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Abstract—A rotor speed of remote generator is used as wide

area measurement signal in this paper. The signal is detected and

transmitted by the phasor measurement unit (PMU). The wide

area signal inputs to the local power system stabilizer (PSS) to

regulate the generator excitation and enhancing the power

system damping. The gains of the wide area controller are

determined by solving linear matrix inequalities (LMI). The LMI

solving method is introduced for the wide area control of power

systems. A proportional plus derivative network is used to

compensate the communication delay. Kundur's four-machine

two-area system is used to test the performance of the wide area

damping control. The simulation results show that the wide area

control can improve power system stability.

Index Terms--Linear matrix inequalities, power system

stability, time delay, wide area control

I. INTRODUCTION

HE stability of power systems is a very important and

common problem. Considerable research effort goes into

investigating the stability of power systems. The power

system stabilizer (PSS) was invented to improve the power

system damping. Power systems are highly nonlinear, large

scale, and multivariable. Conventional power system

stabilizers are not always able to guarantee stability in large

interconnected power system.

Djukanovic and Khammash presented a systematic

procedure for the design of decentralized controllers for

multimachine power systems [1]. The shaft speed deviation is

selected as an input to the controller. But the sequential

synthesis based on μ-approach is complicated for the design of

decentralized controllers.

Befekadu and Erlich introduced a linear matrix inequalities

(LMI) based robust decentralized dynamic output feedback

controller design for power systems [2]. An algorithm based

on iterative the LMI programming method is proposed to

solve for the controller design. However, solving LMIs

iteratively is a challenging problem.

The phasor measurement unit (PMU) can provide wide

area measurement signals. The signals can be used to enhance

H. Wu, Q. Wang and X. Li are with the School of Electrical and

Automation Engineering, Nanjing Normal University, 210042 Nanjing, China

(e-mail: [email protected]).

978-1-4244-1762-9/08/$25.00 ©2008 IEEE

the wide area damping characteristics of a power system. Hui

Ni and Heydt proposed a supervisory level power system

stabilizer (SPSS) using wide area measurements [3]. An SPSS

agent is composed of agent communications, a fuzzy logic

controller switch, and robust controller loops. An LMI-based

method is applied to controller design. The time delay for the

simulation studies falls in range of 10~30 ms. The effect of the

time delay on the performance of the controller was not

analyzed.

Hongxia Wu and Heydt suggested a centralized control

method using system-wide data to enhance the dynamic

performance of a large interconnected power system [4]. This

parameter-dependent controller ensures closed-loop system

stability with a given bound from the disturbance to the

output. The parameters of power systems are measured in real

time and the controller is adjusted accordingly. The system

response is tested by introducing a unit step input disturbance

to the reference voltage. The effects of communication delays

on the controller design and performance was examined.

These delays can be up to 0.25 seconds long.

Hiyama presented a wide area stabilization control system

using power system stabilizers [5]. The input signal to the PSS

is the real power flow signal on one of the trunk lines in the

system. He proposed communication delay compensation in

[5].

This paper introduces wide area damping control of

excitation systems. A rotor speed signal from a remote

generator is used to damp speed oscillation between

generators with feedback control. The wide area controller

includes a compensation network for the communication

delay. A LMI-based design method of wide area damping

controller for interconnected power systems is discussed.

Kundur's four-machine two-area system is used to test the

performance of the wide area damping controller [6].

II. WIDE AREA CONTROLLER DESIGN

This section discusses the controller structure, the

determination of the controller parameters based on LMI, and

a communication delay compensation network.

A. Power System Model

The two-axis model is used to represent the synchronous

machine. Therefore, generator i in the power system is

represented by a fourth order model [7]

'

' ' '

0 di ( )

q i di qi qi qi

T dE E X X I

dt

= − − −

PMU-Based Wide Area Damping Control of

Power Systems

Huaren Wu, Member, IEEE, Qi Wang, and Xiaohui Li

T

fdi qi di di di

qi

d i E E X X I

dt

dE

T ' ( ' )

'

'

0 = − + −

mi di di qi qi i i

i

ji T I E I E D

dt

τ dω = − ( ' + ' ) − ω

i n

in

dt

dδ =ω −ω

where di I , qi I , '

di E , and '

qi E represent the currents, the

damping-winding flux linkage, and the field flux voltage in

the d-q reference frame, respectively. i

ω is the rotor speed.

in δ is the rotor angle difference between generator i and

generator n. fdi E represents the field voltage and Mi T

represents the mechanical torque. '

d 0i T and '

q0i T are the direct

and quadrature-axis open circuit time constants, respectively.

di X , qi X , '

di X , and '

qi X represent the d- and q-axis

synchronous and transient reactances, respectively. i D is the

damping power coefficient. The time constant ji τ depends on

the rotating inertia.

The block diagram of the automatic voltage regulator

(AVR) and the PSS of generator i is shown in Fig. 1. The

conventional PSS uses local signals for feedback control.

Fig. 1. Block diagram of the AVR and PSS.

If two-stage lead-compensated stabilizers are used, the nmachine

system can be described by 7n-1 first-order

differential equations. The linearized state space equations for

the n-machine system are of the form:

x = Ax +Bu (1)

T

1 2 [ , , , ]n = = Δω Δω Δω L L y Cx 􀀢

T

1 2 [ , , , ] n n nn = = ω ω ω W W y C x 􀀢

= + L L W W u K y K y

= + L L W W K C x K C x

where x is state vector, u is control vector, in i n ω =ω −ω ,

and KL and KW are the following diagonal matrices:

KL=diag(KL1, KL2, …, KLn)

KW=diag(KW1, KW2, …, KWn)

nn ω in output equation may be deleted.

B. Determination of the feedback gain KW

The conventional PSS included in (1) is designed according

to the guidelines in [6]. The rotor speed of generator n is used

as a wide area measurement signal. n-1 generators receive the

rotor speed signal from generator n. The time delay of this

signal is not considered. The determination of the gain factor

KW based on LMI is described in the following analysis.

The Lyapunov function is selected so that V = xTPx , and

P > 0 . From

T

V( ) T 0

• • •

x = x Px + x Px < , the following

LMI is derived:

( + )+( + )T + + T T <0 L L L L W W W W P A BKC A BKC P P C C P (2)

where W W P = PBK .

The matrix A, B, CL, CW and KL can be obtained from the

parameters of power systems. The matrix variables P and Pw

in (2) can be obtained by solving the LMI using the MATLAB

LMI toolbox [8].

KW is a n× n diagonal matrix. P is a (7n −1)×(7n −1)

block diagonal matrix. In order to obtain KW, P should have

the structure P=diag(P1, P2, …, Pn), where Pi is a 7×7

symmetric matrix for i=1, 2, …, n-1 and Pn is 6× 6

symmetric matrix.

PW is a (7n −1)× n block diagonal matrix of the form

PW=diag(PW1, PW2, …, PWn), where PWi is a 7 ×1 matrix for

i=1, 2, …, n-1 and PWn is 6×1 matrix.

The structures of P and PW were declared using the Matlab

lmivar(3,struct) function and the LMIs were solved using the

feasp( ) Matlab function to obtain P and PW . KW can be

calculated from W W K = (PB) \\ P .

If a LMI is established for each interesting operating point

and these LMIs are solved simultaneously to obtain the matrix

variables P and Pw, the wide area controller will have robust

performance for a large range of system operating conditions.

C. Compensation for Communication Delay

The wide area measurement signal from the PMU is used

for feedback control. The wide area signal without time delay

could greatly improve the dynamic performance of the

interconnected power system; the communication delay is not

beneficial for power system stability. Thus, the feedback

control signal time delay should be considered in the design of

wide area controllers. The communication delay is expressed

by the Laplace transformation of e−sTd , where Td is the

communication delay. e−sTd may be compensated by esTd .

esTd can be approximated by d

esTd ≈1+ sT . Therefore, the

proportional plus derivative d 1+ sT (PD) network is used to

compensate the time delay for simplification. A filter is

introduced to avoid the influence of the noise in the wide area

signal. Finally, the communication delay is compensated by

the compensator )

1

1 (

f

d

T sT

K sT

+

+ , where KT is the

i Δω

KL Σ (1 )(1 )(1 )

(1 )(1 )

2 4

1 3

sT sT sT

sT sT sT

W

W

+ + +

+ +

Eti

Σ

R 1+ sT

1 +

+

Vrefi

νsi Efdi

ui

uwi +

+

-

KA

compensation factor and Tf is the time constant [5]. The

compensation network is shown in Fig. 2. ωin (t −Td ) in Fig.

2 is the following:

( ) ( ) ( ) in d i d n d ω t −T =ω t −T −ω t −T

Fig. 2. Time delay compensated communication.

The communication delay Td can be obtained from the wide

area signal. The compensation factor KT depends on the time

delay Td. KT is calculated with the following formula obtained

by simulation numerically.

2

2 2

1000 10 1 0.1

1 0.1

d d

T

d

d

T T s

K

T s

T

α

α

⎧⎛' '⎞' − + < '⎜' '⎟' '⎪⎪

= '⎝' '⎠' '⎨⎪

⎪⎩

where α is chosen to get the best power system damping at

time delay Td =0.1 s.

III. SIMULATION AND RESULTS

The design method of the wide area controller presented

above was applied to the four-machine two-area system

shown in Fig. 3. The generators, transformers, and lines

parameters are given in [6]. The parameters of the AVR and

PSS, selected from [6], are as follows:

1 2 200, 0.01, 0.05, 0.02 A R K = T = T = T =

3 4 3, 5.4, 20 L T = T = K =

Fig. 3. Four-machine two-area system.

All four generators are equipped with the local PSS. The

wide area measurement signal is the rotor speed of generator 4.

Generator 1, 2 and 3 have wide area damping controllers and

receive the wide area signal from generator 4.

Two operating conditions are considered. One is the same

as the MATLAB example "Performance of Three PSS for

Interarea Oscillations" [8]. The other has half of the real

power load of the MATLAB example. The 27th-order

linearized state space equations for the test system without

time delay compensation is obtained for each operating

condition. That is, matrix A and B can be obtained for each

operating condition.

P is a 27× 27 matrix., P1, P2 and P3 are declared as 7×7

symmetric matrix, and P4 is defined as a 6× 6 symmetric

matrix. PW is a 27× 4 matrix where PW=diag(PW1, PW2, PW3,

0), and PW1, PW2, and PW3 are 7 ×1 matrices. A LMI of (2) is

created for each operating point. These LMIs were solved

using feasp(LMIs, [0,0,0,0,0],-4000) to obtain P and PW. KW is

calculated from W W K = (PB) \\ P . The results of these

analyses are Kw1=140.7, Kw2=95.6','and Kw3=61.1.

A three-phase fault at the center of one of tie-lines was

created to verify the performance of controllers under transient

conditions. The fault was cleared by opening the circuit

breakers at both ends of the faulted tie-line. The fault-clearing

time was 0.12 s and re-closure was completed in 0.5 s after the

fault-cleared. Fig. 4 shows swing curves with the AVR and

PSS but without wide area control. The swing curves indicate

that the system is stability.

Fig. 4. Swing curves with the PSS.

Fig. 5 presents the swing curves with the PSS and the wide

area control for the time delay of 0.1 s. KT=13.2 is selected for

time delay compensation. Comparing Fig. 5 with Fig. 4 shows

that the wide area control can greatly improve power system

stability.

Fig. 5. Swing curves with the PSS, wide area control,

and time delay compensation.

Fig. 6 depicts swing curves with the PSS and wide area

control for a time delay of 0.1 s. The time delay compensation

was not used with the controller in this simulation. Fig. 6

shows that the communication delay is detrimental to the

power system stability. Fig. 5 and Fig. 6 demonstrate the

effectiveness of the compensator for power system stability

enhancement.

~ ~

~ ~

L7

G1 1 5 6 7 8 9 10 11 3 G3

G2 G4

2 4

L9

C7 C9

( ) in d ω t −T (1 )

1

d

T

f

K sT

sT

+

+ W K wi u

Fig. 6. Swing curves without time delay compensation.

Curves 1 and 2 in Fig. 7 show the swing curves with wide

area control for time delays of 0.1 and 0.25 s, respectively.

Curve 3 shows the swing curve without wide area control. Fig.

7 indicates that wide area control with time delay

compensation can improve power system stability when the

time delay is 0.25 s.

Fig. 7. Effect of time delay compensation on the damping.

The effectiveness of wide area control was also tested at

another operating point with the same fault. Curve 1 in Fig. 8

shows the swing curve with wide area control for a time delay

of 0.1 s. Curve 2 shows the swing curve without wide area

control. Fig. 8 indicates that wide area control has good

robustness at the different operating points.

Fig. 8. Swing curves for another operating condition.

IV. CONCLUSIONS

T

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