The 6th edition of the
Interdisciplinarity in Engineering International Conference
“Petru Maior” University of Tîrgu Mureş, Romania, 2012
ADAPTIVE CONTROL OF STATIC VAR COMPENSATOR
Stelian-Emilian OLTEAN
Electrical Engineering and Computer Science Department, Petru Maior University of Tîrgu Mureș
Nicolae Iorga str., no. 1, Tîrgu Mureș, Romania
stelian.oltean@ing.upm.ro
ABSTRACT
The static var compensators SVC are FACTS devices in shunt connection which can be
used for power system enhancement. The SVC modeled in the paper comprises a fixed
capacitor and a thyristor-controlled inductor to improve the generator damping. The
paper investigates a modern approach for SVC control using adaptive control strategy.
The design methodologies and the characteristics of the self-tuning control of the SVC are
also presented. The least square method with forgetting factor was considered for the
system identification; meanwhile the minimum variance method was used for the SVC
control.
Keywords: static VAR compensator, adaptive control, self-tuning control, power system stability
1. Introduction
The need of more efficient electricity systems
management has given rise to innovative technologies
in power generation and transmission. Flexible AC
transmission systems, FACTS as they are generally
known, are alternating current transmission systems
incorporating power electronic-based and other static
controllers to enhance controllability and increase
power transfer capability [1].
In the literature [1-7], [17], different types of
FACTS are applied to meet these goals:
- Static Var Compensators (SVC), which are the
most important FACTS devices. They have been used
for a number of years to improve transmission line
economics and system losses by resolving dynamic
voltage problems and reactive power control.
- Thyristor controlled series compensators
(TCSC), an extension of conventional series
capacitors through adding a thyristor-controlled
reactor. TCSC increase energy transfer, dampening of
subsynchronous resonances, and control of line power
flow [7].
- STATCOM are GTO (gate turn-off thyristor)
based SVC’s [10]. They don’t require as large
inductive and capacitive components as SVC’s to
provide inductive or capacitive reactive power to high
voltage transmission.
- Unified Power Flow Controller (UPFC).
Actually an UPFC is the result of connecting a
STATCOM with TCSC in the transmission line. This
device combines the benefits of a STATCOM and a
TCSC [11].
Although PID controllers, lead/lag networks and
other conventional controls are simple and easy to
design, their performances deteriorate when the
system operating conditions vary widely and
disturbances occur. During the past two decades
power system has undergone many changes and
variations of the parameters may occur at any time.
Modern solutions like intelligent and adaptive
systems can be used to solve complex problems and
to improve the dynamic and steady state stability.
Depending on the type of the real plant
considered, an adaptive or intelligent systems were
studied in [10-15], [18-22]. In fact, excepting the
intelligent systems, the adaptive systems are the only
way to compensate the large variations of the plant
parameters.
The SVC modeled in the paper is a TCR-FC type
with two components: the thyristor controlled reactor
(TCR) and the fixed capacitor (FC). The total
admittance of the TCR-FC is provided to the power
system using a self-tuning system.
The next chapters describe how work a Static Var
Compensator, the modeling of the TCR-FC, some
theoretical aspects about the indirect self-tuning
control and the design of the self-tuning controller for
power system enhancement.
The adaptive algorithm used for the SVC control
is obtained from the minimum variance (MV) theory
and the controller parameters are determined
commonly after an on-line identification of the plant
parameters. We choose for plant identification the
recursive least square method with exponential
forgetting factor.
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2. The SVC operation principles
The particular SVC modeled in this chapter
consists of a thyristor controlled reactor (TCR) stage
to provide the lagging vars and a fixed capacitor FC
which offer the leading vars.
The lagging reactive power (inductive reactive
power) and TCR current amplitude can be controlled
continuously by varying the thyristor firing angle
between 90 and 180. The TCR firing angle can be
fully changed within one cycle of the fundamental
frequency, thus providing smooth and fast control of
reactive power supplied to the system [13], [17].
Fig. 2 – TSC control
Applications with only TSC's are also available,
providing stepwise control of capacitive reactive
power, but improved performances can be obtained
by using a fixed capacitor (FC) connected in parallel
with thyristor controlled reactor (TCR), resulting a
TCR-FC configuration like in [5], [12].
So, the TCR-FC can be seen as an adjustable
reactance that can perform both inductive and
capacitive compensation. The reactive power
injection of a SVC connected to a busbar and the total
admittance of the SVC are given by (1).
QSVC   BSVC  V 2
(1)
BSVC  BC  B L
In (1) QSVC is the reactive power injection of the
SVC (TCR-FC type), BSVC the admittance of the
SVC, BC the constant admittance of the fixed
capacitor and BL the variable admittance of the
thyristor controlled reactor.
For a TCR-FC compensator the admittance
depends on firing angle α [13].
Fig. 1 – TCR control
B SVC 
The leading vars (capacitive reactive power) are
provided by a different number of capacitor bank
units (only one bank is shown in the diagram) which
are switched on or off in steps. The capacitor
switching operation is completed within one cycle of
the fundamental frequency and the TSC provides a
faster and more reliable solution to capacitor
switching than conventional mechanical switching
devices [13].
An alternative current filter is usually used to
reduce and absorb the harmonic current components
generated by TCR. Thus, the leading vars are
switched in steps, the lagging vars can be varied
smoothly. By combining these two components, fixed
capacitor and continuously controlled reactor, a
smooth variation in reactive power can be achieved
and the sum of the reactive power becomes linear.
1
 BL
XC
2  2  sin 2 
B L   
X L
(2)
The inductive reactance and capacitive reactance
are XL and XC.
3. Theoretical aspects on indirect self-tuning
control with MV and LSM algorithms
Adaptive controls are well suited for systems with
unknown changes (parametrical, nonlinearities or
disturbances). In these modern strategies the
controller parameters can be initially tuned and online
modified by the adaptation mechanism. In the
literature are two major directions: model reference
adaptive control and model identification adaptive
221
control (usually named self-tuning control). Both of
these modern controls it can have a direct or indirect
parameter modification scheme [16], [20], [22].
The adaptive system considered in the paper is the
self-tuning control, which actually has a model
identification indirect adaptive scheme. The block
diagram is presented in figure 3 and contains four
major parts: the adjustable controller, the plant, the
plant identification block and the adjustable
mechanism [16].
Initial value of matrix F determines influence of
initial parameter estimations to the identification.
Using the plant parameters obtained from the
identification block the adjustment mechanism will
modify the parameters of the controller. The
controller designed in the next chapters is a direct
digital control type with minimum variance MV
algorithm.
The direct digital controls DDC are designed to
replace conventional controllers with numerical
algorithms, which in most cases are determined by
minimizing different criteria. The minimum variance
MV algorithm supposes a control signal so that the
variance of the error signal is minimized [16].
2
(5)
J (u (k ))  M y ( k )  y pr (k )

Fig. 3 – Indirect self-tuning control
The plant in our case will be the power system
and SVC connected to the generator busbar. The plant
parameters are identified at every discrete moment
using the input and output data from the plant by the
identification block.
The most practical identification algorithm is the
least squares method LSM or other variant of this
type [16]. These kinds of methods can be used for the
discrete on-line identification of processes that are
described by the following transfer function:
 
H z 1 
b0  b1 z 1  ...  bm z  m d
z
1  a1 z 1  ...  bn z  n

4. Self-tuning control of the SVC for power
system enhancement
The block diagrams from figure 4 show the power
system enhancement using the self-tuning control of
the SVC. We borrowed the single machine infinite
bus theory consists of a synchronous generator
connected via a transmission line, represented by
reactance xe, to a large power system, represented by
the infinite busbar.
The static VAR compensator will be located at the
generator busbar to provide significant damping
during transient conditions [4], [7], [15].
(3)
The main disadvantage of the pure recursive least
square method is the absence of signal weighting.
Each input and output affect result by the same
weight, but actual process parameters can change in
time. Thus newer inputs and outputs should affect
output more than older values. This problem can be
solved by exponential forgetting method.
The parameters are recursively estimated using
the least square method with an exponential
forgetting factor with the algorithm (4).
 k  1   k   K k  1
 k  1  y k  1   T k  1   k 
F k    k  1
K k  1 
T
   k  1  F k    k  1
1
F k  1   F k   K k  1   T k  1  F k  1


where
computed
Fig. 4 – Indirect self-tuning control of the SVC

(4)
 k   [a1 a2 ...an b0 b1...bm ] are the
process
parameter
estimations;
T
k   [ yk  1...  yk  n uk  d  uk  d  m]T
contains the output and input values; F(k) the
covariance matrix updated in each step; K(k+1) the
parameters identification gains, ε(k+1) the
identification error, λ forgetting factor (0..1).
Although the synchronous generator can be
described by Park’s nonlinear relationships, at the
sampling instant t=kTs the adaptive system uses a
discrete second order linear model.
(6)
A q 1  yk   B q 1  u k 
Where y(k) is the sampled output  (generator
speed deviation) at instant k, u(k) sampled input uS of
the SVC, Ts sampling period, q-1 backward shift
operator, k sampling instant, A and B the second order
polynomials (7).
222
 
 
 
A q 1  1  a1q 1  a2 q 2
B (q 1 )  b0 q 1  b1q 2
(7)
The discrete second order model of the power
plant with SVC is transformed in a second order
difference equation.
y (k )  a1 y (k  1)  a2 y (k  2) 
Figure 4 highlights in the second diagram the
auxiliary adaptive control loop diagram of the SVC to
improve the dynamic performance of the integrated
system.
The dynamic equation (11) describes the control
loop of the SVC.

BS 
(8)
 b0u (k  1)  b1u (k  2)
The LMS identification block has the goal to
estimate recursively in real time the four coefficients
of the relation (8) by continuously measuring the
input samples u(k) and the output samples y(k).
If the reference for the speed deviation is zeros the
minimum variance DDC controller has the algorithm
(9), which is the minimization of relation (5).
u k  
 
   
G q 1
 y k 
B q 1  F q 1
(9)
where the G and F are the DDC-MV controller
polynomials.
 
F q 1  1
G (q 1 )  g 0  g1q 1
(10)
The coefficients of the controller polynomials
depend on the coefficients of the plant polynomials
(g0=-a1, g1=-a2).
The plant parameters are considered unknown
(varies in time) and being identified by the LSM
identification block, which means the controller
parameters are also modified in every sampling
instant by the adjustment mechanism. So, because the
coefficients of the DDC controller are updated
continuously using the minimum variance algorithm,
the computed control signal u(k) can be considered an
optimal instant value.
K SVC
B  BS 0 K SVC
 Vref  Vt   S

 u S (11)
TSVC
TSVC
TSVC
In the design procedure the generator is also
equipped with an automatic voltage regulator AVR
for the field voltage Efd, characterized by a first order
model (12), time constant TAVR and constant KAVR.

E fd 
K AVR
1
 Vref  Vt  
 E fd
TAVR
TAVR
(12)
5. Simulations and experimental results
In figure 5 is shown the SVC self-tuning control
diagram for power system stability enhancement used
for simulations.
In the diagram the SMIB block contains the model
of the generator connected through a transmission
line to an infinite busbar. This block has as inputs the
field voltage Efd, the mechanical torque Tm, the
infinite busbar voltage Vb, where we will simulate the
fault and the SVC admittance BS, modified by the
SVC adaptive control loop. In the SMIB model, the
generator and the static VAR compensator are
connected to the same busbar, characterized by
voltage Vt.
The static VAR compensation is adjusted to
exchange capacitive or inductive current to the
system and to damp the rotor angle and speed
oscillations.
Fig. 5 – SVC control scheme (Matlab/Simulink)
223
The following parameters were used for the
simulation (p.u.):
Transmission line
xe=0.2;
Generator
xd=2; xq=2; t’d0=5; H=3; x’d=0.3; Tm=0.5; Kd=2;
AVR
KAVR=100; TAVR=0.1;
SVC
Bsmin=-0.3; Bsmax=0.3; Bs0=0.1; usmin=-0.2;
usmax=0.2; Ksvc=50; Tsvc=0.1;
First case that we have studied was the behavior
of the power system after a 0.5 second fault (3-phase
short-circuit) near the infinite busbar without the
auxiliary signal provided by the adaptive loop.
The figure 6 shows the evolutions of the rotor
angle and the speed deviation after the fault. The
SVC conventional loop tries to damp the oscillation
of the signals, but the performances are not so good,
because the settling time is about 25 seconds.
Fig. 7 – Rotor angle, speed and total admittance
Fig. 6 – Rotor angle and speed
In the second case in the simulations we
considered the same fault (0.5 second 3 phase shortcircuit), but with the auxiliary adaptive loop for the
SVC control.
Figure 7 shows the rotor angle, speed and the total
admittance in presence of the auxiliary signal
provided by the self-tuning controller.
The self-tuning controller has an important role in
damping the oscillation caused by the temporary
fault. So, the SVC control loop including the selftuning controller damps the oscillation in a more
efficient way and the settling time is reduced to 10
seconds.
6. Conclusions
The paper presents the adaptive control of a static
var compensator for power system enhancement. The
single machine infinite busbar SMIB theory and
model were used for power system configuration and
the simulations and experimental results were
obtained using Matlab-Simulink software.
A type of SVC was investigated in this paper to
improve transmission line economics and system
losses by resolving dynamic voltage problems and
reactive power control. The TCR-FC (thyristor
controlled reactor TCR and fixed capacitor FC) was
located on the generator busbar and the behavior of
the power system was studied after the 3 phase shortcircuit that occurs near the infinite busbar. This type
of SVC can be seen as an adjustable reactance that
can perform both inductive and capacitive
compensation to improve the quality of the power
system.
To provide significant damping during transient
conditions on power system the SVC control diagram
uses a conventional SVC loop and an auxiliary signal
224
computed by the self-tuning controller. The plant
parameters were identified at every discrete moment
using the input and output data from the plant by the
identification block using the least squares method
with an exponential forgetting factor. Using the plant
parameters obtained from the identification block the
adjustment mechanism modified continuously the
parameters of the minimum variance based controller.
The main goal of introducing the auxiliary loop was
to damp the oscillations of the rotor angle after the
fault.
Comparative results made after the simulations
with the adaptive controller auxiliary loop
emphasized a shorter settling time and a better
damping of the power system oscillations.
[10]
[11]
[12]
[13]
References
[1] Mithulananthan, N., Cañizares,C.A., Reeve, J.
and Rogers, G.J. (2003), Comparison of PSSS,
SVC and STATCOM Controllers for Damping
Power System Oscillations, IEEE Transactions
on Power Systems, vol. 18, no. 2, pp. 786-792.
[2] Farsangi, M.M., Song, Y.H. and Lee, K.Y.
(2004), Choice of FACTS device control inputs
for damping interarea oscillations, IEEE Trans.
on Power Systems, vol. 19, no. 2, pp. 11351143.
[3] Zellagui, M., Chaghi, A. (2012), Effects of
shunt FACTS devices on MHO distance
protection setting in 400 kV transmission line,
Electrical and Electronic Engineering, vol. 3
(2), pp. 164-169.
[4] Hingorani, N. G. and Gyugyi, L., (2000),
Understanding
FACTS:
Concepts
and
technology of flexible AC transmission systems,
IEEE Press.
[5] Kodsi, S., Cañizares, C.A. and Kazerani, M.
(2006), Reactive current control through SVC
for load power factor correction, Electric Power
Systems Research, vol. 76, pp. 701-708.
[6] Zou, Z., Jiang, Q. J., Cao, Y. J. and Wang, H. F.
(2005), Normal form analysis of interactions
among multiple SVC controllers in power
systems,” Proceedings of IEEE Generation,
Transmission and Distribution, vol. 152, pp.
469-474.
[7] Panda, S. and Padhy, N.P. (2007),
Matlab/Simulink based model of single machine
infinite bus with TCSC for stability studies and
tuning employing GA, International Journal of
Electrical and Electronics Engineering, vol. 1
(5), pp. 314-323.
[8] Li, L. F., Liu, K. P. and Ma, L. (2005),
Intelligent control strategy of SVC, IEEE/PES
Transmission and Distribution Conference &
Exhibition.
[9] Banga, A. and Kaushik, S.S., (2011), Modeling
and simulation of SVC controller for
enhancement of power system stability,
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
225
International Journal of Advances in
Engineering & Technology, vol. 3, pp. 79-84.
Zolghadri, M.R. (2006), Power System
Transient Stability Improvement Using Fuzzy
Controlled STATCOM, IEEE Proc. Power
System Technology, pp. 1-6.
Dash, P. K., Morris, S. and Mishra, S. (2004),
Design of a nonlinear variable-gain fuzzy
controller for FACTS devices, IEEE Trans. on
Control Systems Tech., vol. 12, pp. 428-438.
Mishra, Y., Mishra, S. and Dong, Z.Y. (2008),
Rough Fuzzy Control of SVC for Power System
Stability Enhancement, Journal of Electrical
Engineering & Technology, vol. 3, no. 3, pp.
337-345.
Karpagam, N., and Devaraj, D. (2009), Fuzzy
logic control of static VAR compensator for
power system damping, International Journal of
Electrical and Electronics Eng., pp. 3–10.
Miranda, V. (2007), An improved fuzzy
inference system for voltage/VAR control, IEEE
Transaction on Power Systems, vol. 22, issue 4,
pp. 2013-2020.
Dash, P. K., Mishra, S. and Liew, A. C. (1995),
Fuzzy logic based VAR stabilizer for power
system control, IEEE Proc. Generation,
Transmission and Distribution, vol. 142, pp.
618-624.
Tao, G., (2003), Adaptive control design and
analysis, John Wiley and Sons, New York.
Oltean, S.E. (2012), Modern control of static var
compensator for power system stability
enhancement, Scientific Bulletin of the „Petru
Maior” University of Tîrgu Mureş, vol. 9
(XXVI), no. 1, pp. 33-37.
Hsu, Y.Y. and Cheng C.H., (1987), Design of a
static VAR compensator using model reference
adaptive control, Electric Power Systems
Research, vol. 13, pp. 129 – 138.
Dash, P.K., Sharaf, A.M. and Hill E.F., An
adaptive stabilizer for thyristor controlled static
var compensators for power systems, IEEE
Transactions on Power Systems, vol. 4, no. 2,
pp. 403-410.
Fusco G. and Russo M., (2004), Performance
comparison between self-tuning and model
reference based adaptive schemes for nodal
voltage regulation in power systems,
Proceedings on Control 2004, UK, ID 108.
Djagarov, N.F., Grozdev, Z.G., Bonev, M.B.
and Georgiev, G.D., (2006), An adaptive control
of static var compensator on power systems,
International Conference on Energy &
Environmental Systems, pp. 151-157.
Rahima, A.H.M.A., Nowicki, E.P. and Malik,
O.P., (2006), Enhancement of power system
dynamic performance through an on-line selftuning adaptive SVC controller, Electric Power
Systems Research, vol. 76, pp. 801–807.