c TÜBİTAK
Turk J Elec Eng & Comp Sci, Vol.20, No.Sup.2, 2012, doi:10.3906/elk-1105-4
Dynamic stability enhancement of a multimachine
electric power system using STATCOM
Hasan Fayazi BOROUJENI, Reza HEMMATI∗, Sayed Mojtaba Shirvani BOROUJENI
Department of Electrical Engineering, Boroujen Branch, Islamic Azad University,
Boroujen-IRAN
e-mails: hasanfayazi@gmail.com, reza.hematti@gmail.com, mo shirvani@yahoo.com
Received: 03.05.2011
Abstract
With the expansion of electric power systems, the size and complexity of the network is increased. One
of the most important drawbacks of network expansion is the reduction in the damping torque of the whole
system. The lack of damping torque can lead to fluctuations and instability in the power system. With
regard to this problem, power system stabilizers (PSSs) have been widely utilized to improve power system
stability. However, due to some drawbacks of the conventional PSSs, the need for finding a better substitution
still remains. Therefore, in this paper, the application of a static synchronous compensator (STATCOM)
to improve dynamic stability of a multimachine electric power system is presented and a supplementary
stabilizer based on the STATCOM is incorporated. Intelligence optimization methods such as particle swarm
optimization and genetic algorithms are considered for tuning the parameters of the proposed stabilizer.
Several nonlinear time-domain simulation tests visibly show the ability of the STATCOM in damping power
system oscillations.
Key Words: Flexible AC transmission systems, static synchronous compensator, damping of power system
oscillations, dynamic stability enhancement, multimachine electric power system
1.
Introduction
The rapid development of the high-power electronics industry has made flexible alternating current transmission
system (FACTS) devices viable and attractive for utility applications. FACTS devices have been shown to be
effective in controlling the parameters of the power system and also in damping power system oscillations. In
recent years, new types of FACTS devices have been investigated that may be used to increase power system
operation flexibility and controllability, enhance system stability, and achieve better utilization of existing power
systems [1]. The static synchronous compensator (STATCOM) is one of the most important FACTS devices,
and it is based on the principle that a voltage-source inverter generates a controllable AC voltage source behind
a transformer-leakage reactance. Therefore, the voltage difference across the reactance produces active and
∗ Corresponding author:
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Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen-IRAN
BOROUJENI, HEMMATI, BOROUJENI: Dynamic stability enhancement of a multimachine electric...,
reactive power exchanges between the STATCOM and the transmission network. A STATCOM can be used
for the dynamic compensation of power systems to provide voltage support [2–6]. Moreover, a STATCOM can
be used for transient stability improvement by damping low-frequency power system oscillations [7–10].
The objective of this paper is to investigate the ability of a STATCOM in dynamic stability improvement
via the damping of low-frequency oscillations. Intelligence optimization methods such as particle swarm
optimization (PSO) and the genetic algorithm (GA) are considered for tuning the parameters of a STATCOM
supplementary stabilizer. A multimachine power system installed with a STATCOM is considered as the case
study. A classical power system stabilizer (PSS) is connected to the STATCOM and the parameters of this
STATCOM-based stabilizer are adjusted using PSO and the GA. The advantages of the proposed methods
are their feasibility and simplicity. Different load conditions are considered to show the effectiveness of the
STATCOM and also to compare the performance of PSO and the GA. Simulation results show the validity of
the STATCOM in low-frequency oscillation (LFO) damping and the stability enhancement of large electrical
power systems.
2.
The system under study
Figure 1 shows a multimachine power system installed with the STATCOM [11]. The static excitation system,
model type IEEE-ST1A, has been considered. The STATCOM is assumed to be based on pulse width modulation
(PWM) converters. Details of the system data are given in [11]. To assess the effectiveness and robustness of the
proposed method over a wide range of loading conditions, 3 different cases (nominal, light, and heavy loading)
are considered and listed in Table 1 [12]. In this paper, a turbine-governor system is also modeled to eliminate
steady state error of the responses.
7
Gen 2
8
9
2
3
STATCOM
5
Gen 3
6
Load A
Load B
4
1
Gen 1
Figure 1. Multimachine electric power system installed with STATCOM.
3.
Dynamic model of the system with STATCOM
The nonlinear dynamic model of the system installed with the STATCOM is given in Eq. (1). The dynamic
model of the system is completely presented in [11] and the dynamic model of the system installed with the
STATCOM is presented in [13].
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Turk J Elec Eng & Comp Sci, Vol.20, No.Sup.2, 2012
Table 1. System loading conditions.
Light
P
Q
0.65 0.55
0.45 0.35
0.50 0.25
Load
A
B
C
Nominal
P
Q
1.25 0.50
0.90 0.30
1.00 0.35
Heavy
P
Q
2.00 0.80
1.80 0.66
1.56 0.60
⎧
ω̇ = (Pm − Pe − Dω)/M
⎪
⎪
⎪
⎪
⎪
δ̇ = ω0 (ω − 1)
⎪
⎪
⎨
Ėq = (−Eq + Efd )/Tdo
⎪
⎪
⎪
⎪
Ėfd = (−Efd + Ka (Vref − Vt ))/Ta
⎪
⎪
⎪
⎩
E
V̇dc = 3m
4Cdc (sin (δE ) IEd + cos (δE ) IEq )
(1)
By controlling m E , the output voltage of the shunt converter is controlled. By controlling δE , the exchange of
active power between the STATCOM and the power system is controlled.
4.
STATCOM controllers
In this paper, 2 control strategies are considered for the STATCOM:
1. DC-voltage regulator,
2. STATCOM supplementary stabilizer.
4.1.
DC-voltage regulator
In the STATCOM, the output real power of the shunt converter must be equal to the input real power or vice
versa. In order to maintain the power balance, a DC-voltage regulator is incorporated. The DC voltage is
regulated by modulating the phase angle of the shunt converter voltage. Figure 2 shows the structure of the
DC-voltage regulator. In this paper, the parameters of the DC-voltage regulator are considered as K di = 5.8
and K dp = 3.24. In Figure 2, the δEref is the angle of the phase locked loop in the steady state operation
during the prefault. In fact, the sum of δEref and ΔδE , which is known as δE , is fed into the STATCOM in
order to control the DC voltage. In order to compute δEref , a power flow is performed and the STATCOM
parameters (δE and m E ) are obtained in steady state operation. These parameters are then considered as a
reference during postfault in the power system.
VDCref
VDC
-
+
Eref
Kdp +
Kdi
-
S
Figure 2. DC-voltage regulator.
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BOROUJENI, HEMMATI, BOROUJENI: Dynamic stability enhancement of a multimachine electric...,
4.2.
The STATCOM supplementary stabilizer
A stabilizer controller is provided to improve damping of power system oscillations. This controller is considered
as a lead–lag compensator. It provides an electric torque in phase with the speed deviation in order to improve
the damping of power system oscillations. The transfer function model of the classical stabilizer is given in Eq.
(2), where U in is the input signal, which can be synchronous speed, power of the line, voltage of the bus, etc.
The output signal, U out , is fed as an auxiliary input signal into the STATCOM. This type of stabilizer consists
of a washout filter and a dynamic compensator. The washout filter, which essentially is a high-pass filter, is used
to reset the steady state offset in the output of the PSS. In this paper, the value of the time constant (Tw) is
fixed to 10 s. The dynamic compensator is made up of 2 lead–lag stages and an additional gain. The adjustable
stabilizer parameters are the gain of the stabilizer, K DC , and the time constants, T1–T4. The lead–lag block
presented in the system provides phase-lead compensation for the phase lag, which is introduced in the circuit
between the STATCOM input and the electrical torque.
Uout = K
5.
STW 1 + ST1 1 + ST3
Uin
1 + STW 1 + ST2 1 + ST4
(2)
Stabilizer design
Stabilizer controllers that design themselves have been a topic of interest for decades, especially in classical
PSSs, which are connected to the excitation system of the generator. However, classical PSSs cannot control
the power transmission and also cannot support power system stability under large disturbances, such as a
3-phase fault at terminals of the generator [14]. For these problems, in this paper, a stabilizer controller based
on the STATCOM is provided to mitigate power system oscillations. Two optimization methods, PSO and GA,
are considered for tuning stabilizer parameters. In the next section, an introduction about PSO is presented.
5.1.
Particle swarm optimization
PSO was formulated by Edward and Kennedy in 1995. The thought process behind the algorithm was inspired
by the social behavior of animals, such as bird flocking or fish schooling. PSO is similar to the continuous
GA, which begins with a random population matrix. Unlike the GA, PSO has no evolution operators such as
crossover or mutation. The rows in the matrix are called particles (the same as the GA chromosome). They
contain the variable values and are not binary encoded. Each particle moves about the cost surface with a
velocity. The particles update their velocities and positions based on the best local and global solutions, as
shown in Eqs. (3) and (4) [15]:
new
old
local best
old
global best
old
= w × Vm,n
+ Γ1 × r1 × (Pm,n
− Pm,n
) + Γ2 × r2 × (Pm,n
− Pm,n
).
Vm,n
(3)
new
old
new
Pm,n
= Pm,n
+ ΓVm,n
.
(4)
The PSO algorithm updates the velocity vector for each particle and then adds that velocity to the particle
position or values. Velocity updates are influenced by both the best global solution, associated with the lowest
cost ever found by a particle, and the best local solution, associated with the lowest cost in the present
population. If the best local solution has a cost less than the cost of the current global solution, then the
best local solution replaces the best global solution. The particle velocity is reminiscent of local minima that
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Turk J Elec Eng & Comp Sci, Vol.20, No.Sup.2, 2012
use derivative information, because velocity is the derivative of position. The advantages of PSO are that it
is easy to implement and there are few parameters to adjust. PSO is able to tackle tough cost functions with
many local minima [15].
5.2.
PSO-based stabilizer design
In this section, the parameters of the proposed stabilizer controller are tuned using PSO. In order to produce
the damping torque, 2 control parameters of the STATCOM (m E , δE ) can be modulated. In this paper, the
parameter m E is modulated to the output of the STATCOM supplementary stabilizer and the active power
from bus 7 to bus 8. It is also considered as an input of the STATCOM supplementary stabilizer. Figure 3
clearly shows the structure of the STATCOM supplementary stabilizer. The structure of the supplementary
stabilizer is also shown in Eq. (2). The optimum values of K and T 1 –T 4 , which minimize an array of different
performance indexes, are accurately computed using PSO. In the optimization methods, the first step is to
define a performance index for optimal search. In this study, the performance index is considered as in Eq. (5).
In fact, the performance index is the integral of the time multiplied absolute value of the error (ITAE).
mEref
Active power
from bus 7 to bus 8
-
STATCOM Supplementary
Stabilizer
+
mE
Figure 3. The structure of the STATCOM supplementary stabilizer.
t
t
t |Δω1 | dt+
IT AE =
0
t
t |Δω2 | dt+
0
t |Δω3 | dt
(5)
0
It is easy to understand that a controller with a lower ITAE is better than the other controllers. To compute the
optimum parameter values, a 6-cycle, 3-phase fault is assumed in bus 1 and the performance index is minimized
using PSO. In order to acquire better performance, the number of particles, the particle size, and the number
of iterations Γ1 , Γ2 , and Γ are chosen as 24, 5, 50, 2, 2, and 1, respectively. Moreover, the inertia weight, w,
is linearly decreased from 0.9 to 0.4. The optimum values of the parameters, resulting from the minimization
of the performance index, are presented in Table 2. However, in order to show the effectiveness of the PSO
method, the parameters of the stabilizer controller are tuned using the other optimization method, the GA. In
the case of the GA, the performance index is considered as in the PSO case and the optimal parameters of the
stabilizer controller are obtained, as shown in Table 2.
Table 2. Optimal parameters of the stabilizer using PSO and GA.
K
1.291
6.
T1
0.3412
PSO
T2
0.2291
T3
0.6210
T4
0.3122
K
1.488
T1
0.2022
GA
T2
0.1781
T3
0.7311
T4
0.2827
Results and discussion
In this section, the designed PSO- and GA-based stabilizers are exerted to damp LFOs in the system under study.
In order to study and analyze the system performance under different scenarios, 2 scenarios are considered, as
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BOROUJENI, HEMMATI, BOROUJENI: Dynamic stability enhancement of a multimachine electric...,
follows:
Scenario 1: 6-cycle, 3-phase short circuit in bus 1;
Scenario 2: 6-cycle, 3-phase short circuit in bus 3.
It should be noted that the PSO- and GA-based stabilizers have been designed for nominal operating
conditions. In order to demonstrate the robustness performance of the proposed stabilizers, the ITAE is
calculated under 2 scenarios under all operating conditions (light, nominal, and heavy), and the results are
listed in Table 3. In regard to Table 3, the power system with the PSO-based stabilizer has a lower ITAE than
the GA-based stabilizer. The ITAE is an index for power system oscillation, and the results show that the system
fluctuations have been mitigated with both of the proposed methods. However, in view of the comparison, the
PSO-based stabilizer has better performance than the GA-based stabilizer under all operating conditions and in
all scenarios. The simulation results are presented in Figures 4 and 5. The following cases have been considered
and simulated: in Figure 4, simulation results under Scenario 1 and under nominal operating conditions are
given. In Figure 5, simulation results under Scenario 2 and under heavy operating conditions are given.
1.01
1.01
1.008
1.005
Speed G2 (pu)
Speed G1c (pu)
(b)
(a)
1.006
1.004
1.002
1
1
0.998
0.996
0.994
0
2
4
6
8
10 12
Time (s)
14
16
18
20
0.995
0
2
4
6
8
10 12
Time (s)
14
16
18
20
1.007
1.006
Speed G3 (pu)
1.005
(c)
1.004
1.003
1.002
1.001
1
0.999
0.998
0.997
0
2
4
6
8
10 12
Time (s)
14
16
18
20
Figure 4. System responses under scenario 1 with nominal loading conditions: solid line = PSO-stabilizer, dashed line
= GA-stabilizer, dotted line = without stabilizer, a) ω1 , b) ω2 , c) ω3 .
Figures 4 and 5 both contain 3 plots: the PSO-based stabilizer (solid line), the GA-based stabilizer
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Turk J Elec Eng & Comp Sci, Vol.20, No.Sup.2, 2012
(dashed line), and the system without a stabilizer (dotted line). The simulation results show that applying
the supplementary stabilizer signal greatly enhances damping of the generator angle oscillations; therefore,
the system becomes more stable. Thus, the STATCOM can improve power system stability via damping of
power system oscillations. The results reemphasize that the STATCOM not only controls the power system
parameters, but can also improve power system stability. These 2 control strategies can be incorporated for the
STATCOM separately or simultaneously.
Table 3. Values of the performance index (ITAE).
PSO
GA
Scenario 1
Nominal Heavy
0.0108
0.0415
0.0563
0.1156
Light
0.0391
0.0552
Scenario 2
Nominal Heavy
0.0126
0.0229
0.0582
0.1203
Light
0.0393
0.0644
1.015
1.005
1.004
1.01
(a)
(b)
1.002
Speed G2 (pu)
Speed G1 (pu)
1.003
1.001
1
0.999
1.005
1
0.995
0.998
0.99
0.997
0.996
0
2
4
6
Time(s)
8
10
12
0.985
0
2
4
6
Time (s)
8
10
12
1.001
1.0008
(c)
Speed G3 (pu)
1.0006
1.0004
1.0002
1
0.9998
0.9996
0.9994
0.9992
0.999
0
2
4
6
Time (s)
8
10
12
Figure 5. System responses under Scenario 2 with heavy loading condition: solid line = PSO-stabilizer, dashed line =
GA-stabilizer, a) ω1 , b) ω2 , c) ω3 .
Figure 4 shows the speed of the generators under Scenario 1 and under nominal operating conditions. It is
clearly seen that both the PSO- and GA-based stabilizers can enhance the damping of power system oscillations.
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BOROUJENI, HEMMATI, BOROUJENI: Dynamic stability enhancement of a multimachine electric...,
However, the PSO-based stabilizer performs better than the GA-based stabilizer. Moreover, the system without
a stabilizer does not have enough damping and the responses fluctuate after the disturbance. Figure 5 shows the
speed of the generators under Scenario 2 and under heavy operating conditions. When changing the operating
conditions from nominal to heavy, while the performance of the GA supplementary stabilizer becomes poor,
the PSO stabilizer has a stable and robust performance. It can be concluded that the PSO supplementary
stabilizer has more suitable parameter adaptation in comparison with the GA supplementary stabilizer when
the operating conditions change.
The results clearly show that in large electric power systems, the STATCOM can successfully increase
damping of power system oscillations, and the system with the STATCOM-based stabilizer is more robust and
stable after disturbances. Considering different types of disturbances provides a comprehensive study of the
STATCOM under real-world disturbances.
7.
Conclusions
In this paper, the GA and PSO have been successfully employed to adjust a supplementary stabilizer based on the
STATCOM. A multimachine electric power system installed with a STATCOM, with various load conditions
and disturbances, has been used to demonstrate the ability of the STATCOM in stability enhancement via
LFO damping. Consideration of real-world disturbances such as a 3-phase short circuit guarantees the results
of implementing the controller in industry. Simulation results demonstrated that the designed STATCOMbased stabilizers are capable of guaranteeing the robust stability and robust performance under different load
conditions and disturbances. However, the simulation results show that the PSO technique has excellent
capability in comparison with the GA method. Its application to a multimachine electric power system, which
is similar to practical systems, can increase admission of the technique for real-world applications.
Nomenclature
δ
ω
Δω
Pm
Tm
Pe
Te
mE
δE
M
E’ q
E fd
X’ d
Xq
Xd
T’ do
Ka
Ta
V ref
rotor angle
rotor speed (pu)
frequency deviation
mechanical input power
mechanical torque (pu)
electrical output power (pu)
electric torque (pu)
pulse width modulation of shunt inverter
phase angle of the shunt inverter voltage
system inertia (MJ/MVA)
internal voltage behind x’ d (pu)
equivalent excitation voltage (pu)
transient reactance of d axis (pu)
steady state reactance of q axis (pu)
steady state reactance of d axis (pu)
time constant of excitation circuit (s)
regulator gain
regulator time constant (s)
reference voltage (pu)
Vt
C DC
V DC
V m,n
P m,n
W
r1 , r2
Γ1 , Γ2
local best
Pm,n
global best
Pm,n
t
XT
P
Q
K di
K dp
Tw
T1–T4
K DC
terminal voltage (pu)
DC-link capacitor of the unified power
flow controller (UPFC) (pu)
DC voltage of the UPFC (pu)
particle velocity
particle variables
inertia weight
independent uniform random numbers
learning factors
best local solution
best global solution
simulation time (s)
reactance of transmission line (pu)
active power of load (pu)
reactive power of load (pu)
integrator gain of DC-voltage regulator
proportional gain of DC-voltage regulator
washout filter (s)
time constants of lead–lag dynamic
compensator (s)
gain of the stabilizer
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Turk J Elec Eng & Comp Sci, Vol.20, No.Sup.2, 2012
References
[1] N.G. Hingorani, L. Gyugyi, Understanding FACTS, New York, IEEE Press, pp. 157–235, 2000.
[2] M.N. Slepchenkov, K.M. Smedley, J. Wen, “Hexagram-converter-based STATCOM for voltage support in fixedspeed wind turbine generation systems”, IEEE Transactions on Industrial Electronics, Vol. 58, pp. 1120–1131,
2011.
[3] K. Li, L. Liu, Z. Wang, B. Wei, “Strategies and operating point optimization of STATCOM control for voltage
unbalance mitigation in three-phase three-wire systems”, IEEE Transactions on Power Delivery, Vol. 22, pp. 413–
422, 2007.
[4] B. Singh, S.S. Murthy, S. Gupta, “Analysis and design of STATCOM-based voltage regulator for self-excited
induction generators”, IEEE Transactions on Energy Conversion, Vol. 19, pp. 783–790, 2004.
[5] N.A. Lahaçani, D. Aouzellag, B. Mendil, “Static compensator for maintaining voltage stability of wind farm
integration to a distribution network”, Renewable Energy, Vol. 35, pp. 2476–2482, 2010.
[6] A. Valderrábano, J.M. Ramirez, “DStatCom regulation by a fuzzy segmented PI controller”, Electric Power Systems
Research, Vol. 80, pp. 707–715, 2010.
[7] D. Chatterjee, A. Ghosh, “Improvement of transient stability of power systems with STATCOM-controller using
trajectory sensitivity”, International Journal of Electrical Power & Energy Systems, Vol. 33, pp. 531–539, 2011.
[8] K.R. Padiyar, N. Prabhu, “Design and performance evaluation of subsynchronous damping controller with
STATCOM”, IEEE Transactions on Power Delivery, Vol. 21, pp. 1398–1405, 2006.
[9] M.A. Furini, A.L.S. Pereira, P.B. Araujo, “Pole placement by coordinated tuning of power system stabilizers and
FACTS-POD stabilizers”, International Journal of Electrical Power & Energy Systems, Vol. 33, pp. 615–622, 2011.
[10] R. Hemmati, S.M. Shirvani Boroujeni, E. Behzadipour, H. Delafkar, “Supplementary stabilizer design based on
STATCOM”, Indian Journal of Science and Technology, Vol. 4, pp. 525–529, 2011.
[11] P.W. Sauer, M.A. Pai, Power System Dynamics and Stability, New Jersey, Prentice Hall, pp. 193-260, 1997.
[12] H. Shayeghi, H. Shayanfar, A. Safari, R.A. Aghmasheh, “A robust PSSs design using PSO in a multi-machine
environment”, Energy Conversion and Management, Vol. 51, pp. 696–702, 2010.
[13] H.F. Wang, “Phillips-Heffron model of power systems installed with STATCOM and applications”, IEE Proceedings
– Generation Transmission and Distribution, Vol. 146, pp. 521–527, 1999.
[14] A.R. Mahran, B.W. Hogg, M.L. El-Sayed, “Co-ordinate control of synchronous generator excitation and static VAR
compensator”, IEEE Transactions on Energy Conversion, Vol. 7, pp. 615–622, 1992.
[15] R.L. Haupt, S.E. Haupt, Practical Genetic Algorithms, 2nd ed., New Jersey, John Wiley & Sons, pp. 51–65, 2004.
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