Allocation and design of power system stabilizers for mitigating...

Allocation and design of power system stabilizers for mitigating

low-frequency oscillations in the eastern

interconnected power system in Japan

Masachika Ishimarua,*, Ryuichi Yokoyamaa, Oriane Magela Netob, Kwang Y. Leec

aTokyo Metropolitan University, 1-1 Minamiosawa, Hachioji, Tokyo 192-0397, JapanbFUNREI, Praca Frei Orlando, 170 36307-352 Sao Joao del Rei MG, Brazil

cThe Pennsylvania State University, University Park, PA 16802, USA

Abstract

Low-frequency oscillations have been observed on trunk transmission systems in Japan, and have been the subject for studies in fields of

operation, control, and devices by the many power system utilities. Power system stabilizers (PSSs) are very effective controllers in

enhancing the damping of low-frequency oscillations, since the controllers can increase damping torque for inter area modes by introducing

additional signals into the excitation controllers already equipped with generators. In this paper, allocation of PSSs in an interconnected

power system with inter area modes has been determined by an eigenvalue analysis, and PSSs for the allocated generators have been designed

by a frequency response method. The designed PSSs have been verified in a Japanese power system standard model. This test system is

created as a standard model based on the trunk transmission systems in the eastern area of Japan, and reflects characteristic features of the real

power systems; therefore, realistic allocation and design for enhancement of the stability of low-frequency oscillations have been verified.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Low-frequency oscillation; Power system stability; Frequency response method

1. Introduction

Many electric utility systems are undergoing restructur-

ing worldwide. In 1999, Japan also amended the Electricity

Utility Act effective March 2000. This permitted

participation of power producers and suppliers in the

market. It deregulated the retail market partially, opening

competition up to both domestic and foreign participants.

This may result in a future power system, which is much

more complicated. Recently, the combined effect of various

factors has made it more difficult to maintain system

stability. These include the increased use of heavily loaded

long-distance transmission lines from power sources in

remote and distant locations, an imbalance of power stations

in different areas due to environmental and cost issues

regarding their construction, and the difficulty of securing

transmission line routes. In addition to the increased

complication of the system, the societal requirement to

maintain and supply high quality power is heightened and

stabilization has become a significant issue. Also, under

the present system in Japan, where only conventional

system stabilization control devices are being used to damp

oscillation, there is a concern for the occurrence of

low-frequency oscillation phenomena, and developing

countermeasures is considered as an urgent task.

Two types of oscillation phenomena can occur on the

present power system. One is where the oscillation of one

generator at a specific power plant has an influence on the

system. This type of oscillation is called local-mode

oscillation and its behavior is mainly limited to the local

area in the vicinity of the power plant. It rarely influences

the rest of the system. It has been known that the local

oscillation is likely to occur when power is transmitted over

long-distance transmission lines from a power plant at a

remote location. This type of system can be accurately

modeled using the single-machine-infinite-bus (SMIB)

system model [1]. The other case has been known as

inter-area mode oscillation. This is the case where the

low-frequency oscillation is maintained between sets of

generators in an interconnected power system. The simplest

type of low-frequency oscillation in the inter-area mode is

between two interconnected areas. The inter-area

mode oscillation has a long history. It has been observed

0142-0615/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijepes.2004.04.007

Electrical Power and Energy Systems 26 (2004) 607–618

www.elsevier.com/locate/ijepes

* Corresponding author. Tel.: þ81-3-4586-6361; fax: þ81-3-4586-1185.

E-mail address: [email protected] (M. Ishimaru).

http://www.elsevier.com/locate/ijepes

in the tie-line connecting the large Pacific Southwest and the

Pacific Northwest in the United States. It has also been

observed on the tie-line connecting the northern Midwest

and Canada [2,3]. Observations have also been made of

low-frequency oscillation at 2.5 s per cycle on the trunk

transmission power system of Eastern Japan[4]. In general,

it is difficult to analyze these inter-area mode oscillations

since many generators and complicated network of

transmission lines are involved. Power system stabilizers

(PSSs) have been shown to be effective in stabilizing the

modes where there are different oscillation frequencies, as in

the above case. The PSS is a control device to improve the

stability of the system by introducing a supplementary

signal to an automatic voltage regulator (AVR). The AVR is

an exciter control device, which maintains the terminal

voltage of the generator at a constant level. Unlike AVR,

PSS is not electromechanical but is a supplementary

signal-generating device. Therefore, it is cost effective and

can be easily installed compared with other control devices.

Much research has been done on PSS. Some research has

focused on developing the PSS using multiple signal inputs

such as the generator active power, the generator speed,

and reactive power to maintain the linear characteristics

toward the phase angle on the heavily loaded transmission

system, and the bus voltage for a long distance line from the

generator [5,6]. There are two types of methods for

developing PSSs, where parameter optimization can be

used to damp oscillation between interconnected systems.

The first is to determine the parameters of PSS with

consideration for system operations [7]. The second

includes optimization methods using Artificial Neural

Networks (ANN) [8] or genetic algorithms (GA) [9].

The use of PSS in power system has been both

economical and successful in improving the power system

stability, and is expected to be installed on many

generators connected to the system. However, there are

different kind of power plants connected to the power

system, such as use fossil fuel, hydro and nuclear

power plants, and generators have different characteristics.

In addition, there are pumped storage power plants in

actual use. Whether a PSS is to be installed or not

depends, in part, on the type of power generation. If

low-frequency oscillation is damped by installing an

appropriate number of control devices at appropriate

locations within the power system, even further economic

gain can be expected. For this reason, it is very important

to have a method for determining the locations for PSS on

a realistic power system model. To improve the power

system stability of the entire system, a smaller number of

PSSs have been designed and installed in a real-size

system having inter-area mode oscillations.

The allocation of PSSs have been performed by using an

eigenvalue analysis on the system so that the dominant

generator with the greatest influence on both the power

system stability and the low-frequency oscillation becomes

the candidate for PSS installation. The proposed

approach designed a PSS for this dominant generator with

the capability for damping the system mode. In the design,

the approach used the frequency response method in the

SMIB system model. In the application of the proposed

method, the paper utilized the public domain East10 Model

published from the Institute of Electrical Engineering of

Japan, which is a standard model for the eastern part of the

Japanese interconnection system [10].

2. Power system model and allocation of controllers

It would be desirable to create a model to accurately

analyze each and every equipment in the power system

that is comparable to the real system. However, power

systems are huge systems with connections to

multiple generators and transformers and complicated

network of transmission lines. For this reason, it is

difficult to create a detailed model. The depth of the

system analysis depends on the size of the target power

system, and the accuracy of the model must be

compromised to some degree.

Local mode oscillation has been known to occur at the

generator connected to the system by tie-lines that are

weak for the case of the infinite-bus model. Analysis of

local mode oscillation is done using a detailed model

based on the SMIB system model. However, inter-area

mode occurs in very large system of interconnected,

multi-machine systems; therefore, it is difficult to do a

detailed analysis. In this paper, an aggregated linear

model of a multi-machine power system that does not

involve detailed analysis of a multi-machine power system

but is effective for developing the transmission line

system structure has been used [11].

2.1. Eigenvalue analysis of multi-machine power system

In an analysis of the system stability, eigenvalues of a

power system model have been derived and evaluated.

By analyzing eigenvalues, characteristics of system

dynamics are grasped without a time domain simulation.

Therefore, the eigenvalue analysis is effective in

evaluating the system stability for a multi-machine

power system [14,15].

A swing equation of the ith generator, which indicates

the energy balance between a mechanical input and an

electrical output, is expressed as follows:

Mi

d2

dt2di ¼ Pmi 2 Pei 2 Divi ð1Þ

An active power output of the ith generator in Eq. (1) is

calculated as:

Pei ¼Xn

j¼1

EiEjYij cosðuij 2 di þ djÞ ð2Þ

M. Ishimaru et al. / Electrical Power and Energy Systems 26 (2004) 607–618608

Also, a damping constant of each generator is expressed

as belows:

Di¼e2i v0i

ðX0di2X00

diÞT00doi

X0di2Xei

sin2d0iþðX0

qi2X00qiÞT

00qoi

X0qi2Xei

cos2d0i

( )

ð3Þ

In the case of the stability analysis, the damping constants

are very important coefficients, because the constants affect

real parts of system eigenvalues. In a conventional approach

on power system stability for multi-machine power system,

network reduction has been performed for analysis and

control purpose. This technique is able to deal with

transmission lines, transformers, loads, and other

equipments in the power system by using the per unit (pu)

method. The system eigenvalues have been evaluated by

considering the components and structures of the power

system; that is to say, the eigenvalues reflect electrical

distances between generators. Therefore, the power system

stability has been evaluated in the multi-machine power

system by considering the network configurations.

A condition, that all eigenvalues are in the negative real

half of the complex plane, has been well known for a stable

system. Also, an eigenvalue existing nearby the imaginary

axis, influences the system stability severely. Moreover, the

imaginary parts of system eigenvalues dominate the system

oscillation frequency in the time domain. The parameters in

Eqs. (1)–(3) are listed in Table 1.

2.2. Determination of the dominant generator by utilizing

participation factor

The power system dynamics can be evaluated by

analyzing of the system eigenvalues. In this evaluation,

a dominant root, which is located near the imaginary axis,

can be recognized. In the case of stabilizing the dominant

root by applying an appropriate controller, the power system

stability can be enhanced. This paper proposes an approach

to determine locations of generators, which should be

equipped with the controllers. In the approach, a partici-

pation factor is utilized [12]. The participation factor is

effective in finding state variables affecting the dominant

root. The factor is derived from eigenvectors.

First, eigenvector fj is calculated with an eigenvalue lj of

a system matrix Aðn £ nÞ:

F ¼ ½f1ff2f· · ·fn� ð4Þ

Next, a vector ci is defined as below:

C ¼ ½F21�T ¼ ½c1fc2f· · ·fcn� ð5Þ

In this case, a participation factor pij is expressed as follows:

pij ¼ fij £ cij ð6Þ

Here, these two matrices F and C have been related as

F £CT ¼ I; therefore:

Xn

j¼1

pij ¼Xn

j¼1

fij £ cij ¼ 1:0 þ j0:0 ð7Þ

In a similar way:

Xn

i¼1

pij ¼ 1:0 þ j0:0 ð8Þ

The participation factor pij expresses the influence or

sensitivity upon ith state variable against the eigenvalue

lj; and Eqs. (7) and (8) implies the numerical values are

normalized. In these characteristics, the participation factor

is more effective than normal eigenvectors, and useful for

the eigenvalue analysis. In this paper, the state variable

affecting the dominant root is determined by the evaluation

of the participation factor; moreover, a dominant generator,

which should be equipped with a PSS controller, is selected.

3. Design of power system stabilizer based

on the frequency response method

This paper aims at allocating and designing PSSs against

low-frequency oscillation on the trunk power system in the

eastern area of Japan. The low-frequency oscillation in bulk

power system is related with inter-area mode. However, it is

difficult to prove the cause of the occurrence of the

low-frequency oscillation in the bulk power system. In this

Table 1

List of parameters in Eqs. (1)–(3)

Mi Inertia constant (pu MW s2/rad)

di Rotor angle (rad)

Pmi Mechanical input (pu MW)

Pei Electrical output (pu MW)

Di Damping constant (pu MW s/rad)

vi Deviation from reference speed (rad/s)

Ei Magnitude of internal voltage (pu)

Yij Magnitude of admittance between generators

i and j

(pu)

uij Phase angle of admittance between

generators i and j

(pu)

ei Voltage of infinite bus (pu)

Xei External reactance (pu)

d0i Initial rotor angle of infinite bus voltage (rad)

v0i Rotation speed of generator in steady-state (rad/s)

Xdi0 d-Axis transient reactance (pu)

Xqi0 q-Axis transient reactance (pu)

Xdi00 d-Axis subtransient reactance (pu)

Xqi00 q-Axis subtransient reactance (pu)

Tdoi00 d-Axis subtransient open-circuit time constant (s)

Tqoi00 q-Axis subtransient open-circuit time constant (s)

Fig. 1. Single-machine-infinite-bus (SMIB) system model.

M. Ishimaru et al. / Electrical Power and Energy Systems 26 (2004) 607–618 609

paper, PSS parameters have been designed based on a

frequency response method for a local mode, and the

allocation of PSS controllers has been determined based on

the inter-area mode.

A PSS for the enhancement of the local mode is designed

for SMIB system model shown in Fig. 1. The SMIB system

model ignores power system networks beyond the infinite bus;

therefore, the model has not reflected the electrical distances,

for example components and structures of transmission lines

and other equipments. However, the model is suitable for the

design of PSS parameters, because an exhaustive study on the

generator model has been made already [1].

A generators’ dynamics for small-signal stability anal-

ysis in SMIB system has been expressed, with linearization

by assuming the flux linkages of the field winding is

constant, as follows:

M

v0

s2DdþD

v0

sDdþ KDd ¼ 0 ð9Þ

In the equation above, under condition that the solution

calculated in Eq. (10) is not a positive real number, the

dynamics of the system is stable. In other words, the

condition is that the damping constant D is a positive

number ðD . 0Þ; and the synchronizing coefficient K is also

positive ðK . 0Þ:

s ¼2D ^ j

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4Kv0M 2 D2

p2M

ð10Þ

Block diagrams of damping constant and synchronizing

coefficient of a generator and an AVR with a PSS are shown

in Fig. 2. This figure shows that Dd operates as the

synchronous torque for the electrical oscillation of the

generator, also Dv delaying 908 in phase than Dd signal,

functions as the damping torque. Therefore, each torque of

the generator is, respectively, expressed and analyzed in the

design and evaluation of PSS parameters. The constants K 0

and D0 in the figure, respectively, mean the changes in

synchronous torque and damping torque due to equipping

with both an AVR and a PSS. The synchronous torque and

damping torque of the combined generator and the excitation

Fig. 2. Linearized model of SMIB system.

Fig. 3. IEEJ EAST10 power system standard model.


controller are defined as the synchronizing torque

coefficient Ks and a damping torque coefficient Kd:

4. Allocation of power system stabilizers

in EAST10 model

The allocated and designed PSSs in the proposed

approach have been verified in a Japanese power system

standard model, named ‘East10 Model’ (Fig. 3), released

by the Institute of Electrical Engineering of Japan. This

test system is created as a standard model based on the

trunk transmission systems in the eastern area of Japan,

and reflects characteristic features in the actual power

systems. In addition, operational conditions in peak load

and off-peak load have been set in the system model. In

this paper, the peak load condition, where generators

operate in their output margin, is used for the allocation of

PSSs. The generators in the power system model have

been normally equipped with AVRs shown in Fig. 4. The

normal AVR is not suitable for installing the PSS because

of its slow operation; therefore, a thyristor excited high

performance AVR shown in Fig. 5 has been installed in

the dominant generator instead of the normal AVR. In

view of economics, the least number of replacing AVRs

and installing PSSs is desired. This paper aims at

enhancing the stability against the low-frequency oscil-

lation by replacing AVRs and installing PSSs into the

dominant generator in a test power system. The EURO-

STAG Ver. 4.0 produced by EDF and Tractebel is used in

simulations. A flow chart of the proposed approach is

shown in Fig. 6.

4.1. Eigenvalue analysis of EAST10 model

In this paper, the eigenvalue analysis has been applied to

the test power system model The power system model is

expressed by Eqs. (1)–(3). The eigenvalues of the controlled

system are derived from these expressions with aggregation

of the power system. The obtained eigenvalues are shown in

Fig. 7. The eigenvalue analysis takes notice of conjugate

eigenvalues; therefore, the eigenvalues that take the

positive numbers in the imaginary part are numbered in

Fig. 7. A slant line area in the figure shows that

an eigenvalue in this area has a peculiar oscillation between

2 and 4 s per cycle.

Fig. 4. Block diagram of automatic voltage regulator.

Fig. 5. Block diagram of thyristor excited high performance automatic

voltage regulator.

Fig. 6. Flow chart for allocation and design of PSS.

Fig. 7. System eigenvalues in EAST10 model.


The results of the eigenvalue analysis indicate that Mode 2

dominates the low-frequency oscillation in EAST10 model,

and Mode 5 affects the power system stability. The Mode 2 is

named ‘Low-Frequency dominant mode’, also Mode 5 is

called ‘Stability dominant mode’ just for the sake of

convenience. When these modes have been stabilized, the

low-frequency oscillation is stabilized and the power system

stability is enhanced. The eigenvalues and oscillation periods

of both dominant modes are listed in Table 2.

4.2. Determination of the dominant generator

for installing PSS by utilizing participation factor

The modes dominating the low-frequency oscillation and

the stability have been selected in the eigenvalue analysis.

In the case when a state variable affecting each dominant

mode has been identified, a dominant generator is

determined. The selected generator is a candidate, which

should have the designed PSS installed. In this paper,

the participation factor has been utilized to determine

the dominant generator. The factor is expressed in complex

numbers. The proposed approach deals with the real part

of the factor and ignores the imaginary part, since

the summation of the participation factor in row or column

is 1.0 þ j0.0 by normalization. The factors, ignoring the

imaginary parts, are called participation rates in distinction

from the participation factors. The participation rates for

EAST10 model is shown in Fig. 8. In the figure, the state

variables are numbered as; ½1 : Dv1;…; 10 : Dv10; 11 :

Dd221;…; 19 : Dd1021�

The results of evaluating the participation rates show

that a generator G9 dominates the low-frequency oscil-

lation and a generator G6 influences the power system

stability. This paper replaces the AVRs in these dominant

generators with the thyristor-excited high performance

AVRs, and designs and installs new PSSs into the AVRs

to enhance the damping.

5. Design of PSS focused on the dominant generator

and verification in the East10 model

Through system analysis with the East10 model,

the dominant generator that most effectively damped the

low-frequency oscillation and the generator that most

improved the stability of the entire system have been

identified. In this section, PSSs for each of these generators

are designed. Here, the AVR is replaced with the thyristor-

excited high performance AVR shown in Fig. 5. The design

goal of PSS is to improve the damping torque coefficient

Table 2

Eigenvalue and oscillation period of dominant modes

Mode No. Eigenvalue Oscillation period (s)

Mode 2 20.0590 þ j1.9843 3.1664

Mode 5 20.0350 þ j3.2597 1.9275

Fig. 8. System participation rates in EAST10 model.


with the least influence on the synchronizing torque

coefficient by adding the PSS signal to AVR. Experience

has shown that to do this requires appropriate damping

torque of about 20 pu in the frequency range where the

eigenvalue of the frequency of the given generator is

0.1–1.0 Hz. However, it is desirable to determine the PSS

parameters by examining the damping torque of each

generator. This is because there are differences in capacity

and the inertia constant that are dependent on the power

plant type and because there are influences from the

electrical distance between generators, i.e. influence of

the system structure.

The proposed approach for allocation and design of PSSs

has been examined in the East10 Model. In the power

system model, the low-frequency oscillation between 2 and

4 s per cycle has been observed by opening a single-line at

1.0 s for 0.07 s nearby node No.36. This paper aims at

damping the low-frequency oscillation by a proper

allocation and design of PSSs.

5.1. Design of PSS parameters for the low-frequency

dominant generator

This paper designs a PSS for the low-frequency dominant

generator G9 assuming node No.19 to be the infinite

bus[13]. A block diagram of designed P-Type PSS is

shown in Fig. 9 and effects of the PSS are shown in Fig. 10.

The designed PSS in Fig. 9 realizing 30 pu of the damping

Fig. 9. PSS block diagram for low-freq. dominant generator.

Fig. 10. Kd and Ks in generator No. 9. with P-type PSS.


torque coefficient in the low-frequency domain does not

influence the synchronous torque coefficient. Moreover,

Fig. 10 shows the PSS has an effective damping torque

coefficient in a wide range, including oscillation modes of

generator’s own.

5.2. Verification of the low-frequency dominant PSS

in EAST10 model

The designed PSS has been verified for the contingency,

breaking out the low-frequency oscillation in the EAST10

Fig. 11. Power system oscillations without PSS.


model. Simulation results of not replacing AVRs and not

installing PSSs are shown in Fig. 11, and results of replacing

the AVR and installing the designed PSS into the generator

G9 are shown in Fig. 12. These figures show phase angles of

arbitrary generators in the top row, electrical outputs

of generators in the middle, and active power flows through

arbitrary transmission lines in the bottom.

By comparison of these results, the low-frequency

oscillation at about 4 s per cycle of the electrical output of

generator G9 in Fig. 11 is damped in Fig. 12 by installing

the designed PSS into the dominant one; therefore, the

low-frequency oscillation such as in Fig. 11 are removed

from all outputs in Fig. 12. These results indicate that the

proposed approach can damp the low-frequency oscillation

Fig. 12. PS oscillations with low frequency dominant PSS.


by the excitation controller equipped with the generator

related in the dominant eigenvalue. Therefore, the approach

succeeds allocating and designing of the PSS against

oscillation frequencies in a multi-machine power system.

However, the power system stability has not been

enhanced in Fig. 12 yet, because the stability

dominant mode (Mode 5 in Fig. 7) has not been improved

by this PSS. Mode 5 has the oscillation frequency about 2 s

in the period listed in Table 2; therefore, the

oscillation period of simulation results in Fig. 12

corresponds with one of Mode 5. These results indicate

the necessity of installing a PSS into the stability dominant

generator G6 at the same time.

5.3. Design of PSS parameters for the stability dominant

generator

A PSS equipped with the stability dominant generator

G6 is also designed by utilizing SMIB system A diagram

of a designed PSS for G6 is shown in Fig. 13, and effects

of the PSS are shown in Fig. 14.

The damping torque coefficient in Fig. 14 shows about

3 pu. This coefficient value is especially regulated for the

EAST10 model, because higher damping torque coefficient

has a possibility to make the system unstable; therefore, the

design of PSS parameters needs to regulate or adjust against

the dynamics of the entire power system.

Fig. 14. Kd and Ks in generator No. 6 with P-type PSS.

Fig. 13. PSS block diagram for stability dominant generator.


5.4. Verification of the stability dominant PSS

in EAST10 model

The designed PSS for the stability dominant generator G6

has been verified in the EAST10 model. In the verification,

the low-frequency dominant PSS has been equipped in

the generator G9. The damping torque coefficient in Fig. 14

is smaller than one in the low-frequency dominant PSS.

However, the designed PSS succeeded in enhancing the

power system stability. The results indicate that the design

of PSS needs to consider the system configurations, i.e. the

electrical distance between generators (Fig. 15).

Fig. 15. PS oscillations with stability dominant PSS.


6. Conclusions

In this paper, the allocation and design method of PSSs

have been proposed to suppress the low-frequency

oscillation in the Eastern area of Japan. The proposed

method was applied to the East10 Model, modeled after the

trunk transmission power system of the Eastern area.

The proposed approach created an aggregated model of

the multi-machine power system and performed the

eigenvalue analysis. Among the eigenvalues identified,

two dominant modes, i.e. low-frequency dominant mode

and stability dominant mode have been focused and

stabilized. These modes are intrinsic to the damping torque

of each generator and the transmission system structure and

components, i.e. the electrical distance between generators.

The proposed approach has succeeded in determining the

dominant generator with the ability to influence these modes

by evaluating the participation rates to the low-frequency

dominant mode and the stability dominant mode.

This paper has examined a system by designing and

configuring a PSS at a particular time of the day using the

East10 Model. Since the power system changes over time,

in the future we will need to examine a robust design and

allocation of PSS that ensures stability at various times.

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