Optimal Control for Static Synchronous
Compensator Based on LQR Approach
M.Mahdavian\ G.Shghoiian
2
, S.S.Saiehi Ghaiehsefid
3
, AZareazadeh
2
, MJabbari
2
, S.Bahadory
l
I
Oeptment of Electrical Engineering, Naein Branch, Islamic Azad University, Isfan, Ir
2
0epartment of Electrical Engineering, NajafabadBranch, Islamic Azad University, Isfan, Iran
3
Khuzest Regional Electricity, Khuzestan, Iran
Atract- In this paper an optimal control strategy based on
the linear quadratic regulator (LQR) method for static synchr-
onous compensator (ST A TCOM) is introduced. Simulations
results verify the performance of the controller in improvc the
damping of the power systems.
I. INTRODUCTION
The electric power system is complex dynamic network,
non linear in nature, non-stationary and works in a changing
environment. Flexible ac transmission system (FACTS) co-
ntrollers are power electronic based controllers which can
influence transmission system voltage, currents, impedances
and phase angle rapidly. Three phase voltage source conver-
ter (VSC) is the basic building block of most new FACTS
and custom power equipment. There are widely used in ind-
ustrial applications [1, 2].
A STATCOM is one of the ndamental FACTS devices,
which is connected as a shunt to the network, for voltage re-
gulation and dynamic voltage control. The STA TCOM is
used to control transmission voltage by reactive power shunt
compensation. addition, STATCOM can also increase po-
wer system stability by damping power oscillations.
A number of studies have been performed about the dyna-
mic behavior of STA TCOM and its application to improve
the transient performance of power systems. Some of the co-
ntrollers desied are the loop shaping [3], conventional PI
controllers [
4
], state feedback controller [T5], linear quadra-
tic regulators [5], pole assignment [6] and zzy controllers
[7].
A dc capacitor voltage balance control method for casca-
de multilevel STATCOM and a general analytical method
for balance control strategy is presented in [8]. In [9] solves
the problem of power system stabilization by using the
advanced static var compensator to increase the damping of
the electromechanical and exciter modes of the power syst-
em, which is designed using a two-level optimization output
feedback control and the strip poles assignment method.
This paper presents the mathematical modeling and analy-
sis of STATCOM. An optimal control strategy based on the
LQR approach for STA TCOM in continuous time proposed.
e simulation results show that this proposed technique
good dynamic chteristics and regulation precision.
II. MATHEMATICAL MODEL OF THE COMPENSATOR
The STATCOM is based on a simple concept. Figure 1
presents the topology of a three-phase VSC working either
as STATCOM or as PWM rectifier.
978-1-4673-2025-2112/$31.00 ©2012 IEEE
._
r----------------------------,
: l
U. ' ��' ·�L�. - -:
In Rs Ls
u.
U
. I Rs Ls
Ito In Ire
Figure 1. Three-phase PWM converter topology
The STA TCOM connected through interface impedance
to an infinite bus. Rs and Ls are me resistance and induct-
ance of the line reactor, respectively. In the dc side, a
resistance Roc which represents the sum of the switching
losses of the inverter and the power loss in the capacitor is
in shunt with the capacitor CDC, which produces a set of
controllable three-phase output voltages with the equency
of the ac power system.
The converter phase voltage and three-phase VSC outp-
ut currents are represented by the two vectors:
U
c =
[
UCa UCb UCcl
T
I
s =
[
isa isb ise
]
T
(1)
(2)
Also, the STATCOM bus phase voltage can represent-
ed by
U
M:
UM =
[
UMa UMb UMcl
T
(3)
Based on theses currents and voltages, three vectors defi-
ned as:
I MC =
[
iAB iBC iCA
]
T
1
[
. . . .
=
Isa -Isb Isb -Ise
U
LC =
[U
CAB U CBC
U
CCA
]
T
=
[
UCa -UCb UCb -UCe
ULM =
[
UMAB UMBC UMCA
]
T
=
[
UMa -UMb UMb -UMe
(4)
UCe -UCa
]
T
(5)
UMe -U Ma
]
T
(6)
The basic electronic block for a STATCOM is a voltage
source inverter (VSI) that converter the dc voltage at input
terminal (Uoe) into three phase set of output voltages. The
switches are modeled as ideal switches that can be tued on
and off by a control signal obtained om the controller.