SCSC2003 Abstract S9559
A Robust Design of a Static VAR Compensator Controller for Power
A Robust Design of a Static VAR Compensator Controller for Power
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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