UNITED STATES DEPARTMENT OF AGRICULTURE

Rural Utilities Service 

BULLETIN 1724D-112 

RD-GD-2018-92

SUBJECT: The Application of Capacitors on Rural Electric Systems

TO: RUS Electric Borrowers and RUS Electric Staff

EFFECTIVE DATE: Date of Approval 

OFFICE OF PRIMARY INTEREST: Electric Staff Division 

INSTRUCTIONS: Replaces Bulletin 1724D-112, dated April 27, 2001 

AVAILABILITY: This bulletin is available on the Rural Utilities Service website at 

www.usda.gov/rus/electric. 

PURPOSE: To provide Rural Utilities Service (RUS) borrowers and others guidance on the 

use, characteristics, and benefits of power factor correction capacitors on rural distribution

systems. 

As a rural power distribution system load grows, the system power factor usually declines. This 

gradual load growth and decrease in power factor increases system energy losses, lowers 

voltages at consumers’ premises, degrades the performance of energy utilization equipment, and 

drives up the cost per unit of energy delivered. For optimum performance and avoidance of 

these most undesirable conditions, especially in today’s competitive electric industry, prudent 

utility providers should make every effort to maintain power factor as close to 1.0 as 

economically practical.

To gain optimum performance and advantage, power factor correction capacitors need to be 

efficiently and effectively sized, located, and utilized on power circuits at times appropriate to 

the system’s load cycle. This bulletin presents guidance information on all these considerations.

____________________ 

Date

_________________________________________ 

Christopher A. McLean

Assistant Administrator

Electric Program

Disclaimer: The contents of this guidance document does not have the force and effect of law and is not 

meant to bind the public in any way. This document is intended only to provide clarity to the public 

regarding existing requirements under the law or agency policies.
Bulletin 1724D-112 

Page 2 

TABLE OF CONTENTS

1 Introduction ..............................................................................................................................4

2 How Capacitors Work..............................................................................................................8

3 Capacitor Concerns ................................................................................................................23

4 Capacitor Sizing, Location, and Use......................................................................................40

5 Power Supply Considerations ................................................................................................53

6 Capacitors for Induction Motors ............................................................................................55

7 References ..............................................................................................................................60

Appendices 

Appendix A: Power Factor Table 

Appendix B: Capacitor Rating Table for Motors 

INDEX:

Capacitors

Distribution System Planning

Power Factor

ABBREVIATIONS

Ω Ohms, symbol for the unit of electrical resistance

ACSR Aluminum Cable, Steel-Reinforced

ARC COS Trigonometric Inverse Cosine 

ARC TAN Trigonometric Inverse Tangent 

COS Trigonometric Cosine 

CT Current Transformer

CVR Conservation Voltage Reduction 

EEI Edison Electric Institute

EPA U.S. Environmental Protection Agency

Hz Hertz (cycles per second)

I Current

IEEE Institute of Electrical and Electronics Engineers

+j J Operator, followed by the impedance value, indicates that the voltage across an 

inductor leads the current through it by 90° 

kcmil 1,000 Circular Mils

kV Kilovolt (1,000 volts) 

kVA Kilovolt-Amperes

kVAr Kilovolt-Amperes Reactive

kVArh Kilovolt-Amperes Reactive-Hours 

kW Kilowatts

kWh Kilowatt-Hours 

LTC Load Tap Changing 

MOV Metal-Oxide Varistor
Bulletin 1724D-112

Page 3

NEMA National Electrical Manufacturers Association

NRECA National Rural Electric Cooperative Association

OCR Oil Circuit Recloser

PCB Polychlorinated Biphenyls

p.f. Power Factor

PLC Programmable Logic Controllers

pu Per Unit

rms Root Mean Square

RUS Rural Utilities Service

SCADA System Control and Data Acquisition

TVSS Transient Voltage Surge Suppression

V Volt

V.D. Voltage Drop

VAr Volt-Amperes Reactive

ACKNOWLEDGMENTS

This version of Bulletin 1724D-112 was updated by the Power Quality Subcommittee of the 

National Rural Electric Cooperative Association in 2016. Members of the subcommittee who 

contributed to this revision include:

Ed Bevers, Rural Electric Cooperative, Inc., Lindsay, Okla.

Scott Blecke, Great Lakes Energy, Boyne City, Mich.

Jeff Coleman, Berkeley Electric Cooperative, Moncks Corner, S.C.

Herman Dyal, Clay Electric Cooperative, Inc., Keystone Heights, Fla. (retired)

Varzavand Irani, Nueces Electric Cooperative, Inc., Corpus Christie, Texas

Ted Pejman, Rural Utilities Service, U.S.D.A. (retired)

Tony Thomas, National Rural Electric Cooperative Association, Arlington, Va.

Jeffrey Triplett, Power System Engineering, Inc., Marietta, Ohio

Lewis Shaw, Brunswick Electric Membership Corporation, Shallotte, N.C.
Bulletin 1724D-112

Page 4

1 INTRODUCTION

a. Why Power Factor Correction?

The expansion of power systems for farm electrification and the growth of motor 

and other inductive loads for home and farm uses causes a decline in system

power factor. This downward trend in power factor leads to:

1. Voltage regulation problems,

2. Increased system losses,

3. Power factor penalties in wholesale power contracts, and

4. Reduced system capacity.

Any of these four deficiencies are, in themselves, intolerable for today’s prudent 

utility operator. Utilities, under consumer and regulator scrutiny, have to design, 

construct, operate, and maintain the most reliable, efficient, and economical 

facilities possible.

Capacitors offer a means of improving system power factor and the above

conditions by reducing the reactive kilovar load carried by the utility system.

b. Voltage Regulation

One of the greatest advantages gained by the proper size and location of

distribution capacitors is voltage improvement. By placing leading Volt-Amperes 

Reactive (VAr) loads near lagging VAr load centers, the lagging VAr on a system

basis are cancelled with an associated increase in voltage and gain in system 

capacity.

Care is required not to exceed the lagging VAr requirement at any time.

Capacitors should be sized for peak load requirements and removed from the

system as the load drops, usually through switched controls. Capacitors draw a 

specific leading current that generates a voltage rise through the reactive ohms of

the system impedance (see Section 2f of this bulletin for these calculations).

Today utility systems are increasingly implementing voltage regulation programs 

to reduce system demand on peak as well as reduce system losses both on and off 

peak. These programs are referred to as Conservation Voltage Reduction (CVR). 

This program will be discussed further in Section 2f (2) of this bulletin.

(1) Capacitors or Voltage Regulators

Care should be taken in choosing between capacitors and voltage

regulators for voltage improvement. Often, both are necessary to have a

well-balanced system operating at maximum efficiency. Shunt capacitors

provide some voltage rise and can do so at a lower cost than a line

regulator. Sample calculations are shown in the following sections.
Bulletin 1724D-112

Page 5

However, for some load conditions, the voltage rise offered by capacitors

may be excessive and cause problems for customers’ connected

equipment. Higher cost regulators offer a means for maintaining more

constant system voltage. The combination of regulators and capacitors

provides the best of both worlds.

A 600 Kilovolt-Amperes Reactive (kVAr) capacitor bank—including 

labor and a control—will cost approximately $10,000 and can provide

about a 4-volt rise (more or less, depending on where the capacitors are

located) when connected on a distribution feeder. That rise is either on or

off, depending on whether the capacitor is on-line or off. This capacitance

provides power factor correction by canceling the effects of 600 kVAr of

lagging reactive load.

A single-phase line regulator, at about $13,600, can provide sixteen 3⁄4-volt 

(5⁄8%) steps up or down (on a 120-volt base), depending on whether the

regulator is raising or lowering the voltage. Although this step range

approximates a 12-volt boost or buck capacity, Rural Utility Service 

(RUS) suggests that effective voltage analysis has shown that the system

operator should allow only an 8-volt variation per regulator.

Moreover, from voltage analysis results, the use of only two series 

regulators are recommended in addition to the substation regulator or Load 

Tap Changing (LTC) transformer. If more than two series regulators are

boosting and there is a fault near the end of the line when an Oil Circuit 

Recloser (OCR) opens, the line voltage can go up too high and damage

customer-owned equipment. This means that, if any line regulator needs

to raise to step 11 or greater, the incoming voltage serving the last

consumer prior to the regulator is below 118 volts, which is outside the

Class A voltage limits that RUS recommends be observed as a design

criteria.

Voltage improvement can be gained fairly inexpensively with capacitors,

relative to voltage regulators at $40,600 for a 3-phase bank. But this gain

may be at the cost of higher losses and power factor penalty charges when

the excess capacitors needed for voltage improvement are allowed to drive

the power factor leading.

In general, voltage regulators should be used to maintain accurate control

of voltage throughout the load cycle (control voltage fluctuation), and

shunt capacitors should be used to correct low power factors.

c. Increased System Losses

A distribution utility system serves connected loads that require both reactive 

energy as well as real energy. Both of these energy types must be served by the 

power supplier’s generator. This relationship is discussed in greater detail in 
Bulletin 1724D-112

Page 6

Section 2a of this bulletin. In simple terms, the higher the power factor up to unity 

at the delivery point, the lower the reactive energy being served from the power 

supplier and the more real energy can be delivered to the load. The addition of 

capacitors on the distribution line reduces the reactive energy flow and current,

thereby reducing losses.

Distribution capacitors can reduce system line losses, as long as the system power

factor is not forced into a leading mode. Line losses at 80% leading power factor

are just as detrimental as line losses at 80% lagging power factor. Properly placed

and sized capacitors can usually reduce system line losses sufficiently to justify

the cost of their installation.

If switched capacitors are used to regulate voltage, the system operator will need

to conduct frequent system studies to monitor the load growth and know when

capacitors should be switched on and off. Studies are especially important where

loading is not uniform along the feeder. It is important to remember that costs to

switch capacitor banks add $2,000 to $5,000 per bank, depending upon the

control type used.

The energy loss in an older style standard paper-type capacitor is small (not

exceeding 3.3 watts per kVAr at rated voltage and frequency). Expressed in

terms of efficiency, this is 99.67%. However, new film-type capacitors available

today have energy losses below one watt per kVAr, which results in 99.9%

efficiency. In addition, the size and weight of newer capacitors have been greatly

reduced by use of film in lieu of Kraft paper as the dielectric material.

Capacitors energized at rated voltage always operate at full load. Therefore, 

system load cycles have no effect on the losses of capacitors operating at rated

voltage. Operating capacitors at voltages above their rated values can diminish

capacitor life spans. Operation at voltages below their rated value reduces the 

effective (kVAr) size of the capacitor with a resulting decrease in their benefits.

d. Power Factor Penalty Charges

Power Factor correction may be initiated to reduce power factor penalty charges

in purchased power. Most power purchase rates have penalties for poor power

factor. That penalty takes several forms, but the most common is an adjustment

in Billing Demand rate. The Measured Demand is increased by the ratio of the

contract minimum power factor over the actual metered power factor and is 

calculated as follows:

Measured Power Factor

Contract Power Factor Billing Demand = Metered Peak Demand×

Equation 1: Billing Demand
Bulletin 1724D-112

Page 7

Power Factor is either measured during the system peak or is calculated as an

average power factor for the month as follows:





 



 



 



 × = kWh

kVAr Hours p.f. COS ARCTAN

Equation 2: Power Factor

In some cases, billing departments may only have kilowatts (kWh) and kilovoltamperes reactive-hours (kVArh) data from which to calculate power factor. 

Equation 2 is the inverse of the true power factor formula. However, Table A1 in 

Appendix A, which has been in use for years, corrects the calculation by having 

values greater than unity.

(1) EXAMPLE 1. Find the Power Factor for 244,300 kWh and 200,700

kVArh (Reactive) meter readings.

SOLUTION: kVArh ÷ kWh = 200,700 ÷ 244,300 = 0.82153. Using the

Power Factor Table (Table A1 of Appendix A), we find 0.82153 is closest 

value in the table to 0.821. This value corresponds to value of 0.773 for 

the power factor in Table A1. (This power factor is obtained by reading

the value (0.77) in the left-most cell in the same row as the 0.821 value 

0.821 ratio. Then add to the 0.77 the value (0.003) in the top-most cell in 

the same column as the 0.821 ratio.)

So the Power Factor is 0.773.

ALTERNATIVE SOLUTION: Using Equation 2 from above directly:





 



 



 



 × = kWh

kVAr Hours p.f. COS ARCTAN





 



 



 



 = 244,300

200,700 p.f. COS ARCTAN

p.f. =COS [ ARCTAN (0.82153)]

p.f. =COS [ 39.4 ] = 0.773 

In summary, low system power factor results in higher demand charges. 

With demand charges of $6 to $12 per kilowatt (kW) and full annual 

ratchet, a 1-kW increase costs from $72 to $144 per year. The cost of poor

power factor is then very tangible, but the true costs of poor power factor
Bulletin 1724D-112

Page 8

should also include increased losses, poor voltage, and wasted system 

capacity.

e. Reduced System Capacity

For the reasons discussed in Section 1c of this bulletin, the cause of increased

system losses on the distribution system similarly affect the subtransmission and

bulk transmission system providing power to the distribution plant. These bulk

power facilities also have to provide capacity to satisfy the inductive kVAr load 

installed on the distribution system. The resultant reactive current flow produces

losses on the bulk facilities as well, introducing unnecessary costs. Generators 

too have to provide the reactive needs of distribution plant inductive loads making 

generators less efficient as well.

As will be seen, capacitors will provide improvement on the bulk facilities as a 

by-product of the improvements they bring about on the distribution feeder.

2 HOW CAPACITORS WORK

a. What is Power Factor?

This section explains the power relationships between watts, Volt-Amperes 

Reactive (Var), volt-amperes, and power factor. The total power (Apparent

Power) in Kilovolt-Amperes (kVA) delivered by a distribution line to a load

consists of two parts, Real Power (kW) and Reactive Power (kVAr), as shown in

the container analogy of Figure 1.

REACTIVE

44 kVAr 60 kVAr 70 kVAr POWER

TOTAL

POWER 100 kW

KVA

90 kW 80 kW 70 kW REAL

POWER

Unity Power Factor 0.90 Power Factor 0.80 Power Factor 0.70 Power Factor

Phase Angle (θ) = 0° 25.8° 36.9° 45°

100 kVA loads at various power factors. kW is usable power. Excessive kVAr is wasted power. 

As power factor increases, the useful power delivered is increased. As can be seen, lagging 

kilovars form an appreciable component of the system load.

Figure 1: Real and Reactive Power Analogy

In the Figure 1 analogy, electricity required to serve a system is represented as a

mug of root beer where you have to purchase a whole mug to get what you really

want. Liquid root beer represents kW energy which can perform useful work.

One would prefer a mug full of liquid root beer with little foam. The reactive part
Bulletin 1724D-112

Page 9

(or the foam in this analogy) of the total kVA, while it performs no useful work,

has to be purchased, in the absence of power factor correction. Reactive energy

has to be purchased because connected loads and associated conductors are 

demanding this type of energy. As a result, reactive energy has to be supplied by

the generator at the power plant, be transformed and transmitted along the

transmission grid, and finally be transformed again on the distribution system for

delivery to the reactive load that requires it.

If the reactive part of the total kVA needed to serve a distribution system is to be 

produced by the power supplier’s generator, then the reactive component travels 

through the entire power delivery system. If the distribution system’s reactive

load can be canceled by a capacitor placed at the reactive load center, the entire

power delivery system will be relieved of this kVAr burden and, thereby, gains

capacity. If a capacitor is connected to the distribution system either ahead of or

beyond the system’s load center, the capacitor still provides reactive loading

relief, but the system will not gain the full advantages of voltage and loss

improvement which would be afforded by proper capacitor placement.

Figure 1 depicts an analogy of the relationship between kVA, kW, kVAr, and p.f..

The real power component in kW, which is capable of doing work, is what

utilities sell, and it is measured using kWh meters. The inductive reactive power

component, measured in lagging kVAr, is required by and supplied to motors to

magnetize motor-winding fields, transformers to magnetize transformer windings

and cores, and phase conductors to sustain the magnetic fluxes associated with

current flowing in the conductors.

1 This reactive lagging power component

(kVAr):

1. Performs none of the useful work,

2. Is not measured on kWh meters, and

3. Has to be furnished to the loads.

The leading current developed by capacitors can effectively cancel the lagging

current demanded by the reactive load components. The total power delivered to

the load then consists of a real and a reactive component. Total power is 

measured in kVA. Power factor is defined as the ratio of real power (kW) to total 

power (kVA).

b. Power and Power Factor Relationships

 1 Because inductive reactances associated with circuit phase conductors decrease as the spacing between conductors 

decreases, conductors on narrow profile line construction should contribute less inductive reactance than conductors 

on standard line construction. Assuming all other circuit inductive reactance contributors are the same, required 

power factor correction on narrow profile lines may be less than standard line construction. This narrow profile 

benefit, however, may not be significant enough to justify the associated cost of additional poles, shorter spans, and 

the reduced basic insulation impulse level and possibility of impaired reliability and outages.
Bulletin 1724D-112

Page 10

A more useful way to show the power relationships is with the Power Triangle of

Figure 2. Total Apparent Power (in volt-amperes or VA or kVA) is the vector

sum (not arithmetic sum) of the Real Power (in watts or kilowatts) and the

Reactive Power (in VAr or kilovars). A vector has a length, or magnitude, and a

direction. A vector diagram allows easy calculation of relationships within the

Power Triangle using trigonometry. VAr means volt-ampere reactive, or more

simply Volts times Amps (V×A or VA) shown in the reactive relationship (90

degrees out of phase with the voltage and kW). Therefore, VAr lead or lag by 90

degrees the Real Power (kW) vector. The Real Power vector always lies along

and is in phase with the voltage vector. The Apparent Power vector always lies

along and is in phase with the Current (Amperes) vector. Thus, simple 

trigonometry explains the Power Triangle of Figure 2.

Power Triangle = A vector representation of time relationships where:

• Apparent Power (kVA) is the vector sum of Real Power (kW) and Reactive Power (kVAr)

• Real Power (kW) is in phase with the voltage vector

• Apparent Power (kVA) is in phase with the current vector

• Reactive Power is perpendicular to Real Power

• Lagging Reactive Power is customarily shown pointing Down

• Leading Reactive Power is customarily shown pointing Up

Figure 2: Power Triangle 

As defined, Power Factor equals kW divided by kVA. Power factor is also equal

to the Cosine of the Phase Angle (theta) between the voltage and current vectors. 

Power Factor is the trigonometric Cosine of the angle between the Real and

Apparent Power. This angle is identical to the angle between the voltage and

current vectors.

In trigonometric terms: PHASE ANGLE = ARC COS (kW ÷ kVA)

Explained another way, the phase angle is equal to the angle whose Cosine is kW

÷ kVA. On scientific calculators, the ARC COS is shown as COSINE -1 or 

INVERSE COSINE.

c. Power Factor Effects

VOLTAGE

PHASE ANGLE 

CURRENT

REAL POWER (kW)

POWER FACTOR 

ANGLE (THETA)

APPARENT POWER 

(kVA)

REACTIVE

POWER 

(kVAR)

θ θ
Bulletin 1724D-112

Page 11

A capacitor is a leading reactive power load whose leading VAr requirements 

cancel an equal portion of the system’s lagging VAr requirements, thereby 

reducing the load on the system. The leading current required by the capacitor, 

which flows through the lagging impedance of the system conductors and 

transformers, causes a voltage rise whose magnitude can be calculated.

By the addition of capacitors at a load center, the resulting decrease in VAr 

required of the generator actually lowers the kVA supplied by the generator at the 

power plant to a more pure kW load. This brings about lower losses in the system 

and better voltage at the load due to the resulting lower line currents. In many

cases, the system can then deliver more useful power with the same investment in

equipment. This provides better utilization of existing investment in equipment 

and may make possible the deferral of costly system improvements. This is 

highly desirable as electric utilities move into the era of open competition and 

control of wheeling costs.

A complete understanding of capacitors and their effects on the power system

begins with understanding that capacitors are an unusual load with unusual

characteristics. Capacitors draw current that is advanced 90 degrees (or 1/240th

of a second) ahead in time of the applied voltage wave. This leading current

accomplishes several worthwhile purposes if applied with understanding and in

moderation. The main benefits are that the leading current cancels lagging 

current, which decreases kVAr losses and the voltage drop. Thus, capacitors

actually cause a system voltage rise.

To see how a capacitor affects a power system, look first at the sine-wave-shaped

instantaneous voltage wave generated by a rotating generator. Applied to a purely

resistive load, the current wave is “in-phase” with the voltage wave as shown in

Figure 3.

R

Current

Neutral

Voltage

-150

-100

-50

0

50

100

150

DEGREES

0 30 60 90 120 150 180 210 240 270 300 330 360

VOLTAGE CURRENT

PHASE RELATIONSHIPS

VOLTAGE and CURRENT MAGNITUDES
Bulletin 1724D-112

Page 12

Figure 3: Current in Phase with Voltage

“In phase” means that the current wave starts “positive” at exactly the same time

as does the voltage wave. The current wave also crosses the zero-amplitude axis

going the same direction (positive or negative) at exactly the same time as the

voltage wave and this action repeats itself at all zero-amplitude crossings. The

current wave is usually not the same magnitude (height at peak) as the voltage

wave but it does have the same frequency. The current magnitude is determined

by the load using Ohm’s Law, which, for resistive loads, follows the rise and fall

of the voltage wave exactly, and so current is called “in-phase” with the voltage.

Inductive loads, such as motors, cause the current wave to “slow down” with

respect to the voltage wave as shown in Figure 4. The degree of slowness in time

is measured as an electrical phase angle difference (assuming 360 degrees for one

cycle) between the voltage and current waves. The frequency of power systems

in the United States is 60 hertz (60 cycles per second), so one cycle represents

1/60th of a second. The voltage wave makes one complete revolution, completing

both a positive and negative cycle, during a period of time that is also defined as

360 electrical degrees. So 1⁄2 cycle, or the positive (or negative) half cycle for 

instance, takes 180 degrees. The time to rise from zero to a peak value is 1⁄4 cycle

or 90 degrees.

X

13.3 OHMS

CURRENT

NEUTRAL

7.2 kV

Voltage

L

-150

-100

-50

0

50

100

150

DEGREES

0 30 60 90 120 150 180 210 240 270 300 330 360

VOLTAGE CURRENT

PHASE RELATIONSHIPS

VOLTAGE and CURRENT MAGNITUDES

Figure 4: Current Lags the Voltage

The time to fall back to zero is another 1⁄4 cycle or a second 90 degrees. By 

describing time in terms of degrees, simple trigonometry can be used to solve 

relationships between the sinusoidal waves.

Likewise, capacitive loads cause the current wave to “get ahead” of or “lead” the

voltage wave in time as shown in Figure 5. A pure capacitor with no resistance

will cause the current wave to lead the voltage wave by exactly 90 degrees. A

pure inductance with no resistance will cause the current wave to lag the voltage
Bulletin 1724D-112

Page 13

wave by exactly 90 degrees. But in actuality, inductors have some resistance and 

a small amount of capacitance. Capacitors also have some resistance and a small 

amount of inductance. So a full 90 degrees of lead or lag never is actually 

achieved.

X

13.3 OHMS

CURRENT

NEUTRAL

7.2 kV

Voltage

C

-150

-100

-50

0

50

100

150

DEGREES

0 30 60 90 120 150 180 210 240 270 300 330 360

VOLTAGE CURRENT

PHASE RELATIONSHIPS

VOLTAGE and CURRENT MAGNITUDES

Figure 5: Current Leads the Voltage

Our goal on the power system is to cancel out as much of the effects of the line

inductance and capacitance as possible to allow the most efficient power transfer

from the source to the load. Motor loads and system conductors and service drop

wires are inductive, causing the current to “slow down” in time and lag the

voltage waves by 30–40 degrees.

Lead-lag phase angle can also be expressed by the system power factor. From the 

previous section, power factor has also been defined as the cosine of the phase

angle between the voltage and current waves.

(1) EXAMPLE 2. For an inductive phase angle of 30 degrees, the power

factor equals cosine (30 degrees) or 0.866 lagging (meaning inductive). 

This can be further expressed as power factor of 86.6% (0.866 × 100)

when expressed as a percentage of unity (100%) power factor. For a 40

degree lagging phase angle, the cosine (power factor) is 0.766 or 76.6% 

lagging.

The following table is provided for reference purposes.

Table 1: Trigonometric Power Factor Conversion Table

PHASE

ANGLE

TRIGONOMETRIC

COSINE

POWER

FACTOR

(Degrees) (%)

0.0 1.00 100.0

18.2 0.95 95.0

25.8 0.90 90.0
Bulletin 1724D-112

Page 14

31.8 0.85 85.0

36.9 0.80 80.0

41.4 0.75 75.0

45.6 0.70 70.0

49.5 0.65 65.0

The greater the phase angle between the voltage and current waves, the

poorer or lower the power factor (p.f.). Perfect power factor occurs when

the voltage and current waves are in phase with each other; perfect power 

factor is designated as 100% power factor or unity power factor.

Loads on a distribution power system are usually inductive, as are the

phase conductors and drop wires serving these loads. Capacitors are

added to compensate for the tendency of the inductance to “slow” the

current wave down with respect to the voltage wave. If sized properly,

most of the effects of the inductance can be nullified. Unfortunately, 

because of continuous load variation and available capacitor sizes, 

continuous optimization is not feasible.

d. Load Factor Effects on Power Factor

Typical billing demand data of rural systems show a steady downward trend in

average p.f. This decrease is almost directly proportional to the rising trend in

kWh used. The decrease can be attributed largely to the addition of industrialtype loads and increased usage of motors as residential consumers install more

and more inductive loads (larger freezers, heat pumps, etc.), which lower the

power factor and operate intermittently over a 24-hour period. On a daily basis,

the load distribution of these devices is comparatively uniform. The load factor of

the reactive component is much higher than the load factor of the real component

(that portion of load that is in phase with the voltage) because the real load

component fluctuates widely on a daily basis.

Peak kW Billing Hours

kWh

or

MaximumDemand

AverageDemand Load Factor

× =

Equation 3: Load Factor

Load Factor characteristics help to explain why VAr requirements are 

significantly greater during peak load times than off-peak. Motor driven devices 

that set the peak require additional VAr over the base load, which is more

resistive and less inductive.

Figures 6, 7, and 8 show relationships between load and power factor during 

peak/off-peak periods. Data is courtesy of East Central Oklahoma Electric

Cooperative, Inc., of Okmulgee, Oklahoma.
Bulletin 1724D-112

Page 15

Figure 6: Residential Load—Typical Peak Summer Load

Figure 6 illustrates typical kW and kilovar load curves. Notice that, while the kW

load almost doubles on this peak summer day, the kVAr requirement only

increases about one-third and remains constant, while the kVA rises from 90% to

100% of peak. Figure 6 indicates that, for a residential feeder on a peak airconditioning (a/c) summer day, any capacitors needed should be on-line from

2:00 to 10:00 p.m. on this southwestern U.S. system.

DAILY POWER RELATIONSHIPS - PEAK SUMMER DAY

SMALL COMMERCIAL & RURAL RESIDENTIAL (95% AIR CONDITIONING)

0

10

20

30

40

50

60

70

80

90

100

0:001:002:003:004:005:006:007:008:009:00

10:0011:0012:0013:0014:0015:0016:0017:0018:0019:0020:0021:0022:0023:00

TIME of DAY

PERCENT of DAILY kVA PEAK

kVA

kW

TOTAL kVAR

POWER FACTOR

TEMP

300 kVAR CAPACITOR

BANK

 SWITCHED ON

Figure 7: Effects of 300-kVAr Switched Capacitor Bank

Figure 7 shows how kVAr varies on a system as a 300-kVAr switched capacitor 

bank operates.

DAILY POWER RELATIONSHIPS - RESIDENTIAL FEEDER

PEAK SUMMER DAY WITH 95% AIR CONDITIONING

0

10

20

30

40

50

60

70

80

90

100

0:001:00

2:003:004:00

5:006:007:008:00

9:00

10:0011:0012:00

13:0014:0015:0016:00

17:0018:0019:0020:0021:0022:0023:00

TIME of DAY

PERCENT of DAILY KVA PEAK

kVA

kW

TOTAL kVAR

POWER FACTOR

TEMP
Bulletin 1724D-112

Page 16

Figure 8: Residential Power Off-Peak Day

Figure 8 shows the same circuit for an off-peak (spring or fall) day.

The real power load factor on rural systems often averages about 0.40, while the 

average reactive load factor is about 0.70. A fairly constant kVAr load factor

simplifies the problem of power factor correction. If the power factor of such a

system is corrected to near unity at light load, it will remain nearer unity at peak

load.

The flattening of the power factor curve at peak load in Figures 6 and 7 is not

intuitive, but understandable. As a/c loads come on the system early in the peak

day, when the ambient temperature is 20–30 degrees below the afternoon peak,

the a/c motors are not fully loaded and cycle off for extended periods of time. 

Their power factor approximates 80%. But, as the temperature rises and all a/c

units are on the system, they cycle off less and the motors become more fully

loaded. At peak temperature, with all a/c units fully loaded and with little 

cycling, their power factor improves to near 95%. This helps correct the circuit

power factor without additional capacitors.

e. Capacitor Sizing

Quick approximations of capacitor kVAr needed are fairly simple to make

because the p.f. angles of most uncorrected loads are around 30 degrees (a p.f. of

approximately 87%.). In a 30–60 degree right triangle, the side opposite the 30

degree angle is one-half the hypotenuse. As a “rule of thumb,” this means that the

reactive power (kVAr) is approximately half the apparent power (kVA) at 87% 

p.f. As discussed above, it is prudent to install less capacitor kVAr than one-half

the kVA because residential a/c load p.f. actually improves near-peak load.

DAILY POWER RELATIONSHIPS - RESIDENTIAL

OFF PEAK DAY

0

10

20

30

40

50

60

70

80

90

100

0:001:002:003:004:005:006:007:008:009:00

10:0011:0012:0013:0014:0015:0016:0017:0018:0019:0020:0021:0022:0023:00

TIME of DAY

PERCENT of DAILY KVA PEAK

kVA

kW

TOTAL kVAR

POWER FACTOR

TEMP
Bulletin 1724D-112

Page 17

Graphically, the base of the triangle is the real power (kW) side and is always in 

phase with the voltage. The hypotenuse (kVA) is in phase with the current. As 

the reactive power is reduced, the phase angle decreases and the current moves 

closer to being in phase with the voltage. This improves the power factor.

(1) EXAMPLE 3. For a load of 1,200 kVA at 87% p.f., about 600 kVAr of

reactive power is required. If we provide 600 kVAr of capacitors, the 

leading 600 kVAr added would cancel 600 kVAr of the system’s lagging 

inductive reactance.

θ

V

kVA

kVAr

 I

kW 

V = Voltage Reference I = Current

Figure 9: Power Triangle for Example 3

(2) EXAMPLE 4. For 1,200 kVA at 87% p.f., find kW and kVAr.

SOLUTION:

Power Factor (Phase) Angle = Arc Cosine (0.87) = 29.54 degrees = θ

(Arc Cosine 0.87 means the angle whose Cosine is 0.87)

kW = (1,200 kVA) × (0.87 p.f.) = 1,044 kW

kVAr = (1,200 kVA) × Sine (29.54 degrees) = 592 KVAr

Figure 10: Power Triangle for Example 4

The difference in the 600-kVAr “rule of thumb” sizing method and the

true answer of 592 kVAr is due to an 87% p.f. not being exactly equal to

θ

1,044 kW V

1,200 kVA

592 kVAr
Bulletin 1724D-112

Page 18

30 degrees. Considering that capacitors are available in 50-, 100-, 150- or 

200-kVAr sizes, the 8-kVAr difference is not a significant difference.

(3) EXAMPLE 5. When a 600-kVAr capacitor bank is added, the resulting

kVAr are:

Resulting kVAr = 592 – 600 = –8 kVAr

(New Power Factor = COS (ARC SIN (–8 ÷ 1,200)) = –0.9999

This new Power Factor is virtually 1.00, but the p.f. is slightly leading

because the negative sign means the correction was greater than needed.

592 

kVAr

V

1,044 kW

600 

kVAr

1,044.1 kVA

Figure 11: Power Triangle for Example 5

The 1,200 kVA system load has now been reduced to 1,044.1 kVA. The

current on a 7,200-volt system would be reduced from 56 to 48 Amps. 

The VAr needed to correct any existing power factor and demand can be 

calculated by first determining the existing VAr using the method detailed

in the solution related to Figure 10. Then, using the same demand and the

desired power factor, solve for the resulting VAr that should exist after the 

power factor correction is achieved. The difference in the two VAr values

is the maximum total VAr of capacitors to be added.

f. Voltage Improvement with Capacitors

In addition to improving the system power factor, capacitors also provide voltage

drop improvement. Because of a capacitor’s leading current, which flows through

the system’s lagging inductance, capacitors cause a voltage rise on the system. It

is not uncommon to experience a 2- to 3-volt rise (on a 120-volt base) with 300 

kVAr of capacitors on 7.2-kV systems. For the same kVAr amount of capacitors,

the rise would be half of that on a 14.4-kV system (twice the voltage, half the

current).
Bulletin 1724D-112

Page 19

Voltage rise is determined by multiplying the capacitor’s leading current by the

inductive reactance (XL) of the portion of the distribution system between the

distribution voltage source and the capacitor location. The resistive (R) portion of

the impedance involved causes a voltage drop in phase with the voltage and, thus,

does not play a role with the capacitor in creating voltage rise.

Voltage rise from the power source to the location of a shunt capacitor (or

anywhere on the line between the capacitor and the power source) is calculated as

follows:

Voltage Rise = Capacitor Current (Amps) ×

Conductor (System) Reactance (Ohms)

Equation 4: Capacitor Voltage Rise

where:

Capacitor Current = [kVAr (per phase)] ÷ [kV (line to neutral)]

Equation 5: Capacitor Current

and

Conductor Reactance = R +j X (system component impedance

 near capacitor’s location)

This voltage rise equation provides the total voltage rise from the generator to the

capacitor, but, since most of the impedance is on the distribution system, that is

where most of the rise occurs.

The calculated voltage rise is the actual rise on the primary system. To make it a

usable and understandable number, voltage rise should be referred to the delivery

voltage (120-volt) base. Calculated primary voltage rise is, thus, divided by the

primary line’s potential transformer ratio. This is the primary line-to-neutral

voltage divided by 120 volts (which is 60 for 7,200-volt systems and 120 for 14.4-

kV systems).

(1) EXAMPLE 6. Find the voltage rise caused by a three-phase, 300-kVAr

capacitor station located on a 12.47/7.2-kV feeder whose impedance at the

node point nearest the capacitor station is:

Z = R +j X ohms = 13.4 +j 13.3 ohms (See Figure 12)
Bulletin 1724D-112

Page 20

R = 13.4 OHMS

XL =13.3 OHMS

CURRENT

NEUTRAL

V = 7.2 kV

100 kVAR / φ

XC

Figure 12: Voltage Rise from 300 kVAr of Capacitors

SOLUTION: Capacitor current calculations use capacitor kVAr per phase

divided by line-to-neutral voltage.

Amperes kVAr CapacitorCurrent 13.9

7.2

100

(3) (7.2kV)

300 =



 



 =















× =

(Note: Each 100-kVAr capacitor draws 13.9 Amps on a 7.2-kV system.)

Voltage Rise = (13.9 Amps) × (13.3 ohms) = 184.7 volts (7.2-kV base)

Referred to the delivery base voltage or 120-volt base, divide true volt rise

on the primary by the transformer ratio.

7.2 kV ÷ 120 V = 60 (60:1 ratio)

Voltage Rise on a 120-volt base then = 184.7 ÷ 60 = 3.08 volt rise

This means that the leading 13.9 Amperes per phase capacitor current

flowing through the 13.3 ohms of reactive system impedance causes the

voltage to rise from the distribution voltage source to the capacitor. This

results in a 3.08-volt rise at the capacitor location and beyond the 

capacitor.

Adding a second 100-kVAr capacitor per phase will double the voltage

rise to 6.16 volts on each phase.

This voltage rise starts at near zero at the source and uniformly rises to a

peak of 3.08 volts at the capacitor location. The capacitor voltage rise can

be calculated at any point between the distribution voltage source and the

capacitor (the line section along which the capacitor’s current flows) by

the same method as above. The voltage rise caused by the capacitor levels

out at the capacitor location (the capacitor current has reached its load), 

but the 3-volt rise is seen over the entire system past the capacitor.
Bulletin 1724D-112

Page 21

The percent voltage improvement due to a shunt-connected capacitor

installation, at the capacitor location, is calculated as follows:

100

VoltageBase

VoltageRise %VoltageRise ×















=

Equation 6: Capacitor Percent Voltage Rise

In the above case:

100 2.57%

120

3.08 % × = 

 



 Voltage Rise=

The textbook solution is:

2 10(kV)

(ckVAR) (X) (d) %VoltageRise × × =

Equation 7: Percent Voltage Rise Any Point from Source to Capacitor

Where:

d = length of line, circuit-miles (from distribution voltage 

source to capacitors)

ckVAr = total capacitor kVAr (1φ and 3φ lines, delta-connected

capacitors), or

= 1/2 total capacitor kVAr (Vφ lines), or

= 1/3 total capacitor kVAr (3φ lines, Y-connected capacitors)

X = reactance, ohms per circuit-mile (1φ and 3φ lines), or

= 1/2 single-phase reactance, ohms per circuit-mile (Vφ lines)

kV = line-to-ground kilovolts (1φ and Vφ lines, and 3φ,

Y-connected capacitors), or

= line-to-line kilovolts (3φ, Delta-connected capacitors)

In Example 6, note the closeness of the resistive (13.4 Ω) and the reactive 

impedance (13.3 Ω). This closeness is typical of conductor that has a 

resistance fairly equal to its reactance (1/0 through 4/0 ACSR). Smaller 

conductors have lower X/R ratios. Larger conductors have higher X/R 

ratios. Resistance decreases much faster than reactance as conductor size

gets larger. Reactance is a function of conductor spacing.
Bulletin 1724D-112

Page 22

Table 2: Conductor Impedance

CONDUCTOR IMPEDANCE

ACSR - Ohms per Mile Using

8-foot Crossarm Spacing

% VOLTAGE RISE per

Mile on 120-volt Base

with 100 kVAr per Phase

ACSR

Conductor Size

Line-to-Neutral Voltage

Resistance (R) Reactance (X) 7,200 14,400

4 2.47 0.655 0.126 0.0631

2 1.41 0.642 0.123 0.0619

1/0 0.888 0.656 0.126 0.0632

4/0 0.445 0.581 0.112 0.0560

267 kcmil 0.350 0.465 0.0896 0.0448

477 kcmil 0.196 0.430 0.0829 0.0414

Impedance Source: Westinghouse Electrical Engineering Reference Book—Distribution Systems

System operators should take advantage of the voltage rise associated with

capacitors to help offset normal system voltage drop. However, caution

should be exercised to prevent over application of capacitors for the

purpose of raising voltage because the current drawn by capacitors can

increase line losses, especially if capacitors drive the system into a leading

power factor.

Capacitors can be an inexpensive short-term fix for a voltage problem, but

capacitors can significantly increase line losses and probability of

harmonic influence (interference) on nearby telecommunications lines.

In addition to using capacitors to simply offset normal system voltage 

drop, capacitors can be an integral part of a Conservation Voltage 

reduction (CVR) program.

(2) CVR Considerations with Existing Capacitive Support

Many cooperative are looking at options at saving members energy; CVR 

always comes up as a potential topic. This is typically accomplished via a

load tap changer (LTC) or through voltage regulators. To maximize the 

benefit received from CVR, feeder voltage profiles should be flattened to 

the extent possible. This allows the greatest level of voltage reduction to 

be obtained along the entire feeder length, and capacitors can play a 

significant role in accomplishing this. Study is required to determine the 

proper amount of capacitance, location, and switching parameters.

It is particularly important when using CVR for peak demand reduction to 

ensure the capacitors will quickly switch in as needed during a CVR event 

and then quickly switch out once the CVR event is over. In some cases, it 

may prove beneficial to actually allow the power factor to go slightly 
Bulletin 1724D-112

Page 23

leading during a CVR event to lower peak demand, as long as the duration 

of the event is relatively short.

Capacitors are placed on a distribution system for a variety of reasons:

• Power Factor Correction

• Voltage Support

• Easing of Capacity Constraints

When employing a CVR scheme, special consideration should be given to 

the purpose of the existing capacitor and how it is currently being 

switched. Capacitor banks can be switched using a variety of different 

triggers:

• Voltage

• kVAr

• Current

• Temperature

• Time

Each capacitor bank location should be analyzed based upon its location 

on the distribution system, as well as its impact on the voltage profile of 

the system during a CVR event. Adjustments to the capacitor switching 

scheme may need to be made; for example, a capacitor bank switching on 

voltage may need to have supervised switching to limit the voltage rise 

during a CVR event.

A capacitor bank close to the substation may not need to be adjusted, 

while a bank placed out on the distribution line may require changes to the 

switching scheme. The preferred location of a capacitor bank may need to 

be a hybrid style that isn’t quite optimal for power factor correction or 

other engineering reasons, but rather provides a compromise between 

CVR and the original purpose of the capacitor bank.

3 CAPACITOR CONCERNS

a. Overcurrent and Overvoltage Protection

Lightning surges may cause damage to capacitors. Capacitor units connected

line-to-neutral on a multigrounded neutral system provide a low-impedance path

for lightning surges. This low-impedance characteristic makes capacitors

susceptible to lightning surge events. Lightning strikes have damaged capacitor

bushings as a result of severe instances of flashover. However, the more probable

lightning damage to capacitors is the breakdown of the insulation between the 

capacitor’s internal elements and the capacitor case.
Bulletin 1724D-112

Page 24

A capacitor attempts to maintain constant voltage across its terminals and, if the 

voltage begins to change, the capacitor conducts charging current through itself of 

sufficient amplitude to keep the voltage constant. When lightning strikes a 

capacitor, the surge impresses a very high voltage across the capacitor. The

capacitor then, in an attempt to maintain the impressed voltage, charges to the

surge voltage magnitude by passing enormous charging current. This action can

cause the unit to fail from the internal heat generated by the large charging

current.

Capacitor failure is usually indicated by a severely bulging tank case, ruptured

tank case, other catastrophic physical evidence, or no visible physical evidence on

the capacitor but by simple observation that the fuse protecting the capacitor has

blown. Slight bulging or blooming of a capacitor tank is not necessarily

indicative of capacitor failure because capacitors can withstand considerable 

overcurrent conditions.

Capacitors should conform to the IEEE Standard for Shunt Power Capacitors

(Std. 18-1992). This standard expects a capacitor to provide continuous

operation, provided that none of the following limitations are exceeded:

(1) 135% of nameplate kVAr,

(2) 110% of rated root mean square (rms) voltage and crest voltage not exceeding

2.83 times the rated root mean square voltage (including harmonics but not

transients), and

(3) 180% of rated root mean square current (including fundamental and 

harmonics).

Capacitors suspected of being damaged should be tested using a commercially

available capacitor checker. Testing could also be conducted by using an audio

oscillator, a voltmeter, a resistor, and an inductor of known inductance. The

resistor would be wired in series with the parallel connection of the capacitor and

inductor and the circuit energized with the audio oscillator across this series

parallel connected circuit. The voltmeter would be connected to measure the

voltage across the capacitor or inductor and the frequency of the oscillator

adjusted for a minimum voltage reading. At this frequency, the capacitor and

inductor should be in resonance, where the inductive reactance should equal the

capacitive reactance.

The inductive reactance of the inductor can be calculated by multiplying the

known inductance value by the measured frequency and multiplying this value by

2π. The capacitance should be equal to 1 divided by the product of the calculated

inductance multiplied by 2 times π times the resonant frequency. This calculated

capacitance should be within the rated tolerances of the shunt capacitor’s

capacitance which is calculated according to the following formula.

Capacitance of a power shunt capacitor is equal to:
Bulletin 1724D-112

Page 25

2 2

1000

f V

kVAr C

× ×

× = π

Equation 8: Capacitance

Where:

C = capacitance in microfarads (μF)

kVAr is the capacitor’s rated kVAr

f = rated frequency of capacitor (60 Hz)

V = rated voltage of the capacitor in volts

For example, plugging rated values for a 50-kVAr, 7,200-volt capacitor into the

equation results in a capacitance of 2.56 μF.

If the capacitance calculated from the test varies significantly from the rated

capacitance calculation, then the capacitor should be retired.

Power circuits can remain in operation with part or all of a capacitor bank out of

service. But the portion of a capacitor bank that is not in service does not provide

either voltage improvement (rise) or power factor correction. Wide voltage

variations can occur on multiphase systems that experience the loss of one or

more—but not all—installed capacitors of a capacitor bank. Loss of some—but

not all—capacitors on a multiphase line can also cause shifting of phase angles,

leading to system unbalance.

Shifting phase angles away from the normal 120 degrees causes many problems

on a three-phase power system, such as motor growling, motor overheating,

difficulties in starting loaded three-phase motors, and blowing or tripping of

motor protection devices. Thus, single- or unbalanced-phase capacitor use should

be avoided. When one phase of a three-phase capacitor bank is out of service, the

whole bank should be taken out of service.

In the event of capacitor failure, it is desirable to isolate the failure from the

power system and minimize the damage, with no interruption in service. The 

emphasis, therefore, is upon protection of the circuit instead of the capacitor. 

However, if the capacitor unit contains polychlorinated biphenyls (PCBs), extra

care is required to clear the failed unit before tank rupture and an expensive

cleanup of the affected area as is required by the Environmental Protection

Agency (EPA). System operators would be prudent to remove all PCB capacitors 

from use and properly dispose of them in accordance with EPA regulations (40

CFR Part 761—Polychlorinated Biphenyls (PCBs) Manufacturing, Processing,

Distribution in Commerce, and Use Prohibitions). Capacitors manufactured since

1978 should not contain PCBs and do not have the same health and disposal

concerns as capacitors with PCBs.
Bulletin 1724D-112

Page 26

PCBs proved to be an excellent dielectric material for use in capacitors. 

However, scientific studies conducted raised concerns that PCBs may present a

health hazard to humans, and PCBs were subsequently banned for use in the 

manufacture of capacitors and many other products. Except within the vicinity of 

animal feedlots and grain harvesting facilities, PCB-containing products were 

allowed to remain in use, but EPA issued regulations on the use of such products.

EPA promulgated these PCB product use regulations because PCBs will not

readily decompose or break down and can be expected to retain their chemical

composition for many years. These regulations include the proper method of

disposal of products containing PCBs and PCB waste materials. EPA requires 

that certain PCB-containing products (which includes capacitors) be properly

contained and sent to a suitable toxic disposal facility. The location of the nearest

facility can be obtained by contacting the capacitor manufacturer or the regional

EPA office.

Capacitors need to be provided with lightning arresters and proper fusing or

short-circuit protection for reasons other than lightning. This protection is also

needed to prevent capacitors from being damaged by transient over voltages

caused by switching operations, arcing grounds, accidental conductor contact with

higher voltages, disturbances caused by other arresters, and resonance or near

resonance caused by motors while starting. Protection is best provided with

maxi-block silicone carbide or metal oxide varistor (MOV) lightning arresters. 

Connections to and from the arresters and capacitors and the arrester grounding

provisions should be made using the shortest leads practical, attempting to keep

the leads as straight as possible. A capacitor should also be provided with a fuse

or short-circuit protection that is designed to function under 135% of the 

capacitor’s nameplate current rating. Fusing guidelines are included in Section 4i

of this bulletin.

b. Harmonics

Capacitors act as a path to ground for the harmonic currents of a power system’s

60-Hertz (Hz) power wave. The impedance offered by a capacitor is calculated

using the following formula:

















= f CXc 2π

1

Equation 9: Capacitor Impedance

Where:

Xc = Capacitive reactance

π = 3.1416

f = Frequency (60 Hz for U.S. power systems)

C = Capacitance in Microfarads
Bulletin 1724D-112

Page 27

As can be seen from the formula, a capacitor’s impedance decreases as the

frequency increases. Thus, higher order harmonic currents, or currents at multiple

frequencies of the power system fundamental 60-Hz wave, can flow through a

capacitor easily.

Nonlinear loads such as transformers (especially transformers with poor-quality

cores) generate harmonics. The magnitude and number of harmonics generated

by a transformer is directly related to the magnitude of the voltage used to

energize the transformer. The higher the energizing voltage, especially as the

energizing voltage exceeds the transformer’s nameplate rating, the higher the

magnitude and numbers of harmonics generated by the transformer.

Harmonic currents travel down the lines looking for a low impedance path to

ground. Underground primary power cables are predominately capacitive and

also provide this path. Any odd-numbered triple (180, 540, 900-Hz, etc.) of the

fundamental 60-Hz voltage wave is likely to cause problems, because all three

phases of the odd-numbered triple harmonics are in phase with one another on a

3-phase system and, thus, add up rather than cancel one another where they flow

to ground. This can cause overheating in power equipment and neutral 

conductors. The 9th harmonic, a triple harmonic, can have the greatest effect on 

capacitors because it is a common transformer-generated harmonic and capacitors

offer low impedance at 540 Hz.

With a path to ground, harmonic currents can flow along the phase conductors

and neutral conductors of a power line and can induce currents in parallel

telecommunications cables. If high enough in magnitude, induced harmonic

currents can render a telecommunications system unusable. The power system

operator must design electric facilities to minimize the possibility for harmonic

induction. The primary frequency spectrum for wire-line telecommunications

systems is from 40 Hz to 3,000 Hz. But the frequencies from 100 to 2,500 Hz are

the most critical to causing objectionable harmonic interference. These same

frequencies are within the range of typical harmonics generated on a power

system. Capacitors can exacerbate normal power line harmonic current flow by

providing them a lower impedance path, thus causing their magnitudes to be

higher than they otherwise would be without capacitors connected. In worst-case 

situations, capacitors can also create resonant conditions on the power system that

can cause extremely high magnitudes of harmonic current and voltage that can

severely affect telecommunications operation.

Methods to alleviate harmonic problems associated with capacitors are discussed

below, but you first have to know the issue exists. Placement of capacitor banks 

in areas where higher levels of harmonics are known to exist should prompt 

further investigation before installation. It’s better to avoid potential harmonic 

interference through initial design efforts than be forced to solve a problem once 

equipment is in place.
Bulletin 1724D-112

Page 28

(1) Change Capacitor Location

Telecommunications noise problems created by capacitors can often be

remedied by moving the capacitors to a new location. The ideal objective 

is to move the capacitor bank toward the substation to a location where the

power conductors between the capacitor bank and the substation do not

parallel any telecommunications circuits. Remedial success is high when

the offending capacitors have caused a resonant condition on the power

line and the two utilities parallel one another for a significant distance.

Resonant conditions usually occur at a single frequency, often an odd

multiple of 60 Hz, such as 300, 540, 900 Hz, etc. At the resonant 

frequency, the power circuit’s inductive reactance (between the capacitor

bank and the substation serving the bank) equals the power circuit’s

capacitive reactance. With the circuit impedance so drastically reduced to

only a small resistive component, an abnormally high magnitude of

current can flow at the resonant frequency, significantly improving the

chances for induction and resulting in objectionable harmonic noise in

neighboring telecommunications circuits. At the resonant frequency,

voltage on the power circuit can also become high and could lead to

damage of connected power line equipment and/or system operating

problems.

Moving the capacitor toward the distribution voltage source helps improve

a noise situation in two ways. First, changing the capacitor bank location

can detune the resonance which, by itself, can help to reduce the noise. 

Moving the bank so there is limited parallel exposure of the two utilities’

circuits between the capacitor location and the substation minimizes

possible induction of harmonics into the telecommunications circuits and

adds to the improvement.

Moving a capacitor bank is not necessarily a permanent solution. Noise

problems could arise again as circuit loading and balance changes with

time, possibly creating resonant conditions at different harmonics. In

addition, future utility construction could result in new longer stretches of

parallel exposure between the utilities and cause renewed noise problems. 

Joint utility planning and coordination can help to avoid such problems.

(2) Change Capacitor Size

Adding capacitors at a capacitor bank suspected of causing a resonant

condition can sometimes change the circuit capacitance enough to cancel

the resonance and help alleviate a noise problem. Such a solution,

however, needs to be addressed carefully to be certain that resonance is

not moved to another critical power line harmonic frequency, resulting in

continued or worsened telecommunications noise. Care is also needed to
Bulletin 1724D-112

Page 29

be certain the added capacitance does not cause the power circuit to have

an objectionable leading power factor.

Because of the reduced power/telecommunications circuit exposure,

moving capacitors as discussed in Section 3b (1) of this bulletin can be

more effective in alleviating noise problems than adding capacitance.

For the same reason as noted in Section 3b (1), load growth, new utility 

construction, etc., can upset any success attained in adding capacitance to

a capacitor bank to reduce a noise problem. Again, proper planning,

design, and coordination with all neighboring utilities is extremely useful

in minimizing problems.

(3) Harmonic Filters

Another noise-reducing remedy involves blocking the harmonic ground

path by inserting a tuned filter (specifically manufactured for the purpose)

in the capacitor ground connection. This filter would take the place of the

grounding switch shown in Figure 13. The filter is a harmonic saturable

reactor which, during installation, is experimentally tuned so that, at the 

offending harmonic frequency, it acts as a high impedance, preventing

current at that frequency from flowing on the power line. At 60 Hz, the

filter provides a low-impedance connection to ground, helping to maintain

system grounding integrity.

A filter installation may need to be retuned as the loads and electric

system change. At some point, the electric system could change to such

an extent that the tuning needed for effective noise alleviation may be

outside the range of the filter’s core size as installed and a new filter may

be necessary.

Because the ground wire is hidden in a standard saturable filter 

installation, use of the filter is not acceptable to some utilities.

(4) Ungrounded Capacitor Banks

Another noise-reducing remedy involves blocking the harmonic ground

path by floating the wye point on the capacitor bank and denying

harmonic current a path to ground. However, because of the safety 

concerns, utility systems should consider this solution only as a last 

resort. While the neutral is floated, the ungrounded capacitor cases can

become energized to primary-line voltage levels and present a hazard to

line crews who work on them.

If no other remedial effort is feasible and this solution is determined to be

necessary, then special operating procedures should be implemented and

strictly observed. For safety reasons, to assure the capacitor cases and the

power system neutral are effectively grounded temporarily, the floating
Bulletin 1724D-112

Page 30

wye should be grounded, usually with a solid switch (solid blade cutout). 

This grounding switch would be used during manual switching or repairs

on the capacitor bank or the power system within the vicinity of the

capacitor bank. For normal operation, after the capacitors are energized,

the grounding switch is open and the wye-point of the capacitor bank is 

placed in the ungrounded mode.

It is recommended that a sign be added to the pole for electric line crews 

such as:

WARNING!

UNGROUNDED WYE CAPACITORS

GROUNDING SWITCH

CLOSE GROUNDING SWITCH BEFORE OPERATING

LEAVE SWITCH OPEN WHEN FINISHED

Map records should also show locations of nonstandard capacitor

connections.

c. Switching Transients2

A capacitor is an energy-storage device whose voltage cannot change 

instantaneously. As such, the energization of a capacitor bank results in an 

immediate drop in system voltage toward zero, followed by an oscillating 

transient voltage on the 60-Hz system voltage waveform (as shown in Figure 14), 

which will decay over time as the system recovers and returns to steady-state. 

The initial rebound will overshoot the system voltage by a magnitude equal to the 

 2 Capacitor Switching Transients: A Best Practices Guide. TVPPA R&D Project CS–1, 2011.

Phase A

Phase B

Phase C

Figure 13: Ungrounded Capacitor Bank
Bulletin 1724D-112

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difference between the system voltage and the capacitor voltage at the instant of 

energization. Or, put simply: for every volt the system is pulled below its normal 

level, the overshoot will be one volt above normal. The most severe transient, 

then, will occur when an uncharged capacitor is switched on at a system voltage 

peak, leading to a theoretical peak voltage of 2.0 per unit, or twice the nominal 

system value.

Figure 14: Typical Distribution Capacitor Switching

In practice, capacitor switching transients generally do not reach the theoretical 

maximum magnitude; system losses, loads, and other capacitances will tend to 

damp the excess voltage. Figure 16 shows the feeder voltage transient for the 

simplified model of Figure 15 when the 150-kVAr bank is switched on. Typical 

transient magnitudes fall in the 1.3 to 1.5 per-unit range, with frequencies ranging 

from 300–1,000 Hz (medium- to high-frequency), though there are special cases 

in which these levels could be exceeded. These special cases can result in varying 

degrees of risk to components of the distribution system.

V BCT

Y

V I V I

150 kVAR 600 kVAR

12.47kV Feeder

Feeder Load:

2500 kVA at 80%

power factor

69kV Source
Bulletin 1724D-112

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Figure 15: Simplified Distribution Feeder Model

Figure 16: 150-kVAr Bank Switching; 600-kVAr Bank Off

(1) Back-to-Back Capacitor Switching

“Back-to-back” switching is a term used to describe the energization of a 

shunt capacitor bank when another is already in operation on the 

distribution system. This type of event produces high-frequency, highmagnitude transient currents that flow between the capacitor banks.

The frequency and current level of the transient produced by a back-toback switching event is dependent on a number of factors and generally 

lasts only a fraction of a cycle, but can potentially reach peaks greater than 

2.0 per unit (pu) between the banks. Figure 17 shows the transient 

currents and voltage levels between the capacitor banks in Figure 15 when 

the 600-kVAr bank is energized with the 150-kVAr bank already in 

service.
Bulletin 1724D-112

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Figure 17: Transient Effects of Back-to-Back Switching Event

(2) Capacitor Bank Restrikes

A capacitor switching device must possess sufficient strength to withstand 

the voltage levels across its terminals during a switching event. Capacitor 

banks are de-energized at current zeroes, which correspond to system

voltage peaks; a switch for a grounded-wye-connected bank will be 

subjected to 2.0 volts pu a half-cycle after it interrupts the capacitor 

current.

If the switch cannot withstand this level of potential and restrikes at twice 

the system voltage, a transient voltage magnitude of 3.0 pu can occur. A 

switch on an ungrounded-wye capacitor bank may be subjected to voltages 

greater than 2.0 pu after a de-energization; it is possible, when delays 

occur between the attempted openings of the phases of a switch, to

develop a transient voltage of more than 6.0 volts pu (six times the system 

voltage) during a restrike event.

(3) Capacitor Switching Transients at Consumer Facilities

Because utility distribution systems operate at high voltage and utilize 

equipment that has substantial momentary current withstand capability, 

they are (for the most part) not threatened with damage or failure by 

typical switching transients. Equipment at the utilization level, however, 

tends to utilize sensitive (and sometimes highly frequencydependent)electronic devices at low-voltage levels, meaning that even a 

small overvoltage can, at best, be a severe nuisance and, at worst, cause 

damage or failure.
Bulletin 1724D-112

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The severity of a transient on both the utility and consumer sides of the 

system is dependent on a number of factors, familiarity with which will be 

important when determining expected magnitudes and mitigation 

strategies. The VAr ratings of the capacitor banks in question are 

certainly of great importance. The bank’s configuration whether it is 

connected as a “delta” or “wye” bank plays a role as well.

Of further importance is certain information about the distribution lines on 

which the capacitor bank (or banks) is connected, namely: the distribution 

line impedance and the various lengths of line involved (from the 

substation to the capacitor bank and from the capacitor bank to any 

additional downline banks). The positive sequence and zero sequence

impedance values are of primary concern when predicting transients. 

These factors will all contribute to the severity of transients on the 

consumer system as well as the distribution system. A few other factors 

are in play, however, in certain situations on the consumer side of the 

system.

During a distribution capacitor switching event, typical transient voltages 

produced on consumer systems range from 1.2 to 1.4 pu volts. These 

transient voltages can be magnified, however, if the consumer has 

installed low-voltage capacitors for power factor correction, or by certain 

step-down transformer sizes.

Low-voltage capacitor banks are typically used by commercial and 

industrial facilities to improve the power factor as monitored by their 

electric utility to lower or avoid power factor penalty charges; because 

these consumers tend to have motor loads that draw the reactive power in 

the first place, they also tend to have devices (adjustable-speed drives and 

other process equipment) that use the power electronics components that 

are most sensitive to over voltages. Vulnerability is not limited to these 

devices, of course; computer networks and other electronic devices can be 

damaged or fail due to large over voltages.

In addition to the individual capacitor bank sizes, the relationship between 

the sizes of a distribution bank and a consumer’s power factor-correction 

bank will affect the low-voltage transient level; if the distribution 

capacitor bank is significantly larger (ten times larger or more) than the 

consumer bank, transient voltage magnification is more likely. 

Additionally, the relationship between the energizing frequency of the 

distribution bank and the resonant frequency of the consumer system 

affect the transient magnification. These frequencies are dependent upon 
Bulletin 1724D-112

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the sizes of the capacitor banks and the transformers, the system voltage, 

and the short-circuit power available from the transmission source.

A typical distribution feeder model, down to the consumer level, is shown 

in Figure 18. This is a more detailed feeder model than the one used 

previously, as it places the various connected loads at appropriate points to 

more accurately reflect the behavior of the distribution system and 

represents an actual distribution feeder. The model includes a 600-kVAr

switched capacitor bank on the distribution level and a 60-kVAr fixed 

power factor-correction bank on the consumer level, both connected in a 

grounded-wye configuration. The substation transformer is delta 

(primary)/grounded-wye (secondary), the distribution transformer is 

grounded-wye/grounded-wye, and the line and source impedances are 

modeled based on actual feeder values.

Figure 18: Distribution Feeder Model with Consumer Facility

The transients created on the consumer and utility voltages by the 

switching of the distribution capacitor bank are shown in Figure 19. The 

presence of actual source and load models and conductor impedances has 

the effect of significantly damping the distribution system transient, as is 

seen in the figure. The consumer-level transient, however, is highfrequency and much more severe, exceeding 2.3 pu volts (1,100 V) on the 

A-B phase.

It should be noted here that the kVAr values, transformer properties, and 

transmission source values were not chosen to maximize the transient 

magnification; with the exception of the consumer capacitor bank, every 

quantity in this model is based on a real distribution feeder. Furthermore, 

the size of the consumer bank was chosen not because of its relationship to 

the distribution bank, but because it is a realistic value that would improve 

the facility’s power factor from 84% to 97% (likely reducing the penalty 

charges incurred by the consumer).
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This simulation clearly illustrates the potential consequences of installing 

capacitor equipment without regard to distribution system conditions; the 

level of overvoltage produced by the operation of the utility capacitor 

switch would almost certainly be disastrous for the consumer. Adjustablespeed drive overvoltage protection will typically trip at values as low as 

1.2 pu, meaning that a transient voltage at 2.3 pu would likely cause 

facility-wide process equipment shutdown. An overvoltage of this 

magnitude could also potentially damage any low-energy surge arresters 

or transient suppression equipment in use.

If surge protection equipment is not in use or fails to damp or eliminate the 

transient on the 120-Volt (V) system (allowing a transient voltage of 

nearly 280 V if phase A is used for 120-V service), severe computer 

damage and failure can occur quickly. At the 120-V level, even small 

overvoltages can cause computer issues such as memory alteration and 

data loss. Voltage surges can decrease the life spans of fluorescent bulbs 

and ballasts as well.

Figure 19: 600-kVAr Switching Transients at Consumer and Utility 

Level
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d. Transient Mitigation Strategies

(1) Sizing Capacitor Banks and Detuning Circuits

In certain situations where transients are being magnified at low voltage, 

simply changing one or more circuit parameters can sometimes help to 

reduce the overvoltage. Changing capacitor bank sizes, moving banks or 

removing them from service, or even choosing alternate step-down 

transformer sizes can decrease the severity of transient voltages. This is 

generally a viable option at both the distribution level and the consumer 

level. Transient prediction tools can also prevent transients from 

becoming a problem at all if used by utilities or consumers before 

installing capacitor banks.

(2) Sophisticated Switching Controls

Some capacitor bank control devices are equipped with “zero-crossing” or 

“synchronous closing” capability, which allows them to close in each 

phase of a capacitor bank at or near a voltage zero in order to minimize the 

resulting transient. Figure 20 shows the voltage waveforms for the same 

model shown in Figure 18, but with the capacitor phases switched 

independently at zero crossings. While the transient on the 480-V level is 

not completely eliminated (even the most sophisticated switching controls 

are subject to errors of a fraction of a millisecond, and may not close at a 

perfect zero), the overvoltage is now less than 1.05 pu, appearing as 

merely a blip on the waveform; the feeder voltage experiences no transient 

effects at all.

Many capacitor controls also possess the ability to switch large bank 

installations in smaller sections; these are often called multistep 

installations. This type of control can also reduce the possibility of 

transient voltage magnification, as it will tend to detune the circuit by 

changing the capacitor energization frequency (by connecting smaller 

kVAr quantities into the system separately).

These types of capacitor controls are among the most effective methods of 

eliminating switching transients at the utility level.
Bulletin 1724D-112

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Figure 20: Capacitor Switching with Zero-Crossing Control

(3) Preinsertion Resistors

The installation of a fixed resistance in series with a switched capacitor 

bank will reduce the transient voltages and currents associated with the 

bank’s energization. In order to minimize system losses, this resistance 

must be bypassed by short-circuit and then disconnected once the 

switching transient dissipates. Closing of the switch to create the bypass 

will produce a second transient event, but one that is not disruptive to 

system operation. The most ideal resistance value for a given installation 

is dependent upon the capacitance of the bank and the strength of the 

source. Figure 21 shows a preinsertion resistor configuration.
Bulletin 1724D-112

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Figure 21: Preinsertion Resistor Configuration

(4) Series Inductors

Series inductances introduced at various locations in the circuit can have a 

number of transient-reduction effects, depending on their size and use.

(a) Fixed Inductors on the Distribution Bank. Fixed inductors (also 

called reactors) installed in series with a distribution capacitor 

bank are capable of reducing transient current surges associated 

with capacitor switching. This strategy is particularly effective at 

reducing inrush currents caused by back-to-back switching, but 

does not generally provide transient voltage reduction.

(b) Chokes. Inductors can be used as “chokes,” in series with 

adjustable-speed drives, to effectively “isolate” individual drives 

from transients. This is an effective method at consumer facilities 

for eliminating nuisance tripping of these sensitive devices.

(c) Harmonic Filters. Adding inductors in series with a low-voltage,

power factor-correction capacitor bank will convert the bank into a 

harmonic filter, which can decrease the transients on the consumer 

bus to acceptable levels. The bank will continue to provide power 

factor correction while also acting to control harmonic distortion 

levels within the facility and mitigate transient concerns.

(5) Surge Arresters

Low-voltage, high-energy surge arresters can be used at consumer 

facilities to limit overvoltages to acceptable levels. The use of highenergy MOVs (metal-oxide varistors) is critical in transient-limiting 

applications, as the possibility of voltage magnification at low-voltage 
Bulletin 1724D-112

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terminals leads to the possibility of very high-energy transients. The small 

MOVs normally found in transient voltage surge suppression equipment 

and power electronics are not generally robust enough to withstand a 

magnified transient.

4. CAPACITOR SIZING, LOCATION, AND USE

a Light Load Conditions

The amount of capacitor kVAr needed at minimum load should be permanently

connected/fixed (unswitched) to the power system. Fixed capacitor banks should

be installed on the system in amounts not exceeding the minimum kVAr demand,

without causing leading power factor under light conditions on the respective

feeders.

Experience shows that the minimum load is wholly dependent on the type of

loads being served. Industrial loads may be fairly uniform all day and all year. 

However, most loads are cyclical in nature and most peaks are weather-driven

(either extreme hot or cold). Minimum loads for residential and small

commercial loads may vary from 25% to 50% of peak. A utility system’s demand

on the monthly power bill does not normally show the minimum load. The

demand shown on a bill for an off-peak month is still the maximum demand for

that month, not minimum demand. Selecting capacitor locations for the lightest

load thus requires determining the expected minimum load from the lowest peak

month’s historical load data.

Capacitor or kVAr needs may also be determined by tracking minimummaximum load readings from a feeder’s bus-by-bus metering records or from

Supervisory Control and Data Acquisition (SCADA) loading data. The preferred

methods would be in the following order of priority:

(1) SCADA system with archived load and kW/kVAr data (this may be memory

intensive),

(2) Permanently connected meter readings of amps, kW, and kVAr or power

factor, or

(3) Temporarily connected metering at buses during light-load periods to measure

amperes and power factor.

b. Peak Load Conditions

The capacitor selection discussed so far has dealt only with applications to correct

power factor at minimum load. In order to correct power factor during heavier

loading periods, it is necessary to use switched capacitors. Switching of

capacitors may be done manually. However, automatic controls soon become

cost-effective because of the personnel time spent manually switching and

because of the additional line losses incurred if it is not done in a timely manner.
Bulletin 1724D-112

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Automatic controls can track various parameters and switch the capacitor banks

as needed to optimize the system p.f. The additional capacitors should be

switched either as an entire bank or in steps in order to keep the p.f. from

becoming significantly leading at any time. In addition, proper switching

prevents both overvoltage and undesirable voltage flicker and helps the capacitors

perform the task they were installed to do.

Voltage spikes or surges occur when switching capacitors because the switch

usually closes when the system voltage is not at a zero-voltage crossing point. 

Non-zero current switching causes a capacitor to abruptly charge to the system

voltage and generally creates wide-ranging overswings. This transient will take

several cycles to decay and can affect industrial loads with computer-based

controls. However, there are switches available now that switch only at the next 

zero crossing to minimize switching transients.

Capacitor bank size and location should be selected and designed in a manner that

limits voltage change to 3 volts (on a 120-volt base) to eliminate customer

complaints. For situations where limited switching is expected, customers on

long, lightly loaded feeders may accept up to a 6-volt change.

Since switched capacitors are generally installed to supplement unswitched

capacitors, they are located in the same manner as unswitched units. Results of

computer load-flow studies should be used to determine the optimum sizes and

locations for capacitors. Fixed capacitor installations should be designed to

appropriately accommodate the system’s inductive reactance expected during

minimum loading. The augmenting switched capacitor installations need to be

designed to appropriately accommodate the system’s inductive reactance expected 

during peak-loading periods.

In lieu of load-flow studies and computer-calculated placement schemes, meter

readings should be taken at load centers in the same manner as unswitched units,

but now peak conditions should be investigated instead of minimum load

conditions. Readings should be taken so that peak kVA and kW loading can be 

determined. Since Power Factor = kW ÷ kVA, peak load power factor can then 

be determined along with peak kVAr load. Knowing that 

( ) [( ) ( ) ] 2 2 2 kVAr = kVA − kW , we can calculate [( ) ( ) ] 2 2 kVAr = kVA − kW .

Therefore, the magnitude of switched capacitor kVAr necessary to correct the

peak load power factor to unity is the difference between the kVAr of the

unswitched units and peak load kVAr.

When selecting capacitors for switched units, there are certain limiting factors that

have to be considered. The desired level of correction should be determined

through economics: the cost of the switched capacitor installation (total annual

cost) should be less than the savings derived from the installation (total annual
Bulletin 1724D-112

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savings). Switching devices are expensive, but the installed cost per kVAr of a

capacitor installation generally decreases as the size of the installation increases.

On rural lines especially, the standard sizes of capacitors may be somewhat large

for effective switching. The smallest standard unit for primary use is now 50 

kVAr, and some manufacturers do not make a unit smaller than 100 kVAr. Since

switched steps of capacitors have to be multiples of standard capacitor sizes, it is

impossible to correct exactly to unity or to whatever value is desired. Besides,

system load is dynamic and ever-changing.

Choice of manual or automatic switching depends upon the benefits expected, the

size of the capacitor bank, the amount of variation of kW and kilovar load over a

typical load period, and fluctuation of voltage with load. Manual switching

requires an attendant to make the necessary observations of voltage, power factor,

and kilovar demand. Therefore, automatic switching would almost always be

chosen, in preference to manual switching.

c. Capacitor Location

Maximum benefits are obtained by locating the capacitors as near the inductive

reactance kVAr loads as possible and by matching the magnitude of the inductive

reactance kVAr requirement. Practical considerations of economics and

availability of a limited number of standard kVAr sizes necessitate that capacitors

be clustered near load centers. Computer modeling, or rigorous evaluation of

considerable load metering data, is absolutely necessary to make proper capacitor

placement decisions and keep line losses as low as possible. The loss-reduction

benefits possible with capacitor use can be significant enough to economically

justify feeder metering or a large share of SCADA system costs.

A textbook solution assumes uniform distribution of consumers and suggests that,

as the distance from the substation increases, the number of consumers per main

line mile of feeder increases. To obtain maximum benefits in voltage

improvement and reduction of loss on such a line, a permanently connected

(fixed) capacitor bank should be located at a distance from the substation which is

1⁄2 to 2⁄3 of the total length of the line. This location method is used strictly as a

“Rule of Thumb,” because few rural circuits contain such uniformly distributed

loads.

For industrial loads, it is best to correct the power factor at the load. It is

important to remember that a capacitor bank draws considerable current, so the

existing source-side protective equipment needs to be checked for adequacy. In

an attempt to get the maximum voltage rise by placing a bank at the end of the 3-

phase line, a bank of 15-Amp or 25-Amp circuit reclosers could be loaded to the

point of tripping and could create unnecessary outage problems. Correcting

lagging kVAr requirements at the point of use prevents the utility’s primary line, 

transformer, and service lines—as well as the customer’s internal wiring—from
Bulletin 1724D-112

Page 43

unnecessary losses. Moreover, when corrected on the consumer side, the utility

line never sees the consumer’s kVAr. Appropriate effort should be made to

encourage (perhaps through rate incentives) large consumers to correct their own

power factor. For more information on power factor rates and penalties, see

Section 4g of this bulletin.

As previously stated, optimum benefits are derived by locating capacitors at

industrial loads and at a feeder’s consumer load density center for residential load. 

The residential load center is normally 1⁄2 to 2⁄3 the distance from the substation to

the end of the line for uniformly loaded feeders. However, the installation of

capacitors on all systems within the range specified above is not always feasible

because of possible exposure of long lengths of the power line to 

telecommunications circuits, which may cause excessive noise interference.

Thus, the following methods are recommended for locating capacitors:

(1) Use a computer model of your electric system and allow the computer

program to place the capacitors on the system in blocks of the largest size that

can be used to limit the voltage changes to 3 volts per switched bank. There

are several suppliers of good engineering analysis software and many

engineering consultants offer computer service. Utilities, of course, may

purchase the software themselves and do their own voltage drop and capacitor

placement studies. Studies should be performed in concert with the 

Construction Work Plan.

Computer models calculate proper capacitor placement by trying the smallest

size capacitor a system uses in each line section of every feeder and

calculating the total circuit losses. In this way, the computer selects the line

section with the lowest net losses and then places subsequent additional

capacitors in the same manner. The individual effect on feeder losses is

tabulated for each capacitor placed, with each subsequent unit having less

benefit. At some point, at less than unity power factor, an additional capacitor

offers little additional benefit and adding more actually increases losses. 

Capacitors should be located so as to reduce feeder losses as much as

economically practical. The first capacitor placed provides the most

improvement per unit cost because it is usually a fixed capacitor and it

increases power factor the most. Each subsequent unit is less economically 

practical.

(2) Feeder metering at the substation or point of delivery can provide the

kW/kVAr information that is needed for both kVAr correction and

engineering analysis. Additional kVAr information is available using new

technology kVAr or power factor meters attached to hot sticks. No electrical

connections to the line are necessary. Placing the meter in contact with the

primary wires will allow the necessary measurements to be recorded. Power

factor and phase current data can be used to calculate kVA, kW, and kVAr
Bulletin 1724D-112

Page 44

flow. Example 7 that follows assumes that the system operator is using the

“Rule of Thumb” method for locating an acceptable site for a capacitor bank. 

This means that the system operator travels 1⁄2 to 2⁄3 of the way out the line

from the substation and conducts the sequence of measurements and

determinations suggested in Example 7.

EXAMPLE 7. At a given point on a 12.5/7.2-kV feeder, the following is

measured: 

Currents: 25, 12, and 40 amperes (A, B, and C Phases, respectively)

Average Power Factor: 0.85

What do you know about the system at this point?

CALCULATIONS:

Average Current = (25 + 12 + 40) ÷ 3 = 25.7 Amperes

Circuit Balance = A Phase Good Balance

B Phase 13 Amps low

C Phase 13 Amps high

kVA = [(3) × (Average Current) × (Voltage

(line-to-neutral))] ÷ 1,000

= [(3) × (25.7) × (7,200)] ÷ 1,000

= 554 kVA

Phase Angle = Arccosine (power factor)

Phase Angle = Arccosine (0.85) = 31.8 degrees

kW = (kVA) × (power factor) = (554) × (0.85) = 471 kW

kVAr = (kVA) × Sine (phase angle)

= (kVA) × Sine [(Arccosine (power factor)]

= (554) × Sine (31.8 degrees)

= 292 kVAr

Figure 22 shows a power triangle for this example.
Bulletin 1724D-112

Page 45

471 kW V

CURRENT

554 kVA

292 kVAR

θ = PHASE ANGLE = 31.8

p.f. = 85%

POWER TRIANGLE

Figure 22: Power Triangle for Example 7

So with a few field measurements and an inexpensive scientific calculator,

we know that almost 300 kVAr flows past this point. If capacitors were to

be placed here, then 300 kVAr (three 100-kVAr units) of capacitors

located here (or beyond) would eliminate all lagging kVAr flow under

these load conditions.

The addition of 300 kVAr of capacitors would change the kVAr flow from

(292) – (300) = –8 kVAr. The new phase angle is:

New Phase Angle = ARC TAN (kVAr/kW)

= ARC TAN (–8/471)

= –0.973 degrees (current leading)

New kVA = (kW) × COS (New Phase angle)

= (471) × (0.999)

= 471 kVA

New Average Current = (kVA/3) ÷ (kV)

= (471/3) ÷ (7.2)

= 21.8 Amperes

If you knew that the system impedance at this point (or near this point)

was 14.5 +j 15.3 ohms, the voltage rise here from the 300-kVAr, 3-phase

capacitor bank would be:

Voltage Rise = (Primary Capacitor Current) × (Inductive Reactance)

= [(100 kVAr/Phase) / (7.2 kV)] × (15.3 ohms Reactive)

= 212.5 volts at 7,200 volts, or

= (212.5) ÷ (7,200/120)

= 3.54 volts on 120-volt base
Bulletin 1724D-112

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So by relieving the electric system of 292 lagging kVAr at this point, you

have lowered the load from 554 to 471 kVA, reduced the average current

from 25.7 to 21.8 amps, and gained 3.5 volts at this point and beyond.

d. Three-Phase Capacitor Banks

Capacitors to be installed on 3-phase circuits should be installed in equal kVAr

amounts per phase and not in proportion to the total connected transformer

capacity on each phase. System loads should already be balanced within 20% (at

peak load). In general, capacitors should not be installed on single-phase

extensions of the main three-phase feeder. However, if it is absolutely necessary

to install single-phase capacitor banks on a 3-phase line, they should still be

equally sized per phase and located close to each other so as to appear to be a

Y-connected bank of capacitors.

This balance needs to be maintained to:

1. Minimize power factor phase unbalance, which translates into unbalanced

voltages and unbalanced phase angles for 3-phase loads; and

2. Minimize the effect of certain harmonic currents that would otherwise be

produced and flow in the neutral conductor where it could cause interference

in nearby telecommunications circuits. Power factor unbalance causes more

aggravating noise induction problems than does load unbalance, and these

noise problems occur at higher and more troublesome frequencies.

As noted in Section 3a of this bulletin, when one phase of a capacitor bank is out

of service, take the entire bank out of service. Capacitors should be inspected

regularly, at least before and after peak seasons.

e. Capacitor Installation Drawings

Installation drawings for shunt capacitors on 3-phase lines are provided in RUS

Bulletin 1728F-803, “Specifications and Drawings for 24.9/14.4 kV Line

Construction,” and RUS Bulletin 50-3, “Specifications and Drawings for 12.5/7.2

kV Line Construction.” Only professional engineers should develop major

variations from these RUS standards and such variations should be approved, in 

writing, by RUS.

For convenience, the standard drawing VY3.3, 3-Phase Capacitor Bank, is

provided in Figure 23.
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Figure 23: Three-Phase Capacitor Drawing
Bulletin 1724D-112

Page 48

f. Automatic Capacitor Switching

Additional material and equipment will be required when automatic capacitor

switching is to be installed. In addition to the capacitors and protective

equipment, a switched capacitor bank requires a switching device, control

equipment, and a control power source.

The control equipment for automatic switching consists of a master element, a

time-delay device, and auxiliary devices such as an auto-manual switch and a

close-trip switch. Some controls provide dual controls for summer/winter

conditions or for dual conditions such as thermal/voltage. The master element is

selected to suit the conditions of the system on which the control unit is to be

used. Such stimuli as voltage, current, temperature, kilovar, power factor, or

timing (or a combination thereof) may be used to actuate master elements. It is

common to switch all three phases using one current sensor, so the designer

should verify that all three phases have similar amounts and types of load. In 

brief, the various types of master element control are as follows:

(1) Voltage. Responds to objectionable voltage changes that occur with

varying loads. One type of master element voltage control is essentially a

contact-making voltmeter, which has a range of adjustment from 90 to

110% and a bandwidth adjustable from 3 to 71⁄2%. Another type of master

element voltage control incorporates a resistor inserted in series with a 

voltage-regulating relay, which enables the master element to sense a

lower voltage during high load periods. (This type of master element

sensing has to be coordinated with regulators for proper operation). Most

controls allow dual-sensing actuation or biasing, to allow control by

temperature with voltage override so capacitors can be switched in during

either high-temperature or low-voltage times.

(2) Current. Responds to changes in load current by means of a 

current-sensitive relay. This means of control may be used on systems 

where the voltage is well-regulated and the power factor of the load 

remains substantially constant with variation in kW loading, or on systems 

where the power factor of the circuit varies in a predictable manner with 

variation in kW loading. (This is useful for recreational, seasonal, 

irrigation, or oil well pump-type loads when such loads constitute the bulk 

of the feeder load.) Current sensing is usually located near the primary 

conductors inside the insulators supporting the conductors. Low-voltage 

current leads are neatly and safely trained down the supporting structure 

and connected to the master control.

(3) Temperature. Responds to local air temperature for tracking such

temperature-sensitive loads as ac and electric heat. Controls include both

wide-range and narrow-range settings. Wide-range controls can be set to

switch capacitors “ON” and “OFF” for various temperature 
Bulletin 1724D-112

Page 49

ranges, for example, “ON” between 85 and 90 degrees Fahrenheit and

“OFF” for temperatures between 75 and 80 degrees Fahrenheit. This

feature allows a second tier of capacitors to act as fixed units during a long

spell of hot or cold weather. Other capacitor banks can be controlled with

narrow-range controls and be set to turn “ON” for temperatures between

90 and 92 degrees Fahrenheit and to turn “OFF” for temperatures between 

85 and 88 degrees Fahrenheit, to handle system peak loads.

(4) Kilovar. Responds to inductive loading and is used where load voltage is

regulated, and load power factor varies in an unpredictable manner with

variation in kilowatt loading. KVAr-type controls use an inductiondirectional or solid-state relay for single-phase indication. KVAr control

has been useful for improving system power factor in situations where one

large industrial customer is served, and the customer does not provide its

own power factor correction.

(5) Power Factor. Responds to changes in power factor and is similar to

kVAr control in that it uses an induction-directional or solid-state relay

with a desensitizing adjustment to prevent hunting at light loads. The

desensitizing adjustment is needed to account for the possible occurrence

of the power factor bandwidth being less than the change in sensing

caused by switching the capacitor.

(6) Time Switching. Responds by using a simple clock device to switch

capacitors at some predetermined time. It is primarily used where the load

characteristics are predictable and reasonably constant, as with industrial

loads. Desirable added features are weekend and holiday blocking. This

can be a low-cost method. It is also recommended that the clock be

capable of remaining accurate in case of a power outage.

(7) Centralized Control. In addition to using localized controls and conditions 

to switch capacitor banks, a centralized master element control can be 

used to switch multiple capacitor banks installed across the system based 

on global system conditions. One drawback to this type of control method 

is that communications are required with the capacitor control. Due to the 

low bandwidth requirements, though, the communications channel can be 

basic, such as radio or cellular. One-way communications are all that are 

required, but if two-way communications are employed, local status 

information can be brought back as well. The primary advantage of a 

centralized control scheme is that switching logic can be based on more 

than just local conditions. Typically, a system operator or an automation 

software system determines when one or more capacitor banks should be 

switched on to support the system, possibly not just the distribution system 

but the transmission system, regardless of the local conditions present at 

the capacitor installation. Local overrides are typically programmed into 

the capacitor control to prevent switching from a centralized command if 
Bulletin 1724D-112

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that switching would cause local conditions to reach unacceptable levels, 

such as an overvoltage condition.

g. Leading Power Factor

If the kVAr load on the system becomes less than the kVAr rating of the installed

capacitors, a leading power factor will occur. Leading system p.f. can, in severe

instances, cause generators to become unstable. For example, if a distribution 

circuit peaking at 4,000 kW were to run leading such that kVA was 1⁄2% more 

than kW, the leading p.f. would be 0.995 and the leading kVAr would be 400. A

leading power factor will cause the same losses as a lagging power factor of the

same magnitude. If the power factor does go excessively leading, a system ends

up spending money unnecessarily for capacitors (to reduce system losses) because

it still incurs losses anyway. The solution is to either reduce the capacitors

installed or switch them off when not needed.

Because substation power transformers have predominately inductive (lagging)

reactance, a slight distribution system leading power factor translates into a power

factor closer to unity on the transmission system. In this case, the leading power

factor helps the transmission system.

h. Power Factor Penalty Rates

Most distribution utilities have power factor clauses in their commercial and

industrial retail rates that strongly encourage the customer to maintain a 90–95%

power factor; otherwise, the customer has to pay a penalty charge. Traditionally,

these power factor penalty clauses were added into retail rates because the

utility’s purchased power rates included similar penalties. Lower power factors

usually cause an increased billing demand by the ratio of the target p.f. divided by

the metered p.f., usually on peak.

A traditional method of applying a power factor penalty adjusts (raises) the billing

demand in proportion to the metered power factor deviation from the desired

power factor. This billing demand adjustment is expressed as:

Billing Demand = (Metered Demand) × (Target p.f. ÷ Measured p.f.)

For example, customers that have monthly bills with a metered p.f. of 0.83 and a

target p.f. of 0.95 (minimum allowed by the utility in this example), the billing

demand would be multiplied by 0.95 ÷ 0.83 = 1.145. This 14.5% increase in

billing demand should alert customers and encourage them to improve their

power factors.

You may help persuade consumers to correct their own power factor by pointing

out to them that capacitors help their system in the following ways:
Bulletin 1724D-112

Page 51

(1) Reduce their power factor penalties, if applicable;

(2) Improve their in-plant voltage levels;

(3) Reduce their in-plant line and transformer losses; and

(4) Release (reclaim) substation, transformer, switchboard, and conductor

capacity on their system.

A few utilities offer reduced billing demand if the actual power factor exceeds the

desired power factor.

More information about secondary capacitors and power factor correction for

induction motors is included in Section 6 of this bulletin.

i. Capacitor Fusing

Fuse protection is necessary for each shunt capacitor installation, mainly to

disconnect a faulted capacitor from the line before the capacitor causes other

current protective devices to operate. Capacitor fuse protection has to be

coordinated with any line sectionalizing devices that will be operated on the

feeder. Fuses should be designed to blow before the capacitor case ruptures in 

order to prevent personal injury, damage to adjacent equipment, or capacitor

dielectric fluid leaks.

Shunt capacitors are designed to operate temporarily at 135% of their rated kVAr. 

From Section 6a of this bulletin, Equation 11, we know that a 16.2% overvoltage 

gives 135% of kVAr. This 35% above rated tolerance is to allow for:

(1) Additional kVAr (reactive power) that could be present as a result of

operating the capacitors at voltages above their nameplate fundamental

frequency voltage,

(2) Additional kVAr that could be generated as a result of slightly higher than

normal harmonic voltages that could be present along with the fundamental

frequency voltage, and

(3) Additional kVAr that could be present as a result of the capacitor’s actual

kVAr being on the high side of allowable manufacturing tolerances.

Capacitor current protection devices should have a nominal rating of 135% to

140% of the capacitor line current.

Capacitor units are not normally fused individually, but by phase in a bank of one

or more capacitors per phase. Banks should always contain the same amount of

kVAr in each phase. Capacitor fusing is normally designed to operate at 120% to

135% of the capacitor’s nameplate current rating, although such fusing is

occasionally derated to no less than 108% for multiple units per phase.

In general, a fuse link should melt in 5 minutes at 150% to 300% of rated current. 

Fuses for small capacitors should have at least a 5-ampere rating to minimize the

likelihood of fuse failure due to lightning or transient surges. In high lightning

areas, fuses should be 15 amperes or larger, but no greater than 140% of the
Bulletin 1724D-112

Page 52

capacitor’s nameplate current rating. The choice of fuse rating for a capacitor

installation should always be based on a particular fuse’s time-current 

characteristics. This individual design attention is needed because of the wide

variation in fuse time-current characteristics and the different types and brands of

fuses available.

The following table detailing Edison Electric Institute/National Electrical

Manufacturers Association (EEI/NEMA) Type T and Type K fuse links for

protecting capacitors was created from Table 15A3 on page 102 of Electrical

Distribution-System Protection, 3rd Edition, Bulletin 90020, Cooper Power 

Systems.

Table 3: Capacitor Fusing Table

3-φ

kVAr

Full Load

Amps

12,470/7,200 

Gnd Y

3-φ

kVAr

Full Load

Amps

24,900/14,400 

Gnd Y

150 6.9 8T

300 13.9 15T 300 6.9 8T

450 20.8 20T 450 10.4 10T

600 27.8 25T 600 13.9 15T

900 41.7 40T 900 20.8 20T

If lightning causes excessive fuse blowing but there is no capacitor damage, fuses

should be replaced with the next larger size.

j. Safety Precautions

Capacitors require special precautions when they are taken out of service for

repair or maintenance. Like a battery, a capacitor may retain a charge for an

indefinite time after being disconnected; the capacitor charge can be quite

hazardous to an unsuspecting individual who encounters the charge. Generally,

discharge resistors are manufactured into each capacitor unit to help dissipate

charge when the unit is out of service. The discharging resistors should reduce 

the terminal voltage of a capacitor unit to 50 volts or less in one minute for units

rated at 600 volts or less, and in five minutes for units rated higher than 600 volts.

(1) In Situ Repair

Added precautions should be taken when working with delta and

nongrounded, wye-connected capacitors. A hazardous voltage may be

present on a capacitor even when the phase conductor to which the

capacitor is connected is open-circuited for work. Line voltage can feed

back through the capacitor (via the capacitor’s common connection) with

capacitors connected to other phase conductors that are still energized. 

This is why it is important for line crews to always check phase

conductors for the presence of voltage.
Bulletin 1724D-112

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It is generally good practice before working on a capacitor bank to

completely de-energize the bank and disconnect all line conductors from

all terminals. It is not good practice to rely on a capacitor’s internal

discharging resistors to reduce the terminal voltage to a safe value after

being disconnected from a power line. After disconnecting a capacitor

and waiting for the discharging resistors to bleed voltage down, it is best 

to then short-circuit the capacitor terminals and connect the shorted

terminals and the cases to ground.

(2) Out of Service Repair/Storage

When capacitors are removed from their racks, after waiting several

minutes (during which time the discharging resistors should have reduced

the capacitor terminal voltage practically to zero) the terminals should be

simultaneously short-circuited and solidly connected to their cases. These

connections should be left intact, because capacitors tend to accumulate a 

residual charge (even when not connected to a power source) if not shortcircuited. Number 6 copper wire can be used to make the capacitor

terminal-to-terminal-to-case shorting connections. The connection should

not be removed until the unit is reinstalled.

(3) Load Breaking Considerations

It is important to note that a capacitor bank can be a formidable load as the

kVAr size used increases. A 600-kVAr bank at 7,200 V draws about 28

Amps. A bank drawing this much current cannot be “unloaded” without

the use of load-break cutouts. Therefore, it is recommended that loadbreak cutouts be used on capacitor banks for continuity of service and

safety during maintenance procedures.

5 POWER SUPPLY CONSIDERATIONS

a. Capacitor Effects on Substations

In most cases, greatest efficiency of shunt capacitor use is achieved by placing

capacitors out on the distribution line. In some cases, capacitors may have to be

installed inside substations. This may be the case if the substation is located near

a large industrial load, or the substation feeders are all underground where

capacitors are more difficult and expensive to install.

The voltage improvement at a substation distribution bus with the substation 

transformer carrying full load—due to a shunt-connected capacitor installation at 

that location—may be calculated with the following formula:
Bulletin 1724D-112

Page 54

% Voltage Improvement = tkVA

(ckVAr)×(Z)

Equation 10: Percent Voltage Improvement at Substation

Where:

Z = Percent transformer impedance

tkVA = Transformer kVA rating

ckVAr = Total capacitor kVAr

Voltage rise at a substation is predominantly controlled by the reactance

component of the transformer impedance. However, the impedance of most

substation transformers is practically equal to the reactance. Thus, the percent

impedance value that is provided on a substation transformer nameplate may be

used to calculate voltage rise without appreciable error. If the transformer

reactance is known, using the known value of reactance in lieu of total impedance 

will yield precise results.

The total voltage improvement brought about by the installation of shunt

capacitors at a substation is the sum of the voltage improvements of all

components of the system. When there are no regulators installed at the

substation, the voltage improvement in the substation transformers is added to the

voltage improvement on the distribution line to determine the total effect on the

distribution line voltage. The voltage improvement due to the application of 

capacitors at a substation is neutralized at the distribution regulator within the

operating range of the regulators.

The voltage rise on the distribution line or substation transformers due to

capacitors connected away from the substation out on the system is not dependent

on the system load. The capacitor’s leading current flows through the lagging

system reactance and creates the voltage rise. The benefits from this rise on a

typical distribution system are usually less important than those from the

reduction in system energy losses and the release (reclaiming) of kVA capacity 

for additional useful load.

b. Effects of Distribution Capacitors on Transmission Lines

In addition to the rise in feeder voltage due to a capacitor installation, the

transmission circuit (as well as other substation transformers between the

generating station and the capacitor location) will undergo a similar voltage rise. 

Since the electrical characteristics of these parts of the system vary so widely with

construction practices among power suppliers, their voltage rise cannot be readily

reduced to chart form. But, when you know the total system impedance, you can

easily calculate the voltage rise of any capacitor at any point on the system using

the formulas and methods discussed previously for capacitors out on the 

distribution system.
Bulletin 1724D-112

Page 55

c. Increase in Substation Capacity

Since an increase in power factor reduces the current drawn by a given load, a 

capacitor installation reduces the kVA demand for that load. The decrease in load 

demand due to a capacitor installation corresponds to released (reclaimed)

substation capacity. This released capacity is of particular value when the

substation load approaches the substation design capability. Capacitors may also

relieve existing overloaded conditions.

6 CAPACITORS FOR INDUCTION MOTORS

a. Switched Shunt Capacitor Banks

Capacitors installed on the primary circuit are, in some cases, limited to those 

required for the correction of the power factor of the system without considering

the requirements of large inductive loads. But capacitors can be operated at

voltages above their nameplate ratings for very short times of no more than a few

minutes, effectively increasing their available kVAr.

The most common use of this short-term capacitor overvoltage capability is for

starting large motors with reduced voltage flicker. For this purpose, a

wye-connected capacitor bank is reconnected into a delta-connected switched 

capacitor configuration which overvoltages capacitors in each delta leg by 1.732 

times normal voltage (placing line-to-line voltage on a line-to-neutral unit). This

overvoltage raises the effective kVAr to three times the capacitor’s normal rating

because:

kVAr = [V 2× (2πf )× (C)]÷1,000

Equation 11: kVAr

Where:

V = Rated rms voltage

π = 3.1416

f = Frequency in hertz = 60 Hz for U.S. power systems

C = Capacitance in farads

As switching methods become complex, motors may be controlled by

programmable logic controllers (PLC), which are small computers with

rudimentary programming code used in manufacturing control systems. When a

large motor start button is pressed:

(1) The PLC closes the primary switches on the capacitor bank and monitors

capacitor inrush current or the system voltage to get full use of the capacitors,

then

(2) The PLC closes the motor contactor and monitors the motor starting current as

the motor current falls from its starting high to near its running level, and
Bulletin 1724D-112

Page 56

(3) The PLC finally opens the capacitor primary switches to remove the starting

capacitor bank from the circuit. All this happens within 10 to 20 seconds and

allows a large motor to start with less impact on the distribution feeder. 

Considerable coordination with the customer is required as the control is

installed and tested.

b. Secondary Capacitors

Secondary capacitors are available for installation at a motor at somewhat higher

costs than primary units. However, the benefits of the capacitor at the motor in

decreasing starting and running current and the attendant losses are extended to

the secondary and service wiring, as well as the supply transformer and the

balance of the distribution system.

The motor starter is used to switch on the capacitor, which is wired directly to the

large motor. The resulting load then behaves like a high power-factor load on the

system.

Certain limitations on the size of capacitor installations for various motor sizes

and rotational speeds have to be imposed to avoid the possibility of self-excitation

of the motor with its attendant problems. The maximum size of capacitor that can

be used on an induction motor is one that is not large enough to augment

magnetization current of the motor at any point on its starting and running curve. 

If this limitation is exceeded, the motor may run at a subsynchronous speed and

draw excessive current, which may damage the windings.

If the power source is disconnected momentarily, the motor will operate as an

induction generator while it is coasting. Reconnection of the motor to the supply

will have the same effect as closing the main switch on a generator that is not

synchronized to the supply line.

Motor damage is possible when a motor is disconnected from its supply line. At

the instant the motor is disconnected, current continues to flow in the circuit

consisting of the motor winding inductance and the parallel connected capacitor. 

Resonance may occur at some point on the motor speed curve as the motor slows

down. If this resonance occurs, voltage will rise on the motor windings and only

the “Q” of the tuned circuit will limit the rise. The damping effect of the line

resistance is no longer available to limit this voltage and the motor insulation may

be damaged.

Capacitor manufacturers can provide up-to-date information on suggested

capacitor sizes for various motor sizes and loads. Appendix B is a listing of the

maximum permissible capacitor rating that can be used with various motors so

that no self-excitation voltages will be produced. These values do not necessarily

correspond to standard capacitor ratings, in which case, the next lower rating

should be used.
Bulletin 1724D-112

Page 57

When capacitors are connected to motor terminals, the current flowing in the

supply circuit is reduced. When the capacitors are connected on the motor side of

an overload protective device, this device will no longer provide adequate

protection if the protection device has been selected on the basis of the

uncorrected full-load current. For effective protection, either the circuit breaker

relay needs to be adjusted, or a new fuse needs to be installed. The new fuse 

should have a rating that allows it to operate at a lower current consistent with the

reduced line current.

A 1-kVAr secondary capacitor at the load is equivalent to approximately a 1.04-

kVAr capacitor installed on the primary, from the standpoint of reduction of

losses in the transformer and on the service side of the installation. Secondary

capacitors provide additional voltage rise through the service transformers and

facility wiring. With this type of capacitor application, where the load varies so

widely, the secondary capacitor, which is switched with the load, is a practical

and economical solution.

c. Series Primary Capacitors

(1) Applications and Problems

Series-connected primary capacitors cause a voltage rise quite different

from shunt-connected capacitors. Shunt-connected capacitors cause

voltage rise when the leading current (IC) they draw from the power source

flows through the lagging impedance (XL) of line conductors (IC×XL). 

Conversely, series-connected capacitors cause a voltage rise when the

lagging load current (IL) drawn by the inductive system impedance sources

flow through the leading impedance (XC) of the series-connected

capacitors (IL×XC). See Figure 24.
Bulletin 1724D-112

Page 58

CURRENT

NEUTRAL

MOTOR

LOAD VOLTAGE

R1

XL1 XC R2 XL2

System Impedance Series Cap System Impedance

Figure 24: Series Capacitor Circuit

VOLTAGE

Series Capacitor

Location

Load

Location

Source

Location

STARTING

RUN

Figure 25: Motor Starting with Series Capacitor

This rise through the series-connected capacitor is particularly useful in

canceling voltage dips caused by large motors during starting, as shown in

Figure 25.

A properly sized series capacitor could cancel the entire voltage drop of

motor starting current and even add a rise at the lower running current

levels.

It sounds too good to be true. If series-connected capacitors do all this,

then why are most utilities not using them? Some utilities do use series

capacitors; however, there are other inherent problems which usually

outweigh the benefits.

The biggest problem is lightning. Since neither bushing of the capacitor is

connected to ground, both ends have to be effectively protected with

lightning arresters. And because lightning current traveling down the
Bulletin 1724D-112

Page 59

phase conductor would pass through the capacitor and damage it, some

current bypass method is also needed. Some utilities have tried installing

lightning arresters across the capacitor with limited success. Some

utilities have developed solid-state switching controls that either:

a) Switch the series capacitor into the circuit when a predetermined

current level is sensed; or

b) Bypass the series capacitor when surge current is sensed.

Permanent series capacitor installations have proven to be impractical

because of the considerable design problems. However, utilities have had

some limited success with temporary series capacitor installations and

have used them until major system improvements allow their removal.

Series capacitors are included here to provide a complete discussion of

distribution capacitors.

(2) Sizing Series Capacitors

In order to determine the size of a series-connected capacitor to install on

a system, the designer needs to know the system impedance at various

points along the distribution feeder. A computerized fault current study

can be used to provide the necessary impedance information. The

magnitude of the feeder load current and the feeder’s power factor also

have to be known or calculated. The entire voltage rise occurs across a

series capacitor. A decision has to first be made to determine at what

point on the system the lumped voltage rise is needed and whether nearby

customers will be able to tolerate the resulting voltage fluctuations. 

Knowing the value of the voltage drop that needs to be cancelled and the

prevailing feeder load current, the capacitive reactance necessary to

accomplish the improvement can be calculated as follows:

The voltage drop through a feeder without the series capacitor connected 

is approximately:

V.D. = IX × RX × (COS θ) + IX × XL× (SIN θ)

Equation 12: Voltage Drop

Where:

RX = Feeder Resistance

XL = Feeder Reactance

IX = Feeder Current

θ = Feeder Power Factor Angle

With a series capacitor installed, the voltage drop becomes:

V.D. = IX × RX × (COS θ) + IX× (XL – XC) × (SIN θ)
Bulletin 1724D-112

Page 60

V.D. = IX × RX × (COS θ), when XL = XC

Equation 13: Voltage Drop with Series Capacitor

Where:

RX = Feeder Resistance

XL = Feeder Reactance

XC = Series Capacitor’s Reactance

IX = Feeder Current

θ = Feeder Power Factor Angle

To avoid excessive voltage rise during normal load conditions and to

avoid flicker during motor starts and stops, the capacitive reactance should

be smaller than the feeder’s inductive reactance. If the load power factor

is near 100%, there will not be much capacitive rise. If the load power

factor is leading, there will be a voltage drop. Voltage increases with

series capacitors because the lagging load current produces a voltage rise

through the leading capacitive reactance of the series capacitor. Voltage

increases with shunt capacitors because the leading capacitive current

drawn through the system by a shunt capacitor produces a voltage rise

through the lagging conductor reactance.

XC = 1,000,000 ÷ (2πfC)

Where:

π = 3.1416,

f = Frequency in hertz

C = Capacitance in microfarads

Solving for capacitance, we obtain:

C = 1,000,000 ÷ (2πfXC)

And capacitor kVAr is equal to:

kVAr = [(2πfC) × V2] ÷ 1,000

Where:

V = rated rms voltage of Capacitor units

7 REFERENCES

40 CFR Part 761, Polychlorinated Biphenyls (PCBs) Manufacturing, Processing,

Distribution in Commerce, and Use Prohibitions.

Capacitor Switching Transients: A Best Practices Guide. TVPPA R&D Project CS-1, 

2011.
Bulletin 1724D-112

Page 61

Dai, R., R. Walling, and L. Freeman, Conservation Voltage Reduction (CVR) Evaluation: 

Testing, Methods, and Results, DSTAR Project 13-7 Final Report, 2013.

Electrical Distribution-System Protection: A Textbook and Practical Reference on 

Overcurrent and Overvoltage Fundamentals, Protective Equipment and Applications, 3rd 

Edition, Bulletin 90020, Cooper Power Systems, 1990.

IEEE Standard 18-2012, Standard for Shunt Power Capacitors, 2012.

IEEE Standard 1036-2012, Guide for Application of Shunt Power Capacitors, 2012.

IEEE Standard C37.99-2012, Guide for the Protection of Shunt Capacitor Banks, 2012.

Power Factor Correction: A Guide for the Plant Engineer. Technical Publication No. 

SA02607001E/Z15663. Eaton. August 2014.

RUS Bulletin 1728F-803, Specifications and Drawings for 24.9/14.4 kV Line

Construction, December 1998.

RUS Bulletin 1728F-804, Specifications and Drawings for 12.47/7.2-kV Line 

Construction, October 2005.
Appendix A

Page 1

APPENDIX A

POWER FACTOR TABLE

The following table can be used to calculate power factor using real power (kWh) and reactive 

power (kVArh) data.

Table A1: Power Factors

Power

Factor

Third Decimal Accuracy Power Factor

(Add to Left-Most Column Power Factor Result)

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Tangents Corresponding to Power Factor Angle

1.00 0.000

0.99 0.142 0.135 0.127 0.119 0.110 0.100 0.090 0.078 0.063 0.045

0.98 0.203 0.198 0.192 0.187 0.181 0.175 0.169 0.163 0.156 0.150

0.97 0.251 0.246 0.242 0.237 0.233 0.228 0.223 0.218 0.213 0.208

0.96 0.292 0.288 0.284 0.280 0.276 0.272 0.268 0.263 0.259 0.255

0.95 0.329 0.325 0.322 0.318 0.314 0.311 0.307 0.303 0.299 0.296

0.94 0.363 0.360 0.356 0.353 0.350 0.346 0.343 0.339 0.336 0.332

0.93 0.395 0.392 0.389 0.386 0.383 0.379 0.376 0.373 0.370 0.366

0.92 0.426 0.423 0.420 0.417 0.414 0.411 0.408 0.405 0.401 0.398

0.91 0.456 0.453 0.450 0.447 0.444 0.441 0.438 0.435 0.432 0.429

0.90 0.484 0.481 0.479 0.476 0.473 0.470 0.467 0.464 0.461 0.459

0.89 0.512 0.510 0.507 0.504 0.501 0.498 0.496 0.493 0.490 0.487

0.88 0.540 0.537 0.534 0.532 0.529 0.526 0.523 0.521 0.518 0.515

0.87 0.567 0.564 0.561 0.559 0.556 0.553 0.551 0.548 0.545 0.542

0.86 0.593 0.591 0.588 0.585 0.583 0.580 0.577 0.575 0.572 0.569

0.85 0.620 0.617 0.614 0.612 0.609 0.607 0.604 0.601 0.599 0.596

0.84 0.646 0.643 0.641 0.638 0.635 0.633 0.630 0.628 0.625 0.622

0.83 0.672 0.669 0.667 0.664 0.662 0.659 0.656 0.654 0.651 0.649

0.82 0.698 0.695 0.693 0.690 0.688 0.685 0.682 0.680 0.677 0.675

0.81 0.724 0.721 0.719 0.716 0.714 0.711 0.708 0.706 0.703 0.701

0.80 0.750 0.747 0.745 0.742 0.740 0.737 0.734 0.732 0.729 0.727

0.79 0.776 0.773 0.771 0.768 0.766 0.763 0.760 0.758 0.755 0.753

0.78 0.802 0.800 0.797 0.794 0.792 0.789 0.787 0.784 0.781 0.779

0.77 0.829 0.826 0.823 0.821 0.818 0.815 0.813 0.810 0.808 0.805

0.76 0.855 0.852 0.850 0.847 0.845 0.842 0.839 0.837 0.834 0.831

0.75 0.882 0.879 0.877 0.874 0.871 0.869 0.866 0.863 0.860 0.858

0.74 0.909 0.906 0.904 0.901 0.898 0.895 0.893 0.890 0.887 0.885

0.73 0.936 0.933 0.931 0.928 0.925 0.923 0.920 0.917 0.914 0.912

0.72 0.964 0.961 0.958 0.956 0.953 0.950 0.947 0.944 0.942 0.939

0.71 0.992 0.989 0.986 0.983 0.981 0.978 0.975 0.972 0.969 0.967

0.70 1.020 1.017 1.014 1.012 1.009 1.006 1.003 1.000 0.997 0.995

0.69 1.049 1.046 1.043 1.040 1.037 1.035 1.032 1.029 1.026 1.023

0.68 1.078 1.075 1.072 1.069 1.066 1.064 1.061 1.058 1.055 1.052

0.67 1.108 1.105 1.102 1.099 1.096 1.093 1.090 1.087 1.084 1.081

0.66 1.138 1.135 1.132 1.129 1.126 1.123 1.120 1.117 1.114 1.111

0.65 1.169 1.166 1.163 1.160 1.157 1.154 1.151 1.147 1.144 1.141

0.64 1.201 1.197 1.194 1.191 1.188 1.185 1.182 1.179 1.175 1.172

0.63 1.233 1.229 1.226 1.223 1.220 1.217 1.213 1.210 1.207 1.204

0.62 1.265 1.262 1.259 1.256 1.252 1.249 1.246 1.242 1.239 1.236
Appendix A

Page 2

Power

Factor

Third Decimal Accuracy Power Factor

(Add to Left-Most Column Power Factor Result)

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Tangents Corresponding to Power Factor Angle

0.61 1.299 1.296 1.292 1.289 1.286 1.282 1.279 1.275 1.272 1.269

0.60 1.333 1.330 1.326 1.323 1.320 1.316 1.313 1.309 1.306 1.302

0.59 1.368 1.365 1.361 1.358 1.354 1.351 1.347 1.344 1.340 1.337

0.58 1.405 1.401 1.397 1.394 1.390 1.386 1.383 1.379 1.376 1.372

0.57 1.441 1.438 1.434 1.430 1.427 1.423 1.419 1.416 1.412 1.408

0.56 1.479 1.476 1.472 1.468 1.464 1.460 1.457 1.453 1.449 1.445

0.55 1.518 1.515 1.511 1.507 1.503 1.499 1.495 1.491 1.487 1.483

0.54 1.559 1.555 1.551 1.546 1.542 1.538 1.534 1.530 1.526 1.522

0.53 1.600 1.596 1.592 1.587 1.583 1.579 1.575 1.571 1.567 1.563

0.52 1.643 1.638 1.634 1.630 1.625 1.621 1.617 1.613 1.608 1.604

0.51 1.687 1.682 1.678 1.673 1.669 1.664 1.660 1.656 1.651 1.647

0.50 1.732 1.727 1.723 1.718 1.714 1.709 1.705 1.700 1.696 1.691

0.49 1.779 1.774 1.770 1.765 1.760 1.755 1.751 1.746 1.741 1.737

0.48 1.828 1.823 1.818 1.813 1.808 1.803 1.798 1.793 1.789 1.784

0.47 1.878 1.873 1.868 1.863 1.858 1.853 1.848 1.843 1.838 1.833

0.46 1.930 1.925 1.920 1.914 1.909 1.904 1.899 1.893 1.888 1.883

0.45 1.985 1.979 1.973 1.968 1.963 1.957 1.952 1.946 1.941 1.936

0.44 2.041 2.035 2.029 2.024 2.018 2.012 2.007 2.001 1.996 1.990

0.43 2.100 2.094 2.088 2.082 2.076 2.070 2.064 2.058 2.052 2.047

0.42 2.161 2.155 2.148 2.142 2.136 2.130 2.124 2.118 2.112 2.106

0.41 2.225 2.218 2.212 2.205 2.199 2.192 2.186 2.180 2.173 2.167

0.40 2.291 2.284 2.278 2.271 2.264 2.258 2.251 2.244 2.238 2.231

0.39 2.361 2.354 2.347 2.340 2.333 2.326 2.319 2.312 2.305 2.298

0.38 2.434 2.427 2.419 2.412 2.405 2.397 2.390 2.383 2.375 2.368

0.37 2.511 2.503 2.495 2.487 2.480 2.472 2.464 2.457 2.449 2.442

0.36 2.592 2.583 2.575 2.567 2.559 2.551 2.543 2.535 2.527 2.519

0.35 2.676 2.668 2.659 2.650 2.642 2.633 2.625 2.617 2.608 2.600

0.34 2.766 2.757 2.748 2.739 2.730 2.721 2.712 2.703 2.694 2.685

0.33 2.861 2.851 2.841 2.832 2.822 2.813 2.803 2.794 2.784 2.775

0.32 2.961 2.950 2.940 2.930 2.920 2.910 2.900 2.890 2.880 2.870

0.31 3.067 3.056 3.045 3.034 3.024 3.013 3.002 2.992 2.981 2.971

0.30 3.180 3.168 3.157 3.145 3.134 3.122 3.111 3.100 3.089 3.078

To determine average power factor, divide the measured reactive volt-ampere-hour meter 

reading by the watt-hour meter reading. Find the value that closely approximates your 

calculation in Table A1, then read across the same row to the left-most column for the power

factor. For three-decimal accuracy, find the value that closely approximates your calculated 

value again in Table A1, then read straight up the column in which the value appears to the

table’s second row and add the value in the second row (i.e., 0.000, 0.001, 0.0002, etc.,) to the 

power factor determined previously.
Appendix B

Page 1

APPENDIX B

CAPACITOR RATING TABLE FOR MOTORS

Table B1: Maximum Capacitor Rating for Motors/Capacitors Switched as a Unit

Induction 

Motor 

HorsePower 

Rating

Nominal Motor Speed in RPM

3,600 RPM 1,800 RPM 1,200 RPM 900 RPM 720 RPM 600 RPM

Cap.

Rating

kVAr

Line Current

Reduction %

Cap.

Rating

kVAr

Line Current

Reduction %

Cap.

Rating

kVAr

Line Current

Reduction %

Cap.

Rating

kVAr

Line Current

Reduction %

Cap.

Rating

kVAr

Line Current

Reduction %

Cap.

Rating

kVAr

Line Current

Reduction %

3.0 1.5 14 1.5 15 1.5 20 2.0 27 2.5 35 3.0 41

5.0 2.0 12 2.0 13 2.0 17 3.0 25 4.0 32 4.0 37

7.5 2.5 11 2.5 12 3.0 15 4.0 22 5.0 30 6.0 34

10.0 3.0 10 3.0 11 3.0 14 5.0 21 6.0 27 7.5 31

15.0 4.0 9 4.0 10 5.0 13 6.0 18 8.0 23 9.0 27

20.0 5.0 9 5.0 10 6.0 12 7.5 16 9.0 21 12.5 25

25.0 6.0 9 6.0 10 7.5 11 9.0 15 10.0 20 15.0 23

30.0 7.0 8 7.0 9 9.0 11 10.0 14 12.5 18 17.5 22

40.0 9.0 8 9.0 9 10.0 10 12.5 13 15.0 16 20.0 20

50.0 12.5 8 10.0 9 12.5 10 15.0 12 20.0 15 25.0 19

60.0 15.0 8 15.0 8 15.0 10 17.5 11 22.5 15 27.5 19

75.0 17.5 8 17.5 8 17.5 10 20.0 10 25.0 14 35.0 18

100.0 22.5 8 20.0 8 25.0 9 27.5 10 35.0 13 40.0 17

125.0 27.5 8 25.0 8 30.0 9 30.0 10 40.0 13 50.0 16

150.0 30.0 8 30.0 8 35.0 9 37.5 10 50.0 12 50.0 15

200.0 40.0 8 37.5 8 40.0 9 50.0 10 60.0 12 60.0 14

250.0 50.0 8 45.0 7 50.0 8 60.0 9 70.0 11 75.0 13

300.0 60.0 8 50.0 7 60.0 8 60.0 9 80.0 11 90.0 12

350.0 60.0 8 60.0 7 75.0 8 75.0 9 90.0 10 95.0 11

400.0 75.0 8 60.0 6 75.0 8 85.0 9 95.0 10 100.0 11

450.0 75.0 8 75.0 6 80.0 8 90.0 9 100.0 9 110.0 11

500.0 75.0 8 75.0 6 85.0 8 100.0 9 100.0 9 120.0 10

Table Notes:

For use with 3-phase, 60-hertz, NEMA Design B motors to raise full load power factor to 

approximately 95%.

When manual, reduced-voltage, auto-transformer type starters are used, motor and load 

characteristics have to be considered in order to keep mechanical torque in motor shaft and 

coupling below six times normal.

kVAr is rated kVA of capacitor connected at motor terminals.

Percent reduction in line current due to capacitor is helpful for selecting the proper motor 

overload setting when the overload device carries the sum of motor and capacitor currents.

For new motors and other NEMA standard design motors, follow the manufacturer’s 

recommendation for maximum capacitor rating when motor and capacitor are switched as a

unit.

Taken from Table 3, Page 10, of Power Factor Correction: A Guide for the Plant Engineer.