Embellished Particle Swarm Optimization Algorithm for Solving Reactive Power Problem

Indonesian Journal of Electrical Engineering and Informatics (IJEEI)
Vol. 5, No. 3, September 2017, pp. 192~198
ISSN: 2089-3272, DOI: 10.11591/ijeei.v5i3.291  192
Received April 4, 2017; Revised July 18, 2017; Accepted August 2, 2017
Embellished Particle Swarm Optimization Algorithm for
Solving Reactive Power Problem
Kanagasabai Lenin
Department of EEE, Prasad V. Potluri Siddhartha Institute of Technology
Kanuru, Vijayawada, Andhra Pradesh -520007
e-mail: gklenin@gmail.com
Abstract
This paper proposes Embellished Particle Swarm Optimization (EPSO) algorithm for solving
reactive power problem .The main concept of Embellished Particle Swarm Optimization is to extend the
single population PSO to the interacting multi-swarm model. Through this multi-swarm cooperative
approach, diversity in the whole swarm community can be upheld. Concurrently, the swarm-to-swarm
mechanism drastically speeds up the swarm community to converge to the global near optimum. In order
to evaluate the performance of the proposed algorithm, it has been tested in standard IEEE 57,118 bus
systems and results show that Embellished Particle Swarm Optimization (EPSO) is more efficient in
reducing the Real power losses when compared to other standard reported algorithms.
Keywords: reactive power, transmission loss, embellished particle swarm, optimization.
1. Introduction
Optimal reactive power dispatch problem is one of the difficult optimization problems in
power systems. The sources of the reactive power are the generators, synchronous
condensers, capacitors, static compensators and tap changing transformers. The problem that
has to be solved in a reactive power optimization is to determine the required reactive
generation at various locations so as to optimize the objective function. Here the reactive power
dispatch problem involves best utilization of the existing generator bus voltage magnitudes,
transformer tap setting and the output of reactive power sources so as to minimize the loss and
to maintain voltage stability of the system. It involves a nonlinear optimization problem. Various
mathematical techniques have been adopted to solve this optimal reactive power dispatch
problem. These include the gradient method [1, 2], Newton method [3] and linear programming
[4-7].The gradient and Newton methods suffer from the difficulty in handling inequality
constraints. To apply linear programming, the input- output function is to be expressed as a set
of linear functions which may lead to loss of accuracy. Recently many global optimization
techniques have been proposed to solve the reactive power flow problem [8-10]. In this paper
Embellished Particle Swarm Optimization (EPSO) algorithm is used for solving the reactive
power problem. By using the multi-swarm cooperative approach, diversity in the entire swarm
community can be maintained. While at the meantime, the colony-to-colony communication
mechanism speeds up the convergence rate of global optimum .The performance of EPSO has
been evaluated in standard IEEE 57,118 bus test systems and the results analysis shows that
our proposed approach outperforms all approaches investigated in this paper.
2. Objective Function
2.1. Active Power Loss
The objective of the reactive power dispatch problem is to minimize the active power
loss and can be written in equations as follows:
∑ ( ) (1)
where F- objective function, PL – power loss, gk - conductance of branch,Vi and Vj are voltages
at buses i,j, Nbr- total number of transmission lines in power systems.

IJEEI ISSN: 2089-3272 
Embellished Particle Swarm Optimization Algorithm for Solving… ( Kanagasabai Lenin)
193
2.2. Voltage Profile Improvement
To minimize the voltage deviation in PQ buses, the objective function (F) can be written
as:
(2)
where VD - voltage deviation, - is a weighting factor of voltage deviation.
And the Voltage deviation given by:
∑ | | (3)
where Npq- number of load buses
2.3. Equality Constraint
The equality constraint of the problem is indicated by the power balance equation as
follows:
(4)
where PG- total power generation, PD - total power demand.
2.4. Inequality Constraints
The inequality constraint implies the limits on components in the power system in
addition to the limits created to make sure system security. Upper and lower bounds on the
active power of slack bus (Pg), and reactive power of generators (Qg) are written as follows:
(5)
(6)
Upper and lower bounds on the bus voltage magnitudes (Vi) is given by:
(7)
Upper and lower bounds on the transformers tap ratios (Ti) is given by:
(8)
Upper and lower bounds on the compensators (Qc) is given by:
(9)
where N is the total number of buses, Ng is the total number of generators, NT is the total
number of Transformers, Nc is the total number of shunt reactive compensators.
3. Particle Swarm Optimization Algorithm (PSO)
Particle Swarm Optimization Algorithm (PSO) is a population based optimization tool
[11-19], where the system is initialized with a population of random particles and the algorithm
searches for optima by updating generations. Suppose that the search space is D-dimensional.
The position of the i-th particle can be represented by a D-dimensional vector
( ) and the velocity of this particle is ( ).The best previously
visited position of the i-th particle is represented by ( ) and the global best
position of the swarm found so far is denoted by ( ). The fitness of each
particle can be evaluated through putting its position into a designated objective function. The
particle's velocity and its new position are updated as follows:

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( ) ( ) (10)
(11)
where * + * + N is the population size, the superscript t denotes the
iteration number, is the inertia weight, r1 and r2 are two random values in the range [0,1], c1
and c2 are the cognitive and social scaling parameters which are positive constants.
4. Embellished Particle Swarm Optimization Algorithm
Embellished Particle Swarm Optimization Algorithm (EPSO) algorithm following the
principle and it utilizes the concept of PSO algorithm. EPSO is a robust (it performs excellent in
an unusual condition also), stochastic (selection is based on the random objective function)
optimization technique based on the movement and the intelligence of swarms. EPSO algorithm
follows the five basic principles of the swarm intelligence and it utilizes the concept of PSO
algorithm. The five basic principles are Proximity principle (population should be able to carry
out simple space and time computation), Quality principle (population should respond to the
quality factors pbest and gbest), Diverse Response principle (allocation of responses between
pbest and gbest should ensure the diversity of responses), Stability principle (the population
should not change its behavioral mode every time when the environment changes) and
Adaptability principle ( the population should adapt the changes when gbest changes). EPSO is
initialized by a group of random particles. Consider each particle as a bird. After initialization the
particles are sorted in a descending order. Then the sorted particles are placed into the different
colonies (i.e. the entire swarm or community is divided into several colonies). Intra-Swarm-
Communication is described as follows: The community consists of set of colonies. Each colony
performs a local search and it finally gives one best solution. Within each colony, the individual
birds having their own ideas they share their ideas with each other.
Inter-Swarm-Communication is described as follows: This can be evolved through a
process of iterations. After a defined number of iterations, the information obtained is passed
among the colonies and the knowledge among each colony is shared. These colonies co-
ordinately and cooperatively work together and it provides the optimal solution. With these intra
and inter-birds communication mechanisms, the birds can jump out from local optima and it
quickly fly through the neighbourhood of the possible global optimum. Therefore a balance
between local search and global search is attained. Through this, MC - PSO overcome the
problem of Premature Convergence in the PSO algorithm. The proposed methodology includes
constriction factor concept. By including the constriction factor the performance of the algorithm
is improved. The process is initialized with a group of random particles P. For S-dimensional
problems (S variables), a bird i is represented as,
( ) (12)
Then the birds are sorted in a descending order according to their fitness. Then the
entire community is divided into m colonies, each containing n birds (i.e. P = m × n). In this
process, the first bird goes to the first colony, the second bird goes to the second colony, bird m
goes to the mth colony, and the bird m+1 goes back to the first colony. Within each colony, the
birds with the best and the worst fitness are represented as and , and the bird with the
global fitness is represented as Xg .Then, a process similar to PSO is applied to improve only
the bird with the worst fitness not for all birds in each iteration. In each iteration, the
communication is formulated as (V),
( ) ( ) ( ) ( ) (13)
Current position = current position + velocity
where
is the velocity,
is the performance improvement factor,
is the best position found so far by the particle in the colony,

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is the best position found so far by the multi-colony community.
is the social learning rate between the particles within each colony,
is the social learning rate between different colonies,
is a random number between 0 and 1.
The term ( ) ( ) describes the cooperation between
individuals of the same colony and the term ( ) ( ) describes the
cooperation between different colonies in the community. Then the position of the bird with the
worst fitness is represented as follows
( ) ( ) (14)
(15)
If this process produces a better solution, it replaces the worst bird, else the calculations
in this equation are repeated but with respect to the global best bird ( replaces ). If no
updation is possible then a new solution is randomly generated to replace that bird.
EPSO Algorithm for Reactive power optimization problem.
Begin;
Initialization:
Generate random population of P solutions (i particles);
For each individual i ϵ P;
Fitness Evaluation:
Calculate fitness (i);
Sorting:
Sort the population P in descending order of their fitness;
Divide the entire community P into m Colonies (Community);
Intra Colony Communication:
For each colony;
Determine the best and worst particles;
Improve the worst particle by using equations 3 and 4;
Repeat for a specific number of iterations;
Self- attraction within the colony is achieved by equation 1 in the 2nd term;
End;
Inter Colony Communication:
Combine the evolved colonies;
Sorting: Sort the population P in descending order of their fitness;
Cooperation between different colonies is achieved by equation 1 in the 3rd term;
Termination:
Check if termination = true;
End;
5. Simulation Results
Proposed Embellished Particle Swarm Optimization (EPSO) algorithm is tested in
standard IEEE-57 bus power system. The reactive power compensation buses are 18, 25 and
53. Bus 2, 3, 6, 8, 9 and 12 are PV buses and bus 1 is selected as slack-bus. The system
variable limits are given in Table 1.
The preliminary conditions for the IEEE-57 bus power system are given as follows:
Pload = 12.018 p.u. Qload = 3.012 p.u.
The total initial generations and power losses are obtained as follows:
∑ = 12.5048 p.u. ∑ = 3.3217 p.u.
Ploss = 0.25625 p.u. Qloss = -1.2017 p.u.
Table 2 shows the various system control variables i.e. generator bus voltages, shunt
capacitances and transformer tap settings obtained after EPSO based optimization which are

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within the acceptable limits. In Table 3, shows the comparison of optimum results obtained from
proposed EPSO with other optimization techniques. These results indicate the robustness of
proposed EPSO approach for providing better optimal solution in case of IEEE-57 bus system.
Table 1. Variable limits
Reactive Power Generation
Limits
Voltage And Tap Setting
Limits
Shunt Capacitor Limits
Bus no Qgmin Qgmax vgmin 0.9 Bus no Qcmin Qcmax
1 -1.4 1 Vgmax 1.0 18 0 10
2 -.015 0.3 vpqmin 0.91 25 0 5.2
3 -.02 0.4 Vpqmax 1.05 53 0 6.1
6 -0.04 0.21 tkmin 0.9
8 -1.3 1 tkmax 1.0
9 -0.03 0.04
12 -0.4 1.50
Table 2. Control variables obtained after optimization
Control
Variables
EPSO
V1 1.1
V2 1.031
V3 1.040
V6 1.039
V8 1.030
V9 1.010
V12 1.020
Qc18 0.0654
Qc25 0.200
Qc53 0.0452
T4-18 1.010
T21-20 1.057
T24-25 0.871
T24-26 0.819
T7-29 1.051
T34-32 0.880
T11-41 1.021
T15-45 1.040
T14-46 0.910
T10-51 1.021
T13-49 1.060
T11-43 0.910
T40-56 0.900
T39-57 0.950
T9-55 0.950
Table 3. Comparison results
S.No. Optimization
Algorithm
Finest Solution Poorest Solution Normal
Solution
1 NLP [20] 0.25902 0.30854 0.27858
2 CGA [20] 0.25244 0.27507 0.26293
3 AGA [20] 0.24564 0.26671 0.25127
4 PSO-w [20] 0.24270 0.26152 0.24725
5 PSO-cf [20] 0.24280 0.26032 0.24698
6 CLPSO [20] 0.24515 0.24780 0.24673
7 SPSO-07 [20] 0.24430 0.25457 0.24752
8 L-DE [20] 0.27812 0.41909 0.33177
9 L-SACP-DE [20] 0.27915 0.36978 0.31032
10 L-SaDE [20] 0.24267 0.24391 0.24311
11 SOA [20] 0.24265 0.24280 0.24270
12 LM [21] 0.2484 0.2922 0.2641
13 MBEP1 [21] 0.2474 0.2848 0.2643
14 MBEP2 [21] 0.2482 0.283 0.2592
15 BES100 [21] 0.2438 0.263 0.2541
16 BES200 [21] 0.3417 0.2486 0.2443
17 Proposed EPSO 0.22107 0.23128 0.22172

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Proposed Embellished Particle Swarm Optimization (EPSO) has been tested in
standard IEEE 118-bus test system [22] .The system has 54 generator buses, 64 load buses,
186 branches and 9 of them are with the tap setting transformers. The limits of voltage on
generator buses are 0.95 -1.1 per-unit., and on load buses are 0.95 -1.05 per-unit. The limit of
transformer rate is 0.9 -1.1, with the changes step of 0.025. The limitations of reactive power
source are listed in Table 4, with the change in step of 0.01.
Table 4. Limitation of reactive power sources
BUS 5 34 37 44 45 46 48
QCMAX 0 14 0 10 10 10 15
QCMIN -40 0 -25 0 0 0 0
BUS 74 79 82 83 105 107 110
QCMAX 12 20 20 10 20 6 6
QCMIN 0 0 0 0 0 0 0
The statistical comparison results of 50 trial runs have been list in Table 5 and the
results clearly show the better performance of proposed EPSO algorithm.
Table 5. Comparison Results
Active power loss (MW) BBO
[23]
ILSBBO/
strategy1
[23]
ILSBBO/
strategy1
[23]
Proposed
EPSO
Min 128.77 126.98 124.78 115.97
Max 132.64 137.34 132.39 121.02
Average 130.21 130.37 129.22 119.52
6. Conclusion
In this paper an innovative approach Embellished Particle Swarm Optimization (EPSO)
algorithm successfully reactive power problem. Swarm-to-swarm mechanism drastically speeds
up the swarm community to converge to the global near optimum. The performance of the
proposed algorithm has been demonstrated by testing it on standard IEEE 57,118 test bus
systems. Proposed Embellished Particle Swarm Optimization EPSO algorithm out performs
other reported standard algorithm’s in reducing real power loss.
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