553 

27.6828 113.927 109.9438 110.3059 101.2362 

27.8391 113.9117 109.9295 110.2915 101.224 

27.9641 113.9016 109.92 110.282 101.216 

28.1491 113.8866 109.906 110.2679 101.2041 

28.4312 113.864 109.8849 110.2466 101.1862 

28.6137 113.8538 109.8753 110.237 101.1781 

28.983 113.834 109.8568 110.2183 101.1624 

29.633 113.8004 109.8254 110.1867 101.1357 

29.925 113.7873 109.8131 110.1744 101.1253 

30.264 113.7798 109.8061 110.1673 101.1193 

30.904 113.7682 109.7952 110.1564 101.11 

31.183 113.7661 109.7932 110.1544 101.1083 

31.4215 113.7646 109.7919 110.153 101.1072 

31.6365 113.7643 109.7916 110.1528 101.107 

31.7505 113.7644 109.7917 110.1528 101.1071 

31.8455 113.7634 109.7908 110.1519 101.1063 

32.0297 113.7589 109.7865 110.1477 101.1027 

157
 
Table 21. Voltage Profile Data for Light Load Tests 1 Through 8 

at 95% and 105% Substation Primary Voltage 

Distance 

Test 8 105 

LL 

Test 8 95 

LL 

Test 7 105 

LL 

Test 7 95 

LL 

Test 6 105 

LL 

Test 6 95 

LL 

0.1034 125.9754 113.9697 125.9744 113.9687 125.5215 113.4715 

0.2378 125.6501 126.1978 125.648 126.1954 126.246 125.7513 

0.3218 125.6232 126.1708 125.6211 126.1683 126.2194 125.7247 

0.3218 125.6232 126.1708 125.6211 126.1683 126.2194 125.7247 

0.5288 125.617 126.1647 125.6149 126.1621 126.1918 125.6973 

0.7648 125.6046 126.1523 125.6024 126.1496 126.1567 125.6622 

1.3788 125.572 126.1198 125.5696 126.1168 126.0648 125.5707 

2.583 125.5091 126.057 125.5064 126.0535 125.8856 125.392 

2.666 125.5048 126.0527 125.5021 126.0492 125.8732 125.3798 

3.206 125.4822 126.0303 125.4794 126.0265 125.7984 125.3052 

3.429 125.4729 126.0211 125.4701 126.0172 125.7676 125.2745 

3.716 125.4611 126.0093 125.4582 126.0053 125.7279 125.2349 

5.754 125.3787 125.9272 125.3753 125.9223 125.4476 124.9556 

6.798 125.3473 125.8961 125.3437 125.8907 125.3146 124.823 

6.9262 125.3436 125.8925 125.34 125.887 125.2984 124.807 

7.0603 125.3329 125.8817 125.3292 125.8762 125.2746 124.7832 

7.2034 125.3214 125.8703 125.3177 125.8647 125.2492 124.7579 

7.3784 125.3075 125.8563 125.3037 125.8506 125.2181 124.727 

7.7094 125.2813 125.8302 125.2776 125.8244 125.1597 124.6687 

7.9064 125.2659 125.8148 125.2621 125.8089 125.1251 124.6342 

7.9064 125.2659 125.8148 125.2621 125.8089 125.1251 124.6342 

8.2464 125.2381 125.787 125.2342 125.7809 125.064 124.5734 

8.4174 125.2241 125.7729 125.2201 125.7668 125.0333 124.5427 

8.8571 125.1886 125.7375 125.1846 125.7312 124.9548 124.4646 

9.4411 125.1418 125.6906 125.1376 125.684 124.8508 124.3609 

9.6082 125.1295 125.6784 125.1253 125.6717 124.8222 124.3324 

10.0174 125.1 125.6488 125.0957 125.642 124.7525 124.263 

10.3374 125.077 125.6259 125.0727 125.6189 124.6981 124.2088 

10.5075 125.0646 125.6135 125.0602 125.6064 124.6691 124.1798 

10.8129 125.0425 125.5914 125.038 125.5842 124.617 124.1279 

10.9501 125.0326 125.5815 125.0281 125.5742 124.5936 124.1046 

11.0961 125.0222 125.5711 125.0177 125.5637 124.5688 124.0799 

11.6971 124.9798 125.5287 124.9752 125.5211 124.4674 123.9789 

12.0081 124.9582 125.5072 124.9536 125.4994 124.4152 123.9269 

12.0291 124.9564 125.5054 124.9517 125.4976 124.4134 123.9251 

12.0292 124.9564 125.5054 124.9517 125.4976 124.4134 123.9251 

12.2671 124.9358 125.4847 124.9311 125.4769 124.3929 123.9047 

12.3884 124.9253 125.4742 124.9205 125.4663 124.3825 123.8942 

12.5244 124.9136 125.4626 124.9089 125.4546 124.3709 123.8827 

12.6619 124.284 125.3955 124.8416 125.3871 124.3038 123.8159 

12.7589 124.2758 125.3873 124.8334 125.3789 124.2957 123.8078 

12.9495 124.2597 125.3713 124.8173 125.3628 124.2798 123.7919 

158
 
Distance 

Test 8 105 

LL 

Test 8 95 

LL 

Test 7 105 

LL 

Test 7 95 

LL 

Test 6 105 

LL 

Test 6 95 

LL 

13.0549 124.2508 125.3624 124.8085 125.3539 124.271 123.7831 

13.3859 124.2215 125.3332 124.7792 125.3245 124.2419 123.7542 

13.6541 124.2 125.3118 124.7578 125.303 124.2207 123.733 

13.9121 124.1789 125.2909 124.7368 125.282 124.1998 123.7122 

14.1148 124.1626 125.2747 124.7206 125.2656 124.1837 123.6961 

14.5219 124.1228 125.2349 124.6808 125.2257 124.1442 123.6568 

15.0699 124.0693 125.1816 124.6274 125.1722 124.0912 123.604 

15.2599 124.0508 125.1632 124.609 125.1537 124.0729 123.5858 

15.4019 124.0375 125.1499 124.5957 125.1404 124.0597 123.5726 

15.5403 124.0247 125.1372 124.5829 125.1275 124.047 123.56 

15.8453 123.9958 125.1084 124.5541 125.0987 124.0184 123.5315 

16.1153 123.9701 125.0828 124.5285 125.0729 123.9929 123.5061 

17.4453 123.8498 124.9629 124.4085 124.9525 123.8737 123.3873 

17.6035 123.8375 124.9507 124.3962 124.9401 123.8615 123.3751 

17.8465 123.8185 124.9317 124.3772 124.9211 123.8427 123.3563 

18.2915 123.7842 124.8977 124.3431 124.8869 123.8088 123.3226 

18.4488 123.772 124.8855 124.3309 124.8747 123.7967 123.3105 

18.6148 123.7591 124.8727 124.3181 124.8618 123.7839 123.2978 

18.7818 123.7461 124.8597 124.3051 124.8487 123.771 123.2849 

19.1128 123.7203 124.8341 124.2794 124.823 123.7455 123.2595 

19.4183 123.6947 124.8086 124.2538 124.7973 123.7202 123.2342 

20.0144 123.6585 124.7728 124.2179 124.7613 123.6845 123.1987 

20.3923 123.6362 124.7507 124.1957 124.739 123.6624 123.1767 

20.7652 123.6182 124.733 124.1779 124.7211 123.6447 123.1591 

20.9525 123.6088 124.7237 124.1686 124.7118 123.6355 123.1499 

21.4666 123.583 124.6983 124.143 124.6861 123.6101 123.1245 

21.7311 123.5696 124.685 124.1297 124.6727 123.5969 123.1114 

21.9173 123.5612 124.6768 124.1214 124.6644 123.5886 123.1032 

22.0473 123.5534 124.669 124.1136 124.6566 123.5809 123.0955 

22.1883 123.5448 124.6605 124.105 124.648 123.5723 123.0869 

22.3543 123.5347 124.6504 124.0949 124.6379 123.5623 123.0769 

22.4763 123.5277 124.6435 124.088 124.6309 123.5554 123.07 

22.8133 123.5082 124.6242 124.0686 124.6114 123.5361 123.0508 

22.9733 123.5073 124.6234 124.0678 124.6106 123.5353 123.05 

23.1957 123.5057 124.622 124.0663 124.6091 123.5337 123.0485 

23.3361 123.5027 124.619 124.0633 124.6061 123.5308 123.0455 

23.3575 123.5022 124.6186 124.0628 124.6057 123.5304 123.0451 

23.5515 123.498 124.6146 124.0588 124.6016 123.5263 123.041 

23.7088 123.4948 124.6114 124.0556 124.5983 123.5231 123.0379 

159
 
Distance 

Test 8 105 

LL 

Test 8 95 

LL 

Test 7 105 

LL 

Test 7 95 

LL 

Test 6 105 

LL 

Test 6 95 

LL 

24.0118 123.4884 124.6053 124.0494 124.5921 123.5169 123.0317 

24.1251 123.4861 124.6031 124.047 124.5898 123.5146 123.0294 

24.3851 123.4808 124.598 124.0419 124.5846 123.5095 123.0243 

24.6292 123.4755 124.5929 124.0367 124.5795 123.5044 123.0192 

24.8032 123.4722 124.5897 124.0335 124.5762 123.5011 123.016 

25.0212 123.4678 124.5855 124.0292 124.5719 123.4969 123.0117 

25.1302 123.4656 124.5834 124.027 124.5697 123.4947 123.0096 

25.3432 123.4642 124.5823 124.0258 124.5684 123.4935 123.0083 

26.3495 123.4459 124.5648 124.0079 124.5505 123.4757 122.9907 

26.5235 123.4425 124.5615 124.0046 124.5472 123.4724 122.9873 

26.9295 123.4337 124.553 123.996 124.5385 123.4639 122.9788 

27.0567 123.4311 124.5505 123.9934 124.5359 123.4613 122.9763 

27.3222 123.4239 124.5435 123.9864 124.5289 123.4543 122.9693 

27.3813 123.4218 124.5415 123.9843 124.5268 123.4523 122.9673 

27.6828 123.4112 124.5311 123.9738 124.5162 123.4418 122.9568 

27.8391 124.232 123.6907 123.9678 124.5102 123.4358 122.9509 

27.9641 124.2276 123.6863 123.9634 124.5058 123.4314 122.9465 

28.1491 124.221 123.6798 123.9568 124.4992 123.4249 122.9401 

28.4312 124.2111 123.67 123.947 124.4893 123.4151 122.9303 

28.6137 124.2065 123.6654 123.9423 124.4847 123.4105 122.9257 

28.983 124.1976 123.6565 123.9335 124.4758 123.4018 122.917 

29.633 124.1829 123.6419 123.9189 124.4611 123.3872 122.9025 

29.925 124.1772 123.6362 123.9131 124.4553 123.3815 122.8968 

30.264 124.1739 123.6329 123.9098 124.452 123.3782 122.8935 

30.904 124.1685 123.6276 123.9045 124.4467 123.373 122.8883 

31.183 124.1674 123.6265 123.9034 124.4456 123.3718 122.8872 

31.4215 124.1666 123.6257 123.9026 124.4448 123.3711 122.8864 

31.6365 124.1662 123.6253 123.9022 124.4444 123.3707 122.886 

31.7505 124.1662 123.6253 123.9022 124.4444 123.3707 122.886 

31.8455 124.1658 123.6249 123.9018 124.444 123.3703 122.8856 

32.0297 124.1639 123.6231 123.9 124.4422 123.3685 122.8838 

160
 
Distance 

Test 5 105 

LL 

Test 5 95 

LL 

Test 4 105 

LL 

Test 4 95 

LL 

Test 3 105 

LL 

Test 3 95 

LL 

0.1034 125.1863 113.1052 124.8272 112.684 124.8297 112.6858 

0.2378 126.275 125.6313 126.2478 126.1644 126.2539 126.1689 

0.3218 126.2487 125.6051 126.2214 126.1377 126.2276 126.1422 

0.3218 126.2487 125.6051 126.2214 126.1377 126.2276 126.1422 

0.5288 126.2059 125.5625 126.162 126.0775 126.1685 126.0822 

0.7648 126.1545 125.5114 126.0928 126.0072 126.0996 126.0122 

1.3788 126.0206 125.378 125.9124 125.8242 125.9201 125.8297 

2.583 125.7585 125.1171 125.5592 125.4657 125.5685 125.4725 

2.666 125.7404 125.0992 125.5349 125.441 125.5443 125.4478 

3.206 125.6284 124.9877 125.3819 125.2857 125.3921 125.2931 

3.429 125.5822 124.9417 125.3188 125.2216 125.3293 125.2292 

3.716 125.5227 124.8825 125.2376 125.1391 125.2485 125.147 

5.754 125.1016 124.4633 124.6618 124.5544 124.6755 124.5643 

6.798 124.8962 124.2589 124.377 124.2651 124.3921 124.276 

6.9262 124.8712 124.234 124.3422 124.2297 124.3575 124.2408 

7.0603 124.838 124.201 124.3088 124.1957 124.3243 124.2069 

7.2034 124.8027 124.1659 124.2732 124.1595 124.289 124.1709 

7.3784 124.7596 124.1229 124.2297 124.1153 124.2457 124.1268 

7.7094 124.6782 124.0419 124.1477 124.0318 124.1642 124.0437 

7.9064 124.6299 123.9939 124.0991 123.9823 124.1158 123.9943 

7.9064 124.6299 123.9939 124.0991 123.9823 124.1158 123.9943 

8.2464 124.5453 123.9096 124.0138 123.8955 124.031 123.9079 

8.4174 124.5026 123.8672 123.9709 123.8519 123.9883 123.8644 

8.8571 124.3937 123.7588 123.8611 123.7402 123.8791 123.7532 

9.4411 124.2491 123.6149 123.7154 123.592 123.7343 123.6055 

9.6082 124.2089 123.5748 123.6749 123.5507 123.694 123.5644 

10.0174 124.1107 123.4772 123.576 123.45 123.5956 123.4641 

10.3374 124.0341 123.4009 123.4987 123.3714 123.5188 123.3858 

10.5075 123.9932 123.3602 123.4575 123.3294 123.4778 123.344 

10.8129 123.9198 123.2871 123.3836 123.2541 123.4043 123.269 

10.9501 123.8869 123.2544 123.3504 123.2203 123.3713 123.2354 

11.0961 123.8519 123.2196 123.3151 123.1845 123.3363 123.1996 

11.6971 123.7086 123.0769 123.1707 123.0374 123.1926 123.0531 

12.0081 123.6347 123.0034 123.0962 122.9616 123.1186 122.9776 

12.0291 123.6315 123.0002 123.093 122.9583 123.1154 122.9743 

12.0292 123.6315 123.0002 123.093 122.9583 123.1154 122.9743 

12.2671 123.5952 122.9641 123.0562 122.9205 123.079 122.9368 

12.3884 123.5767 122.9457 123.0374 122.9012 123.0604 122.9176 

12.5244 123.5561 122.9251 123.0165 122.8797 123.0396 122.8963 

12.6619 123.3715 122.7414 123.5686 125.2723 123.5931 125.29 

12.7589 123.3569 122.7269 123.5539 125.2574 123.5785 125.2752 

12.9495 123.3283 122.6984 123.525 125.2282 123.5499 125.2462 

161
 
Distance 

Test 5 105 

LL 

Test 5 95 

LL 

Test 4 105 

LL 

Test 4 95 

LL 

Test 3 105 

LL 

Test 3 95 

LL 

13.0549 123.3125 122.6827 123.5091 125.2121 123.5341 125.2302 

13.3859 123.2614 122.6319 123.4576 125.1601 123.483 125.1785 

13.6541 123.2223 122.5929 123.4181 125.1202 123.4439 125.1388 

13.9121 123.1843 122.5551 123.3797 125.0814 123.4059 125.1003 

14.1148 123.1546 122.5256 123.3498 125.0512 123.3762 125.0703 

14.5219 123.0881 122.4594 123.2827 124.9834 123.3097 125.0029 

15.0699 122.9986 122.3704 123.1925 124.8923 123.2202 124.9123 

15.2599 122.9677 122.3396 123.1613 124.8607 123.1893 124.8809 

15.4019 122.9451 122.3171 123.1385 124.8377 123.1667 124.858 

15.5403 122.9231 122.2952 123.1164 124.8153 123.1447 124.8358 

15.8453 122.8743 122.2466 123.0671 124.7655 123.0959 124.7863 

16.1153 122.8308 122.2033 123.0233 124.7212 123.0524 124.7422 

17.4453 122.6228 121.9964 122.8135 124.5093 122.8444 124.5315 

17.6035 122.6001 121.9737 122.7905 124.486 122.8216 124.5085 

17.8465 122.565 121.9388 122.7551 124.4503 122.7866 124.4729 

18.2915 122.5014 121.8755 122.6909 124.3854 122.7229 124.4085 

18.4488 122.4787 121.8529 122.668 124.3623 122.7003 124.3855 

18.6148 122.4548 121.8292 122.6439 124.338 122.6764 124.3613 

18.7818 122.4308 121.8052 122.6196 124.3134 122.6524 124.337 

19.1128 122.3831 121.7578 122.5715 124.2648 122.6047 124.2887 

19.4183 122.3373 121.7122 122.5253 124.2181 122.5589 124.2423 

20.0144 122.2616 121.6369 122.4487 124.1408 122.4831 124.1656 

20.3923 122.2142 121.5896 122.4007 124.0924 122.4357 124.1175 

20.7652 122.1714 121.5471 122.3574 124.0487 122.3929 124.0742 

20.9525 122.1495 121.5253 122.3353 124.0264 122.371 124.052 

21.4666 122.0895 121.4656 122.2746 123.9651 122.311 123.9912 

21.7311 122.0585 121.4347 122.2432 123.9334 122.28 123.9598 

21.9173 122.0377 121.414 122.2221 123.9122 122.2592 123.9387 

22.0473 122.0301 121.4064 122.2143 123.9043 122.2515 123.9309 

22.1883 122.0216 121.398 122.2057 123.8956 122.2431 123.9224 

22.3543 122.0117 121.3881 122.1955 123.8854 122.2331 123.9123 

22.4763 122.0048 121.3813 122.1885 123.8783 122.2263 123.9054 

22.8133 121.9857 121.3623 122.169 123.8586 122.2072 123.886 

22.9733 121.9849 121.3615 122.168 123.8577 122.2064 123.8852 

23.1957 121.9834 121.36 122.1662 123.856 122.2049 123.8837 

23.3361 121.9805 121.3571 122.1631 123.8529 122.202 123.8807 

23.3575 121.9801 121.3567 122.1626 123.8524 122.2015 123.8803 

23.5515 121.9761 121.3527 122.1583 123.8481 122.1975 123.8762 

23.7088 121.9729 121.3495 122.155 123.8448 122.1944 123.873 

24.0118 121.9668 121.3435 122.1485 123.8383 122.1883 123.8668 

24.1251 121.9645 121.3412 122.146 123.8359 122.186 123.8645 

24.3851 121.9595 121.3362 122.1406 123.8305 122.181 123.8594 

162
 
Distance 

Test 5 105 

LL 

Test 5 95 

LL 

Test 4 105 

LL 

Test 4 95 

LL 

Test 3 105 

LL 

Test 3 95 

LL 

24.6292 121.9544 121.3311 122.1352 123.8252 122.1759 123.8543 

24.8032 121.9512 121.3279 122.1318 123.8217 122.1727 123.851 

25.0212 121.947 121.3237 122.1273 123.8172 122.1685 123.8467 

25.1302 121.9449 121.3216 122.125 123.815 122.1664 123.8446 

25.3432 121.9437 121.3204 122.1235 123.8136 122.1652 123.8434 

26.3495 121.9262 121.303 122.1046 123.7948 122.1477 123.8256 

26.5235 121.9229 121.2997 122.1011 123.7914 122.1444 123.8223 

26.9295 121.9145 121.2913 122.0921 123.7824 122.136 123.8138 

27.0567 121.9119 121.2888 122.0894 123.7797 122.1335 123.8112 

27.3222 121.905 121.2819 122.0821 123.7725 122.1266 123.8042 

27.3813 121.903 121.2799 122.08 123.7704 122.1246 123.8022 

27.6828 121.8927 121.2697 122.0693 123.7596 122.1142 123.7917 

27.8391 121.8868 121.2638 124.5168 125.412 122.1083 123.7857 

27.9641 121.8825 121.2595 124.5124 125.4075 122.104 123.7813 

28.1491 121.8761 121.2531 124.5059 125.4009 122.0976 123.7749 

28.4312 121.8664 121.2435 124.496 125.391 122.0879 123.7651 

28.6137 121.8619 121.239 124.4914 125.3864 122.0834 123.7605 

28.983 121.8532 121.2304 124.4826 125.3775 122.0747 123.7517 

29.633 121.8389 121.2161 124.468 125.3628 122.0604 123.7372 

29.925 121.8332 121.2105 124.4622 125.357 122.0548 123.7315 

30.264 121.83 121.2073 124.459 125.3537 122.0516 123.7283 

30.904 121.8249 121.2022 124.4537 125.3484 122.0464 123.723 

31.183 121.8238 121.2011 124.4526 125.3472 122.0453 123.7219 

31.4215 121.823 121.2003 124.4517 125.3464 122.0445 123.7211 

31.6365 121.8226 121.1999 124.4514 125.346 122.0442 123.7208 

31.7505 121.8226 121.1999 124.4513 125.346 122.0441 123.7207 

31.8455 121.8222 121.1995 124.4509 125.3456 122.0437 123.7203 

32.0297 121.8204 121.1977 124.4491 125.3438 122.0419 123.7185 

163
 
Distance 

Test 2 105 

LL 

Test 2 95 

LL 

Test 1 105 

LL 

Test 1 95 

LL 

0.1034 124.8365 112.7094 124.8365 112.9372 

0.2378 126.2705 126.2252 126.2705 114.2202 

0.3218 126.2443 126.199 126.2443 114.1963 

0.3218 126.2443 126.199 126.2443 114.1963 

0.5288 126.1855 126.1402 126.1855 114.1426 

0.7648 126.1169 126.0717 126.1169 114.08 

1.3788 125.9383 125.8932 125.9383 113.917 

2.583 125.5886 125.5436 125.5886 113.5978 

2.666 125.5645 125.5195 125.5645 113.5758 

3.206 125.4131 125.3682 125.4131 113.4376 

3.429 125.3507 125.3058 125.3507 113.3806 

3.716 125.2703 125.2255 125.2703 113.3072 

5.754 124.7003 124.6557 124.7003 112.7869 

6.798 124.4185 124.3741 124.4185 112.5297 

6.9262 124.3841 124.3397 124.3841 112.4983 

7.0603 124.3511 124.3067 124.3511 112.4681 

7.2034 124.3159 124.2715 124.3159 112.436 

7.3784 124.2729 124.2286 124.2729 112.3968 

7.7094 124.1919 124.1475 124.1919 112.3228 

7.9064 124.1438 124.0995 124.1438 112.2789 

7.9064 124.1438 124.0995 124.1438 112.2789 

8.2464 124.0595 124.0152 124.0595 112.202 

8.4174 124.0171 123.9728 124.0171 112.1632 

8.8571 123.9086 123.8643 123.9086 112.0642 

9.4411 123.7646 123.7204 123.7646 111.9327 

9.6082 123.7245 123.6803 123.7245 111.8962 

10.0174 123.6268 123.5827 123.6268 111.807 

10.3374 123.5505 123.5064 123.5505 111.7373 

10.5075 123.5097 123.4656 123.5097 111.7001 

10.8129 123.4366 123.3926 123.4366 111.6334 

10.9501 123.4038 123.3598 123.4038 111.6035 

11.0961 123.369 123.325 123.369 111.5717 

11.6971 123.2263 123.1823 123.2263 111.4414 

12.0081 123.1527 123.1088 123.1527 111.3743 

12.0291 123.1495 123.1056 123.1495 111.3714 

12.0292 123.1495 123.1056 123.1495 111.3714 

12.2671 123.1134 123.0695 123.1134 111.3383 

12.3884 123.0949 123.051 123.0949 111.3215 

12.5244 123.0744 123.0305 123.0744 111.3028 

12.6619 122.8905 122.8467 122.8905 111.1349 

12.7589 122.876 122.8322 122.876 111.1217 

12.9495 122.8475 122.8037 122.8475 111.0956 

164
 
Distance 

Test 2 105 

LL 

Test 2 95 

LL 

Test 1 105 

LL 

Test 1 95 

LL 

13.0549 122.8317 122.7879 122.8317 111.0813 

13.3859 122.7809 122.7371 122.7809 111.0349 

13.6541 122.7419 122.6982 122.7419 110.9993 

13.9121 122.7041 122.6603 122.7041 110.9647 

14.1148 122.6746 122.6308 122.6746 110.9378 

14.5219 122.6083 122.5646 122.6083 110.8773 

15.0699 122.5192 122.4756 122.5192 110.796 

15.2599 122.4884 122.4448 122.4884 110.7679 

15.4019 122.4659 122.4223 122.4659 110.7473 

15.5403 122.4441 122.4004 122.4441 110.7274 

15.8453 122.3954 122.3518 122.3954 110.683 

16.1153 122.3521 122.3085 122.3521 110.6435 

17.4453 122.145 122.1015 122.145 110.4545 

17.6035 122.1223 122.0788 122.1223 110.4338 

17.8465 122.0874 122.0439 122.0874 110.4019 

18.2915 122.024 121.9806 122.024 110.3441 

18.4488 122.0015 121.9581 122.0015 110.3235 

18.6148 121.9777 121.9343 121.9777 110.3018 

18.7818 121.9537 121.9103 121.9537 110.2799 

19.1128 121.9063 121.8629 121.9063 110.2366 

19.4183 121.8607 121.8173 121.8607 110.195 

20.0144 121.7853 121.7419 121.7853 110.1261 

20.3923 121.738 121.6947 121.738 110.083 

20.7652 121.6954 121.6522 121.6954 110.0442 

20.9525 121.6736 121.6304 121.6736 110.0243 

21.4666 121.6139 121.5707 121.6139 109.9697 

21.7311 121.583 121.5398 121.583 109.9416 

21.9173 121.5623 121.5191 121.5623 109.9226 

22.0473 121.5547 121.5114 121.5547 109.9157 

22.1883 121.5462 121.503 121.5462 109.908 

22.3543 121.5363 121.4931 121.5363 109.899 

22.4763 121.5295 121.4863 121.5295 109.8928 

22.8133 121.5105 121.4673 121.5105 109.8754 

22.9733 121.5097 121.4665 121.5097 109.8747 

23.1957 121.5082 121.465 121.5082 109.8733 

23.3361 121.5053 121.4621 121.5053 109.8706 

23.3575 121.5049 121.4617 121.5049 109.8702 

23.5515 121.5009 121.4577 121.5009 109.8666 

23.7088 121.4977 121.4545 121.4977 109.8637 

24.0118 121.4916 121.4484 121.4916 109.8582 

24.1251 121.4894 121.4462 121.4894 109.8561 

24.3851 121.4843 121.4411 121.4843 109.8515 

165
 
Distance 

Test 2 105 

LL 

Test 2 95 

LL 

Test 1 105 

LL 

Test 1 95 

LL 

24.6292 121.4793 121.4361 121.4793 109.8469 

24.8032 121.4761 121.4329 121.4761 109.844 

25.0212 121.4719 121.4287 121.4719 109.8401 

25.1302 121.4698 121.4266 121.4698 109.8382 

25.3432 121.4686 121.4254 121.4686 109.8371 

26.3495 121.4512 121.408 121.4512 109.8212 

26.5235 121.4479 121.4047 121.4479 109.8182 

26.9295 121.4395 121.3963 121.4395 109.8106 

27.0567 121.437 121.3938 121.437 109.8083 

27.3222 121.4301 121.3869 121.4301 109.802 

27.3813 121.4281 121.3849 121.4281 109.8002 

27.6828 121.4178 121.3746 121.4178 109.7908 

27.8391 121.4119 121.3688 121.4119 109.7854 

27.9641 121.4076 121.3645 121.4076 109.7815 

28.1491 121.4013 121.3581 121.4013 109.7757 

28.4312 121.3916 121.3485 121.3916 109.7669 

28.6137 121.3871 121.344 121.3871 109.7628 

28.983 121.3785 121.3353 121.3785 109.7549 

29.633 121.3642 121.3211 121.3642 109.7419 

29.925 121.3586 121.3155 121.3586 109.7368 

30.264 121.3554 121.3123 121.3554 109.7339 

30.904 121.3503 121.3072 121.3503 109.7292 

31.183 121.3492 121.3061 121.3492 109.7282 

31.4215 121.3484 121.3053 121.3484 109.7274 

31.6365 121.3481 121.3049 121.3481 109.7271 

31.7505 121.348 121.3049 121.348 109.7271 

31.8455 121.3476 121.3045 121.3476 109.7267 

32.0297 121.3459 121.3027 121.3459 109.7251 

A summary of simulation information for each test, load condition, primary substation 

voltage, and traditional voltage regulation method is displayed in Table 22. This table 

summarizes the significant information collected from each simulation to show how these 

significant data change for each simulation. The data given for each test are: 

•	 Test number 

•	 Primary voltage: 95% or 105% 

•	 Load condition: HL or LL 

•	 Substation transformer LTC tap 

setting (±16) 

•	 Step VR tap settings (±32) 

•	 Capacitor kVArc applied 

•	 Line currents (IA, IB, IC) at Node 

[0] 

•	 Lowest three-phase voltage: VA, 

VB, VC 

•	 Lowest single-phase voltage 

•	 Highest unbalanced current: I2/I1% 

•	 Highest unbalanced voltage: 

V2/V1% 

•	 Kilowatt losses per phase and total 

•	 Kilovar losses per phase and total 

•	 Released capacity per phase and 

total. 

166
 
Table 22. Simulation Summary Data for Tests 1 Through 8 

Lowest 

1Φ

Node 01 Lowest 3Φ Voltage Voltage 

LTC Tap 

Pri. Volt / Reg 

Test No. % Load Tap IA IB IC VA VB VC 

1 95 HL NA 451.10 511.63 498.20 101.10 102.32 102.04 100.81 

1 95 LL NA 208.36 240.56 234.39 109.72 110.18 110.01 109.59 

1 105 HL NA 542.98 614.92 598.73 110.14 111.60 111.22 109.80 

1 105 LL NA 228.26 263.55 256.78 123.06 118.60 117.22 121.20 

2 95 HL 16 539.33 610.54 594.13 109.78 111.21 110.80 109.44 

2 95 LL 16 228.19 263.43 256.63 123.02 118.60 117.22 121.16 

2 105 HL 6 579.58 655.94 638.52 113.75 115.29 114.86 113.39 

2 105 LL 0 228.26 263.55 256.78 123.06 118.60 117.22 121.20 

3 95 HL 16 566.73 640.04 620.83 112.87 113.35 111.81 111.25 

VR (1) 32, 32, 32 

3 95 LL 16 232.26 267.90 260.58 122.89 118.60 117.22 121.79 

VR (1) 14, 14, 14 

3 105 HL 6 608.51 687.11 666.73 117.11 117.64 116.00 115.40 

VR (1) 32, 32, 32 

3 105 LL 0 229.42 264.82 258.19 123.03 118.60 117.22 121.89 

VR (1) 4, 4, 5 

4 95 HL 16 576.90 650.25 626.60 112.49 112.98 111.65 111.10 

VR (1) 32, 32, 32 

VR (2) 16, 13, 13 

4 95 LL 16 232.70 268.15 260.71 122.87 118.60 117.22 121.78 

VR (1) 14, 14, 14 

VR (2) 2, 1, 1 

4 105 HL 6 614.37 692.81 669.94 116.90 117.44 115.92 115.32 

VR (1) 32, 32, 32 

VR (2) 9, 7, 7 

4 105 LL 0 230.08 265.30 258.44 123.00 118.60 117.22 121.93 

VR (1) 4, 4, 5 

VR (2) 3, 2, 2 

5 95 HL 16 529.93 603.50 586.65 110.75 112.16 111.80 110.40 

Cap (1) 900 kVAr 

5 95 LL 14 211.04 245.95 238.81 122.91 118.60 117.22 121.05 

Cap (1) 900 kVAr 

5 105 HL 5 563.43 641.46 623.81 114.12 115.63 115.26 113.75 

Cap (1) 900 kVAr 

5 105 LL -1 212.02 247.12 239.99 123.54 118.60 117.22 121.67 

Cap (1) 900 kVAr 

167 
6 95 HL 16 527.76 603.59 586.63 112.50 113.97 113.78 112.14 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

6 95 LL 13 203.64 237.46 230.10 123.83 118.60 117.22 122.74 

Cap (1) 900 kVAr 

Cap (1) 900 kVAr 

6 105 HL 4 554.81 634.37 616.83 115.28 116.83 116.64 114.90 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

6 105 LL -2 204.37 238.34 230.99 124.32 118.60 117.22 123.22 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

7 95 HL 16 524.72 601.75 586.04 114.16 115.66 115.53 113.79 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 95 LL 12 205.36 235.24 228.50 125.76 118.60 117.22 124.29 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 105 HL 3 545.03 624.99 608.99 116.29 117.87 117.76 115.91 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 105 LL -4 204.54 234.33 227.66 125.21 118.60 117.22 123.75 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 HL 16 558.30 636.77 616.27 116.97 117.43 116.20 115.60 

VR (1) 32, 32, 32 

VR (2) 9, 6, 6 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 LL 12 205.19 235.04 228.39 125.77 118.60 117.22 123.47 

VR (1) 0, 0, 0 

VR (2) -1, -1, -1 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 105 HL 3 573.87 651.88 632.58 119.45 120.10 118.73 118.11 

VR (1) 28, 24, 24 

VR (2) 6, 4, 5 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 105 LL -4 203.94 233.47 226.89 125.22 118.60 117.22 123.61 

VR (1) -3, -3, -3 

VR (2) 1, 0, 0 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

168
 
Highest Highest kW Losses/Φ & Total kVAr Losses/Φ & Total 

Released Capacity % / 

Total 

I2/I1 % V2/V1 % A B C A B C A B C 

100.06 1.32 159.26 131.82 144.29 509.98 664.33 637.60 32.23 32.07 32.03 

435.37 1811.91 32.11 

100.15 1.26 53.79 43.90 53.40 111.47 150.07 146.52 16.88 16.87 16.87 

151.09 408.06 16.87 

100.06 1.43 218.89 180.17 195.86 739.94 959.69 921.89 9.84 9.76 9.72 

594.92 2621.52 9.77 

100.15 1.26 59.67 48.78 58.90 133.79 180.12 175.86 -0.65 -0.66 -0.66 

167.35 489.77 -0.66 

100.06 1.44 218.28 179.34 197.37 768.13 992.13 951.65 10.29 10.25 10.25 

594.99 2711.91 10.26 

100.15 1.26 60.03 48.98 59.62 140.56 188.56 183.80 -0.79 -0.79 -0.78 

168.63 512.92 -0.79 

100.06 1.48 246.50 202.37 220.58 859.41 1111.33 1067.28 -0.10 -0.13 -0.15 

669.45 3038.02 -0.13 

100.15 1.26 59.67 48.78 58.90 133.79 180.12 175.86 -0.65 -0.66 -0.66 

167.35 489.77 -0.66 

100.06 1.49 240.17 192.88 208.79 856.27 1101.07 1048.32 5.73 5.91 6.22 

641.84 3005.66 5.96 

100.15 1.26 61.32 49.78 60.28 145.82 195.31 189.69 -2.59 -2.50 -2.33 

171.38 530.82 -2.47 

100.06 1.52 271.04 217.50 233.26 956.33 1231.29 1173.85 -5.10 -4.88 -4.58 

721.80 3361.47 -4.85 

100.15 1.26 59.99 49.02 59.15 135.22 181.91 177.88 -1.16 -1.14 -1.21 

168.16 495.01 -1.17 

100.06 1.44 251.98 196.59 210.46 894.06 1146.18 1070.86 4.04 4.41 5.35 

659.03 3111.10 4.62 

100.15 1.26 61.52 49.75 60.31 146.51 195.74 189.85 -2.79 -2.59 -2.38 

171.58 532.10 -2.58 

100.06 1.48 278.24 219.52 234.25 979.06 1257.47 1186.79 -6.11 -5.75 -5.08 

732.01 3423.32 -5.64 

100.15 1.26 60.29 49.03 59.19 136.17 182.72 178.21 -1.45 -1.33 -1.31 

168.51 497.10 -1.36 

100.06 1.42 215.79 182.39 200.36 752.38 977.98 941.40 11.85 11.28 11.38 

598.54 2671.76 11.49 

100.15 1.26 56.68 47.82 58.36 124.56 167.85 165.15 7.91 7.04 7.35 

162.86 457.56 7.41 

100.06 1.45 238.77 201.82 219.42 821.34 1069.08 1030.55 3.31 2.72 2.78 

660.01 2920.97 2.92 

100.15 1.26 56.63 47.95 58.06 120.21 162.41 160.21 7.14 6.25 6.55 

162.64 442.83 6.62 

169
 
100.06 1.36 213.16 187.86 201.94 739.70 973.85 939.19 12.21 11.27 11.39 

602.96 2652.74 11.60 

100.15 1.26 53.44 47.69 57.06 113.31 153.72 152.76 11.68 10.80 11.28 

158.19 419.79 11.23 

100.06 1.38 231.00 203.74 216.63 786.79 1037.76 1002.45 5.41 4.41 4.50 

651.37 2827.00 4.75 

100.15 1.26 53.28 47.79 56.74 109.03 148.31 147.93 11.09 10.19 10.66 

157.81 405.27 10.63 

100.06 1.31 214.50 191.42 207.62 735.61 974.26 940.81 12.72 11.54 11.48 

613.54 2650.68 11.88 

100.15 1.26 54.09 47.32 57.86 116.29 151.68 151.31 11.49 12.18 12.44 

159.27 419.28 12.06 

100.05 1.33 227.32 203.40 218.10 761.52 1011.00 978.17 7.68 6.44 6.32 

648.82 2750.69 6.79 

100.15 1.26 53.41 47.01 57.10 109.99 143.76 144.07 12.23 12.90 13.15 

157.52 397.82 12.78 

100.06 1.31 242.97 207.48 220.18 843.99 1105.93 1049.85 7.13 6.39 6.91 

670.63 2999.77 6.80 

100.15 1.26 54.02 47.28 57.86 116.06 151.36 151.16 11.56 12.25 12.48 

159.16 418.58 12.12 

100.05 1.27 252.36 214.40 228.29 854.80 1111.50 1061.88 2.80 2.42 2.70 

695.05 3028.18 2.63 

100.15 1.26 53.29 46.80 56.98 109.40 142.70 143.05 12.49 13.22 13.44 

157.07 395.15 13.07 

170
 
Because line-to-line loads and line-to-neutral single-phase loads create a 100% load 

imbalance at that node on the circuit, the highest load imbalance data are not very 

meaningful. For proof of 100% load imbalance, see Appendix B.2. 

Therefore, a separate load imbalance, Table 23, was assembled to show the imbalance at 

Node 0 and at the source of the circuit and the range of imbalance throughout the circuit (low 

to high excluding 100%). 

171
 
Table 23. Simulation Summary Data for Unbalanced Loading (Tests 1 Through 8) 

I2 / I1% 

Test No. Pri. Volt % Load 

LTC Tap / 

Reg Tap Node 01 Low 

High 

(<100) Max 

1 95 HL NA 3.77 1.0444 88.45 100.06 

1 95 LL NA 4.72 2.4117 85.38 100.15 

1 105 HL NA 3.73 1.1119 88.42 100.06 

1 105 LL NA 4.72 2.4123 85.38 100.15 

2 95 HL 16 3.70 1.1098 88.41 100.06 

2 95 LL 16 4.71 2.399 85.38 100.15 

2 105 HL 6 3.71 1.1348 88.40 100.06 

2 105 LL 0 4.72 2.4123 85.38 100.15 

3 95 HL 16 3.59 1.1817 88.42 100.06 

VR (1) 32, 32, 32 

3 95 LL 16 4.66 2.3741 85.38 100.15 

VR (1) 14, 14, 14 

3 105 HL 6 3.60 1.1907 88.41 100.06 

VR (1) 32, 32, 32 

3 105 LL 0 4.71 2.4308 85.38 100.15 

VR (1) 4, 4, 5 

4 95 HL 16 3.44 0.9068 88.46 100.06 

VR (1) 32, 32, 32 

VR (2) 16, 13, 13 

4 95 LL 16 4.63 2.3226 85.38 100.15 

VR (1) 14, 14, 14 

VR (2) 2, 1, 1 

4 105 HL 6 3.51 1.0169 88.44 100.06 

VR (1) 32, 32, 32 

VR (2) 9, 7, 7 

4 105 LL 0 4.67 2.3681 85.38 100.15 

VR (1) 4, 4, 5 

VR (2) 3, 2, 2 

5 95 HL 16 3.87 0.7447 88.41 100.06 

Cap (1) 900 kVAr 

5 95 LL 14 5.11 0.291 85.39 100.15 

Cap (1) 900 kVAr 

5 105 HL 5 3.88 0.747 88.41 100.06 

Cap (1) 900 kVAr 

5 105 LL -1 5.12 0.2758 85.39 100.15 

172
 
Cap (1) 900 kVAr 

6 95 HL 16 4.02 0.7303 88.43 100.06 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

6 95 LL 13 5.38 0.25 85.40 100.15 

Cap (1) 900 kVAr 

Cap (1) 900 kVAr 

6 105 HL 4 4.03 0.727 88.43 100.06 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

6 105 LL -2 5.38 0.2343 85.41 100.15 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

7 95 HL 16 4.18 0.701 88.45 100.06 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 95 LL 12 5.44 0.1901 85.43 100.15 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 105 HL 3 4.19 0.6916 88.45 100.05 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 105 LL -4 5.44 0.1729 85.44 100.15 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 HL 16 3.89 0.6814 88.49 100.06 

VR (1) 32, 32, 32 

VR (2) 9, 6, 6 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 LL 12 5.45 0.1907 85.43 100.15 

VR (1) 0, 0, 0 

VR (2) -1, -1, -1 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 105 HL 3 3.80 0.6566 88.50 100.05 

VR (1) 28, 24, 24 

VR (2) 6, 4, 5 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 105 LL -4 5.42 0.171 85.44 100.15 

VR (1) -3, -3, -3 

VR (2) 1, 0, 0 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

173
 
Finally, Appendix B contains selected simulation data by node for each item listed. 

6.2.1	 Heavy Load Circuit Voltage Profiles (First Set 95% and 105% 

Primary Voltage)

Figure 103 shows the voltage profiles for each test, 1 through 8, at 105% and 95% substation 

primary voltage and HL condition. The figure shows a vast range of voltage spread (highest to 

lowest) throughout the circuit. The voltages shown are located at the secondary of the circuit 

distribution transformer. Therefore, an additional 3 V have been added to Range A (i.e., 114 

V + 3 V = 117 V) for a minimum acceptable level of 117 V and a maximum acceptable level 

of 129 V (126 V + 3 V = 129 V). This addition accounts for the voltage drop in the secondary 

and service drop to the customer because Range A of ANSI Standard C84.1 is the voltage at 

the customer’s meter. The regulated voltage is to remain within these maximum and 

minimum values of 129 V and 117 V. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V)
 

128
 

123 

118
 

MIN (117 V)
 

113 

108 

103 

98 

93 

88 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Test 8 105 HL 

Test 8 95 HL 

Test 7 105 HL 

Test 7 95 HL 

Test 6 105 HL 

Test 6 95 HL 

Test 5 105 HL 

Test 5 95 HL 

Test 4 105 HL 

Test 4 95 HL 

Test 3 105 HL 

Test 3 95 HL 

Test 2 105 HL 

Test 2 95 HL 

Test 1 105 HL 

Test 1 95 HL 

Volts 

Figure 103. HL circuit voltage profiles for all tests 

(first set – 95% and 105% substation primary voltage) 

In Table 24, the voltage spread throughout the circuit for Test 1 has a range of 25.2 V 

with no LTC regulation. For Test 8, it is only 10.4 V with all methods of regulation. As more 

regulation is sequentially added to the circuit, the voltage spread reduces. 

174
 
Table 24. HL Circuit Voltage Profiles (First Set) 

Test No. Substation Primary Voltage 

Spread and Load Condition Voltage Regulation Method 

Voltage Spread 

Highest 

ThreePhase 

Lowest 

SinglePhase 

Test 1 95%, 105%, HL No LTC 126.01 100.81 

Test 2 95%, 105%, HL LTC 126.08 109.44 

Test 3 95%, 105%, HL LTC, VR 1 126.00 111.25 

Test 4 95%, 105%, HL LTC, VR 1, VR 2 126.00 111.10 

Test 5 95%, 105%, HL LTC, CAP 1 126.05 110.40 

Test 6 95%, 105%, HL LTC, CAP 1, CAP 2 126.00 112.14 

Test 7 95%, 105%, HL LTC, CAP 1, CAP 2, CAP 3 126.20 113.79 

Test 8 95%, 105%, HL LTC, VR 1, VR 2 

CAP 1, CAP 2, CAP 3 126.00 115.6 

In the individual voltage profiles for Test 1, Figure 104, the voltage spread because of the 

10% change (95% to105%) in the substation primary voltage is 9.05 V (or 110.15–101.1 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 1 105 HL 

Test 1 95 HL 

MAX (129 V) 

MIN (117 V) 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 104. Test 1 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (no LTC) 

175
 
For Test 2, Figure 105 shows a significant improvement in voltage spread with the addition of 

the LTC at the substation, even though the primary substation voltage spread is 10%. Here, 

the spread is only 3.97 V (or 113.76 V–109.79 V). Because the deadband for the LTC is ±1 V, 

the spread could be as much as 5.97 V. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 2 105 HL 108 Test 2 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 105. Test 2 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC) 

176
 
Test 3, Figure 106, shows the benefit of adding the first step VR. The voltage profile with 

105% primary voltage bumps the tag end voltage up to 118.04 V, and with a 95% primary 

voltage, the tag end voltage is 113.9 V. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 3 105 HL 

Test 3 95 HL 

MAX (129 V) 

MIN (117 V) 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 106. Test 3 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC and VR 1) 

177
 
When two step regulators are added, as in Test 4 (Figure 107), the tag end voltage at Node 17 

reaches almost 124.67 V with 105% primary voltage, but at 95% primary voltage, this 

becomes 125.24 V. At Node 8 with a primary voltage of 95%, the voltage gets down to 

112.34 V. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 4 105 HL 

108 Test 4 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 107. Test 4 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC, VR 1, and VR 2)
 

178
 
Test 5 uses the LTC at the substation transformer and Capacitor 1, located at Node 6, which 

has a reactive capability of 900 kVArc to improve the voltage regulation. Notice that the rate 

of change of voltage drop (or slope) in Figure 108 is less than that of Test 4 from the 

substation to Node 8 because of the addition of the capacitor and less reactive current. 

However, the voltage improvement compared with the two-step regulator test is considerably 

less. The tag end voltage at Node 17 is 114.13 V for 105% primary voltage and 110.76 V for 

95% primary voltage. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 5 105 HL 

108 Test 5 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 108. Test 5 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC and CAP 1)
 

179
 
Test 6 results, shown in Figure 109, are based on two capacitors (1 and 2) located at nodes 6 

and 12 of Figure 102 and the LTC transformer to regulate the circuit voltage. Here, the 

voltage gradient is less than that of Test 5 because of the additional capacitor (2), and the tag 

end voltage at Node 17 is 112.51 V compared with 110.76 V for Test 5 at 95% primary 

voltage. It is common to gain about 2 V with the addition of the second capacitor. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 6 105 HL 

108 Test 6 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 109. Test 6 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC, CAP 1, and CAP 2)
 

180
 
Test 7 involves the LTC and three capacitors. Its results are shown in Figure 110. These 

capacitors consist of a 900 kVArc at Node 6 (Capacitor 1), a 900 kVArc at Node 12 

(Capacitor 2), and a 1,200 kVArc at Node 13 (Capacitor 3). Now, the tag end voltage is up to 

114.17 V at 95% primary voltage. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 7 105 HL 

108 Test 7 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 110. Test 7 HL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC, CAP 1, CAP 2, and CAP 3)
 

181
 
Test 8, which uses all forms of regulation (i.e., the LTC, two step regulators, and three 

capacitors), yields the best overall voltage profile with the lowest voltage at Node 8 of 116.53 

V. The tag end voltage of 125.47 V is almost 11 V (10.96 V) more than that of Test 7 with 

three capacitors and a primary voltage of 95%. See Figure 111. With105% primary voltage, 

the lowest voltage of 118.99 V occurs at Node 8, just ahead of the first step regulator. Test 8 

is the only voltage profile under HL conditions that almost meets a minimum voltage criteria 

of 117 V (actual minimum = 116.53 V); all other profiles fail. This indicates a need for DG to 

add more regulation at Node 10, where the 1,000-kW synchronous generator is sited. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 8 105 HL 

108 Test 8 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 111. Test 8 HL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3) 

6.2.2	 Heavy Load Comparison Circuit Voltage Profiles (Second Set 95% 

Primary Voltage)

Because it is difficult to see how each voltage regulation method taken in succession 

improves the voltage profile, voltage profile comparisons A through F are given in Figure 112 

through Figure 118. The comparisons are also provided in Table 25 at 95% primary voltage. 

182
 
Table 25. Voltage Profile Comparison for HL and 95% Primary Voltage 

F 

Test 2
 95% HL LTC 

VR 1 Test 3 95% HL LTC 

Test 4
 

D 

B 

A 

C 95% HL LTC VR 1, VR 2 

CAP 1 Test 5 95% HL LTC 

CAP 1, CAP 2 Test 6 95% HL LTC 

E Test 7
 95% HL LTC CAP 1, CAP 2, CAP 3 G 

Test 8 95% HL LTC VR 1, VR 2, CAP 1, CAP 2, CAP 3 

Comparison A, of Tests 2 and 3, is depicted in Figure 112. The Node 17 voltage
 

improvement, from adding the first step regulator, is 4.11 V. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17
 

MAX (129 V)
 

128
 

123
 

118
 

MIN (117 V)
 

113
 

Test 3 95 HL
 108
 Test 2 95 HL
 

103
 

98
 

93
 

88
 

Volts

0 5 10 15 20 25 30 35
 

Distance from Substation (1000 ft) 

Figure 112. Comparison A: Test 2 and Test 3 HL circuit voltage profiles 

for 95% substation primary voltage (LTC versus LTC and VR 1) 

183
 
When the second regulator is added (Comparison B), the tag end voltage, shown in Figure 

113 at Node 17, goes up to 125.24 V, for a gain of 11.34 V. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 4 95 HL 

Test 3 95 HL 

MAX (129 V) 

MIN (117 V) 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 113. Comparison B: Test 3 and Test 4 HL circuit voltage profiles 

for 95% substation primary voltage (LTC and VR 1 versus LTC, VR 1, and VR 2) 

184
 
As seen from Comparison C in Figure 114, the addition of the first capacitor for Test 5 

marginally increases the voltage at Node 17 by 0.97 V (110.76–109.79 V). 

Voltage Profiles 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 114. Comparison C: Test 2 and Test 5 HL circuit voltage profiles 

for 95% substation primary voltage (LTC versus LTC and CAP 1) 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 5 95 HL 

Test 2 95 HL 

MAX (129 V) 

MIN (117 V) 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

185
 
Comparison D, for Tests 5 and 6, shows the voltage improvement from adding the second 

capacitor. Figure 115 at Node 17 shows a 1.75-V improvement. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 6 95 HL 

Test 5 95 HL 

MAX (129 V) 

MIN (117 V) 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 115. Comparison D: Test 5 and Test 6 HL circuit voltage profiles 

for 95% substation primary voltage (LTC and CAP 1 versus LTC, CAP 1, and CAP 2) 

186
 
Comparison E, Figure 116, shows a voltage rise at Node 17 of only 1.66 V with the addition 

of the third capacitor. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 7 95 HL 

Test 6 95 HL 

MAX (129 V) 

MIN (117 V) 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 116. Comparison E: Test 6 and Test 7 HL circuit voltage profiles for 95% substation 

primary voltage (LTC, CAP 1, and CAP 2 versus LTC, CAP 1, CAP 2, and CAP 3) 

187
 
Comparison F shows the greatest improvement when Test 2, with the LTC, is compared with 

Test 8, with all methods of regulation. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 8 95 HL 108 Test 2 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 117. Comparison F: Test 2 and Test 8 HL circuit voltage profiles for 95% substation 

primary voltage (LTC vs. LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3) 

At Node 17 of Figure 117, the voltage difference between the two tests is 15.35 V (125.14– 

109.79 V). Of course, there are lower voltage gains at Node 8 and Node 14, which are the 

voltages at the points just before the first and second step regulators. 

188
 
Comparison G of Figure 118 shows the difference of voltage between Test 7 (with the LTC 

and all capacitors on) and Test 8 (with all methods of regulation on). The voltage 

improvement at Node 17 is 10.97 V (125.14–114.17 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

MAX (129 V) 

128 

123 

118 

MIN (117 V) 

113 

Test 8 95 HL 

108 Test 7 95 HL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 118. Comparison G: Test 7 and Test 8 HL circuit voltage profiles for 95% substation
 

primary voltage (LTC, CAP 1, CAP 2, and CAP 3 versus 

LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3)
 

6.2.3	 Voltage Profile Data as a Function of Distance from Substation 

to Tag End

Specific data for the highest three-phase and lowest single-phase voltage were provided in 

Table 24 for tests 1–8 at 95% and 105% primary voltage during HL conditions. The distance 

is given in thousands of feet from the substation to the end of the regulation path in Table 20. 

6.2.4	 Light Load Circuit Voltage Profiles (Third Set 95% and 105% Primary 

Voltage)

A process similar to that for the HL voltage profiles is repeated for the LL voltage profiles 

beginning with Figure 119 and ending with Figure 134. The LL circuit is 5.91 MVA 

compared with the LL base case of 5.96 MVA. Even though the LL base case is 5.96 MVA 

compared with the HL base case of 14.89 MVA, there is one test, Test 1 at 95% with no LTC 

regulation, in which the voltage is below the minimum acceptable level of 114.7 V. All the 

rest of the test voltage profiles are above the minimum voltage level. 

189
 
The voltage spread throughout the circuit for Test 1 is shown in Table 26 to be only 16.65 V 

(126.24–109.59 V). This compares to 25.2 V for the same test during HL conditions and no 

LTC regulation. As additional regulation is added to the circuit, the voltage spread diminishes 

to its lowest value of only 2.91 V for Test 8. During the LL period, the highest voltage on the 

circuit reaches 126.38 V. Care should be exercised not to exceed 129 V when operating 

distribution generation near the substation bus or near the load side of any of the two step 

regulators. It may be necessary to operate DG with a strategy to absorb volt-amperes reactive 

to prevent HV during light load. 

Table 26. LL Circuit Voltage Profiles (Third Set) 

Test 

Substation Primary 

Voltage Spread and Load 

Condition 

Voltage Regulation 

Method Voltage Spread 

Highest 

Three-Phase 

Lowest 

Single-Phase 

Test 1 95%, 105%, LL No LTC 126.24 109.59 

Test 2 95%, 105%, LL LTC 126.24 121.16 

Test 3 95%, 105%, LL LTC, VR 1 126.23 121.79 

Test 4 95%, 105%, LL LTC, VR 1, VR 2 126.22 121.78 

Test 5 95%, 105%, LL LTC, CAP 1 126.25 121.05 

Test 6 95%, 105%, LL LTC, CAP 1, CAP 2 126.22 122.74 

Test 7 95%, 105%, LL LTC, CAP 1, CAP 2, CAP 3 126.37 123.75 

Test 8 95%, 105%, LL LTC, VR 1, VR 2, CAP 1, 

CAP 2, CAP 3 

126.38 123.47 

190
 
Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

128 

MAX 126.7 V 

123 

118 

MIN 114.7 V 

113 

108 

103 

98 

93 

88 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Test 8 105 LL 

Test 8 95 LL 

Test 7 105 LL 

Test 7 95 LL 

Test 6 105 LL 

Test 6 95 LL 

Test 5 105 LL 

Test 5 95 LL 

Test 4 105 LL 

Test 4 95 LL 

Test 3 105 LL 

Test 3 95 LL 

Test 2 105 LL 

Test 2 95 LL 

Test 1 105 LL 

Test 1 95 LL 

Volts 

Figure 119. LL circuit voltage profiles for all tests 

(third set – 95% and 105% substation primary voltage) 

191
 
The Test 1 voltage profile shown in Figure 120 shows a uniformly wide voltage spread at 

each node on the circuit as the primary voltage ranges from 95% to 105%. The voltage spread 

at the tag end is 11.62 V (121.35–109.73 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 1 105 LL 

Test 1 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 120. Test 1 LL circuit voltage profiles 

for 95% and 105% substation primary voltage (no LTC) 

192
 
When the LTC is added in Test 2, Figure 121, the voltage spread is still uniform, but it is 

reduced considerably to only 0.05 V (121.35–121.3 V) at Node 17. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 2 105 LL 

Test 2 95 LL 

MAX 126.7 V 

MIN 114.7 V 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 121. Test 2 LL circuit voltage profiles 

for 95% and 105% substation primary voltage (LTC) 

193
 
The Test 3 profile, with the LTC and the first step VR, of Figure 122 shows a 1.68-V spread 

beginning at Node 8 and continuing to the tag end of the circuit. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 3 105 LL 

Test 3 95 LL 

MAX 126.7 V 

MIN 114.7 V 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 122. Test 3 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC and VR 1) 

194
 
Test 4 shows a similar condition when the second regulator is added. As shown in Figure 123, 

there is no voltage spread up to Node 8, and at the tag end, the voltage spread is only 0.9 V. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 4 105 LL 

Test 4 95 LL 

MAX 126.7 V 

MIN 114.7 V 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 123. Test 4 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC, VR 1, and VR 2) 

195
 
Test 5, with the first capacitor on, shows a worsening condition in voltage spread. But the
 

voltage spread at any node of Figure 124 is still very small. It is only 0.62 V 

(121.82–121.2 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17
 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 5 105 LL 

Test 5 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35
 

Distance from Substation (1000 ft) 

Figure 124. Test 5 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC and CAP 1) 

196
 
When the second capacitor is added in Test 6, the voltage profile of Figure 125 shows little
 

change throughout the length of the circuit, and the voltage spread is very low—only 0.48 V 

(123.37–122.98 V) at Node 17. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17
 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 6 105 LL 

Test 6 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35
 

Distance from Substation (1000 ft) 

Figure 125. Test 6 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC, CAP 1, and CAP 2) 

197
 
Test 7, shown in Figure 126 and with the LTC and three capacitors on, is near the ultimate 

voltage regulation test. The voltage profile is nearly at the same level throughout the circuit, 

and the spread is only 0.54 V (124.44 V – 123.9 V = 0.54 V) at Node 17. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 7 105 LL 

Test 7 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 126. Test 7 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC, CAP 1, CAP 2, and CAP 3) 

198
 
Test 8, with all regulation and shown in Figure 127, is the ultimate test. It has no voltage 

spread from Node 8 to Node 17 and a spread of only 0.54 V (124.17–123.63 V) at Node 17. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 8 105 LL 

Test 8 95 LL 

MAX 126.7 V 

MIN 114.7 V 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 127. Test 8 LL circuit voltage profiles for 95% and 105% substation primary voltage 

(LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3) 

199
 
6.2.5	 Light Load Comparison Circuit Voltage Profiles (Fourth Set 95% Primary 

Voltage)

The voltage comparison Test A of Figure 128 shows the improvement in voltage throughout 

the circuit when the first step regulator is added. The voltage profile drops from 126.07 V at 

the source (with the LTC) to 121.31 V at Node 17 for Test 2. When the regulator is added in 

Test 3, the voltage rise at Node 17 is 2.41 V (123.72–121.81 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17
 

128
 

MAX 126.7 V
 

123
 

118
 

MIN 114.7 V
 

113
 

Test 3 95 LL
 108
 Test 2 95 LL
 

103
 

98
 

93
 

88
 

Volts

0 5 10 15 20 25 30 35
 

Distance from Substation (1000 ft) 

Figure 128. Comparison A: Test 2 and Test 3 LL circuit voltage profiles 

for 95% substation primary voltage (LTC versus LTC and VR 1) 

200
 
Comparison B, for Tests 3 and 4, is shown in Figure 129. The profiles of Tests 3 and 4 are the 

same until the second regulator is added. Beyond Node 14, there is a slight voltage spread of 

1.63 V (125.35–123.72 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 129. Comparison B: Test 3 and Test 4 LL circuit voltage profiles 

for 95% substation primary voltage (LTC versus LTC, VR 1, and VR 2) 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 4 95 LL 

Test 3 95 LL 

MAX 126.7 V 

MIN 114.7 V 

201
 
Figure 130 shows Comparison C, in which a slight voltage spread exists throughout 

the circuit. 

Voltage Profiles 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 5 95 LL 

Test 2 95 LL 

MAX 126.7 V 

MIN 114.7 V 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 130. Comparison C: Test 2 and Test 5 LL circuit voltage profiles 

for 95% substation primary voltage (LTC versus LTC and CAP 1) 

202
 
The tests 6 and 5 comparison (D) of Figure 131 shows the rise in voltage at the tag end is 

greater than the rise at the source with the addition of the second capacitor. This is because 

this capacitor reduces the reactive and total current from its location back to the source. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 6 95 LL 

Test 5 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 131. Comparison D: Test 5 and Test 6 LL circuit voltage profiles 

for 95% substation primary voltage (LTC and CAP 1 versus LTC, CAP 1, and CAP 2) 

203
 
When all three capacitors are added, as in Comparison E of Figure 132, the voltage rise (less 

voltage drop) effect is even greater. It shows a nearly level voltage throughout the circuit for 

Test 7. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 7 95 LL 

Test 6 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 132. Comparison E: Test 6 and Test 7 LL circuit voltage profiles for 95% substation 

primary voltage (LTC, CAP 1, and CAP 2 versus LTC, CAP 1, CAP 2, and CAP 3) 

204
 
Comparison F shows the improvement in regulation between using only the LTC of Test 2 

and all the regulation of Test 8. The difference in voltage at Node 17 in Figure 133 is 2.32 V 

(123.72–121.3 V). 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17
 

88 

93 

98 

103 

108 

113 

118 

123 

128 

Volts

Test 8 95 LL 

Test 2 95 LL 

MAX 126.7 V 

MIN 114.7 V 

0 5 10 15 20 25 30 35
 

Distance from Substation (1000 ft) 

Figure 133. Comparison F: Test 2 and Test 8 LL circuit voltage profiles for 95% substation 

primary voltage (LTC versus LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3) 

205
 
Comparison G, shown in Figure 134, shows the effect of adding the two regulators to the 

three capacitors of Test 7. The voltage is more uniform throughout the circuit for Test 7 than 

it is with the two regulators added in Test 8. But, as stated earlier, the voltage spread is better 

with the two regulators turned on when the primary voltage ranges from 95% to 105%. 

Voltage Profiles 

Node 1 Node 3 Node 8 Node 11 Node 14 Node 17 

128
 

MAX 126.7 V
 

123 

118 

MIN 114.7 V 

113 

Test 8 95 LL
 108
 Test 7 95 LL 

103 

98 

93 

88 

Volts

0 5 10 15 20 25 30 35 

Distance from Substation (1000 ft) 

Figure 134. Comparison G: Test 7 and Test 8 LL circuit voltage profiles 

for 95% substation primary voltage (LTC, CAP 1, CAP 2, and CAP 3 

versus LTC, VR 1, VR 2, CAP 1, CAP 2, and CAP 3) 

6.3 Distribution Circuit Simulation Summary Data for Tests 1– 8 

As noted earlier, for each test, summary data were assembled (see Table 22). These data 

consist of the primary voltage (either 95% or 105%), load condition (either HL or LL), tap 

settings for the LTC and step regulators, line currents at Node 0, the lowest three-phase 

voltage, the lowest single-phase voltage, the highest load imbalance, the highest voltage 

imbalance, the kilowatt losses per phase and total, the kilovar losses per phase and total, and 

the release capacity per phase and total when the capacitors are applied. Because the 

maximum imbalance load can be 100% for any line-to-line load connected to the wye system, 

Table 23 is provided to show the range of unbalance other than 100%. 

6.3.1 Unbalanced Voltage 

Unbalanced voltage is determined by calculating the negative sequence V2 and positive 

sequence V1 and dividing V2 by V1. Table 22 shows the highest unbalanced voltage in percent 

for each test. The voltage unbalance is very important for siting DG because most 

synchronous generators trip when the unbalance reaches 3%. The highest unbalanced voltages 

on the circuit range from 1.52% to 1.26%. The highest unbalanced voltages for each test are 

shown in Table 27. 

206
 
It is interesting to note that the highest measured imbalance from the unbalance voltage 

survey of Section 4.5.1.2 and Table 9 was 5.94% with the average being 0.83% for wye and 

closed delta transformer connections. Although these measured data are taken on the 

secondary side of the distribution transformers, whereas the simulated data are for the primary 

in Table 27, there is reasonably close agreement—especially when one considers the data in 

Table 27 are for one circuit while the measured data are for a large population of 1,209 tests 

across a multiplicity of circuits from 13 utilities. 

Table 27. Highest Unbalanced Voltages 

Regulation Method 95% HL 95% LL 105% HL 105% LL 

Test 1 No LTC 1.32% 1.26% 1.43% 1.26% 

Test 2 LTC 1.44% 1.26% 1.48% 1.26% 

Test 3 LTC, VR 1 1.49% 1.26% 1.52% 1.26% 

Test 4 LTC, VR 1, VR 2 1.44% 1.26% 1.48% 1.26% 

Test 5 LTC, CAP 1 1.42% 1.26% 1.45% 1.26% 

Test 6 LTC, CAP 1, CAP 2 1.36% 1.26% 1.38% 1.26% 

Test 7 LTC, CAP 1, CAP 2, CAP 3 1.31% 1.26% 1.33% 1.26% 

Test 8 LTC, VR 1, VR 2, CAP 1, CAP 2, CAP 3 1.31% 1.26% 1.27% 1.26% 

Notice that all the unbalanced voltages are greater during HL conditions. Increasing the 

voltage increases the load, and thus, the unbalance increases. Adding an LTC increased the 

voltage unbalance from 1.32% to 1.44% at 95% HL. Another finding was that the highest 

unbalanced voltages occur at 105% primary voltage, as would be expected. In fact, with no 

LTC, the voltage unbalance at 105% primary voltage was 1.43% versus 1.32% at 95% 

primary voltage. Lowering the primary voltage to 95% reduced the voltage unbalance because 

of the effect of the VDC source model. Adding capacitors reduced the unbalanced voltage, 

and adding a step VR increased the unbalance from 1.44% with the LTC up to 1.49% with 

one step regulator and a 95% primary voltage. 

When the LTC and all three capacitors were on, the voltage unbalanced was reduced to 1.31% 

at 95% primary voltage and down to 1.33% at 105% primary voltage. The highest unbalanced 

voltage on the circuit was reduced to 1.31% with all regulation. It is obvious from these 

results that the voltage regulation method and the amount of regulation on the circuit are 

important in reducing the imbalance to acceptable levels. 

207
 
6.3.2 Unbalanced Loading

Table 23 summarizes the load imbalance for each test. It is calculated as the negative sequence 

load I2 divided by the positive sequence load I1 in percent. Most synchronous generators trip 

when the load imbalance becomes more than 10%–20%. However, inverter-based generation has 

been tested and successfully operated even when the unbalance reached 100%. However, the 

total capability was reduced to 75%. The data in Table 23 show there are locations on the circuit 

where the unbalanced load was greater than 10%–20%. Care should be given to discover the 

magnitude of unbalanced load before a synchronous generator is sited on the circuit. At Node 10, 

where the 1,000-kW generator is interconnected to the distribution circuit, the load unbalance is 

1.22% for 95% primary voltage and HL, and when all regulation is turned on, the voltage 

unbalance is 1.29%. Notice from Table 23 that the load unbalance is always higher at LL than 

HL. This is good because most DR operate during peak load conditions. 

The load imbalance at the substation Node 01 ranges from about 4% for HL and about 5.45% 

at LL. This is an excellent location to site synchronous generators. There are points on the 

circuit where the load unbalance is lower than at the substation, but there are many points 

where the imbalance is up to 90%. Adding regulation did not necessarily improve load 

imbalance. In fact, with all regulation on, the Node 10 value was 3.89% at 95% primary 

voltage versus 3.77% with no regulation and HL conditions. 

6.4 Significant Results and Conclusions 

The Milford Circuit DC 8103 is typical of residential and light commercial load characteristics. 

•	 The CC load model, the CP load model, and the VDC load model were applied in tests 

7 and 8 at 95% source voltages for HL conditions. However, as shown in Appendix 

B.1, the VDC model was better than the CC model (i.e., 2.0% error versus 5.3%). 

Therefore, the best overall method to represent the load characteristics as a function of 

source voltage changes was the VDC model. 

Heavy Load 

•	 The highest voltage spread, measured as the difference between the highest threephase voltage and the lowest single-phase voltage, was 25.2 V and occurred with no 

LTC regulation at the substation transformer during HL conditions and with the 

primary voltage on the substation transformer ranging from 95% to 105%. This spread 

was reduced to 10.4 V with all regulation methods turned on. 

•	 When the LTC and first step regulator were added, the tag end voltage improved 4.11 

V, and with the second regulator turned on, the voltage increased another 11.34 V. 

•	 When the LTC and first capacitor were added, the voltage increased only 0.97 V, and 

with the addition of the second capacitor, the voltage gain was 1.75 V at the tag end. 

The third capacitor added another 1.66 V rise at the tag end. 

•	 When all regulation was turned on, the tag end voltage improvement was 15.35 V over 

only the LTC transformer to regulate voltage. Also, when DR are added to the circuit, 

this method of voltage regulation reduces the voltage spread even further. 

208
 
Light Load 

•	 During LL and no LTC regulation, the voltage spread, as determined by subtracting 

the highest three-phase voltage from the lowest single-phase voltage, was 16.65 V 

compared to 25.2 V for HL. With all regulation turned on, this difference diminished 

to 2.91 V. 

•	 Care should be exercised when operating DR during LL because the highest threephase voltage on the Milford Circuit was 126.24 V. It may be necessary to operate DR 

to absorb volt-amperes reactive to prevent HV. 

Unbalanced Conditions 

•	 Raising the source voltage during HL conditions with the LTC and a step regulator 

turned on created the highest unbalance voltage of 1.52%. Most synchronous 

generators trip at unbalanced voltages more than 3%. Studies should always be 

conducted to ensure the unbalanced voltage does not exceed 3% at the point of 

interconnection (not point of common coupling) for the DR. Of course, if an isolation 

transformer is installed at the point of interconnection with a delta-wye transformer 

connection, it will improve the voltage unbalance seen by the generator. 

•	 Adding the LTC regulation at HL and 95% primary substation voltage lowered the 

maximum unbalance voltage to 1.44%. Adding a step regulator worsened the 

unbalanced voltage by raising it to 1.49%, but adding a second step regulator reduced 

the unbalanced voltage to 1.44%. 

•	 Adding capacitors reduced the maximum unbalanced voltage. The first capacitor 

turned on lowered this unbalanced voltage to 1.42%. With both capacitors turned on, 

the unbalanced voltage went down to 1.36%. All three capacitors turned on lowered 

the unbalance to 1.31%. 

•	 Having all regulation turned on lowered the maximum unbalanced voltage to 1.31% 

for 95% primary voltage and HL (worst-case condition). The 13-utility unbalanced 

voltage survey showed the maximum measured voltage unbalance of 5.94%. 

•	 The highest voltage unbalance during LL was 1.26%, even though the primary voltage 

on the transformer ranged from 95% to 105%. 

•	 At many locations on the circuit, the current imbalance exceeded 20%. Most 

synchronous generators trip between 10% and 20% current imbalance. Inverter-based 

generation can operate under 100% load imbalance, but typically, they do so at 75% of 

rated capacity. The greatest unbalance current was 100% at locations where line-toline loads or line-to-neutral loads were connected to the three-phase, wye-grounded 

system. Unbalances of 20%–90% were apparent at many nodes, but, generally, the 

load magnitudes were small and, thus, not causing the generator to trip. The greater 

load imbalances occurred at LL. 

209
 
•	 The current imbalance at Node 10, where the 1,000-kW synchronous generator is 

interconnected, was 1.22% during HL conditions, and the voltage unbalance was 

1.29%. Even the load imbalance at the substation was about 4% at HL but reached 

about 6% at LL. If a DR is installed at the substation and operated in an isolated mode 

(i.e. as a microgrid), it may see 10% current imbalance during LL. However, on other 

circuits on the system, the load imbalance at the substation could be as high as 20%. It 

is important to determine the imbalanced current at the point of interconnection before 

ever siting a synchronous DR generator. 

•	 The zero sequence current ranged from 45.43 A to 50.24 A for the simulations 

conducted. See Table B-3. This level of zero sequence current is not a problem from a 

system standpoint, but when the system is lost, a portion of the circuit is operated as a 

microgrid or island, and there are line-to-neutral loads and line-to-line loads, high 

negative sequence currents can be expected. When the wye ungrounded synchronous 

generator windings are connected to a delta-wye high-side transformer with neutral 

solidly grounded, zero sequence currents from a line-to-ground load on one phase of 

the system will create 100% negative sequence currents on the generator windings, or 

the negative sequence current will be equal to the positive sequence current. Most 

small generators are wye ungrounded with a delta-wye high-side transformer and 

grounded neutral connection, so this represents the most common installation. 

Appendix A.3 shows that a generator with only 33.34 A of zero sequence current on 

the high side will see 100% unbalanced currents on the generator windings. The 

negative sequence current is 33% of the full rated three-phase capacity of the 

generator. This will cause the generator negative sequence relays to trip at 10% 

negative sequence current. This means the generator will trip if it serves only 30 A of 

single-phase load, even though the rated current is 100 A per phase of load current. 

Because the other two phases are unloaded, the generator can produce only 1/10 of its 

full rated three-phase machine capacity (i.e., 30 A single-phase load ÷ 300 A threephase capacity). 

210
 
7 Project Results – Design of Field Voltage Regulation and 

Metering Equipment 

7.1 Introduction 

This section defines the equipment installed on Milford Circuit DC 8103 to control voltage 

and the metering equipment used to validate the models. 

7.2 Voltage Regulation Equipment 

Figure 135 shows the locations of the voltage regulation equipment on Milford Circuit DC 

8103. Table 28 describes this equipment. 

Table 28. Voltage Regulation Equipment 

Location Description 

A. 10-MVA delta-wye transformer #1 

Z = 7.02%, 41.57 kV/13.8 kV, 0, ±2.5, ±5.0 high-side setting = 0, low-side setting = ±5, 

LTC + 16 steps + 10%, aN = 3 (See Figure 136) 

B. Three 167-kVA single-phase step VRs, 32 steps 

D. 1,000-kW synchronous generator, 1,050-kW power prime mover, rated output = 1,312 kVA 

@ PF = 0.8, 1,800 rpm, 480 V, 60 Hz, voltage regulation ±5%. 

F.	 (1) 900-kVAr three-phase capacitor, Y-connected, neutral grounded 

G.	 (2) 900-kVAr three-phase capacitor, Y-connected, neutral grounded 

H. (3) 1,200-kVAr three-phase capacitor, Y-connected, neutral grounded 

211
 
. F.

E. 

osercl

G. 

Φ

Φ

M

M 

1 

M

M Φ

1

M Φ

2 

Φ

M Φ

6 

28 

26
 

M Φ 3	 

MTSΦ

Φ

K. J.24

MTS

19 Φ19

L.

MTSΦ 18

Phas e B MTSΦ

Ph ase C h 111V

Phase A I.

MT3Φ

125K16 80K 

17

80K20 80K 40K 65K

21 100K22 15 40KFar End Far End

65K DR

40K 3 - SΦ	 (Study) H.	 23 400 kW Inverter 400 kW Inverter 0 kW Inverter RegulatorsRegulatorsegulators GeneratorGenerator 400 kW Induction 400 kW Induction kW Induction (Study)

MT3Φ 3 43199 17 	 43199 (Study) 1200 kVAr 1200 kVAr 14 2 Generator (Study) Generator (Study) nerator (Study) 13 B. E.

Y, Z P1 P5 MTSΦ 14 900 kVAr 900 kVAr Regulation

M P6 2Path 43244 11 12 8 3Φ

80K10 43090 7 9

43052 C. 43052 C. Midpoint DR Midpoint DRidpoint DR 43095 100K G.

65K 3 M Φ K (actual site) (actual site)actual site) MT3Φ PTS

3 - SΦ 1000 kW

2Φ Regulators Regulators egulators	 Sync. Generator Sync. Generator

M3Φ D. ync. Generator

1

65K	 8 11

A. M3Φ 43283 P

3Φ 3Φ 3Φ

Near EndNear End R F..

DR (Study)DR (Study) R-1 125K R-1 125K 

5 40K65KR-3MT3Φ 65K 0 1 4 3Φ

2 recloser recloser 3-SΦ re scloser 65K 80K 140K

3 mov e ZX

6 1 2Φ

25 L

65K	 900 kVAr 900 kVAr ZX

80K 65K 2Φ

S 3

80K 2Φ 2Φ 40K

80K

L4

26

Note (1):	 Note (2): 2Φ

65K PCC VA, VB, VC 

PCC VA, VB, VC Metering ROC M 3Φ I

A, IB, IC IA, IB, IC MPermanent (SOC) 25K P, Q Installations

28 40K

40K 40K 65K	 DTECH 65K DTECH MeteringMetering 3Φ M

25K(SOC) MTTemporary

Installations 27 1000 kW 1000 kW

Synchronous Machine Synchronous Machine ynchronous Machine

Note (3): Nodes where low voltage, high voltage, highest unbalance voltage, highest unbalanced load and nodes where Note (3): Nodes where low voltage, high voltage, highest unbalance voltage, highest unbalanced load and nodes where

actual values exceed pre-set values (criteria violations) may be different than the nodes indicated above. actual values exceed pre-set values (criteria violations) may be different than the nodes indicated above.

Note (4): The LTC voltage regulator is gang operated using the C phase as reference. Note (4): The LTC voltage regulator is gang operated using the C phase as reference.

Note (5): The "P" reclosure data is sent to midpoint DR consisting of I , IB, IC, VCN, VBN, VCN, kWA, kWB, kW C Note (5): The "P" reclosure data is sent to midpoint DR consisting of I , I , B, IC, VCN, VBN, VCN, kWA, kWB, kWC, A

kVArA, kVArB, kVArC kVArA, kVArB, kVArC

Figure 135. Milford Circuit DC 8103 

212
 
Tie Line Trunk Line Tie Line

8623 3107 2819

Proud Page Cody - Proud

CAP 2 

12 MVAr 

N.O. 

41.57 kV 

Tie Line 

6117 

Placid Tie Line 

6147 

Placid 

Section 

Breaker 

Tie Line 

5831 

"A" Cable "B" Cable 

DC 8066 

13.8 kV 13.2 kV 

PTS 43283 

#1 #2 

0% Fixed 

10 MVA 

ed 

41.57/13.2 kV 

N.O. 

5% Fixed 

10 MVA 

57/13.8 kV 

CAP 2

12 MVAr

N.O.

41.57 kV

Tie Line

6117

Placid T

+10% 

+5% Fix

+10% +10% 

0% Fixed 41.

+

ie Line

6147

Placid

Section

Breaker

Tie Line

5831

"A" Cable "B" Cable

DC 8103 DC 8066

13.8 kV 13.2 kV

PTS 43283

#1 #2

0% Fixed

10 MVA

+5% Fixed

41.57/13.2 kV

N.O.

5% Fixed

10 MVA

10%

0% Fixed 41.57/13.8 kV

Figure 136. Milford substation one-line diagram 

7.3 Major System Protection Equipment

The major system protection equipment is listed in Table 29. It consists of three-phase and 

single-phase reclosers and single-phase sectionalizers. 

Table 29. Major System Protection Equipment 

Location Description 

1. R Three three-phase reclosers – 280 A vacuum V4L, 2A, 2D 

2. P One three-phase recloser – 680 A vacuum VWE, R, C 

3. P5 Three single-phase reclosers – 280 A vacuum V4L, 2A, 2D 

4. P1 Three single-phase reclosers – 280 A vacuum V4L, 2A, 2D 

5. S Three single-phase reclosers – 140 A vacuum V4L, 1A, 3D 

6. L Three single-phase reclosers – 140 A vacuum V4L, 1A, 3D 

7. L4 Three single-phase sectionalizers – 140 A hydraulic 

8. P6 Three single-phase reclosers – 140 A V4L, 2A, 2D 

213
 
Table 30. Measurement Locations and Data Collection 

Permanent Metering Locations 

A. Substation M3Φ VAN, VBN, VCN IA, IB, IC P, Q, PF 

B. Regulators (1) M3Φ VAN, VBN, VCN IA, IB, IC P, Q, PF 

D. 1,000-kW synchronous DR M3Φ VAN, VBN, VCN IA, IB, IC P, Q, PF 

Temporary Metering Locations 

F. 900-kVAr capacitor MT 3Φ VAN, VBN, VCN IA, IB, IC 

G. 900-kVAr capacitor MT 3Φ VAN, VBN, VCN IA, IB, IC 

H. 1,200-kVAr capacitor MT 3Φ VAN, VBN, VCN IA, IB, IC 

I. Three-phase circuit tag end MT 3Φ IA, IB, IC 

K.L. Single-phase tag ends MT SΦ VAN VBN 

7.4 Metering Equipment and Accuracy of Measurements 

7.4.1 Substation Metering 

The substation metering consists of an ION 7600 Power Measurements Meter, which 

measures the three-phase voltages, three line currents, and phase power factors and calculates 

the kilowatts per phase and total kilowatts, kilovars per phase and total kilovars, kilovoltamperes per phase and total kilovolt-amperes, and unbalanced voltage and current. The 

integration period is 15 minutes. The accuracy of the metered data is 0.1% for voltage, 0.1% 

for current, ±0.01 Hz for frequency, and 0.5% for power factor. The kilowatt, kilovar, and 

kilovolt-ampere accuracy is Class 0.2. 

7.4.2 Synchronous Generator Metering 

The generator metering is a 3720 ACM meter that measures the three-phase voltages, three 

line currents, three-phase kilowatts, three-phase kilovars, three-phase kilovolt-amperes, power 

factor, frequency, and circuit load including generation. The data are 30-second samples 

integrated over 5 minutes. The SOC data are 5-minute samples averaged over 15 minutes. The 

accuracy of the measured data is shown in Table 31. 

Table 31. Accuracy of 3720 ACM 

Parameter Accuracy 

Current 

Kilowatts

Kilovars

Kilovolt-amperes

Voltage 

Power factor 

Frequency

0.2% 

0.4% 

0.4% 

0.4% 

0.2% 

1.0% 

 0.05 Hz 

214
 
7.4.3 Capacitor Location Metering 

The metering at the capacitor locations (nodes F, G, and H) is the Line Tracker LT40 from 

Grid Sense. These metering devices measure the three-phase voltages and three line currents. 

The voltage is sampled at 600 samples per second, and the current is sampled at 1,200 

samples per second. The accuracy of the current measurement is ±5%. The integration period 

is 15 minutes. 

7.4.4 Voltage Regulator Locations 

The CL-6 control of the VRs at Location B measures the load and source phase voltages, line 

currents, phase kilowatts, phase kilovars, phase kilovolt-amperes, and phase power factor. 

The data are integrated over 15 minutes, and the accuracy is Class 1 metering or 1% for all 

power quantities (i.e., voltage, current, kilowatts, kilovars, and kilovolt-amperes). 

7.4.5 Single-Phase Voltage Customer Metering 

The Rustrak measured voltage and current. The accuracy is 0.25% for voltage and 0.5% for 

current. Each is in percent of reading. The integration period is 15 minutes. 

215
 
8 Project Results – Distributed Generation Control Strategies 

for Field Verification 

8.1 Introduction 

This section defines the generation equipment voltage regulation capability and the control 

strategies used to regulate voltage on the Milford Circuit DC 8103. 

8.2 1,000-kW Synchronous Generator 

The voltage regulation control capabilities for the 1,000-kW synchronous generator located at 

the midpoint on the circuit Node D is given in Figure 137. 

8.3 400-kW High-Speed Generator and Inverter 

The voltage regulation control capability for the 400-kW high-speed generator and inverter is 

shown in Figure 138. 

8.4 400-kW Self-Excited Induction Generator 

The voltage regulation control capability for the 400-kW self-excited induction generator is 

shown in Figure 139. 

8.5 Voltage Regulation Simulations and Field Verification Strategy 17 

The voltage regulation simulations and Strategy 17 used for field verification is outlined in 

Table 32. 

216
 
I

max. 

a d 

Rated

Fixed P.F. Fixed P.F. 

kVArs

Field

6 Current Current

Limit

1230 kV A

Synchronous Rated kVA and Rated kVA and ated kVA and 2Condensor 3 P.F. = .80P.F. = .80F. = .80

ArmatureArmature 7

Current Limit Current Limit urrent Limit I.

OperatingOperatingperating

1 5 Quadrants I., Quadrants I., uadrants I., 984 kW IV.

246 kW kWs

1050

kW

max.

8 IV.

1

I

f Rated f 4 Xd

I

f Lead

Figure 8.0 DR Control Strategies for 1000 kW Synchronous Machine Figure 8.0 DR Control Strategies for 1000 kW Synchronous Machine gure 8.0 DR Control Strategies for 1000 kW Synchronous Machine

Operating Points

(a) points 1 and2 is rated kW and rated KVArs is rated kW and rated KVArs

(b) point 3 rated kVA and rated lagging P.F. rated kVA and rated lagging P.F.

(c) point (c) point 4 leading P.F.

(d) point 5 maximum kW maximum kW

(e) point 6 minimum kW and maximum kVArs (synchronous condensor) minimum kW and maximum kVArs (synchronous condensor)

(f) points 7 and 8 fixed power factor lagging and leading fixed power factor lagging and leading

Figure 137. DR control strategies for a 1,000-kW synchronous machine 

217
 
+QRated kVA = 400 kVA Rated kVA = 400 kVA

Rated P.F. = 0.8 lag (producin Rated P.F. = 0.8 lag (producing

VArs = +Q = +240 kVArs VArs = +Q = +240 kVArs

Rated kWRated = 320 kW kW = 320 kW

Pmax= 400 kW

Operating

Quadrants

I. and IV. I. and IV.

Rated P.F. = 0.8 lead (absorbing

VArs = -Q = -240 kVArs) VArs = -Q = -240 kVArs)

II 

I 

III 

IV 

-Q 

II

I

III

IV

-Q

Note (4): DR Control Strategies Note (4): DR Control Strategies

(a) Peak Shave P fix (a) Peak Shave P fi exd

(b) P.F. = unity, P variable (b) P.F. = unity, P variable

(c) + P.F. constant, P variabl (c) + P.F. constant, P variable

(d) + Q (VArs volt. reg.) P = (d) + Q (VArs volt. reg.) P = 0

(e) P + jQ (optimizing) - see synchronous machine (e) P + jQ (optimizing) - see synchronous machine

(f) Frequency Dithering (anti-islanding)

Note (5): (f) not included in model Note (5): (f) not included in model

Figure 138. DR control strategies for a 400-kW high-speed generator 

and inverter – current mode 

218
 
Rated kVA = 470.59 kVA +Q 

normal 

Rated P.F. = .85 

-Q 

(a) Peak Shave P fixed 

(b) P.F. = unity, P fixed 

(c) + P.F. constant at P fixed 

(d) + Q fixed, P fixed same as (c) 

Note (4) Induction machine with inverter is the same as Inverter where the speed is 

varied to create variable dc output after the rectifier and the ac current output 

from the inverter is phase shifted (switching) to produce a variable P.F. with 

respect to the system voltage. 

Figure 139. DR control strategies for a 400-kW self-excited induction generator 

switched capacitor 2 

"on" (producing VArs 

= +Q = +247.91 kVArs 

P = 400 kW max 

switched 

capacitor 1 

"on" 

P.F. = .85
 

(absorbing VArs = -Q
 

= -247.91 kVArs)
 

switched 

capacitor 

"off" 

219
 
Table 32. Matrix of Voltage Regulation Simulations 

and Control Strategy 17 for Field Verification 

Test NumbersReference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourly quantities Light Load Day 24 Hourlyquantities LTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (Synchronous Machine) 

Locations (1) 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P variable 

(c) + P.F. Constant, Variable P & 

Q 

(d) + Q (Vars Volt reg) P Min 

(e) P+ jQ (Optimizing) 

(f) Fixed P.F. Anti-island 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 I.A. (a) (d) (f) x x 

2 I.B. (d) (f) x x x 

3 I.C. (d) (f) x x x x 

4 I.C '. (d) (f) x x x x x 

5 I.D (d) (f) x x x x 

6 I.D ' (d) (f) x x x x x 

7 I.D." (d) (f) x x x x x x 

8 I.E. (d) (f) x x x x x x x x 

9 II.A. x x x (b) (d) (e) 

10 II.B. x x x (b) (d) (e) 

11 II.C. x x x (b) (d) (e) 

12 II.D. Repeat IIA., IIB., IIC. turn on LTC 

13 II.E. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) 

14 II.F. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) 

15 II.G. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1) 

16 II.H. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1), (2) 

17 II.I. Repeat IIA., IIB., IIC. turn on LTC, and Regulator (1) and (2) and Cap. (1), (2), (3) 

18 

19 

20 

21 

22 

23 

24 

25 

Note (1): DR Control Strategies 

(a.) The DR is operated at fixed real power output and normally Is scheduled to run during peak periods when 

the cost of DR generation is lower than host utility cost. The Q is zero at the PCC. 984 kW rated 

(b.) The DR is operated at unity P.F. with variable power output. 492 kW (50%) to 1050 kW max. 

(c.) DR is operated at a fixed power factor either lead or lag (for example + 0.8 P.F.) with variable P and Q to 

not violate voltage criteria. 

(d.) The DR is operated as a synchronous condenser with minimum watts and variable VArs to regulate 

voltage. 246 kW (25% of rated) 

(e.) DR is operated with variable P and Q and is used to optimize to a specific set of criteria such as minimize 

real losses, minimize reactive losses, regulate voltage and maximize released capacity. 

220
 
Test Numbers

Reference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourlyquantities Light Load Day 24 Hourly quantitiesLTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (Induction Generator) 

Locations 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P fixed 

(c) + P.F. Constant, P fixed 

(d) + Q fixed, P fixed 

same as (c) 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 (a) (d) (f) 

2 (d) (f) 

3 (d) (f) 

4 (d) (f) 

5 (d) (f) 

6 (d) (f) 

7 (d) (f) 

8 (d) (f) 

9 II.A. x x x (b) (d) 

10 II.B. x x x (b) (d) 

11 II.C. x x x (b) (d) 

12 II.D. Repeat II.A., II.B., II.C. turn on LTC 

13 II.E. Repeat II.A., II.B., II.C. turn on LTC and Regualator (1) 

14 II.F. Repeat II.A., II.B., II.C. turn on LTC and Regulators (1) & (2) 

15 II.G. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) 

16 II.H. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) and (2) 

17 II.I. Repeat II.A., II.B., II.C. turn on LTC, Reg (1) & (2) and Cap (1), (2) & (3) 

18 III. Repeat synchronous and inverter generation 

19 IV. Repeat synchronous, inverter and induction generation 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

221
 
Test Numbers

Reference. Section 

Primary 

Voltage 

Spread 

(a)87% 

(b) 92% 

(c)93% 

(d) 95% 

(e) 98% 

(f) 105% 

Peak Load Day 24 Hourlyquantities Light Load Day 24 Hourly quantitiesLTC + 16 steps & neutral 

Line 

Regulator Capacitors 

DR (Induction Generator) 

Locations 

(a)Peak shave, P fixed 

(b) P.F.= Unity, P fixed 

(c) + P.F. Constant, P fixed 

(d) + Q fixed, P fixed 

same as (c) 

#1 #2 #1 #2 #3 Near End 

Midpoint 

(Actual 

Site) Far End 

1 (a) (d) (f) 

2 (d) (f) 

3 (d) (f) 

4 (d) (f) 

5 (d) (f) 

6 (d) (f) 

7 (d) (f) 

8 (d) (f) 

9 II.A. x x x (b) (d) 

10 II.B. x x x (b) (d) 

11 II.C. x x x (b) (d) 

12 II.D. Repeat II.A., II.B., II.C. turn on LTC 

13 II.E. Repeat II.A., II.B., II.C. turn on LTC and Regualator (1) 

14 II.F. Repeat II.A., II.B., II.C. turn on LTC and Regulators (1) & (2) 

15 II.G. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) 

16 II.H. Repeat II.A., II.B., II.C. turn on LTC, Reg. (1) & (2) and Cap (1) and (2) 

17 II.I. Repeat II.A., II.B., II.C. turn on LTC, Reg (1) & (2) and Cap (1), (2) & (3) 

18 III. Repeat synchronous and inverter generation 

19 IV. Repeat synchronous, inverter and induction generation 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

222
 
9 Project Results – Field Verification of Models 

9.1 Introduction 

This section verifies the models using field test data. Voltage regulation models were 

developed for the LTC transformer at the substation, the bidirectional step regulators, the 

capacitors, all the distribution circuit transformer connections, and the line sections. In 

addition, models for synchronous, induction, and inverter generators were created. 

The field verification was conducted using the metering equipment defined in Section 7 and 

the DG control for the 1,000-kW synchronous generator defined in Section 8. The Strategy 17 

control strategy was used. In it, all three capacitors (1, 2, and 3), the regulator (1), and the 

substation LTC were turned on. 

The field verification studies were conducted for the circuit peak days of July 17, 2006, at 

17:43 and July 29, 2006, at 17:11, when the 1,000-kW DR was running, and on July 31, 2006 

at 17:56, when this DR was turned off. 

9.2 Circuit and Generation Measured Data 

The nodes at which measured data were taken on the circuit and Node D (Node 10), where the 

generation is interconnected with the circuit, are described in Figure 135. The test dates and 

data collection periods are shown in Table 33. 

Table 33. Test Dates and Data Collection Periods 

Generation Start Generation End 

Date 

Circuit 

Start 

Circuit 

Peak 

Circuit 

End 

(Post-Generation 

Start) 

(Pre-Generation 

Off) 

7/17/06 

7/29/06 

7/31/06 

8/02/06 

10:42 

00:11 

00:11 

00:11 

17:43 

17:11 

17:56 

17:56 

23:58 

23:56 

23:56 

23:56 

17:28 

17:11 

10:26 

generator 

21:23 

20:16 

12:16 

Because there is a time delay between the initiation of the “start” generator command and 

when the unit is synchronized and carrying load and a delay between the initiation of the 

“stop” generator command and when the generator is not carrying load, the times given in the 

Table 33 are the post-generation start (the time the unit is carrying load) and the pre-generation 

off (the time the unit is still carrying load but has received the “stop” generator command). 

223
 
Illustrative Example of Generation Run Time and 

Distribution Circuit Time Stamps for Simulation Studies 

and Field Verification 

Load, MVA 

Light Load Pre-generation 

Start 

Post generation 

Start 

Pre-generation 

Off 

Post generation 

Off 24 hr 

Circuit Peak 

Generator 

Run 

0 hr 

Figure 140. Daily circuit load profile and time stamps 

These times are described in Figure 140. As shown in Table 33, there were four days during 

the summer when tests were conducted and four days when measured data were collected. The 

first two days, July 17 and July 29, 2006, the 1,000-kW DG was turned on to offset the circuit 

peak load. On July 31, 2006, this DG was turned off. This was to determine if there is a 

difference in the variance between simulation and field-measured data when the DG was 

running and when it was not. Simulations and comparisons with field-measured data were not 

conducted on the last test day (Aug. 2, 2006) because the load of the South Branch of the 

Milford Circuit DC 8103 was cut over to a circuit fed from the Page Substation on Aug. 1 at 

19:00. This removed approximately 2 MVA of load (i.e., a 15.92 MVA peak prior to cut-over 

versus a 13.98-MVA peak after the cut-over) from the Milford Circuit DC 8103. See Table 34. 

The times of circuit peak data and generation data are given in Table 34 for the four test days. 

The measured data consist of: 

• Circuit peak kilovolt-amperes 

• Circuit phase currents at Substation Node 1 

• Generation line currents at Node 10 

• Generation line-to-line voltages at Node 10 

• Generation three-phase PF at Node 10 

• Generation three-phase kilowatts, kilovars, and kilovolt-amperes at Node 10. 

224
 
9.3 Bidirectional Voltage Regulator Measured Data

The bidirectional VR measured data for the circuit peak time of each test day are given in 

Table 35 and listed below for each phase regulator at Node 9. 

• Load current 

• Load PF 

• Kilowatt load 

• Kilovolt-ampere load 

• Kilovar load 

• Voltage 120-V base 

9.4 Circuit Equipment (Capacitors) and Customer-Measured Data

The measured data at the time of circuit peak for each of the three capacitors at nodes 6, 12, 

and 13 on the respective test days are given in Table 36. They consist of the phase currents 

and phase voltages. Also, the customer-measured data for Node I, which consist of Ia and Ic 

phase currents; Node L and the VC phase voltage; and Node K and the VA phase voltage are 

given in this table. 

9.5 Percent Variance Between Simulated and Field-Measured Data 

Table 37 and Table 38 compare simulated data and field-measured data for the two test days 

when DG was running. Table 39 shows similar data for when the DG was turned off. The 

field data for the phase currents, phase voltages, and phase power factors of the circuit, 

generator, and the VR1 bidirectional regulator are given for Node 1, Node 10, and Node 9 on 

the left. The corresponding simulation data are shown on the right. The measured phase 

currents and phase voltages for the three capacitors and their respective simulation data are 

also given in these tables, but the simulated voltage data have been reduced by 3.67 V to 

reduce the measured primary voltage to secondary voltage values. Finally, customermeasured current and voltage data and simulation data for Nodes I and L are listed. 

Table 40 summarizes the differences between measured and simulated values. For three-phase 

quantities, the percent variance is calculated as the absolute value of the sum of the 

differences between the actual and simulated values divided by three and then divided by the 

average of the actual three-phase values. The result is multiplied by 100 to represent the 

percent difference using the average of the actuals as the base. For single-phase quantities, the 

percent variance is the absolute value of the difference divided by the actual as the base, 

multiplied by 100. 

225
 
Table 34. Circuit and Generation Measured Data 

Circuit Start: 7/17/2006 10:42 End: 7/17/2006 23:58 Generator Start: 7/17/2006 17:28 End: 7/17/2006 21:23 

Circuit Start Circuit Peak 

Date Time East Regulator Phase A North Regulator Phase B South Regul

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load 

7/17/2006 10:42 132.20 0.98 1,039.00 1,021.00 190.00 7,857.51 123.72 126.90 0.99 998.00 984.00 169.00 7,868.23 123.89 120.50 0.98 946.00 92

7/17/2006 17:43 282.60 0.94 2,216.00 2,088.00 742.00 7841.79 123.48 255.70 0.95 2,009.00 1,913.00 612.00 7855.34 123.69 238.00 0.94 1,877.00 1,77

Circuit Start: 7/29/2006 00:11 End: 7/29/2006 23:56
 

Generator Start: 7/29/2006 17:11 End: 7/29/2006 20:16
 Date Time East Regulator Phase A North Regulator Phase B South Regul

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load 

7/29/2006 0:11 157.80 0.89 1,248.00 1,110.00 570.00 7,908.95 124.53 138.80 0.90 1,096.00 991.00 468.00 7,896.23 124.33 143.40 0.88 1,133.00 1,00

7/29/2006 17:11 312.30 0.93 2,464.00 2,286.00 917.00 7887.81 124.20 296.60 0.94 2,331.00 2,190.00 798.00 7859.16 123.75 279.70 0.93 2,195.00 2,04

Circuit Start Circuit Peak 

Circuit Start: 7/31/2006 00:11 End: 7/31/2006 23:56
 

Generator Start: 7/31/2006 16:11 End: 7/31/2006 17:11
 Date Time East Regulator Phase A North Regulator Phase B South Regul

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load 

I 

7/31/2006 0:11 271.10 0.89 2,139.00 1,903.00 977.00 7,891.57 124.26 256.90 0.90 2,029.00 1,829.00 878.00 7,898.27 124.37 241.10 0.89 1,892.00 1,68

7/31/2006 17:56 369.00 0.94 2,882.00 2,695.00 1,021.00 7811.26 123.00 355.00 0.94 2,813.00 2,640.00 971.00 7924.79 124.78 314.00 0.93 2,486.00 2,31

Circuit Start 

Circuit Peak 

Circuit Start: 8/2/2006 00:11 End: 8/2/2006 23:56
 

Generator Start: 8/2/2006 10:26 End: 8/2/2006 12:16
 Date Time East Regulator Phase A North Regulator Phase B South Regul

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load 

8/2/2006 

8/2/2006 

8/2/2006 

0:11 

12:16 

17:56 

116.00 

170.10 

259.70 

0.91 

0.96 

0.93 

917.00 

1,334.00 

2,059.00 

833.00 

1,287.00 

1,924.00 

384.00 

352.00 

734.00 

7,907.76 

7,844.62 

7,929.52 

124.52 123.52 

124.86 

113.00 

154.10 

247.60 

0.91 

0.98 

0.95 

895.00 

1,210.00 

1,950.00 

818.00 

1,185.00 

1,856.00 

361.00 246.00 595.00 

7,914.87 

7,854.76 7,873.08 

124.63 

123.68 123.97 

107.30 149.40 

227.90 

0.89 0.97 

0.94 

845.00 

1,167.00 

1,794.00 

75

1,13

1,69

Circuit Start 

Generator 

Circuit Peak 

August 1st moved south branch to Page Substation at 19:00 

226
 
Table 35. Bidirectional VR Measured Data 

Circuit Start: 7/17/2006 10:42 End: 7/17/2006 23:58
 Generator Start: 7/17/2006 17:28 End: 7/17/2006 21:23
 Date Time East Regulator Phase A North Regulator Phase B S

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load 

7/17/2006 10:42 132.20 0.98 1,039.00 1,021.00 190.00 7,857.51 123.72 126.90 0.99 998.00 984.00 169.00 7,868.23 123.89 120.50 0.98 94

7/17/2006 17:43 282.60 0.94 2,216.00 2,088.00 742.00 7841.79 123.48 255.70 0.95 2,009.00 1,913.00 612.00 7855.34 123.69 238.00 0.94 1,87

Circuit Start Circuit Peak 

Circuit Start: 7/29/2006 00:11 End: 7/29/2006 23:56 

Generator Start: 7/29/2006 17:11 End: 7/29/2006 20:16 

Circuit Start Circuit Peak 

Date Time East Regulator Phase A North Regulator Phase B S

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load 

7/29/2006 0:11 157.80 0.89 1,248.00 1,110.00 570.00 7,908.95 124.53 138.80 0.90 1,096.00 991.00 468.00 7,896.23 124.33 143.40 0.88 1,13

7/29/2006 17:11 312.30 0.93 2,464.00 2,286.00 917.00 7887.81 124.20 296.60 0.94 2,331.00 2,190.00 798.00 7859.16 123.75 279.70 0.93 2,19

Circuit Start: 7/31/2006 00:11 End: 7/31/2006 23:56 Generator Start: 7/31/2006 16:11 End: 7/31/2006 17:11 

Circuit Start Circuit Peak 

Date Time East Regulator Phase A North Regulator Phase B S

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load 

I 

7/31/2006 0:11 271.10 0.89 2,139.00 1,903.00 977.00 7,891.57 124.26 256.90 0.90 2,029.00 1,829.00 878.00 7,898.27 124.37 241.10 0.89 1,89

7/31/2006 17:56 369.00 0.94 2,882.00 2,695.00 1,021.00 7811.26 123.00 355.00 0.94 2,813.00 2,640.00 971.00 7924.79 124.78 314.00 0.93 2,48

Circuit Start: 8/2/2006 00:11 End: 8/2/2006 23:56
 

Generator Start: 8/2/2006 10:26 End: 8/2/2006 12:16
 Date Time East Regulator Phase A North Regulator Phase B S

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load Kva Load KW Load Kvar 

Load 

Voltage 

Load 

Voltage 

120V Base 

Load 

Current 

Load Power 

Factor Load 

8/2/2006 8/2/2006 

8/2/2006 

0:11 

12:16 

17:56 

116.00 170.10 

259.70 

0.91 

0.96 

0.93 

917.00 

1,334.00 

2,059.00 

833.00 

1,287.00 

1,924.00 

384.00 

352.00 

734.00 

7,907.76 

7,844.62 

7,929.52 

124.52 123.52 

124.86 

113.00 154.10 

247.60 

0.91 0.98 

0.95 

895.00 

1,210.00 

1,950.00 

818.00 

1,185.00 

1,856.00 

361.00 

246.00 595.00 

7,914.87 

7,854.76 7,873.08 

124.63 

123.68 123.97 

107.30 

149.40 227.90 

0.89 

0.97 0.94 

84

1,161,79

Circuit Start Generator 

Circuit Peak 

August 1st moved south branch to Page Substation at 19:00 

227
 
Table 36. Circuit Equipment and Customer-Measured Data 

Circuit Start: 7/17/2006 10:42 End: 7/17/2006 23:58 Generator Start: 7/17/2006 17:28 End: 7/17/2006 21:23 

Circuit Start 

Circuit Peak 

Date Time Node F/6 Capacitor 1 (900 Kvar) Node G/12 Capacitor 2 (900 Kvar) Node H/13 Capacito

Phase Currents Phase Voltages Phase Currents Phase Voltages Phase Currents 

Ia Ib Ic Va Vb Vc Ia Ib Ic Va Vb Vc Ia Ib Ic 

7/17/2006 10:42 33.50 62.41 8.37 121.40 120.90 121.55 33.36 11.00 12.35 121.85 121.20 120.90 44.01 21.49 42.76 

7/17/2006 17:43 48.57 108.20 13.00 118.25 117.75 121.08 51.96 14.00 23.83 120.65 118.40 118.65 65.84 27.09 53.70 

Circuit Start 

Circuit Peak 

Date Time Node I Node K Node L 

Ia Ib Ic Va Vc 

7/17/2006 10:42 32.00 - 19.00 - 120.05 

7/17/2006 17:43 46.00 - 31.00 - 117.60 

Circuit Start: 7/29/2006 00:11 End: 7/29/2006 23:56 

Generator Start: 7/29/2006 17:11 End: 7/29/2006 20:16 

Circuit Start Circuit Peak 

Date Time Node F/6 Capacitor 1 (900 Kvar) Node G/12 Capacitor 2 (900 Kvar) Node H/13 Capacito

Phase Currents Phase Voltages Phase Currents Phase Voltages Phase Currents 

Ia Ib Ic Va Vb Vc Ia Ib Ic Va Vb Vc Ia Ib Ic 

7/29/2006 0:11 23.82 47.09 8.78 24.69 5.42 10.78 27.23 12.53 31.53 

7/29/2006 17:11 50.45 103.25 10.34 54.29 13.02 24.72 50.05 18.57 47.97 

Circuit Start: 7/31/2006 00:11 End: 7/31/2006 23:56 Generator Start: 7/31/2006 16:11 End: 7/31/2006 17:11 

Circuit Start Circuit Peak 

Date Time Node F/6 Capacitor 1 (900 Kvar) Node G/12 Capacitor 2 (900 Kvar) Node H/13 Capacito

Phase Currents Phase Voltages Phase Currents Phase Voltages Phase Currents 

Ia Ib Ic Va Vb Vc Ia Ib Ic Va Vb Vc Ia Ib Ic 

7/31/2006 0:11 22.12 44.79 7.74 21.23 5.81 10.16 30.38 14.65 31.88 

7/31/2006 17:56 51.53 108.84 11.78 49.30 14.93 23.96 62.18 27.37 54.05 

Circuit Start: 8/2/2006 00:11 End: 8/2/2006 23:56 Generator Start: 8/2/2006 10:26 End: 8/2/2006 12:16 

Circuit Start Generator 

Circuit Peak 

Date Time Node F/6 Capacitor 1 (900 Kvar) Node G/12 Capacitor 2 (900 Kvar) Node H/13 Capacito

Phase Currents Phase Voltages Phase Currents Phase Voltages Phase Currents 

Ia Ib Ic Va Vb Vc Ia Ib Ic Va Vb Vc Ia Ib Ic 

8/2/2006 8/2/2006 

8/2/2006 

0:11 

12:16 

17:56 

34.58 

37.82 

52.56 

77.96 

86.89 

109.82 

10.80 

12.02 

13.40 

41.65 

42.15 

51.40 

9.95 

13.98 

15.32 

18.72 

18.46 24.46 

47.89 

52.82 52.27 

23.05 

23.95 20.09 

52.07 

50.02 

55.17 

Date Time Node K Node L 

Va Vc 

8/2/2006 

8/2/2006 8/2/2006 

0:11 

12:16 17:56 

119.15 118.25 

-

--

Notes (1): August 1st moved south branch to Page Substation at 19:00 

Circuit Start (2): Voltage Data At Capacitor Locations Not Available from July 26 until August 22 

(3): All Capacitor Phase Voltages Are Measured On The Secondary Side At The Customer's Meter 

Generator (4): All Capacitor Phase Currents Are Measured On The Primary Circuit Peak 

228
 
Table 37. Field Verification Data – July 17, 2006 – DR Generation On 

Field Data - 7/17/06 - Circuit Peak 17:43 Simulation 

Current Voltage PF Current Voltage 

Location Node A B C A B C A B C A B C A B 

Start of Circuit 1 565.00 651.00 637.00 126.00 126.00 126.00 0.95 0.95 0.95 554.54 637.77 619.97 125.86 125.80 

2.2% 0.3% 5.7% 

Generator 10 18.31 17.24 17.00 122.50 122.50 120.25 0.96 0.96 0.96 17.49 17.25 17.36 121.68 123.38 

2.3% 1.1% 0.0% 

VR 1 9 282.60 255.70 238.00 123.48 123.69 124.19 0.94 0.95 0.94 274.07 246.07 227.56 123.60 123.82 

3.7% 0.2% 2.4% 

Cap 1* 6 48.57 108.20 13.00 118.25 117.75 121.08 48.03 104.47 13.77 121.25 121.14 

3.0% 0.7% 117.58 117.47 

Cap 2* 12 51.96 14.00 23.83 120.65 118.40 118.65 52.18 14.87 24.53 120.51 123.09 

2.0% 1.5% 116.84 119.42 

Cap 3* 13 65.84 27.09 53.70 117.05 116.93 118.15 64.44 27.92 50.18 119.04 121.44 

3.9% 1.2% 115.37 117.77 

Node I 16 46.00 31.00 32.73 22.94 

38.3% 

Node L* 18 117.60 121.42 

0.1% 117.75 

*The voltage measurements were taken at the customer's meter. Therefore, an average voltage drop of 3.67 V was included to reduce the primary voltage to the comparison shown in the table. 

Table 38. Field Verification Data – July 29, 2006 – DR Generation On 

Field Data - 7/29/06 - Circuit Peak 17:11 Simulation 

Current Voltage PF Current Voltage 

Location Node A B C A B C A B C A B C A B 

Start of Circuit 1 635.00 562.00 615.00 564.59 636.69 616.03 126.46 126.34 

0.3% 

Generator 10 8.07 7.08 6.84 122.25 122.25 120.75 0.98 0.98 0.98 7.30 7.19 7.22 121.76 123.67 

5.7% 1.2% 0.0% 

VR 1 9 296.60 312.30 279.70 124.20 123.75 123.56 0.93 0.94 0.93 316.35 299.29 284.46 123.92 124.46 

1.3% 0.5% 3.4% 

Cap 1 6 50.45 10.34 103.25 49.80 100.44 11.10 

2.6% 

Cap 2 12 54.29 13.02 24.72 54.48 13.91 25.46 

2.0% 

Cap 3 13 50.05 18.57 47.97 49.11 19.56 45.29 

4.0% 

229
 
Table 39. Field Verification Data – July 31, 2006 – DR Generation Off 

Field Data - 7/31/06 - Circuit Peak 17:56 Simulation 

Current Voltage PF Current Voltage 

Location Node A B C A B C A B C A B C A B 

Start of Circuit 1 696.00 604.00 678.00 608.76 699.59 678.97 126.26 126.14 

0.5% 

Generator 10 N/A N/A N/A N/A N/A N/A N/A N/A N/A 

VR 1 9 355.00 369.00 314.00 123.00 124.78 124.35 0.94 0.94 0.93 376.11 362.02 324.22 122.93 123.63 

2.3% 0.5% 3.4% 

Cap 1 6 51.53 11.78 108.84 50.82 105.52 12.49 

2.8% 

Cap 2 12 49.30 14.93 23.96 48.74 15.69 24.55 

2.2% 

Cap 3 13 62.18 27.37 54.05 60.45 28.03 49.14 

5.1% 

230
 
Table 40. Percent Variance Between Actual and Simulated
 

Currents, Voltages, and Power Factors 

Location Node Current Voltage PF 

Test Day 7/17/06 DR Generation Running 

Start of circuit 

Generator 

1 

10 

2.2 

2.3 

0.3 

1.1 

5.7 

0.0 

VR 9 3.7 

Capacitor 1 6 3.0 

Capacitor 2 12 2.0 

Capacitor 3 13 3.9 

Node I 16 38.3 

Node L 18 --

0.2 2.4 

0.7 --

1.5 --

1.2 --

-- --

0.1 --

Test Day 7/29/06 DR Generation Running 

Start of circuit 1 0.3 -- --

Generator 10 5.7 1.2 0.0 

VR 9 1.3 0.5 3.4 

Capacitor 1 6 2.6 -- --

Capacitor 2 12 2.0 -- --

Capacitor 3 13 4.0 -- --

Test Day 7/31/06 DR Generation Off 

Start of circuit 1 0.5 -- --

Generator N/A N/A N/A N/A 

VR 9 2.3 0.5 3.4 

Capacitor 1 6 2.8 -- --

Capacitor 2 12 2.2 -- --

Capacitor 3 13 5.1 -- --

9.6 Summary of Variance Results 

From Table 40, the variance between actual field-measured data and simulated data is less 

than 6% (i.e., 5.7% actual) for the phase currents throughout the circuit (except for Node I, 

where the percent unbalanced current is very high). The highest variance for the phase 

voltages throughout the circuit is 1.5% percent, whereas the highest variance for the PF is 

5.7% at the start of the circuit. It should be noted that the lowest variances occur on the load 

side of the step regulators because these regulators are individually phase-controlled and not 

gang-operated as the LTC at the substation. 

As shown in the variance data in Table 40, the simulated data closely match the actual fieldmeasured data in most cases, and the models developed in Section 5 can be used to estimate 

phase currents, phase voltages, and power factors without the use of extensive circuit metering. 

However, knowing the phasing of the loads is paramount to accurate simulated data. No 

significant difference in percent variance occurred when the DR was turned on or off. 

231
 
10 Project Results – Distributed Generation Penetration Limits 

Using Maximum Real Power and Maximum Real and 

Reactive Power Methods of Voltage Control 

10.1 Introduction 

In this section, the largest synchronous generator that can be installed on the distribution 

circuit is determined. This is determined based on three criteria: 

•	 The lowest single-phase voltage must not be less than 114 meter V or 117.67 V on the 

secondary of the distribution transformer, and the highest single-phase voltage cannot 

exceed 126 meter V. 

•	 The generator must not exceed 100% of the thermal rating on the most limiting 

element. 

•	 The generator must not create a reverse-power condition (i.e., there can be no flow 

back through the substation transformer). 

Although these criteria were used for testing, a fourth criterion was that no system protection 

device could misoperate. This criterion was not applied because it was the subject of a prior 

Department of Energy contract. 

10.2 Real Power Distributed Generation Size Limitation 

Table 41 summarizes the results of applying the highest acceptable real power injection at the 

beginning point, BP, Node 2; the middle point, Node 10; and the end point, Node 17. The 

limiting criterion in all cases was reverse power. The optimum location was at the midpoint, 

which had the lowest single-phase voltage improvement of 1.7% and a real power loss 

savings of 2.04%. The base case real power losses were 5.4%. The largest real power 

injection was 13,980 kW at the end point; the beginning and midpoints were slightly less at 

13,290 kW and 13,740 kW, respectively. 

232
 
Table 41. Maximum Limit for Real Power Injection 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

k

Machine 

Type 

Real 

Power 

Reactive 

Power 

Reason for 

Failure Location LTC Tap IA IB IC VA VB VC 

SG 13290 0 Reverse Power BP 10 220.1696 271.2878 260.5665 119.6138 120.2031 118.6864 118.0618 100.0552 1.3408 4.5% 

VR (1) 32, 30, 32 

SG 13740 0 Reverse Power MP 9 209.6296 236.8509 231.5352 123.4694 121.8682 120.5033 119.8612 100.0533 0.9978 3.4% 

VR (1) 14, 23, 22 

SG 13980 0 Reverse Power EP 11 259.8293 283.9373 288.2117 122.7994 121.6083 119.4167 118.7864 100.0536 1.3867 5.4% 

VR (1) 11, 17, 21 

Improvement 

Machine Real Reactive Reason for Lowest Node 1 

Type Power Power Failure Location Voltage Losses Capacity 

SG 13290 0 Reverse Power BP 0.18% 0.93% 59.78% 

VR (1) 32, 30, 32 

SG 13740 0 Reverse Power MP 1.70% 2.04% 76.64% 

VR (1) 14, 23, 22 

SG 13980 0 Reverse Power EP 0.79% 0.00% 71.95% 

VR (1) 11, 17, 21 

Table 42. Maximum Limit for Real and Reactive Power Injection 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

k

Machine 

Type 

Real 

Power 

Reactive 

Power 

Reason for 

Failure Location LTC Tap IA IB IC VA VB VC 

SG 13220 1893 Reverse Power BP 8 142.0642 196.0875 183.4428 119.7491 120.385 118.8633 118.2371 100.0551 1.3197 4.4% 

VR (1) 32, 29, 31 

SG 14250 3480 Reverse Power MP 6 67.2904 105.9963 101.8954 126.4554 124.0628 126.3554 123.2218 100.0518 0.7465 3.1% 

VR (1) -10, 0, -2 

SG 14490 2007 Reverse Power EP 8 177.3008 200.7446 203.7936 124.1336 122.7252 120.8493 120.205 100.0529 1.2065 5.1% 

VR (1) 1, 9, 10 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power 

Reason for 

Failure Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 13220 1893 Reverse Power BP 0.32% 1.00% 70.98% 

VR (1) 32, 29, 31 

SG 14250 3480 Reverse Power MP 4.55% 2.30% 84.41% 

VR (1) -10, 0, -2 

SG 14490 2007 Reverse Power EP 1.99% 0.28% 70.29% 

VR (1) 1, 9, 10 

233
 
10.3 Real and Reactive Distributed Generation Size Limitation 

Table 42 shows the results of applying the maximum real and reactive power without 

exceeding study criteria. Notice that a much larger DG can be used when injecting both real 

and reactive power because, now, the real power limit is 14,490 kW (versus 13,980 kW for 

real power injection only). Again, the optimum location is at the midpoint. However, in this 

case, the lowest single-phase voltage was improved 4.55% versus only 1.7% in the real power 

case. The real power loss savings were marginally better (2.3% versus 2.04%) than the 

optimum real power injection case. 

10.4 Findings

It should be remembered that the three-phase feeder conductor size of 636 kcmil aluminum is 

uniform throughout the Milford Circuit. Therefore, maximum size was not limited because of 

location of DG on the circuit. The optimum location for the greatest voltage improvement and 

real power loss savings is the midpoint. 

234
 
11 Project Results – Distributed Generation Voltage Regulation 

and Optimum Generator Conditions for Maximum 

Improvement of Voltage Regulation, Loss Reduction, and 

Released Capacity 

11.1 Introduction 

In this section, three generation types are employed to determine their effect on distribution 

circuit voltage regulation when the magnitude of the real power injection and the reactive 

power export or import (absorption) is varied. The three types of generation are a 400-kW 

induction generator with two fixed reactive values, a 400-kW inverter-based generator with a 

±0.8 power factor, and a 1,000-kW synchronous machine with a ±0.8 power factor. 

Three effects may occur when DG is operated on a distribution circuit: voltage regulation 

improvement, released capacity savings, and real power loss reduction. These improvements 

were tabulated for each generator type for both high (105%) and low (95%) substation 

primary voltage. The data are summarized for the actual locations of the induction generator 

and the high-speed generator and inverter; the data for the synchronous machine are 

summarized for its actual location on the distribution circuit or the midlocation (ML, Node 

10), at the beginning location (BL, Node 1), on the secondary of the substation after the LTC, 

and at the end location (EL, Node 17) near the tag end of the circuit. 

This analysis was conducted for the actual peak-load, or HL, condition at 17:43 on July 17, 

2006, and at the LL condition at 05:00 the same day. The results are tabulated and 

displayed in graphical form for voltage improvement, released capacity savings, and real 

energy loss reduction. 

11.2 Factors to Consider for Test Result Evaluation 

Two factors must be considered for simulation test result evaluation: (1) the dead band of the 

VR and (2) the effect the VDC source model on the increase or decrease in kilowatt and 

kilovar load as the voltage changes. 

11.2.1 Regulator Dead Ban

The regulator dead band is set for 1 V. Because the regulator has a +5% boost in voltage over 

32 steps and a -5% buck in voltage over 32 steps, the number of steps within the dead band is 

5% voltage change = 0.15625%/step x 120 volts, or 0.1875 volts/tap. 32 steps 

The number of steps within the deadband is then 

1 volt deadband

 = 5 steps. 0.1875 volts / tap 

235
 
So the voltage can change as much as 1 volt and not result in a change of the VR tap setting. 

When DG is run during an HV condition on the primary of the substation and at different real 

and plus or minus reactive power flows, the voltage will decrease or increase. This will cause 

the kilowatt and kilovar loads to decrease or increase. The change in voltage may not be 

enough to cause a reduction in the regulator settings (see Figure 141, Figure 155, and Figure 

161). During the LV condition on the primary of the substation, the LTC and step regulator 

taps are typically set at the highest tap settings, and there is less effect because of the step 

regulator step-changing interventions. 

11.2.2 Voltage-Dependent Current Source 

The model that best represents how load characteristics change with a change in voltage is the 

VDC source model. Adding real and positive reactive power from DG sources will increase 

the voltage and cause an increase in current or kilovolt-ampere load, which, in turn, increases 

the real power energy losses and reduces the released capacity (see Figure 144). The model 

will cause a 1.8% increase in current with a 1% increase in voltage and a 1.8% decrease in 

current with a 1% decrease in voltage. 

11.3 Interpreting the Distributed Generation Voltage Regulation 

Application Results 

Two sets of tables summarize the results of the DG applications. The first set, Table 44 

through Table 51, summarizes the results of applying each of the three generation types for 

both HV and LV substation primary conditions. Table 43 explains how to interpret the results. 

In the second set, Table 52 shows a summary of the benefits of running each type of DG. In 

the cases of the induction and inverter-based generators, the results are given for the location 

where the units are installed on the circuit. The induction generator is located at Node 17, or 

the EL, and the inverter generator is located at Node 22, or the midpoint. For the synchronous 

generator, the findings are summarized for generator locations at the beginning (Node 1), 

middle or actual location site (Node 10), and end (Node 17). 

11.3.1 Induction Generator Voltage Regulation Application (High Voltage) – 

Heavy Load, Table 44

Each of the generator applications consists of different real power and reactive power 

injections (+) or absorption (-) for both HV (105%) and LV (95%) conditions on the primary 

of the substation. The LTC tap setting at the secondary of the substation transformer is 

recorded for each real and reactive power case considered, as well as the tap settings of the 

step regulator for each case. The phase currents IA, IB, and IC at Node 1; the lowest three 

phase voltages VA, VB, and VC; and the lowest single-phase voltage on the circuit are 

recorded along with the highest current unbalance I2/I1%, the highest voltage unbalance 

V2/V1%, the percent circuit losses (excluding the substation transformer), kilovar losses, and 

capacity savings. 

Six cases were studied for the real power and reactive power. These are: 

236
 
Substation Primary 

P (kW) Q (kVAr) Voltage 

1 400 0 LV 

2 400 247.91 LV 

3 400 -247.91 LV 

4 400 0 HV 

5 400 247.91 HV 

6 400 -247.91 HV 

Table 43 explains the meaning of each improvement from the base case with no DG 

application. For the substation primary LV case, notice that when plus reactive and real power 

are injected (400 kW, +247.91 kVAr), the lowest three-phase voltages increase, the lowest 

single-phase voltage increases, and the percent losses on the circuit are slightly lower (i.e., 

5.145% compared with 5.4% for the base case). The percent loss improvement is then 0.25%, 

and the released capacity savings are 6.10%. For the substation primary HV case, the phase 

currents IA, IB, and IC are about 20 A more because the higher voltage levels cause an increase 

in the load. Here, when the DG injects 400 kW of real power and +247.91 kVArs of reactive 

power, the lowest single-phase voltage improves by 0.12%, the percent energy loss savings 

improves 0.30%, and the released capacity improves only by 3.80%. This reduction in 

released capacity is due to the higher voltage and increased load. For the LV case, the 

released capacity was 6.10%. For the LV case, when the generator is absorbing volt-amperes 

reactive (i.e., -247.91 Vars), there is a drop in voltage. The lowest single-phase voltage is now 

2.63% less than the base case. The loss savings is 0.2%, but the released capacity is 6.44%. 

For the HV case and the same P and –Q, the lowest voltage drops only 0.06%, the loss 

savings are 0.19%, and the released capacity is only 2.31%. Again, the higher the voltage, the 

greater the load and less released capacity. 

237
 
Table 43. Explaining the Meaning of 

Positive and Negative Improvements for DG ApplicationsA, B, C
 

Improvement Parameter Negative % Numbers Positive % Numbers 

% Lowest single-phase 

voltage 

% Real energy losses 

% Released capacity 

Voltage drop from base case 

(negative improvement) 

Higher losses than base case 

(negative improvement) 

Higher capacity needed to 

serve the load 

(negative improvement) 

Voltage rise from base case 

(positive improvement) 

Lower losses than base case 

(positive improvement) 

Lower capacity needed to 

serve load 

(positive improvement) 

Notes: 

A.	 The percent voltage improvement is the percent difference between the lowest single-phase 

voltage on the circuit for the base case and the lowest single-phase voltage for the DG 

application being considered divided by the base case and multiplied by 100%. 

B.	 The energy losses are the sum of all feeder lateral distribution transformer, secondary, and 

service losses, and the percent improvement is the difference between the base case percent 

losses for the circuit and the percent losses for the DG application. 

C. The kilovolt-ampere released capacity percent improvement is the difference between the 

percent capacity needed to serve the load at Node 1 and the percent base case capacity. 

11.3.2 Inverter Generator Voltage Regulation Application (High Voltage) – 

Heavy Load, Table 45 

Because the real and reactive power capability of the high-speed generator inverter is about 

the same as that of the induction generator, the results are very similar to the induction 

generator voltage regulation application. 

Six cases were studied for the inverter-based generation. These represent a full range of real 

and reactive capability. 

Substation Primary 

P (kW) Q (kVAr) Voltage 

1 400 0 LV 

2 320 240 LV 

3 320 -240 LV 

4 400 0 HV 

5 320 240 HV 

6 320 -240 HV 

The savings in losses, voltage improvement, and released capacity are, in general, less than 

those of the induction generator application because the real power at maximum +Var output 

is less. 

238 
11.3.3 Synchronous Generator Voltage Regulation Application (Beginning 

Location, High Voltage) – Heavy Load, Table 46 

Thirteen cases, with the range of real and reactive power shown below, were studied for the 

synchronous generator. Because regulation results differ depending on location, three 

locations were selected: the BL, ML, and EL. 

Location P Q 

Substation Primary 

Voltage 

1 BL 50% 0 HV 

2 BL 75% 0 HV 

3 BL 100% 0 HV 

4 BL 106.7% 0 HV 

5 BL 100% 100% HV 

6 BL 100% -100% HV 

7 BL 25% 100% HV 

8 BL 25% 75% HV 

9 BL 25% 50% HV 

10 BL 25% 25% HV 

11 BL 25% 0% HV 

12 BL 25% -50% HV 

13 BL 25% -100% HV 

When the synchronous generator is located at the source end (near the substation), its 

maximum generation of real and reactive power reduces these requirements from the source 

and, as such, results in the highest released capacity of 7.36% when operated at P = 100% and 

Q = +100%. Although the losses are less than those of the base case, the loss savings are not 

as good as when the generation is closer to the load. The lowest single-phase voltage is, in 

general, better than the previous cases but still less than the base case. 

11.3.4 Synchronous Generator Voltage Regulation Application (End Location, 

High Voltage) – Heavy Load, Table 47 

Installing generation at the end of the circuit (EL) resulted in a released capacity savings of 

6.85%, a loss savings of 0.53%, and near-base case conditions for voltage when the real 

power was 106.7% of nameplate and the reactive was 0%. When 100% reactive and 100% 

real power were applied, the voltage improved above the base case by 0.82%, and the released 

capacity was 5.97%. The worst-case voltage occurred when the unit was operated at -100% 

reactive and 100% real power. The lowest single-phase voltage dropped 0.44% below the 

base case. Both the voltage and the released capacity improvement parameters were worse 

than those of the base case when the unit was operated at 25% real power and -100% reactive. 

Here, the voltage dropped -0.7%, and the released capacity was only 1.5%. 

239
 
11.3.5 Synchronous Generator Voltage Regulation Application (Midlocation, 

High Voltage) – Heavy Load, Table 48 

The mid-location is the actual site of the 1,000-kW synchronous generator. The maximum 

released capacity of 6.88% occurs when the machine is operated at its maximum real power 

output of 106.7% and zero reactive power. This is to be expected because this input power to 

the circuit just offsets the same required power plus losses that the source provides to the 

circuit. Also, this case results in the second-highest loss savings of 0.48%, the highest loss 

saving being when the real power and reactive power are 100% each. The minimum released 

capacity of 1.15%, the lowest loss saving of 0.03%, and the worst-case single-phase voltage 

improvement of -0.81% occurs when the real power is only 25% and the reactive is -100%. 

Here, the voltage is reduced because of the high value of the generation reactive absorption. 

The best-case voltage improvement is 0.5% when the reactive is 100% export. 

11.3.6 Synchronous Generator Voltage Regulation Application (Beginning 

Location, Low Voltage) Heavy Load, Table 49 

When the primary of the substation is operating at the LV condition of 95%, the LTC at the 

substation is in the all-raise position (16), and the step regulator on the circuit operates at the 

all-raise position on all three phases (32, 32, 32). The released capacity savings reached their 

highest levels in this case with a 10.44% savings occurring at 100% real power and 100% 

reactive power. The voltages are lower than those of the base case by about 2% to 3%. The 

worst case occurred at -2.96% with 25% real and -100% reactive. This is obvious because the 

negative reactive is reducing the voltage. The best-case voltage of -1.93% occurred when 

100% real power and 100% reactive export power were delivered at the BL. The loss 

improvements are quite low and range from only 0.02% to 0.13%. 

11.3.7 Synchronous Generator Voltage Regulation Application (End Location, 

Low Voltage) – Heavy Load, Table 50 

As before (see 11.3.6), the LTC regulator and the step regulator are operating at full-raise 

position during this LV condition on the primary of the substation. The capacity savings of 

9.98% are slightly lower than those of the previous case, with the maximum real power output 

of 106.7%. All the voltage improvements are still negative, with the worst case occurring at ­

3.33% when P = 25% and Q -100%. The loss savings were better than the previous cases, 

with the maximum of 0.56% at P = 100% and Q = 100%. This is because a portion of the tag 

end load of the circuit is now being served by the DG. Again, this LV condition results in less 

kilovolt-amperes of load and, hence, lower losses. 

11.3.8 Synchronous Generator Voltage Regulation Application (Midlocation, 

Low Voltage) – Heavy Load, Table 51 

The midlocation performance is somewhat between the BL and EL performances. The released 

capacity is now 10.01% at 106.7% real power, whereas the released capacity was 10.44% at 

the BL and 9.98% at the EL. The greatest loss savings of 0.51% occurred at P = 100% and Q = 

100%, which is slightly less than the maximum loss savings of 0.56% when the DG is located 

at the EL. The worst-case lowest single-phase voltage was -3.36%, compared with the best 

case of -2.96% when the DG is located at the BL and operating at P = 25% and Q = -100%. 

The best-case lowest single-phase voltage is -1.14% when P = 100% and Q = 100%, which is 

almost the same result as when the unit was located at the EL (-1.15%). 

240
 
Table 44. Induction Generator Voltage Regulation Application (LV, HV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 L

IG 400 0 LV N/A 16 552.457 630.2362 612.8234 116.9241 117.2165 115.8406 115.1259 100.0563 1.3398 5.2% 2924.33 3.9985 0

VR (1) 32, 32, 32 

IG 400 247.91 LV N/A 16 553.1808 631.4567 614.1055 117.2827 117.5672 116.2048 115.4859 100.0561 1.3216 5.1% 2931.47 4.0372 0

VR (1) 32, 32, 32 

IG 400 -247.91 LV N/A 16 551.9444 629.1895 611.7199 116.5597 116.8611 115.4707 114.7603 100.0564 1.3594 5.2% 2920.77 3.9577 0

VR (1) 32, 32, 32 

IG 400 0 HV N/A 3 571.6509 648.8639 632.2462 119.2617 119.7564 118.2793 117.5369 100.0553 1.2632 5.1% 2990.79 3.8551 0

VR (1) 30, 26, 27 

IG 400 247.91 HV N/A 3 568.6085 646.8681 629.8217 119.7302 120.1709 118.7389 117.9912 100.0551 1.2666 5.1% 2960.5 3.9362 0

VR (1) 26, 23, 23 

IG 400 -247.91 HV N/A 4 579.2854 656.8888 639.831 119.523 120.0307 118.5256 117.7804 100.0552 1.2836 5.2% 3082.02 3.8059 0

VR (1) 32, 28, 29 

Improvement 

Lowest 

Machine Real Reactive 1Φ kW Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

IG 400 0 LV N/A -2.32% 0.23% 6.28% 

VR (1) 32, 32, 32 

IG 400 247.91 LV N/A -2.01% 0.25% 6.10% 

VR (1) 32, 32, 32 

IG 400 -247.91 LV N/A -2.63% 0.20% 6.44% 

VR (1) 32, 32, 32 

IG 400 0 HV N/A -0.27% 0.25% 3.51% 

VR (1) 30, 26, 27 

IG 400 247.91 HV N/A 0.12% 0.30% 3.80% 

VR (1) 26, 23, 23 

IG 400 -247.91 HV N/A -0.06% 0.19% 2.31% 

VR (1) 32, 28, 29 

241
 
Table 45. Inverter Generator Voltage Regulation Application (LV, HV) – HL 

Table 11.2 Inverter Generator Voltage Regulation Application (LV, HV) - Heavy Load 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 L

InvG 400 0 LV N/A 16 552.4406 630.1595 612.4781 117.0235 117.1949 115.8796 115.1541 100.0562 1.3684 5.2% 2952.59 3.9782 0

VR (1) 32, 32, 32 

InvG 320 240 LV N/A 16 555.3521 633.2756 616.0219 117.5087 117.6895 116.3973 115.6369 107.5141 1.363 5.2% 2985.68 3.9892 0

VR (1) 32, 32, 32 

InvG 320 -240 LV N/A 16 555.7432 633.3703 615.2559 116.3862 116.6189 115.2498 114.5651 100.0565 1.3826 5.3% 2978.01 3.9493 0

VR (1) 32, 32, 32 

InvG 400 0 HV N/A 3 570.7684 648.7027 631.0691 119.3939 119.7258 118.3498 117.5964 100.0552 1.3194 5.2% 3013.17 3.8672 0

VR (1) 29, 26, 26 

InvG 320 240 HV N/A 3 576.2127 653.6868 637.0627 119.765 120.1514 118.7634 117.9769 122.1077 1.2764 5.2% 3070.41 3.8373 0

VR (1) 32, 28, 29 

InvG 320 -240 HV N/A 4 583.018 660.9927 643.3038 119.355 119.7961 118.3125 117.5922 100.0553 1.3048 5.2% 3139.33 3.7977 0

VR (1) 32, 28, 29 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

InvG 400 0 LV N/A -2.29% 0.22% 6.29% 

VR (1) 32, 32, 32 

InvG 320 240 LV N/A -1.88% 0.16% 5.83% 

VR (1) 32, 32, 32 

InvG 320 -240 LV N/A -2.79% 0.13% 5.81% 

VR (1) 32, 32, 32 

InvG 400 0 HV N/A -0.22% 0.24% 3.53% 

VR (1) 29, 26, 26 

InvG 320 240 HV N/A 0.10% 0.21% 2.79% 

VR (1) 32, 28, 29 

InvG 320 -240 HV N/A -0.22% 0.16% 1.70% 

VR (1) 32, 28, 29 

242
 
Table 46. Synchronous Generator Voltage Regulation Application (BL, HV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Lo

SG 50% 0 HV BL 3 569.7675 647.5676 630.3888 118.9988 119.5496 118.0643 117.3244 100.0554 1.3032 5.3% 3085.62 3.9085 0.6

VR (1) 32, 28, 29 

SG 75% 0 HV BL 3 560.5307 638.4113 621.1837 119.0267 119.5778 118.0917 117.3515 100.0554 1.3034 5.3% 3040.39 3.9695 0.6

VR (1) 32, 28, 29 

SG 100% 0 HV BL 3 551.3242 629.2837 612.0087 119.0544 119.6056 118.1188 117.3782 100.0554 1.3037 5.3% 2995.99 4.0321 0.0

VR (1) 32, 28, 29 

SG 106.7% 0 HV BL 3 548.8595 626.8399 609.5523 119.0618 119.613 118.126 117.3854 100.0554 1.3037 5.3% 2984.23 4.0492 0.0

VR (1) 32, 28, 29 

SG 100% 100% HV BL 3 545.0327 623.0061 605.5145 119.5898 120.1441 118.643 117.8965 100.0552 1.3085 5.3% 2989.46 4.1082 0.0

VR (1) 32, 28, 29 

SG 100% -100% HV BL 3 565.4395 644.8146 627.551 119.1903 119.6974 118.2112 117.4696 100.0554 1.3253 5.3% 3089.67 3.9899 0.0

VR (1) 32, 29, 30 

SG 25% 100% HV BL 3 573.1587 650.8478 633.5213 119.5061 120.0599 118.561 117.8155 100.0552 1.3078 5.3% 3125.69 3.9176 0.6

VR (1) 32, 28, 29 

SG 25% 75% HV BL 3 574.5047 652.2184 634.9375 119.3716 119.9246 118.4293 117.6853 100.0553 1.3066 5.3% 3126.54 3.901 0.6

VR (1) 32, 28, 29 

SG 25% 50% HV BL 3 575.9175 653.6441 636.4107 119.2389 119.7912 118.2994 117.5568 100.0553 1.3054 5.3% 3127.81 3.8843 0.6

VR (1) 32, 28, 29 

SG 25% 25% HV BL 3 577.4435 655.1716 637.9895 119.1038 119.6552 118.1671 117.426 100.0554 1.3041 5.3% 3129.55 3.8668 0.6

VR (1) 32, 28, 29 

SG 25% 0% HV BL 3 579.0334 656.7516 639.6228 118.9705 119.5212 118.0366 117.297 100.0554 1.3029 5.3% 3131.69 3.8492 0.6

VR (1) 32, 28, 29 

SG 25% -50% HV BL 4 588.6396 667.0585 649.8389 119.3703 119.9216 118.4242 117.6801 100.0553 1.3072 5.4% 3211.77 3.8093 0.6

VR (1) 32, 28, 29 

SG 25% -100% HV BL 4 592.5017 671.6892 654.5498 119.1057 119.6124 118.1285 117.3878 100.0554 1.3245 5.4% 3226.28 3.8167 0.6

VR (1) 32, 29, 30 

Improvement 

Machine Real Reactive Lowest Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

SG 50% 0 HV BL -0.45% 0.08% 3.70% 

VR (1) 32, 28, 29 

SG 75% 0 HV BL -0.43% 0.11% 5.06% 

VR (1) 32, 28, 29 

SG 100% 0 HV BL -0.40% 0.13% 6.42% 

VR (1) 32, 28, 29 

SG 106.7% 0 HV BL -0.40% 0.13% 6.79% 

VR (1) 32, 28, 29 

SG 100% 100% HV BL 0.04% 0.14% 7.36% 

VR (1) 32, 28, 29 

SG 100% -100% HV BL -0.33% 0.08% 4.11% 

VR (1) 32, 29, 30 

SG 25% 100% HV BL -0.03% 0.08% 3.21% 

VR (1) 32, 28, 29 

SG 25% 75% HV BL -0.14% 0.07% 3.01% 

VR (1) 32, 28, 29 

SG 25% 50% HV BL -0.25% 0.07% 2.79% 

VR (1) 32, 28, 29 

SG 25% 25% HV BL -0.36% 0.07% 2.57% 

VR (1) 32, 28, 29 

SG 25% 0% HV BL -0.47% 0.06% 2.33% 

VR (1) 32, 28, 29 

SG 25% -50% HV BL -0.15% 0.03% 0.79% 

VR (1) 32, 28, 29 

SG 25% -100% HV BL -0.40% 0.02% 0.10% 

VR (1) 32, 29, 30 

243
 
Table 47. Synchronous Generator Voltage Regulation Application (EL, HV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Lo

SG 50% 0 HV EL 3 570.0817 647.3645 630.642 119.2577 119.742 118.2744 117.532 100.0553 1.2618 5.1% 2973.1 3.8604 0.6

VR (1) 32, 28, 29 

SG 75% 0 HV EL 3 561.0321 638.1117 621.5711 119.4095 119.8616 118.401 117.6572 100.0552 1.2525 5.0% 2875.42 3.8957 0.6

VR (1) 32, 28, 29 

SG 100% 0 HV EL 3 552.0319 628.8905 612.534 119.5571 119.9779 118.5236 117.7784 100.0552 1.2434 4.9% 2781.08 3.9317 0.6

VR (1) 32, 28, 29 

SG 106.7% 0 HV EL 3 549.6257 626.4219 610.115 119.596 120.0085 118.5558 117.8102 100.0551 1.241 4.9% 2756.33 3.9415 0.6

VR (1) 32, 28, 29 

SG 100% 100% HV EL 3 553.2643 632.3135 615.4063 120.6019 120.9582 119.5848 118.8273 100.0547 1.2115 4.8% 2797.7 4.0748 0.6

VR (1) 31, 28, 28 

SG 100% -100% HV EL 4 558.1387 634.894 618.1221 119.1788 119.5887 118.0735 117.3335 100.0554 1.2939 5.0% 2867.19 3.8478 0.6

VR (1) 32, 29, 30 

SG 25% 100% HV EL 3 581.5285 660.3106 643.6109 120.1129 120.6085 119.1723 118.4197 100.0549 1.2474 5.2% 3101.21 3.9285 0.6

VR (1) 32, 28, 29 

SG 25% 75% HV EL 3 580.7804 659.2589 642.5056 119.8622 120.3626 118.9172 118.1675 100.055 1.2532 5.2% 3091.66 3.9041 0.6

VR (1) 32, 28, 29 

SG 25% 50% HV EL 3 580.1452 658.3071 641.5027 119.6129 120.1184 118.6635 117.9167 100.0551 1.259 5.2% 3084.02 3.879 0.6

VR (1) 32, 28, 29 

SG 25% 25% HV EL 3 579.605 657.4265 640.572 119.3567 119.8678 118.4028 117.659 100.0552 1.2651 5.2% 3078.1 3.8526 0.6

VR (1) 32, 28, 29 

SG 25% 0% HV EL 3 579.1803 656.6483 639.7466 119.1019 119.6189 118.1435 117.4027 100.0554 1.2734 5.2% 3074.16 3.8256 0.6

VR (1) 32, 28, 29 

SG 25% -50% HV EL 4 584.876 663.1896 645.9419 119.2565 119.7462 118.2349 117.493 100.0554 1.3302 5.3% 3152.87 3.8112 0.6

VR (1) 32, 29, 30 

SG 25% -100% HV EL 4 584.8512 662.3115 645.7803 118.7268 119.2323 117.6578 116.9226 100.0556 1.3404 5.4% 3161.99 3.768 0.7

VR (1) 32, 29, 31 

Improvement 

Machine Real Reactive Lowest Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

SG 50% 0 HV EL -0.27% 0.28% 3.73% 

VR (1) 32, 28, 29 

SG 75% 0 HV EL -0.17% 0.39% 5.11% 

VR (1) 32, 28, 29 

SG 100% 0 HV EL -0.06% 0.50% 6.48% 

VR (1) 32, 28, 29 

SG 106.7% 0 HV EL -0.04% 0.53% 6.85% 

VR (1) 32, 28, 29 

SG 100% 100% HV EL 0.82% 0.56% 5.97% 

VR (1) 31, 28, 28 

SG 100% -100% HV EL -0.44% 0.37% 5.59% 

VR (1) 32, 29, 30 

SG 25% 100% HV EL 0.48% 0.22% 1.80% 

VR (1) 32, 28, 29 

SG 25% 75% HV EL 0.27% 0.21% 1.96% 

VR (1) 32, 28, 29 

SG 25% 50% HV EL 0.05% 0.20% 2.10% 

VR (1) 32, 28, 29 

SG 25% 25% HV EL -0.17% 0.18% 2.23% 

VR (1) 32, 28, 29 

SG 25% 0% HV EL -0.38% 0.16% 2.35% 

VR (1) 32, 28, 29 

SG 25% -50% HV EL -0.31% 0.09% 1.37% 

VR (1) 32, 29, 30 

SG 25% -100% HV EL -0.79% 0.03% 1.50% 

VR (1) 32, 29, 31 

244
 
Table 48. Synchronous Generator Voltage Regulation Application (ML, HV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 % 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 HV ML 4 576.1912 654.2454 637.2163 119.9124 120.3898 118.9073 118.1577 100.0551 1.2761 5.2% 3062.53 3.8547 0.6735 8

VR (1) 32, 28, 29 

SG 75% 0 HV ML 4 567.1353 645.0019 628.1048 120.0596 120.5 119.0274 118.2764 100.055 1.2599 5.1% 2970.4 3.8887 0.6722 8

VR (1) 32, 28, 29 

SG 100% 0 HV ML 3 551.7973 628.6983 612.1472 119.5362 119.9369 118.4938 117.7489 100.0552 1.2387 5.0% 2808.4 3.9286 0.6662 8

VR (1) 32, 28, 29 

SG 106.7% 0 HV ML 3 549.37 626.2141 609.6999 119.5748 119.9656 118.525 117.7798 100.0551 1.236 4.9% 2784.82 3.9382 0.6659 8

VR (1) 32, 28, 29 

SG 100% 100% HV ML 3 551.6677 630.5463 613.5866 120.6176 120.9517 119.5915 118.8339 100.0547 1.231 4.9% 2817.49 4.0656 0.6485 

VR (1) 31, 28, 28 

SG 100% -100% HV ML 4 559.1494 636.2131 619.1058 119.1376 119.526 118.0228 117.2833 100.0554 1.3092 5.1% 2891.46 3.8543 0.696 8

VR (1) 32, 29, 30 

SG 25% 100% HV ML 3 580.1401 658.7236 642.1133 120.143 120.6317 119.2001 118.4472 100.0549 1.2438 5.2% 3101 3.9212 0.6527 8

VR (1) 32, 28, 29 

SG 25% 75% HV ML 3 579.7367 658.0634 641.3639 119.8813 120.3756 118.9341 118.1842 100.055 1.2525 5.2% 3094.6 3.898 0.657 8

VR (1) 32, 28, 29 

SG 25% 50% HV ML 3 579.4374 657.4961 640.7111 119.6221 120.1221 118.6705 117.9236 100.0551 1.2632 5.2% 3089.47 3.8745 0.6613 8

VR (1) 32, 28, 29 

SG 25% 25% HV ML 3 579.2344 657.005 640.1354 119.3568 119.8629 118.4008 117.657 100.0552 1.2744 5.2% 3085.46 3.8498 0.6656 8

VR (1) 32, 28, 29 

SG 25% 0% HV ML 4 585.2859 663.5147 646.3563 119.7628 120.2777 118.7848 118.0366 100.0551 1.2926 5.3% 3156.84 3.8214 0.6748 8

VR (1) 32, 28, 29 

SG 25% -50% HV ML 4 585.4652 663.9017 646.5384 119.2355 119.7207 118.2116 117.47 100.0554 1.3345 5.3% 3161.93 3.8146 0.6908 8

VR (1) 32, 29, 30 

SG 25% -100% HV ML 4 586.0652 664.643 647.0848 118.7006 119.1573 117.6306 116.8956 100.0556 1.3769 5.4% 3172.1 3.8039 0.7068 8

VR (1) 32, 30, 31 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 HV ML 0.26% 0.23% 2.70% 

VR (1) 32, 28, 29 

SG 75% 0 HV ML 0.36% 0.33% 4.08% 

VR (1) 32, 28, 29 

SG 100% 0 HV ML -0.09% 0.45% 6.51% 

VR (1) 32, 28, 29 

SG 106.7% 0 HV ML -0.06% 0.48% 6.88% 

VR (1) 32, 28, 29 

SG 100% 100% HV ML 0.83% 0.51% 6.24% 

VR (1) 31, 28, 28 

SG 100% -100% HV ML -0.49% 0.34% 5.39% 

VR (1) 32, 29, 30 

SG 25% 100% HV ML 0.50% 0.20% 2.04% 

VR (1) 32, 28, 29 

SG 25% 75% HV ML 0.28% 0.19% 2.13% 

VR (1) 32, 28, 29 

SG 25% 50% HV ML 0.06% 0.18% 2.22% 

VR (1) 32, 28, 29 

SG 25% 25% HV ML -0.17% 0.16% 2.29% 

VR (1) 32, 28, 29 

SG 25% 0% HV ML 0.15% 0.13% 1.32% 

VR (1) 32, 28, 29 

SG 25% -50% HV ML -0.33% 0.08% 1.26% 

VR (1) 32, 29, 30 

SG 25% -100% HV ML -0.81% 0.03% 1.15% 

VR (1) 32, 30, 31 

245
 
Table 49. Synchronous Generator Voltage Regulation Application (BL, LV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 % 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 LV BL 16 548.6123 626.86 609.0336 116.7192 117.0647 115.6745 114.9617 100.0564 1.3905 5.3% 2996.76 4.0662 0.701

VR (1) 32, 32, 32 

SG 75% 0 LV BL 16 539.1941 617.5306 599.6492 116.7506 117.0963 115.7052 114.9921 100.0563 1.3908 5.3% 2948.95 4.1333 0.702 

VR (1) 32, 32, 32 

SG 100% 0 LV BL 16 529.8083 608.2319 590.297 116.7817 117.1274 115.7356 115.0221 100.0563 1.3911 5.3% 2902.08 4.2024 0.003

VR (1) 32, 32, 32 

SG 106.7% 0 LV BL 16 527.2958 605.7425 587.7935 116.79 117.1357 115.7437 115.0301 100.0563 1.3912 5.3% 2889.65 4.2212 0.003

VR (1) 32, 32, 32 

SG 100% 100% LV BL 16 523.8771 602.3187 584.1404 117.3644 117.7121 116.3049 115.585 100.0561 1.3965 5.3% 2897.59 4.2846 0.003

VR (1) 32, 32, 32 

SG 100% -100% LV BL 16 537.3505 615.5354 597.8991 116.1926 116.5363 115.1599 114.453 100.0566 1.3855 5.3% 2914.53 4.111 0.003

VR (1) 32, 32, 32 

SG 25% 100% LV BL 16 552.5664 630.6959 612.7041 117.2703 117.6177 116.213 115.4941 100.0561 1.3957 5.3% 3041.67 4.0744 0.003

VR (1) 32, 32, 32 

SG 25% 75% LV BL 16 553.8063 631.9622 614.0214 117.124 117.4709 116.07 115.3527 100.0562 1.3943 5.3% 3041.9 4.0567 0.703

VR (1) 32, 32, 32 

SG 25% 50% LV BL 16 555.1215 633.2907 615.4032 116.9796 117.326 115.929 115.2133 100.0563 1.393 5.3% 3042.61 4.0387 0.703

VR (1) 32, 32, 32 

SG 25% 25% LV BL 16 556.5554 634.725 616.8951 116.8325 117.1784 115.7852 115.0712 100.0563 1.3916 5.3% 3043.81 4.0199 0.702

VR (1) 32, 32, 32 

SG 25% 0% LV BL 16 558.0616 636.2191 618.449 116.6874 117.0328 115.6434 114.931 100.0564 1.3902 5.4% 3045.5 4.0009 0.701

VR (1) 32, 32, 32 

SG 25% -50% LV BL 16 561.387 639.4819 621.8422 116.3935 116.7379 115.3562 114.6471 100.0565 1.3875 5.4% 3050.38 3.961 0.7 

VR (1) 32, 32, 32 

SG 25% -100% LV BL 16 565.0973 643.0796 625.5829 116.098 116.4414 115.0675 114.3616 100.0566 1.3847 5.4% 3057.28 3.9192 0.003

VR (1) 32, 32, 32 

Improvement 

Machine Real Reactive Lowest Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

SG 50% 0 LV BL -2.45% 0.07% 6.78% 

VR (1) 32, 32, 32 

SG 75% 0 LV BL -2.43% 0.09% 8.17% 

VR (1) 32, 32, 32 

SG 100% 0 LV BL -2.40% 0.12% 9.56% 

VR (1) 32, 32, 32 

SG 106.7% 0 LV BL -2.40% 0.12% 9.93% 

VR (1) 32, 32, 32 

SG 100% 100% LV BL -1.93% 0.13% 10.44% 

VR (1) 32, 32, 32 

SG 100% -100% LV BL -2.89% 0.10% 8.47% 

VR (1) 32, 32, 32 

SG 25% 100% LV BL -2.00% 0.06% 6.21% 

VR (1) 32, 32, 32 

SG 25% 75% LV BL -2.12% 0.06% 6.02% 

VR (1) 32, 32, 32 

SG 25% 50% LV BL -2.24% 0.05% 5.83% 

VR (1) 32, 32, 32 

SG 25% 25% LV BL -2.36% 0.05% 5.61% 

VR (1) 32, 32, 32 

SG 25% 0% LV BL -2.48% 0.05% 5.39% 

VR (1) 32, 32, 32 

SG 25% -50% LV BL -2.72% 0.04% 4.90% 

VR (1) 32, 32, 32 

SG 25% -100% LV BL -2.96% 0.02% 4.37% 

VR (1) 32, 32, 32 

246
 
Table 50. Synchronous Generator Voltage Regulation Application (EL, LV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 % 

Type Power Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 LV EL 16 549.006 626.7122 609.3697 116.9842 117.2648 115.8915 115.1763 100.0562 1.3285 5.1% 2886.35 4.0128 0.7003 

VR (1) 32, 32, 32 

SG 75% 0 LV EL 16 539.8146 617.3121 600.1594 117.1419 117.3913 116.0245 115.3077 100.0561 1.2987 5.0% 2787.26 4.0515 0.6999 

VR (1) 32, 32, 32 

SG 100% 0 LV EL 16 530.6745 607.9443 590.9841 117.2951 117.5141 116.1531 115.4348 100.0561 1.2695 4.9% 2691.66 4.0909 0.6994 

VR (1) 32, 32, 32 

SG 106.7% 0 LV EL 16 528.2311 605.4366 588.5284 117.3354 117.5464 116.1868 115.4681 100.0561 1.2617 4.9% 2666.6 4.1016 0.6993 

VR (1) 32, 32, 32 

SG 100% 100% LV EL 16 533.2555 611.9855 595.217 118.3551 118.5527 117.2303 116.4997 100.0556 1.2174 4.8% 2719.58 4.2068 0.685 

VR (1) 32, 32, 32 

SG 100% -100% LV EL 16 530.0755 605.5359 588.4268 116.1839 116.4322 115.0243 114.3189 100.0566 1.3493 5.0% 2696.18 3.9554 0.7147 

VR (1) 32, 32, 32 

SG 25% 100% LV EL 16 561.0616 640.3213 622.989 117.8818 118.1728 116.8302 116.1042 100.0558 1.3084 5.2% 3021.61 4.0834 0.6866 

VR (1) 32, 32, 32 

SG 25% 75% LV EL 16 560.1873 639.133 621.7479 117.6192 117.915 116.5635 115.8405 100.056 1.32 5.2% 3010.52 4.0577 0.6901 

VR (1) 32, 32, 32 

SG 25% 50% LV EL 16 559.4335 638.051 620.6159 117.358 117.6588 116.2982 115.5783 100.0561 1.3322 5.2% 3001.46 4.0314 0.6936 

VR (1) 32, 32, 32 

SG 25% 25% LV EL 16 558.779 637.0428 619.5591 117.0894 117.3959 116.0254 115.3086 100.0562 1.3453 5.2% 2994.18 4.0034 0.6973 

VR (1) 32, 32, 32 

SG 25% 0% LV EL 16 558.2482 636.1438 618.6145 116.822 117.1345 115.754 115.0403 100.0563 1.3589 5.2% 2988.98 3.9748 0.7009 

VR (1) 32, 32, 32 

SG 25% -50% LV EL 16 557.5336 634.6244 617.0118 116.2731 116.5994 115.1969 114.4896 100.0565 1.3886 5.3% 2984.61 3.9137 0.7083 

VR (1) 32, 32, 32 

SG 25% -100% LV EL 16 557.3193 633.5188 615.8361 115.7105 116.0528 114.626 113.9253 100.0568 1.4216 5.4% 2988.86 3.8481 0.7159 

VR (1) 32, 32, 32 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 LV EL -2.27% 0.28% 6.81% 

VR (1) 32, 32, 32 

SG 75% 0 LV EL -2.16% 0.39% 8.21% 

VR (1) 32, 32, 32 

SG 100% 0 LV EL -2.05% 0.51% 9.60% 

VR (1) 32, 32, 32 

SG 106.7% 0 LV EL -2.03% 0.54% 9.98% 

VR (1) 32, 32, 32 

SG 100% 100% LV EL -1.15% 0.56% 9.00% 

VR (1) 32, 32, 32 

SG 100% -100% LV EL -3.00% 0.40% 9.96% 

VR (1) 32, 32, 32 

SG 25% 100% LV EL -1.49% 0.21% 4.78% 

VR (1) 32, 32, 32 

SG 25% 75% LV EL -1.71% 0.20% 4.96% 

VR (1) 32, 32, 32 

SG 25% 50% LV EL -1.93% 0.19% 5.12% 

VR (1) 32, 32, 32 

SG 25% 25% LV EL -2.16% 0.17% 5.27% 

VR (1) 32, 32, 32 

SG 25% 0% LV EL -2.39% 0.15% 5.40% 

VR (1) 32, 32, 32 

SG 25% -50% LV EL -2.86% 0.10% 5.63% 

VR (1) 32, 32, 32 

SG 25% -100% LV EL -3.33% 0.04% 5.79% 

VR (1) 32, 32, 32 

VR (1) 32, 28, 29 

247
 
Table 51. Synchronous Generator Voltage Regulation Application (ML, LV) – HL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 % 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

H

(<

SG 50% 0 LV ML 16 548.8954 626.6189 609.1722 116.97 117.2405 115.8728 115.1577 100.0562 1.3534 5.2% 2901.89 4.0115 0.6993 88

VR (1) 32, 32, 32 

SG 75% 0 LV ML 16 539.6345 617.1659 599.8566 117.1235 117.3573 115.9993 115.2827 100.0562 1.3356 5.0% 2808.77 4.0498 0.6983 88

VR (1) 32, 32, 32 

SG 100% 0 LV ML 16 530.4157 607.7407 590.5718 117.2744 117.472 116.1231 115.4052 100.0561 1.3181 4.9% 2717.96 4.089 0.6974 88

VR (1) 32, 32, 32 

SG 106.7% 0 LV ML 16 527.9495 605.2168 588.0861 117.3145 117.5024 116.1559 115.4376 100.0561 1.3134 4.9% 2694 4.0996 0.6971 88

VR (1) 32, 32, 32 

SG 100% 100% LV ML 16 531.6213 610.1927 593.3617 118.373 118.547 117.2388 116.508 100.0556 1.277 4.9% 2737.94 4.1987 0.6806 88

VR (1) 32, 32, 32 

SG 100% -100% LV ML 16 531.0778 606.8617 589.4042 116.1427 116.3682 114.973 114.2682 100.0566 1.364 5.0% 2719.09 3.9633 0.7148 8

VR (1) 32, 32, 32 

SG 25% 100% LV ML 16 559.6553 638.7202 621.4732 117.9141 118.1974 116.8601 116.1337 100.0558 1.3311 5.2% 3020.68 4.0764 0.6836 88

VR (1) 32, 32, 32 

SG 25% 75% LV ML 16 559.128 637.9253 620.5903 117.6398 117.9289 116.5818 115.8586 100.0559 1.3409 5.2% 3012.89 4.052 0.6878 88

VR (1) 32, 32, 32 

SG 25% 50% LV ML 16 558.713 637.2304 619.8111 117.368 117.663 116.306 115.586 100.0561 1.3507 5.2% 3006.48 4.0271 0.6919 88

VR (1) 32, 32, 32 

SG 25% 25% LV ML 16 558.3989 636.6144 619.1121 117.0897 117.3909 116.0236 115.3068 100.0562 1.3611 5.2% 3001.22 4.0008 0.6961 88

VR (1) 32, 32, 32 

SG 25% 0% LV ML 16 558.1977 636.0994 618.5182 116.8139 117.1215 115.7437 115.0301 100.0563 1.3715 5.3% 2997.36 3.9741 0.7003 88

VR (1) 32, 32, 32 

SG 25% -50% LV ML 16 558.1264 635.3429 617.6118 116.2514 116.5729 115.1727 114.4656 100.0566 1.3936 5.3% 2993.51 3.9175 0.7089 88

VR (1) 32, 32, 32 

SG 25% -100% LV ML 16 558.5165 634.977 617.1095 115.6802 116.0168 114.5926 113.8923 100.0568 1.4169 5.4% 2995.16 3.8573 0.7177 88

VR (1) 32, 32, 32 

Improvement 

Machine Real Reactive Lowest Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

SG 50% 0 LV ML -2.29% 0.24% 6.82% 

VR (1) 32, 32, 32 

SG 75% 0 LV ML -2.18% 0.35% 8.23% 

VR (1) 32, 32, 32 

SG 100% 0 LV ML -2.08% 0.45% 9.63% 

VR (1) 32, 32, 32 

SG 106.7% 0 LV ML -2.05% 0.48% 10.01% 

VR (1) 32, 32, 32 

SG 100% 100% LV ML -1.14% 0.51% 9.27% 

VR (1) 32, 32, 32 

SG 100% -100% LV ML -3.04% 0.37% 9.76% 

VR (1) 32, 32, 32 

SG 25% 100% LV ML -1.46% 0.19% 5.02% 

VR (1) 32, 32, 32 

SG 25% 75% LV ML -1.69% 0.18% 5.14% 

VR (1) 32, 32, 32 

SG 25% 50% LV ML -1.93% 0.17% 5.24% 

VR (1) 32, 32, 32 

SG 25% 25% LV ML -2.16% 0.15% 5.33% 

VR (1) 32, 32, 32 

SG 25% 0% LV ML -2.40% 0.13% 5.41% 

VR (1) 32, 32, 32 

SG 25% -50% LV ML -2.88% 0.09% 5.52% 

VR (1) 32, 32, 32 

SG 25% -100% LV ML -3.36% 0.04% 5.57% 

VR (1) 32, 32, 32 

248
 
11.4 Plotted Performance Data 

To help the reader follow the evaluation of the data, Table 52 and Table 53 show the results of 

each generator application and its improvement for HL and LL conditions. These data are 

plotted in Figure 141 through Figure 164 for the HL circuit condition. 

249
 
Table 52. Distributed Generator Voltage Regulation Application Summary – HL 

g g pp y y 

Ind Gen 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

247.91 115.4859 -2.01% 0.25% 6.10% 117.9912 0.12% 0.30% 3.80% 

0 115.1259 -2.32% 0.23% 6.28% 117.5369 -0.27% 0.25% 3.51% 

-247.91 114.7603 -2.63% 0.20% 6.44% 117.7804 -0.06% 0.19% 2.31% 

Inv Gen - P = 400 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

0 115.1541 -2.29% 0.22% 6.29% 117.5964 -0.22% 0.24% 3.53% 

Inv Gen - P = 320 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

240 115.6369 -1.88% 0.16% 5.83% 117.9769 0.10% 0.21% 2.79% 

-240 114.5651 -2.79% 0.13% 5.81% 117.5922 -0.22% 0.16% 1.70% 

SG - Voltage - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 115.585 116.508 116.4997 117.8965 118.8339 118.8273 

0 0 115.0221 115.4052 115.4348 117.3782 117.7489 117.7784 

-100% -738 114.453 114.2682 114.3189 117.4696 117.2833 117.3335 

SG - Voltage - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 115.4941 116.1337 116.1042 117.8155 118.4472 118.4197 

75% 553.5 115.3527 115.8586 115.8405 117.6853 118.1842 118.1675 

50% 369 115.2133 115.586 115.5783 117.5568 117.9236 117.9167 

25% 184.5 115.0712 115.3068 115.3086 117.426 117.657 117.659 

0% 0 114.931 115.0301 115.0403 117.297 118.0366 117.4027 

-50% -369 114.6471 114.4656 114.4896 117.6801 117.47 117.493 

-100% -738 114.3616 113.8923 113.9253 117.3878 116.8956 116.9226 

SG - Loss - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.13% 0.51% 0.56% 0.14% 0.51% 0.56% 

0 0 0.12% 0.45% 0.51% 0.13% 0.45% 0.50% 

-100% -738 0.10% 0.37% 0.40% 0.08% 0.34% 0.37% 

SG - Loss - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.06% 0.19% 0.21% 0.08% 0.20% 0.22% 

75% 553.5 0.06% 0.18% 0.20% 0.07% 0.19% 0.21% 

50% 369 0.05% 0.17% 0.19% 0.07% 0.18% 0.20% 

25% 184.5 0.05% 0.15% 0.17% 0.07% 0.16% 0.18% 

0% 0 0.05% 0.13% 0.15% 0.06% 0.13% 0.16% 

-50% -369 0.04% 0.09% 0.10% 0.03% 0.08% 0.09% 

-100% -738 0.02% 0.04% 0.04% 0.02% 0.03% 0.03% 

250
 
SG - Cap - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 10.44% 9.27% 9.00% 7.36% 6.24% 5.97% 

0 0 9.56% 9.63% 9.60% 6.42% 6.51% 6.48% 

-100% -738 8.47% 9.76% 9.96% 4.11% 5.39% 5.59% 

SG - Cap - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 6.21% 5.02% 4.78% 3.21% 2.04% 1.80% 

75% 553.5 6.02% 5.14% 4.96% 3.01% 2.13% 1.96% 

50% 369 5.83% 5.24% 5.12% 2.79% 2.22% 2.10% 

25% 184.5 5.61% 5.33% 5.27% 2.57% 2.29% 2.23% 

0% 0 5.39% 5.41% 5.40% 2.33% 1.32% 2.35% 

-50% -369 4.90% 5.52% 5.63% 0.79% 1.26% 1.37% 

-100% -738 4.37% 5.57% 5.79% 0.10% 1.15% 1.50% 

SG - VImp - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 -1.93% -1.14% -1.15% 0.04% 0.83% 0.82% 

0 0 -2.40% -2.08% -2.05% -0.40% -0.09% -0.06% 

-100% -738 -2.89% -3.04% -3.00% -0.33% -0.49% -0.44% 

SG - VImp - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 -2.00% -1.46% -1.49% -0.03% 0.50% 0.48% 

75% 553.5 -2.12% -1.69% -1.71% -0.14% 0.28% 0.27% 

50% 369 -2.24% -1.93% -1.93% -0.25% 0.06% 0.05% 

25% 184.5 -2.36% -2.16% -2.16% -0.36% -0.17% -0.17% 

0% 0 -2.48% -2.40% -2.39% -0.47% 0.15% -0.38% 

-50% -369 -2.72% -2.88% -2.86% -0.15% -0.33% -0.31% 

-100% -738 -2.96% -3.36% -3.33% -0.40% -0.81% -0.79% 

Base Case: 

Lowest Voltage: 117.855 

Losses: 5.40% 

Node 1 Capacity: -0.21% 

251
 
Table 53. Distributed Generator Voltage Regulation Application Summary – LL 

g g pp y g 

Ind Gen 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

247.91 122.4196 0.98% 0.37% 2.64% 121.6783 0.37% 0.38% 2.89% 

0 121.9696 0.61% 0.31% 2.04% 122.048 0.67% 0.33% 2.02% 

-247.91 121.5126 0.23% 0.23% 1.38% 121.6023 0.30% 0.25% 1.31% 

Inv Gen - P = 400 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

0 122.0019 0.63% 0.28% 2.01% 122.0808 0.70% 0.30% 1.99% 

Inv Gen - P = 320 

LV HV 

Q V V Imp Loss Cap V V Imp Loss Cap 

240 122.5691 1.10% 0.29% 2.20% 122.6307 1.15% 0.33% 2.19% 

-240 121.361 0.10% 0.18% 0.90% 121.4598 0.19% 0.22% 0.87% 

SG - Voltage - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 121.8718 122.7779 122.7609 121.8101 122.7128 122.7038 

0 0 121.9196 122.1461 122.1478 121.995 122.2167 122.2183 

-100% -738 121.2282 120.7316 120.7239 121.3707 120.8687 120.8612 

SG - Voltage - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 121.8061 122.5474 122.5393 121.7512 122.4923 122.4845 

75% 553.5 121.6368 122.2038 122.2004 121.5958 122.1624 122.1591 

50% 369 121.4698 121.871 121.8712 121.4425 121.8429 121.8431 

25% 184.5 121.2997 122.2507 121.5328 122.0896 121.5158 122.3202 

0% 0 121.8535 121.9139 121.9097 121.9358 121.9948 121.9985 

-50% -369 121.5057 121.2191 121.2214 121.6166 121.3288 121.331 

-100% -738 121.1639 120.4784 120.4737 121.3036 120.6267 120.6221 

SG - Loss - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.26% 0.63% 0.66% 0.27% 0.65% 0.67% 

0 0 0.22% 0.49% 0.51% 0.24% 0.51% 0.53% 

-100% -738 0.16% 0.26% 0.23% 0.61% 0.29% 0.26% 

SG - Loss - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.19% 0.38% 0.39% 0.21% 0.40% 0.41% 

75% 553.5 0.18% 0.34% 0.36% 0.20% 0.37% 0.38% 

50% 369 0.17% 0.31% 0.32% 0.19% 0.33% 0.35% 

25% 184.5 0.15% 0.28% 0.28% 0.19% 0.29% 0.32% 

0% 0 0.16% 0.23% 0.24% 0.18% 0.26% 0.27% 

-50% -369 0.12% 0.12% 0.12% 0.15% 0.15% 0.15% 

-100% -738 0.09% 0.00% -0.04% 0.12% 0.03% 0.00% 

252
 
SG - Cap - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 7.40% 7.32% 7.20% 7.43% 7.35% 7.28% 

0 0 4.93% 5.14% 5.15% 4.91% 5.13% 5.13% 

-100% -738 2.29% 2.56% 2.59% 2.25% 2.57% 2.61% 

SG - Cap - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 3.34% 3.13% 3.06% 3.37% 3.15% 3.09% 

75% 553.5 2.88% 2.71% 2.66% 2.91% 2.73% 2.68% 

50% 369 2.41% 2.31% 2.29% 2.42% 2.33% 2.30% 

25% 184.5 1.89% 1.65% 1.87% 1.65% 1.89% 1.63% 

0% 0 1.14% 1.19% 1.15% 1.12% 1.17% 1.18% 

-50% -369 -0.06% 0.13% 0.15% -0.09% 0.10% 0.13% 

-100% -738 -1.31% -1.20% -1.16% -1.34% -1.19% -1.15% 

SG - VImp - P=100% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.53% 1.27% 1.26% 0.47% 1.22% 1.21% 

0 0 0.57% 0.75% 0.75% 0.63% 0.81% 0.81% 

-100% -738 -0.01% -0.41% -0.42% 0.11% -0.30% -0.31% 

SG - VImp - P=25% 

LV HV 

Q Q - Mag BL ML EL BL ML EL 

100% 738 0.47% 1.08% 1.08% 0.43% 1.04% 1.03% 

75% 553.5 0.33% 0.80% 0.80% 0.30% 0.77% 0.76% 

50% 369 0.19% 0.53% 0.53% 0.17% 0.50% 0.50% 

25% 184.5 0.05% 0.84% 0.25% 0.71% 0.23% 0.90% 

0% 0 0.51% 0.56% 0.56% 0.58% 0.63% 0.63% 

-50% -369 0.22% -0.01% -0.01% 0.32% 0.08% 0.08% 

-100% -738 -0.06% -0.62% -0.63% 0.06% -0.50% -0.50% 

Base Case: 

Lowest Voltage: 121.2343 

Losses: 3.40% 

Node 1 Capacity: 60.58% 

253
 
114.5 

115 

115.5 

116 

116.5 

117 

117.5 

118 

118.5 

-300 -200 -100 0 100 200 300 

Reactive Power (kVar) 

Volts (V) 

Base Case = 117.855 

Lowest Single Phase Voltage for High Substation Primary Voltage (105 %) 

Lowest Single Phase Voltage for Low Substation Primary Voltage (95 %) 

Figure 141. HL condition – voltage rise or drop (in volts on a 120-V base) as a function of 

induction generator +/- reactive power with a constant real power output of 400 kW 

0.50% 

0.00% 

Voltage % Improvement from Base Case -0.50% 

-1.00% 

-1.50% 

-2.00% 

-2.50% 

-3.00% 

High Substation Primary Voltage (105 %) Low Substation Primary Voltage (95 %) 

-300 -200 -100 0 100 200 300 

Reactive Power (kVar) 

Figure 142. HL condition – reduction or increase in voltage (in percent on a 120-V base) as a 

function of induction generator +/- reactive power with a constant real power output of 400 kW 

254 
Capacity % Improvement from Base Case 

0.15% 

0.17% 

0.19% 

0.21% 

0.23% 

0.25% 

0.27% 

0.29% 

0.31% 

Real Loss % Improvement from Base Case 

-300 -200 -100 0 100 200 

Reactive Power (kVar) 

High Substation Primary Voltage (105 %) Low Substation Primary Voltage (95 %) 

-

Figure 143. HL condition – reduction or increase of real power 

(in percent of total circuit kilowatts) as a function of induction generator +/- reactive power 

with a constant real power output of 400 kW 

7.00%
 

6.50%
 

2.50% 

3.00% 

3.50% 

4.00% 

4.50% 

5.00% 

5.50% 

6.00% 

2.00% 

-300 -200 -100 0 100 200 

Reactive Power (kVar) 

High Substation Primary Voltage (105 %) Low Substation Primary Voltage (95 %) 

gure eavy on e on or ncrease o apac ty n o rc t 

Figure 144. HL load condition – reduction or increase of capacity
 

(in percent of total circuit kilovolt-amperes) as a function of induction generator
 

+/- reactive power with a CP output of 400 kW
 

255
 

300 

300 
Volts (V) 

114.5 

115 

115.5 

116 

116.5 

117 

117.5 

118 

118.5 

Base Case = 117.855 

114 

-300 -200 -100 0 100 200 300 

Reactive Power (kVar) 

Lowest Single Phase Voltage for High Substation Primary Voltage (105 %), P = 320 kW 

Lowest Single Phase Voltage for Low Substation Primary Voltage (95 %), P = 320 kW 

Lowest Single Phase Voltage for High Substation Primary Voltage (105 %), P = 400 kW 

Lowest Single Phase Voltage for Low Substation Primary Voltage (95 %), P = 400 kW 

Fi 6 5 H L d C diti V lt Ri D (i V lt 120 V B ) F ti f 

Figure 145. HL condition – voltage rise or drop (in volts on a 120-V base) as a function 

of inverter generator +/- reactive power with a constant real power output of 400 kW 

-3.00% 

-2.50% 

-2.00% 

-1.50% 

-1.00% 

-0.50% 

0.00% 

0.50% 

Voltage % Improvement from Base Case 

-300 -200 -100 0 100 200 

Reactive Power (kVar) 

High Substation Primary Voltage (105 %), P = 320 kW 

Low Substation Primary Voltage (95 %), P = 320 kW 

High Substation Primary Voltage (105 %), P = 400 kW 

Low Substation Primary Voltage (95 %), P = 400 kW 

Figure 146. HL condition – reduction or increase in voltage (in percent on a 120-V base) 

as a function of inverter generator +/- reactive power 

with a constant real power output of 320 kW or 400 kW 

256
 

300 
Real Loss % Change from Base Case 

0.05% 

0.10% 

0.15% 

0.20% 

0.25% 

0.30% 

0.00% 

-300 -200 -100 0 100 200 

Reactive Power (kVar) 

High Substation Primary Voltage (105 %), P = 320 kW 

Low Substation Primary Voltage (95 %), P = 320 kW 

High Substation Primary Voltage (105 %), P = 400 kW 

Low Substation Primary Voltage (95 %), P = 400 kW 

Figure 147. HL condition – reduction or increase of real power 

5.00% 

4.00% 

3.00% 

2.00% 

1.00% 

0.00% 

-300 -200 -100 0 100 200 300 

Reactive Power (kVar) 

High Substation Primary Voltage (105 %), P = 320 kW 

Low Substation Primary Voltage (95 %), P = 320 kW 

High Substation Primary Voltage (105 %), P = 400 kW 

Low Substation Primary Voltage (95 %), P = 400 kW 

(in percent of total circuit kilowatts) as a function of induction generator +/- reactive power 

with a constant real power output of 320 kW or 400 kW 

7.00% 

6.00% 

Capacity % Change from Base Case 

Figure 148. HL condition – reduction or increase of capacity
 

(in percent of total circuit kilovolt-amperes) as a function of induction generator
 

+/- reactive power with a CP output of 320 kW or 400 kW
 

257
 

300 
Volts (V) Volts (V) 

117.4 

117.6 

117.8 

118 

118.2 

118.4 

118.6 

118.8 

119 

Base Case = 117.855 

117.2 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

Lowest Single Phase Voltage, Beginning Location 

Lowest Single Phase Voltage, Mid Location 

Lowest Single Phase Voltage, End Location 

Figure 149. High substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 984 kW 

117 

116.5 

116 

115.5 

115 

114.5 

114 

-800 -600 -400 -200 0 200 400 600 800 

Base Case = 117.855 

Reactive Power (kVar) 

Lowest Single Phase Voltage, Beginning Location 

Lowest Single Phase Voltage, Mid Location 

Lowest Single Phase Voltage, End Location 

Figure 150. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 984 kW 

258
 
Volts (V) 

116.8 

117 

117.2 

117.4 

117.6 

117.8 

118 

118.2 

118.4 

118.6 

Volts (V) 

Base Case = 117.855 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Lowest Single Phase Voltage, Beginning Location 

Lowest Single Phase Voltage, Mid Location 

Lowest Single Phase Voltage, End Location 

Figure 151. High substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 246 kW
 

116.5 

116 

115.5 

115 

114.5 

114 

113.5 

Base Case = 117.855 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Lowest Single Phase Voltage, Beginning Location 

Lowest Single Phase Voltage, Mid Location 

Lowest Single Phase Voltage, End Location 

Figure 152. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 246 kW
 

259
 

800 

800 
Voltage % improvement from Base Case 

1.00% 

0.80% 

0.60% 

0.40% 

0.20% 

0.00% 

-0.20% 

-0.40% 

-0.60% 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 153. High substation primary voltage, HL condition – reduction or increase in voltage
 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 984 kW
 

0.00% 

-0.50% 

Voltage % Improvement from Base Case 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 154. Low substation primary voltage, HL condition – voltage rise or drop 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 984 kW 

-1.00% 

-1.50% 

-2.00% 

-2.50% 

-3.00% 

-3.50% 

260
 

800 

800 
Voltage % improvement from Base Case 

0.60% 

0.40% 

0.20% 

0.00% 

-0.20% 

-0.40% 

-0.60% 

-0.80% 

-1.00% 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 155. High substation primary voltage, HL condition – reduction or increase in voltage
 

(in volts on 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 246 kW
 

0.00% 

-0.50% 

Voltage % improvement from Base Case -1.00% 

-1.50% 

-2.00% 

-2.50% 

-3.00% 

-3.50% 

-4.00% 

Beginning Location Mid Location End Location 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

Figure 156. Low substation primary voltage, HL condition – reduction or increase in voltage 

(in volts on a 120-V base) as a function of location and synchronous generator 

+/- reactive power with a constant real power output of 246 kW
 

261 

800 
Real Loss % Change from Base Case Real Loss % Change from Base Case 

0.60% 

0.50% 

0.40% 

0.30% 

0.20% 

0.10% 

0.00% 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 157. High substation primary voltage, HL condition – reduction or increase 

of real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power output of 984 kW 

0.60% 

0.50% 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

0.40% 

0.30% 

0.20% 

0.10% 

0.00% 

Beginning Location Mid Location End Location 

Figure 158. Low substation primary voltage, HL condition – reduction or increase 

of real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power output of 984 kW 

262 

800 
Real Loss % Change from Base Case Real Loss % Change from Base Case 

0.25% 

0.20% 

0.15% 

0.10% 

0.05% 

0.00% 

Beginning Location Mid Location End Location 

Figure 159. High substation primary voltage, HL condition – reduction or increase 

of real power loss (in percent total circuit kilowatts) as a function of location 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

and synchronous generator +/- reactive power with a constant real power output of 246 kW 

0.25% 

0.20% 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

0.15% 

0.10% 

0.05% 

0.00% 

Beginning Location Mid Location End Location 

Fi 6 20 L S b t ti P i V lt H L d C diti R d ti I f R 

Figure 160. Low substation primary voltage, HL condition – reduction or increase 

of real power loss (in percent total circuit kilowatts) as a function of location 

and synchronous generator +/- reactive power with a constant real power output of 246 kW 

263 

l 

800 
0.60% 

1.60% 

2.60% 

3.60% 

4.60% 

5.60% 

6.60% 

7.60% 

8.60% 

Capacity % Improvement from Base Case 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 161. High substation primary voltage, HL condition – reduction or increase
 

of capacity (in percent total circuit kilowatts) as a function of location and synchronous
 

generator +/- reactive power with a constant real power output of 984 kW
 

12.60% 

10.60% 

Capacity % Improvement from Base Case 

8.60% 

6.60% 

4.60% 

2.60% 

0.60% 

Beginning Location Mid Location End Location 

-800 -600 -400 -200 0 200 400 600 800 

Reactive Power (kVar) 

Figure 162. Low substation primary voltage, HL condition – reduction or increase of capacity
 

(in percent total circuit kilowatts) as a function of location and synchronous generator
 

+/- reactive power with a constant real power output of 984 kW
 

264 
Capacity % Improvement from Base Case 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

0.00% 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

Beginning Location Mid Location End Location 

Figure 163. High substation primary voltage, HL condition – reduction or increase of capacity
 

(in percent total circuit kilowatts) as a function of location and synchronous generator
 

+/- reactive power with a constant real power output of 246 kW
 

6.60% 

5.60% 

Capacity % Improvement from Base Case 

-800 -600 -400 -200 0 200 400 600 

Reactive Power (kVar) 

4.60% 

3.60% 

2.60% 

1.60% 

0.60% 

Beginning Location Mid Location End Location 

Figure 164. Low substation primary voltage, HL condition – reduction or increase of capacity
 

(in percent total circuit kilowatts) as a function of location and synchronous generator
 

+/- reactive power with a constant real power output of 246 kW
 

265 

800 

800 
11.5 Findings and Conclusions 

11.5.1 Synchronous Generator (Low Voltage on Primary of Substation) – Heavy 

Load Condition 

• Released capacity improvement – BL 

The best-case released capacity improvement occurred when the DG was located at 

the BL of the circuit, with a 10.44% savings when the synchronous generator was 

operating at its highest real and reactive power output. This occurred with all LTC 

regulator taps and step regulator taps in their full-raise position because of the LV 

condition of 95% on the primary of the substation. Adding reactive from the generator 

improves the voltage but causes an increase in kilovolt-ampere load that reduces the 

released capacity. 

There is a 1.8% change in current for a 1% change in voltage. When the primary of the 

substation is operating at LV, or 95%, there is a 5% drop from nominal (100%) that 

causes a 9% (1.8% x 5%) drop in current. The base case peak load kilovolt-amperes at 

the start of the circuit without generation are 14,187 kW + j5846 kVAr, or 15,344 

kVA. When the generator is running at 984 kW + j 738 kVAr, or 1,230 kVA, the 

circuit load drops to 12,347 kW + j 5415 kVArs, or 13,482 kVA. This example shows 

a released capacity of 

15,344 kVA (w/o generation) – 13,482 kVA (with generation) = 1,862 kVA load 

reduction. 

The percent load reduction is then 

1,862 kVA x 100% = 12.14% road reduction. 

15,344 kVA 

The example given is based on balanced circuit loading, so the maximum released 

capacity of 10.44% indicates an unbalanced condition exists and, as such, the released 

capacity will be less because one of the phases has a lower load current than the other 

two before the generation is added. Therefore, the reduction in load or released 

capacity will be less on the phase with the lowest load. 

266
 
• Loss savings – EL 

The greatest reduction in real power losses occurs when the synchronous generator is 

located at the EL on the circuit, P = 100%, and Q = 100%. Here, the loss reduction 

was 0.56% better than the base case (5.7%). There were marginal loss savings (a range 

of only 0.02% to 0.13%) when the DG was applied at the head-end of the circuit. 

Locating the generation at the EL with 100% reactive and 100% real power reduces 

the current magnitude and, hence, the I2

R losses. 

• Voltage improvement – ML 

The best case for voltage improvement occurs when the synchronous generator is at 

the ML of the circuit and delivering 100% real power and 100% reactive power. The 

lowest single-phase voltage was -1.14% (down from the base case). The EL DG 

voltage improvement is almost the same (-1.15% from the base case). The BL DG had 

voltages about 2%–3% less than the base case. It should be noted that the criteria of 

114 V could not be met under the LV condition on the primary of the substation for 

customers with secondary and services. 

11.5.2 Synchronous Generator (High Voltage on Primary of Generator 

Substation) – Heavy Load Condition 

• Released capacity improvement – BL 

During HV conditions on the primary of the substation, the highest released capacity 

of 7.36% occurs when the synchronous generator is located at the head-end of the 

circuit, P = 100%, and Q = 100%. When the HV condition exists, the load increases so 

that reactive has to be at its highest value to reduce the load. Notice that the released 

capacity is lower for the HV case than for the LV case, in which the value was 

10.44%. This is because when the voltage increases, the load increases because of the 

VDC source model, which best represents how the load magnitude changes with 

changes in voltage. 

• Loss savings – EL 

The greatest loss savings of 0.56% was obtained at the EL for the HV case when P = 

100% and Q = 100%. This is the same result as for the LV case. For the LV case, the 

step regulator taps and the LTC tap were at full raise, and the magnitude of the current 

being served from the source was reduced because of the added generation. In addition, 

the I2

R losses are less. In the HV case, the step regulator tap settings and the LTC tap 

setting were low, which reduced the voltage and, thus, the load. The worst-case loss 

savings at the BL is only 0.02%, whereas the best case at the BL is 0.14% at full real 

and reactive power. This is because the load being served is just offset by the DG 

power output at the source end, and the load seen by the circuit is essentially the same. 

267
 
• Voltage improvement – ML 

The best voltage improvement of 0.83% occurs at the ML when the unit is operated at 

P = 100% and Q = 100%. The EL had about the same improvement of 0.82%. Notice 

these voltage improvement levels are better than the LV case, in which the substation 

primary voltage is 10% less than the HV level of 105%. This is because the LTC and 

step regulator are not in the full-raise position, as is the case for the LV condition, and, 

thus, the step regulator and the LTC raise the voltage. The generator is delivering 

100% reactive power, thus further reducing the voltage drop. It should be noted that 

the voltage criteria of 114 V was met during the HV condition. 

11.5.3 Induction Generator for Heavy Load Condition 

• Released capacity improvement 

The induction generator is located at the tag end of the circuit, so its released capacity 

is less than the synchronous generator at the BL. The highest released capacity of 

6.44% occurs during the LV case when P = 400 kW and Q = -247.91 kVAr. The 

absorbed kilovars cause the voltage to drop, which causes a lower circuit load, which 

produces the highest released capacity for the induction generator case. The capacity 

savings is less than that of the synchronous generator (10.44%) because the maximum 

real power capability of the induction generator is only 400 kW with a reactive 

capability of ±247.91 kVAr. The maximum kilovolt-ampere capacity is 1,230 kVA, 

and the maximum real power output of the synchronous generator is much bigger— 

1,050 kW (106.7%) with a reactive capability of ±738 kVAr. Obviously, the larger 

machine will realize a greater released capacity, especially because it is located at the 

optimum location on the circuit (the BL) for the greatest released capacity. 

The induction generator is located at the tag end, which is the least optimum location 

for released capacity. With the induction generator operating at 400 kW and a –Q of 

247.91 kVAr, this caused the voltage to drop and thus lowered the circuit load. The 

synchronous generator under the LV case had its highest released capacity at the BL 

of 10.44% with full-rated real power and full-rated-plus reactive power. Notice that 

the released capacity for the synchronous generator with zero reactive and maximum 

real power of 106.7% was 9.93%, which is not that different from the maximum 

released capacity of 10.44%. The released capacity for the HV case was only 3.8% for 

the induction generator. 

• Loss savings 

The maximum loss savings of 0.3% was achieved at P = 400 kW and Q = 247.91 

kVAr during the HV condition because the LTC tap setting was down to 3 and the 

step regulator tap settings were low (24, 21, 19). The current on the circuit was 

lowered with the reactive injection, which caused the losses to be at their lowest. 

268
 
• Voltage improvement 

The best voltage is obtained under HV conditions with full reactive and real power, 

which is 0.12% better than the base case. With the synchronous machine, the best 

voltage improvement during HV conditions is 0.83% at the ML with full real and 

reactive power output. Again, the synchronous machine’s better improvement in 

voltage is due to its ability to produce more real and reactive power. 

11.5.4 Inverter Generator for Heavy Load Condition 

• Released capacity improvement 

The inverter generator is located near the midpoint of the circuit; therefore, like the 

induction generator (at the tag end), it will not produce high values of released 

capacity. Its highest released capacity was 6.29% at P = 400 kW and Q = 0 under LV 

conditions, which is essentially the same as the induction generator capacity saving of 

6.44%, because their real power capabilities are the same. At HV, the released 

capacity is about half (3.53%) because the load increased because of the higher 

primary voltage. 

• Loss savings 

It would be expected that the inverter generator would have the highest loss savings at 

full real power and full reactive to reduce the magnitude of the current to its lowest 

value. But this is not the case because the real power capability drops down to 320 kW 

when the full reactive capability is 240 kVAr. Here, the greatest loss saving of 0.24% 

occurs at full rated real power of 400 kW at the HV condition. This is because the 

LTC and the step regulator reduced the voltage and lowered the current. 

• Voltage improvement 

As expected, the best voltage improvement of 0.10% is realized at full real power of 320 

kW and full reactive power of 240 kVAr for the HV condition. The voltage improvement 

is -1.88% at the LV condition with full-rated real (320) and reactive (240). 

11.6 Optimum Generator Conditions for Maximum Improvements – Heavy Load 

Conditions 

To summarize the findings and conclusions, Table 54 shows the optimum generator 

conditions for released capacity, loss savings, and voltage improvement. 

11.7 Optimum Generator Conditions for Maximum Improvements – Light Load 

Conditions 

The optimum generator conditions for improvements during light load conditions are given in 

Table 55. 

269
 
Table 54. Optimum Generator Conditions for Maximum Improvements – HL 

Generator 

Type 

Substation 

Primary 

Voltage 

Optimum Condition 

Location P, % Q, % 

Released 

Capacity 

% 

LossE 

Reduction% 

VoltageE 

Improvement% 

Synchronous 

generatorF LV BL 100 100 10.44 

LV EL 100 100 0.56 

LV ML 100 100 -1.14A

 HV BL 100 100 7.36 

HV EL 100 100 0.56 

HV ML 100 100 0.82 

P, Q, 

kW kVAr 

Induction 

generator LV ELB

 400 -247.9 6.44 

LV EL 400B

 247.9B 0.25 

LV EL 400 247.9 -2.01A

 HV EL 400 247.9 3.80 

HV EL 400 247.9 0.30 

HV EL 400 247.9 0.12 

Inverter 

generator LV MLC

 400 0 6.29 

LV ML 320D

 240D 0.16 

LV ML 320 240 -1.88A

 HV ML 400 0 3.53 

HV ML 400 0 0.24 

HV ML 320 240 0.10 

Notes: 

A. The voltage criterion of 114 V is not met for customers with secondary and services (3.67 V drop). 

Only for customers with services is the voltage criterion met. 

B. The kilovolt-ampere capability of the induction generator is 400 + j 247.9 = 470.6 kVA. It is located at 

the tag end of circuit, or EL. 

C. The inverter generator location is at the midpoint of the circuit, or ML. 

D. The kilovolt-ampere capability of the inverter generator is 320 + j240 = 400 kVA. 

E.	 The base case energy losses are 5.4%, and the base case lowest single-phase voltage is 117.855 V. 

F.	 The kilovolt-ampere capability of the synchronous machine is 984 + j738 = 1,236 kVA. The unit is 

located at midpoint. 

270
 
 

Table 55. Optimum Generator Conditions for Maximum Improvement – LL 

Generator 

Type 

Substation 

Primary 

Voltage 

Optimum Condition 

Location P, % Q, % 

Released 

Capacity 

% 

LossD 

Reduction% 

VoltageD 

Improvement% 

Synchronous 

generatorE LV BL 100 100 7.40 

LV EL 100 100 0.66 

LV ML 100 100 1.27 

HV BL 100 100 7.43 

HV EL 100 100 0.67 

HV ML 100 100 1.22 

P, Q, 

kW kVAr 

Induction 

generator LV ELA

 400 +247.9 2.64 

LV EL 400A

 247.9A 0.37 

LV EL 400 247.9 0.98 

HV EL 400 247.9 2.89 

HV EL 400 247.9 0.38 

HV EL 400 0 0.67 

Inverter 

generator LV MLB

 320 240 2.20 

LV ML 320C

 240C 0.29 

LV ML 320 240 1.10 

HV ML 320 0 2.19 

HV ML 320 240 0.33 

HV ML 400 0 1.15 

Notes: 

A.	 The kilovolt-ampere capability of the induction generator is 400 + j 247.9 = 470.6 kVA. It is located at 

the tag end of the circuit, or EL. 

B.	 The inverter generator is at the midpoint of the circuit, or ML. 

C. The kilovolt-ampere capability of the inverter generator is 320 + j240 = 400 kVA. 

D. The base case energy losses are 3.4%, and the base case lowest single-phase voltage is 121.33 V. 

E.	 The kilovolt-ampere capability of the synchronous machine is 984 + j738 = 1,236 kVA. The unit is 

located at midpoint. 

271
 
Table 56. Induction Generator Voltage Regulation Application (LV, HV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC N

IG 400 0 LV N/A 16 215.5865 250.8556 244.2324 123.2152 123.0762 122.3465 121.9696 100.1499 0.5791 3.1% 457.01 4

VR (1) 7, 7, 8 

IG 400 247.91 LV N/A 16 211.3691 246.811 240.07 123.6507 123.4998 122.7978 122.4196 100.1498 0.5601 3.0% 438.8 5

VR (1) 7, 7, 8 

IG 400 -247.91 LV N/A 16 220.2762 255.3078 248.8162 122.7733 122.6469 121.8883 121.5126 100.1499 0.5984 3.2% 478.96 4

VR (1) 7, 7, 8 

IG 400 0 HV N/A 0 215.6606 250.9707 244.3936 123.2559 123.1314 122.4251 122.048 100.1499 0.57 3.1% 436.17 4

VR (1) 7, 7, 8 

IG 400 247.91 HV N/A -1 209.897 245.1622 238.5137 122.8626 122.7266 122.0544 121.6783 100.1497 0.5505 3.0% 411.4 5

VR (1) 7, 7, 8 

IG 400 -247.91 HV N/A 0 220.6714 255.7775 249.293 122.8241 122.7128 121.9782 121.6023 100.1499 0.5895 3.1% 458.58 4

VR (1) 8, 8, 9 

Improvement 

Machine Real Reactive Lowest kW Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

IG 400 0 LV N/A 0.61% 0.31% 2.04% 

VR (1) 7, 7, 8 

IG 400 247.91 LV N/A 0.98% 0.37% 2.64% 

VR (1) 7, 7, 8 

IG 400 -247.91 LV N/A 0.23% 0.23% 1.38% 

VR (1) 7, 7, 8 

IG 400 0 HV N/A 0.67% 0.33% 2.02% 

VR (1) 7, 7, 8 

IG 400 247.91 HV N/A 0.37% 0.38% 2.89% 

VR (1) 7, 7, 8 

IG 400 -247.91 HV N/A 0.30% 0.25% 1.31% 

VR (1) 8, 8, 9 

272
 
Table 57. Inverter Generator Voltage Regulation Application (LV, HV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC N

InvG 400 0 LV N/A 16 215.7648 251.0805 244.2842 123.3158 123.0805 122.3867 122.0019 100.1498 0.5704 3.1% 467.04 4

VR (1) 7, 7, 8 

InvG 320 240 LV N/A 16 214.3897 249.7643 242.9851 123.8584 123.6347 122.9837 122.5691 189.5674 0.5357 3.1% 461.97 4

VR (1) 7, 7, 8 

InvG 320 -240 LV N/A 16 223.2678 258.5274 251.7314 122.6213 122.4607 121.6974 121.361 100.1499 0.6131 3.2% 495.7 4

VR (1) 7, 7, 8 

InvG 400 0 HV N/A 0 215.8399 251.1973 244.4464 123.3571 123.1364 122.4658 122.0808 100.1498 0.5606 3.1% 446.17 4

VR (1) 7, 7, 8 

InvG 320 240 HV N/A 0 214.4339 249.8456 243.1133 123.8825 123.6733 123.0455 122.6307 189.2126 0.5253 3.1% 441.2 4

VR (1) 7, 7, 8 

InvG 320 -240 HV N/A 0 223.374 258.6802 251.9266 122.6821 122.5365 121.7965 121.4598 100.1499 0.6034 3.2% 473.61 4

VR (1) 7, 7, 8 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

InvG 400 0 LV N/A 0.63% 0.28% 2.01% 

VR (1) 7, 7, 8 

InvG 320 240 LV N/A 1.10% 0.29% 2.20% 

VR (1) 7, 7, 8 

InvG 320 -240 LV N/A 0.10% 0.18% 0.90% 

VR (1) 7, 7, 8 

InvG 400 0 HV N/A 0.70% 0.30% 1.99% 

VR (1) 7, 7, 8 

InvG 320 240 HV N/A 1.15% 0.33% 2.19% 

VR (1) 7, 7, 8 

InvG 320 -240 HV N/A 0.19% 0.22% 0.87% 

VR (1) 7, 7, 8 

273
 
Table 58. Synchronous Generator Voltage Regulation Application (BL, HV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 % 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 HV BL 0 212.8733 248.4197 241.7729 123.0971 123.0572 122.3328 121.9559 100.15 0.5814 3.2% 464.51 5.0537 2.4249 

VR (1) 7, 7, 8 

SG 75% 0 HV BL 0 204.3709 239.9243 233.3379 123.117 123.0771 122.3526 121.9756 100.15 0.5814 3.2% 448.7 5.2441 2.4249 

VR (1) 7, 7, 8 

SG 100% 0 HV BL 0 196.0316 231.5685 225.0531 123.1365 123.0966 122.372 121.995 100.15 0.5813 3.2% 433.75 5.4457 2.4249 

VR (1) 7, 7, 8 

SG 106.7% 0 HV BL 0 193.8247 229.3523 222.8581 123.1417 123.1018 122.3772 122.0001 100.15 0.5813 3.2% 429.88 5.5017 2.4249 

VR (1) 7, 7, 8 

SG 100% 100% HV BL -1 179.4087 214.7065 207.7869 122.9478 122.9088 122.1866 121.8101 100.1499 0.5809 3.1% 403.36 5.8977 2.4257 

VR (1) 7, 7, 8 

SG 100% -100% HV BL 0 214.3268 249.4135 243.3793 122.507 122.4672 121.746 121.3707 100.1499 0.5816 2.8% 464.99 5.0029 2.4248 

VR (1) 7, 7, 8 

SG 25% 100% HV BL -1 206.9496 241.9569 234.9388 122.8884 122.8494 122.1275 121.7512 100.1499 0.581 3.2% 450.51 5.1888 2.4257 

VR (1) 7, 7, 8 

SG 25% 75% HV BL -1 209.9137 245.0483 238.1157 122.7317 122.6927 121.9717 121.5958 100.1499 0.581 3.2% 455.68 5.1136 2.4256 

VR (1) 7, 7, 8 

SG 25% 50% HV BL -1 213.0619 248.2864 241.4423 122.5771 122.5382 121.818 121.4425 100.1499 0.5811 3.2% 461.23 5.037 2.4256 

VR (1) 7, 7, 8 

SG 25% 25% HV BL 0 217.9593 253.4542 246.661 123.232 123.192 122.4669 122.0896 100.15 0.5813 3.2% 474.63 4.953 2.4249 

VR (1) 7, 7, 8 

SG 25% 0% HV BL 0 221.5205 257.0412 250.3433 123.0768 123.0369 122.3126 121.9358 100.15 0.5814 3.2% 481.16 4.8738 2.4249 

VR (1) 7, 7, 8 

SG 25% -50% HV BL 0 229.5958 265.1166 258.5824 122.7537 122.7143 121.9926 121.6166 100.1499 0.5818 3.2% 497.01 4.7075 2.423 

VR (1) 8, 8, 9 

SG 25% -100% HV BL 0 238.1321 273.5304 267.2042 122.438 122.3987 121.6786 121.3036 100.1499 0.5819 3.3% 513.6 4.5422 2.4229 

VR (1) 8, 8, 9 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 HV BL 0.60% 0.20% 2.40% 

VR (1) 7, 7, 8 

SG 75% 0 HV BL 0.61% 0.22% 3.67% 

VR (1) 7, 7, 8 

SG 100% 0 HV BL 0.63% 0.24% 4.91% 

VR (1) 7, 7, 8 

SG 106.7% 0 HV BL 0.63% 0.25% 5.24% 

VR (1) 7, 7, 8 

SG 100% 100% HV BL 0.47% 0.27% 7.43% 

VR (1) 7, 7, 8 

SG 100% -100% HV BL 0.11% 0.61% 2.25% 

VR (1) 7, 7, 8 

SG 25% 100% HV BL 0.43% 0.21% 3.37% 

VR (1) 7, 7, 8 

SG 25% 75% HV BL 0.30% 0.20% 2.91% 

VR (1) 7, 7, 8 

SG 25% 50% HV BL 0.17% 0.19% 2.42% 

VR (1) 7, 7, 8 

SG 25% 25% HV BL 0.71% 0.19% 1.65% 

VR (1) 7, 7, 8 

SG 25% 0% HV BL 0.58% 0.18% 1.12% 

VR (1) 7, 7, 8 

SG 25% -50% HV BL 0.32% 0.15% -0.09% 

VR (1) 8, 8, 9 

SG 25% -100% HV BL 0.06% 0.12% -1.34% 

VR (1) 8, 8, 9 

274
 
Table 59. Synchronous Generator Voltage Regulation Application (EL, HV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 

SG 50% 0 HV EL 0 212.3632 247.6197 241.0869 123.3 123.1564 122.4539 122.0766 100.1498 0.5676 3.0% 423.13 5.0172 

VR (1) 7, 7, 8 

SG 75% 0 HV EL 0 203.6864 238.771 232.3689 123.415 123.2206 122.5274 122.1499 100.1498 0.5618 2.9% 390.74 5.1848 

VR (1) 7, 7, 8 

SG 100% 0 HV EL 0 195.2284 230.0957 223.8435 123.5254 123.281 122.5959 122.2183 100.1497 0.5567 2.9% 361.9 5.3601 

VR (1) 7, 7, 8 

SG 106.7% 0 HV EL 0 192.9993 227.7999 221.5913 123.5543 123.2966 122.6135 122.2358 100.1497 0.5554 2.9% 354.76 5.4084 

VR (1) 7, 7, 8 

SG 100% 100% HV EL -1 180.5095 215.6699 209.1265 123.9599 123.6821 123.0829 122.7038 100.1496 0.4985 2.7% 311.07 5.8389 

VR (1) 6, 6, 7 

SG 100% -100% HV EL 0 212.9442 247.0417 241.1703 122.2241 122.007 121.235 120.8612 100.1499 0.6197 3.1% 440.76 4.8856 

VR (1) 9, 10, 11 

SG 25% 100% HV EL -1 208.4481 243.8298 236.9695 123.6157 123.4901 122.8629 122.4845 100.1497 0.5178 3.0% 408.59 5.2074 

VR (1) 6, 6, 7 

SG 25% 75% HV EL -1 211.1141 246.5272 239.6941 123.2996 123.1822 122.5366 122.1591 100.1497 0.5318 3.0% 417.38 5.1233 

VR (1) 7, 7, 8 

SG 25% 50% HV EL -1 213.7232 249.0965 242.3328 122.9942 122.8849 122.2196 121.8431 100.1498 0.5455 3.1% 426.84 5.0399 

VR (1) 7, 7, 8 

SG 25% 25% HV EL 0 218.1168 253.6216 246.8922 123.4912 123.39 122.6982 122.3202 175.2828 0.5601 3.1% 445.68 4.947 

VR (1) 7, 7, 8 

SG 25% 0% HV EL 0 221.2389 256.6262 249.9807 123.1805 123.0883 122.3755 121.9985 100.1499 0.5741 3.1% 459.1 4.857 

VR (1) 7, 7, 8 

SG 25% -50% HV EL 0 228.6036 263.6773 257.1874 122.5345 122.4624 121.7061 121.331 100.15 0.6033 3.3% 493.54 4.6634 

VR (1) 8, 8, 9 

SG 25% -100% HV EL 0 237.5644 272.2539 266.1526 120.9778 121.3988 121.4231 120.6221 100.15 0.6374 3.4% 539.55 4.4658 

VR (1) 11, 11, 13 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 HV EL 0.69% 0.37% 2.52% 

VR (1) 7, 7, 8 

SG 75% 0 HV EL 0.76% 0.45% 3.84% 

VR (1) 7, 7, 8 

SG 100% 0 HV EL 0.81% 0.53% 5.13% 

VR (1) 7, 7, 8 

SG 106.7% 0 HV EL 0.83% 0.55% 5.48% 

VR (1) 7, 7, 8 

SG 100% 100% HV EL 1.21% 0.67% 7.28% 

VR (1) 6, 6, 7 

SG 100% -100% HV EL -0.31% 0.26% 2.61% 

VR (1) 9, 10, 11 

SG 25% 100% HV EL 1.03% 0.41% 3.09% 

VR (1) 6, 6, 7 

SG 25% 75% HV EL 0.76% 0.38% 2.68% 

VR (1) 7, 7, 8 

SG 25% 50% HV EL 0.50% 0.35% 2.30% 

VR (1) 7, 7, 8 

SG 25% 25% HV EL 0.90% 0.32% 1.63% 

VR (1) 7, 7, 8 

SG 25% 0% HV EL 0.63% 0.27% 1.18% 

VR (1) 7, 7, 8 

SG 25% -50% HV EL 0.08% 0.15% 0.13% 

VR (1) 8, 8, 9 

SG 25% -100% HV EL -0.50% 0.00% -1.15% 

VR (1) 11, 11, 13 

275
 
Table 60. Synchronous Generator Voltage Regulation Application (ML, HV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 HV ML 0 212.4129 247.6931 241.1176 123.2956 123.148 122.4488 122.0716 100.1498 0.5669 3.1% 427.69 5.0118 0.52

VR (1) 7, 7, 8 

SG 75% 0 HV ML 0 203.7158 238.8462 232.3743 123.4114 123.2107 122.523 122.1455 100.1498 0.5606 3.0% 395.73 5.1779 0.52

VR (1) 7, 7, 8 

SG 100% 0 HV ML 0 195.2055 230.1473 223.7941 123.5246 123.2713 122.5943 122.2167 100.1497 0.555 2.9% 366.13 5.3526 0.52

VR (1) 7, 7, 8 

SG 106.7% 0 HV ML 0 192.9567 227.8406 221.522 123.5546 123.2872 122.613 122.2353 100.1497 0.5536 2.9% 358.59 5.4009 0.52

VR (1) 7, 7, 8 

SG 100% 100% HV ML -1 180.0864 215.2308 208.6781 123.9702 123.6826 123.0919 122.7128 100.1496 0.4961 2.7% 314.73 5.8244 0.49

VR (1) 6, 6, 7 

SG 100% -100% HV ML 0 212.9588 247.2812 241.2013 122.231 122.0028 121.2425 120.8687 100.1499 0.6183 3.1% 434.31 4.8977 0.56

VR (1) 9, 10, 11 

SG 25% 100% HV ML -1 208.0818 243.3935 236.593 123.6243 123.4957 122.8707 122.4923 100.1497 0.5168 3.0% 410.4 5.1974 0.48

VR (1) 6, 6, 7 

SG 25% 75% HV ML -1 210.8721 246.2299 239.4376 123.3036 123.1838 122.5398 122.1624 100.1497 0.531 3.0% 420.44 5.114 0.49

VR (1) 7, 7, 8 

SG 25% 50% HV ML -1 213.5907 248.9264 242.1842 122.9947 122.8834 122.2195 121.8429 100.1498 0.5449 3.1% 430.49 5.0319 0.50

VR (1) 7, 7, 8 

SG 25% 25% HV ML -1 216.6113 251.8874 245.2029 122.6785 122.5761 121.8915 121.5158 100.1498 0.5592 3.1% 442.03 4.945 0.51

VR (1) 7, 7, 8 

SG 25% 0% HV ML 0 221.2784 256.6741 250.0092 123.1772 123.0832 122.3719 121.9948 100.1499 0.5738 3.1% 462 4.854 0.51

VR (1) 7, 7, 8 

SG 25% -50% HV ML 0 228.7312 263.8744 257.3197 122.5323 122.4578 121.704 121.3288 100.15 0.6032 3.2% 492.86 4.6678 0.53

VR (1) 8, 8, 9 

SG 25% -100% HV ML 0 237.6779 272.5148 266.2969 121.8619 121.8078 120.9998 120.6267 100.15 0.6372 3.4% 532.26 4.4801 0.5

VR (1) 11, 11, 13 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 HV ML 0.69% 0.35% 2.51% 

VR (1) 7, 7, 8 

SG 75% 0 HV ML 0.75% 0.43% 3.83% 

VR (1) 7, 7, 8 

SG 100% 0 HV ML 0.81% 0.51% 5.13% 

VR (1) 7, 7, 8 

SG 106.7% 0 HV ML 0.83% 0.53% 5.47% 

VR (1) 7, 7, 8 

SG 100% 100% HV ML 1.22% 0.65% 7.35% 

VR (1) 6, 6, 7 

SG 100% -100% HV ML -0.30% 0.29% 2.57% 

VR (1) 9, 10, 11 

SG 25% 100% HV ML 1.04% 0.40% 3.15% 

VR (1) 6, 6, 7 

SG 25% 75% HV ML 0.77% 0.37% 2.73% 

VR (1) 7, 7, 8 

SG 25% 50% HV ML 0.50% 0.33% 2.33% 

VR (1) 7, 7, 8 

SG 25% 25% HV ML 0.23% 0.29% 1.89% 

VR (1) 7, 7, 8 

SG 25% 0% HV ML 0.63% 0.26% 1.17% 

VR (1) 7, 7, 8 

SG 25% -50% HV ML 0.08% 0.15% 0.10% 

VR (1) 8, 8, 9 

SG 25% -100% HV ML -0.50% 0.03% -1.19% 

VR (1) 11, 11, 13 

276
 
Table 61. Synchronous Generator Voltage Regulation Application (BL, LV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2/I1 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 Low 

SG 50% 0 LV BL 16 212.7966 248.3 241.6071 123.0554 123.0003 122.2526 121.876 100.15 0.5896 3.2% 484.87 5.0431 2.41

VR (1) 7, 7, 8 

SG 75% 0 LV BL 16 204.296 239.806 233.172 123.0777 123.0225 122.2747 121.898 100.15 0.5896 3.2% 467.61 5.2333 2.41

VR (1) 7, 7, 8 

SG 100% 0 LV BL 16 195.9588 231.4519 224.8876 123.0995 123.0443 122.2964 121.9196 100.15 0.5896 3.2% 451.28 5.4346 2.41

VR (1) 7, 7, 8 

SG 106.7% 0 LV BL 16 193.7525 229.2363 222.6927 123.1053 123.0501 122.3022 121.9254 100.15 0.5896 3.2% 447.05 5.4905 2.41

VR (1) 7, 7, 8 

SG 100% 100% LV BL 15 179.6222 214.9111 207.9322 123.0487 122.9945 122.2484 121.8718 100.15 0.589 3.1% 419.17 5.8832 2.41

VR (1) 7, 7, 8 

SG 100% -100% LV BL 16 214.4479 249.197 243.3917 122.4026 122.3609 121.603 121.2282 100.1499 0.5913 3.2% 485.98 4.961 2.38

VR (1) 8, 7, 9 

SG 25% 100% LV BL 15 207.126 242.1265 235.0549 122.9824 122.9283 122.1826 121.8061 100.15 0.5891 3.2% 470.68 5.177 2.41

VR (1) 7, 7, 8 

SG 25% 75% LV BL 15 210.0627 245.1867 238.2018 122.8117 122.7576 122.0128 121.6368 100.1499 0.5891 3.2% 476.27 5.1021 2.41

VR (1) 7, 7, 8 

SG 25% 50% LV BL 15 213.1836 248.3942 241.499 122.6432 122.5892 121.8454 121.4698 100.1499 0.5892 3.2% 482.29 5.0259 2.41

VR (1) 7, 7, 8 

SG 25% 25% LV BL 15 216.5831 251.8481 245.0485 122.4716 122.4176 121.6747 121.2997 100.1499 0.5893 3.2% 488.93 4.9462 2.41

VR (1) 7, 7, 8 

SG 25% 0% LV BL 16 221.4424 256.9205 250.1782 123.0328 122.9777 122.2301 121.8535 100.15 0.5896 3.2% 503.07 4.8634 2.41

VR (1) 7, 7, 8 

SG 25% -50% LV BL 16 229.4716 264.9431 258.3683 122.6806 122.626 121.8813 121.5057 100.1499 0.59 3.3% 520.22 4.6972 2.40

VR (1) 8, 8, 9 

SG 25% -100% LV BL 16 237.9682 273.3106 266.9479 122.3359 122.2815 121.5386 121.1639 100.1499 0.5901 3.3% 538.25 4.532 2.40

VR (1) 8, 8, 9 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 LV BL 0.53% 0.18% 2.42% 

VR (1) 7, 7, 8 

SG 75% 0 LV BL 0.55% 0.20% 3.69% 

VR (1) 7, 7, 8 

SG 100% 0 LV BL 0.57% 0.22% 4.93% 

VR (1) 7, 7, 8 

SG 106.7% 0 LV BL 0.57% 0.23% 5.26% 

VR (1) 7, 7, 8 

SG 100% 100% LV BL 0.53% 0.26% 7.40% 

VR (1) 7, 7, 8 

SG 100% -100% LV BL -0.01% 0.16% 2.29% 

VR (1) 8, 7, 9 

SG 25% 100% LV BL 0.47% 0.19% 3.34% 

VR (1) 7, 7, 8 

SG 25% 75% LV BL 0.33% 0.18% 2.88% 

VR (1) 7, 7, 8 

SG 25% 50% LV BL 0.19% 0.17% 2.41% 

VR (1) 7, 7, 8 

SG 25% 25% LV BL 0.05% 0.15% 1.89% 

VR (1) 7, 7, 8 

SG 25% 0% LV BL 0.51% 0.16% 1.14% 

VR (1) 7, 7, 8 

SG 25% -50% LV BL 0.22% 0.12% -0.06% 

VR (1) 8, 8, 9 

SG 25% -100% LV BL -0.06% 0.09% -1.31% 

VR (1) 8, 8, 9 

277
 
Table 62. Synchronous Generator Voltage Regulation Application (EL, LV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I2

Type Power Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 L

SG 50% 0 LV EL 16 212.2903 247.5062 240.9265 123.2606 123.1026 122.3766 121.9996 100.1499 0.5769 3.1% 443.41 5.0066 0

VR (1) 7, 7, 8 

SG 75% 0 LV EL 16 203.6169 238.6617 232.2108 123.3787 123.1704 122.4535 122.0762 100.1498 0.5716 3.0% 409.53 5.1741 0

VR (1) 7, 7, 8 

SG 100% 0 LV EL 16 195.1622 229.9907 223.688 123.4919 123.2341 122.5252 122.1478 100.1498 0.567 2.9% 379.28 5.3492 0

VR (1) 7, 7, 8 

SG 106.7% 0 LV EL 16 192.934 227.6962 221.4365 123.5215 123.2505 122.5436 122.1661 100.1497 0.5659 2.9% 371.78 5.3975 0

VR (1) 7, 7, 8 

SG 100% 100% LV EL 15 181.0127 216.1996 209.5588 124.0533 123.7631 123.14 122.7609 100.1496 0.5089 2.7% 327.99 5.8192 0

VR (1) 7, 7, 8 

SG 100% -100% LV EL 16 213.0625 247.1357 241.1868 122.1223 121.8917 121.0974 120.7239 100.1499 0.6305 3.2% 461.79 4.8718 0

VR (1) 10, 11, 12 

SG 25% 100% LV EL 15 208.6222 243.9988 237.0845 123.7093 123.5693 122.9178 122.5393 100.1497 0.5263 3.0% 429.05 5.1957 0

VR (1) 6, 6, 7 

SG 25% 75% LV EL 15 211.2622 246.6659 239.7802 123.3795 123.2477 122.5779 122.2004 100.1498 0.5403 3.0% 438.23 5.1119 0

VR (1) 7, 7, 8 

SG 25% 50% LV EL 15 213.8455 249.2062 242.3909 123.0608 122.937 122.2478 121.8712 100.1498 0.5541 3.1% 448.04 5.0287 0

VR (1) 7, 7, 8 

SG 25% 25% LV EL 15 216.7438 252.02 245.2842 122.7333 122.6182 121.9086 121.5328 173.4712 0.5683 3.1% 460.03 4.94 0

VR (1) 7, 7, 8 

SG 25% 0% LV EL 16 221.4532 256.8277 250.101 123.1283 123.0217 122.2865 121.9097 100.1499 0.5832 3.2% 482.19 4.8432 0

VR (1) 8, 8, 9 

SG 25% -50% LV EL 16 228.481 263.5061 256.9753 122.4626 122.3755 121.5962 121.2214 100.15 0.6122 3.3% 516.53 4.6532 0

VR (1) 8, 8, 9 

SG 25% -100% LV EL 16 237.6856 272.3481 266.1733 121.7458 121.681 120.8464 120.4737 100.15 0.6467 3.4% 565.3 4.453 0

VR (1) 12, 12, 14 

Improvement 

Machine Real Reactive Lowest Node 1 

Type Power Power HV / LV Location Voltage Losses Capacity 

SG 50% 0 LV EL 0.63% 0.34% 2.54% 

VR (1) 7, 7, 8 

SG 75% 0 LV EL 0.69% 0.43% 3.86% 

VR (1) 7, 7, 8 

SG 100% 0 LV EL 0.75% 0.51% 5.15% 

VR (1) 7, 7, 8 

SG 106.7% 0 LV EL 0.77% 0.52% 5.49% 

VR (1) 7, 7, 8 

SG 100% 100% LV EL 1.26% 0.66% 7.20% 

VR (1) 7, 7, 8 

SG 100% -100% LV EL -0.42% 0.23% 2.59% 

VR (1) 10, 11, 12 

SG 25% 100% LV EL 1.08% 0.39% 3.06% 

VR (1) 6, 6, 7 

SG 25% 75% LV EL 0.80% 0.36% 2.66% 

VR (1) 7, 7, 8 

SG 25% 50% LV EL 0.53% 0.32% 2.29% 

VR (1) 7, 7, 8 

SG 25% 25% LV EL 0.25% 0.28% 1.87% 

VR (1) 7, 7, 8 

SG 25% 0% LV EL 0.56% 0.24% 1.15% 

VR (1) 8, 8, 9 

SG 25% -50% LV EL -0.01% 0.12% 0.15% 

VR (1) 8, 8, 9 

SG 25% -100% LV EL -0.63% -0.04% -1.16% 

VR (1) 12, 12, 14 

278
 
Table 63. Synchronous Generator Voltage Regulation Application (ML, LV) – LL 

Node 01 Lowest 3Φ Voltage Lowest 

1Φ

Voltage 

Highest 

I2/I1 % 

Highest 

V2/V1 % 

% kW 

Loss 

Total 

kVar Loss 

I

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location LTC Tap IA IB IC VA VB VC Node 0 

SG 50% 0 LV ML 16 212.3396 247.5788 240.9566 123.2559 123.0939 122.3713 121.9943 100.1499 0.5762 3.1% 447.96 5.0013 0

VR (1) 7, 7, 8 

SG 75% 0 LV ML 16 203.6459 238.736 232.2155 123.3749 123.1601 122.4489 122.0716 100.1498 0.5704 3.0% 414.53 5.1672 0

VR (1) 7, 7, 8 

SG 100% 0 LV ML 16 195.1391 230.0414 223.638 123.491 123.224 122.5235 122.1461 100.1497 0.5653 2.9% 383.51 5.3416 0

VR (1) 7, 7, 8 

SG 106.7% 0 LV ML 16 192.8913 227.7359 221.3666 123.5217 123.2408 122.543 122.1655 100.1497 0.564 2.9% 375.61 5.3899 0

VR (1) 7, 7, 8 

SG 100% 100% LV ML 15 180.3035 215.4447 208.831 124.0729 123.7724 123.1571 122.7779 100.1496 0.5063 2.8% 330.64 5.8102 0

VR (1) 6, 6, 7 

SG 100% -100% LV ML 16 213.0786 247.3756 241.2184 122.1295 121.8875 121.1051 120.7316 100.1498 0.629 3.1% 455.38 4.8838 0

VR (1) 10, 11, 12 

SG 25% 100% LV ML 15 208.257 243.5636 236.709 123.7181 123.5753 122.926 122.5474 100.1497 0.5252 3.0% 430.81 5.1856 0

VR (1) 6, 6, 7 

SG 25% 75% LV ML 15 211.0207 246.3693 239.5242 123.3835 123.2494 122.5814 122.2038 100.1498 0.5395 3.1% 441.23 5.1026 

VR (1) 7, 7, 8 

SG 25% 50% LV ML 15 213.7131 249.0361 242.2424 123.0612 122.9354 122.2477 121.871 100.1498 0.5534 3.1% 451.66 5.0208 0

VR (1) 7, 7, 8 

SG 25% 25% LV ML 16 218.0283 253.4786 246.7043 123.4602 123.3425 122.6284 122.2507 100.1499 0.5684 3.1% 470.68 4.9307 0

VR (1) 7, 7, 8 

SG 25% 0% LV ML 16 221.202 256.556 249.8464 123.1342 123.0254 122.2907 121.9139 100.1499 0.5826 3.2% 0 4.8436 

VR (1) 7, 7, 8 

SG 25% -50% LV ML 16 228.6085 263.7029 257.1074 122.4603 122.3707 121.5939 121.2191 100.15 0.612 3.3% 515.86 4.6577 0

VR (1) 8, 8, 9 

SG 25% -100% LV ML 16 237.7999 272.6093 266.318 121.7498 121.6811 120.8512 120.4784 100.15 0.6466 3.4% 558.04 4.4672 0

VR (1) 12, 12, 14 

Improvement 

Machine 

Type 

Real 

Power 

Reactive 

Power HV / LV Location 

Lowest 

Voltage Losses 

Node 1 

Capacity 

SG 50% 0 LV ML 0.63% 0.32% 2.53% 

VR (1) 7, 7, 8 

SG 75% 0 LV ML 0.69% 0.41% 3.85% 

VR (1) 7, 7, 8 

SG 100% 0 LV ML 0.75% 0.49% 5.14% 

VR (1) 7, 7, 8 

SG 106.7% 0 LV ML 0.77% 0.51% 5.49% 

VR (1) 7, 7, 8 

SG 100% 100% LV ML 1.27% 0.63% 7.32% 

VR (1) 6, 6, 7 

SG 100% -100% LV ML -0.41% 0.26% 2.56% 

VR (1) 10, 11, 12 

SG 25% 100% LV ML 1.08% 0.38% 3.13% 

VR (1) 6, 6, 7 

SG 25% 75% LV ML 0.80% 0.34% 2.71% 

VR (1) 7, 7, 8 

SG 25% 50% LV ML 0.53% 0.31% 2.31% 

VR (1) 7, 7, 8 

SG 25% 25% LV ML 0.84% 0.28% 1.65% 

VR (1) 7, 7, 8 

SG 25% 0% LV ML 0.56% 0.23% 1.19% 

VR (1) 7, 7, 8 

SG 25% -50% LV ML -0.01% 0.12% 0.13% 

VR (1) 8, 8, 9 

SG 25% -100% LV ML -0.62% 0.00% -1.20% 

VR (1) 12, 12, 14 

279
 
12 Conclusions and Recommendations 

12.1 Conclusions 

•	 Five methods to improve voltage regulation at the substation were explained and seven 

methods to improve voltage regulation on the distribution circuit were defined. It was 

shown that the voltage drop is six times less for three-phase circuit than single-phase 

circuit portions with the same load, yet most of the load is served by the single-phase 

portions of the circuit. Voltage and current equations were developed for the Type A 

and Type B step VRs and the bidirectional regulator, which is required for operation of 

DG on the circuit. The operation of the line drop compensator and how the settings are 

calculated when loads are tapped off the circuit before the regulation point were 

explained. In addition, equations were developed to determine the settings of the 

regulator when shunt capacitors are added to the circuit. Why grounded wye capacitors 

are used on four-wire wye-grounded systems and why delta-connected capacitors are 

used on ungrounded systems to alleviate series resonant conditions were explained. 

•	 Causes for unbalanced voltage and current and how these conditions affect protective 

relaying were explained. The neutral relay is set to trip for ground faults, and the trip 

value may have to be increased to account for increased neutral current because of 

unbalance. This may cause a loss of sensitivity in clearing for faults. 

•	 Significant unbalanced loading can occur even though voltages are balanced at the 

source. Reclosers and the substation breaker with ground fault-sensing circuits are 

affected by load imbalance. Unequal single-phase load connected line-to-line does not 

produce neutral current in the ground relay. 

•	 Fuse preload because of unbalanced loading can cause fuses to become unselective 

with other protective devices such as reclosers and cause misoperation. 

•	 Reducing unbalanced loading reduces the losses created by the neutral current in the 

neutral conductor. 

•	 Unbalanced three-phase voltages have a significant effect on the heating of induction 

and synchronous generators. For example, a 5.5% voltage unbalance can cause an 

approximate 25% increase in temperature rise. The phase currents with unbalanced 

voltages are greatly unbalanced, on the order of four to five times the voltage 

unbalance. If overload relay protection settings are raised because of unbalance, the 

generator may not be protected against overload and open phases. 

•	 Heating of induction generators because of voltage unbalance is affected by phase 

rotation. Phase rotation affects which of the phases has the highest line currents. This 

means negative sequence current protection must be used to protect the induction 

generator to prevent failure because of voltage unbalance. The negative sequence losses 

are proportional to the square of the negative sequence voltage. The generator may have 

to reduce output below nameplate rating to avoid overheating with voltage unbalance. 

280
 
An equation was developed to calculate machine derating with unbalanced voltages with 

only the percent unbalanced voltage and ratio of the positive-to-negative sequence 

impedances of the induction generator. It was shown that a 5% voltage unbalance causes 

a 3.2%–10.7% power output derate, depending on the positive-to-negative sequence 

impedance ratio. 

•	 The 13-utility voltage survey showed a maximum percent unbalance of 5.94%, with 

an average of 1.1%. Eighty-five percent of all tests were <2% voltage unbalance. The 

Milford Circuit showed the maximum percent unbalance to be 1.52% on the primary 

during HL conditions and 1.26% for LL. Typically, the maximum permissible current 

unbalance for synchronous generators is 10% of the rated stator current. A 15.44% 

negative sequence current is produced from a 3% voltage unbalance for a single-cage 

induction generator, so care must be exercised to locate generating units on a 

distribution circuit for which the voltage unbalance is less than 3% and the unbalance 

current is less than 10%–20%. 

•	 Models were developed for the 10-MVA LTC delta-wye-grounded substation 

transformer, the 167-kVA bidirectional VRs, the three wye-grounded capacitors, the 

line impedances, and all (nine cases) the distribution circuit transformer connections. 

•	 The line loss model was validated using three line configurations and balanced and 

unbalanced load conditions. The three line configurations were the balanced 

impedance triangular spacing configuration, or equilateral; the flat configuration nontransposed; and the flat configuration transposed. The purpose of the validation was to 

show that, with a balanced line impedance and balanced load, the kilowatt losses are 

the same in each phase and the total kilowatt losses are lowest. In addition, an example 

showed that, even though the kilowatt losses per phase are not correct because of the 

Kron reduction process from a four-by-four matrix to a three-by-three matrix, the total 

losses for the three phases are, in fact, correct. 

•	 Models were developed for the 1,000-kW synchronous generator, the self-excited 400­

kW induction generator, and the 400-kW high-speed generator and inverter system. 

•	 The line, equipment, and generation models were verified with the maximum phase 

current variance of 3.9% on July 17, 2006, and 5.7% on July 29, 2006—except for 

Node I, where the percent unbalance current was very high. The maximum phase 

voltage variance was 1.5% on July 17 and 1.2% on July 29. The maximum PF 

variance was 5.7% on July 17 and 3.4% on July 29. 

•	 The selected distribution circuit was a 13.2-kV, three-phase wye multi-grounded 

system that serves approximately 76.2% residential, 4% commercial, and 19.8% light 

industrial loads. The load on the summer peak day was 15.3 MVA, and the summer 

peak day minimum load was 5.91 MVA. Eight regulation tests were conducted for the 

HL load condition, and eight were conducted for the LL condition. The primary 

voltage to the substation was ranged from 95% to 105%. The regulation methods 

consisted of the: 

281
 
o	 LTC 

o	 LTC and VR 1 

o	 LTC, VR 1, and VR 2 

o	 LTC and Cap 1 

o	 LTC, Cap 1, and Cap 2 

o	 LTC, Cap 1, Cap 2, and Cap 3 

o	 LTC, VR 1, VR 2, Cap 1, Cap 2, and Cap3. 

The voltage spread, measured as the difference between the highest three-phase 

voltage and the lowest single-phase voltage, for the HL condition was 25.2 V with no 

regulation at the substation and on the distribution circuit. When all regulation was 

implemented, this voltage spread was reduced to only 10.4 V, and there were no 

voltage criteria violations. For the LL condition, the voltage spread was 16.65 V for no 

regulation. With all regulation operating, the spread was only 2.91 V. 

•	 The load imbalance at the substation was 4% for HL and 5.45% for LL. Adding 

regulation does not necessarily improve load imbalance; in fact, higher voltages 

generally cause higher loads and more imbalance. 

•	 The VDC model best represented how the circuit load changes with changes in source 

voltage. The model consisted of % ΔP/% ΔV = 1.26 and % ΔQ/% ΔV = 4.66%. The 

CC model percent error was 3.9%, the CP model percent error was 12.5%, and the 

VDC model percent error was only 2%. 

•	 Three voltage control strategies were tested for the 400-kW induction generator at LV 

and HV substation primary voltage for a total of six simulations. Three voltage control 

strategies were tested for the 400-kW inverter-based generation at LV and HV 

substation primary voltage for a total of six simulations. And 13 voltage control 

strategies for HV and 13 for LV were tested for the synchronous generator located at 

the BL, ML, and EL of the circuit, for a total of 78 simulations. The maximum 

released capacity of 10.44% was achieved with the 1,000-kW synchronous generator 

with P = 100% and Q = 100%. The voltage improvement was 0.82%, and the loss 

reduction was 0.56% out of a 5.4% base. 

•	 The optimum location for the DG with the highest released capacity of 10.44% was at 

the source of the circuit because it directly offset the load current and load losses of 

the circuit. The optimum DR location to achieve the greatest loss reduction was at the 

EL of the circuit because adding generation here reduces on a prorata basis the load 

and the length of the circuit. There was little difference for improving the voltage 

regulation between locating the DR at the midpoint or end of the circuit. There was a 

slightly better improvement at the midpoint for circuits in which the conductor size of 

the entire three-phase backbone was the same. 

282
 
•	 The DG penetration study showed that a synchronous DG had a real power limit of 

13,980 kW at the tag end of the circuit. The optimum location was at the midpoint, 

with the lowest single-phase voltage improvement of 1.7% and a real power loss 

savings of 2.04%. The base case real power losses were 5.4%. The DG penetration 

study found that the maximum real and reactive power output limit was 14,490 kW 

and 2,007 kVAr, which allows a larger DG to be installed than when only real power 

was injected. Again, the optimum location was at the midpoint of the circuit, but, in 

this case, the lowest single-phase voltage was improved 4.55% versus only 1.7% in 

the real power limit case. The real power loss savings were marginally better, with a 

2.3% savings versus 2.04%. This saving in losses represents a 57.4% reduction when 

the DG is located at the midpoint of the circuit. 

12.2 Recommendations 

•	 This project used validated circuit equipment and line models and a validated VDC 

source load model to test 78 synchronous generator voltage control strategies. It found 

the greatest improvement in released capacity reduced real losses and improvement in 

voltage regulation occurred when the synchronous generator produced the maximum 

real and reactive power. DG can be sized and located to produce these improvements, 

but the effects on system protection systems must be evaluated. 

•	 It is recommended that a validated unbalanced three-phase power flow program be 

used to determine the percent unbalanced voltage and percent unbalanced current 

throughout the circuit. If the percent unbalanced voltage exceeds 3% and the percent 

unbalanced current exceeds 10% at the location where a synchronous generator is to 

be sited, it is highly possible it will never operate and could trip on voltage or current 

imbalance. 

•	 It is highly recommended that a VDC source be used for the load model because it is 

more accurate than the CP and CC models. 

•	 The optimum voltage regulation method that produced the least voltage spread used 

the substation transformer LTC, step regulators, capacitors, and DG. It is 

recommended that the DG be located at the midpoint of the circuit to produce the best 

overall improvements in voltage regulation, loss reduction, and released capacity. 

•	 The circuit selected had voltage unbalance conditions that closely agreed with the 

average voltage unbalance measurements taken at 13 major utilities. Therefore, the 

results should be representative of what would be experienced on the average 

distribution circuit. 

•	 Voltage regulation and system protection issues represent the most difficult problems 

for interconnecting DG with the distribution circuit. This report explains how voltage 

unbalance and current imbalance can affect system protection performance and the 

rating of the DG output. It is recommended that inverter-based generation be 

considered as the preferred DG type if the level of unbalanced voltage and current 

may prevent synchronous and induction generators from operating on the circuit. 

283
 
•	 Future research should fund the development of a real-time optimal control of DG to 

accomplish the optimum generator voltage control condition, including the control of 

the substation transformer LTC, the bidirectional step regulators, and the switched 

capacitors. The cost to perform this development work on the Milford Circuit DC 

8103 would be substantially less than installing DG and metering equipment on a new 

circuit because all of this equipment is already installed and tested. Furthermore, the 

newly developed control strategies can be tested in the summer of 2008. The estimated 

cost for this project is less than $500,000, and the development, testing, and analysis 

schedule is estimated to be approximately 1.5 years. 

12.3 Benefits to California 

Models were developed and validated with actual measured circuit and generator test data. 

This project showed that adding DG to a distribution circuit can reduce generation capacity by 

10% (released capacity), and these results can be achieved in 1 year—not 7–10 years—for 

traditional central-station generation. Also, improved voltage regulation results in fewer 

service voltage criteria violations and less distribution energy losses (i.e., approximately 10%). 

284
 
13 References 

Davis, M.W. (2003). Determine the Market Penetration Limits of Distributed Energy 

Resources (by Distributed Generation Type) by the Year 2015. Department of 

Energy/National Renewable Energy Laboratory report. 

Davis, M.W.; Krupa, T.J.; Diedzic, M.J. “The Economics of Load Management on the Design 

and Operation of the Distribution System, Part II Load Characteristics.” IEEE Transactions 

on Power Apparatus and Systems; Vol. PA8-102 No. 3, March 1983; pp. 654–674. 

Electrical Distribution System Protection. 3rd edition. Pewaukee, WI: Cooper Power. Cooper 

Power Systems Bulletin 90020 February 2005. Available at www.cooperpower.com. 

Gafford, B.N.; Duesterohoeft, N.C.; Mosher, C.C. III. “Heating of Induction Motors on 

Unbalanced Voltages.” Prepared for the American Institute of Electrical Engineers Winter 

General Meeting, New York, Feb. 1–6, 1959; p. 284. 

Kersting, W.H. “The Computation of Neutral and Dirt Currents and Power Losses.” Prepared 

for the Power Systems Conference and Exposition 2004. IEEE PES, Vol. 10–13, October 

2004; pp. 213–218. 

G. E. Multilin SR 469 Motor Management Relay, 1998. 

Mason, C.R. The Art and Science of Protective Relaying. General Electric online, 

http://www.geindustrial.com/industrialsystems/pm/notes/artsci/index.htm. 

National Electrical Manufacturers Association Standard for Motors and Generators MG1, 

1978. 

Elmore, W.A. Protective Relaying Theory and Applications. 2nd edition. New York: Marcel 

Dekker Inc., 1994. 

S&C Electric Co. “Data Bulletin 350-195,” July 17, 2000; p. 1 of 4. 

S&C Electric Co. “Coordinaide: The S&C Protection and Coordination Assistant.” S&C 

Electric Co. online, http://www.sandc.com/FSA/coordinaide.asp. 

Tracey, G.F. “Maximum Allowable Continuous Output of Induction Motors Operating Under 

Unbalanced Voltages.” April 1954. Discussion of J. E. Williams “Operation of Three-Phase 

Induction Motors on Unbalanced Voltages,” Power Apparatus and Systems, April 1954, p. 

132. 

Wagner, C.F.; Evans, R.D. Symmetrical Components. New York: McGraw Hill Book Co. 

Inc., 1933; pp. 345–350. 

Williams, J.E. “Operation of Three-Phase Induction Motors on Unbalanced Voltages.” 

American Institute of Electrical Engineers Winter General Meeting; Jan. 18–22, 1954, New 

York. 

285
 
286
 
Appendix A: Ground Detector and Ungrounded Systems 

For ungrounded delta systems, there is a normal leakage current of about 2 A to ground 

because of the distributed capacitance, as shown in Figure A-1. The VTs with a ratio of 40:1 

are connected in a broken delta configuration on the secondary side. Under normal 

circumstances, the line-to-neutral voltages on the primary of the VT are 2,770 V, and the 

voltage vectors on the secondary side have a magnitude of 69 V with an angle of 120° 

between these vectors. These vectors add to zero, as in the phasor diagram of Figure A-2. 

When a ground is applied to Phase Conductor A, as in Figure A-3, this phase goes to ground 

potential, while the two unfaulted phases have 4,800 V applied across each. This causes an 

increase in the ground current IG from 2 A to 6 A and an increase in voltage on the secondary 

of the broken delta from 0 V to 208 V. This phasor diagram is shown in Figure A-4. 

Grounding phase conductors of an ungrounded delta system produces a minimum current 

unbalance of 3.46 A in this case. Overcurrent relays are not normally installed to detect this 

small current unbalance. But there are instances in which as much as 20–30 A have been 

detected. This is still less than the typical overcurrent settings of 70 A for a recloser on the 

circuit and 1,000 A or higher for a breaker at the substation. 

A.1. Ungrounded Delta Ground Detection – Normal Condition, No Ground 

Applied to Phase Conductor 

C 

System Transformation 

Wye - Delta 

B 

VT = 40:1 = = 69V 40 

2771 

2771V 

2771V 

2771V 40:1 

I'CA = 2A 180 

I'CB = 2A 60o 

I'CC = 2A - 60 

4.8 kV 

N 

2.771 kV 

V ref. 

69V 

69V 

69V 

Broken 

Delta 

0 Volts 

I

C = capacitive curr 

to ground 

I

CA = capacitive cur 

phase A to gro 

Figure A-1. Normal leakage currents to ground because of distributed capacitance 

287
 
VA= 69V

VB VC 

Vref. 

2.771 

I

C = 2A 60o 

B 

I

C = 2A -60o 

I

C = 2A 80o 

A 

VB VC

Vref.

2.771

I

C = 2A 60o

B

I

C = 2A -60o

I

C = 2A 80o

A

C

VB + VC V = 0 B + VC V = 0 A + 

Figure A-2. Normal leakage currents to ground 

because of distributed capacitance – phasor diagram 

A Phase Conductors 

C B

System Transformation 

Wye - Delta 

4800V 4800V 40:1 

I'CB = 3.464 A 30o 

4.8 kV 

120V 

120V 

4.8 kV 

4.8 kV 

I'CA = 0 

I

G = I'CB + I'CC = 6A 0o 

I'CC = 3.464A -30o 

A 

C B

208V 

Figure A-3. Increased leakage current on the unfaulted phases 

and resultant ground current IG and resultant zero sequence voltage 3 VO 

288
 
 

 

 

I'CB = 2A 3 = 3.4 6A

VC VB 

I

G = I'CB + I'CC = 6A 0O 

VT = 40:1 

120V 

120V 

A 

= 120V 40 

4,800 

3.46A 

6A 

3.46A 

I'CC (unfaulted phases 

are B and C.) 

3VO V = 208V

C VB

I

G = I'CB + I'CC = 6A 0O

VT = 40:1

120V

120V

A

=120V 40

4,800

3.46A

6A

3.46A

I'CC (unfaulted phases

are B and C.)

3VO = 208V

Figure A-4. Increased leakage current on the unfaulted phases 

and resultant ground current IG and resultant zero sequence voltage 3 VO – phasor diagram 

A.2. Relay Settings 

Phase Settings at Substation 

---------------------------------------------------------------------------

STATION: MILFD POSITION: T1-L

 EQUIPMENT: TRF 1 TO DC 8103 

SHEET#: 

SCHEME: A_REL

1 

FUNCTION: OVERCURRENT XYZ-51 

RELAY TYPE: CO-8 (4-12) 

PT RATIO: 0 : 1 

CT RATIO: 120 : 1 NORM: 

CT NOTE: 600:5 MR T.O.: 

PU = 7.5 X 120 10 MVA TRF'S. 

L = 1.75 

40 CYCLES AT 37.5 AMPS 

198 CYCLES AT 15 AMPS 

289
 
 

 

 

 

 

 

 

Neutral Settings at Substation 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: T1-L SHEET#: 2 

 EQUIPMENT: TRF 1 TO DC 8103 SCHEME: A_REL

 FUNCTION: OVERCURRENT N-51 

 RELAY TYPE: CO-8 (4-12) 

 PT RATIO: 0 : 1 

 CT RATIO: 120 : 1 NORM: 

CT NOTE: 600:5 MR T.O.: 

 EMERGENCY TAP = 5 

PU = 9 X 120 ( WHEN VWE #47316 IS JUMPERED OUT) 

L = 1.5 

33 CYCLES AT 45 AMPS 

 166 CYCLES AT 18 AMPS 

Reclosing Settings at Substation 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: T1-L SHEET#: 3 

 EQUIPMENT: TRF 1 TO DC 8103 SCHEME: A_REL

 FUNCTION: RECLOSING 179 

 RELAY TYPE: PART OF PR 

 CT RATIO: 0 : 1 

CT NOTE: 

 PT RATIO: 0 : 1 

NORM: 

T.O.: 

 RECLOSE: 30 SEC 30 SEC 30 SEC 

RESET: 5 MIN MAX 

290
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Phase Settings on Recloser 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 SHEET#: 1 

 EQUIPMENT: VWE RECLOSER ON DC 8103 SCHEME: OHRCL

 FUNCTION: OVERCURRENT (ESSENTIAL ME) 

 RELAY TYPE: ME RECL - C CURVE STOCK NO. 680-0341 

 PT RATIO: 0 : 1 

 CT RATIO: 1000 : 1 NORM: 

CT NOTE: T.O.: 

 PHASE TIME DELAY NOTES: 1) PLUG C CURVE TIMING CAN INTO THE 

 PHASE TRIP TIMING NO. 2 SOCKET 

 PU = 0.68 X 1000 = 680 AMPS 

 RESISTOR SIZE: 680 AMPS 2) 3 TIME DELAY OPERATIONS 

 173 CYCLES AT 1.36 AMPS (+ OR - 17 CYCLES) 

 47 CYCLES AT 2.72 AMPS (+ OR - 4 CYCLES) 

LOCATION: LW N GOING WIXOM 4PS RED OAK LN

 FAULT INDICATOR: AUTO 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 SHEET#: 2 

 EQUIPMENT: VWE RECLOSER ON DC 8103 SCHEME: OHRCL

 FUNCTION: OVERCURRENT 

 RELAY TYPE: ME RECL - R CURVE 

 PT RATIO: 0 : 1 

 CT RATIO: 1000 : 1 NORM: 

CT NOTE: T.O.: 

 PHASE FAST TIME NOTES: 1) PLUG R CURVE TIMING CAN INTO THE 

 PHASE TRIP TIMING NO. 1 SOCKET 

 2) SET PHASE TRIP SOCKET 1 DIAL AT 1 

 PU = 0.68 X 1000 = 680 AMPS 

 RESISTOR SIZE: 680 AMPS 3) 1 FAST TIME OPERATION 

 15 CYCLES AT 1.36 AMPS (+ OR - 1 CYCLE) 

 7 CYCLES AT 2.72 AMPS (+ OR - 1 CYCLE) 

291
 

 

 

 

 

 

 

 

 

 

 

 

 

 Neutral Settings on Recloser 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 

 EQUIPMENT: VWE RECLOSER ON DC 8103 

SHEET#: 3 

SCHEME: OHRCL

 FUNCTION: OVERCURRENT 

 RELAY TYPE: ME RECL - 6 CURVE 

 PT RATIO: 0 : 1 

 CT RATIO: 1000 : 1 NORM: 

CT NOTE: T.O.: 

 NEUTRAL TIME DELAY NOTES: 1) PLUG 6 CURVE TIMING CAN INTO THE 

 GROUND TRIP TIMING NO. 2 SOCKET

 2) SET GROUND TRIP SWITCH TO NORMAL

 PU = 0.80 X 1000 = 800 AMPS 

 RESISTOR SIZE: 800 AMPS 3) 3 TIME DELAY OPERATIONS 

 143 CYCLES AT 1.60 AMPS (+ OR - 14 CYCLES) 

 46 CYCLES AT 3.20 AMPS (+ OR - 4 CYCLES) 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 SHEET#: 4 

 EQUIPMENT: VWE RECLOSER ON DC 8103 SCHEME: OHRCL

 FUNCTION: OVERCURRENT 

 RELAY TYPE: ME RECL - 4 CURVE 

 PT RATIO: 0 : 1 

 CT RATIO: 1000 : 1 NORM: 

CT NOTE: T.O.: 

 NEUTRAL FAST TIME NOTES: 1) PLUG 4 CURVE TIMING CAN INTO THE 

 GROUND TRIP TIMING NO. 1 SOCKET 

 2) SET GROUND TRIP SOCKET 1 DIAL AT 1 

 PU = 0.80 X 1000 = 800 AMPS 

 RESISTOR SIZE: 800 AMPS 3) 1 FAST TIME OPERATION 

 12 CYCLES AT 1.60 AMPS (+ OR - 1 CYCLE) 

 4 CYCLES AT 3.20 AMPS (+ OR - 1 CYCLE) 

292
 

 

 

 

 

 

 

 

 

 

 

Reclosing Setting on Recloser 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 SHEET#: 5 

 EQUIPMENT: VWE RECLOSER ON DC 8103 SCHEME: OHRCL

 FUNCTION: RECLOSING 

 RELAY TYPE: ME RECL - RECLOSING

 PT RATIO: 0 : 1 

 CT RATIO: 1000 : 1 NORM: 

CT NOTE: T.O.: 

1ST - 0 SEC NOTE: SET RECLOSING SWITCH IN 

2ND - 30 SEC NORMAL RECLOSING POSITION 

3RD - 30 SEC 

LOCKOUT DIAL = 4 OPERATIONS 

 RESET DELAY TIMING PLUG = 45 SEC 

Phase Neutral and Reclosing Setting on Form 5 Control 

 --------------------------------------------------------------------------- 

 STATION: MILFD POSITION: 47316 SHEET#: 2 

 EQUIPMENT: VWE RECLOSER ON DC 8103 SCHEME: OHRCL

 FUNCTION: OVERCURRRENT

 RELAY TYPE: FORM5 (SHEET 2 OF 7) 

 PT RATIO: 0 : 1 

 CT RATIO: 0 : 1 NORM: 

CT NOTE: T.O.: 

NORMAL ALT1 ALT2 ALT3 PHASE PROFILE|NORMAL ALT1 ALT2 ALT3 

GROUND PROFILE 

OPERATIONS TO LOCKOUT:4 |OPERATIONS TO LOCKOUT:4 

 NORMAL PU = 0.68 X 1000 = 680 AMPS |NORMAL PU = 0.60 X 1000 = 600 

AMPS 

ALT1 PU = 0.68 X 1000 = 680 AMPS |ALT1 PU = 0.60 X 1000 = 600 AMPS 

ALT2 PU = 0.68 X 1000 = 680 AMPS |ALT2 PU = 0.60 X 1000 = 600 AMPS 

ALT3 PU = 0.68 X 1000 = 680 AMPS |ALT3 PU = 0.60 X 1000 = 600 AMPS 

TCC1 = KYLE_105 |TCC1 = KYLE_106 

TCC2, TCC3, TCC4 = KYLE_133 |TCC2, TCC3, TCC4 = KYLE_136 

HOT LINE TAG = KYLE_105 |HOT LINE TAG = KYLE_106 

FAST TRIPS DISABLED = KYLE_133 |FAST TRIPS DISABLED = KYLE_136 

1ST RECLOSE INTERVAL: 20 SEC. |1ST RECLOSE INTERVAL: 20 SEC. 

2ND RECLOSE INTERVAL: 30 SEC. |2ND RECLOSE INTERVAL: 30 SEC. 

3RD RECLOSE INTERVAL: 30 SEC. |3RD RECLOSE INTERVAL: 30 SEC. 

RESET TIME FOR PHASE AND NEUTRAL: 45 SEC 

293
 
294
 
Appendix B: Circuit Modeling 

B.1 Circuit Modeling Verification 

The circuit was modeled using CC, CP, and VDC. Based on actual circuit-measured data 

taken from a circuit with a similar composition of load (Davis, Krups, and Diedzic 1983) as 

the Milford Circuit DC 8103, equations, B.1 and B.2 were developed for the summer period 

when the ambient temperature ranged from 80°F to 90°F. The resultant change in real power 

P and reactive power Q for the range of source voltage -2.8% (119.5 V) to 0% (122.9 V) to 

+4.2% (128.0 V) was 

% Δ P 

= 1.26 Equation B.1 % Δ V 

and 

% Δ Q = 4.66 . Equation B.2 % Δ V 

To see which of the three model simulations best agrees with the measured circuit data, tests 7 

and 8 were repeated for 95% primary voltage and HL conditions. By viewing the line current 

data of Table B-1 and comparing the differences between the actual and simulated values for 

each load model in Table B-2, it can be seen that the CC and VDC models best represent the 

load characteristics for the circuit. 

To check the accuracy, the actual line currents at Node 0 were subtracted from the simulated 

values (shown as δ). Then the absolute values of these phase current differences were 

summed and divided by three (the number of phases). For example, Test 7 for the CC model 

shows an absolute difference of 94. To obtain a percent difference between the actual and 

simulated currents, the actual line current magnitudes were summed and divided by three. 

I 3 δ Φ This value ‡” forms the basis for comparing the deviation ‡” with the basis for each 3 3 

model applied. 

This resulted in 3.9% for the Test 7 CC model. The CP model had a deviation of 12.5%. The 

VDC model was slightly better (3.6%) than the CC model. When this process was repeated for 

Test 8 at 95% primary voltage, the VDC model had a deviation of only 2%, which is less than 

the measurement accuracy of 3%. 

The change in real power P and the change in reactive power Q as a function of change in 

source voltage V was defined (in (Davis, Krups, and Diedzic 1983) as 

%ΔP %ΔQ = 1.26% and = 4.66 . %ΔV %ΔV 

295
 
These percent changes in P and Q represent changes in flow at the source for changes in 

source voltage from 99.58% (119.5 V) to 106.67% (128.0 V). 

To implement the load characteristics into the power flow algorithm, it becomes necessary to 

represent the percent changes in P and Q as percent change in current. 

θ0 

θ1 

S0 = P0+jQ0 

S1

= P1+jQ1 

P0 ΔP

ΔQ 

Q0 

Figure B-1. Percent change in kilovolt-amperes or current from percent change in P and Q 

The three-phase kilovolt-ampere flow S is proportional to the phase circuit I. Therefore, the 

percent change in current (I) for a 1% change in voltage is equal to the percent change in 

kilovolt-amperes, or 

S - S

% ΔS = % ΔI = 1 0 x 100. S0 

For this study, at HL condition, the % ΔI = 1.8% for a 1% change in voltage. The example below 

shows how the percent change in current of 1.9% is calculated for the initial values of P0 = 2,000 

kW and Q0 = 1,000 kVArs for a 13.2-kV system and a 1% change in voltage at the source. 

θ0 =26.56° 

θ1 = 

27.33° 

S0 = 2236 kVA 

S1 = 2279 kVA 

Q0 = 1000 kVar 

1.26% = 25.2 kW = ΔP 

P0 = 2000 kW 

4.66% = 46.6 kVar = ΔQ 

Figure B-2. Percent change in kilovolt-amperes or current 

296
 
S - S 2279 - 2236

%ΔS = 1 0 x 100 = x 100 = 1.9% S0 2236 

2279 kVA

I1 = = 99.68A 

3 13.2 kV
 

2236 kVA

I0 = = 97.80A 

3 13.2 kV
 

I1 - I 0 99.68 - 97.80

%ΔI = x 100 = x 100 = 1.9% 

I0 97.80 

B.2 Load Imbalance 

As previously noted, a 100% load imbalance occurs at any node at which a line-to-line load or 

line-to-neutral load is connected to the wye-grounded systems. Proof of this statement is 

given below. 

In Table B-4 (Test 8) at 95% primary voltage and HL conditions with LTC, VR 1, VR 2, and 

capacitors 1, 2, and 3 turned on, at Node 22 E, the phase current is 27.153 amperes, which 

indicates a line-to-neutral load. Now, from the zero sequence I0, positive sequence I1, and 

negative sequence I2 currents of 9.051 A from Table B-4, it can be shown that 

IA1 = (IA + IB a + IC a2

)/3 Equation B.3 

= (27.153 0° + 0 + 0)/3 

= 9.051 0o 

IA2 = (IA + IB a2

 + IC a)/3 Equation B.4

 = (27.153 0° + 0 + 0)/3 

= 9.051 0° 

IA0 = (IA + IB + IC)/3 Equation B.5 

= (27.153 0° + 0 + 0)/3 

= 9.051 0° 

Furthermore, 

IB1 = IA1 a2 = 9.051 -120° Equation B.6 

IC1 = IA1 a = 9.051 120° Equation B.7 

IB2 = IA1 a = 9.051 120° Equation B.8 

IC2 = IA1 a2

 = 9.051 -120° Equation B.9 

IA0 = IB0 = ICO = 9.051 0° Equation B.10 

297
 
and 

IA = IA1 + IA2 + IA0 Equation B.11 

= 9.051 0° + 9.051 0° + 9.051 0° 

= 27.153 0° . 

The percent unbalanced current is then calculated from equations B.3 and B.4, or 

I A2 9.051

x 100 = x 100 =100% . Equation B.12 IA1 9.051 

B.3 System Zero Sequence Currents Become Negative Sequence Currents on 

the Generator Windings 

The zero sequence currents for each test are given in Table B-3. The values range from 45.43 

A for Test 2 up to 50.24 A for Test 8. Because most small synchronous machines are wyeconnected with an ungrounded neutral and the output terminals of these machines are 

normally connected to delta-wye transformers with the high-side wye grounded, there is no 

problem with these zero sequence current magnitudes if interconnected to the power system. 

For machines operating in an islanded mode with a delta-wye high-side transformer and a 

solidly grounded neutral, high zero sequence currents on the high side will appear as negative 

sequence currents on the machine windings. This is a very serious problem because it results 

in 100% negative sequence currents in the generator windings. 

The zero sequence relays in the neutral at the substation are set to trip at current levels higher 

than the phase currents to ensure the neutral relay does not trip for single-phase switching 

operations on the circuit. But a time delay could be added to permit a lower neutral relay trip 

setting (to ignore single-phase switching conditions and maintain selectivity) so it becomes 

more sensitive to line-to-ground faults. 

It will be shown that 100-A rated output current (on Phase A only) on the 13.2 kV on the high 

side of the transformer of a generating unit results in 33.34 A of zero sequence current on the 

load side of the generator step-up transformer. This is a common value of zero sequence 

currents. This produces a negative sequence current of 916 A on the generator windings, or a 

100% current imbalance or 

I 2 916A

% = x 100 =100% .

I1 916A 

298
 
C B 

A 

277 V 

C B 

A 

916A 

916A 

480 V 

C 

B 

A I

A 100A +120o 

7620 V 

I

AB = 1587 A 120o 

0o 

120o 

LOAD 

I

CG 

I

AG 

I

BG

 - IBG = 1587 A 120o 

I

AG = 1587 A 120o 

Generator Step-up Transformer 

Figure B-3. Zero sequence current on load side 

becomes negative sequence current to the generator 

V1 7620 N1 Let, = or =15.875, where V1 is the load-side voltage and V2 is the

V2 480 N2 

generator terminal voltage. The turns ratio is 15.875. 

By applying symmetrical components to the load side, 

IA = IA1 + IA2 + IA0 = 100 A +120° 

IA1 = (IA + IB a + IC a2

)/3

 (100 + 120° + 0 + 0)/3 

= 33.34 + 120° 

IA2 = (IA + IB a2

 + IC a)/3

 = 33.34 + 120° + 0 + 0 

and 

IA0 = (IA + IB + IC)/3 

 = 33.34 + 120° + 0 + 0 

∴ 3 IA0 = 100 amperes. 

Applying symmetrical components to the generator side, 

IAG1 = (IAG + IBG a + ICG a2

)/3, 

IAG2 = (IAG + IBG a2

 + ICG a)/3,

Equation B.13 

 Equation B.14 

 Equation B.15 

 Equation B.16 

 Equation B.17 

 Equation B.18 

299
 
300

and 

IAG0 = (IAG + IBG + ICG)/3. Equation B.19 

Substituting the rated phase current from the generator into the three equations above results in: 

IAG1 = (1,587 A + 120° + 1,587 A -60° a + 0)/3, Equation B.20 

IAG2 = (1,587 A + 120° + 1,587 A -60° a2 + 0)/3, Equation B.21 

and 

IAG0 = (1,587 A + 120° + 1,587 A -60° + 0)/3. Equation B.22 

Note: -IBG in Figure B-3 shows the current flow path, but polarity on –IBG must be the 

opposite direction +IBG for correct symmetrical component calculation (i.e. -IBG = 1,587 120° 

ˆ IBG = 1,587 -60°). 

I

AG a IBG

-60o a = 120o

I

BG

120o

o o AG1 9091690 3

2749

3

1587 = 3I = =

I

AG a IBG

-60o a = 120o

I

BG

120o

o o AG1 9091690 3

2749

3

1587 = 3I = =

Figure B-4. Determining IAG1 
a2 IBG 

IAG 

- 60o 

a2 = 240o 

IBG 

120o 

o o AG2 150 150916 3 

2749 

3 

1587

= 3I = =

Note: 

Notice the negative sequence current 

is equal to the positive sequence 

current or 100% load imbalance. 

a2 IBG

IAG

- 60o

a2 = 240o

IBG

120o

o o AG2 150 150916 3

2749

3

1587 = 3I = =

Note:

Notice the negative sequence current

is equal to the positive sequence

current or 100% load imbalance.

Figure B-5. Determining IAG2 

IAG 

IBG 

120o 

- 60o 

IAG0 = 0 because there is no ground on the generator 

wye connection. 

Figure B-6. Determining IAG0 

301
 
The rated power for the generator is 

Prated generator = 3 VL-L IL Equation B.23 

= 3 (13.2 kV) (100 A) = 2,286 kVA machine rating, 

and the rated current is 

2286 kVA

Irated generator = = 2749A full-load rated current, or IAG1. 3 480V 

The percent unbalance loading based on machine rating is 

I AG2 916A 

x100 = x100 = 33.3%.

IAG1 2749A 

For a balanced load, IAG = IBG =ICG, and 

IAG1 = (IAG + IBG a + ICG a2

)/3, 

IAG1 = (2,749 +90° + 2,749 + 90° + 2,749 + 90°)/3, 

and 

IAG1 = 2,749 A 90°. 

Even though the rated output on the high side of the transformer is 100 A, only 33.34 A of 

I 2 zero sequence current (on the high side) causes a 100% unbalanced current % on the

I1 

generator, which has a rated generator currency of 2,747 A per phase. The negative sequence 

current of 916 A is 33% of the generator machine rating (2,749 A) current. 

This negative sequence current of 916 A will cause the generator negative sequence relay to 

trip the unit because it is common to set this relay to 10% of the machine rating. Even with 

33.4 A of single-phase load, which is one-third of the 100 A of rated phase current on the high 

side, the negative sequence relay will trip the unit. Notice that the generating unit could only 

run at 10% of full rated output (or 30 A divided by 300 A full-rated three-phase capacity) 

without tripping. 

302
 
Table B-1. Simulation Summary Data for Tests 7 and 8 at 95% Voltage 

and HL Conditions and a Comparison of Modeling Results
 

for CC, CP, and VDC 

Lowest 

1Φ

Node 00 Lowest 3Φ Voltage Voltage Highest Highest kW Losses/Φ & Total kVAr Losses/Φ & Total 

Test No. 

Pri. Volt 

% 

Load 

Type 

LTC Tap 

/ Reg 

Tap IA IB IC VA VB VC I2/I1 % V2/V1 % A B C A B C 

7 95 CC 15 807.02 736.28 908.03 109.79 120.08 108.81 109.05 100.05 3.32 210.93 20.38 228.47 1119.86 820.68 1369.59 

Cap (1) 900 kVAr 459.78 3310.13 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 95 CP 16 871.31 720.56 1037.24 108.43 124.00 102.64 102.89 100.04 5.15 204.93 -31.59 419.29 1392.44 729.90 1982.90 

Cap (1) 900 kVAr 592.63 4105.24 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

7 95 VDC 14 756.47 723.87 844.61 110.88 118.45 110.72 110.79 100.05 2.61 190.80 40.20 170.49 953.41 811.06 1162.98 

Cap (1) 900 kVAr 401.49 2927.45 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 CC 15 828.54 744.03 928.42 114.70 122.11 111.24 110.46 100.05 3.08 221.99 16.61 244.04 1205.74 850.27 1447.40 

VR (1) 32, 14, 32 482.64 3503.41 

VR (2) 32, 10, 32 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 CP 16 866.95 723.58 1038.01 115.00 124.94 106.69 105.38 100.04 4.33 200.30 -18.75 403.81 1371.63 751.93 1988.70 

VR (1) 32, 8, 32 585.36 4112.26 

VR (2) 32, 4, 32 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

8 95 VDC 15 801.31 756.68 888.74 115.48 121.15 113.13 112.50 100.05 2.52 215.99 38.73 193.39 1092.14 894.21 1295.33 

VR (1) 32, 22, 32 448.11 3281.68 

VR (2) 32, 15, 32 

Cap (1) 900 kVAr 

Cap (2) 900 kVAr 

Cap (3) 1200 kVAr 

303
 
Table B-2. Comparison of Line Currents for Simulated and Actual Measurements 

for Each Load Model and Each Test 7 and 8 

Test 

No. 

Primary 

Voltage 

Load 

Type 

Voltage Regulation 

Method 

Node 0 

Line Amperes

 Simulated Actual 

Line Amperes 

Difference 

(δ) Amps % 

IA 807 794 +13 

IB 736 764 -28 

7 95% CC LTC, CAP 1, CAP 2, 

CAP 3 

IC 908 855 +53 

3 

δ

= 804, ‡” 3 

I 

‡” 3Φ

3 

94 

= 3.9 

IA 871 794 +77 

IB 721 764 -43 

7 95% CP LTC, CAP 1, CAP 2, CAP 3 IC 1037 855 182 

3 

δ

= 804, ‡” 3 

I 

‡” 3Φ

3 

302 

= 12.5 

IA 757 794 -37 

IB 724 764 -40 

7 95% VDC LTC, CAP 1, CAP 2, CAP 3 IC 845 855 -10 

3 

δ

= 804, ‡” 3 

I 

‡” 3Φ

3 

87 

= 3.6 

IA 829 794 +35 

IB 744 764 -20 

8 95% CC LTC, VR 1, VR 2, CAP 1, 

CAP 2, CAP 3 

IC 928 855 +73 

3 

δ

= 804, ‡” 3 

I 

‡” 3Φ

3 

128 

= 5.3 

IA 867 794 +73 

IB 724 764 -40 

8 95% CP LTC, VR 1, VR 2, CAP 1, 

CAP 2, CAP 3 

IC 1038 855 183 

3 

δ

= 804, ‡” 3 

I 

‡” 3Φ

3 

296 

= 12.3 

IA 801 794 +7 

IB 757 764 -7 

8 95% VDC LTC, VR 1, VR 2, CAP 1, 

CAP 2, CAP 3 

IC 889 855 +34 

3 

δ = 804, ‡” 3 

I 

‡” 3Φ

3 

48 

= 2.0 

304
 
Table B-3. Sequence Currents for Each Test 

Substation Secondary Bus 

Sequence Currents* 

Amps 

Test 

No. 

Primary 

Voltage 

Load Voltage Regulation I0 I1 I2 

1 

1 

95% 

105% 

HL 

HL 

No LTC 

No LTC 

45.46 

45.44 

799.94 

780.11 

45.21 

45.08 

2 

2 

95% 

105% 

HL 

HL 

LTC + 16 

LTC + 1 

45.43 

45.43 

780.12 

780.13 

45.08 

45.08 

3 

3 

95% 

105% 

HL 

HL 

LTC + 16 

VR 1, 32, 32, 32 

LTC + 3 

VR 1, 32, 20, 32 

45.86 

47.37 

796.86 

794.95 

45.72 

47.34 

4 

4 

95% 

105% 

HL 

HL 

LTC + 16 

VR 1, 32, 32, 32 

VR 2, 32, 23, 32 

LTC + 3 

VR 1, 32, 20, 32 

VR 2, 32, 11, 32 

45.82 

47.61 

799.26 

796.96 

45.70 

47.69 

5 

5 

95% 

105% 

HL 

HL 

LTC + 16 

CAP 1 

LTC + 1 

CAP 2 

45.34 

45.34 

760.27 

760.18 

45.87 

45.87 

6 

6 

95% 

105% 

HL 

HL 

LTC + 16 

CAP 1, CAP 2 

LTC + 1 

CAP 1, CAP 2 

45.19 

45.18 

744.66 

744.49 

47.59 

47.59 

7 

7 

95% 

105% 

HL 

HL 

LTC + 15 

CAP 1, 2, 3 

LTC + 1 

CAP 1, 2, 3 

45.69 

45.67 

724.07 

723.50 

49.55 

49.54 

8 

8 

95% 

105% 

HL 

HL 

LTC + 15 

VR 1, 32, 14, 32 

VR 2, 32, 10, 32 

CAP 1, 2, 3 

LTC + 1 

VR 1, 32, 4, 32 

VR 2, 32, 7, 32 

CAP 1, 2, 3 

48.82 

50.24 

738.71 

736.56 

52.76 

53.90 

*Note: The sequence currents are measured at the secondary of the transformer to indicate 

the magnitude of zero sequence current to be used to calculate the neutral relay settings. 

305
 
Table B-4. Simulation Data by Node for Test 8 at 95% HL with LTC, VR 1, VR 2, 

and Capacitors 1, 2, and 3 Regulation Methods Implemented (CC Model) 

KW Losses: KVAR Losses: 

Phase A Phase B Phase C Phase A Phase B Phase C 

221.99 16.61 244.04 1205.74 850.27 1447.4 

LTC Tap VR 1 A Tap VR 1 B Tap VR 1 C Tap 

15 32 14 32 

Local Name Amps A Amps B Amps C Cust Volts A Cust Volts B 

======Node 0====== 

MILFD8103 828.5427 744.0258 928.4221 114.0001 114.0001 

======Node 1====== 

Node 1 734.6588 659.7188 823.2208 123.5558 124.6471 

======Node 2====== 

======Node 3====== 

Node 3 622.6234 573.6905 685.2835 118.8883 122.7722 

Node 3 N 602.6146 562.2695 673.3692 118.0738 122.4304 

Node 3 E 20.145 11.5252 11.923 118.8822 122.7727 

======Node 4====== 

Node 4 602.6207 553.9184 673.3727 117.9749 122.3914 

Node 4 E 57.6258 117.3591 87.9715 117.9713 122.3544 

Node 4 N 552.4512 437.5563 589.768 117.8738 122.3733 

======Node 5====== 

Node 5 51.8035 112.1439 77.187 117.9394 121.8941 

Node 5 E 49.3877 112.1465 68.3351 117.937 121.8709 

Node 5 N 3.2219 0.0186 9.8124 117.9387 121.8952 

======Node 6====== 

Node 6 38.6448 39.825 38.713 117.8053 121.4029 

======Node 7====== 

Node 7 533.9893 425.5483 579.9824 114.3333 121.7128 

Node 7 E 370.1802 322.0644 363.0935 114.3225 121.709 

Node 7 N 90.3277 48.7249 107.2539 114.33 121.7336 

Node 7 W 81.0404 83.8447 114.1217 114.3293 121.7005 

======Node 8====== 

Node 8 370.1825 312.0715 363.0953 114.0694 121.6228 

======Node 9====== 

Node 9 370.1834 312.0719 363.0959 119.0288 123.7469 

======Node 10====== 

Node 10 0 0 0 116.5839 123.0896 

======Node 11====== 

Node 11 239.1742 154.4999 183.0159 114.7319 122.7623 

Node 11 N 167.2796 62.2984 150.2312 114.7044 122.7646 

Node 11 E 76.7785 94.8149 43.9618 114.7126 122.7557 

======Node 12====== 

Node 12 37.5633 40.2759 37.6143 114.5085 122.7774 

======Node 13====== 

Node 13 50.0483 53.442 49.2189 114.426 122.1848 

======Node 14====== 

Node 14 61.5139 60.0707 44.4666 114.3284 122.5585 

======Node 15====== 

Node 15 61.5159 60.0719 44.4681 119.7258 124.3025 

306
 
======Node 16====== 

Node 16 58.7012 55.1948 41.1831 119.6476 124.2664 

Node 16 E 40.1441 55.2021 32.9683 119.6339 124.2491 

Node 16 W 18.5601 0.0147 8.2176 119.6416 124.2715 

======Node 17====== 

Node 17 0.002 0.0025 0.0024 119.502 124.0212 

======Node 18====== 

Node 18 0 1.535 0.0033 0 123.6049 

======Node 19====== 

Node 19 0.4804 0 0 119.4087 0 

======Node 20====== 

Node 20 48.058 25.0014 110.0025 114.4173 122.2138 

Node 20 W 26.9459 0 0 114.4173 0 

Node 20 N 21.113 25.0019 110.003 114.492 122.1791 

======Node 21====== 

Node 21 21.1279 23.5647 92.8119 114.6153 122.1214 

Node 21 N 19.5842 21.9699 56.157 114.6153 122.1214 

Node 21 E 1.5578 1.6084 36.794 114.6235 122.1199 

======Node 22====== 

Node 22 1.5647 0.4098 28.8641 114.6728 122.1126 

Node 22 E 0.0064 0.0071 27.1533 114.6955 122.1091 

Node 22 S 0.4156 0.4137 1.7122 114.6744 122.1114 

Node 22 N 1.1561 0 0 114.2154 0 

======Node 23====== 

======Node 24====== 

Node 24 0 0 0.0076 0 0 

======Node 25====== 

Node 25 734.6591 659.719 823.2209 123.3711 124.5002 

Node 25 W 96.1194 83.4757 130.2754 123.3665 124.4941 

Node 25 E 638.7186 576.8384 693.052 123.1598 124.4218 

======Node 26====== 

Node 26 31.4495 25.1278 86.48 122.9961 124.2321 

Node 26 E 0 0 46.5381 0 0 

Node 26 W 0 0 0.4618 0 0 

Node 26 S 31.4495 25.1278 39.4887 122.9867 124.2275 

======Node 27====== 

Node 27 0.6914 0.7947 0.003 122.9003 124.2241 

======Node 28====== 

Node 28 0 0 1.586 0 0 

======Node 29====== 

Node 29 0 0 0 0 123.4408 

======Feeder Path Trace====== 

Distance (1000mCustvoltsA CustVoltsB CustVoltsC %CapacityA %CapacityB 

0.1034 114.0001 114.0001 114.0001 23.6916 31.4756 

0.2378 123.6421 124.7267 123.8458 21.0044 29.0625 

0.3218 123.5558 124.6471 123.7504 -9.4872 1.6813 

0.3218 123.5558 124.6471 123.7504 26.8996 34.3563 

0.5288 123.3711 124.5002 123.5386 26.8996 34.3563 

0.7648 123.1598 124.4218 123.3099 36.4459 42.6031 

1.3788 122.6107 124.2194 122.7203 36.4458 42.6031 

307
 
2.583 121.5436 123.832 121.5709 36.4454 42.7524 

2.666 121.4705 123.8056 121.4921 36.4446 42.7622 

3.206 121.0131 123.62 120.9913 38.0481 42.7622 

3.429 120.825 123.5443 120.785 38.0477 42.8685 

3.716 120.5835 123.4475 120.5199 38.0476 42.9016 

5.754 118.8883 122.7722 118.6597 38.0474 42.9164 

6.798 118.0738 122.4304 117.7378 40.0383 44.0528 

6.9262 117.9749 122.3914 117.6237 40.0377 44.8837 

7.0603 117.8738 122.3733 117.5038 45.0297 56.4621 

7.2034 117.7663 122.3538 117.3759 45.1101 56.462 

7.3784 117.6352 122.33 117.2198 45.11 56.462 

7.7094 117.3887 122.2846 116.925 45.2256 56.4619 

7.9064 117.243 122.2573 116.75 45.3336 56.4618 

7.9064 117.243 122.2573 116.75 45.3335 56.4617 

8.2464 116.9892 122.2113 116.4532 45.3335 56.4617 

8.4174 116.8617 122.1883 116.3046 45.3333 56.4616 

8.8571 116.5373 122.1278 115.9235 45.5525 56.4616 

9.4411 116.1091 122.0486 115.419 45.5522 56.4911 

9.6082 115.9912 122.0231 115.2754 46.5649 56.4909 

10.0174 115.7046 121.9659 114.9215 46.5648 56.9883 

10.3374 115.4816 121.9213 114.6456 46.5885 56.9882 

10.5075 115.3628 121.8978 114.5002 46.5883 56.9881 

10.8129 115.1505 121.8583 114.2381 46.5882 57.2977 

10.9501 115.0555 121.8415 114.1201 46.588 57.5374 

11.0961 114.9547 121.824 113.9944 46.5879 57.6571 

11.6971 114.5436 121.7511 113.4784 46.7157 57.6571 

12.0081 114.3333 121.7128 113.2125 46.8667 57.6569 

12.0291 114.3225 121.709 113.2014 63.1661 67.9538 

12.0292 114.3225 121.709 113.2014 63.1661 67.9538 

12.2671 114.2006 121.6659 113.075 63.1661 67.9538 

12.3884 114.1384 121.6439 113.0107 63.166 67.9537 

12.5244 114.0694 121.6228 112.9367 63.1659 68.9481 

12.6619 118.9621 123.7245 117.7881 64.8529 69.5867 

12.7589 118.9155 123.7084 117.7392 65.0307 69.5867 

12.9495 118.824 123.6769 117.6433 65.0527 69.6087 

13.0549 118.7736 123.6594 117.5903 65.0905 69.6086 

13.3859 118.6107 123.605 117.4322 65.0904 69.6086 

13.6541 118.4865 123.5557 117.3054 66.2643 69.6085 

13.9121 118.3656 123.5085 117.1863 66.2641 69.6084 

14.1148 118.2716 123.4708 117.0929 66.4581 69.6083 

14.5219 118.0595 123.4005 116.9433 66.458 69.7846 

15.0699 117.7751 123.3105 116.74 66.4578 70.0693 

15.2599 117.6769 123.2793 116.6696 66.5157 70.0691 

15.4019 117.6053 123.2547 116.6173 67.0263 70.069 

15.5403 117.5361 123.2329 116.5651 67.0262 70.6868 

15.8453 117.3817 123.1853 116.4533 67.0261 70.6868 

16.1153 117.2443 123.1434 116.3557 67.0259 70.6867 

17.4453 116.5956 123.0812 115.7992 67.0258 74.9083 

17.6035 116.5257 123.0682 115.7365 69.1939 74.9076 

17.8465 116.4182 123.0483 115.641 69.1938 74.9076 

18.2915 116.2227 123.0111 115.4664 69.3132 74.9075 

18.4488 116.1534 122.9981 115.4051 69.313 74.9074 

308
 
18.6148 116.0804 122.9844 115.3405 69.3129 74.9074 

18.7818 116.0068 122.9707 115.2757 69.3128 74.9073 

19.1128 115.8612 122.9436 115.1473 69.3127 74.9073 

19.4183 115.7205 122.9196 115.0395 69.3125 74.9072 

20.0144 115.4673 122.8774 114.9176 74.42 78.4082 

20.3923 115.3085 122.8579 114.8363 74.4197 79.167 

20.7652 115.1688 122.8272 114.7579 76.2023 79.1669 

20.9525 115.0971 122.8121 114.7215 76.2021 79.1668 

21.4666 114.9004 122.7715 114.621 76.202 79.2307 

21.7311 114.7988 122.7509 114.5703 76.2017 79.2306 

21.9173 114.7319 122.7623 114.5207 76.2016 84.6269 

22.0473 114.7044 122.7646 114.4802 83.3553 93.8012 

22.1883 114.6741 122.7673 114.4374 83.3552 93.8011 

22.3543 114.6384 122.7703 114.3869 83.3552 93.801 

22.4763 114.6142 122.7716 114.3501 84.0002 93.8009 

22.8133 114.5463 122.7752 114.25 84.0002 93.8008 

22.9733 114.5484 122.7649 114.2008 91.0257 93.8006 

23.1957 114.5496 122.7507 114.135 91.0257 93.8005 

23.3361 114.5427 122.7479 114.0953 91.0256 93.8003 

23.3575 114.5417 122.7474 114.0893 91.0496 93.8244 

23.5515 114.5322 122.7435 114.0346 91.0496 93.8244 

23.7088 114.5248 122.74 113.9903 91.1444 93.8243 

24.0118 114.5108 122.7334 113.905 91.1443 93.8243 

24.1251 114.5055 122.7309 113.8731 91.1441 93.8241 

24.3851 114.4941 122.7247 113.8002 91.2696 93.8241 

24.6292 114.4822 122.719 113.734 91.2694 93.824 

24.8032 114.4753 122.7138 113.687 91.6332 93.8239 

25.0212 114.4659 122.7074 113.6295 91.6331 93.8238 

25.1302 114.4612 122.7044 113.6006 91.633 93.9099 

25.3432 114.4633 122.6909 113.5454 93.7495 93.9098 

26.3495 114.4243 122.6322 113.3672 93.7494 93.9098 

26.5235 114.4166 122.6221 113.3381 93.7487 93.9094 

26.9295 114.395 122.5991 113.2762 93.7486 93.9093 

27.0567 114.3887 122.5915 113.2569 93.8795 93.9091 

27.3222 114.3686 122.5765 113.2282 93.8794 93.9091 

27.3813 114.3621 122.5736 113.2252 93.8792 94.0228 

27.6828 114.3284 122.5585 113.2109 93.8792 94.0228 

27.8391 119.7117 124.2937 118.5691 94.5939 94.5492 

27.9641 119.698 124.2872 118.5641 94.1593 94.111 

28.1491 119.6779 124.2782 118.5565 94.1592 94.2556 

28.4312 119.6476 124.2664 118.5438 94.1591 94.508 

28.6137 119.6339 124.2491 118.5441 95.8614 94.3091 

28.983 119.607 124.2135 118.5448 95.9843 94.3089 

29.633 119.5614 124.1497 118.5465 96.1026 94.3087 

29.925 119.5436 124.1195 118.5476 96.4791 94.3082 

30.264 119.5336 124.0781 118.5499 97.7923 94.308 

30.904 119.5189 123.9977 118.5547 98.0387 94.3078 

31.183 119.5178 124.0023 118.5297 98.0383 99.9981 

31.4215 119.5173 124.0062 118.5092 98.1065 99.9985 

31.6365 119.5183 124.0089 118.4909 98.3796 99.9987 

31.7505 119.5191 124.0102 118.4812 98.4935 99.999 

31.8455 119.5177 124.0117 118.477 98.4935 99.9991 

32.0297 119.5114 124.0156 118.4756 98.4934 99.9992 

309
 
kVA Flow SOC Released Capacity 

Phase A Phase B Phase C Phase A Phase B Phase C 

5998.63 5386.73 6721.75 6.55 8.84 6.36 

7.17 

VR 2 A Tap VR 2 B Tap VR 2 C Tap 

32 10 32

 Cust Volts C Seq Amps 0 Seq Amps 1 Seq Amps 2 I2/I1 (%) Seq Volts 0 Seq Volts 1 Seq Volts 2 

114.0001 55.0565 833.1159 59.4993 7.1418 0 7239.8662 0.1059 

123.7504 48.8179 738.7138 52.7574 7.1418 0.4098 7873.8943 42.2513 

118.6597 34.2333 626.6931 39.1943 6.2542 72.9172 7627.4228 114.1174 

117.7378 33.4637 612.2335 40.1371 6.5558 85.5513 7583.3448 127.8616 

118.6573 2.7552 14.5262 2.8859 19.8671 73.0231 7627.2546 114.1589 

117.6237 36.2142 609.4338 41.6729 6.838 87.2579 7577.9977 129.5801 

117.6249 18.2699 87.0192 19.2667 22.1408 85.6853 7577.1623 129.6009 

117.5038 50.857 526.0247 46.8835 8.9128 90.0076 7572.923 131.3654 

117.6675 18.7746 79.5263 19.8846 25.0038 65.6593 7567.6039 129.5358 

117.6747 20.0504 75.5901 21.1139 27.9321 64.5089 7567.2157 129.4562 

117.6499 2.8653 4.3419 2.9142 67.1179 66.1558 7567.2383 129.7394 

118.0132 0.1811 39.0583 0.6485 1.6602 35.0707 7561.6856 125.5384 

113.2125 50.5017 512.5785 47.365 9.2405 188.9092 7392.3764 196.3087 

113.2014 16.9106 351.6674 15.4637 4.3973 189.062 7391.8311 196.4311 

113.1866 28.4113 76.8408 25.1711 32.7574 190.4583 7392.1802 196.8204 

113.1848 10.0303 92.9083 11.8693 12.7752 189.3063 7391.44 196.3231 

112.9367 19.9915 348.328 18.7552 5.3844 192.8739 7379.0356 199.3641 

117.8575 19.9915 348.328 18.7552 5.3844 152.7909 7633.059 147.8634 

115.7925 0 0 0 NA 177.6127 7523.7794 169.5996 

114.5207 27.8802 191.9652 23.6843 12.3378 201.5767 7450.8418 184.3941 

114.4802 33.0006 126.5865 32.1058 25.3628 203.2963 7449.4322 184.7586 

114.5306 18.1433 70.9456 15.5961 21.9831 201.1182 7450.5149 184.3036 

114.6636 1.0233 38.4793 0.956 2.4844 198.1103 7449.5857 185.0702 

112.5295 1.5608 50.8907 1.4428 2.8351 226.6332 7389.3299 209.4912 

113.2109 5.8404 55.3422 5.127 9.2642 231.6821 7409.7747 196.8352 

118.5772 5.8404 55.3422 5.127 9.2642 175.4698 7674.5193 132.419 

310
 
118.5438 5.762 51.6853 4.9805 9.6362 174.758 7671.4176 132.3578 

118.5441 6.4845 42.7659 6.6492 15.5479 174.2237 7670.7728 132.2688 

118.5394 5.4573 8.9227 5.2855 59.2369 175.0594 7671.3023 132.4698 

118.4747 0 0.0023 0 0 169.8666 7661.7073 131.9398 

118.7155 0 0.5114 0.5109 NA 0 5128.758 2650.3923 

0 0.1601 0 0 NA 2527.8226 0 0 

112.0482 25.6513 60.9544 25.2617 41.4437 242.4023 7379.2661 216.0309 

0 8.982 0 0 NA 2422.1572 0 0 

111.8079 28.4826 51.9765 29.6231 56.9932 248.7786 7374.8441 219.1163 

111.3929 23.03 45.7673 24.0853 52.6255 260.5602 7367.1183 224.4831 

111.3929 11.3733 32.4807 12.4718 38.3975 260.5602 7367.1183 224.4831 

111.3767 11.7106 13.3076 11.7767 88.4961 261.0967 7366.9025 224.7192 

111.2784 9.337 10.2756 9.2633 90.1485 264.4658 7365.61 226.1654 

111.2374 9.0519 9.0484 9.0526 100.0456 265.8927 7365.1032 226.776 

111.2734 0.4259 0.8465 0.4403 52.0152 264.6239 7365.5058 226.2304 

0 9.337 0 0 NA 76.1436 0 0 

110.4629 0 0 0.0025 NA 0 0 2338.3935 

123.5386 48.818 738.714 52.7573 7.1418 3.6133 7862.3871 43.5241 

123.5279 14.1559 103.2862 13.8139 13.3744 3.8854 7861.9354 43.618 

123.3099 37.0466 635.6931 38.9572 6.1283 6.7013 7851.4117 46.75 

122.3175 19.4346 47.6817 19.5383 40.9765 38.9384 7822.8104 60.8002 

122.2857 0 0 15.5124 NA 0 0 2588.6705 

122.3169 0 0 0.1539 NA 0 0 2589.3317 

122.3 4.0966 32.0209 4.2183 13.1736 39.3434 7822.1417 61.0528 

121.86 0.2209 0.4938 0.2777 56.238 55.2611 7810.8523 67.7209 

121.3932 0 0 0.5287 NA 0 0 2569.776 

0 0 0 0 NA 0 2613.1221 0 

311
 
V2/V1 (%) pf A pf B pf C kW Flow A kW Flow B kW Flow C 

0.0015 0.8584 0.8849 0.8406 5149.1606 4766.8566 5650.2696 

0.5366 0.8879 0.9128 0.8763 5122.0445 4770.1754 5674.0669 

1.4961 0.9047 0.9274 0.8933 4313.6989 4171.0642 4685.7275 

1.6861 0.9133 0.933 0.9015 4155.377 4090.1585 4574.6012 

1.4967 0.8616 0.8777 0.8942 131.0445 78.8687 80.3424 

1.71 0.9167 0.936 0.9056 4142.5374 4031.3237 4559.5452 

1.7104 -0.9968 0.9706 0.99 430.3626 885.3978 650.5856 

1.7347 0.8965 0.9249 0.8868 3710.6449 3145.7893 3907.0391 

1.7117 -0.9868 0.975 0.9965 382.8852 846.4462 574.7759 

1.7108 -0.9791 0.975 0.9997 362.179 846.4345 510.4917 

1.7145 0.858 -0.081 0.8767 20.7062 0.0117 64.2842 

1.6602 -1 -1 -1 0 0 0 

2.6556 0.9148 0.9339 0.9025 3553.3654 3073.0376 3772.1753 

2.6574 0.8864 0.8959 0.8899 2382.5191 2230.3426 2323.1687 

2.6625 0.9993 -0.7408 0.9812 655.4244 279.0285 756.6251 

2.6561 0.8719 0.8705 0.8383 513.0646 564.1957 687.8519 

2.7018 0.8872 0.8979 0.8906 2380.7169 2164.8146 2320.9673 

1.9371 0.8872 0.8979 0.8906 2380.1093 2165.0119 2320.1343 

2.2542 0.014 -0.1051 0.101 0 0 0 

2.4748 0.92 0.9521 0.932 1604.2112 1146.7663 1241.0627 

2.4802 0.8593 0.8597 0.8538 1047.4059 417.5658 932.8863 

2.4737 0.9945 0.9868 -0.9626 556.3686 729.4639 307.7802 

2.4843 -1 -1 -1 0 0 0 

2.835 -1 -1 -1 0 0 0 

2.6564 0.8728 0.8599 0.8593 389.9266 402.0834 274.7443 

1.7254 0.8728 0.8599 0.8593 389.8517 402.1026 274.7275 

312
 
1.7253 

1.7243 

1.7268 

0.8735 

0.8755 

0.8692 

0.8611 

0.861 

-0.098 

0.8598 

0.8619 

0.8514 

389.7086 

267.0694 

122.5788 

375.1131 

375.1165 

0.0114 

266.6114 

213.9266 

52.6708 

1.7221 0.0786 0.0777 -0.1562 -0.0012 -0.0016 0.0028 

NA 0 0.8569 -0.2548 0 10.3257 0.0064 

NA 0.9293 0 0 3.3855 0 0 

NA 

2.9275 

2.9711 

0.8611 

0.8602 

0.8624 

0.8725 

0 

0.8725 

0.8317 

0 

0.8318 

300.7089 

168.4344 

132.3024 

169.3145 

0 

169.3082 

651.1819 

0 

651.1001 

3.0471 

3.0471 

3.0504 

0.8627 

0.8581 

0.9149 

0.8721 

0.8677 

0.9225 

0.8292 

0.8043 

0.8652 

132.6442 

122.3268 

10.3743 

159.397 

147.8421 

11.5081 

544.9446 

319.5401 

225.2152 

NA 

3.0706 

3.0791 

3.0715 

0.9123 

0.1803 

0.8774 

0.9209 

0.8937 

-0.1022 

0.8826 

0 

0.8678 

0.8683 

0.8593 

0 

10.3955 

-0.0084 

2.6557 

7.7537 

2.8404 

0.0056 

2.8318 

0 

177.045 

166.6303 

10.3979 

0 

NA 0 0 0 0 0 0 

0.5536 

0.5548 

0.5954 

0.8877 

0.8613 

0.8926 

0.9127 

0.8621 

0.9196 

0.8761 

0.8588 

0.8804 

5117.5113 

648.6462 

4466.9384 

4766.5191 

568.9836 

4194.1674 

5668.3741 

877.767 

4787.3572 

NA 

NA 

0.7772 

0.7805 

0.8651 

0 

0 

0.8651 

0.8701 

0 

0 

0.8701 

0.8628 

0.8562 

0.8614 

0.8705 

212.5206 

0 

0 

212.5206 

172.4914 

0 

0 

172.4914 

579.6498 

309.537 

3.0899 

267.0229 

0.867 0.9235 0.8599 -0.0702 4.9835 5.3911 0.0016 

NA 0 0 0.8578 0 0 10.4887 

0 0 0 0 0 0 0 

313
 
 kVAR Flow A kVAR Flow B kVAR Flow C 

3077.2811 2508.765 3640.9319 

2653.9563 2134.0307 3119.0733 

2031.446 1682.7564 2357.103 

1853.4526 1578.1536 2196.1263 

77.2185 43.07 40.2268 

1805.4186 1515.9154 2135.9344 

-34.6628 219.5798 92.699 

1834.1241 1292.804 2035.8337 

-62.8923 192.8663 48.3931 

-75.2874 193.01 13.1168 

12.3951 -0.1436 35.2763 

-289.1261 -307.0551 -290.1482 

1569.381 1176.185 1800.4953 

1244.4147 1105.9595 1190.9072 

24.4915 -252.9738 148.9699 

288.1546 318.9365 447.3585 

1237.9948 1061.1047 1185.0185 

1235.644 1059.7503 1182.8978 

-0.0028 -0.0027 -0.0025 

683.4916 368.2371 482.7818 

623.3742 248.0914 568.8417 

58.5656 119.7008 -86.6172 

-273.1699 -314.0477 -273.9112 

-363.7023 -414.6977 -351.747 

218.0912 238.7374 163.5691 

217.9555 238.5926 163.5184 

314
217.2283 221.5176 158.3322 

147.3893 221.5439 125.8585 

69.7442 -0.1153 32.4542 

-0.0154 -0.02 -0.0175 

0 6.2119 -0.0243 

1.3455 0 0 

177.5406 94.8042 434.753 

99.8401 0 0 

77.671 94.8264 434.5321 

77.7599 89.4539 367.2787 

73.1979 84.7146 236.0576 

4.5774 4.814 130.505 

4.665 1.4261 101.3997 

-0.0457 -0.0546 95.1758 

1.4522 1.5085 6.1891 

3.2815 0 0 

0 0 -0.0531 

2653.9597 2134.0345 3119.0764 

382.6578 334.5056 523.6688 

2256.2813 1792.011 2578.3209 

123.2254 97.73 339.5784 

0 0 186.7663 

0 0 1.8222 

123.2254 97.73 150.99 

2.07 3.2 -0.0231 

0 0 6.2854 

0 0 0 

315
 
B.4. Heavy- and Light-Load Base Case Data and Measured Data at Node 01 

Table B-5. Summary of HL Base Case

 (LTC control only, tap = 14)

 [#0 MXAT services included] 

Location Simulated Data Measured Data July 17, 2006 

Node 01 IA 

578.13 

IB 

654.17 

IC 

636.62 

IA 

565 

IB 

651 

IC 

637 

Node 01 VA 

125.90 

VB 

125.55 

VC 

124.98 

VA 

126.0 

VB 

126.0 

VC 

126.0 

Node 01 

Node 01 

PFA 

0.843 

PFB 

0.843 

PFC 

0.841 

kVA Flow Total 

Node 01 

Phase A 

4,622.62 

Phase B 

5,216.17 

Phase C 

5,053.13 14,891.92 

kW Flow 

Node 01 

Phase A 

3,897.94 

Phase B 

4,399.49 

Phase C 

4,249.92 12,547.35 

kVAr Flow 

Node 01 

Phase A 

2,484.88 

Phase B 

2,802.29 

Phase C 

2,735.55 8,020.72 

kVAr Losses Total % 

Node 01 

Phase A 

877.31 

Phase B 

1,132.1 

Phase C 

1,086.42 

3095.83 

38.59% 

kW Losses Total %

 Phase A 

246.56 

Phase B 

202.22 

Phase C 

221.79 

670.57 

5.34% 

Node 01 I0 

23.01 

V0 

0.1936 

I1 

622.96 

V1 

7968.87 

I2 

23.01 

V2 

33.92 

I2/I1% 

3.69 

V2/V1% 

0.4257 

Note: All capacitors and line regulators were turned off. The substation primary voltage was set at 

100% (120 V). The base case used for the synchronous generator, inverter-based generator, and 

induction generator simulations had all three capacitors on one regulator turned on and all generation 

turned off. The losses in this case were 5.4%. 

316
 
Phase A Phase B Phase C Phase A Phase B Phase C Phase A 

246.56 202.22 221.79 877.31 1132.1 1086.42 4622.62 

LTC Tap VR 1 A Tap VR 1 B Tap VR 1 C Tap 

14 NA NA NA 

Local Name Amps A Amps B Amps C Cust Volts A Cust Volts B Cust Volts C 

======Node 0====== 

MILFD8103 648.0396 733.271 713.601 120.0001 120.0001 120.0001 

======Node 1====== 

StPole_MILFD8 578.1287 654.1653 636.6173 125.9017 125.5546 124.9828 

======Node 2====== 

======Node 3====== 

Node 3 481.8032 564.0023 523.93 121.8937 121.6459 121.6163 

Node 3 N 465.5588 552.767 513.7795 121.1734 120.9197 121.0038 

Node 3 E 16.2788 11.2809 10.2472 121.889 121.6455 121.6148 

======Node 4====== 

Node 4 465.5661 544.3872 513.7841 121.0855 120.8334 120.9275 

Node 4 E 53.0644 126.2385 80.5565 121.0701 120.7819 120.9227 

Node 4 N 412.5386 418.2472 433.3739 121.0031 120.7747 120.8507 

======Node 5====== 

Node 5 47.2952 121.2589 71.1749 120.8873 120.142 120.8823 

Node 5 E 44.7918 121.2666 63.0488 120.8773 120.1099 120.8842 

Node 5 N 2.5035 0.0186 8.1287 120.8869 120.1427 120.868 

======Node 6====== 

Node 6 0 0 0 120.5488 119.378 121.0163 

======Node 7====== 

Node 7 398.3378 406.7628 425.2631 118.0492 118.635 118.1037 

Node 7 E 250.6805 282.5334 245.4241 118.0415 118.6281 118.0974 

Node 7 N 81.6264 41.7154 90.1658 118.0364 118.6371 118.0811 

Node 7 W 66.1638 82.7247 89.7199 118.0454 118.6206 118.0853 

======Node 8====== 

Node 8 250.683 273.7643 245.4261 117.8587 118.469 117.9463 

======Node 9====== 

Node 9 250.6839 273.7649 245.4268 117.4472 118.0253 117.5559 

======Node 10====== 

Node 10 20.4 20.2112 20.2746 115.5999 116.6792 116.3151 

======Node 11====== 

Node 11 181.9956 152.9444 140.0598 114.0857 115.7246 115.4564 

Node 11 N 118.6435 55.1258 103.8657 114.066 115.7222 115.4317 

Node 11 E 63.3539 97.8194 36.195 114.0665 115.7056 115.4596 

======Node 12====== 

Node 12 0 0 0 113.7463 115.3602 115.4034 

======Node 13====== 

Node 13 0 0 0 117.8356 118.6261 117.5034 

======Node 14====== 

Node 14 42.5463 53.1638 27.7177 113.7832 115.4145 114.681 

======Node 15====== 

Node 15 42.5481 53.1649 27.7191 113.7822 115.4132 114.6804 

kW Losses: kVAr Losses: 

317
 
Node 17 0.0019 0.0024 0.0022 113.6089 115.1328 114.6841 

======Node 18====== 

Node 18 0 1.3445 0.0032 0 114.7666 114.8794 

======Node 19====== 

Node 19 0.3952 0 0 113.2432 0 0 

======Node 20====== 

Node 20 37.9451 26.6195 77.7292 117.8058 118.6012 117.2153 

Node 20 W 19.3002 0 0 117.8058 0 0 

Node 20 N 18.6457 26.62 77.7296 117.8475 118.553 117.0723 

======Node 21====== 

Node 21 18.6604 25.3668 65.2933 117.9146 118.4698 116.8272 

Node 21 N 17.3276 23.6725 37.8338 117.9146 118.4698 116.8272 

Node 21 E 1.3462 1.7079 27.4619 117.9204 118.4682 116.8158 

======Node 22====== 

Node 22 1.3529 0.411 21.7288 117.9554 118.4604 116.7453 

Node 22 E 0.0066 0.007 20.4099 117.9718 118.457 116.7157 

Node 22 S 0.3388 0.4147 1.3202 117.9565 118.4591 116.7418 

Node 22 N 1.0205 0 0 117.118 0 0 

======Node 23====== 

======Node 24====== 

Node 24 0 0 0 0 0 116.1101 

======Node 25====== 

Node 25 578.129 654.1655 636.6175 125.7425 125.3385 124.8545 

Node 25 W 82.7048 87.1324 106.8792 125.7381 125.3313 124.848 

Node 25 E 495.5384 567.2441 530.0965 125.5643 125.1707 124.7026 

======Node 26====== 

Node 26 26.4142 25.8686 69.1744 125.3649 124.9546 124.0365 

Node 26 E 0 0 36.6633 0 0 123.9562 

Node 26 W 0 0 0.3888 0 0 124.0349 

Node 26 S 26.4142 25.8686 32.1314 125.3562 124.9477 124.0252 

======Node 27====== 

Node 27 0.6813 0.7658 0.003 125.2701 124.9092 123.7098 

======Node 28====== 

Node 28 0 0 1.293 0 0 122.477 

======Node 29====== 

Node 29 0 0 0 0 114.6208 0 

======Feeder Path Trace====== 

Distance (1000m CustvoltsA CustVoltsB CustVoltsC %CapacityA %CapacityB %CapacityC 

0.1034 116.4234 116.2687 116.0501 40.3159 32.4661 34.2777 

0.2168 125.9662 125.6275 125.0536 37.8356 29.6596 31.5465 

0.3008 125.9017 125.5546 124.9828 13.8407 2.5089 5.1241 

0.3008 125.9017 125.5546 124.9828 42.4748 34.9089 36.655 

0.5078 125.7425 125.3385 124.8545 42.4747 34.9089 36.655 

0.7438 125.5643 125.1707 124.7026 50.6927 43.5578 47.2541 

1.3578 125.0996 124.7357 124.3115 50.6925 43.5577 47.4227 

2.562 124.191 123.8923 123.5481 50.6921 43.7146 47.4224 

318
 
2.645 124.1284 123.8344 123.4958 50.6912 43.7247 47.4219 

3.185 123.7363 123.4468 123.1639 52.0601 43.7247 47.8681 

3.408 123.5746 123.2877 123.0271 52.0598 43.8324 47.8679 

3.695 123.3667 123.0835 122.8512 52.0596 43.8643 47.8678 

5.733 121.8937 121.6459 121.6163 52.0594 43.8804 47.8677 

6.777 121.1734 120.9197 121.0038 53.6757 44.9983 48.8777 

6.9052 121.0855 120.8334 120.9275 53.675 45.8321 48.8772 

7.0393 121.0031 120.7747 120.8507 58.9514 58.3834 56.8782 

7.1824 120.9154 120.712 120.7689 59.0161 58.3833 56.8782 

7.3574 120.8081 120.6353 120.6689 59.016 58.3832 56.8781 

7.6884 120.6062 120.49 120.4802 59.1066 58.3831 56.878 

7.8854 120.4865 120.4034 120.3681 59.1883 58.383 56.8779 

7.8854 120.4865 120.4034 120.3681 59.1882 58.3829 56.9812 

8.2254 120.2777 120.255 120.1788 59.1882 58.3829 57.413 

8.3964 120.1726 120.1804 120.0841 59.1879 58.3827 57.4847 

8.8361 119.9043 119.9879 119.8411 59.3508 58.3826 57.4846 

9.4201 119.5486 119.7333 119.5193 59.3505 58.4097 57.4844 

9.5872 119.4502 119.6584 119.4278 60.131 58.4094 57.4842 

9.9964 119.2101 119.48 119.2011 60.1309 58.9101 57.4841 

10.3164 119.0227 119.3406 119.0243 60.152 58.9099 57.4839 

10.4865 118.9227 119.2667 118.9312 60.1518 58.9098 57.6858 

10.7919 118.7436 119.1363 118.7632 60.1517 59.188 57.6858 

10.9291 118.6633 119.0785 118.6874 60.1514 59.3977 57.6856 

11.0751 118.578 119.0175 118.6066 60.1514 59.5265 57.6856 

11.6761 118.2288 118.7656 118.2748 60.2484 59.5264 57.6855 

11.9871 118.0492 118.635 118.1037 60.3644 59.5261 57.6853 

12.0081 118.0415 118.6281 118.0974 75.0567 71.8872 75.5797 

12.0082 118.0415 118.6281 118.0974 75.0567 71.8872 75.5797 

12.2461 117.9535 118.5502 118.0255 75.0567 71.8872 75.5797 

12.3674 117.9086 118.5105 117.9889 75.0565 71.8871 75.5796 

12.5034 117.8587 118.469 117.9463 75.0564 72.7598 75.5795 

12.6409 117.3969 117.9836 117.5131 75.0563 72.7597 75.5794 

12.7379 117.3617 117.954 117.4829 75.1868 72.7597 75.5794 

12.9285 117.2927 117.8959 117.4238 75.2038 72.7806 75.5962 

13.0339 117.2546 117.8638 117.3911 75.2311 72.7805 75.5961 

13.3649 117.1317 117.7635 117.2942 75.231 72.7804 76.3121 

13.6331 117.0379 117.6782 117.2165 76.1338 72.7803 76.3119 

13.8911 116.9465 117.5965 117.144 76.1336 72.7802 76.6399 

14.0938 116.8754 117.5319 117.0871 76.2787 72.7801 76.6398 

14.5009 116.7155 117.4069 117.0003 76.2786 72.9292 79.6292 

15.0489 116.5008 117.2425 116.8818 76.2783 73.1781 79.629 

15.2389 116.4266 117.1856 116.8408 76.3222 73.1779 79.6287 

15.3809 116.3724 117.1421 116.8104 76.7063 73.1778 79.6286 

15.5193 116.32 117.1016 116.7796 76.7062 73.7591 79.6285 

15.8243 116.2031 117.0129 116.714 76.7061 73.7591 79.9307 

16.0943 116.0991 116.9345 116.657 76.7059 73.759 80.0757 

17.4243 115.6043 116.6686 116.3121 76.7057 77.462 80.0756 

17.5825 115.5473 116.6314 116.2701 76.29 75.5126 78.5313 

17.8255 115.4594 116.5744 116.2061 76.2899 75.5126 78.604 

18.2705 115.2994 116.4695 116.0892 76.391 75.5125 78.6039 

18.4278 115.2427 116.4325 116.0483 76.3907 75.5123 78.7047 

18.5938 115.1828 116.3936 116.0051 76.3906 75.5123 78.7047 

319
 
18.7608 115.1225 116.3544 115.9618 76.3905 75.5122 78.7362 

19.0918 115.0031 116.277 115.876 76.3904 75.5121 78.7361 

19.3973 114.8882 116.2064 115.8045 76.3902 75.512 79.7979 

19.9934 114.6846 116.0857 115.7242 80.5779 79.2287 85.5329 

20.3713 114.5566 116.0157 115.6697 80.5775 79.9467 85.5325 

20.7442 114.4426 115.9384 115.6173 81.8918 79.9466 85.5323 

20.9315 114.3841 115.8998 115.5929 81.8916 79.9464 85.9615 

21.4456 114.2239 115.7948 115.5258 81.8915 80.0014 85.9614 

21.7101 114.1411 115.741 115.4919 81.8912 80.0012 86.0638 

21.8963 114.0857 115.7246 115.4564 81.891 84.7817 86.0637 

22.0263 114.066 115.7222 115.4317 88.1947 94.5148 89.6651 

22.1673 114.0442 115.7197 115.4055 88.1946 94.5148 89.8794 

22.3333 114.0185 115.7167 115.3747 88.1946 94.5147 89.8793 

22.4553 114.001 115.7138 115.3522 88.6467 94.5146 89.8792 

22.7923 113.952 115.706 115.2914 88.6466 94.5145 90.0361 

22.9523 113.953 115.694 115.2609 93.6863 94.5143 90.0359 

23.1747 113.9531 115.6775 115.2202 93.6862 94.5142 90.3605 

23.3151 113.9476 115.6713 115.1959 93.6861 94.5141 90.6615 

23.3365 113.9468 115.6704 115.1922 93.7046 94.5372 90.6802 

23.5305 113.9392 115.6619 115.1587 93.7046 94.5372 90.6802 

23.6878 113.9334 115.6548 115.1315 93.7713 94.5371 90.6801 

23.9908 113.9222 115.6412 115.0792 93.7712 94.5371 90.68 

24.1041 113.918 115.6361 115.0597 93.771 94.537 90.6953 

24.3641 113.9089 115.624 115.015 93.8589 94.5369 90.6953 

24.6082 113.8994 115.6128 114.9746 93.8588 94.5368 90.9637 

24.7822 113.8938 115.604 114.946 94.1175 94.5368 90.9636 

25.0002 113.8862 115.5932 114.9111 94.1173 94.5367 91.1438 

25.1092 113.8824 115.5879 114.8935 94.1172 94.6128 91.1437 

25.3222 113.8832 115.5721 114.8601 95.6735 94.6127 91.1436 

26.3285 113.8533 115.5023 114.7593 95.6734 94.6127 93.4976 

26.5025 113.8474 115.4904 114.7431 95.6728 94.6123 93.7918 

26.9085 113.8313 115.4628 114.7094 95.6727 94.6122 94.2053 

27.0357 113.8266 115.454 114.6989 95.7668 94.6121 94.2051 

27.3012 113.8119 115.4363 114.685 95.7667 94.612 95.4719 

27.3603 113.8073 115.4327 114.6843 95.7666 94.7101 97.1667 

27.6618 113.7832 115.4145 114.681 95.7665 94.7101 97.242 

27.8754 113.768 115.3986 114.6763 96.0813 95.1035 97.4471 

28.0004 113.7579 115.391 114.6752 95.7663 94.7099 97.3313 

28.1854 113.743 115.3805 114.6733 95.7662 94.8365 97.3313 

28.4675 113.7204 115.3658 114.6696 95.7661 95.0503 97.3312 

28.65 113.7102 115.3493 114.674 96.9771 94.871 97.8451 

29.0193 113.6904 115.3154 114.683 97.0786 94.8709 97.845 

29.6693 113.657 115.2549 114.6991 97.1762 94.8707 97.8449 

29.9613 113.6438 115.2265 114.7065 97.4539 94.8703 97.8447 

30.3003 113.6364 115.1891 114.7161 98.4128 94.8701 97.8446 

30.9403 113.6248 115.1169 114.7343 98.575 94.8699 97.8444 

31.2193 113.6227 115.12 114.7189 98.5747 99.9982 97.8437 

31.4578 113.6212 115.1226 114.7062 98.6242 99.9986 97.9187 

31.6728 113.621 115.1243 114.6949 98.8229 99.9988 97.9186 

31.7868 113.621 115.1251 114.6889 98.9169 99.9991 97.9185 

31.8818 113.6201 115.126 114.6859 98.9169 99.9992 98.786 

32.066 113.6155 115.1288 114.6849 98.9168 99.9993 99.8769 

320
 
kVA Flow SOC Released Capacity 

Phase B Phase C Phase A Phase B Phase C 

5216.17 5053.13 NA NA NA 

Seq Amps 0 Seq Amps 1 Seq Amps 2 I2/I1 (%) Seq Volts 0 Seq Volts 1 Seq Volts 2 

25.7965 698.2907 25.7941 3.6939 0 7620.9118 0.1115 

23.0135 622.9587 23.0114 3.6939 0.1936 7968.8747 33.9196 

22.4991 523.2323 24.9978 4.7776 49.9693 7729.7254 51.729 

23.9031 510.6884 26.5738 5.2035 60.3815 7686.0193 57.4956 

1.7735 12.597 1.9806 15.7225 49.9106 7729.5842 51.7098 

21.8127 507.8991 24.1295 4.7508 61.516 7680.7011 58.2175 

21.6972 86.6161 20.9846 24.2271 63.5193 7679.1639 58.5285 

7.5855 421.3687 5.4263 1.2878 61.4762 7676.0831 58.7883 

21.9777 79.9071 21.6109 27.045 88.9736 7660.636 62.4304 

23.1378 76.367 22.9815 30.0935 90.3389 7659.7703 62.5919 

2.3733 3.5412 2.4374 68.828 88.6572 7660.3411 62.6375 

0 0 0 NA 122.8907 7639.7369 64.7177 

9.2072 410.102 7.2384 1.765 61.7245 7509.8745 83.3577 

10.8543 259.536 12.4159 4.7839 61.8074 7509.4287 83.4209 

15.1231 71.1666 14.7461 20.7205 60.9885 7509.1726 83.5844 

5.932 79.493 8.307 10.45 61.7607 7509.0973 83.4723 

7.9299 256.6139 9.5945 3.7389 63.6226 7498.9618 84.9248 

7.9299 256.6139 9.5945 3.7389 64.834 7472.586 83.9778 

0.2618 20.2921 0.2301 1.1341 83.6019 7378.426 94.7981 

11.8567 158.322 13.0377 8.2349 103.7461 7307.7226 101.2307 

19.7917 92.5382 18.5969 20.0965 102.826 7306.745 101.1012 

17.419 65.7855 18.2442 27.7329 104.7716 7306.9653 101.1667 

0 0 0 NA 118.8639 7291.4843 101.5956 

0 0 0 NA 47.9228 7492.5132 90.5568 

6.7516 41.1329 8.0044 19.4599 87.6444 7278.4331 107.7743 

6.7516 41.1329 8.0044 19.4599 87.6602 7278.3672 107.7566 

6.15 39.6964 7.3816 18.5952 89.473 7275.8145 107.4898 

8.1408 33.3165 8.9997 27.0127 90.1313 7275.3363 107.3031 

3.9063 6.3814 3.7501 58.7658 89.2813 7275.737 107.4865 

321
 
0 0.0022 0 0 96.7325 7268.7484 105.6876 

0 0.4479 0.4474 99.8923 0 4861.3551 2416.1432 

0.1317 0 0 NA 2397.3029 0 0 

15.4031 47.4282 15.5983 32.8881 45.8041 7485.2458 94.603 

6.4334 0 0 NA 2493.8892 0 0 

18.3321 40.9954 18.6891 45.5884 48.7395 7482.0428 97.0537 

14.3794 36.4373 14.735 40.4393 55.2777 7476.4375 101.2469 

5.8922 26.2761 6.2311 23.714 55.2777 7476.4375 101.2469 

8.6301 10.1643 8.6697 85.2956 55.6248 7476.2813 101.4468 

6.9913 7.8281 6.9199 88.3989 57.7939 7475.3449 102.6636 

6.8041 6.8009 6.8047 100.056 58.8266 7474.9831 103.1873 

0.3134 0.691 0.3175 45.9455 57.9135 7475.2644 102.7101 

6.9913 0 0 NA 78.0787 0 0 

0 0 0 NA 0 0 2457.9386 

23.0135 622.9589 23.0114 3.6939 2.9102 7958.2171 32.5265 

7.3151 92.2339 7.587 8.2258 3.0394 7957.833 32.4707 

19.3679 530.9452 22.1074 4.1638 4.6354 7947.6736 32.8143 

14.1796 40.4839 14.5118 35.8459 19.7449 7924.7918 34.2899 

0 0 12.2208 NA 0 0 2624.0328 

0 0 0.1296 NA 0 0 2625.6999 

1.8314 28.1349 2.1963 7.8065 19.8955 7924.2239 34.3331 

0.2178 0.4812 0.267 55.4879 29.4606 7914.9081 35.5305 

0 0 0.431 NA 0 0 2592.7205 

0 0 0 NA 0 2426.4122 0 

322
 
pf FLOW 

V2/V1 (%) pf A pf B pf C kW Flow A kW Flow B kW Flow C 

0.0015 0.7952 0.7913 0.7921 3927.3825 4422.1394 4307.9145 

0.4257 0.8432 0.8434 0.841 3897.9469 4399.4995 4249.9173 

0.6692 0.8446 0.849 0.8452 3188.3499 3743.2235 3454.8722 

0.7481 0.8476 0.8549 0.8514 3054.845 3650.9841 3378.6615 

0.669 0.8733 0.8936 0.9131 110.047 77.876 72.2701 

0.758 0.8495 0.8578 0.8553 3043.6655 3586.0975 3376.8882 

0.7622 0.8675 0.8754 0.883 354.002 848.0526 546.2885 

0.7659 0.8474 0.8528 0.8504 2688.3306 2737.1724 2830.3302 

0.815 0.8673 0.8779 0.8829 314.935 812.2552 482.4273 

0.8172 0.8675 0.8778 0.8814 298.3348 812.2442 426.6433 

0.8177 0.8637 -0.0773 0.8939 16.6002 0.011 55.784 

0.8471 -1 -1 -1 0 0 0 

1.11 0.8568 0.8628 0.8628 2562.5809 2647.2655 2755.9769 

1.1109 0.8478 0.8526 0.8594 1593.3367 1815.0299 1582.0433 

1.1131 0.8666 0.8835 0.8775 530.33 277.6918 593.4315 

1.1116 0.8809 0.8884 0.861 436.9675 553.7387 579.382 

1.1325 0.8482 0.8529 0.86 1592.1555 1757.4092 1581.5949 

1.1238 0.8482 0.8529 0.86 1591.7548 1757.3321 1581.4082 

1.2848 0.9637 0.9637 0.9637 -144.3264 -144.3264 -144.3265 

1.3853 0.8659 0.8754 0.8739 1142.3289 984.1866 897.71 

1.3837 0.8671 0.8766 0.8741 745.3779 355.1598 665.6767 

1.3845 0.8641 0.8751 0.8737 396.658 629.1174 231.8776 

1.3933 -1 -1 -1 0 0 0 

1.2086 -1 -1 -1 0 0 0 

1.4807 0.8804 0.8773 0.8798 270.7401 341.9209 177.6084 

1.4805 0.8804 0.8773 0.8798 270.6931 341.9206 177.6115 

323
 
1.4774 

1.4749 

1.4773 

0.8805 

0.883 

0.8749 

0.878 

0.8779 

-0.0824 

0.88 

0.8817 

0.8738 

270.6305 

186.9862 

83.604 

320.0234 

320.0152 

0.0084 

171.8888 

134.214 

37.6769 

1.454 0.0586 0.097 -0.1554 0 -0.0017 0.0025 

49.701 0 0.8733 -0.2558 0 8.558 0.0059 

NA 0.9297 0 0 2.6429 0 0 

NA 

1.2639 

1.2972 

0.8665 

0.866 

0.867 

0.8856 

0 

0.8856 

0.8791 

0 

0.8791 

245.9844 

125.055 

120.9412 

177.5682 

0 

177.5618 

508.7365 

0 

508.7018 

1.3542 

1.3542 

1.3569 

0.8669 

0.8622 

0.9201 

0.8854 

0.8815 

0.932 

0.8807 

0.879 

0.8835 

121.1206 

111.8729 

9.2763 

169.0124 

156.9953 

11.9755 

426.8469 

246.7566 

180.0152 

NA 

1.3734 

1.3804 

1.374 

0.9171 

0.1516 

0.885 

0.9235 

0.9059 

-0.0919 

0.8955 

0 

0.8858 

0.8862 

0.881 

0 

9.2938 

-0.0075 

2.246 

7.0599 

2.8014 

0.0049 

2.794 

0 

142.7331 

134.0994 

8.6234 

0 

NA 0 0 0 0 0 0 

0.4087 

0.408 

0.4129 

0.8432 

0.8688 

0.8395 

0.8434 

0.8769 

0.8387 

0.841 

0.8799 

0.8338 

3897.9475 

573.8255 

3322.0806 

4399.4991 

608.1993 

3786.9672 

4249.9171 

745.6672 

3504.6396 

NA 

NA 

0.4327 

0.4333 

0.8735 

0 

0 

0.8735 

0.886 

0 

0 

0.886 

0.8836 

0.8765 

0.8747 

0.8916 

183.6974 

0 

0 

183.6974 

181.8916 

0 

0 

181.8916 

481.4931 

253.1318 

2.679 

225.6823 

0.4489 0.9254 0.875 -0.0565 5.016 5.3157 0.0013 

NA 0 0 0.8751 0 0 8.8011 

0 0 0 0 0 0 0 

324
 
 kVAR Flow A kVAR Flow B kVAR Flow C 

2994.4404 3416.6517 3319.2982 

2484.8771 2802.2932 2733.5539 

2020.8649 2329.1825 2184.851 

1912.3068 2215.1469 2081.2881 

61.4043 39.1233 32.2663 

1890.091 2148.7621 2045.9234 

202.9733 468.2726 290.3765 

1684.3503 1676.1461 1751.1922 

180.7191 443.0079 256.5759 

171.0321 443.1493 228.6038 

9.6871 -0.1414 27.9721 

0 0 0 

1542.3544 1550.7972 1615.0629 

996.676 1112.2177 941.1572 

305.3682 147.2087 324.3699 

234.7624 286.0857 342.3179 

994.3771 1075.6567 938.4383 

993.5189 1074.3983 937.4523 

-40.0011 -40.0009 -40.0006 

659.9751 543.3731 499.4587 

428.2069 194.9498 369.9944 

231.0125 347.9404 129.1095 

0 0 0 

0 0 0 

145.8217 187.0529 95.9727 

145.772 186.9251 95.955 

325
145.7273 174.5042 92.7921 

99.4138 174.5241 71.8258 

46.2855 -0.1015 20.9698 

-0.014 -0.0174 -0.016 

0 4.7749 -0.0224 

1.047 0 0 

141.7294 93.1255 275.851 

72.193 0 0 

69.5248 93.1382 275.7495 

69.6617 88.7318 229.5944 

65.7403 84.1135 133.8224 

3.9478 4.6589 95.4486 

4.0411 1.3092 74.7599 

-0.0486 -0.0527 70.1198 

1.1817 1.3887 4.6312 

2.9325 0 0 

0 0 0 

2484.8807 2802.297 2733.557 

326.9982 333.3856 402.7434 

2150.222 2459.0224 2320.6186 

102.3847 95.1695 255.1357 

0 0 139.0539 

0 0 1.4846 

102.3847 95.1695 114.5972 

2.055 2.9415 -0.0236 

0 0 4.8678 

0 0 0 

326
 
Table B-6. Summary of LL Base Case

 (LTC control only, tap = 7)

 [#0 MXAT services included] 

Location Simulated Data Measured Data July 17, 2006 

Node 01 IA 

227.46 

IB 

262.61 

IC 

255.85 

IA 

225 

IB 

260 

IC 

254 

Node 01 VA 

125.76 

VB 

125.60 

VC 

125.31 

VA 

126.0 

VB 

126.0 

VC 

126.0 

Node 01 

PFA 

0.867 

PFB 

0.862 

PFC 

0.857 

kVA Flow Total 

Node 01 

Phase A 

1,816.66 

Phase B 

2,094.65 

Phase C 

2,036.10 5,947.41 

kW Flow 

Node 01 

Phase A 

1,575.70 

Phase B 

1,806.23 

Phase C 

1,743.88 5,125.81 

kVAr Flow 

Node 01 

Phase A 

904.12 

Phase B 

1,060.70 

Phase C 

1,050.99 3,015.81 

kW Losses Total % 

Node 01 

Phase A 

59.58 

Phase B 

48.67 

Phase C 

58.98 

167.23 

3.26% 

kVAr Losses Total %

 Phase A 

135.74 

Phase B 

182.47 

Phase C 

178.03 

496.24 

16.45% 

Node 01 

Node 01 

I0 

9.97 

V0 

0.084 

I1 

248.62 

V1 

7973.66 

I2 

11.71 

V2 

16.65 

I2/I1% 

4.71 

V2/V1% 

0.2088 

Note: All capacitors and line regulators were turned off, and the substation primary voltage was set at 

100% (120 V). 

327
 
 kW Losses: kVAr Losses: 

Phase A Phase B Phase C Phase A Phase B Phase C Phase A 

59.58 48.67 58.98 135.74 182.47 178.03 1816.66 

LTC Tap VR 1 A Tap VR 1 B Tap VR 1 C Tap 

7 NA NA NA 

Local Name Amps A Amps B Amps C Cust Volts A Cust Volts B Cust Volts C 

======Node 0====== 

MILFD8103 244.0341 281.7392 274.4897 120.0001 120.0001 120.0001 

======Node 1====== 

StPole_MILFD8 227.4606 262.605 255.8479 125.7579 125.5965 125.3097 

======Node 2====== 

======Node 3====== 

Node 3 195.3918 233.8487 218.4801 124.2194 124.0145 123.9459 

Node 3 N 189.6574 229.6123 213.8667 123.9386 123.7173 123.6939 

Node 3 E 5.7509 4.256 4.6576 124.2179 124.0142 123.945 

======Node 4====== 

Node 4 189.6645 226.3778 213.8713 123.9043 123.6818 123.6624 

Node 4 E 17.4388 45.8427 29.0388 123.8995 123.6625 123.6608 

Node 4 N 172.2271 180.5432 184.8588 123.8714 123.6565 123.6305 

======Node 5====== 

Node 5 15.6842 44.2623 25.1048 123.8405 123.4232 123.6495 

Node 5 E 14.9015 44.27 22.0038 123.8371 123.4112 123.6505 

Node 5 N 0.7828 0.019 3.1026 123.8407 123.4233 123.6441 

======Node 6====== 

Node 6 0 0 0 123.7265 123.1477 123.7001 

======Node 7====== 

Node 7 167.4328 176.0287 180.8732 122.6773 122.732 122.4825 

Node 7 E 105.0159 118.6366 102.1838 122.6741 122.7292 122.48 

Node 7 N 32.9179 20.8533 41.1011 122.6728 122.7314 122.4726 

Node 7 W 29.5179 36.562 37.6357 122.6751 122.7259 122.4746 

======Node 8====== 

Node 8 105.0185 115.4683 102.1858 122.5993 122.665 122.4185 

======Node 9====== 

Node 9 105.0194 115.4688 102.1865 122.4367 122.4842 122.2595 

======Node 10====== 

Node 10 0 0 0 121.6699 121.9238 121.7519 

======Node 11====== 

Node 11 65.79 55.7814 48.2718 121.0926 121.5547 121.4505 

Node 11 N 43.6761 19.9716 35.7606 121.085 121.5542 121.4419 

Node 11 E 22.1163 35.8106 12.5122 121.0856 121.5474 121.4519 

======Node 12====== 

Node 12 0 0 0 120.9692 121.414 121.4392 

======Node 13====== 

Node 13 0 0 0 122.5989 122.6963 122.2159 

======Node 14====== 

Node 14 17.687 19.3124 9.9032 120.9486 121.4649 121.1777 

======Node 15====== 

636_B 17.6897 19.3144 9.6032 120.9384 121.4575 121.1755 

328
======Node 16====== 

Node 16 17.6916 18.157 9.6048 120.9225 121.4499 121.1732 

Node 16 E 12.5106 18.164 7.5572 120.918 121.4443 121.1746 

Node 16 W 5.1835 0.0146 2.0498 120.9208 121.4513 121.1721 

======Node 17====== 

Node 17 0.0021 0.0025 0.0024 120.8743 121.3688 121.1773 

======Node 18====== 

Node 18 0 0.455 0.0033 0 121.2314 121.2496 

======Node 19====== 

Node 19 0.2497 0 0 120.7303 0 0 

======Node 20====== 

Node 20 17.4798 15.5017 36.3913 122.5861 122.6707 122.0873 

Node 20 W 6.4988 26.6195 77.7292 122.5861 118.6012 117.2153 

Node 20 N 10.9817 15.5022 36.3918 122.5995 122.6446 122.0226 

======Node 21====== 

Node 21 10.997 15.1054 31.9865 122.6209 122.5986 121.9099 

Node 21 N 10.2902 14.1955 21.7833 122.6209 122.5986 121.9099 

Node 21 E 0.719 0.9229 10.2065 122.623 122.598 121.9057 

======Node 22====== 

Node 22 0.7256 0.1491 8.3349 122.6357 122.5952 121.8787 

Node 22 E 0.0068 0.0073 7.8109 122.642 122.5939 121.8673 

Node 22 S 0.1233 0.1521 0.5253 122.6362 122.5947 121.8773 

======Node 23====== 

======Node 24====== 

Node 24 0 0 0 0 0 121.4917 

======Node 25====== 

Node 25 227.4609 262.6052 255.8481 125.6992 125.5116 125.26 

Node 25 W 27.1253 27.7831 35.5414 125.6979 125.5094 125.2576 

Node 25 E 200.3418 234.828 220.3332 125.6309 125.4443 125.1993 

======Node 26====== 

Node 26 8.9683 8.8416 23.2341 125.5836 125.3932 124.9689 

Node 26 E 0 0 11.2573 0 0 124.9446 

Node 26 W 0 0 0.1154 0 0 124.9685 

Node 26 S 8.9683 8.8416 11.8722 125.5812 125.3907 124.9644 

======Node 27====== 

Node 27 0.371 0.2275 0.003 125.5605 125.3781 124.8424 

======Node 28====== 

Node 28 0 0 0.3933 0 0 124.3938 

======Node 29====== 

Node 29 0 0 0 0 121.183 0 

======Feeder Path Trace====== 

Distance (1000m CustvoltsA CustVoltsB CustVoltsC %CapacityA %CapacityB %CapacityC 

0.1034 118.7851 118.7178 118.6043 77.5246 74.052 74.7196 

0.2168 125.7839 125.6264 125.3387 75.5419 71.7629 72.4895 

0.3008 125.7579 125.5965 125.3097 66.1013 60.8636 61.8707 

0.3008 125.7579 125.5965 125.3097 77.3671 73.8702 74.5425 

0.5078 125.6992 125.5116 125.26 77.3671 73.8701 74.5425 

0.7438 125.6309 125.4443 125.1993 80.0655 76.634 78.0763 

1.3578 125.453 125.2693 125.0424 80.0653 76.6339 78.1271 

2.562 125.1045 124.9284 124.7351 80.0649 76.6811 78.1268 

329
 
2.645 125.0805 124.905 124.714 80.0641 76.6837 78.1263 

3.185 124.9297 124.7482 124.5792 80.5588 76.6837 78.2612 

3.408 124.8674 124.6837 124.5236 80.5584 76.7162 78.2609 

3.695 124.7873 124.6008 124.4519 80.5582 76.7257 78.2608 

5.733 124.2194 124.0145 123.9459 80.558 76.7315 78.2607 

6.777 123.9386 123.7173 123.6939 81.1286 77.153 78.7197 

6.9052 123.9043 123.6818 123.6624 81.1279 77.4748 78.7193 

7.0393 123.8714 123.6565 123.6305 82.863 82.0355 81.6061 

7.1824 123.8364 123.6295 123.5964 82.8828 82.0354 81.606 

7.3574 123.7935 123.5965 123.5548 82.8827 82.0354 81.606 

7.6884 123.7128 123.5339 123.4762 82.9105 82.0353 81.6059 

7.8854 123.6649 123.4965 123.4294 82.9353 82.0351 81.6057 

7.8854 123.6649 123.4965 123.4294 82.9352 82.035 81.6379 

8.2254 123.5809 123.4326 123.3508 82.9352 82.035 81.8885 

8.3964 123.5386 123.4004 123.3114 82.935 82.0349 81.9108 

8.8361 123.4305 123.3175 123.2102 82.9856 82.0348 81.9107 

9.4201 123.287 123.2075 123.076 82.9853 82.0431 81.9105 

9.5872 123.2471 123.1753 123.0377 83.2611 82.0428 81.9103 

9.9964 123.1497 123.0984 122.9429 83.261 82.2412 81.9102 

10.3164 123.0736 123.0382 122.8689 83.2733 82.241 81.91 

10.4865 123.033 123.0063 122.8299 83.2731 82.2409 82.0033 

10.7919 122.9602 122.9497 122.7596 83.2729 82.3374 82.0032 

10.9291 122.9275 122.9246 122.7279 83.2727 82.4083 82.0031 

11.0751 122.8929 122.8981 122.6939 83.2726 82.4851 82.003 

11.6761 122.7506 122.7887 122.5546 83.3033 82.485 82.0029 

11.9871 122.6773 122.732 122.4825 83.34 82.4847 82.0027 

12.0081 122.6741 122.7292 122.48 89.5507 88.1954 89.8325 

12.0082 122.6741 122.7292 122.48 89.5506 88.1954 89.8325 

12.2461 122.6381 122.6978 122.4507 89.5506 88.1954 89.8325 

12.3674 122.6197 122.6818 122.4358 89.5505 88.1953 89.8323 

12.5034 122.5993 122.665 122.4185 89.5504 88.5106 89.8323 

12.6409 122.416 122.4672 122.2421 89.5503 88.5106 89.8322 

12.7379 122.4016 122.4551 122.2298 89.5935 88.5105 89.8321 

12.9285 122.3732 122.4315 122.2057 89.5989 88.5171 89.8375 

13.0339 122.3575 122.4184 122.1924 89.6074 88.5171 89.8374 

13.3649 122.3068 122.3775 122.153 89.6074 88.517 90.1356 

13.6331 122.268 122.3427 122.1214 89.958 88.5169 90.1354 

13.8911 122.2303 122.3094 122.0917 89.9579 88.5168 90.2428 

14.0938 122.2008 122.283 122.0684 90.0051 88.5167 90.2427 

14.5009 122.1348 122.2319 122.0327 90.0049 88.5661 91.4448 

15.0489 122.0461 122.1643 121.9841 90.0047 88.6493 91.4446 

15.2389 122.0154 122.1409 121.9673 90.0186 88.6491 91.4443 

15.3809 121.9929 122.123 121.9548 90.16 88.649 91.4442 

15.5193 121.9712 122.1063 121.9422 90.1599 88.8767 91.4442 

15.8243 121.9227 122.0697 121.9153 90.1598 88.8766 91.5733 

16.0943 121.8795 122.0374 121.8918 90.1596 88.8765 91.6211 

17.4243 121.6732 121.9215 121.7536 90.1594 90.1983 91.621 

17.5825 121.6506 121.9062 121.738 90.7546 90.1974 91.7572 

17.8255 121.6158 121.8827 121.7141 90.7545 90.1973 91.7819 

18.2705 121.5526 121.8392 121.6706 90.8164 90.1972 91.7818 

18.4278 121.5302 121.8238 121.6555 90.8161 90.1971 91.8435 

18.5938 121.5065 121.8076 121.6395 90.816 90.197 91.8434 

330
 
18.7608 121.4826 121.7914 121.6234 90.8159 90.1969 91.8536 

19.0918 121.4353 121.7591 121.5916 90.8158 90.1969 91.8535 

19.3973 121.3899 121.7297 121.5652 90.8156 90.1968 92.2613 

19.9934 121.3147 121.6853 121.5392 93.0173 92.4638 95.0126 

20.3713 121.2676 121.6599 121.5211 93.0169 92.7741 95.0121 

20.7442 121.2252 121.6321 121.5037 93.4546 92.7739 95.0119 

20.9315 121.2035 121.6182 121.4957 93.4544 92.7738 95.1624 

21.4456 121.144 121.5803 121.4735 93.4542 92.7918 95.1623 

21.7101 121.1132 121.5608 121.4623 93.4539 92.7916 95.197 

21.8963 121.0926 121.5547 121.4505 93.4537 94.4496 95.1968 

22.0263 121.085 121.5542 121.4419 95.6541 98.0128 96.4417 

22.1673 121.0766 121.5536 121.4329 95.6541 98.0127 96.5147 

22.3333 121.0667 121.5529 121.4222 95.654 98.0126 96.5146 

22.4553 121.0599 121.5522 121.4144 95.8112 98.0125 96.5145 

22.7923 121.041 121.5502 121.3934 95.8111 98.0124 96.5674 

22.9523 121.0402 121.5465 121.3827 97.5132 98.0122 96.5672 

23.1747 121.0387 121.5413 121.3683 97.5131 98.0121 96.6775 

23.3151 121.0358 121.5397 121.3597 97.513 98.012 96.7796 

23.3365 121.0353 121.5394 121.3584 97.5204 98.0212 96.787 

23.5305 121.0313 121.5372 121.3467 97.5204 98.0211 96.787 

23.6878 121.0282 121.5353 121.3371 97.5426 98.0211 96.7869 

23.9908 121.0222 121.5317 121.3187 97.5425 98.021 96.7868 

24.1041 121.0199 121.5303 121.3118 97.5423 98.0209 96.7918 

24.3641 121.0149 121.5271 121.2961 97.5718 98.0209 96.7917 

24.6082 121.0099 121.5241 121.2818 97.5716 98.0208 96.8826 

24.7822 121.0067 121.5217 121.2717 97.6614 98.0207 96.8825 

25.0002 121.0025 121.5187 121.2594 97.6613 98.0206 96.9438 

25.1092 121.0004 121.5173 121.2532 97.6611 98.0462 96.9437 

25.3222 120.9992 121.5125 121.2414 98.21 98.0461 96.9437 

26.3285 120.9818 121.4915 121.2059 98.2098 98.0461 97.7627 

26.5025 120.9786 121.4879 121.2001 98.2092 98.0457 97.8604 

26.9085 120.9702 121.4796 121.1882 98.2091 98.0456 97.9984 

27.0357 120.9677 121.4769 121.1844 98.2404 98.0455 97.9982 

27.3012 120.9608 121.4715 121.1794 98.2403 98.0454 98.422 

27.3603 120.9588 121.4705 121.1791 98.2401 98.0784 98.9894 

27.6618 120.9486 121.4649 121.1777 98.2401 98.0784 99.0146 

27.858 120.9427 121.4598 121.176 98.3709 98.2212 99.0878 

27.983 120.9384 121.4575 121.1755 98.2398 98.0782 99.0445 

28.168 120.9321 121.4543 121.1747 98.2398 98.1203 99.0444 

28.4501 120.9225 121.4499 121.1732 98.2396 98.1933 99.0443 

28.6326 120.918 121.4443 121.1746 98.7102 98.1274 99.2209 

29.0019 120.9094 121.4327 121.1777 98.7743 98.1273 99.2208 

29.6519 120.8952 121.4116 121.1833 98.8357 98.1271 99.2207 

29.9439 120.8896 121.4016 121.186 98.9576 98.1266 99.2205 

30.2829 120.8864 121.388 121.1894 99.373 98.1264 99.2203 

30.9229 120.8813 121.3619 121.1959 99.4283 98.1262 99.2202 

31.2019 120.8802 121.3633 121.1902 99.4279 99.9981 99.2194 

31.4404 120.8794 121.3645 121.1855 99.4477 99.9985 99.2464 

31.6554 120.8791 121.3653 121.1813 99.5151 99.9988 99.2464 

31.7694 120.8791 121.3657 121.1791 99.5744 99.999 99.2463 

31.8644 120.8787 121.3661 121.178 99.5744 99.9991 99.5357 

32.0486 120.8769 121.3672 121.1776 99.5743 99.9992 99.9585 

331
 
kVA Flow SOC Released Capacity 

Phase B Phase C Phase A Phase B Phase C 

2094.65 2036.10 NA NA NA 

Seq Amps 0 Seq Amps 1 Seq Amps 2 I2/I1 (%) Seq Volts 0 Seq Volts 1 Seq Volts 2 

10.6997 266.7397 12.5661 4.711 0 7620.9118 0.1115 

9.973 248.6242 11.7127 4.711 0.084 7973.6646 16.649 

10.0093 215.8935 12.4044 5.7456 21.2443 7878.6813 24.3383 

10.3777 211.0309 12.9244 6.1244 25.6344 7861.0895 26.6788 

0.3748 4.886 0.5281 10.8088 21.2226 7878.627 24.3351 

9.6275 209.9567 12.0089 5.7197 26.1204 7858.9441 26.9705 

8.3286 30.7726 8.1616 26.5225 26.8884 7858.3973 27.1083 

3.754 179.1924 4.3125 2.4066 26.1587 7857.0354 27.1938 

8.4174 28.3499 8.3981 29.6229 36.6073 7851.8011 28.8003 

8.8219 27.0579 8.8711 32.7856 37.1205 7851.4935 28.871 

0.9194 1.2925 0.9472 73.2813 36.506 7851.6931 28.8793 

0 0 0 NA 48.6106 7844.5683 29.8772 

3.9833 174.7588 4.5671 2.6134 28.0842 7787.8378 36.715 

4.5087 108.6062 5.673 5.2234 28.1123 7787.6568 36.7426 

5.9934 31.6231 5.769 18.243 27.8664 7787.5197 36.811 

1.8431 34.5322 3.5023 10.142 28.1004 7787.4935 36.7669 

3.4602 107.5518 4.6405 4.3146 28.733 7783.4062 37.3958 

3.4602 107.5518 4.6405 4.3146 29.1752 7772.7694 37.063 

0 0 0 NA 35.9934 7733.8786 41.7965 

5.0211 56.61 5.1669 9.1272 43.847 7707.4137 44.0908 

7.2945 33.1324 6.6414 20.0449 43.514 7707.0621 44.0182 

6.6666 23.4789 6.8538 29.1915 44.2314 7707.1408 44.0789 

0 0 0 NA 49.8449 7701.5484 44.3862 

0 0 0 NA 24.7761 7779.7819 39.7308 

2.6065 15.6289 3.198 20.4621 38.0717 7696.7125 45.7633 

2.7067 15.5305 3.2965 21.2261 38.2758 7696.2939 45.6723 

332
 
2.5008 15.1462 3.0505 20.1403 38.6129 7695.7453 45.627 

2.8332 12.7392 3.2962 25.8747 38.8364 7695.5626 45.5523 

1.55 2.4084 1.4676 60.9367 38.5379 7695.7163 45.6194 

0 0.0023 0 0 41.1339 7693.0855 44.9112 

0 0.1514 0.1509 99.6866 0 5133.0788 2558.1215 

0.0832 0 0 NA 2555.801 0 0 

6.6367 23.1235 6.6805 28.8905 25.1359 7776.2405 41.4469 

2.1663 47.4282 15.5983 32.8881 2595.0857 7485.2458 94.603 

7.7805 20.9578 7.8723 37.5624 26.7462 7774.5972 42.5068 

6.3754 19.3623 6.4694 33.4126 29.9628 7771.6767 44.346 

3.3308 15.4226 3.4172 22.157 29.9628 7771.6767 44.346 

3.1224 3.9442 3.1421 79.6646 30.0955 7771.6168 44.4178 

2.659 3.0675 2.619 85.3787 30.9206 7771.2542 44.8628 

2.6044 2.6012 2.6051 100.1499 31.3241 7771.1159 45.0595 

0.1292 0.2665 0.1305 48.9528 30.9698 7771.2238 44.8812 

0 0 0 NA 0 0 2571.8618 

9.973 248.6244 11.7127 4.711 1.214 7969.5736 16.1522 

2.8208 30.149 2.5843 8.5717 1.2553 7969.4473 16.1338 

8.7835 218.4865 11.2937 5.169 1.9729 7965.4167 16.3163 

4.7697 13.6807 4.7844 34.9721 7.611 7958.4629 16.5635 

0 0 3.7523 NA 0 0 2644.9557 

0 0 0.0385 NA 0 0 2645.4616 

0.9805 9.8936 1.0013 10.1203 7.7004 7958.2634 16.5774 

0.0977 0.1987 0.1188 59.808 11.8744 7954.9772 16.8805 

0 0 0.1311 NA 0 0 2633.2957 

0 0 0 NA 0 2565.3263 0 

333
 
pf FLOW 

V2/V1 (%) pf A pf B pf C kW Flow A kW Flow B kW Flow C 

0.0015 0.8498 0.8427 0.838 1580.4571 1809.311 1752.9747 

0.2088 0.8674 0.8623 0.8565 1575.6953 1806.2348 1743.876 

0.3089 0.8682 0.8656 0.8586 1344.3375 1601.8058 1482.6379 

0.3394 0.8692 0.8676 0.8603 1300.5374 1568.9705 1448.3102 

0.3089 0.8833 0.8992 0.917 40.0761 30.1402 33.6184 

0.3432 0.87 0.8686 0.8619 1298.7358 1544.9531 1447.9904 

0.345 0.8734 0.8766 0.8812 119.8594 315.6539 200.9773 

0.3461 0.8697 0.8667 0.8589 1178.6613 1229.138 1246.9655 

0.3668 0.8736 0.8777 0.8789 107.7664 304.5262 173.2681 

0.3677 0.8739 0.8775 0.8769 102.4174 304.5142 151.515 

0.3678 0.8689 -0.0799 0.8928 5.349 0.0119 21.7531 

0.3809 -1 -1 -1 0 0 0 

0.4714 0.8735 0.8707 0.8631 1140.0921 1195.1526 1215.1032 

0.4718 0.8703 0.8658 0.8684 712.0695 800.647 690.2474 

0.4727 0.8711 0.8755 0.8713 223.4181 142.3008 278.5733 

0.4721 0.8882 0.8844 0.8406 204.2579 252.041 246.0894 

0.4805 0.8704 0.8664 0.8686 711.8635 779.4645 690.1703 

0.4768 0.8704 0.8664 0.8686 711.792 779.4513 690.1382 

0.5404 -0.0038 -0.1003 0.1056 0 0 0 

0.5721 0.871 0.8715 0.8649 440.7576 375.3048 322.0443 

0.5711 0.8731 0.8727 0.8648 293.2731 134.5544 238.5249 

0.5719 0.8669 0.8709 0.8652 147.4439 240.7619 83.502 

0.5763 -1 -1 -1 0 0 0 

0.5107 -1 -1 -1 0 0 0 

0.5946 0.8897 0.8722 0.8735 120.8866 129.9473 66.5753 

0.5934 0.8896 0.8722 0.8738 120.8783 129.9443 64.5752 

334
 
0.5929 

0.5919 

0.5928 

0.8896 

0.8923 

0.8828 

0.8729 

0.8725 

-0.0877 

0.8737 

0.8766 

0.8621 

120.8727 

85.7247 

35.1431 

122.2559 

122.2442 

0.0099 

64.5766 

50.9787 

13.599 

0.5838 0.0618 0.0941 -0.1546 0 -0.0018 0.0028 

49.836 0 0.8623 -0.2553 0 3.0209 0.0066 

NA 0.9291 0 0 1.7787 0 0 

0.533 

1.2639 

0.5467 

0.8675 

0.8668 

0.8679 

0.8753 

0.8856 

0.8753 

0.8709 

0.8791 

0.8709 

118.0516 

43.8564 

74.1985 

105.7122 

177.5682 

105.7093 

245.7587 

508.7365 

245.7518 

0.5706 

0.5706 

0.5715 

0.8672 

0.8617 

0.933 

0.8748 

0.8699 

0.9368 

0.8714 

0.8684 

0.878 

74.2613 

69.0483 

5.2243 

102.8992 

96.1532 

6.7311 

215.8611 

146.4653 

69.3783 

0.5773 

0.5798 

0.5775 

0.9273 

0.1525 

0.9217 

0.9447 

-0.0924 

0.9196 

0.8814 

0.8814 

0.8792 

5.2405 

-0.0081 

0.8852 

1.0966 

0.0052 

1.0887 

56.8652 

53.2874 

3.575 

NA 0 0 0 0 0 0 

0.2027 

0.2024 

0.2048 

0.8674 

0.8765 

0.8664 

0.8623 

0.871 

0.8615 

0.8565 

0.8745 

0.8539 

1575.6959 

189.8084 

1385.5885 

1806.2345 

192.8982 

1612.6247 

1743.8758 

247.2446 

1496.6866 

NA 

NA 

0.2081 

0.2083 

0.8819 

0 

0 

0.8819 

0.8846 

0 

0 

0.8846 

0.876 

0.8606 

0.8599 

0.89 

63.0834 

0 

0 

63.0834 

62.2831 

0 

0 

62.2831 

161.5408 

76.8906 

0.7877 

83.8625 

0.2122 0.9261 0.8671 -0.0568 2.7398 1.5706 0.0014 

NA 0 0 0.8601 0 0 2.6726 

0 0 0 0 0 0 0 

335
 
 kVAR Flow A kVAR Flow B kVAR Flow C 

980.2917 1156.1179 1141.532 

904.118 1060.7034 1050.9932 

768.4928 926.5778 885.2514 

739.75 899.2868 858.1904 

21.2659 14.6679 14.6282 

736.1879 881.3615 852.071 

66.8173 173.2785 107.7932 

668.9267 707.346 743.5245 

60.0243 166.2396 94.0404 

56.9766 166.3883 83.067 

3.0477 -0.1486 10.9734 

0 0 0 

635.5206 675.2037 710.8971 

402.9679 462.6705 394.1484 

125.9318 78.5502 156.8848 

105.6756 133.0068 158.5757 

402.5919 449.2327 393.7029 

402.4412 449.008 393.533 

-0.003 -0.0027 -0.0027 

248.6105 211.181 186.9282 

163.7406 75.2687 138.5139 

84.785 135.8595 48.387 

0 0 0 

0 0 0 

62.0248 72.8681 37.0982 

62.046 72.8788 35.9416 

336
62.063 68.3221 35.9626 

43.3819 68.4443 27.9884 

18.6962 -0.1121 7.9934 

-0.0158 -0.0193 -0.0179 

0 1.774 -0.0249 

0.7079 0 0 

67.6977 58.3967 138.6665 

25.2285 93.1255 275.851 

42.4745 58.4064 138.6507 

42.6478 56.9816 121.4951 

40.6686 54.5054 83.6167 

2.0144 2.5146 37.8295 

2.1153 0.3805 30.4788 

-0.0525 -0.0563 28.5605 

0.3725 0.4652 1.937 

0 0 0 

904.1216 1060.7072 1050.9963 

104.2233 108.7893 137.1452 

798.7348 950.3567 912.2053 

33.7157 32.8395 88.9252 

0 0 45.5001 

0 0 0.4675 

33.7157 32.8395 42.9576 

1.1161 0.9025 -0.024 

0 0 1.5853 

0 0 0 

337
 
F1147-E(12/2004) 

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5a. CONTRACT NUMBER

DE-AC36-99-GO10337 

5b. GRANT NUMBER

4. TITLE AND SUBTITLE

Modeling and Testing of Unbalanced Loading and Voltage 

Regulation: Final Report 

5c. PROGRAM ELEMENT NUMBER

5d. PROJECT NUMBER

NREL/SR-581-41805 

5e. TASK NUMBER

WW88.2003 

6. AUTHOR(S)

M.W. Davis, R. Broadwater, and J. Hambrick 

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National Renewable Energy Laboratory 

1617 Cole Blvd. 

Golden, CO 80401-3393 

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NREL/SR-581-41805 

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14. ABSTRACT (Maximum 200 Words)

This paper is a final report on a project to (1) explain how voltage regulation reduces voltage spread; (2) define the 

effects of unbalanced loading and voltage on system protection and distributed generation output ratings; (3) develop 

models for an actual distribution circuit, its voltage regulation equipment, and distributed generation; (4) validate the 

models by comparing power flow simulations and voltage profiles with actual measured circuit data; (5) determine the 

optimum generator operating conditions to provide the greatest improvement in released capacity, reduced energy 

losses, and voltage regulation, and (6) determine the maximum distributed generation penetration limits with 

synchronous generator real and reactive power injections. 

15. SUBJECT TERMS

distributed generation; DG; distributed resources; DR; interconnection; voltage regulation; modeling; penetration limit; 

National Renewable Energy Laboratory; NREL; DTE Energy 

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