System Stability Improvement

A.H.M.A.Rahim

S.A.Al-Baiyat

Department of Electrical Engineering

K.F.University of Petroleum and Minerals

Dhahran, Saudi Arabia.

Mailing address:

Dr.A.H.Rahim

KFUPM Box 349

Dhahran 31261

Saudi Arabia

Email: ahrahim@kfupm.edu.sa

Tel : (9663)860 4986

Fax: (9663)860 3535

A Robust Design of a Static VAR Compensator Controller for Power

System Stability Improvement

(An extended summary)

Introduction

The static var compensators (SVC) are the first generation of flexible ac transmission

systems (FACTS) devices used for control of power system voltages. Static VAR

compensators are also known to increase transient stability limits, prevent voltage

instability and control severe over-voltages.

The SVC in the voltage control mode, does not improve damping of a power system.

In the transient state, however, the static var compensators with properly designed

supplementary controls, can provide damping to power swings. Design for optimum

damping control generally is operating point dependent requiring expensive electronic

circuits for tuning the parameters. One of the important goals of the control engineers is

to design ‘robust’ fixed parameter controllers which will be effective of a large range of

operation. This article presents such an SVC controller employing a relatively new ‘loopshaping’

method. The controller designed has been tested on a single machine-infinite

bus system. It has been observed to provide excellent damping control over a wide range

of power system operation.

The Power System and SVC Model

Fig. 1 gives the configuration of a single machine system connected to a remote bus.

The SVC is located at the mid-bus. Fig. 2 shows the block diagram of the SVC and its

controller. The input to the normal voltage control loop is the bus voltage Vm. An extra

stabilizing block is connected to the output of the voltage regulator. The objective of this

article is to design the robust damping controller(C).

The Robust Control Design

Consider a multi-input control system given in Fig.3. A controller C provides robust

stability if it provides internal stability for every plant in the uncertainty set P. The

perturbed plant functions P~ in P are related to nominal plant P through,

P W P ) 1 ( 2

~

? + = (1)

W2 is a fixed stable transfer function, also called the weight, and ? is a variable transfer

function satisfying ? ? < 1.

Fig.3 Plant and controller configuration

A necessary and a sufficient condition for robust performance for the plant is given as,

? + T W S W 2 1 < 1 (2)

where, S is the sensitivity function and is the complement of the input-output transfer

function T. Through a ‘loop-shaping’ technique, it can be shown that the open-loop

transfer function L should satisfy the conditions at low and high frequencies, respectively

for robustness.

The algorithm to generate a robust control function C involves generation of W2

from the uncertainty modeling, choice of an appropriate monotonically decreasing real

and rational function W1, choice of open-loop function L so as to satisfy (3). Then the

robust controller is determined through the relation L=PC.

Results

For nominal generator power output of 0.86pu at 0.91 lagging power factor the plant

transfer function, with SVC susceptance as the input and generator speed as output, is

obtained as,

35.97) 0.1282s 33.03)(s 0.548)(s (s

0.74) 32.7)(s (s 0.0339s P 2 + + + +

+ + = (4)

(12)

Off-nominal power output between the range of 0.2-1.3 pu and power factor of up to

0.8 lag/lead were considered in the robust design. The W2 function arrived at is,

125 . 21 9 . 42 8 . 1

5625 . 10 1633 . 14 8506 . 3 2428 . 0 ) ( 2 3

2 3

2 + + +

+ + + =

s s s

s s s s W (5)

A Butterworth filter was selected for the functionW1(s). For a choice of L as,

) 3 . 1677 42 . 80 )( 03 . 33 )( 1 . 0 (

) 2 )( 74 . 0 )( 7 . 32 ( 10

2 + + + +

+ + + =

s s s s

s s s L (6)

The robust controller transfer function obtained through the loop-shaping procedure is,

0.1) s(s

2) 0.5)(s 294.98(s C

+

+ + = (7)

6

For a 100% torque pulse for 0.1 sec. duration, the rotor angle variations of the

generator for a number of operating conditions are shown in Fig.4. The corresponding

terminal voltage variations are presented in Fig. 5. As can be observed, the robust

controller provides extremely good damping to the rotor oscillations as well as the

electrical transients. The uncontrolled system is very oscillatory (not shown).

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

30

40

50

60

70

80

90

100

Generator Rotor Angle(deg.)

Time (sec.)

a

b

c

d

Fig.4 Generator rotor angle with robust controller following a 100% torque pulse for 0.1 sec, with a)1.3pu

output power at 0.95lagging pf, b)1.00 pu power and 0.85 lag, c)0.8 pu power with 0.9 lag, and d)0.5 pu

power with 0.95 leading pf.

7

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.5

0.6

0.7

0.8

0.9

1

1.1

Generator Term. Voltage(pu)

Time (sec.)

a

b

c

d

Fig.5 Terminal voltage variation of the generator corresponding to Fig. 4

Conclusions

A robust fixed parameter SVC controller has been designed through a novel loopshaping

technique. Simulation results indicate that the controller provides excellent

damping properties to the power system over a good range of operating conditions.

8

Acknowledgement

The authors wish to acknowledge the facilities provided at the K.F.University of

Petroleum and Minerals. This work was performed under KFUPM project

EE/ROBUST/252.

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