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Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 190-195
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Advances in Natural and Applied Sciences
ISSN:1995-0772 EISSN: 1998-1090
Journal home page: www.aensiweb.com/ANAS
Auxiliary Stabilizer of STATCOM based on the State Feedback Theory
Reza Saki, Somayeh Yarahmadi, Faranak Nikabadi, Vahid Chegeni
Department of Electrical Engineering, Doroud Branch, Islamic Azad University, Doroud, Iran
ARTICLE INFO
Article history:
Received 25 January 2014
Received in revised form 12
March 2014
Accepted 14 April 2014
Available online 5 May 2014
ABSTRACT
This paper addresses an auxiliary stabilizer based on the static synchronous
compensator (STATCOM) to improve small signal stability of power system. The
proposed stabilizer is designed by using state feedback theory. A single machine power
system which is installed with STATCOM is considered as case study and nonlinear
simulations are carried out in MATLAB software. Several nonlinear time-domain
simulations demonstrate the validity of proposed method in damping power system
oscillations.
Keywords:
State Feedback Theory
Power System Stability
Static Synchronous Compensator
Low Frequency Oscillations
© 2014 AENSI Publisher All rights reserved.
To Cite This Article: Reza Saki, Somayeh Yarahmadi, Faranak Nikabadi, Vahid Chegeni, Auxiliary Stabilizer of STATCOM based on the State
Feedback Theory. Adv. in Nat. Appl. Sci., 8(8): 190-195, 2014
INTRODUCTION
Recently development in the field of high-power electronic has made Flexible AC Transmission System
(FACTS) devices viable and attractive for power system applications. FACTS devices have been widely used
for different purposes in power systems such as stability improvement, voltage control, power control, etc
(Nilsson, 1995; El-Sadek et al., 1997; Mihalič and Papič, 1998; Oliveira et al., 1999; Fang and Ngan, 2000;
Hingorani et al., 2000; Kazemi and Sohrforouzani, 2006; Taher et al., 2010; Nguimfack-Ndongmo et al., 2014;
Zamora-Cárdenas et al., 2014). Paper (Nilsson, 1995) discusses that the AC transmission system is emerging as
a key recourse for the electric utilities. It is increasingly being stressed by wheeling demands for which it may
not have been built. However, the power flows in a network are not easily controlled because line parameters,
which determine the distribution of power in the system, are not easily changed. Power electronics based
systems which can provide the operators the needed flexibility in controlling the system power flows have been
in use for some time and more such systems are being developed. These systems are broadly referred to as
FACTS which stands for flexible AC transmission system. This paper discusses the implications of FACTS
technologies for the security and reliability of the AC transmission system and discusses how the new systems
fits into the existing systems for control of the power system as a whole. Paper (Zamora-Cárdenas et al., 2014)
proposes a practical approach to incorporate synchronized phasor measurements into a weighted least squares
state estimation algorithm suitable for electric networks containing flexible AC transmission systems (FACTS)
controllers. Equations relating the branch current phasors to FACTS controllers’ state variables are derived from
first principles in order to directly append synchronized phasor measurements of currents and voltages to the set
of measurement data collected from the supervisory control and data acquisition system to estimate the
equilibrium point of the electric power system. The phase angle measured by a perfect phasor measurement unit
at one of the buses is selected as the global reference for the estimation, such that the voltage phasor
measurements provided as data to the estimator correspond to the angle differences between all remaining
voltage phasor measurements and the reference angle. Furthermore, the synchronized current phasor
measurements are transformed to rectangular coordinates to enhance the convergence properties of the proposed
state estimation approach. In both cases, the variance of the new set of synchronized measurements is calculated
based on the uncertainty propagation theory. The proposed approach simultaneously upgrades the estimated
values of the state variables of FACTS devices and the electric network for a unified estimation of the system
state. Lastly, numerical simulations with two real-life electric power networks are reported to demonstrate the
prowess of the proposed approach. Paper (El-Sadek et al., 1997) discusses that a flexible AC transmission
system (FACTS) is a proposed new technique for balancing unbalanced three phase arc furnace loads. Although
reactances of conductors can be balanced by traditional methods, the method proposed here is a unique method
Corresponding Author: Reza Saki. Islamic Azad University, Department of Electrical Engineering, Doroud, Iran.
E-mail: [email protected]
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Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 190-195
for balancing inevitably unbalanced arc resistances. Compensator controller elements and relations between
their variables and the actual firing angles are derived. The influence of furnace load balancing on its
characteristics is discussed.
Current paper aims at investigating an auxiliary stabilizer of STATCOM based on the state feedback theory.
Single machine infinite bus power system which is installed with STATCOM is considered as case study.
Simulation results demonstrate the effectiveness of the proposed method to damp out the oscillations.
Test System:
Figure 1 shows a single machine infinite bus power system installed with STATCOM. A non-linear
dynamic model of the system is derived by disregarding the resistances of all components and the
transients of the transmission lines and transformer of the STATCOM. The nonlinear dynamic model is
given as (1).

   Pm  Pe  D M


δ      1
0



Eq   E q  E fd  Tdo
 
E   E  K  V  V   T
fd
a
ref
t
a
 fd
 
3m E
sin  δE  IEd  cos  δE  IEq 
Vdc 
4C
dc

(1)
A linear dynamic model is obtained by linearising the non-linear model around the nominal operating
condition. The linear model is given as (2).
δ  w 0 w

   Pe  D /M

 /
/
E q  (  E q  E fd )/Tdo
 
E fd   1 TA  E fd   K A TA  Vt
 
/
v dc  K 7 δ  K 8 E q  K 9 v dc  K ce m E  K cδe δ E
(2)
Where,
Pe  K1δ  K 2 E q/  K pd vdc  K pem E  K pδE δ E
E q  K 4 δ  K 3E q/  K qd v dc  K qem E  K qδE δ E
Vt  K 5δ  K 6 E q/  K vd vdc  K ve m E  K vδE δ E
mE: Deviation of pulse width modulation index mE at shunt inverter. By controlling mE, the
output voltage of the shunt converter is controlled. E: Deviation of the phase angle at shunt inverter. By
controlling E, the exchanged active power between STATCOM and power system is controlled. The dynamic
model of the system in the state-space form is obtained as (3).
    0
 δ   K
     1
M
 w  
    K
  E q/     /4
    Tdo
 E   K K
 fd    A 5
    TA
  vdc  

  K 7
w0
0
K
 2
M
K3
 /
Tdo
0
0
0

0
Supplementary Stabilizer:
KAK6
TA
K8
0
0
1
Tdo/

1
TA
0
0
0
 
 
  
K pd  
K

   pe

M   w  
M
K qd   /   K qe
 /
  E    /
Tdo   q  
Tdo
 

K A K vd   E fd   K A K ve

 

TA   v dc  
TA
 
 
  Kce
K 9  
0

K pe 

M 
K qe   m E 
 /

Tdo   E 

K K
 A ve 
TA 

K ce 
(3)
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The stabilizer is mainly provided to increase damping in power system. This controller is generally made as
a lead-lag compensator. Figure 2 shows the block diagram of conventional stabilizer. In this paper, state
feedback is used to design stabilizer. This method is introduced in the next section.
Fig. 1: A single-machine infinite-bus power system installed with STATCOM.
Fig. 2: The Structure of classical stabilizer.
State feedback:
The state of a dynamical system is a collection of variables that permits prediction of the future
development of a system. We now explore the idea of designing the dynamics a system through feedback of the
state. We will assume that the system to be controlled is described by a linear state model and has a single input.
The feedback control will be developed step by step using one single idea: the positioning of closed loop
eigenvalues in desired locations. Figure 3 shows a diagram of a typical control system using state feedback. The
full system consists of the process dynamics, which we take to be linear, the controller elements, K and kr , the
reference input, r, and processes disturbances, d. The goal of the feedback controller is to regulate the output of
the system, y, such that it tracks the reference input in the presence of disturbances and also uncertainty in the
process dynamics. An important element of the control design is the performance specification. The simplest
performance specification is that of stability: in the absence of any disturbances, we would like the equilibrium
point of the system to be asymptotically stable. More sophisticated performance specifications typically involve
giving desired properties of the step or frequency response of the system, such as specifying the desired rise
time, overshoot and settling time of the step response. Finally, we are often concerned with the disturbance
rejection properties of the system: to what extent can we tolerate disturbance inputs d and still hold the output y
near the desired value (Aström and Murray, 2010).
Fig. 3: A feedback control system with state feedback (Aström and Murray, 2010).
State feedback theory or pole placement, is a method employed in feedback control system theory to place
the closed-loop poles of a plant in pre-determined locations in the s-plane. Placing poles is desirable because the
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Advances in Natural and Applied Sciences, 8(8) July 2014, Pages: 190-195
location of the poles corresponds directly to the Eigen-values of the system, which control the characteristics of
the response of the system. The system must be considered controllable in order to implement this method. The
state space model of system can be represented as (4) and then, the poles of the system are the roots of the
characteristic equation given by (5).
 x  A x  Bu

 y  C x  Du
(4)
sI  A  0
(5)
Full state feedback is utilized by commanding the input vector u as (6).
u  K x
(6)
Eventually, the state space equations can be derived as follows;
 x  A  BK x
 y  C  DK x

(7)
The roots of the state feedback system are given by the characteristic equation as follows:
det sI  A  BK
(8)
Comparing the terms of this equation with those of the desired characteristic equation yields the values of
the feedback matrix K which force the closed-loop Eigen-values to the pole locations specified by the desired
characteristic equation.
Simulation Results:
As stated before, in this paper, state feedback is used to design supplementary stabilizer of STATCOM. The
output signal Δω is assumed as input of feedback and ΔmE is considered as output of state feedback. Simulation
results are carried out following 5-cycles three-phase short circuit at bus 1. Figure 4 shows the generator speed
following disturbance. It is clear that the oscillations are damped out and system stability is passed after 15
seconds. Figure 5 indicates the rotor angle following 5-cycles three-phase short circuit at bus 1. This figure
shows that rotor angle is driven back to nominal value after disturbance. Figures 6 and 7 show the voltage angle
and magnitude at bus 1 respectively. The voltage stability is clear in these figures. Figure 8 shows the stabilizer
output signal following disturbance. It is clear that stabilizer injects extra signal to the STATCOM and provides
more damping to the system.
1.0004
1.0003
1.0002
Speed G (p.u.)
1.0001
1
0.9999
0.9998
0.9997
0.9996
0.9995
0
5
10
Time (s)
15
Fig. 4: Generator speed following 5-cycles three-phase short circuit at bus 1.
20
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1.245
1.24
Rotor angle (Rad)
1.235
1.23
1.225
1.22
1.215
1.21
1.205
1.2
0
5
10
Time (s)
15
20
Fig. 5: Rotor angle following 5-cycles three-phase short circuit at bus 1.
0.505
Voltage angle at bus 1 (Rad)
0.5
0.495
0.49
0.485
0.48
0.475
0.47
0
5
10
Time (s)
15
20
Fig. 6: Voltage angle at bus 1 following 5-cycles three-phase short circuit at bus 1.
Voltage magnitude at bus 1 (p.u.)
1.005
1
0.995
0.99
0.985
0
5
10
Time (s)
15
20
Fig. 7: Voltage magnitude at bus 1 following 5-cycles three-phase short circuit at bus 1.
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Fig. 8: Stabilizer output signal following 5-cycles three-phase short circuit at bus 1.
Conclusions:
In this paper, state feedback theory was applied to design stabilizer based on the STATCOM. A single
machine infinite bus power system installed with STATCOM was considered as case study. Simulation results
demonstrated that the designed stabilizer could guarantee the system stability following large signal
disturbances such as three-phase short circuit.
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