1630
Vol. 4
Indian Journal of Science and Technology
No. 12 (Dec 2011)
ISSN: 0974- 6846
Low frequency oscillation at a multi machine environment by using UPFC tuned based on simulated
annealing
Hasan Fayazi Boroujeni*, Meysam Eghtedari, Ahmad Memaripour and Elahe Behzadipour
Department of Electrical Engineering, Boroujen Branch, Islamic Azad University, Boroujen, Iran
hasanfayaziboroujeni@gmail.com*; meysameghtedari@yahoo.com; memarpor@yahoo.com;
e.behzadipour@yahoo.com
Abstract
Unified Power Flow Controller (UPFC) is one of the most viable and important Flexible AC Transmission Systems
(FACTS) devises. Application of UPFC in single machine and multi machine electric power systems has been
investigated with different purposes such as power transfer capability, damping of Low Frequency Oscillations (LFO),
voltage support and so forth. But, an important issue in UPFC applications is to find optimal parameters of UPFC
controllers. This paper presents the application of Unified Power Flow Controller (UPFC) to enhance dynamic stability
of a multi-machine electric power system. A supplementary stabilizer based on UPFC (like power system stabilizer) is
designed to reach the defined purpose. An intelligence optimization method based on Simulated Annealing (SA) is
considered for tuning the parameters of UPFC supplementary stabilizer. Several nonlinear time-domain simulation
tests visibly show the ability of UPFC in damping of power system oscillations and consequently stability enhancement.
Keywords: Unified Power Flow Controller; Low Frequency Oscillations; Multi Machine Electric Power System;
Simulated Annealing.
Introduction
(Wang, 1999; Tambey & Kothari, 2003; Guo & Crow,
The rapid development of the high-power electronics 2009; Zarghami et al., 2010). They are designed for a
industry has made Flexible AC Transmission System specific operating condition using linearized models.
(FACTS) devices viable and attractive for utility More advanced control schemes such as Particle-Swarm
applications. FACTS devices have been shown to be method, Fuzzy logic and genetic algorithms (Eldamaty et
effective in controlling power flow and damping power al., 2005; Al-Awami, 2007; Hao et al., 2008; Singh et al.,
system oscillations. In recent years, new types of FACTS 2009) offer better dynamic performances than fixed
devices have been investigated that may be used to parameter controllers.
increase power system operation flexibility and
The objective of this paper is to investigate the ability
controllability, to enhance system stability and to achieve of UPFC for dynamic stability enhancement via damping
better utilization of existing power systems (Hingorani & of low frequency oscillations at a multi machine electric
Gyugyi, 2000). UPFC is one of the most complex FACTS power system. Simulated Annealing (SA) is incorporated
devices in a power system today. It is primarily used for for tuning the parameters of UPFC supplementary
independent control of real and reactive power in stabilizer. The proposed method is evaluated on a multi
transmission lines for flexible, reliable and economic machine power system installed with a UPFC. A classical
operation and loading of power systems. Until recently all Power System Stabilizer (PSS) is connected to UPFC
three parameters that affect real and reactive power flows and the parameters of this UPFC based stabilizer are
on the line, i.e., line impedance, voltage magnitudes at adjusted using SA. The advantages of the proposed
the terminals of the line, and power angle, were methods are their feasibility and simplicity. Different load
controlled separately using either mechanical or other conditions are considered to show effectiveness of
FACTS devices. But UPFC allows simultaneous or UPFC. Simulation results show the validity of UPFC in
independent control of all these three parameters, with LFO damping and stability enhancement at large electric
possible switching from one control scheme to another in power systems.
real time (Faried & Billinton, 2009; Mehraeen et al., 2010; System under study
Jiang et al., 2010; Jiang et al., 2010; Farrag & Putrus,
Fig.1 shows a multi machine power system installed
2011; Mehdi Nikzad et al., 2011; Reza Hemmati et al., with UPFC (Kundur, 1993). The static excitation system,
2011). Also, the UPFC can be used for voltage support model type IEEE – ST1A, has been considered. The
and transient stability improvement by damping of low UPFC is assumed to be based on Pulse Width
frequency power system oscillations. Low Frequency Modulation (PWM) converters. Details of the system data
Oscillations (LFO) in electric power system occur are given earlier (Kundur, 1993). To assess the
frequently due to disturbances such as changes in effectiveness and robustness of the proposed method
loading conditions or a loss of a transmission line or a over a wide range of loading conditions, three different
generating unit. These oscillations need to be controlled cases as nominal, light and heavy loading are considered
to maintain system stability. Many in the past have and listed in Table 1.
presented lead-Lag type UPFC damping controllers
Research article
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H.F.Boroujeni et al.
Indian J.Sci.Technol.
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Indian Journal of Science and Technology
No. 12 (Dec 2011)
ISSN: 0974- 6846
Fig.1.Four-machine eleven-bus power system
Dynamic model of the system
controlled.
Table.1.System loading conditions
Nominal
Heavy
Load
Light
P
Q
P
Q
P
A
17.6258
-2.1000
18.5535
-2.625
20.4089 -2.630
B
9.64580
-0.8400
10.1535
-1.050
11.1689 -1.055
Q
Dynamic model of the system
The nonlinear dynamic model of the system installed
with UPFC is given as (1). The dynamic model of the
system is completely presented in (Kundur, 1993) and
also dynamic model of the system installed with UPFC is
presented in (Nabavi-Niaki & Iravani, 1996; Wang, 2000).

.
Pm  Pe  Dω
ωi 
M

.
δ  ω ω 1
0
 i

 E q  Efd 
 .
Eqi 

Tdo

 .
 E fd  K a Vref  Vt 
E fdi 
Ta

 .
3mE
3m

sinδ E I Ed  cosδE I Eq   B sinδB I Bd  cosδB I Bq 
Vdc 
4Cdc
4Cdc

……………………….. (1)
Where:
i=1, 2, 3, 4 (the generators 1 to 4)
δ, rotor angle; ω, rotor speed; Pm, mechanical input
power; Pe, electrical output power; E´q, internal voltage
behind x´d; Efd, equivalent excitation voltage; Te, electric
´
torque; T do, time constant of excitation circuit; Ka,
regulator gain; Ta, regulator time constant; Vref, reference
voltage; Vt, terminal voltage.
mB: pulse width modulation of series inverter. By
controlling mB, the magnitude of series- injected voltage
can be controlled.
δB: phase angle of series injected voltage.
mE: pulse width modulation of shunt inverter. By
controlling mE, the output voltage of the shunt converter is
Research article
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δE: phase angle of the shunt inverter voltage.
The series and shunt converters are controlled in a
coordinated manner to ensure that the real power output
of the shunt converter is equal to the power input to the
series converter. The fact that the DC-voltage remains
constant ensures that this equality is maintained.
UPFC controllers
In this paper two control strategies are considered for
UPFC:
i. DC-voltage regulator
ii. UPFC supplementary stabilizer
DC-voltage regulator
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 maintain the
power balance between the two converters, a DC-voltage
regulator is incorporated. DC-voltage is regulated by
modulating the phase angle of the shunt converter
voltage. Fig. 2 shows the structure of DC-voltage
Fig.2.DC-voltage regulator
regulator. In this paper the parameters of DC-voltage
regulator are considered as Kdi=39.5 and Kdp=6.54.
UPFC supplementary stabilizer
A stabilizer controller is provided to improve damping
of power system oscillations. This controller is considered
as a lead-lag compensator and provides an electrical
torque in phase with the speed deviation in order to
improve damping of power system oscillations. The
transfer function model of the classical stabilizer is as (2).
Where, ∆ω is the deviation in speed from the
synchronous speed. This type of stabilizer consists of a
washout filter, a dynamic compensator. The output signal
is fed as a supplementary input signal to the UPFC. The
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H.F.Boroujeni et al.
Indian J.Sci.Technol.
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Indian Journal of Science and Technology
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 to
two lead–lag stages and an additional gain. The
adjustable stabilizer parameters are the gain of the
Stabilizer, KDC, and the time constants, T1–T4. The lead–
lag block present in the system provides phase lead
compensation for the phase lag that is introduced in the
circuit between the UPFC input and the electrical torque.
UK
STW 1  ST1 1  ST3
Δω …………………………. (2)
1  STW 1  ST2 1  ST4
Stabilizer design
Stabilizer controllers design themselves have been a
topic of interest for decades, especially in form of
classical Power System Stabilizers (PSS) which are
connected to the excitation system of generator. But
classical PSS cannot control power transmission and also
cannot support power system stability under large
disturbances like 3-phase fault at terminals of generator
(Mahran et al., 1992). For these problems, in this paper a
stabilizer controller based on UPFC is provided to
mitigate power system oscillations. An optimization
method such as SA is handled for tuning stabilizer
parameters. In the next section an introduction about SA
is presented.
Simulated annealing
In the early 1980s the method of simulated annealing
(SA) was introduced based on ideas formulated in the
early 1950s. This method simulates the annealing
process in which a substance is heated above its melting
temperature and then gradually cooled to produce the
crystalline lattice, which minimizes its energy probability
distribution. This crystalline lattice, composed of millions
of atoms perfectly aligned, is a beautiful example of
nature finding an optimal structure. However, quickly
cooling or quenching the liquid retards the crystal
formation, and the substance becomes an amorphous
mass with a higher than optimum energy state. The key
to crystal formation is carefully controlling the rate of
change of temperature.
The algorithmic analog to this process begins with a
random guess of the cost function variable values.
Heating means randomly modifying the variable values.
Higher heat implies greater random fluctuations. The cost
function returns the output, f, associated with a set of
variables. If the output decreases, then the new variable
set replaces the old variable set. If the output increases,
then the output is accepted provided that:
r≤
[ (
[ (
)
)
(
(
)]/
)]/
r≤
ISSN: 0974- 6846
Where, r is a uniform random number and T is a variable
analogous to temperature. Otherwise, the new variable
set is rejected. Thus, even if a variable set leads to a
worse cost, it can be accepted with a certain probability.
The new variable set is found by taking a random step
from the old variable Set as (4).
Pnew=dPold …………………………………………………………………..(4)
The variable d is either uniformly or normally
old
distributed about p . This control variable sets the step
size so that, at the beginning of the process, the algorithm
is forced to make large changes in variable values. At
times the changes move the algorithm away from the
optimum, which forces the algorithm to explore new
regions of variable space. After a certain number of
iterations, the new variable sets no longer lead to lower
costs. At this point the value of T and d decrease by a
certain percent and the algorithm repeats. The algorithm
stops when T 0.The decrease in T is known as the
cooling schedule. Many different cooling schedules are
possible. If the initial temperature is T0 and the ending
temperature is TN, then the temperature at step n is given
by (5).
Tn=f(T0, TN, N, n) …………………………………………………………………(5)
Where, f decreases with time. Some potential cooling
schedules are as follows:
a. Linearly decreasing: Tn=T0-n(T0-Tn)/N
b. Geometrically decreasing: Tn=0.99 Tn-1
c. Hayjek optimal: Tn=c/log(1+n), where c is the smallest
variation required to get out of any local minimum.
Many other variations are possible. The temperature is
usually lowered slowly so that the algorithm has a chance
to find the correct valley before trying to get to the lowest
point in the valley. This algorithm has been applied
successfully to a wide variety of problems (Randy & Sue,
2004).
SA based stabilizer design
In this section the parameters of the proposed
stabilizer are tuned using SA. Four control parameters of
the UPFC (mE, δE, mB and δB) can be modulated in order
to produce the damping torque. The parameter mE is
modulated to output of damping controller and speed
deviation  is also considered as input of damping
controller. The optimum values of stabilizer parameters
(K and T1-T4) which minimize an array of different
performance indexes are accurately computed using SA.
In optimization methods, the first step is to define a
performance index for optimal search. In this study the
performance index is considered as (6). In fact, the
performance index is the Integral of the Time multiplied
Absolute value of the Error (ITAE).
t
ITAE 
“Unified power flow controller”
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t
t
t
 t Δω 1 dt   t Δω 2 dt   t Δω 3 dt   t Δω 4 dt
0
………………………….(3)
Research article
Indian Society for Education and Environment (iSee)
No. 12 (Dec 2011)
0
0
0
(6)
H.F.Boroujeni et al.
Indian J.Sci.Technol.
1633
Vol. 4
Indian Journal of Science and Technology
K
T1
T2
T3
T4
value
1.881
0.32.12
19.342
0.791
0.23
Results and discussion
The designed HS based stabilizer is exerted to
damping LFO in study system. In order to study and
analysis system performance, a three phase short circuit
at bus 1 is considered as disturbances. The simulation
results under proposed disturbance are presented in
Fig.3-6. Each figure contains two parameters as follows:
SA based stabilizer (solid line) and system without
stabilizer (dashed line). The simulation results show that
applying the supplementary stabilizer signal greatly
enhances the damping of the generator angle oscillations
and therefore the system becomes more stable. Under
this scenario, while the performance of system without
stabilizer becomes poor, the SA stabilizer has a stable
and robust performance. Also in all figures, the system
responses without any supplementary stabilizer have
been shown. The system without stabilizer does not have
enough damping and the responses fluctuate after
disturbance.
The results clearly show that in large electric power
systems, UPFC can successfully increase damping of
power system oscillations and the system with UPFC
based stabilizer is more robust and stable after
disturbances. In earlier investigations, short circuit is
considered in order to study of system under disturbance.
But our approach, considering different types of
disturbances (disconnection of line and short circuit),
helps to make comprehensive study of UPFC under real
world disturbances.
Conclusions
In this paper simulated annealing has been
successfully exerted to design a supplementary stabilizer
based on UPFC. A multi machine electric power system
installed with a UPFC with various load conditions and
disturbances has been assumed to demonstrate the
ability of UPFC in stability enhancement via LFO
damping. Considering real world type disturbances such
as disconnection of line and three phase short circuit
guarantee the results in order to implementation of
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Indian Society for Education and Environment (iSee)
Speed deviations G1 (p.u.)
Parameter
Fig.3. Speed deviations of generator 1 in the
nominal loading condition Solid (SA-stabilizer),
Dashed (without-stabilizer)
1.01
1.005
1
0.995
0
2
4
6
8
10
Time(s)
12
14
16
18
20
Fig.4. Speed deviations of generator 2 in the
nominal loading condition Solid (SAstabilizer), Dashed (without-stabilizer)
1.01
1.008
Speed deviations G2 (p.u.)
Table 2. Optimal parameters of stabilizer using SA
ISSN: 0974- 6846
controller in industry. Simulation results demonstrated
that the designed UPFC based stabilizers capable to
guarantee the robust stability and robust performance
under a different load conditions and disturbances.
1.006
1.004
1.002
1
0.998
0.996
0
2
4
6
8
10
Time(s)
12
14
16
18
20
Fig.5. Speed deviations of generator 3 in
the nominal loading condition Solid (SAstabilizer), Dashed (without stabilizer)
1.008
1.006
Speed deviations G3 (p.u.)
Where,  is the frequency deviation and parameter "t" in
ITAE is the simulation time. In this paper 100 seconds
time period is considered for simulation. It is clear to
understand that the controller with lower ITAE is better
than the other controllers. To compute the optimum
parameter values, a 6 cycle three phase fault is assumed
in bus 8 and the performance index is minimized using
SA. The optimum values of parameters, resulting from
minimizing the performance index is presented in Table
2.
No. 12 (Dec 2011)
1.004
1.002
1
0.998
0.996
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0
2
4
6
8
10
Time(s)
12
14
16
18
20
H.F.Boroujeni et al.
Indian J.Sci.Technol.
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Indian Journal of Science and Technology
Application to a multi machine electric power system
which is near to practical systems can increase
admission of the technique for real world applications.
10.
Fig.6.Speed deviations of generator 4 in the
nominal loading condition Solid (SAstabilizer), Dashed (without stabilizer)
1.007
1.006
9.
11.
Speed deviations G4 (p.u.)
1.005
1.004
12.
1.003
1.002
1.001
1
13.
0.999
0.998
0.997
0
2
4
6
8
10
Time(s)
12
14
16
18
20
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