Bonfring International Journal of Power Systems and Integrated Circuits, Vol. 1, Special Issue, December 2011
60
PSO Based Optimal Placement and Setting of
FACTS Devicesfor Improving the Performance of
Power Distribution System
J. Tibin, X. Sini, S. Chitra, V.I. Cherian and SasidharanSreedharan
Abstract--- Power systems, under heavily loaded
conditions, are at high risks of probable line outage and
consequent voltage instability problem. Real power loss and
voltage deviation minimization are reliable indicators of
voltage security of power system networks. This paper
proposes a Particle Swarm Optimization (PSO) based
algorithm for the optimal location and setting of FACTS
devicesto improve voltage stability. Particle swarm
optimization technique optimizes the locationand setting of
SVC, which is used in this paper as FACTS device.The
effectiveness of the proposedalgorithm has been tested in
IEEE-14 Bus standard test system.
Keywords— Power System, Optimization, Particle Swarm
Optimization, SVC, Real Power Losses
I.
INTRODUCTION
T
HE modern power system networks are forced to be
operatedmuch closer to stability limits due to ever
increasing load demand, the environmental constraints in
expansion of transmission and distribution networks and. In
such a stressed condition, the system may enter into voltage
instability problem and it has been found responsible for
several block outs across the world. A power system needs to
be with sufficient reactive power capability to remain voltage
secured even under highlystressed conditions. In a deregulated
environment, the optimum bidders are chosen only based on
real power cost characteristics and this results in reactive
power shortage and ultimately the probable voltage instability.
Distribution lines, in a deregulated environment, are operated
under heavily loaded conditions andit results in increased
voltage drop and is in high risks ofoutages.
To ensure uninterrupted and quality power supply tothe
consumers the power system should be stable
undercontingency conditions.The introduction of Flexible AC
Transmission System (FACTS) controllers [2] are increasingly
used to provide voltage andpower flow controls. Insertion of
J. Tibin, PG Scholar, Department of EEE, AmalJyothi College of
Engineering, Kanjirapally, India. E-mail:josephtibin@gmai.com
X. Sini X, PG Scholar, Department of EEE, AmalJyothi College of
Engineering, Kanjirapally, India.
S. Chitra, PG Scholar, Department of EEE, AmalJyothi College of
Engineering, Kanjirapally, India.
V.I. Cherian, Professor, Department of EEE, AmalJyothi College of
Engineering, Kanjirapally, India.
SasidharanSreedharan, Professor, Department of EEE, Vidya Academy
of Science & Technology, Thrissur, India.
FACTS devices is found to behighly effective in preventing
voltage instability [6].However, the benefits and performance
of FACTS controllers aredetermined by their location and size
[3].Owing to high cost, thenumber of FACTS devices to be
used should be minimized andtheir benefits may be
maximized through efficient optimizationmethods [6].Static
VAR Compensator is a shunt connectedcontroller capable of
all possible benefits of FACTS devices [1]-[2]. It is also easy
to incorporate in load flow solution andhighly suitable for
VAR support
As a result of today’s power electronics technologies,
newdevices capable of providing control to one or more of
themain transmission and distribution system parameters have
been developed. The definition of a FACTSdevice given by
the IEEE is "a power electronic basedsystem and other static
equipment that provide control ofone or more AC
transmission and distribution system parameters to enhance
controllability and increase power transfercapability" [13].
FACTS devices include Thyristor controlled series
compensator (TCSC), Static VAR Compensator (SVC),
Thyristor controlled phase angle regulator (TCPST), Static
compensator (STATCOM), Unified power flow controller
(UPFC) etc. FACTS devices have been widely used for
voltage stability and reactive power compensations.
The loss of one of the power sources could
suddenlyincrease the load demand on the remaining part of the
system, causing severe voltage depression that could results in
an ultimate voltage collapse. The changes that are going to
occur in the network configuration during contingencies, like
generator outages or branch outages, the reactive power flow
in the system differs widely under different contingencies. It
has long been recognized that the steady-state transmittable
power can be increased and the voltage profile along line
controlled by appropriate reactive shunt compensation. The
voltage magnitude at all or some load buses may fall below
the specified lower limits during heavy load conditions and at
light loads, the voltage magnitude may exceed the specified
upper limits. Thus, shunt connected, fixed or thyristor
switched reactors are applied to maintain the voltage levels
within the specified limits[5-7].
The Particle Swarm Optimization algorithm belongs to the
category of Swarm Intelligence methods. It is a population
based algorithm that exploits a population of individuals to
probe promising regions of the search space. In every
iteration, the velocity vector is adjusted so that the prior best
positions (cognitive aspect) and the best positions found by the
ISSN 2250 – 1088 | © 2011 Bonfring
Bonfring International Journal of Power Systems and Integrated Circuits, Vol. 1, Special Issue, December 2011
particles within a specific neighbourhood (social aspect) act as
attractors. Each particle moves with an adaptable velocity
throughout the search space, and retains in its memory the best
position it has encountered so far [12].
In this paper, identification of optimal location for
placement of SVC in IEEE 14 bus bar system is first
formulated as an optimization problem and the solution is then
achieved through the steps of PSO. The formulation of the
problem and sequential steps of PSO as applied to the problem
are explained in this paper. Extensive simulation results are
supplied to illustrate the new approach.
II.
61
power by working as an inductor. The rating of SVC at bus-i
is obtained by using (2).
B. Objective Functions and Constraints
The goal of voltage stability improvement under
contingency condition is to minimize the active power losses
and voltage deviation by optimal positioning of SVC and its
corresponding parameter. Hence, the objective function can be
expressed as:
Min F = ∑ PLK(5)
Subjected to the following equality constraints
PROBLEM FORMULATION
A. Modelling of SVC
A Static VAr Compensator (SVC) is a shunt connected
device and is installed in parallel with a bus. It has the ability
to generate or absorb reactive power at the point where it is
connected. Figure 1 shows the steady state model of the SVC.
The effect of SVC is incorporated in power flow problem as
reactive power generation/absorption.
(6)
(7)
And the inequality constraints
Power flow limits: The apparent power that is transmitted
through a branch l must not exceed a limit value, Sl max,
which represents the thermal limit of the line or transformer in
steady-state operation:
Sl≤ Slmax
(8)
Bus voltages: For several reasons (stability, power quality,
etc.), the bus voltages must be maintained around thenominal
value:
Uimin ≤ Ui≤ Uimax
III.
Figure 1: SVC Connections to a Bus Terminal
The model is completed by the algebraic equation
expressing the reactive power injected at the SVC node. The
model of SVC in this paper interprets the FACTS as a shunt
element with varying susceptance B [14]. The active and
reactive power value of an SVC from the injected power
equations [14] is:
Pi = 0
Qi=Vi2 Bt
(1)
(2)
Where Pi and Qi are injected real and reactive power to a
bus respectively and Vi is the voltage at bus-i at which an
SVC is shunted.
The total susceptance with SVC shunted at bus-i is:
Bt= Bi+ BSVC
(3)
The net reactive power generated by SVC is
QSVC= QC-QL
(4)
In case, the bus voltage that falls below the specified
lowerlimits, the SVC will supply reactive power by working
as a capacitor. On the other hand if the bus voltage exceeds the
specified upper limits, then the SVC will absorb reactive
(9)
IMPLEMENTATION OF PSO ALGORITHM
PSO is an evolutionary computation technique developed
byEberhart and Kennedy in 1995, and was inspired by the
socialbehaviour of bird flocking and fish schooling [16]. PSO
has its roots in artificial life and social psychology as well as
in engineering and computer science. It utilizes a population
of individuals, called particles, which fly through the problem
hyperspace with some given initial velocities. In each
iteration, the velocities of the particles are stochastically
adjustedconsidering the historical best position of the particles
and their neighbourhood best position; where these positions
are determined according to some predefined fitness function.
Then, the movement of each particle naturally evolves to an
optimal or near-optimal solution.
Each particle keeps track of its coordinates in the problem
spacewhich are associated with the best solution (fitness) it
hasachieved so far. The fitness value is also stored. This value
is called Pbest. When a particle takes all the population as its
topological neighbours, the best value is a global best and is
called Gbest. After finding the two best values, the particle
updates its velocity and positions with following equation (10)
and (11).
C. Algorithm of Proposed Methodology
Step 1: Input line data, bus data, svc data, voltage limits, line
limits and PSO settings.
Step 2: Identify the best location for svc placement by the
ISSN 2250 – 1088 | © 2011 Bonfring
Bonfring International Journal of Power Systems and Integrated Circuits, Vol. 1, Special Issue, December 2011
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calculation of total active power loss of the system and
connect the svc to that particular bus.
Step 3: Calculate the base case power flow with the svc
connected at the identified bus.
Step 4: Randomly generate an initial population (array) of
particles with random positions and velocities on dimensions
in the solution space. Set the iteration counter i = 0
Step 5: For each particle, calculate and compare its objective
function value with the individual best. If the objective value
is higher than Pbest, set this value as the current Pbest and
record the corresponding particle position.
Step 6: Choose the particle associated with the minimum
individual best Pbest of all particles, and set the value of Pbest
as the current overall Gbest.
Step 7: Update the velocity and position of particle using the
velocity and position update equations.
Vik+i =W* Vik + C1 * rand1 * P best i - Sik
+ C2 * rand2 * Gbest -Sik
(10)
Sik+1 = Sik + Vik+1
(11)
Step 8: If the iteration number reaches the maximum limit, go
to step 9. Else set iteration index i = i+1 and go back to step 5.
Step 9: Display the optimal solution to the target problem. The
best position gives the location for svc resulting in minimum
total active power loss for the system.
Vik+i = Velocity of agent i at kth iteration
Vik+1 = Velocity of agent i at (k +1)th iteration
W = The inertia weight
C1 = C2 = individual and social acceleration constants (0 to 3)
rand1=rand2=random numbers (0 to1)
Sik = Current position of agent i at kth iteration
Sik+1 = Current position of agent i at (k+1)th iteration
itermax = Maximum iteration number
iter= Current iteration number
Pbest i= Particle best of agent i
Gbest= Global best of the group
D. Optimal Parameter Value
Table1: Optimal Value of PSO Parameters
Parameters
Optimal value
Number of particles
Number of iterations
50
50
2.5
Individual acceleration
Constant
Social acceleration constant
Initial inertia weight
Final inertia weight
Particle velocity
Figure 2: Flow Chart for the PSO Algorithm
IV.
CASE STUDY AND SIMULATION RESULTS
E. Specification of Test System
The proposed solution method was tested on an IEEE 14
bus test system, shown in Figure 3. The network consists of 6
generators, of which one is slack and there are 20 lines. The
results consist of two steps. The first step is to access the best
location and setting of SVC and the second is the calculation
of minimum active power loss. The proposed methodology
has been tested on IEEE14-bus system as shown in figure 5.
Bus-2, 10 are PV buses and 3, 6 and 8 are synchronous
compensator buses. Loads were modeled as constant power
loads (PQ load) and were solved by using Newton Raphson
Power flow Routine. The program was coded in MATLAB.
2
0.9
0.4
1
Figure 3: IEEE- 14 Bus Systems with SVC on Bus 10
ISSN 2250 – 1088 | © 2011 Bonfring
Bonfring International Journal of Power Systems and Integrated Circuits, Vol. 1, Special Issue, December 2011
base case (without SVC)
Rective power generation
(pu)
F. Results and Discussions
The base case without SVC bus voltage level is compared
against the base case with SVC and the voltageprofile is as
given in Figure.4.The figure shows that optimal placement of
SVC slightly adjusted the voltages of PV buses and for
minimising the losses. The figure clearly states that all the bus
voltages are within the set limits at minimum active power
loss with SVC at optimum location
0.40
0.20
0.00
Bus voltage (pu)
1.10
1.00
0.95
1
3
5
7
9
11
13
3
5
7 No
9 . 11 13
Bus
Table 2: Active Power Loss without and with SVC
Figure 4: Typicalvoltage Levels with and without SVC
The active power flows in various lines are given in
Figure. 5 The thick black stacked area corresponds to the
power flow with SVC and the white area represents the power
flow without SVC.
Figure 6 shows the bus generations at minimum active
power loss using SVC at optimum location. The thick dark
black bar represents the reactive power generation at
minimum active power loss using SVC and the white bars, the
base case without SVC.
Power flow (without SVC)
6
4
Line Real power flow
(pu)
1
Figure 6: Typical Real Power Generation with and without
DG
Table.2 shows the active power loss of the system with and
without SVC. The losses are reduced when the SVC is
optimally located. The optimal SVC bus is identified as bus
number 14.
Bus No.
Power Flow (with SVC)
Rective Power Generation (without SVC)
Reactive Power Generation (with SVC)
0.60
base case (with SVC)
1.05
63
2
0
-2 1 2 3 4 5 6 7 8 91011121314151617181920
Line No.
Figure 5: Typical Line Flows with and without SVC
Without
SVC
With SVC
Active Power
Loss(p.u)
0.3269
Total Reactive power
generation (p.u)
0.223
0.2225
0.210
V.
CONCLUSION
This work shows the step by step application of the
Particle
Swarm Optimization algorithm to solve the problem of
optimal placement in a medium size power network The
algorithm is easy to implement and is able to find the optimal
solution with regard to global best position and size of SVC.
The settings of the PSO parameters are shown to be optimal
for this type of application and the algorithm is able to find the
optimal solutions with a relatively small number of iterations
and particles, therefore with a reasonable computational effort.
In this paper, a method for determining the minimum
voltage deviations by using the FACTS device has been
presented. The particle swarm optimization based algorithm
has been used to obtain the minimum voltage deviation and
active power loss by optimally locating SVC device. The
result seemed to be quite promising when tested on IEEE 14bus system.
ACKNOWLEDGMENT
The authors gratefully acknowledge Dr Federico Milano,
for his excellent simulation software PSAT [11].
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