815
Vol. 4
Indian Journal of Science and Technology
No. 7 (July 2011)
ISSN: 0974- 6846
Stabilizer design based on UPFC using simulated annealing
Reza Hemmati, Sayed Mojtaba Shirvani Boroujeni, Hamideh Delafkar and Amin Safarnezhad Boroujeni
Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen, Iran
reza.hematti@gmail.com, mo_shirvani@yahoo.com, delafkar@aut.ac.ir, safarnezhad@gmail.com
Abstract
This paper presents the application of Unified Power Flow Controller (UPFC) to enhance damping of Low Frequency
Oscillations (LFO) at a Single-Machine Infinite-Bus (SMIB) power system installed with UPFC. Since UPFC is
considered to mitigate LFO, a supplementary UPFC like power system stabilizer is designed to reach the defined
purpose. Simulated Annealing (SA) is used to tune UPFC supplementary stabilizer. To show effectiveness, the
proposed method is compared with another optimization method named Genetic Algorithms (GA). Several linear timedomain simulation tests visibly show the validity of proposed method in damping of power system oscillations. Also
simulation results emphasis on the better performance of SA in comparison with GA.
Keywords: Flexible AC Transmission Systems, Unified Power Flow Controller, Low Frequency Oscillations, Simulated
Annealing, Genetic Algorithms
Introduction
method, Fuzzy logic and genetic algorithms (Taher et al.,
The rapid development of the high-power electronics 2008; Al-Awami et al., 2007; Eldamaty et al., 2005) offer
industry has made Flexible AC Transmission System better dynamic performances than fixed parameter
(FACTS) devices viable and attractive for utility controllers.
applications. FACTS devices have been shown to be
The objective of this paper is to investigate the ability
effective in controlling power flow and damping power of optimization methods such as Simulated Annealing
system oscillations. In recent years, new types of FACTS (SA) and Genetic Algorithms (GA) for UPFC
devices have been investigated that may be used to supplementary stabilizer controller design. A Sigel
increase power system operation flexibility and Machine Infinite Bus (SMIB) power system installed with
controllability, to enhance system stability and to achieve a UPFC is considered as case study and a UPFC based
better utilization of existing power systems (Hingorani et stabilizer controller whose parameters are tuned using
al., 2010). UPFC is one of the most complex FACTS SA and GA is considered as power system stabilizer.
devices in a power system today. It is primarily used for Different load conditions are considered to show
independent control of real and reactive power in effectiveness of the proposed methods and also
transmission lines for flexible, reliable and economic comparing the performance of these two methods.
operation and loading of power systems. Until recently all Simulation results show the validity of proposed methods
three parameters that affect real and reactive power flows in LFO damping.
on the line, i.e., line impedance, voltage magnitudes at System under study
the terminals of the line, and power angle, were controlled
Fig. 1 shows a SMIB power system installed with
separately using either mechanical or other FACTS UPFC (Hingorani et al., 2010). The UPFC is installed in
devices. But UPFC allows simultaneous or independent one of the two parallel transmission lines. This
control of all these three parameters, with possible configuration (comprising two parallel transmission lines)
switching from one control scheme to another in real time permits to control of real and reactive power flow through
(Faried et al., 2009; Alasooly et al., 2010; Mehraeen et a line. The static excitation system, model type IEEE–
al., 2010; Jiang et al., 2010; Jiange et al., 2010). Also ST1A, has been considered. The UPFC is assumed to be
UPFC can be used for transient stability improvement by based on Pulse Width Modulation (PWM) converters. The
damping of Low Frequency Oscillations (LFO) in power nominal system parameters are given in appendix.
system. Low Frequency Oscillations in electric power Dynamic model of the system
system occur frequently due to disturbances such as Nonlinear dynamic model
changes in loading conditions or a loss of a transmission
A non-linear dynamic model of the system is derived
line or a generating unit. These oscillations need to be by disregarding the resistances of all components of the
controlled to maintain system stability. Many in the past system (generator, transformers, transmission lines and
have presented lead-Lag type UPFC damping controllers converters) and the transients of the transmission lines
(Zarghami et al., 2010; Guo et al., 2009; Tambey et al., and transformers of the UPFC (Nabavi-Niaki et al., 1996;
2003; Wang et al., 1999). They are designed for a Wang et al., 2000). The nonlinear dynamic model of the
specific operating condition using linear models. More system installed with UPFC is given as (1).
advanced control schemes such as Particle-Swarm
Research article
Indian Society for Education and Environment (iSee)
“Stabilizer design based UPFC”
http://www.indjst.org
Reza Hemmati et al.
Indian J.Sci.Technol.
816
Vol. 4
Indian Journal of Science and Technology

 .  Pm  Pe  DΔω 
ω 
M
.
δ  ω  ω  1
0

(1)
 .
E q  E fd 

 Eq 
Tdo

 .
E fd  K a  Vref  Vt 
 E fd 
Ta

 .
 Vdc  3m E  sin  δ E  I Ed  cos  δ E  I Eq   3m B  sin  δ B  I Bd  cos  δ B  I Bq 
4Cdc
4Cdc

No. 7 (July 2011)
ISSN: 0974- 6846
series converter. The fact that the DC-voltage remains
constant ensures that this equality is maintained.
Dynamic model in state-space form
The dynamic model of the system in state-space form
is as (5).
w0
0
0
0 
 0
0
0
0 
 0
Kpδe
Kpb
Kpδb 
Δ   K1
Kpd  Δ   Kpe
K




0  2
0

 

 ΔmE 

  
M
M
M
M
M  Δ   M
Δ   M
Kqδe
Kqb
Kqδb  ΔδE 
Kqd   /   Kqe
K3
1
ΔE /     K4

 /
 /
 /
0  /
 /   ΔEq    /

/
/
 q   Tdo
Tdo
Tdo
Tdo  ΔmB

  Tdo
Tdo
Tdo
Tdo
 ΔE  
ΔE   K K
KAKvc KAKvδe
KAKvb KAKvδb  Δδ 
fd
K
K
1
K
K
fd
A
5
A
6
A
vd



 
  B



0 



 
 dc  TA
TA
TA
TA 
ΔV
TA
TA
TA  Δvdc  TA
 


Kce
K
K
K
K
0
K
0

K

cδ
e
cb
cδ
b

8
9 
 7
(5)
UPFC controllers
In this research two control strategies are
The equation for real power balance between the series
considered
for UPFC:
and shunt converters is given as (2).
i. DC-voltage regulator


(2)
Re VB I B  VE I E  0
ii. Power system oscillation-damping controller
Linear dynamic model
DC-voltage regulator
A linear dynamic model is obtained by linearizing the
In UPFC, The output real power of the shunt
converter must be equal to the input real power

of the series converter or vice versa. In order to
 Δδ  w Δw
0

maintain the power balance between the two
 Δω    ΔPe  DΔω  /M
converters, a DC-voltage regulator is
(3)
 /
/
incorporated. DC-voltage is regulated by
 ΔE q  (  ΔE q  ΔE fd )/Tdo
modulating the phase angle of the shunt

converter voltage. In this paper a PI type
 ΔE fd   1 ΔE fd  K A ΔV

controller is considered to control of DC
TA
TA

voltage. The parameters of this PI type DC/
 Δv dc  K 7 Δδ  K 8 ΔE q  K 9 Δv dc  K ce Δm E  K cδeΔδ E  K cb Δm B  K cδb Δδ B voltage regulator are considered as K =39.5
I
nonlinear dynamic model around nominal operating
and KP=6.54.
condition. The linear model of the system is given as (3).
Power system stabilizer
Where
A stabilizer controller is provided to improve
damping of power system
/
Δ Pe  K 1 Δ δ  K 2 Δ E q  K p d Δ v d c  K p e Δ m E  K p δ e Δ δ E  K p b Δ m B  K p δ b Δ δ B
oscillations. This controller may
/
Δ E q  K 4 Δ δ  K 3 Δ E q  K q d Δ v d c  K q e Δ m E  K q δ e Δ δ E  K q b Δ m B  K q δ b Δ δ B be considered as a lead-lag
compensator.
However
an
Δ V t  K 5 Δ δ  K 6 Δ E q/  K vd Δ v d c  K v e Δ m E  K v δ e Δ δ E  K v b Δ m B  K v δ b Δ δ B electrical torque in phase with the
speed deviation should be
Fig. 2 shows the transfer function model of the system produced to improve damping of power system
including UPFC. The model has numerous constants oscillations. The transfer function model of the stabilizer
denoted by Kij. These constants are function of the controller is shown in Fig. 3 (Yu et al., 1983).
system parameters and the initial operating condition. Eigen value analysis
For the nominal operating condition the eigenvalues
Also the control vector U in Fig. 2 is defined as (4).
of the system are obtained using state-space model of
T
U  [Δm E Δδ E Δm B Δδ B ]
(4)
the system presented in (5) and these eigenvalues are
Where:
shown in Table 1. It is clearly seen that the system is
∆mB: Deviation in pulse width modulation index mB of unstable and needs to power system stabilizer (damping
series inverter. By controlling mB, the magnitude of controller)
for
Table 1. Eigen-values of the closedseries- injected voltage can be controlled.
stability.
loop system without stabilizer
∆δB : Deviation in phase angle of series injected voltage.
Stabilizer
-15.3583
∆mE : Deviation in pulse width modulation index mE of controllers
design
-5.9138
shunt inverter. By controlling mE, the output voltage of the themselves
have
0.7542 + 3.3055i
shunt converter is controlled.
been a topic of
0.7542 - 3.3055i
∆δE: Deviation in phase angle of the shunt inverter interest for decades,
-0.7669
voltage.
especially in form of
The series and shunt converters are controlled in a Power System Stabilizers (PSS). But PSS cannot control
coordinated manner to ensure that the real power output power transmission and also cannot support power
of the shunt converter is equal to the power input to the


Research article
Indian Society for Education and Environment (iSee)
“Stabilizer design based UPFC”
http://www.indjst.org
Reza Hemmati et al.
Indian J.Sci.Technol.
817
Vol. 4
Indian Journal of Science and Technology
Fig. 1. A Single Machine Infinite Bus (SMIB)
power system installed with UPFC
No. 7 (July 2011)
ISSN: 0974- 6846
Fig. 2. Transfer function model of the system including
UPFC
K1
  P
e


K pu
Pm


w0
S
1
MS  D
K4
K2
K pd
K5
K6
K qu
K8
Fig 3. The structure of damping controller
U


K cu


1
K 3  STdo/
E q/
1
S  K9

 Vref

ka
1  STa





K vd
K vu
K qd
Vdc
K7
-5
6
x 10
-4
18
GA
SA
4
GA
SA
16
2
14
0
12
-2
10
VDC (pu)
W (pu)
Fig. 5. Dynamic response VDC for case 1
x 10
-4
-6
8
6
-8
4
-10
2
Fig. 4. Dynamic response ω for case 1
0
-12
-2
-14
0
1
2
3
4
5
Time (s)
6
7
8
9
10
1
2
3
4
5
Time (s)
6
7
8
9
10
-4
-5
8
0
x 10
20
x 10
GA
SA
GA
SA
6
15
4
2
10
VDC (pu)
W (pu)
0
-2
-4
5
-6
-8
0
Fig. 6. Dynamic response ω for case 2
-10
-12
0
1
2
3
4
5
Time (s)
6
Research article
Indian Society for Education and Environment (iSee)
7
8
9
10
Fig. 7. Dynamic response VDC for case 2
-5
0
1
“Stabilizer design based UPFC”
http://www.indjst.org
2
3
4
5
Time (s)
6
7
8
9
10
Reza Hemmati et al.
Indian J.Sci.Technol.
818
Vol. 4
Indian Journal of Science and Technology
No. 7 (July 2011)
ISSN: 0974- 6846
system stability under large disturbances like 3-phase a. Linearly decreasing: Tn=T0-n(T0-Tn)/N
fault at terminals of generator. For these problems, in this b. Geometrically decreasing: Tn=0.99 Tn-1
paper a stabilizer controller based UPFC is provided to c. Hayjek optimal: Tn=c/log(1+n), where c is the smallest
mitigate power system oscillations. Two optimization
variation required to get out of any local minimum.
methods such as SA and GA are considered for tuning Many other variations are possible. The temperature is
stabilizer controller parameters. In the next section an usually lowered slowly so that the algorithm has a chance
introduction about SA is presented.
to find the correct valley before trying to get to the lowest
Simulated annealing
point in the valley. This algorithm has been applied
In the early 1980s the method of simulated annealing successfully to a wide variety of problems (Randy and
(SA) was introduced in 1983 based on ideas formulated Sue, 2004).
in the early 1950s. This method simulates the annealing Stabilizer design using SA
process in which a substance is heated above its melting
In this section the parameters of the proposed
temperature and then gradually cooled to produce the stabilizer controller are tuned using SA. Four control
crystalline lattice, which minimizes its energy probability parameters of the UPFC (mE, δE, mB and δB) can be
distribution. This crystalline lattice, composed of millions modulated in order to produce the damping torque. The
of atoms perfectly aligned, is a beautiful example of parameter mE is modulated to output of damping
nature finding an optimal structure. However, quickly controller and speed deviation  is also considered as
cooling or quenching the liquid retards the crystal input of damping controller. The structure of
formation, and the substance becomes an amorphous supplementary stabilizer controller has been shown in
mass with a higher than optimum energy state. The key Fig. 3. The parameters in Fig. 3 are as follow:
to crystal formation is carefully controlling the rate of KDC: the stabilizer gain
change of temperature.
TW: the parameter of washout block
The algorithmic analog to this process begins with a T1 and T2: the parameters of compensation block
random guess of the cost function variable values. The optimum values of KDC, T1 and T2 which minimize an
Heating means randomly modifying the variable values. array of different performance indexes are accurately
Higher heat implies greater random fluctuations. The cost computed using SA and TW is considered equal to 10. In
function returns the output, f, associated with a set of optimization methods, the first step is to define a
variables. If the output decreases, then the new variable performance index for optimal search. In this study the
set replaces the old variable set. If the output increases, performance index is considered as (9). In fact, the
then the output is accepted provided that:
performance index is the Integral of the Time multiplied
Absolute value of the Error (ITAE).
r≤e[f(Pold)-f (Pnew)]/T
(6)
t
t
Where, r is a uniform random number and T is a variable
(9)
ITAE   t Δω dt   t ΔV DC dt
analogous to temperature. Otherwise, the new variable
0
0
set is rejected. Thus, even if a variable set leads to a
Where,  is the frequency deviation, VDC is the
worse cost, it can be accepted with a certain probability.
deviation
of DC voltage and parameter "t" in ITAE is the
The new variable set is found by taking a random step
simulation time and a 100 seconds time
from the old variable Set as (7).
Table 2. Optimum values of
period is considered. It is clear to
Pnew=dPold
(7)
stabilizer controller
understand that the controller with lower
The variable d is either uniformly or
parameters using SA
ITAE is better than the other controllers. To
normally distributed about pold. This control
KDC
561.443
compute the optimum parameter values, a
variable sets the step size so that, at the
T1
42.933
0.1 step change in mechanical torque
beginning of the process, the algorithm is
T2
0.0219
(Tm) is assumed and the performance
forced to make large changes in variable
values. At times the changes move the algorithm away index is minimized using SA. The optimum values of KDC,
from the optimum, which forces the algorithm to explore T1 and T2, resulting from minimizing the performance
new regions of variable space. After a certain number of index is presented in Table 2. Also in order to show
iterations, the new variable sets no longer lead to lower effectiveness of SA method, the parameters of stabilizer
costs. At this point the value of T and d decrease by a controller are tuned using the other optimization method,
certain percent and the algorithm repeats. The algorithm GA. In continuous GA case, the performance index is
stops when T≃0.The decrease in T is known as the considered as SA case and the optimal parameters of
cooling schedule. Many different cooling schedules are stabilizer controller are obtained as shown in Table 3.
The search limits are as follows:
possible. If the initial temperature is T0 and
Table 3. Optimum values
<1KDC<1000, 0.01<T<1.
the ending temperature is TN, then the
of
stabilizer
controller
Simulation results
temperature at step n is given by (8).
parameters using GA
In this section, the designed SA and GA
Tn=f(T0, TN, N, n)
(8)
KDC
622.78
based stabilizer controllers are applied to
Where, f decreases with time. Some
T1
0.2819
damping LFO in the under study system. In
potential cooling schedules are as follows:
T2
Research article
Indian Society for Education and Environment (iSee)
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“Stabilizer design based UPFC”
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Reza Hemmati et al.
Indian J.Sci.Technol.
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Vol. 4
Indian Journal of Science and Technology
order to study and analysis system performance under
system uncertainties (controller robustness), two
operating conditions are considered as follow:
Case 1: Nominal operating condition
Case 2: Heavy operating condition
The parameters for two cases are presented in
appendix. SA and GA stabilizer controllers have been
designed for the nominal operating condition. In order to
demonstrate the robustness performance of the proposed
method, The ITAE is calculated following 10% step
change in the reference torque (Tm) at all operating
conditions (Nominal and Heavy) and results are shown at
Tables 4. Following step change, the SA based stabilizer
has better performance than the GA based stabilizer at all
operating conditions.
No. 7 (July 2011)
ISSN: 0974- 6846
stability enhancement under small disturbances in
comparison with GA method.
Appendix
The nominal parameters and nominal operating condition of
the system are listed in Table 5. Also system operating
conditions are defined as Table 6 (Operating condition 1 is the
nominal operating condition).
References
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load flow control and voltage flicker elimination and current
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& Energy Systems. 29, 251-259.
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Power Flow Controller. IEEE CCGEI 2005.1(1), 1950-1953.
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The calculated ITAE
sizing FACTS devices for steady-state voltage profile
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enhancement. IET Gen., Trans., & Dist. 3(4), 385 – 392.
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0.0019
0.0021
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S, Jagannathan S and Crow ML (2010) Novel
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and dynamic models of Unified Power Flow Controller
M = 8 Mj/MVA T´do = 5.044 s Xd = 1 p.u.
for power system studies. IEEE Transactions on Power
Generator
Systems. 11 (4), 1937-1950.
Xq = 0.6 p.u. X´d = 0.3 p.u.
D=0
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Excitation system
Ka = 10
Ta = 0.05 s
Algorithms. 2nd Ed., John Wiley & Sons.
Transformers
Xte = 0.1 p.u.
XSDT = 0.1 p.u.
12. Taher SA and Hematti R (2008) Optimal
Transmission lines
XT1 = 1 p.u.
XT2 = 1.25 p.u.
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Q = 0.30 p.u. Vt =1.05 p.u.
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In this paper Simulated Annealing and Genetic
15. Wang HF (2000) A unified model for the analysis of FACTS
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devices in damping power system oscillation Part III: Unified
stabilizer controller based UPFC. A Single Machine
Power Flow Controller. IEEE Trans. Power Delivery. 15 (3),
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978-983.
various load conditions has been assumed to 16. Yu NY (1983) Electric power system dynamics. Acad. Press,
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the
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Simulation
results
Inc., London.
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Atcitty (2010) A novel approach to inter-area oscillations
to guarantee the robust stability and robust performance
damping by UPFC utilizing ultra-capacitors. IEEE
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show that the SA method has an excellent capability in
power system oscillations damping and power system
Research article
Indian Society for Education and Environment (iSee)
“Stabilizer design based UPFC”
http://www.indjst.org
Reza Hemmati et al.
Indian J.Sci.Technol.