National Renewable Energy Laboratory 

Innovation for Our Energy Future 

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

Office of Energy Efficiency & Renewable Energy

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

Study and Development of 

Anti-Islanding Control for 

Synchronous Machine-Based 

Distributed Generators 

November 2001 — March 2004 

Z. Ye 

GE Global Research Center 

Niskayuna, New York 

Subcontract Report 

NREL/SR-560-38018 

March 2006 
Study and Development of 

Anti-Islanding Control for 

Synchronous Machine-Based 

Distributed Generators 

November 2001 — March 2004 

Z. Ye 

GE Global Research Center 

Niskayuna, New York 

NREL Technical Monitor: B. Kroposki 

Prepared under Subcontract No. NAD-1-30605-01 

Subcontract Report 

NREL/SR-560-38018 

March 2006 

National Renewable Energy Laboratory 

1617 Cole Boulevard, Golden, Colorado 80401-3393 

303-275-3000 • www.nrel.gov 

Operated for the U.S. Department of Energy 

Office of Energy Efficiency and Renewable Energy 

by Midwest Research Institute • Battelle 

Contract No. DE-AC36-99-GO10337
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Table of Contents 

EXECUTIVE SUMMARY ........................................................................................................................1

1 INTRODUCTION..............................................................................................................................3

2 SYNCHRONOUS MACHINE AND POWER SYSTEM MODELING .......................................5

2.1 SYNCHRONOUS GENERATOR MODEL FOR ISLANDING STUDIES .................................................6 

2.2 EXCITATION SYSTEM MODEL AND REACTIVE POWER REGULATION .........................................8 

2.3 GOVERNOR MODEL AND ACTIVE POWER REGULATION .............................................................9 

2.4 RLC LOAD MODEL AND INDUCTION MOTOR LOAD MODEL ....................................................10 

2.5 GRID MODEL .............................................................................................................................13

2.6 SMALL-SIGNAL ANALYSIS ........................................................................................................13 

3 ANTI-ISLANDING CONCEPT AND IMPLEMENTATION.....................................................15

3.1 INTRODUCTION OF POSITIVE FEEDBACK ...................................................................................15 

3.2 IMPLEMENTATION OF THE ACTIVE/REACTIVE POWER SCHEMES..............................................15 

3.3 DESIGN GUIDELINE BASED ON FREQUENCY-DOMAIN ANALYSIS.............................................17 

3.4 PRACTICAL DESIGN CONSIDERATIONS......................................................................................19 

3.4.1 Power Level...........................................................................................................................19

3.4.2 Quality Factor.......................................................................................................................21

3.4.3 Grid Impedance.....................................................................................................................22

3.4.4 Motor Load............................................................................................................................22

3.4.5 Conclusions...........................................................................................................................23

4 PERFORMANCE EVALUATION WITH TIME-DOMAIN SIMULATIONS.........................24

4.1 PERFORMANCE EVALUATION WITH RLC LOAD .......................................................................24 

4.1.1 Case 1: Baseline without AI Scheme.....................................................................................24

4.1.2 Case 2: Active Power Scheme with Qf=1.8...........................................................................24

4.1.3 Case 3: Reactive Power Scheme with Qf=1.8 .......................................................................25

4.1.4 Case 4: Active Power Scheme with Qf=0.0...........................................................................25

4.1.5 Case 5: Reactive Power Scheme with Qf=0.0 .......................................................................25

4.2 PERFORMANCE EVALUATION WITH INDUCTION MOTOR LOAD ................................................27 

4.2.1 Case 6: Baseline without AI Scheme and with Induction Motor Load..................................27

4.2.2 Case 7: Active Power AI Scheme with Induction Motor Load..............................................27

4.2.3 Case 8: Reactive Power AI Scheme with Induction Motor Load ..........................................27

4.3 PERFORMANCE EVALUATION WHEN THE GRID IS CONNECTED................................................29 

4.3.1 Grid Disturbances.................................................................................................................29

iii
4.3.2 Grid Impedances...................................................................................................................30

4.3.3 Grid Frequency Oscillations.................................................................................................32

5 SUMMARY.......................................................................................................................................33

5.1 CONCLUSIONS............................................................................................................................33 

5.2 FUTURE WORK ..........................................................................................................................34 

6 APPENDIX .......................................................................................................................................35

6.1 SYNCHRONOUS MACHINE DATA ...............................................................................................35 

6.2 INDUCTION MOTOR DATA .........................................................................................................36 

7 REFERENCES.................................................................................................................................37

List of Figures 

Figure 1: Synchronous generator system and its control block diagram......................................................5

Figure 2: Synchronous generator d- and q-axis equivalent circuits..............................................................8

Figure 3: Control block diagram of excitation system ...................................................................................9

Figure 4: Control block diagram of governor...............................................................................................10

Figure 5: DQ equivalent circuit model of RLC load.....................................................................................11

Figure 6: DQ equivalent circuit model of induction motor...........................................................................12

Figure 7: DQ equivalent circuit model of grid..............................................................................................13

Figure 8: DQ equivalent circuit model of the overall system.......................................................................14

Figure 9: Schematic of the machine with the AI compensators..................................................................16

Figure 10: Schematic of the machine with the AI loops opened.................................................................17

Figure 11: Active and reactive AI compensators ........................................................................................18

Figure 12: Loop gains with different generator output power .....................................................................20

Figure 13: Loop gains with different quality factors ....................................................................................21

Figure 14: Loop gains with different grid impedance ..................................................................................22

Figure 15: Loop gains with RLC and motor load ........................................................................................23

Figure 16: Simulation results of the active power scheme in response to islanding at 1s .........................25

Figure 17: Simulation results of the reactive power scheme in response to islanding at 1s ......................26

Figure 18: Simulation results with the induction motor load in response to islanding at 1s .......................28

Figure 19: Simulation results of the generator response to a three-phase fault.........................................30

Figure 20: Simulation results with high grid impedance .............................................................................31

Figure 21: Simulation results of the generator response to the grid frequency oscillation .........................32

iv
List of Symbols 

di , q Direct-axis and quadrature-axis currents of the generator; i

ud , uq Direct-axis and quadrature-axis voltage of the generator; 

fd i Field winding current of the generator; 

fd e Field voltage applied to the generator; 

di1 , q Direct-axis and quadrature-axis damper winding currents of the generator; i

1

Ra Stator winding resistance of the generator;

Rfd Field winding resistance of the generator;

R1d , R1q Damper winding resistance of the generator; 

Ll Stator winding inductance of the generator; 

Lfd Field winding leakage inductance of the generator; 

L1d , L1q Direct and quadrature damper winding inductance of the generator; 

Lad , Direct and quadrature magnetizing inductances of the generator; Laq

ωr Rotating speed of the generator; 

δ Power angle of the generator; 

Tm Mechanical torque of the generator; 

Te Electromagnetic torque of the generator; 

H Inertia constant of the generator; 

Ψd , Direct and quadrature flux linkage of the generator; Ψq

Ψfd Field flux linkage of the generator; 

Ψ1d , Direct and quadrature damper windings flux linkage of the generator; Ψ1q

VA , VB State variables of the exciter; 

K1 , , Constant gain of the excitation system controller; K2 K3

T1 , T2 , T3 Time constant of the excitation system controller; 

Pref , Reference value for the active and reactive power; Qref

Qe Reactive power output of the generator; 

Vref Reference of the generator terminal voltage; 

v
Vt Terminal voltage of the generator; 

TG Time constant of the prime mover of the generator; 

RG The governor droop constant; 

dR i , D-axis and q-axis currents of the resistance load; qR i

dL i , D-axis and q-axis currents of the inductance load; qL i

dC i , D-axis and q-axis currents of the capacitance load; qC i

 , , R L C Load resistance, capacitance and inductance; 

dm e , D-axis and q-axis components of the induction motor transient stator voltage; qm e

dm i , D-axis and q-axis components of induction motor transient stator current; qm i

X sm Synchronous inductance of the induction motor;

' X sm Transient inductance of the induction motor;

Hm Inertia constant of the induction motor;

D Load model exponent of the motor; 

Tnorm Normal value of mechanical torque of the motor; 

Re , Grid resistance and inductance; Le

∞ V Rms value of the infinite bus voltage; 

α Phase angle of the infinite bus; 

dgrid i , D-axis and q-axis currents flowing into the grid; qgrid i

Gpai , Active power and reactive power AI compensator transfer functions. Gqai

List of Acronyms 

AI Anti-islanding 

AVR Automatic voltage regulator 

DG Distributed generator 

kW Kilowatt 

PI Proportional - Integral 

ROCOF Rate of change of frequency relay 

THD Total Harmonic Distortion

vi
Executive Summary 

This report summarizes the study and development of new active anti-islanding (AI) control schemes for 

synchronous machine-based distributed generators (DGs). These DGs include engine generators (diesel, 

natural gas, biomass, hydrogen) and gas turbines. 

The accomplishments of the work include: 

1. Advancing new AI control schemes that exhibit substantial improvement on non-detection zone for a 

static load, without power quality degradation. The schemes also lower costs and feature robustness 

for system disturbances 

2. Providing design guidelines and evaluating the effectiveness of the new schemes under various load 

conditions 

3. Validating the new anti-islanding control schemes with a time-domain simulation in PSCAD. 

The report presented here is divided into four parts. The first part discusses the modeling of basic system 

components, including the synchronous machine, and the RLC and induction motor loads, and the grid. 

The second part of the report discusses in detail the basic principles and design guidelines of the new AI 

schemes, denoted as active power AI scheme and reactive power AI scheme respectively. Frequencydomain results in MATLAB are used for the analysis. In the third part, time domain simulations are 

carried out using PSCAD to validate the effectiveness of the proposed schemes. Finally, conclusions 

based on the theoretical analysis and the simulation results are provided. The future scope of work along 

with issues to be addressed is also established. 

1
2 
1. Introduction 

The phenomenon of islanding in the presence of distributed generation systems (DGs) requires 

considerable attention due to its potential result in an unsafe operating condition of the system. Almost all 

utilities require that, in case of islanding, generators should disconnect from the grid as soon as possible. 

IEEE standard 1547 stipulates a maximum delay of 2s for detection of an island and also establishes the 

need for proper coordination of the auto-reclosing scheme with the anti-islanding (AI) protection [1]. 

While the past decade has seen the introduction of many new concepts, several outstanding issues remain 

especially with regard to availability of reliable and economical AI schemes for rotating-machine-based 

distributed generators. 

To prevent unintentional islanding, transfer trip is traditionally used, mostly for larger units in megawatt 

ranges. For smaller DGs connected at distribution level, transfer trip is too expensive. Also, an increasing 

number of distribution systems are configured to provide multiple alternate feed points to a particular 

feeder section. Transfer trip can be exceedingly complicated and expensive to implement when trip 

signals from multiple points need to be communicated, as well as the current status of the system 

configuration to determine which trip signal is relevant at any given time. While other low-cost 

communication means and infrastructures are under development, it is always desirable for DG to have 

local intelligence to detect islanding events. 

The most basic and universal means of detecting an island is to establish an under/over frequency and 

under/over voltage window within which a synchronous DG is allowed to operate. When the synchronous 

DG is islanded from the utility system, either due to a fault or other abnormal condition, the frequency 

and voltage will quickly move outside the operating window if there is a significant difference between 

loads and the generation level. For generations that are not designed to export power to the utility 

network, the loss of the grid connection inherently causes power to flow from the generator into the utility 

network to supply other loads left connected to the islanded subsystem. This can be detected using a 

reverse power relay to monitor the power flow in the inter-tie, which can be used to trip the inter-tie 

breaker. 

With large generators, there is a reasonable possibility that the system voltage and frequency will be 

maintained within the specified limits following loss of the grid. Therefore, special means are required to 

detect the loss of the grid. Depending whether there is interaction with the system or not, they can be 

divided into two categories: passive and active. 

Active schemes detect the islanding by directly interacting with the system under consideration. The two 

main methods used for synchronous machines are reactive error export detection and fault level 

monitoring [3-4]. The reactive error export detector controls the embedded generator excitation current so 

that it generates a known value of reactive current, which cannot be supported unless the generator is 

connected to the grid. The fault level monitoring scheme uses point-on-wave thyristor switching, which 

triggers near the voltage zero point, and then measures the current through a shunt inductor, enabling 

calculation of system impedance and fault level. The fault level monitoring scheme provides a very fast 

response to the condition with detection possible in half a cycle. 

Passive devices function by monitoring various system parameters and make their decision to trip without 

directly interacting with the system operation. Typical passive techniques include the rate of change of 

frequency relay (ROCOF) [5-6]; rate of change of output power [7-8]; ratio of the frequency change to 

the output power change [9]; rate of change of voltage and power factor [10]; detection of islanding using 

an elliptical trajectory technique [11]; voltage unbalance; and total harmonic distortion (THD) [12], etc. 

These technologies were developed based on the fact that a loss of the grid will cause variations in system 

3
voltage, current, or frequency under almost all circumstances. Nevertheless, when the amount of power 

mismatch between utility and local load is not significant, it may fail to signal the abnormality. 

The main drawback to the passive schemes is that they cannot effectively differentiate between the loss of 

the grid and other non-islanding transients. Active schemes are more effective and robust than the passive 

schemes, but most existing active schemes have the disadvantages of high cost and degradation of power 

quality. Therefore, it is imperative to find new means of protecting DG against islanding reliably and 

economically. Otherwise, as other technologies in the field of distributed resources are advancing, the 

lack of reliable protection against islanding is impeding the wide deployment of these alternative energy 

resources. 

The objective of this study is to develop new effective AI schemes for synchronous machine-based 

distributed generators. 

4
2. Synchronous Machine and Power System Modeling 

Unintentional islanding is considered undesirable for a number of reasons including worker and public 

safety. The effective detection of islanding is a real issue confronting power system engineers. The worstcase islanding is when the power mismatch between the DG and the load is zero, and the system is 

operating at steady state before islanding. This is the case on which this study will focus. 

Synchronous generators can be analyzed conveniently using the Park’s transformation, which results in a 

time-invariant nonlinear system. A linearized model can be obtained from the time-invariant model at a 

steady-state operating point. In the event that the system experiences a small perturbation, the linearized 

power system models can be used with advantage for both analysis and controller design. Such a linear 

design on a nonlinear system generally provides asymptotic stability over a small region about the 

equilibrium and is appropriate for the dynamic stability problem where the primary concern is providing 

damping following small disturbances. 

 

The mathematical model of a synchronous machine along with various control strategies has been well 

documented in the literature [13]. For completeness, the model of a machine used in the analysis is 

reported here again in detail. The overall control block diagram of machine model is shown in the Figure 

1. The most noticeable feature here is that when the generator is connected to the grid, the main task of 

the generator is to maintain its real and reactive power output as a typical DG operational mode (in some 

cases, instead of reactive power, power factor regulation is used). The regulation of the real power is 

achieved through a feed-forward controller applied to the governor while the regulation of the reactive 

power is carried out through a feedback PI (Proportional-Integral) controller cascaded with the exciter. 

+

Grid

Load

Generator

Qe

Σ PI

Q

Calculation

+

-

LPF

ωr

Σ

Tm

-

+

Prime

Mover

Σ +

Governor

Pref

AVR Exciter

Vref

Vt

Σ

Σ LPF

ω0

+

-

fd e -

+

Vabc

I Qref abc

Figure 1: Synchronous generator system and its control block diagram 

5 
2.1 Synchronous Generator Model for Islanding Studies 

The dynamics of the synchronous machine can be described by a set of nonlinear differential equations. 

Typically, the states can be associated with each machine’s armature currents, rotor currents resolved 

through the Park’s equations, rotor dynamics, automatic voltage regulator (AVR) and the turbinegovernor dynamics. 

In developing the model of a synchronous machine for islanding studies, the following assumptions were 

made. The worst-case islanding is when the power mismatch is small and the system is operating under 

steady-state conditions before islanding. This provides solid justification for the following assumptions: 

1. The air gap flux is distributed sinusoidally along the air gap. 

2. Magnetic hysteresis is negligible. 

3. Magnetic saturation effects are neglected. 

After simplifications, the following set of equations of the machine model can be obtained. 

Voltage equations 

darqdd = pu Ψ −Ψ ω − iR (2.1) 

qardqq = pu Ψ + Ψ ω − iR (2.2) 

fdfdfdfd +Ψ= iRpe (2.3) 

ddd 0 +Ψ= iRp 111 (2.4) 

qqq iRp 111 0 +Ψ= (2.5) 

Flux linkage equations 

dadfdaddladd iLiLiLL 1 )( +++−=Ψ (2.6) 

qaqqlaqq iLiLL 1 Ψ = − + )( + (2.7) 

daddadfdfdadfd Ψ = + )( + 1 − iLiLiLL (2.8) 

daddfdaddfdadd Ψ1 = + ( 1 + ) 1 − iLiiLLiL (2.9) 

qaqqaqqq Ψ = + )( 111 − iLiLL (2.10) 

Air-gap torque 

dqqde = Ψ − Ψ iiT (2.11) 

6
Here the flux is denoted by Ψ. Inductance is denoted by L, and terminal voltage is expressed in the D-Q 

frame [13]. Generally, in case of synchronous machines, the prime mover and other essential mechanical 

assemblies are mounted on the same shaft. Based on the time frame involved, it is fairly a good 

approximation to assume the rotor mass as a rigid body. Hence for the islanding studies, the following 

differential equations are used to represent the synchronous machine rotor dynamics.

)

2

( 2H

1 TT em

dt

d = − δ (2.12)

ωω 0

δ r −= dt

d (2.13) 

where: 

di and q are direct-axis and quadrature-axis currents of the generator; i

ud and are direct-axis and quadrature-axis voltage of the generator; q u

fd i is field winding current of the generator; 

fd e is field voltage applied to the generator; 

di1 and q are direct-axis and quadrature-axis damper winding currents of the generator; i

1

Ra is stator winding resistance of the generator; 

Rfd is field resistance of the generator; 

R1d and are damper winding resistance of the generator; R1q

Ll is stator winding inductance of the generator; 

Lfd is field leakage inductance of the generator; 

L1d and, are direct and quadrature leakage inductance of the generator; L1q

Lad and are direct and quadrature magnetizing inductance of the generator; Laq

ωr is rotating speed of the generator; 

δ is power angle of the generator; 

Tm is mechanical torque of the generator; 

Te is electromagnetic torque of the generator; 

H is inertia constant of the generator; 

Ψd and are direct and quadrature flux linkage of the generator; Ψq

Ψfd is field winding flux linkage of the generator; 

Ψ1d and Ψ1q are direct and quadrature damper winding flux linkage of the generator. 

7
Based on equations (2.1)–(2.13), an equivalent circuit of the synchronous machine can be developed as 

shown in the Figure 2. 

d u

Efd

Ra Ll

Lad

R1d

+ -

ω ψ qr

L1d

Lfd

Rfd

+

-

di

d i1 fd i

(a) d-axis equivalent circuit 

q u

Ra Ll

Laq

L1q

R1q

+ - ω ψ dr

+

-

qi

q i1

(b) q-axis equivalent circuit 

Figure 2: Synchronous generator d- and q-axis equivalent circuits 

2.2 Excitation System Model and Reactive Power Regulation 

Most generators are equipped with an AVR. These devices maintain the terminal voltage of the generator 

at a specified value by modulating the field voltage and hence the field current to supply the required 

reactive power to the load. However, as a distributed generation, the voltage regulation is prohibited by 

IEEE 1547, unless special agreements are made. A common operation mode for DG is reactive power (or 

power factor) regulation. 

The exciter systems widely used for synchronous machines are commonly subdivided into the four 

different categories. More detailed aspects of modeling an excitation system for simulation studies can be 

found in [14]. For simplicity of analysis in the time frame involved, the excitation system here is 

represented as a tuned PI controller with a necessary lag circuit. The parameters of the circuit model are 

approximated from the aggregate response of terminal voltage of a generator. Figure 3 shows the model 

of the excitation system used for the machine simulation. A feedback PI controller is cascaded with the 

exciter to regulate the reactive power of the machine. Therefore, when the grid is connected, the reactive 

power output of the machine will follow the desired reference value. The parameters of the PI controller 

are given in the Appendix of this report. 

8
+

-

33

1

K + sT

-

+

K2

+

+

1 sT

1

Σ Σ

VA Vt

Vref

Qe

Qref

VB

fd e K1

2 sT

1

+

+

Σ Σ

Reactive Power

Regulation

AVR

Exciter

Figure 3: Control block diagram of excitation system 

The description of the reactive power regulator and the exciter is given by: 

1 −= erefA /)( TQQV& (2.14) 

1 2 [ AtrefB −++−= eref /)]( TQQKVVVV& (2.15) 

23 1 3 [ ( /))]( TQQKVVVKeKVe fdBfd Atref −++−+−= eref & (2.16) 

where: 

VA and are the intermediate variables indicated in Figure 3; VB

K1 , and are constant in the controller; K2 K3

T1 , and are time constant in the controller; T2 T3

Qref is the reference value of the reactive power; 

Qe is the reactive power output of the generator; 

Vref is the reference for the terminal voltage; 

Vt is the terminal voltage of the generator; 

fd e is the field voltage as the input to the generator. 

2.3 Governor Model and Active Power Regulation 

The governor system consists of a prime mover and provides the necessary mechanical power required by 

the generator. The governor is represented by a droop function with input and the prime mover is 

described by a lag function. Figure 4 shows the typical representation of a governor and the real power 

regulation for these islanding studies: 

Pref

9
ω0 -

+

Tm +

Pref

1+ sTG

1

+

ωr

RG Σ − /1 Σ

Governor Prime

Mover

Figure 4: Control block diagram of governor 

The governor dynamics is (including the prime mover) 

( ) 1 0

m

G

r

ref

G

m T

R

P

T

T − − +=

ω ω & (2.17) 

where: 

TG is the time constant of the prime mover of the generator; 

RG is the governor droop. 

2.4 RLC Load Model and Induction Motor Load Model 

Load characteristics have an important influence on the dynamical behavior of the generator when it is 

islanded. The modeling of actual loads is complicated because a typical load bus is composed of a large 

number of devices, such as fluorescent and incandescent lamps, refrigerators, heaters, compressors, 

motors, furnaces, and so on. Based on a considerable amount of simplification, two types of the loads are 

most often investigated in the islanding studies: a RLC load and an induction motor load. 

The RLC load is as simple as the aggregation of a resistor—an inductor and a capacitor in parallel. While 

such a load can represent the steady-state fundamental frequency characteristics of an actual load, this 

type of model is not a realistic representation of a load because the dynamic and non-fundamental 

characteristics of actual loads are not accurately simulated. Given the terminal voltage, the current 

through the resistance, inductance and the capacitance is determined by the following equations. 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

dL

qL

q

d

qL

dL

i

i

u

u

i L

i

dt

d

ω

1

 (2.18) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

qc

dc

d

q

qC

dC

i

i

u C

u

u

u

dt

d 1

ω (2.19) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

q

d

qR

dR

u

u

R

i

i

/1 (2.20) 

where: 

10
dR i , and are the d-axis and q-axis currents through the load resistance, inductance and 

capacitance, respectively 

qR i dL i qL i dC i qC i

ud are d-axis and q-axis terminal voltage q u

R , L , andC are the value of load resistance, capacitance and inductance, respectively. 

The RLC load equivalent circuit in DQ is shown in Figure 5. 

d u

+

+

-

ωLiqL

R

- ωCu q

q u

+

+

-

- ωLidL R ωCud

L

L

C

C

Figure 5: DQ equivalent circuit model of RLC load 

Typically, motors consume 20% to 70% of the total energy supplied by a feeder. Therefore, the dynamics 

attributable to motors are usually the most significant aspects of dynamic characteristics of the overall 

system load. Motor loads, however, vary largely in characteristics due to different applications. The motor 

load used in the simulation studies described in this report is a compromise; it is intended to represent a 

general population of motors ranging in types from those in small residential/industrial applications to 

large motors. The default motor load uses only a single-cage representation. This is adequate for dynamic 

stability studies where damping of oscillations, rather than stalling of motors and motor starting, is the 

main focus. 

The induction motor to be studied is represented by a standard single-cage model with the transient 

variations of its rotor flux linkage handled explicitly. The motor can be described by performance-based 

parameters or equivalent circuit parameters. The driven load is characterized by the inertia constant 

of the combined motor-load rotor and the exponent D, relating driven load to its speed. The detailed 

modeling of the motor load can be found in reference [15]. The dynamics of the induction motor is 

described by 

Hm

11
dm dm sm qmsm qmrepiXXe T

e ))(( +−+−= θ 1 '

'

0

& (2.21) 

qm qm sm dmsm dmrepiXXe T

e ))(( −−−−= θ 1 '

'

0

& (2.22) 

m D (2 dmdmqmqmmm TieieH norm )()

ω0

ω

ω& −+= (2.23) 

where: 

dm e , are D-axis and q-axis components of the motor transient stator voltage; qm e

dm i , are D-axis and q-axis components of the motor transient stator current; qm i

X sm is the motor synchronous inductance; 

' X sm is the motor transient inductance; 

Hm is inertia constant of the motor; 

D is load model exponent of the motor; 

Tnorm is normal value of mechanical torque of the motor; 

ωm is rotating speed of the motor. 

Figure 6 shows the DQ equivalent circuit of the induction motor. 

dm i '

sm − XX sm

sT

' 1 0

1

+

qm e

qmi

dm e

+

d u

+ +

-

sm qm iX '

-

q u

+

-

+ -

Rsm

Rsm

sm dm iX '

dm e

qm e

+

+

-

-

'

00 m −ωω )( T

'

00 m −ωω )( T

sT

' 1 0

1

+

' X sm

' X sm

dm i

qm i

Σ

' Σ sm − XX sm

+

- -

Figure 6: DQ equivalent circuit model of induction motor 

12
2.5 Grid Model 

Since the synchronous machine is connected to an infinite bus, the d-q terminal voltage of the machine 

are constrained by the grid voltage, described in DQ frame below: 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− −⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ∞

)cos(

)sin(

αδ

αδ

ω V

i

i

L

i

i

L

i

i

R

u

u

dgrid

qgrid

e

qgrid

dgrid

e qgrid

dgrid

e q

d

&

&

 (2.24) 

where: 

Re and are the grid resistance and inductance respectively; Le

∞ V is the rms value of the bus voltage and α is its phase angle; 

dgrid i and are the d-axis and q-axis currents flowing into the grid. qgrid i

Figure 7 shows the grid DQ equivalent circuit. 

d u

+

+

-

e qgrid ω iL

-

q u

+

-

Le Re

+ -

Re

sin( +αδ ) ∞ V

cos( +αδ ) ∞ V

Le e dgrid ω iL

+

+

-

-

dgrid i

qgrid i

Figure 7: DQ equivalent circuit model of grid 

2.6 Small-Signal Analysis 

In the preceding section, we have developed the equivalent DQ circuit model for the generator, load and 

the grid respectively. The equivalent circuit of the overall system to be studied can be easily obtained by 

combining those components together. One circuit model of such a system consisting of the DG and the 

RLC load, and the grid is shown in Figure 8. This equivalent circuit is highly nonlinear and crosscoupled. If the perturbation applied to the power system is small, the linearized model, also called smallsignal model, can be obtained by linearizing the equations from (2.1) to (2.24) around an operation point. 

Therefore, the highly nonlinear model can be greatly simplified and the dynamical characteristics of the 

power system can be approximately analyzed from the small-signal model. 

13
e qgrid ω iL

q u

- +

+ -

Re

sin( +αδ ) ∞ V

cos( +αδ ) ∞ V

Le e dgrid ω iL

+

-

Lad

ω ψ qr Lfd

Ll Ra

Laq

L1q

R1q

ω ψ dr

d u

+ - -+

Re Le

+

-

Ll

Ra

R1d

L1d

Efd

Rfd

+ ωLiqL

R

- ωCu q

+ ωLidL - R ωCud

L

L

C

C

di

qi

dL i

qL i

dgrid i

qgrid i

Generator RLC Load Grid

Figure 8: DQ equivalent circuit model of the overall system 

14
3. Anti-Islanding Concept and Implementation 

3.1 Introduction of Positive Feedback 

The proposed AI schemes for the synchronous machine DG are implemented on the basis of a positive 

feedback. The principle behind the method is to destabilize frequency or voltage by introducing positive 

feedback. This results in under/over frequency or voltage trip vary quickly once the DG is islanded. In the 

presence of the grid, the positive feedback will have little effect on the grid frequency or voltage 

regulation. In contrast to the passive methods, these active schemes can detect islanding effectively and 

reliably without causing false trip. 

Although the positive feedback concept has been successfully used for the inverter-based DG for AI 

protection, the application of the concept to synchronous machine has not yet been explored extensively. 

Typically, a rotating-machine-based DG is characterized by higher inertia—longer time constants than an 

inverter-based DG. Due to these factors, the machine and the inverter-based DG respond in fundamentally 

different ways. 

In support of the design and implementation, both frequency-domain and the time-domain analysis are 

conducted to provide the insights into the characteristics of the proposed schemes. 

3.2 Implementation of the Active/Reactive Power Schemes 

The positive feedback for the synchronous machine comes in two different ways, denoted as active power 

AI scheme and reactive power AI scheme, because the feedback modifies the active power and reactive 

power references, respectively. The structures of the active and reactive power AI scheme are shown in 

Fig. 3-1. The active power AI compensator takes the variations in the frequency as input to modify the 

active power reference to the DG. The reactive power AI compensator uses the variation in the voltage 

magnitude to change the reactive power reference. 

15
+

Grid

Load

Generator

Qe

Σ PI

Q

Calculation

Qref

+

-

LPF

ωr

Σ

Tm

-

+

Prime

Mover

Σ +

Governor

+ Pref

AVR Exciter

Vref

Vt

Σ

qai sG )( Σ LPF

sG )( pai

ω0

+

-

fd

+ e -

+

Vabc

I

abc

Figure 9: Schematic of the machine with the AI compensators 

The AI compensators both consist of a washout filter and a proportional gain. The washout filter is 

designed to ensure that the AI compensators only react to the transient of the frequency/voltage, but not 

causing any DC steady-state error. When there is a voltage or frequency variation, the responses of the AI 

loop will amplify the voltage or frequency variation in the same direction. Therefore, the loops are called 

positive feedback. The mechanism can be further illustrated below. 

When there is a generator terminal voltage variation, for instance, voltage increases slightly, and the 

reactive power reference will be increased due to the reactive power AI loop, which will lead to a boosted 

voltage reference, thus causing the terminal voltage to further increase. When properly designed, the 

effect of the reactive power AI loop is insignificant when the grid is connected because the grid will 

regulate the terminal voltage magnitude. Once grid is lost, the reactive power AI loop becomes dominant 

and drives the voltage away from nominal. 

A similar mechanism applies to the frequency. When there is a generator speed (frequency) variation, e.g., 

when frequency increases slightly (due to under loading), the active power reference will be increased due 

to the active power AI loop, which will further generate a greater mechanical torque (resulting in more 

under loaded), causing higher speed (frequency). When properly designed, the mechanism will create this 

instability only in an islanded system and cause a frequency relay to trip. 

In summary, the main idea is that the active/reactive power AI compensators have a dominant effect in 

the frequency/voltage oscillations when the grid connection is lost. But, with a proper design, these 

destabilization effects are negligible, when the machine is connected to the grid. 

16
3.3 Design Guideline Based on Frequency-Domain Analysis 

The basic principles of the positive feedback for islanding detection have been introduced. This section 

will emphasize on the design and implementation of the AI compensator. In order to illustrate the design 

guideline, a loop gain concept is used. MATLAB is used for the following frequency-domain analysis. 

+

Vabc

I

abc

Grid

Load

Generator

Qe

Σ PI

Q

Calculation

Qref

+

-

LPF

ωr Σ

Tm

-

+

Prime

Mover

Σ +

Governor

+

Pref

AVR Exciter

Vref

Vt

Σ

Σ LPF sG )( qai

sG )( pai

ω0

+

-

fd e

+ -

+

qin

qout

pin

pout

Figure 10: Schematic of the machine with the AI loops opened 

The loop gains of the active and reactive AI loops can be measured by breaking the loops, shown in 

Figure 10, where pin and pout are at the breaking point for the active power loop, while qin and qout are for 

the reactive power loop. The loop gain is defined as the small-signal transfer function from the 

perturbation signal pin (or qin) to the output pout (or qout). Therefore, the active power loop gain is given by: 

in

out

p p

p sT )( = (3.5) 

Similarly, the reactive power AI loop gain is defined as the small signal transfer function from the 

perturbation signal from to the output . qin qout

in

out

q q

q sT )( = (3.6) 

From the loop gain, the system dynamics can be characterized by, for example, the stability margins. For 

AI control, the design principles are: 

17
(1) When the grid is connected, the loop gain should indicate a stable system, i.e., the peak of the AI 

loop gain must be less than 0dB. The lower the loop gain is below 0dB, the less impact of the AI 

loop on the DG’s normal grid-connected operation. 

(2) When the grid is disconnected, the loop gain should indicate an unstable system, i.e., the peak of 

the AI loop gain must be greater than 0dB, while the phase is lagging more than 180 degrees. The 

unstable system will ensure that the islanded system can be detected even when there is 100% 

active and reactive power matching. The higher the loop gain, the more quickly the island voltage 

or frequency will move outside the normal operational windows to trigger voltage or frequency 

protection. However, on the other hand, the gain should not be too high to insure that criterion (1) 

is met. Basically, criterion (1) sets the upper bound of the loop gain, while criterion (2) sets the 

lower bound of the loop gain. 

If both criteria are satisfied, the AI compensator will amplify the frequency/voltage transients when the 

machine is islanded but with minimal effect on the frequency/voltage dynamics when the grid is 

connected. 

1( )( )1 1 sTsT

sT K w

w

++

sG )( pai

∆ω ∆p

(a) Active power AI compensator 

1( )( )1 1 sT sT

sT K

w

w

++

sG )( qai

∆V ∆q

(b) Reactive power AI compensator 

Figure 11: Active and reactive AI compensators 

Figure 11 shows the formula of the active/reactive power AI compensator. The AI compensator basically 

consists of a washout filter, a gain and a first-order filter. The crucial step in the design is to determine the 

setting for the active/reactive power AI compensator. The critical settings include: 

(1) The corner frequency of the washout filter, TW

(2) The gain, K 

(3) The low pass filter conner frequency T1.

The washout function serves as a high-pass filter, with a time constant to allow signals with frequency 

higher than 1/ to pass. For the signal with frequency lower than 1/ , especially for DC signal, will be 

attenuated by the washout filter. This is to minimize the AI loop impact on the steady-state regulation. 

The low pass filter corner frequency T1 is set to attenuate high-frequency noise. The combined washout 

filter and the low-pass filter constitute a band-pass filter. The selection of gain, K is a compromise 

between the high enough gain to ensure islanding detection quickly and the low enough gain to have 

minimal impact on the DG under the grid-connected conditions. The gain selection should leave certain 

margins for both grid-connected and islanded conditions. 

TW

TW TW

18
3.4 Practical Design Considerations 

The basic criteria for the AI design have been discussed. However, the parametric design of the AI 

compensator is still an issue since the active/reactive power loop gains may vary with the different load 

conditions. In order to ensure that the AI control is effective under all circumstances, the AI compensator 

must be designed under the worst-case situation. The critical gain can only be approximately determined 

after the study of a range of different load conditions. Consequently, the impact of the various passive and 

motor load conditions on the loop gains must also be examined. The preliminary study concludes that the 

situations important to this AI scheme design are those where the grid impedance is high or there is a high 

penetration of induction motor load. 

After the worst cases have been identified, the active and reactive power AI compensators are chosen as 

in (3.7) and (3.8), respectively. 

)29.01)(32.01(

1.61

ss

p s

++ = ∆

∆

ω

 (3.7) 

)016.01)(048.01(

41.2

ss

s

V

q

+ + = ∆

∆ (3.8) 

When the analysis of the loop gains are carried out in the following, it is assumed that 

1. The power output of the machine and the local load are closely matched. 

2. The machine operates at a power factor of 1.0 (due to the choice of the RLC load with unity power 

factor). 

3. The loss of the grid is caused by the tripping of the utility breaker at a moment when the system is 

operating at steady state. 

With these assumptions, the impact of four different factors (power level, load quality factor, motor load 

and grid impedance) on the proposed AI schemes is investigated. 

3.4.1 Power Level 

In order to examine the impact of the different power level on the loop gain, the generator active power, 

which matches the active power of the RLC load (with =1.8), is varied from 30% to 90%. The Bode 

plots of the loop gains under different power levels are shown in Figure 12. 

Qf

19
10-2 10-1 100

-80

-60

-40

-20

0

Active Power Loop Gain Without Compensator

Magnitude (dB)

10-2 10-1 100 -60

-40

-20

0

20

Active Power Loop Gain With Compensator

Frequency(Hz)

Magnitude (dB)

(a) (b) 

(c) 

(d) (e) (f) 

(a) (b) 

(c) 

(d) (e) (f) 

 

10-1 100101 -80

-60

-40

-20

0

Reactive Power Loop Gain Without Compensator

Magnitude (dB)

10-1 100101

-40

-20

0

20

Reactive Power Loop Gain With Compensator

Frequency(Hz)

Magnitude (dB)

(a) 

(b) 

(c) 

(e) (d) (f) 

(a) (b) 

(c) 

(d) (e) (f) 

(i) Active power loop gains (ii) Reactive power loop gains 

[(a) (b) (c) Grid-connected 30% power; 60% power; 90% power, (d) (e) (f) Grid-disconnected 30% power; 

60% power; 90% power] 

Figure 12: Loop gains with different generator output power 

Without any compensator, both the active power and reactive power loop gains are much less than 0dB,

under both grid connected [cases (a)(b)(c)] and islanded conditions [cases (d)(e)(f)]. The gain below 0 dB 

even when the grid is disconnected (cases (d)(e)(f)) implies that the isolated DG and load system is stable, 

thus can be islanded. It is consistent with the time-domain simulation results in a later section that show, 

without any compensator, the islanding can be easily sustained. 

The loop gains difference between grid-connected [(a)(b)(c)] and islanded [(d)(e)(f)] is due to the system 

structural change. One has a grid with relatively low impedance. The islanded system has no grid 

connected, or, equivalently, a grid with infinite impedance. 

After being compensated, both the active power and reactive power loop gains are reshaped (the bottom 

two figures in Figure 12). The compensator design should be such that, the grid-connected loop gains 

[cases (a)(b)(c)] are below 0dB in order to keep the system stable, while the islanded loop gains [cases 

(d)(e)(f)] are above 0dB in order for effective AI detection. For the purpose of illustration, the peak value 

of the open loop gain is denoted as , and the corresponding frequency is called . Basically and 

 together determine the dynamic characteristics of the AI control. From the design point of view, the 

larger and , the stronger dynamics of the islanded system. However, there are some fundamental 

limits on the maxima of and . For the active power AI scheme [Figure 12 (i) bottom figure], the 

limit on is due to the inertia of the DG. In this design, under the grid-disconnected condition is 

about 0.3Hz. This small indicates the slow response of the active power AI scheme to the loss of the 

Gp Fp Gp

Fp

Fp Gp

Gp Fp

Fp Fp

Fp

20
grid. In order to overcome the slow response due to small , a high gain is necessary so that the 

frequency can be effectively driven out of the normal range for a given time. However, a high gain may 

potentially cause the DG instability, which sets the upper bound of the loop gain. 

Fp Gp

From the Bode plot shown in Figure 12 (ii) bottom figure, it can be seen that the of the reactive power 

AI loop gain is around 2.5Hz. In this case, the gain can be lower than the gain for the active power 

loop gain. This indicates that the reactive power AI scheme can respond faster than the active power AI 

scheme. 

Fp

Gp

Another observation is that, once the rotating-machine-based DG is islanded, the difference in the loop 

gain due to the different power levels is insignificant while the previous study has shown that the loop 

gain of an inverter-based DG is very sensitive to the load power level [16]. 

3.4.2 Quality Factor 

The loop gains with the different quality factors, =0.0 and =1.8, are compared with each other in 

Figure 13. The quality factor of a RLC load is defined as the ratio of the reactive power stored in the load 

inductor or capacitor to real power consumed by the resistor. For a load with fixed active power, the 

different quality factors imply varying the reactive power of the load, i.e. inductance and capacitance. 

Usually, a load with the quality factor of 1.8 is considered an extreme case for the islanding study. From 

Figure 13, it can be seen that the loop gains vary little with different quality factors for both gridconnected ((a)(b)) and islanded ((c)(d)) conditions. This is again quite different from the case in the 

inverter-based DG. The fundamental reason is the inertia difference. Generally, represents the load 

inertia. The machine-based DG has large inertia and dominates the overall DG/load system inertia. As a 

result, different Qf makes little difference in the system dynamics. 

Qf Qf

Qf

10-1 100 -30

-20

-10

0

10

20

30

Active Power Loop Gain With Compensator

Magnitude (dB)

Freqency(Hz) 

(a) (b) 

(c) (d) 

 100

10

1 -50

-40

-30

-20

-10

0

10

Reactive Power Loop Gain With Compensator

Magnitude (dB)

Frequency(Hz) 

(a) 

(b) 

(c) (d) 

(i) Active power loops (ii) Reactive power loop gains 

((a) (b) Grid-connected =0.0 and =1.8, (c)(d) Grid-disconnected =0.0 and =1.8) Qf Qf Qf Qf

Figure 13: Loop gains with different quality factors 

21
3.4.3 Grid Impedance 

The impact of the AI scheme on the grid stability is also investigated. With different grid impedance, 

especially high grid impedance (weak grid), the AI schemes may cause a stability issue (islanding is 

actually a special case with infinite grid impedance). Therefore, it is necessary to investigate its impact 

and specify its application limits. 

 

The active and reactive power AI loop gains have been evaluated for the varying grid impedance from 5% 

to 40% (on the base of the DG power rating), as shown in Figure 14. It can be seen that the gridconnected active/reactive power AI loop gains [cases (a)(b)(c)] increase with the increasing grid 

impedance. When the grid impedance is approaching 40% (a rare but possible case), the system becomes 

marginally stable. Another observation is that the reactive power loop gains are more sensitive to the grid 

impedance than the active power loop gains. 

As far as grid impedance is concerned, islanding is actually a special case that has infinite grid impedance. 

Between the infinite grid impedance (islanded) and finite grid impedance (grid-connected), the active AI 

controls always have certain design room by choosing appropriate gain so that their loop gains is 

separated by 0dB. The higher the grid impedance, however, will result in less design margins. Without 

sufficient margins, the system may risk instability. 

10-210-1100101 -100

-80

-60

-40

-20

0

20

40

Active Power Loop Gain With Compensator

Magnitude (dB)

Frequency(Hz)

(a) (b) 

(c) 

(d) (e) (f) 

 10-2

10-1100101102 -100

-80

-60

-40

-20

0

20

Reactive Power Loop Gain With Compensator

Magnitude (dB)

Frequency(Hz) 

(a) 

(b) 

(c) 

(d) (e) (f) 

(i) Active power loop gains (ii) Reactive power loop gains 

 [(a) (b) (c) Grid-connected Xe=0.05 p.u.; Xe=0.2 p.u.; Xe=0.4 p.u. (d)(e)(f) Grid-disconnected Xe=0.05 

p.u.; Xe=0.2 p.u.; Xe=0.4 p.u.] 

Figure 14: Loop gains with different grid impedance 

3.4.4 Motor Load 

Induction motors constitute major part of the distribution load. Studies [15] show that the most important 

sensitivity influencing the system dynamics is the percentage of motors in a feeder. Variations in the 

motor inertia and impedances are not as great an influence on the system dynamics as the percentage of 

motors. The effects of the motor load on active/reactive power loop gains are evaluated when the load is 

composed of an induction motor (H=0.5MW/MVA, Power Rating=150kVA, comparable to the generator 

rating) and a capacitor for power factor correction. 

22
Figure 15 shows the loop gains comparison between RLC load and motor load (with capacitor), both at 

unity power factor with the same power level. It can be seen that the active power loop gain of the 

induction motor load (Figure 15 (i) ((b)(d)) is lower than the loop gain with the RLC load (Figure 15 (i) 

((a)(c)). It implies that the dynamics of the islanded system is slowed down by the induction motor load. 

In contrast, the reactive power AI scheme is still very effective with the motor load, shown in Fig. 3-7 (ii). 

It indicates that, the motor load is a worse case than RLC load for the active power scheme. For reactive 

power scheme, however, the motor load is easier to detect than RLC load. 

10-2 10-1 100

-60

-40

-20

0

20

Active Power Loop Gain With Compensator

Magnitude (dB)

Frequency(Hz) 

(a) (b) 

(c) 

(d) 

 10-1 100

101 -50

-40

-30

-20

-10

0

10

20

30

Reactive Power Lopp Gain With Compensator

Magnitude (dB)

Frequency(Hz) 

(a) 

(b) 

(c) (d) 

(i) Compensated active power loop gains (ii) Compensated reactive power loop gains 

 [(a) (c) Grid-connected/disconnected RLC load(P=0.54 p.u. and =1.8) (b) (d) Gridconnected/disconnected motor load(P=0.54 p.u., Q=0.34 p.u. and C=600μF)] 

Qf

Figure 15: Loop gains with RLC and motor load 

3.4.5 Conclusions 

In this chapter, we have investigated the dependence of the AI loop gains on various factors such as 

power output of the DG, quality factor, grid impedance, and motor loads. The effectiveness of both 

schemes is insensitive to power level and quality factor. The active power scheme is less effective with 

motor load than with RLC load, while the reactive power scheme is effective for both load conditions. 

When grid connected, the reactive power scheme is more sensitive to the grid impedance than the active 

power scheme. With the higher grid impedance, the stability margin of the reactive power scheme is 

reducing quicker than the active power scheme. 

23
4. Performance Evaluation with Time-Domain Simulations 

In the preceding chapter, the basic principles and design guidelines of the proposed two AI schemes have 

been discussed. In this section, time-domain simulations are carried out using PSCAD to validate the 

proposed schemes and to evaluate their effectiveness. The parameters of the DG and the load used in the 

simulations are given in the Appendix. The system used in the simulation consists of the grid, the 

synchronous generator, and the RLC or motor loads. A constant voltage source behind impedance is used 

to represent the grid. The local load and the DG are closely balanced. The loss of the grid is due to the trip 

of a utility breaker at steady state, and this is considered as the worst case for islanding detection. 

The performance of the AI schemes is evaluated for both a static load and the induction machine load. For 

all islanding simulations, the grid is disconnected at t=1s. 

4.1 Performance Evaluation With RLC Load 

4.1.1 Case 1: Baseline without AI Scheme 

Before evaluating the performance of the proposed AI schemes, a baseline case without any AI schemes 

is simulated, shown in both Figure 16 and 17. The DG is operating at 88 kilowatts (kW), 60% of its rated 

power. The RLC load is 88 kW with quality factor Qf=1.8. Since the load and the DG are closely 

matched, the island can be sustained after the loss of the grid, because the variation in the frequency and 

the terminal voltage is so small that any passive scheme may not detect the islanding. 

4.1.2 Case 2: Active Power Scheme with Qf=1.8 

The same DG output and load conditions, but with the active power AI scheme enabled, have been 

simulated. The simulation results are shown in Figure 16 (case 2). After the grid disconnection at t=1s, 

the frequency drifts quickly (within 2s) to go out of normal ranges (Figure 16(b)), while the voltage 

magnitude almost remains unchanged [Figure 16(a)]. Therefore, the active power AI scheme dominates 

the frequency dynamics, but has little effect on excitation (voltage) dynamics. Figure 16(c) shows the 

field voltage dynamics after islanding. Figure 16(d) shows the AI compensator output. 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.90

0.95

1.00

1.05

1.10 case 1

 case 2

 case 4

Voltage Magnitude(p.u.)

Time(seconds)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

58.4

58.6

58.8

59.0

59.2

59.4

59.6

59.8

60.0

60.2

 case 1

 case 2

 case 4

Frequency(Hz)

Time(seconds)

(a) Terminal voltage (b) Frequency 

24 
0.0 0.5 1.0 1.5 2.0 2.5 3.0

1.0

1.1

1.2

1.3

1.4

1.5

1.6

 case 1

 case 2

 case 4

Field Voltage(p.u.)

Time(seconds)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

 case 1

 case 2

 case 4

Output of Active Power AI Compensator(p.u.)

Time(seconds)

(c) Field voltage (d) AI compensator output 

 (Case 1: baseline without AI scheme P=88kW and Qf=1.8; Case 2: active power AI scheme with P=88kW 

and Qf=1.8; Case 4: active power AI scheme with P=88kW and Qf=0.0) 

Figure 16: Simulation results of the active power scheme in response to islanding at 1s 

4.1.3 Case 3: Reactive Power Scheme with Qf=1.8 

Figure 17 shows that simulation results with the reactive power scheme is enabled. It can be seen that 

after islanding, the frequency [Figure 17(b) and the terminal voltage (Figure 17(a)] oscillate away quickly. 

The changes in frequency are caused by the fluctuating active power of the load when the terminal 

voltage is varying. In this case, the detection of the islanding can be triggered by either under/over 

frequency or an under/over voltage relay. Figure 17(c) shows the field voltage, which is saturated at 2 p.u., 

but the scheme is still effective. 

4.1.4 Case 4: Active Power Scheme with Qf=0.0 

Figure 16 also shows the simulation results for a resistive load only (Qf=0) (case 4) and with the active 

power AI scheme enabled. Compared with the simulation results for the load with Qf=1.8 (case 2), the 

difference between the variations in the frequency and terminal voltage is negligible. This is well 

consistent with the analysis in the frequency domain. 

4.1.5 Case 5: Reactive Power Scheme with Qf=0.0 

Figure 17 shows the simulation results for a resistive load only (Qf=0) (case 5) , and with the reactive 

power AI scheme also enabled. Compared with the simulation results for the load of (Qf=1.8) (case 3), the 

variations in the frequency [Figure 17(b)] and the terminal voltage[Figure 17(a)] 0 magnitude are only 

slightly different. It indicates that Qf has only a little impact on the reactive power AI scheme. This is also 

consistent with the analysis in the frequency domain. 

25
0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

 case 1

 case 3

 case 5

Voltage Magnitude(p.u.)

Time(seconds) 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

59.0

59.5

60.0

60.5

61.0

61.5

62.0

62.5

 case 1

 case 3

 case 5

Frequency(Hz)

Time(seconds)

(a) Terminal voltage (b) Frequency 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

 case 1

 case 3

 case 5

Field Voltage(p.u.)

Time(seconds) 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-12

-10

-8

-6

-4

-2

0

2

4

6

8

 case 1

 case 3

 case 5

Output of Reactive Power AI Compensator(p.u.)

Time(seconds)

(c) Field voltage (d) AI compensator output 

(Case 1: baseline without AI scheme P=88kW and Qf=1.8; Case 3: reactive power AI scheme with 

P=88kW and Qf=1.8; Case 5: reactive power AI scheme with P=88kW and Qf=0.0) 

Figure 17: Simulation results of the reactive power scheme in response to islanding at 1s 

26
4.2 Performance Evaluation with Induction Motor Load 

As indicated in the previous section, motors form a major portion of system loads. Hence, it is important 

to investigate the motor load impact on the islanding protection. In this study, a generic induction motor is 

modeled to represent a general population of motors ranging in types from those in small 

residential/industrial applications to large motors. Studies [15] show that the most important sensitivity 

influencing the system dynamics is the percentage of motors at the load bus. Variations in the motor 

inertia and impedances are not as great an influence on the system dynamics as the percentage of motors. 

Here, the extreme case with 100% penetration of induction motor load (H=0.5MW/MVA, Power 

Rating=150 kVA) is simulated to evaluate its impact on the performance of the AI schemes. In the 

simulation, a capacitor is connected in parallel to the motor so as to compensate the reactive power of the 

induction motor. 

4.2.1 Case 6: Baseline without AI Scheme and with Induction Motor Load 

Before evaluating the performance of the proposed AI scheme for the induction motor load, a baseline 

case without any AI scheme is simulated, shown in Figure 18 (case 6). Since the power mismatch 

between the generator output and the motor load is very small, the initial oscillation of the islanded 

system is small and slow. However, the islanded system drastically changes its behavior after 

approximately 3 seconds of islanding. The voltage magnitude continues to drop so that the islanding 

cannot be sustained indefinitely. 

Although the islanded system with the motor load seems to be unstable eventually, the detection of the 

islanding within 2 seconds is still difficult with the motor load due to its slow response in the first few 

seconds. 

4.2.2 Case 7: Active Power AI Scheme with Induction Motor Load 

The same conditions have been simulated except that the active power scheme is enabled and the 

simulation results are also shown in Figure 18 (case 7). Compared with the previous simulation results for 

RLC load, the active power AI scheme for the induction motor is not as effective as for the RLC load. In 

this case, actually, it fails to detect the islanding within a 2-second time window because the voltage and 

frequency are still within the normal ranges. This is consistent with the frequency-domain analysis. 

4.2.3 Case 8: Reactive Power AI Scheme with Induction Motor Load 

The same conditions have been simulated except that the reactive power scheme is enabled, and the 

simulation results are shown in Figure 18 (case 8). In this case, the voltage magnitude oscillates 

dramatically due to the reactive power AI scheme. The islanding can be easily detected by an overvoltage relay. The frequency also drifts away quickly. It concludes that the reactive power scheme is more 

effective for motor load than the active power scheme. The same conclusion is drawn in the frequencydomain analysis. 

27
01234567

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

 case 6

 case 7

 case 8

Voltage Magnitude(p.u.)

Time(seconds)

01234567

59

60

61

62

63

64

 case 6

 case 7

 case 8

Frequency(Hz)

Time(seconds)

(a) Voltage magnitude (b) Frequency 

01234567

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

 case 6

 case 7

 case 8

Field Voltage(p.u.)

Time(seconds)

0123456

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0 case 7

Output of Active Power AI Compensator(p.u.)

Time(seconds)

-10

-8

-6

-4

-2

0

2

4

6

8

10

 Output of Reactive Power AI Compensator(p.u.)

 case 8

(c) Field voltage (d) AI compensator output 

(Case 6: baseline without any AI scheme for the Induction motor load; Case 7: active power AI scheme 

for the induction motor load; Case 8: reactive power AI scheme for the induction motor load) 

Figure 18: Simulation results with the induction motor load in response to islanding at 1s 

28
4.3 Performance Evaluation When the Grid Is Connected 

In the preceding section, the AI control performance of the active power and reactive power AI schemes 

have been demonstrated. Another major issue related to the performance of the AI schemes is the 

potential impact on the DG’s normal operation under the grid-connected conditions. The following study 

will simulate a range of situations including oscillation in the grid frequency, a low voltage event and 

high grid impedance to investigate whether the proposed AI schemes have a significant impact or not. 

4.3.1 Grid Disturbances 

A robust AI scheme must distinguish between the actual loss of the grid and a grid disturbance with 

increasing penetration, distributed generation may become an integral part of the overall power generation 

system. Therefore, an unexpected tripping off line from the DG may cause severe impact on the system 

reliability and stability. One of those disturbances is a transient low voltage event. For some reasons (fault 

or start-up of large motors), the voltage could be lower than the normal ranges for an extended period of 

time. It’s very difficult for any passive scheme to differentiate between the disturbance and the actual 

islanding. 

 

In the following simulations, the active power and reactive power AI schemes are evaluated under a 

typical low-voltage ride through event. The performance is compared against the case without any AI 

scheme. A three-phase fault is applied at the high-voltage side of the distribution transformer at t=1s and 

lasts about 0.3 seconds. The responses of the frequency and voltage from the simulations are shown in 

Figure 19. It is demonstrated that the active power AI scheme is robust and resilient to this low voltage 

event. But the impact of the reactive power AI scheme has some negative effect, exaggerating the event 

when the DG is subjected to a low-voltage event. If widely deployed, this could compromise grid voltage 

stability following faults. 

29
0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.5

0.6

0.7

0.8

0.9

1.0

1.1

 Without AI Scheme

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Voltage Magnitude(p.u.)

Time(seconds)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

59.0

59.2

59.4

59.6

59.8

60.0

60.2

60.4

60.6

60.8

61.0

 Without AI Scheme

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Frequency(Hz)

Time(second)

(a) Voltage magnitude (b) Frequency 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

 With Active Power AI Scheme

Output of Active Power AI Compensator(p.u.)

Time(seconds)

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

Output of Reactive Power AI Compensator(p.u.)

 With Reactive Power AI Scheme

(c) AI compensator output 

Figure 19: Simulation results of the generator response to a three-phase fault 

4.3.2 Grid Impedances 

There have been concerns over the stability impact caused by the positive feedback schemes, since the 

grid is not an ideal voltage source. Conceptually, if the gain of the positive feedback is too high or the 

grid is too weak, the DG may not operate stably due to the AI schemes. Therefore, there always has been 

the question of what are the stability bounds of the positive feedback schemes. Here the discussion only 

focuses on the strength of the grid. In the following simulation, the active power, and reactive power AI 

schemes are evaluated under extremely high grid impedance. The case with active power AI scheme has 

been simulated with a grid impedance Xe=0.5 p.u. (on the base of the DG power rating), and the AI 

scheme is enabled at t=1.0s. Here the grid is always connected even after 1s. As shown in Figure 20(a), 

the system is dynamically stable when the active power AI scheme is enabled. The case with reactive 

power AI scheme has been simulated with a grid impedance Xe=0.50 p.u. and the reactive power AI 

scheme is enabled at t=1.0s. As shown in Figure 20(b), the system is dynamically unstable when the 

30
reactive power AI scheme is enabled. The high grid impedance causes the reactive power AI loop gain 

approaches 0dB, thus losing stability margins. 

In order to maintain stability (especially transient stability, which imposes more margin requirement than 

small-signal stability), the design with sufficient margin is necessary. Therefore, for a given design, an 

upper bound of grid impedance must be specified as an application note, when applying the positive 

feedback AI schemes. 

0 2 4 6 8 10 12

59.4

59.6

59.8

60.0

60.2

60.4

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Frequency(Hz)

Time(seconds)

0 2 4 6 8 10 12

0.90

0.95

1.00

1.05

1.10

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Voltage Magnitude(p.u.)

Time(Seconds)

(a) Voltage magnitude (b) Frequency 

0 2 4 6 8 10 12

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Field Voltage(p.u.)

Time(Seconds)

0 2 4 6 8 10 12

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

 With Active Power AI Scheme

Output of Active Power AI Compensator(p.u.)

Time(Seconds)

-4

-2

0

2

4

Output of Reactive Power AI Compensator(p.u)

 With Reactive Power AI Scheme

(c) Field voltage (d) AI compensator output 

 Figure 20: Simulation results with high grid impedance 

31
4.3.3 Grid Frequency Oscillations 

Another disturbance event to test the performance of the new proposed schemes is a fluctuation in the 

grid frequency. This variation in the frequency may be attributed to some severe disturbances (faults or 

loss of a transmission line) occurring in the high-voltage level of the grid. Usually due to the large inertia 

of the power system, the rate of change of frequency is very low. One rare case simulated here is that the 

frequency oscillates between 59Hz and 61Hz at frequency of 1Hz. The simulation results with 

active/reactive power AI scheme enabled are shown in Figure 21. Even tested by so large variations in the 

frequency, there is little negative impact caused by the active/reactive power AI schemes. 

012345

59.0

59.5

60.0

60.5

61.0

 Without AI Scheme

 With Active AI Scheme

 With Reactive AI Scheme

Frequency(Hz)

Time(seconds)

012345

0.90

0.95

1.00

1.05

1.10

 Without AI Scheme

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Voltage Magnitude(p.u.)

Time(seconds)

(a) Frequency oscillation (Hz) (b) Voltage magnitude 

012345

1.0

1.2

1.4

1.6

1.8

 Without AI Scheme

 With Active Power AI Scheme

 With Reactive Power AI Scheme

Field Voltage(p.u.)

Time(seconds)

012345

-1.0

-0.5

0.0

0.5

1.0

 With Active Power AI Scheme

Output of Active Power AI Compensator(p.u.)

Time(second)

-10

-8

-6

-4

-2

0

2

4

6

8

10

 Output of Reactive Power AI Compensator(p.u.)

 With Reactive Power AI Scheme

(c) Field voltage (d) AI compensators output 

Figure 21: Simulation results of the generator response to the grid frequency oscillation 

32
Summary 

5.1 Conclusions 

This report has proposed two new AI control schemes: namely the active power AI scheme and the 

reactive power AI scheme for synchronous machine-based distributed generations. These DGs include 

engine generators (diesel, natural gas, biomass, hydrogen) and gas turbines. In the report, the detailed 

discussions and simulation studies, including theoretical analysis and the design guidelines for the new AI 

schemes, have been covered. 

The positive feedback created by the active/reactive power AI compensator will drive the 

frequency/voltage to be out of the normal ranges once the DG is islanded. One of the outstanding features 

is that the proposed schemes can show discrimination between actual islanding and other non-islanding 

disturbances. This is very hard for any passive scheme to achieve. Since the new schemes are designed as 

part of the DG control, the cost to implement the schemes is basically negligible. 

In the first part of this report, the characteristics and modeling of the power system using Park’s 

transformation was covered in considerable detail. After that, the positive feedback concept with the 

principles of the applications was introduced. With the frequency-domain analysis in MATLAB, the 

effectiveness of the new active/reactive power AI schemes have been evaluated over a wide range of load 

conditions. The preliminary study concludes that the reactive power AI scheme is more effective than the 

active power AI scheme. But the reactive power AI scheme is more likely to cause the DG to be unstable 

when the grid impedance is high (weak grid). The frequency-domain analysis conducted in MATLAB has 

been validated by the illustrative time-domain simulations conducted in PSCAD. The time-domain 

simulation also implies that the reactive power AI scheme has a slightly adverse effect when the DG is 

subjected to a low voltage event. 

The preliminary study has discovered the following findings: 

1. Without any active schemes, both the RLC load and induction motor load can be islanded for more 

than 2 seconds without being detected. 

2. Both active power and reactive power AI schemes are very effective for RLC load, i.e., detecting 

islanding within 2.0s even when the power is closely matched between the generation and the load. 

3. The impact of different power levels is very insignificant. That is, for a given scheme, it works at full 

power as well as at partial power. 

4. The impact of different quality factor Qf is also insignificant. That is, for a given scheme, it works as 

effective with a high Qf load as with a low Qf load. This indicates that for synchronous machinebased DG AI testing, a resonant tank (RLC) load is not necessary.1

5. Substantial differences in performance were observed for the same AI scheme (e.g. active power AI 

scheme) with RLC load and induction motor load. Because induction motors form a large portion of 

actual loads, these results raise concern that passive load may not be adequate to evaluate the 

effectiveness of certain AI schemes. 

 

1

 Latest IEEE P1547.1 testing standard draft is considering to use a simplified load other than RLC 

resonant tank for testing synchronous machine unintentional islanding protection function. 

33 
6. The reactive power AI scheme is superior to the active power AI scheme due to its high effectiveness 

for a high penetration of motor loads. However, the nominal operation of the DG equipped with the 

reactive power AI scheme can be affected more adversely by the grid impedance and voltage 

disturbances. 

In summary, the new proposed AI schemes are highly reliable, robust to other non-islanding disturbances 

and easy for implementation. 

5.2 Future Work 

In view of the progress described in the previous Chapters, the following directions are suggested as 

possible areas for further investigation: 

1. Optimum design of AI compensator

This report has provided a systematic discussion on how to design the active/reactive 

power AI compensators with the assumption that such a compensator is linear. This is 

simple in the design but not optimum. The performance of the new proposed AI scheme 

could be improved if the AI compensator can adjust its gain to the variations of frequency 

or terminal voltage in real time. In doing so, the new AI schemes can be more effective 

and less sensitive to the grid impedance. This possibility can be explored in the further 

study. 

2. Multiple DG

The discussion here is only limited to the situation with only one rotating machine DG 

present in the islanding. The proposed schemes, conceptually should work for the 

multiple DG but this has not been validated. Furthermore, the dynamical interaction 

between the inverter-based DG and rotating machine DG is an important consideration 

for the design of AI schemes. Therefore, extending the concept of positive feedback to 

multiple DGs will be the major task of next step. 

3. Test load for AI characterization

This report shows that the RLC load representation may not represent the worst case to 

test some AI scheme. Further research is needed to develop models, which are 

simultaneously realistic and achievable in a test laboratory environment. 

34
6. Appendix 

6.1 Synchronous Machine Data 

The data for the generator used in the simulation studies is obtained from [17]. 

Machine rating: 150 kW. 

Machine rated voltage (line-to-line RMS): 480V. 

Inertia Constant : H =2.00 MW/MVA 

Machine Reactance values (in pu): 

Xd=10.823 pu ; Xq=5.325 pu; X’d=0.863 pu; X’’d= 0.258 pu; X’’q=0.304 pu; 

Time constant value (in pu): 

T’d0=2.11s; T”d0=0.0227s; T”q0=0.176s; Xl=0.0892 pu; Ra=0.22 pu. 

Load Parameters (100 % of Load): 

R=1.536 ohms 

L=2.26354 [mH] 

C=3.108295 [mF] 

For the system with voltage and frequency control 

Exciter Data: 

K1=0.0625 pu; T1=100 pu; 

K2=33 pu; K2=0.02 sec; 

K3=1.0 pu; K2=0.0159 sec. 

Governor Data: 

TG=1.0 sec; 

RG=5% pu. 

35 
6.2 Induction Motor Data 

The data for the induction motor used in the simulation studies is obtained from [15]. 

Stator winding resistance Ra= 0.0068 pu; 

Stator leakage inductance L1= 0.1 pu; 

Magnetizing inductance Lm= 3.4 pu; 

Synchronous inductance Ls= 3.5 pu; 

Rotor resistance R2=0.018 pu; 

Rotor leakage inductance L2=0.07 pu; 

Inertia constant H=0.5 MW/MVA 

Load model exponent D=2 pu; 

36
7. References 

[1] IEEE Standard for Interconnecting Distributed Resources with electric power systems, IEEE Std 

1547-2003, 2003. 

[2] Warin, J.W. “Loss of mains protection,” in ERA Conference on Circuit protection for industrial 

and commercial installations, 1990,ERA 90-0001, pp. 4/3/1-12. 

[3] Cooper, C.B. “Standby generation, problems and prospective gains from parallel running,”

Keynote address, International Power System Protection ’89, Power System Conference, 

Singapore Polytechnic, Singapore, 1989.

[4] Hopewell, P.D.; Jenkins, N.; Cross, A.D. “Loss-of-mains detection for small generators,” Electric 

Power Applications, IEE Proceedings- , Volume: 143 Issue: 3 , pp. 225 –230, May 1996. 

[5] Salman, S.K.; King, D.J. “Monitoring changes in system variables due to islanding condition and 

those due to disturbances at the utilities' network,” in Transmission and Distribution Conference, 

1999 IEEE , Volume: 2 , pp. 460 –465. 

[6] Guillot, M.; Collombet, C.; Bertrand, P.; Gotzig, B. “Protection of embedded generation connected 

to a distribution network and loss of mains detection,” in Electricity Distribution, 2001. Part 1: 

Contributions. CIRED. 16th International Conference and Exhibition on (IEE Conf. Publ No. 

482), Volume: vol. 4 , pp. 5. 

[7] Redfern, M.A.; Usta, O.; Fielding, G., “Protection against loss of utility grid supply for a 

dispersed storage and generation unit,” Power Delivery, IEEE Transactions on , Volume: 8 Issue: 

3 , pp. 948 –954, July 1993. 

[8] Redfern, M.A.; Barrett, J.I.; Usta, O, “A new loss of grid protection based on power 

measurements,” in Developments in Power System Protection,1997., Sixth International 

Conference on (Conf. Publ. No. 434) , pp. 91 –94. 

[9] Fu-Sheng, P.; Shyh-Jier, H, “A detection algorithm for islanding-prevention of dispersed 

consumer-owned storage and generating units ,“ Energy Conversion, IEEE Transaction on , 

Volume: 16 Issue: 4 , pp.346 –351, Dec. 2001. 

[10] Salman, S.K.; King, D.J.; Weller, G., “New loss of mains detection algorithm for embedded 

generation using rate of change of voltage and changes in power factors,” in Developments in 

Power System Protection, 2001, Seventh International Conference on (IEE), pp.82 –85. 

[11] Salman, S.K. “Detection of embedded generator islanding condition using elliptical trajectory 

technique,” in Developments in Power System Protection, Sixth International Conference on 

(Conf. Publ. No. 434) , 1997, pp.103 –106. 

[12] Jang, S.-I.; Kim, K.-H. “An Islanding Detection Method for Distributed Generations Using Voltage 

Unbalance and Total Harmonic Distortion of Current”, Power Delivery, IEEE Transactions on , 

Volume: 19 , Issue: 2 , April 2004, pp 745 – 752. 

[13] Kundur, P. Power System Stability and Control, EPRI, McGraw-Hill Inc., New-York, 1996. 

[14] IEEE recommended practices for excitation System Models for Power System Stability Studies, 

IEEE Std 421.5-1992, Aug. 1992. 

[15] Pereira, L.; Kosterev, D.; Mackin, P.; Davies, D.; Undrill, J.; Zhu, W. “An interim dynamic 

induction motor model for stability studies in WSCC,” IEEE Transactions on Power Systems, 

Vol.17, No. 4, pp.1108-1115, November 2002. 

37 
[16] Zhihong, Y., et al. "Study and development of anti-islanding control for grid-connected inverters”, 

GE global research center, Niskayuna, NY, 2003, report submitted to National Renewable Energy 

Laboratory (NREL). 

[17] Jadric, I.; Boroyevich, D.; Jadric, M. “Modeling and Control of a Synchronous Generator with an 

Active DC Load”, IEEE transactions on Power Electronics, Vol. 15 No.2, ,pp.303 – 311, March 

2000. 

38
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Study and Development of Anti-Islanding Control for Synchronous 

Machine-Based Distributed Generators 

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14. ABSTRACT (Maximum 200 Words)

This report summarizes the study and development of new active anti-islanding (AI) control schemes for synchronous 

machine-based distributed generators (DGs). These DGs include engine generators (diesel, natural gas, biomass, 

hydrogen) and gas turbines. The accomplishments of the work include advancing new AI control schemes that 

exhibit substantial improvement on non-detection zone for a static load, without power quality degradation; providing 

design guidelines and evaluating the effectiveness of the new schemes under various load conditions; and validating 

the new anti-islanding control schemes with a time-domain simulation in PSCAD. 

15. SUBJECT TERMS

anti-islanding; synchronous distributed generators; engine generators; gas turbines; motor loads; power system 

modeling 

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