Research Journal of Applied Sciences, Engineering and Technology 4(2): 206-213, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: October 02, 2011
Accepted: October 24 , 2011
Published: February 01, 2012
Robust Design a PSO Based IPFC Output Feedback Damping Controller
1
Amin Safari and 2Navid Rezaei
Young Researchers Club, Ahar Branch, Islamic Azad University, Ahar, Iran
2
Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran
1
Abstract: In this study, on basis of a novel control scheme for Interline Power Flow Controller (IPFC), the
dynamic performance of the IPFC is investigated. For this purpose, the Heffron-Phillips model of a Single
machine power system is extracted and a novel feedback-based supplementary IPFC controller is applied to
the power system. The Particle Swarm Optimization (PSO) algorithm which has a powerful potential to find
the optimal solutions is employed to achieve the global optimum design of the feedback controller parameters.
Thus, to better assessment, the potential of various IPFC control signals upon the power system's different
operating conditions is investigated through the time domain simulation. The results in time-domain simulation
analysis reveals that the designed PSO based IPFC controller tuned by the proposed objective function has an
excellent capability in damping power system low frequency oscillations and enhance greatly the dynamic
stability of the power systems. Moreover, the system performance analysis under different operating conditions
show that the m1 (magnitude of injected voltage) based controller is superior to the other based controller.
Key words: Dynamic stability, IPFC, output feedback, power system oscillation, PSO
applied to the interconnected power systems, it can also
provide significant damping effect on the tie line power
oscillations through its supplementary control.
IPFC consists of two or more series Voltage Source
Converters (VSC), connected through a DC link, which
can inject series voltages into the compensated
transmission lines. In the view of controllability, the IPFC
can control the magnitude and phase of the series injected
voltages, independently. The basic theory and the
operating characteristics of the IPFC is first introduced by
(Gyugyi et al., 1999). They proposed IPFC as a new
concept for the compensation and the effective power
flow management of a multi-line transmission system.
After that, the IPFC’s impacts in power flow management
and steady-state analysis perused in some studies
(Vasquez-Arnez et al., 2008; Zhang et al., 2006;
Bhowmick et al., 2009). Recent publications on the
modeling of the IPFC in Newton power flow calculation
and the application of IPFC to Optimal Power Flow
(OPF) control due to its constraints have greatly deepened
people’s understanding of the performance of IPFC in the
steady-state analysis. However, detailed and quantities
research on the topic of dynamic performance of IPFC is
still not sufficient. (Azeb and Mihalic, 2009) constructed
the structure-preserving energy function of an electric
power system using the power injection model of an IPFC
to show the adequate effect of the IPFC in mastering the
dynamic phenomena. (Parimi et al., 2008; Kazemi and
Kalini, 2006) use the linearized Heffron-Phillips model of
a single machine infinite bus power system and the phase
compensation method, to design the IPFC’s damping
INTRODUCTION
Nowadays, power systems are interconnected large
nonlinear systems that have electromechanical oscillatory
modes with light damping. Low Frequency Oscillation
(LFO) is a one of the phenomena that may threat the
dynamic stability of power systems. LFOs usually occur
after a disturbance in the power system and these
oscillations emerging in power system variables such as
bus voltage, line current, power flow and generator speed.
Traditionally, extension of the stability ranges in the
power systems is exerted by Power System Stabilizers
(PSSs). PSSs provide the supplementary control signals
for AVR and the turbine regulatory system. However,
PSSs suffer a drawback of being liable to cause great
variations in the voltage profile and they may even result
in leading power factor operation and losing system
stability under severe disturbances, especially those of
three-phase faults which may occur at the generator
terminals (Keri et al., 1999). Besides, in recent years, due
to the fast progress in design, manufacture and application
of power-electronics devices, consequently, imparting of
power system from power-electronics’ productions such
as FACTS devices have been an advanced process.
Because of the extremely fast control action associated
with FACTS-device operations, they have been very
promising candidates for utilization in power system
damping enhancement. The Interline Power Flow
Controller (IPFC) is one of the FACTS devices which can
be employed for regulating power flow between parallel
lines or in the transmission hallways. When the IPFC is
Corresponding Author: Amin Safari, Young Researchers Club, Ahar Branch, Islamic Azad University, Ahar, Iran
206
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
controller parameters. However, the optimal signal
selection has not been investigated in those papers.
Recently, PSO technique such as other evolutionary
computational techniques based on swarm intelligence
like Ant Colony Optimization (ACO) is exerted in power
system analysis to improve the stability problem of the
power system due to the complex and multi-agent
constraints. The PSO is a novel population based metaheuristic, which utilizes the swarm intelligence between
the particles in a swarm and has emerged as a useful tool
for the optimization. In this paper, the optimal
decentralized design of a supplementary output feedback
controller of the IPFC is investigated. The
accomplishment of the designed controller is practical by
using the local and available states (DT and DVt) as the
input of the controller. The problem of the robust
controller design is formulated as an optimization
problem and PSO technique is used to solve it. A
performance index is defined based on the system
dynamics after an impulse disturbance alternately occurs
in the system and it is organized for a wide range of
operating conditions and used to form the objective
function of the designed problem. The effectiveness of the
designed controller is demonstrated through the nonlinear
time simulation studies to damp low frequency
oscillations under different operating conditions. In this
study, we also compare the IPFC’s parameter controls in
order to determine the most effective control signal for
damping power system oscillations better. This
comparison executed under various operating conditions.
Results show the good robustness of this design using the
PSO algorithm and the superiority of the m1 based
controller to the other three based controllers due to
different operating conditions.
Start
Select parameters of PSO: N, c1 , c 2 , c and ω
Generate the randomly position and
velocities of particles
Initialization, pbest with a copy often position
for particle, determine gbest
Update velocities and position according to
Eq. (1, 2)
Evaluate the fitness of each particle
Update pbest and gbest
Satisfying stopping
criterion
No
Optimal vale of the damping controller parameters
End
Fig. 1: Flowchart of the proposed PSO technique
version of the PSO keeps track of the overall best value
(gbest), and its location, obtained thus far by any particle
in the population. The PSO consists of, at each step,
changing the velocity of each particle toward its pbest and
gbest according to Eq. (1). The velocity of particle i is
represented as Vi = (vi1, vi2. . . viD). The position of the ith
particle is then updated according to Eq. (2) (Del Valle
et al., 2008).
Review of PSO technique: (Kennedy and Eberhart,
1995) presented a multi-agent general meta-heuristic
method based on the swarm intelligence which is called
Particle Swarm Optimization algorithm. In other words,
PSO is a nature-inspired stochastic search algorithm that
can provide a near-optimal solution in a reasonable time.
It has also been found to be robust in solving problem
featuring non-linearity, non-differentiability and highdimensionality. This search algorithm is based on the
knowledge gained by both the swarm and each individual,
called a particle. Each particle in the swarm represents a
candidate solution of the optimum design problem (Del
Valle et al., 2008). The PSO is initialized with a group of
random particles and searches for the optimal point by
updating generations. In each iteration, particles are
updated by the best values of itself and the swarm’s. The
ith particle is represented by Xi = (xi1, xi2, . . . , xiD). Each
particle keeps track of its coordinates in hyperspace,
which are associated with the fittest solution it has
achieved so far. The value of the fitness for particle i
(pbest) is also stored as Pi = (pi1, pi2, . . . ,piD). The global
vid  w  vid  c1  rand ()  ( Pid  xid )
 c2  rand ()  ( Pgd  xid )
(1)
xid  xid  cv id
(2)
where, Pid and Pgd are pbest and gbest. In the PSO
algorithm, the trade-off between the local and global
exploration abilities is mainly controlled by the inertia
weights (T). The inertia weight which is formulated as in
Eq. (3) varies linearly from 0.9 to 0.4 during the run (Del
Valle et al., 2008).
  max   min 
 .iter
 itermax 
   max  
207
(3)
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
Vi
Vt
i2
Gen
X t1
i1
Tr : Line
Vb
Xt 2
VSC 2 Vdc VSC 1
m2 2
m1 1
Fig. 2: SMIB power system equipped with the IPFC
Table 1: System parameters
Controller Parameters
Control signal *1
m1
*2
m2
168.2944
195.0985
163.0298
199.5966
and transients of the transformers, the IPFC’s dynamic
model in order to study the small-signal stability of a
power system can be modeled as the following (7):
K1K2
9.8057
1.2259
6.0265
2.1342
Vinjkd   0

 
Vinjkq    xtk
where, Tmax is the initial value of the inertia weight, Tmin
is the final value of the inertia weight, itermax is the
maximum iteration number and iter is the current iteration
number. Figure 1 shows the flowchart of the PSO
algorithm.
x tk 
0 
 mkVdc cos k 

 ikd  
2
 i    m V sin   , k  1, 2
k 
 kd   k dc


2
METHODOLOGY
Dynamic model of power system: The IPFC consists of
two series coupled transformers to each transmission
lines, two three-phase GTO based Voltage Source
Converters (VSCs), and a DC link capacitor. The control
parameters of each IPFC’s branch are the magnitude and
the angle of series injected voltage, i.e., m1, m2, *1, and *2,
respectively (Parimi et al., 2008). Consequently, by
changing these parameters other system parameters such
as bus voltages, active and reactive power flows, could be
controlled. According to the independence of the
magnitude of the series-injected voltages generating by
VSCs of the magnitude of the bus voltage, in an IPFC
with 2 branches, 3 parameters can be independently
controlled as one parameter control the active power
balance in the IPFC. Figure 2 shows a SMIB power
system equipped with an IPFC. The synchronous
generator is delivering power to the infinite-bus through
a double circuit transmission line and an IPFC. The
nominal parameters and operating condition of the system
are listed in Table 1.
2
Vdc 
 4C
k 1
3m
(ikd cos k  ikd sin  k )
(4)
(5)
dc
From the above equations, we can obtain: The xt1, xt2,
xd, x'd and xq which are the transformer 1 and 2
reactance's, d-axis reactance, d-axis transient reactance,
and q-axis reactance, respectively. Where, Vinj1, i1, Vinj2,
and i2 are the voltage of the transformer of line 1,current
of line 1, voltage of the transformer of line 2 and the
current of line 2, respectively; Cdc and Vdc are the DC link
capacitance and voltage; It and Vb, are the armature
current and infinite bus voltage. The nonlinear model of
the SMIB system as shown in Fig. 2 is described by
(Kazemi and Kasimi 2006):
  0 (  1)
Power system nonlinear model with IPFC: By applying
the Park’s transformation and neglecting the resistance
 
208
Pm  Pe  D 
M
(6)
(7)
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
E q 
E fd  Eq
E fd 
0


K
  1
M


K4
A 

 Tdo
 K A K5

T
 KA
7

(8)
Tdo
K A (Vref  Vt )  E fd
TA
(9)
0

K pm1

 
M

K qm1

B 
Tdo


 K A K vm1

TA
 K
cm1

The linearized model of power system as shown in
Fig. 2 is given as follows:
    0  
  
(10)
 (  Pe  D  )
M
(11)
Tdo

(12)
 E fd 
K A (  Vref   Vt )   E fd
TA
0
0
0
0



0
K p 1
M
K q 1
Tdo

K A K v 1
TA
K c 1
IPFC output feedback controller design using PSO: A
power system can be described by using a state-space
model as follows:
(13)
x  Ax  Bu, y  Cx
 Pe  K1   K2  Eq  K pd  Vdc
 K pm1 m1  K p 1 1  K pm2  m2  K p 2  2
 Eq  K4    K3 Eq  Kqd  Vdc  Kqm1 m1
 Kq 1 1  Kqm2  m2  Kq 2   2
 Vt  K5   K6  Eq  K pv  Vdc
 Kvm1 m1  Kv 1 1  Kvm2  m2  Kv 2  2
 Vdc  K7    K8  Eq  K9  Vdc  Kcm1 m1
 Kc 1 1  Kcm2  m2  Kc 2  2
(14)
(19)
where, x, y and u denote the system linearized state,
output and input variable vectors, respectively. A, B and
C are constant matrixes with appropriate dimensions
which are dependent on the operating point of the system.
The eigenvalues of the state matrix A define the stability
of the system when it is affected by a small interruption
(Shayeghi et al., 2009). As long as all eigenvalues have
negative real parts, the power system is stable when it is
subjected to a small disturbance. If one of these
eigenvalues has a positive real part the system is unstable.
In this case, using either the output or the state feedback
controller can move the unstable mode to the left hand
side of the complex plane in the area of the negative real
parts. An output feedback controller has the following
structures:
(15)
(16)
(17)
u   Ky
The state-space model of the power system is given by:
x  Ax  Bu
0

K pv 

0

M 
K
1
qv 


Tdo
Tdo

 
K A K vd 
1

TA
TA 
 K 9 
0
0
0

K
K

 pm 2
 q 2 
M
M 
K qm2
K q 2 



Tdo
Tdo



K A K v 2 
K A K vm2


TA
TA 
K cm2
K c 2 
0
In order to improve damping low frequency
oscillations, the task of damping controller is producing
an in-phase electrical torque, with the speed deviation )T,
considering as the input for the damping controller.
 E fd  Eq
 E q 
0
K
 2
M
K3

Tdo

K A K6

TA
K8
w0
(20)
Substituting (19) into (20) the resulting state equation is:
(18)
x  Ac x
where, the state vector x, control vector u, A and B are:
(21)
where, AC = A-BKC. By properly choosing the feedback
gain K, the eigenvalues of closed-loop matrix Ac are
moved to the left-hand side of the complex plane and the
desired performance of controller can be achieved. Once
the output feedback signals are selected, only the selected
x  [      Eq  E fd  vdc ]T
: u  [  m1  1  m2  2 ]T
209
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
Table 2: The optimal parameter settings of the proposed controllers
based on the different objective function based on the different
control signals (*1, m1, *2, m2)
Xd = 1pu
Generator M = 8 MJ/MVA TTido= 5.044s
XXid = 0.3 pu
D=0
Xq = 0.6pu
Ta = 0.01s
Excitation System
Ka = 100
Xt = 0.8 pu
Transformers
Xt1 = 0.2 pu
Xt2 = 0.2 pu
Xtie-line = 0.4 pu
Transmission Lines
XL1 = 0.4pu
XL2 = 0.4 pu
Operating Condition
P = 0.8 pu
Vb = 1pu
Vt = 1 pu
Cdc = 1pu
DC Link Parameter
Vdc = 2 pu
*1 = -70.56o
IPFC Parameter
m1 = 0.15
m2 = 0.1
*2 = -82.44o
Ks = 1
Ts = 0.05
Speed deviation
0.025
-0.025


i 1 0
t  i dt
K2min  K2  K2max
10
Angle deviation
2
0
0
5
Time (sec)
10
(b)
0.025
(22)
0.00
-0.02
In Eq. (33) NP is the total number of operating points
to carry out the optimization, tsim is the time range of
simulation and )T is the deviation of the rotor speed of
the generator in SMIB. The optimization purpose is
minimizing the objective function bounded to following
constraints:
Minimize J subject to:
K1min  K1  K1max
5
Time (sec)
4
Speed deviation
J
0
(a)
signals are used in forming Eq. (30). Thus, the remaining
problem in the design of output feedback controller is the
selection of K to achieve the required objectives. The
control objective is to increase the damping of the critical
modes to the desired level. It should be noted that the four
control parameters of the IPFC can be modulated in order
to produce the damping torque. In this paper, the four
control parameters of the IPFC (m1, m2, *1 and *2)
modulated in order to produce the damping torque. The
parameters of the damping controller are obtained using
PSO algorithm. In this study, an Integral of Time
multiplied Absolute value of the Error (ITAE) is taken as
the objective function. Since the operating conditions in
power systems are often varied, a performance index for
a wide range of operating points is defined as follows:
Np t sim
0.00
0
5
Time (sec)
10
(c)
Fig. 3:
(23)
C
C
The PSO algorithm searches for an optimal or near
optimal set of controller parameters, with typical ranges
are [0.01-200] for K1 and [0.01-10] for K2 of the
optimized parameters. Using the time domain simulation
model of the power sy stem on the simulation period, the
objective function is calculated and by considering the
multiple operating conditions, the optimal parameters of
the controller is carried out. The operating conditions are
considered as:
C
C
Dynamic responses for )T with controller at (a) Base
case (b) Case 1 and (c) Case 2 loading; Solid
(m1),Dot-dashed (m2), Dashed (*1) and Dotted (*2)
Base case: P = 0.7 pu, Q = 0.15 pu and XL1 = 0.4 pu.
(Nominal loading)
Case 1: P = 1.25 pu, Q = 0.25 and XL1 = 0.4 pu.
(Heavy loading)
Case 2: P = 0.2 pu, Q = 0.02 and XL1 = 0.4 pu. (Light
loading)
Case 3: P = 0.7 pu, Q = 0.15 pu and XL1 = 0.5 pu.
(25% increase in the line reactance)
In this study, the value of NP is 4 corresponding to the
above four cases and the simulation run-time equals to
210
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
4
Speed deviation
Angle deviation
0.03
2
0
0
5
Time (sec)
10
0
-0.005
0
(a)
5
Time (sec)
10
(a)
0.05
0.00
-0.04
0
5
Time (sec)
Speed deviation
Speed deviation
0.05
10
0
-0.03
(b)
0
5
Time (sec)
18
10
0.035
9
Speed deviation
Angle deviation
(b)
0
0
5
Time (sec)
10
0
-0.01
0
(c)
Fig. 4: Dynamic responses for )* with controller at (a)Base
case (b)Case 1 and (c)Case 2 loading; Solid(m1),Dotdashed(m2), Dashed (*1) and Dotted (*2)
5
Time (sec)
10
(c)
Fig. 5: Dynamic responses for )Pe with controller at (a) Base
case (b)Case 1 and (c) Case 2 loading; Solid (m1),Dotdashed (m2), Dashed (*1) and Dotted (*2)
tsim = 10. In order to acquire better performance, number
of particle, particle size, number of iteration, c1, c2 and c
is chosen as 40, 5, 100, 2, 2 and 1, respectively. It should
be noted that PSO algorithm is run several times and then
optimal set of IPFC controller parameters is selected.
Also, the inertia weight, T, is linearly decreasing from 0.9
to 0.4. The final values of the optimized parameters with
the objective functions, J, are given in the Table 2.
RESULTS
Simulation studies are carried out for a fault
disturbance occurred in an occasional scenario. As such,
we can assess the robustness of the designed damping
controller by PSO algorithm.
211
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
4
Control signal deviation
Speed deviation
0.05
0
-0.04
0
-4
0
10
5
Time (sec)
0
5
Time (sec)
(a)
10
(b)
Power deviation
10
0
-1
0
5
Time (sec)
10
(c)
Fig. 6: Dynamic responses for )u with controller at (a) Base case (b) Case 1 and (c) Case 2 loading; Solid (m1), Dot-dashed (m2),
Dashed (*1) and Dotted (*2)
1
Power deviation
Control signal deviation
4
0
0
-0.8
-3
0
5
Time (sec)
0
10
(a)
1
Power deviation
Control signal deviation
10
(b)
1
0
-8
5
Time (sec)
0
-1
0
5
Time (sec)
10
(c)
0
5
Time (sec)
10
(d)
Fig. 7: Dynamic response of VSC1: (a) m1, (b) *1 and VSC2, (c) m2 d *2 in various load conditions: Solid (heavy), dashed (nominal)
and dotted (light)
212
Res. J. Appl. Sci. Eng. Technol., 4(3): 206-213, 2012
Description the considered scenario: A 6-cycle threephase fault occurred at t = 1 sec at the middle of the of
one transmission line is considered. The fault is cleared
without line tripping and the original system is restored
upon the clearance of the fault. This severe disturbance is
considered for different loading conditions and the
performance of the proposed controller under these
conditions is verified. The system response to this
disturbance is shown in Fig. 3, 4, 5, 6 and 7. From the
above conducted test and the figures, it can be concluded
that the m1 controller is superior to the other three
controllers. As such, it can be concluded that the m1
controller is the most robust controller. Moreover, in a
constant line reactance, with decreasing in load,
therewith, decreasing in the transmission angle (*), the
line current is dropping. As a result, the active power
which the series VSCs interchange with the
uncompensated lines will be decreased. The active power
injection decreases with decreasing the transmission
angle. Therefore, LFOs which are occurred in light load
conditions are damped posterior due to nominal or heavy
loading conditions. Moreover, decreasing the load and
increasing in the line reactance may have a castrating
effect in weakening these four controller performances.
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CONCLUSION
In this study, IPFC’s effect on the dynamic stability
of power system has been investigated. The design
problem of the IPFC’s output feedback controller is
converted into an optimization problem which is solved
by a PSO technique with an ITAE performance index
applied as an objective function. The effectiveness of the
proposed IPFC signal controllers for improving dynamic
stability performance of a power system are demonstrated
by a weakly connected example power system subjected
to a severe disturbance. Then, we compare the IPFC’s
different control signals in order to demonstrate the most
effective control signal to provide good damping low
frequency oscillations in single-machine power system.
The non-linear time domain analysis results reveal that
the proposed controller based on m1 control signal has
superiority than other three signal based controllers due to
the different operating conditions.
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