Solution for optimal power flow problem in wind energy system using hybrid multi objective artificial physical optimization algorithm

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 10, No. 1, March 2019, pp. 486~503
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v10.i1.pp486-503  486
Journal homepage: http://iaescore.com/journals/index.php/IJPEDS
Solution for optimal power flow problem in wind energy system
using hybrid multi objective artificial physical
optimization algorithm
P. Nagaleshmi
Panacorp Software Solutions, Nagercoil, India
Article Info ABSTRACT
Article history:
Received Dec 16, 2017
Revised Apr 13, 2018
Accepted Oct 3, 2018
Normally, the character of the wind energy as a renewable energy sources
has uncertainty in generation. To resolve the Optimal Power Flow (OPF)
drawback, this paper proposed a replacement Hybrid Multi Objective
Artificial Physical Optimization (HMOAPO) algorithmic rule, which does
not require any management parameters compared to different meta-heuristic
algorithms within the literature. Artificial Physical Optimization (APO), a
moderately new population-based intelligence algorithm, shows fine
performance on improvement issues. Moreover, this paper presents hybrid
variety of Animal Migration Optimization (AMO) algorithmic rule to express
the convergence characteristic of APO. The OPF drawback is taken into
account with six totally different check cases, the effectiveness of the
proposed HMOAPO technique is tested on IEEE 30-bus, IEEE 118-bus and
IEEE 300-bus check system. The obtained results from the HMOAPO
algorithm is compared with the other improvement techniques within the
literature. The obtained comparison results indicate that proposed technique
is effective to succeed in best resolution for the OPF drawback.
Keywords:
Animal migration optimization
(AMO)
Meta-heuristic algorithms
artificial physical optimization
(APO)
Renewable energy sources
optimal power flow (OPF)
Copyright © 2019 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
P. Nagalashmi,
Panacorp Software Solutions,
Nagercoil – 629001, India.
Email: nagaleshmip17@gmail.com
1. INTRODUCTION
Today’s technological word fully depends on electricity; but the availability of electric source is
low. The deficiency of electricity becomes the breaking point for emerging countries. Therefore, the research
organizations tend into research to discover an appropriate solution for giving uninterruptable electricity. In
this situation the usage of renewable energy sources are the superior solution, so these renewable energy
systems are encouraged for electricity production [1], [2]. The most available renewable source in the world
is wind and solar, the researches on these to area are under progressing but wind energy conversion is most
promising research area because of its low complexity in installation and maintenance [3]. The wind energy
systems are directly integrated into the power system for power system usage. The integration of wind energy
into existing power system presents a technical problems and that needs attention of voltage regulation,
stability, power quality issues [4].
The power quality is an important customer focused measure and is significantly affected by the
operation of a distribution and transmission network. The issue of power quality is of great importance to the
wind turbine [6]. By aggregating multiple wind turbines as wind farm or park, greater amount of electrical
power can be generated from it. To interconnect wind power to the utility grid, there must be an appropriate
grid interconnection, control system and regulation to ensure high power quality, reliability and stability.
However, the one of the most critical problems associated with wind power is that, the amount of power
generated by the same is affected by the intermittent nature of wind flow which is difficult to predict [7]. It

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Solution for optimal power flow problem in wind energy system using hybrid... (P. Nagaleshmi)
487
follows that, the grid integrated wind powered units, may introduce severe challenges to traditional
generation scheduling methodologies and operation of power system [8]. For satisfactory grid integration, the
wind power fluctuation may have to be balanced by other types of generation. Alternatively, to compensate
for the power imbalance due to uncertainty of wind, additional cost may have to be added with the total
power generation cost of the system [9].
The major goal of Optimal Power Flow (OPF) is to improve a target capacity such as cost of fuel by
means of ideal change of the control variables simultaneously different equality and inequality constraints.
For the main intend of economical and secure operation and planning of power systems, optimal power flow
(OPF) is employed [10]. The objective of OPF is to reduce the cost of fuel, environmental pollution and also
the power lost by the network. In power system economic load dispatch (ELD) is commonly used to find
generation or fuel cost. The major goal of Economic Dispatch (ED) is to minimize the amount of total
pollution caused by the environment. This can be done by avoiding the burning of fuels [11]. Economic Load
Dispatch (ELD) is determined as the technique in which the generation levels are allocated to the generating
units. As a result the load of the system is totally and economically supplied. The ELD is a large-scale, highly
non-linear, constrained optimization problem [12]. The main aim of ELD is conflicting in nature and to
achieve an acceptable strategy of power dispatch within different system constraints and also it helps to keep
the pollution within the limits and it reduces the fuel cost [13].
Application with renewable energy sources such as solar cell array, wind turbines, or fuel cells have
increased significantly during the past decade. To obtain the clean energy, we are using the hybrid solar-wind
power generation. Consumers prefer quality power from suppliers. The quality of power can be measured by
using parameters such as voltage sag, harmonic and power factor. To obtain quality power we have different
topologies. In our paper we present a new possible topology which improves power quality [14].
The hybrid power system is normally equipped with control system which functions to reduce the
system frequency oscillations and makes the wind turbine generator power output follow the performance
curve when the system is subjected to wind/load disturbances. Usually PI controllers are employed in these
systems. Unfortunately since the operating point changes depending on the demand of consumers, this
constant gain PI controller are unsuitable to other operating points. Therefore, it describes the application of
fuzzy gain scheduling of PI controller for an isolated wind-diesel hybrid power system with superconducting
magnetic energy storage [15].
Reduction of operating costs in power system in order to return the investment costs and more
profitability has vital importance in power industry. Economic Load Dispatch (ELD) is one of the most
important issues in reducing operating costs. ELD is formulated as a nonlinear optimization problem with
continuous variables within the power plants. The main purpose of this problem is optimal planning of power
generation in power plants with minimum cost by total units, regarded to equality and inequality constraints
including load demand and the range of units' power productivity. In this article, Economic Load Dispatch
problem has been modeled by considering the valve-point loading effects with power plants' constraints such
as: the balance of production and consumption in system, the forbidden zones, range of production,
increasing and decreasing rates, reliability constraints and network security [16].
In recent years wind turbine technology has undergone rapid developments, growth in size. The
wind energy become increasingly competitive with conventional energy sources based on the optimization of
wind turbines. The penetration of wind energy in the grid raises questions about the compatibility of the wind
turbine power production with the grid. In particular, the contribution to grid stability, power quality and
behavior during fault situations plays therefore as important a role as the reliability. In this paper, a vector
control scheme is developed to control the rotor side voltage source converter [17].
A new control method for quasi-Z-source cascaded multilevel inverter-based grid-connected
photovoltaic (PV) system is proposed. The proposed method is capable of boosting the PV array voltage to a
higher level and solves the imbalance problem of DC-link voltage in traditional cascaded H-bridge inverters.
This system adjusts the grid injected current in phase with the grid voltage and achieves independent
maximum power point tracking (MPPT) for the separate PV arrays. To achieve these goals, the proportional-
integral (PI) controllers are employed for each module. For achieving the best performance, this paper
presents an optimum approach to design the controller parameters using particle swarm optimization (PSO).
The primary design goal is to obtain good response by minimizing the integral absolute error. Also, the
transient response is guaranteed by minimizing the overshoot, settling time and rise time of the system
response. The effectiveness of the new proposed control method has been verified through simulation studies
based on a seven level quasi-Z-Source cascaded multilevel inverter [18].
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

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 10, No. 1, March 2019 : 486 – 503
488
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 [19].
The problem of Optimal Power Flow can be solved by utilizing various techniques like linear
programming, non-linear programming, interior-point technique, quadratic programming, sequential
unconstrained minimization and Newton based techniques and also it can be solved by the integration of
optimization techniques like evolutionary programming (EP), particle swarm optimization (PSO), and
sequential quadratic programming (SQP)[20]. There are two steps involved. In the first step, the solution
space is investigated by both EP and PSO techniques. In the second step, SQP is utilized when there is a
development in the result of first phase [21]. EP is a kind of global searching technique. It begins at the
population of candidate solution and at last evaluation process is utilized to find the near global solution in
parallel. GA is a search algorithm based on the mechanics of natural genetics and natural selection. The
evolution procedure of organs with functional optimizations is integrated here. Reproduction, crossover and
mutation are the three basic prime operators associated with GA. Based on the chromosomes, GA works. A
set of binary digits which describes the control parameter coding is contained in these chromosomes which is
composed themselves with genes [22], [23].
It is necessary to control the power flow at the optimal range while the renewable energy sources are
used in power systems. The main contribution of this paper is i) To formulate the optimal power flow
problem as a multi objective optimization problem ii) And to utilize the Artificial Physical Optimization
(APO) algorithm with Animal migration optimization as a solution to the OPF problem. The remainder of
this paper is organized as follows: Some of the recent related researches to our proposed method is explained
in section 2. The proposed methodology with problem formulation is explained in section 3. The
Experimental results of the proposed method and the comparison with existing methods are presented in
section 4 followed by the conclusion in section 5.
2. RELATED WORKS
Some of the recent research work related to the OPF problem in wind energy system is listed
as follows:
Shanhe Jiang et.al [24] introduced “A hybrid particle swarm optimization and gravitational search
algorithm for solving economic emission load dispatch problems with various practical constraints”. To solve
economic emission load dispatch problem, in this paper PSO was integrated with GSA. Both the utilized
approach was based on population. In PSO technique, the agents were taken as particle. Here the movement
of each particle was based on both the past best solution of its own and the past best solution of its group. In
GSA, the agents were taken as objects. Here the one object was fascinated by other objects through
gravitational force. The agent in GSA was described through four types of parameters. The first parameter
was the position of the mass in which solution to the problem was stated at specified search space. The
second parameter was the inertial mass which decelerates its motion by reflection of its resistance. The third
and fourth parameter was the active and passive gravitational mass. The estimation of both gravitational and
inertial mass was done through fitness function. Both the algorithms were integrated by any one of the two
procedures. (i.e.) one work starts after the completeness of the previous work and the other way was to
employ co-evolutionary method to consider the swarm components as the components introduced by
PSO-GSA.
Aniruddha Bhattacharya and Pranab Kumar Chattopadhyay [25] developed “Hybrid Differential
Evolution with Biogeography-Based Optimization for Solution of Economic Load Dispatch”. Here the issue
of both convex and non-convex economic load dispatch was solved by the combination of differential
evolution (DE) algorithm and biogeography-based optimization algorithm. The above combination of
algorithms also solves problems like degradation of solution quality and low speed. The DE algorithm was
based on population. Here functions like non-differentiable, nonlinear and multi-modal objective can be
handled and a trial vector was constructed by each parent individual in order to produce new offspring. There
were three types of basic operators was involved to enhance the population namely mutation, crossover, and
selection. In Biogeography activities like the movement of one island to another, appearance and
disappearance of new species were expressed. The quality of the solution will be degraded in later stage due
to the existence of cross-over operation in evolutionary based algorithm whereas in BBO, cross-over
operation was not restricted.
IejinCai et.al [26] presented “A hybrid CPSO–SQP method for economic dispatch considering the
valve-point effects”. In this paper, chaotic particle swarm optimization (CPSO) algorithm and sequential
quadratic programming (SQP) were incorporated to retrieve the solution for economic power dispatch
problem. Here the central optimizer was the CPSO and to enhance quality of the solution, the results were

489
adjusted by SQP. The CPSO was designed based on tent equation. CPSO was a combination of PSO and
CLS. Where global exploration was carried out in PSO and local search was done to the solutions of the PSO
through CLS. IN SQP, there were three stages. In the first stage, the Hessian matrix contained in the
lagrangian function was updated. Estimation of line search and merit function was done at the second stage
and finally solution was acquired for the problem of quadratic programming. The optimal power generation
of each unit which was submitted to operation was found by the hybridization of CPSO-SQP technique.
Behnam Mohammadi-Ivatloo et.al [27] discussed “Nonconvex Dynamic Economic Power Dispatch
Problems Solution Using Hybrid Immune-Genetic Algorithm”. The cost needed for operation was reduced
and also the solution for the problem of dynamic economic dispatch (DED) in a non-convex solution space
was found by the consolidation of immune algorithm (IA) and genetic algorithm (GA). In IA, when the
extraneous molecules was arrived in the immune system of human body a reaction occurs. Even though this
algorithm does not contain any knowledge about that molecule, they were analyzed by this algorithm after
some time and also solution for the removal of these molecules was found. Here the extraneous molecule was
known as antigens and the reaction of the immune system was known as antibodies. The antibodies should be
balanced with the unknown antigens. The antibodies were given by the objective function, its combined
constraints from the antigens and the solutions which enhance them. Some antibodies was generated by the
human body at the initial stage and those antibodies was compared with the newcomer antigens and the
identical properties between them was estimated. This estimation was known as affinity factor.
K. Vaisakh et.al [28] designed “Solving dynamic economic dispatch drawback with security
constraints exploitation bacterial forage PSO-DE algorithm”. Here problems like non-smooth, non-convex
nature attributable to valve-point loading effects, ramp rate limits, spinning reserve capability, prohibited in
operation zones and security constraints was shown in DED drawback. The on top of mentioned issues is
often defeated by the mixing of bacterial forage Particle Swarm improvement (BPSO) with differential
evolution (DE) algorithmic rule. The BPSO was a mixture of microorganism forage optimization algorithmic
rule and PSO. The bacterium with positive foraging methods was chosen by the PSO operator within the
change method of each chemo-tactic step, so as to get reduced price. In our new BPSO-DE approach, the
primary step was the substitution of velocity in place of delta. Within the second step, through the calculation
of fitness operate the population of best fitness within the current generation and also the worth for world
best fitness was obtained. Within the third step, the position of generation was modified to a replacement
position. Within the fourth step, to retrieve the losses from power, apparent power within the lines and
voltages of load was retrieved by the load flow operation that was done with those new populations made at
the previous step. Within the fifth step the violations was verified for the line flows and cargo voltages. If it
contains violations then penalty terms were additional to the fitness operate of each BPSO and Delaware.
Each the fitness functions were compared for each bacterial population and also the best worth was keeping
in an exceedingly separate variable. The simplest value of fitness, real power generation price, voltages, line
flows, power losses for the given interval were updated for all the microorganism population as pbest and
global best (gbest). Then the procedure for next chemo-tactic step was continual.
3. PROPOSED OPTIMIZATION SOLUTION TO OPF PROBLEM
In a wind energy system, Optimal Power Flow (OPF) is a Multi-objective optimization problem that
seeks to find out a compromise solution to minimize the fuel cost, power loss, emission and
maintaining voltage stability. The Solution of optimal power flow (OPF) problem aims to optimize a selected
objective function through optimal adjustment of the power system control variables while at the same time
satisfying the various equality and inequality constraints. According to the results of previous investigations,
Animal Migration Optimization (AMO) and Artificial Physical Optimization (APO) have better performance
for solving optimizations problems. In this work, we intend to propose a Hybrid Multi objective Artificial
Physical Optimization (HMOAPO) is to solving the OPF (Optimal Power Flow) problem in wind energy
system. The architecture of our proposed work is shown in Figure 1.

 ISSN: 2088-8694
490
cv
Animal migration
with artificial
physical
optimization
Adaptive penalty
function
Hybrid optimization for optimal power flow control
Figure 1. Architecture of our proposed work
To enhance the performance of APO, this work applies an Animal Migration algorithm (AMO)
which follows three main rules for each individual and also to overcome the drawback of premature
convergence. In addition, the MOAPO is combined with Adaptive Penalty Function to handle equality and
inequality constrains associated with OPF problems. The adaptive penalty function (APF), which convert a
constrained problem into an unconstrained one where the ‘Penalty Function’ penalize the infeasible solutions
to move towards desirable feasible solutions.
3.1. OPF problem definition
The OPF problem is considered as a general optimization problem. The OPF problem expects to
reduce the whole fuel cost perform whereas fulfilling the whole load, completely different equality and
difference constraints. Likewise, the best values of the management variables within the power grid are
resolved within the OPF problem. Mathematical expression belonging to the matter is delineating as follows.
T
OF
OF
OF
OF
OF
OF
Min )
,
,
,
,
,
( 6
5
4
3
2
1
(1)
Subject to:
 ,
sin
cos
|
|
|
|
1
ij
ij
ij
ij
N
j
j
i
Di
Gi
B
G
V
V
P
P 
 




,
N
i 
 (2)
 ,
cos
sin
|
|
|
|
1
 




N
j
ij
ij
ij
ij
j
i
Di
Ci
Gi
B
G
V
V
Q
Q
Q 
 ,
N
i

 (3)
,
,
max
min
g
Gi
Gi
Gi
N
i
P
P
P 


 (4)
,
,
max
min
g
Gi
Gi
Gi N
i
Q
Q
Q 


 (5)
,
|,
|
|
|
|
| max
min
N
i
V
V
V i
i
i



 (6)
,
,
max
min
t
k
k
k
N
k
t
t
t 


 (7)
,
, nbr
i
S
S rated
li
li 

 (8)
,
,
max
min
c
ci
ci
ci N
i
Q
Q
Q 


 (9)
 
 
1
sin
|
|
4
2




j
i
i
j
ij
ij
V
Q
X
LSI



(10)

491
,
tan 1








 
ij
ij
R
X
 (11)
  .
sin
|
|
|
|
sin
|
|
|
||
| 2




ij
j
j
i
ij
j
i
j
Z
V
Z
V
V
Q 


 (12)
In this work, the target perform of the OPF problem is proposed because the total generation value
as well as valve-point impact, loss minimization and prohibited zones. The power flow equations are
thought-about because the equality constraints. The transmission limits and alternative security limits are
used as difference constraints. The vectors are outlined as state variable and control variable vectors are
outlined as follows:
 .
........
,
........
,
.......
,
...... 1
1
1
1 Nc
c
c
Nt
Ng
g
g
Ng
g
g
Q
Q
T
T
V
V
P
P 





(13)
Where g
P , g
V , Nt
T , c
Q are described as the active power of the slack bus, the voltage magnitude of
the load buses, active power output of the generators except at the slack bus, the reactive power of the
generators respectively.
 .
......
,
.......
,
...... 1
1
1 nbr
PQ l
l
N
PQ
PQ
Ng
g
g S
S
V
V
Q
Q 



(14)
Where g
Q , PQ
V and l
S are defined as the reactive power generation at bus, the voltage of load bus
and the line flow, respectively.
Objective function
In this paper, the objective function of the OPF problem is defined as minimization of the total fuel
cost of the power generation system. The total fuel cost can be mathematically defined as follows:
 
 



Ng
i
i
Gi
i
Gi
i
c
P
b
P
a
OF
1
2
1
(15)
Where i
PG are represented as the active power output of the
th
i generator, respectively. i
a , i
b
and i
c are the fuel cost coefficients of the
th
i generator.
3.2. The generation cost minimization with valve point loading (VPL) effect
The generation cost with valve-point effect is presented as follows:
   
 
Gi
Gi
i
i
Ng
i
i
Gi
i
Gi
i
P
P
e
d
c
P
b
P
a
OF 



 



min
1
2
2
sin (16)
Where i
d and i
e are coefficients of the valve-point effect of the
th
i generator. Typical curve
related to fuel cost with and without valve-point effect of the generation units is shown in Figure2.
Unit
Cost
With valve point effect
Without valve point effect
Figure 2. Typical curve related to fuel cost with and without valve-point effect of the generation units

 ISSN: 2088-8694
492
Let  
k
j
W
k
j P
W ,
,
be the electrical energy cost of wind power of the th
j wind farm and the
th
k wind
power generator. Therefore, the cost of the wind unit can be defined by:
     
k
j
k
j
k
j
z
k
j
k
j
k
j
z
k
j
k
j
k
j
W
k
j P
P
P
P
P
P
W ,
,
,
,
,
,
,
,
,
,
,
,
~
ˆ
~
2
1







 

 (17)
Which, k
j
k
j
P
P ,
,
~
,

are expected and available generation output of the unit j in the wind farm k (MW).
k
j,
 , k
j
z ,
,
1
 and k
j
z ,
,
2
 are namely direct, overestimation and underestimation electrical wind energy cost
coefficient of the unit j in the wind farm k ($/MWh).
3.3. Generating units with prohibited operating zones (POZs)
The physical limitations of the power plant components, prohibited operating zones (POZs) are
occurred in a hydro-generating unit. This constraint dictates several feasible sub-regions for hydro-generating
units as shown in Figure 3 and can be expressed by:
Valve
point
effect
Prohibited
zone
Cost
The unit
th
i
k
LB
i
P
1

k
UB
i
P
Figure 3. Topology of cost function with prohibit zone constraint and valve point effect
k
g
i
i
UB
i
LB
i
i
UB
i
LB
i
i
i
N
k
N
i
P
P
P
P
P
P
P
P
P
k
k
k
,.....,
2
,
1
,
,......,
2
,
1
,
max
min
1
1

















(18)
Which, 1

k
UB
i
P and k
LB
i
P are upper and lower limits of the
th
k sub-regions of the
th
i unit, respectively.
g
N and k
N are the number of thermal units and sub-regions.
Power Loss Minimization
The total real power loss in power systems is represented by
   
 
  



 
N
i
N
j
j
i
j
i
ij
j
i
j
i
ij
Q
P
P
Q
Q
Q
P
P
OF
1 1
3

 (19)
Which
   
j
i
j
i
ij
ij
j
i
j
i
ij
ij
V
V
r
V
V
r





 


 sin
,
cos
, i
i
V 
 is the complex voltage at the bus
th
i . ij
ij
ij
jx
r
Z 
 is the
th
ij element of [Zbus] impedance matrix. i
P and j
P are the active power injections at the
th
i and th
j buses,
respectively. i
Q and j
Q are the reactive power injections at the
th
i and th
j buses, respectively. N is the
number of buses.
L-index minimization
The voltage stability index (VSI) which ensures secure operations and is written as follows

493
and
V
V
V
dV
V
V
OF avg
N
i
avg
i





 

 






 

 2
|
|
|
|
,
|
| min
max
1
4
(20)
,
2
|
| min
max







 

V
V
dV
(21)
Where n is selected to be equal 1.Finally, wind power can be expressed by the piecewise linear
as follows:

































f
w
k
j
co
k
j
k
j
h
k
j
h
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
k
j
k
j
ci
k
j
k
j
k
j
h
k
i
N
k
N
j
otherwise
T
T
T
T
T
T
T
T
D
T
T
D
T
T
D
T
T
T
T
T
D
T
T
D
T
T
T
T
D
P
P
,...
2
,
1
,
,...
2
,
1
,
0
,
1
),
(
)
(
)
(
),
(
)
(
,
,
,
,
,
,
,
,
,
2
,
,
2
,
,
,
3
,
,
1
,
,
2
,
,
2
,
,
,
,
1
,
,
1
,
,
2
,
,
,
1
,
,
1
,
,
,
2
,
,
,
,
1
,
,
1
,
,
1
,
,
,
,
,
,
1
,
,
,


(22)
Which, Di,j,k is slope of section j of the wind unit w in wind farm f (MWs/m). Tci,j,k, Tco,j,k, Ti,j,k
and Th,j,k are cut-in wind speed, cut-out wind speed, breakpoint of segment i and rated wind speed, for all
the wind units w in the wind farm (m/s), respectively.
Artificial Physical Optimization
APO is a nature-inspired metaheuristic method inspired by natural physical forces based on artificial
physics (AP) framework [29]which is developed by Spear et al. Based on the similarity among the AP
method and population-based optimization algorithm, recently some authors proposed APO and tested its
optimization performance [30–32]. APO can be described briefly as follows
Assume the optimization problem can be expressed as
D
d
x
x
x
t
s
x
f
d
d
d
d
,........,
2
,
1
,
.
.
)
(
min
max
min



Where D is the dimension of the problem, d
xmin
and
d
xmax are the minimum and maximum limits of
variable
d
x .
The particle’s position signifies the solution to the optimization problem. The position of particle i
is defined as
  .
,.........
2
,
1
,
,.......,
,.......,
, 2
1
NP
i
x
x
x
x
X D
i
d
i
i
i
i


Where NP is the number of individuals in APO;
d
i
x is the position of the
th
i individual in
th
d
dimension.
Step 1: Population Initialization.
The NP individual’s positions are randomly formed in the n-dimensional decision space.
The NP individual’s velocities are set to be zero.
Step 2: Fitness calculation.
Compute the fitness of each individual according to the objective function.
Step 3: Force calculation.
In the APO, the process of optimization is continuously performed by moving the individual toward
the promising region until the optimal solutions is found. And the rules for moving the individuals are
decided by the forces act on each other. The rules can be expressed by the following equations:
4. SIMULATION RESULTS AND COMPARISONS
The proposed algorithm is developed using MATLAB version 6.5 programming language and the
proposed methodology is tested in IEEE 30-bus system and the samples are tested on 2.6-Ghz Pentium-IV
PC. The generators data and cost coefficients are gathered from [25].

 ISSN: 2088-8694
494
4.1. Case studies on the IEEE 30-bus System
4.1.1. Comparison with global optimization
Initially the sample is tested in IEEE 30-bus, 41-branch system with the voltage constraint of lower
and upper limits are 0.9 p.u and 1.1 p.u., respectively. The APO population size is taken equal 30, the most
range of generation is 100, and crossover and mutation are applied with initial likelihood zero.9 and 0.01
severally. Figure 4 shows the topology of normal IEEE 30 bus system.
Figure 4. IEEE 30 bus system
For the aim of supportive the efficiency of the proposed approach, we have a tendency to created a
comparison of our efficiency with others competitive OPF efficiency. In [25], they conferred a typical GA, in
[3] the authors conferred associate enhanced GA, and so in [26], they proposed an Improved evolutionary
programming (IEP). In [27] they presented an optimum power flow solution using GA-Fuzzy system
approach (FGA), and in [11] a changed differential evolution is proposed (MDE). The budget items in our
proposed approach is 800.8336 and therefore the power loss is 8.92 that area unit higher than the others
strategies reported within the literature. Result in Table 1 show clearly that the proposed approach provides
higher results.
Table 1. Results of the minimum cost and power generation compared with:
SGA, EGA, IEP, FGA and MDE for IEEE 30-bus
Variables Our approach EPGA Global optimization methods
NP=1 NP=2 NP=3 SGA [19] EGA [3] IEP [20] FGA [21] MDE [11]
P1(MW) 180.12 175.12 174.63 179.367 176.20 176.2358 175.137 175.974
P2(MW) 44.18 48.18 47.70 44.24 48.75 49.0093 50.353 48.884
P5(MW) 19.64 20.12 21.64 24.61 21.44 21.5023 21.451 21.510
P8MW) 20.96 22.70 20.24 19.90 21.95 21.8115 21.176 22.240
P11(MW) 14.90 12.96 15.04 10.71 12.42 12.3387 12.667 12.251
P13(MW) 12.72 13.24 12.98 14.09 12.02 12.0129 12.11 12.000
Q1(Mvar) -4.50 -2.11 -2.03 -3.156 - - -6.562 -
Q2(Mvar) 30.71 32.57 32.42 42.543 - - 22.356 -
Q5(Mvar) 22.59 24.31 23.67 26.292 - - 30.372 -
Q8(Mvar) 37.85 27.82 28.22 22.768 - - 18.89 -
Q11(Mvar) -2.52 0.490 0.48 29.923 - - 21.737 -
Q13(Mvar) -13.08 -11.43 -11.43 32.346 - - 22.635 -
1(deg) 0.00 0.00 0.00 0.000 - - 0.00 -
2(deg) -3.448 -3.324 -3.313 -3.674 - - -3.608 -
5(deg) -9.858 -9.725 -9.623 -10.14 - - -10.509 -
8(deg) -7.638 -7.381 -7.421 -10.00 - - -8.154 -
11(deg) -7.507 -7.680 -7.322 -8.851 - - -8.783 -
13(deg) -9.102 -8.942 -8.926 -10.13 - - -10.228 -
Cost ($/hr) 801.34 800.83 800.92 803.699 802.06 802.465 802.0003 802.376
Ploss (MW) 9.120 8.920 8.833 9.5177 9.3900 9.494 9.459
CPU time(s) ~0.954 - - 594.08 - 23.07

495
Table 1 denotes the cost consumption of the proposed and prevailing global methodologies.It is
clearly seen that the cost consumption of the prevailing methodologies such as Sga, tga,Iep,Fga and Mde.are
comparatively higher than that of the cost consumption of our proposed methodology implying EPGA.This
clearly depicts the cost efficiency of our framework from others.
Table 2 shows the best solution of shunt compensation obtained at the standard load demand
(Pd=283.4 MW) using reactive power planning. This describes the shunt reactive power compensation of
Epga and Ega where comparatively betterment is shown in favour of Epga. The transmission line loading
after optimization compared to aco and fga for ieee 30-bus as shown in Table 3.
Table 2. Comparative results of the shunt reactive power compensation between
EPGA and EGA [7] for ieee 30-bus
Shunt N° 1 2 3 4 6 7 8 9
Bus N° 10 12 15 17 21 23 24 29
Best Qsvc [pu] 0.1517 0.0781 0.029 0.0485 0.0602 0.0376 0.0448 0.0245
Best case bsh [pu] [7] 0.05 0.05 0.03 0.05 0.05 0.04 0.05 0.03
Table 3. Transmission line loading after optimization compared to ACO and FGA for ieee 30-bus
EPGA: PD=283.4 MW ACO [22] FGA [21]
Line Rating
(MVA)
From Bus
P(MW)
To Bus
P(MW)
To Bus
P(MW)
To Bus
+(P(MW))
1-2 130 113.9200 -7.7300 -119.5488 117.211
1-3 130 60.7100 5.7000 -58.3682 58.3995
2-4 65 32.0600 4.3000 -34.2334 34.0758
3-4 130 56.8600 3.7900 -55.5742 54.5622
2-5 130 62.4200 4.9000 -62.4522 63.7783
2-6 65 43.3000 2.4400 -44.5805 45.3399
4-6 90 49.1700 -8.0100 -49.0123 50.2703
5-7 70 -11.7900 7.2300 11.2939 14.1355
6-7 130 34.9800 0.8800 -34.0939 33.9924
6-8 32 11.8500 -1.3200 -11.0638 13.6882
6-9 65 16.5700 -3.3400 -19.7631 22.4033
6-10 32 12.5400 0.0700 -13.1277 14.6187
9-11 65 -15.0400 -0.0700 10.4330 24.1764
9-10 65 31.6100 -3.8000 -30.1961 32.7929
4-12 65 31.2200 16.7200 -33.1670 30.5889
12-13 65 -12.9800 11.8000 12.1730 24.9376
12-14 32 7.6600 1.0500 -8.0453 7.6911
12-15 32 18.1000 1.4900 -18.1566 17.4525
12-16 32 7.2400 1.3600 -7.4961 6.34027
14-15 16 1.4000 -0.6800 -1.8340 1.2313
16-17 16 3.6900 -0.5400 -3.9715 3.2983
15-18 16 5.8900 1.9700 -6.2224 5.4066
18-19 16 2.6500 1.0000 -3.0140 2.3627
19-20 32 -6.8500 -2.4100 6.5015 8.5117
10-20 32 9.1500 3.3200 -8.7015 11.0315
10-17 32 5.3200 0.8600 -5.0285 9.861616
10-21 32 16.1000 3.9800 -15.8419 18.96153
10-22 32 7.7800 1.7400 -7.6778 9.0741
21-22 32 -1.4800 -0.6100 1.6585 2.0887
15-23 16 5.2100 -0.7000 -5.4613 4.5343
22-24 16 6.2600 1.0400 -5.9593 6.9397
23-24 16 1.9900 1.8800 -2.2388 1.14447
24-25 16 -0.5000 1.1200 0.5027 1.3934
25-26 16 3.5400 2.3600 -3.5000 4.2647
25-27 16 -4.0500 -1.2400 4.0748 5.633
27-28 65 17.3200 2.9500 -17.3814 19.7428
27-29 16 6.1900 -0.2900 -6.1070 6.4154
27-30 16 7.0600 0.8900 -6.9295 7.2897
29-30 16 3.7200 1.3500 -3.6705 3.7542
8-28 32 2.0700 -2.1900 -2.2067 3.3685
6-28 32 15.2900 -0.6800 -15.1747 16.5409
Ploss (MW) 8.8836 9.8520 9.494

 ISSN: 2088-8694
496
The operation costs of the most effective solutions for the new system composed by 2 partitions and
for the new system composed by 3 partitions area unit 800.8336 $/h and 800.9265, severally , (0.0929
difference). The variations between the values are not important compared to the initial network while not
partitioning. This proves that the new subsystems generated conserve the physical proprieties and
performances of the initial network. Table three shows that the road flows obtained area unit well underneath
security limits compared to FGA algorithm and ACO algorithm [28].
4.1.2. Comparison with PSAT and MATPOWER OPF solver
For the purpose of verifying the robustness of the proposed algorithm we made a second comparison
with PSAT and MATPOWER packages under severe loading conditions. In this work the increase in the load
is regarded as a parameter which affects the power system to voltage collapse.





oL
L
oL
L
Q
Kld
Q
P
Kld
P
.
.
(23)
Where, oL
P and oL
Q are the active and reactive base loads, L
P and L
Q are the active and reactive
loads at bus L for the current operating point. Kld Represents the loading factor.
Table 4. Results of the minimum cost and power generation compared with:
PSAT and MATPOWER package for ieee 30-bus
Variables Our Approach EPGA MATPOWER PSAT
Kld=18% Kld=32% Kld=18% Kld=32% Kld=18% Kld=32%
P1(MW) 192.66 199.30 200.00 200.0 200.00 200.0
P2(MW) 58.94 70.60 55.00 69.74 54.9925 69.9368
P5(MW) 23.22 29.08 23.70 28.40 23.6957 28.5135
P8(MW) 33.98 33.66 35.00 35.00 35.00 35.00
P11(MW) 16.60 29.32 17.01 28.03 17.0154 28.2596
P13(MW) 20.40 25.10 15.84 26.47 15.8827 26.7635
Q1(Mvar) -5.26 -6.18 -13.94 -17.66 -15.6226 -9.4127
Q2(Mvar) 38.07 40.02 37.18 43.69 38.5416 60.4752
Q5(Mvar) 35.25 42.28 36.10 42.62 36.5254 49.5412
Q8(Mvar) 35.95 43.54 47.96 60.00 49.525 50.00
Q11(Mvar) 1.150 2.06 3.680 6.910 4.6425 21.1631
Q13(Mvar) -11.73 -11.04 -11.68 -2.270 2.3642 19.7389
1(deg) 0.00 0.00 0.00 0.00 0.00 0.00
2(deg) -3.684 -3.972 -4.028 -4.022 -4.0412 -4.026
5(deg) -11.218 -12.002 -11.841 -12.518 -11.8475 -12.6009
8(deg) -8.055 -8.588 -8.737 -9.065 -8.7607 -8.7792
11(deg) -11.995 -6.847 8.931 -7.386 -8.9022 -7.0128
13(deg) -9.344 -9.423 -10.642 -9.751 -10.6419 -9.8547
Cost ($/hr) 993.6802 1159.6 993.98 1160.56 994.1047 1164.1706
Ploss MW 11.390 12.975 12.141 13.556 12.174 14.385
The results together with the generation cost, the ability losses, reactive power generation, and also
the angles are shown in Table 4. We can clearly observe that the whole cost of generation and power losses
are higher than the results obtained by PSAT and MATPOWER at each loading issue (kld=18% and
kld=32%). as an example, at loading issue 32nd (PD=374.088) the distinction in generation cost between our
approach and to the 2 Packages (1159.6 $/h compared to 1160.56 $/h and 1164.1706 $/h) and in real power
loss (12.975 MW compared to thirteen.556 MW and 14.385 MW) obtained from MATPOWER and
PSAT severally.
Table 5 depicts the results of minimum cost, power generation, power losses, reactive power
generation, and angles. At loading issue kld=48.5%, the two simulation Package (PSAT and
MATPOWER) did not converge. A wider comparison is done with the PSAT and MATPOWER in order to
verify the robustness of this framework. Similarly, the cost factor also analyzed for betterment with both
methods. The approach proposed provides acceptable answer, the minimum total cost is 1403.5 $/h.
Voltage profile at loading factor: kld=48.5% as shown in Figure 5. Lines power flow at critical
loading factor kld= 48.5% as shown in Figure 6. Reactive power exchanged between SVC controllers and the
network at loading factor: kld=48.5% as shown ini Figure 7.

497
Table 5. Results of the minimum cost and power generation compared with PSAT And MATPOWER
package for ieee 30-bus
Variables Loading Factor Kld=48.5%
PD=420.85 MW
Our Approach PSAT MATPOWER
P1(MW) 199.98
Did not Converge Did not Converge
P2(MW) 79.96
P5(MW) 49.98
P8(MW) 34.92
P11(MW) 30.00
P13(MW) 39.90
Q1(Mvar) -5.680
Q2(Mvar) 41.62
Q5(Mvar) 45.14
Q8(Mvar) 53.31
Q11(Mvar) 2.910
Q13(Mvar) -10.33
1(deg) 0.000
2(deg) -3.761
5(deg) -11.907
8(deg) -8.972
11(deg) -7.228
13(deg) -8.237
Cost ($/hr) 1403.5
Ploss (MW) 13.8960
Figure 5. Voltage profile at loading factor:
kld=48.5%
Figure 6. Lines power flow at critical loading factor
kld= 48.5%
Figure 7. Reactive power exchanged between SVC controllers and the network at loading factor:
kld=48.5%
0 5 10 15 20 25 30
0.95
1
1.05
1.1
Bus Number
V
olatage
Magnitude
Loading Factor kld=48.5%
PD=420.85 MW
0 10 20 30 40
-150
-100
-50
0
50
100
150
Lines Number
Line
P
ow
er
Flow
Rating Level(+)
Pji
Pij
Rating Level(-)
PD=420.85 MW
Loading Factor =48.5%
1 2 3 4 5 6 7 8
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Bus Number
Reactive
Power
Exchanged
(SVC)
SVC at Bus 12
SVC at Bus 15
SVC at Bus 17
SVC at Bus 21
SVC at Bus 23
SVC at Bus 24
SVC at Bus 10
SVC at Bus 29
Loading Factor =48.5%
PD=420.85 MW
SVC Max =0.35 p.u
SVC Min =-0.35 p.u

 ISSN: 2088-8694
498
Figure 8. Convergence of IEEE 30 bus system
The protection constraints are checked for voltage magnitudes, angles and branch flows. The
protection constraints are checked for voltage magnitudes, angles and branch flows. Figure 5 shows that the
voltages magnitudes are within the desired security limits. Fig. 6 shows clearly that the transmission lines
loading do not exceed their higher limits. Figure 7 shows the reactive power changed between SVC
Controllers installed in at a specified buses and also the network.
The convergence values of IEEE 30 bus system on multi objective basis is shown in above Figure 8.
The variation with real power loss, reactive power loss, voltage profile and fuel cost for the standard IEEE 30
bus system with combined APO with AMO and APO is presented and it shows the importance of utilizing
APO with AMO than APO.
4.2. Case study 2 on IEEE 26-Bus test system with non-smooth cost function
This case study comprises of 6 generation units, 26 buses and 46 transmission lines [29] and all the
thermal units are within the ramp rate limits and prohibited zones. The data for this system is taken from the
reference [29], [30] and the load demand required for this system taken as PD=1263. The transmission loss
coefficient of the B matrix is determined as follows.








































 
0
.
15
2
.
0
8
.
0
6
.
0
1
.
0
2
.
0
2
.
0
9
.
12
6
.
0
6
.
0
6
.
0
5
.
0
8
.
0
6
.
0
24
.
0
0
.
0
1
.
0
1
.
0
6
.
0
0
.
1
0
.
0
1
.
3
9
.
0
7
.
0
1
.
0
6
.
0
1
.
0
9
.
0
4
.
1
2
.
1
2
.
0
5
.
0
1
.
0
7
.
0
2
.
1
7
.
1
.
10 3
ij
B
(24)
 
6635
.
0
2161
.
0
0591
.
0
7047
.
0
1297
.
0
3908
.
0
.
10 3
0 




 
i
B (25)
056
.
0
00 
B (26)
Table 6 shows the performance comparison among the proposed algorithms, a particle swarm
optimization (PSO) approach [29], a novel string based GA [12], standard genetic algorithm (GA) method
[29], multiple task search algorithm (MTS) [13], and the simulated annealing (SA) method [13]. The
simulation results of the proposed approach outperformed recent optimization methods presented in the

499
literature in terms of solution quality and time convergence. The computational time of the proposed
approach is reduced significantly in comparison to the other methods.
Table 6. Results of the minimum cost and power generation compared with
global optimùization methods for 26-bus test system
Generators
(MW)
SA [13] New-string
GA [12]
GA [23] MTS [13] PSO [23] Our Approach
Pg1 Part1 478.1258 446.7100 474.8066 448.1277 447.4970 448.0451
Pg2 163.0249 173.0100 178.6363 172.8082 173.3221 172.0835
Pg3 Part2 261.7143 265.0000 262.2089 262.5932 263.4745 264.5932
Pg4 125.7665 139.0000 134.2826 136.9605 139.0594 134.9605
Pg5 Part3 153.7056 165.2300 151.9039 168.2031 165.4761 170.2452
Pg6 90.7965 86.7800 74.1812 87.3304 87.1280 85.2884
Total PG 1276.1339 1275.73 1276.03 1276.0232 1276.01 1275.20
Ploss (MW) 13.1317 12.733 13.0217 13.0205 12.9584 12.2160
Cost[$/hr] 15461.10 15447.00 15459.00 15450.06 15450.00 15439
CPU time(s) - 8.36 - 1.29 14.89 1.4380
4.3. Case study 3 on the IEEE 118-Bus
To investigate the strength of the projected approach the algorithmic program was enforced and
tested to the quality IEEE 118-bus model system (54 generators, 186 (line + transformer) and ninety nine
loads). The system load is 4242 MW and base MVA is 100 MVA. During this model, there are 54 generators
and that they are consists of various 18 characteristic generators [25]. The projected approach is compared to
the $64000 Genetic algorithmic program projected in [25]. The results pictured in Table 6 show clearly that
the projected approach provides far better results than the other technique. The distinction in generation value
between these 2 studies (6347.2$/h compared to 8278.9$/h) and in real power loss (106.788 MW compared
to 94.305 MW).
Figure 9. Topology of the IEEE 118-bus test system

 ISSN: 2088-8694
500
The optimum active powers ars bushed their secure limits values and are off from the physical
constraints limits. The protection constraints also are checked for voltage magnitudes and angles. Reactive
power designing [11], [12] applied within the second step based mostly in sensible fuzzy rules. Figure 9
show the topology the quality IEEE 118-Bus. Figure 10 shows that the reactive power generations are on
their security limits; Figure 11 shows the reactive power changed between the SVC Compensators put in at
crucial buses and also the network. Figure 12 demonstrates that the voltage profiles for all buses are
increased based mostly in reactive power designing sub problem.
The convergence values of IEEE 118 bus system on multi objective basis is shown in above
Figure 13. The variation with real power loss, reactive power loss, voltage profile and fuel cost for the
standard IEEE 30 bus system with combined APO with AMO and APO is presented and it shows the
importance of utilizing APO with AMO than APO.
The comparison Results of proposed method with GA for IEEE 118-Bus in terms of the Minimum
Cost and Power Generation is shown in Table 7.
Figure 10. Reactive power generation of IEEE 118-
bus electrical network with shunt compensation
(pd=4242 mw)
Figure 11. Reactive power compensation based
SVC compensators exchanged with the IEEE 118-
bus electrical network (pd=4242 mw)
Figure 12. Voltage profiles of IEEE 118-bus electrical network
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
51
53
55 57 59 61 63 65
67
69
71
73
75
77
79
81
83
85
87
89
91
93
95
97
99
101
103
105
107
109
111
113
115
117
Vmax Vmin

501
Figure 13. Convergence of IEEE 118 bus system
Table 7. Results of the minimum cost and power generation compared with GA for IEEE 118-bus
Gen Type EPGA GA [19] Gen Type EPGA GA [19]
1
4
6
8
10
12
15
18
19
24
25
26
27
31
32
34
36
40
42
46
49
54
55
56
59
61
62
#1
#1
#1
#1
#2
#3
#1
#1
#1
#1
#4
#5
#1
#6
#1
#1
#1
#1
#1
#7
#8
#9
#1
#1
#10
#10
#1
10.840
11.280
16.840
21.380
258.86
92.760
10.000
10.000
10.780
10.060
289.98
411.80
13.700
43.100
11.020
12.160
10.300
14.180
15.100
73.420
101.24
40.820
13.140
14.520
157.26
41.920
11.820
11.99 33.603
10.191
10.038
162.09 63.06
28.439
10.398
10.023
13.178
282.02
376.55
29.683
67.232
14.144
12.912
12.639
66.505
19.805
13.345
217.88 52.24
14.431
23.335
59.497
195.11
43.015
65
66
69
70
72
73
74
76
77
80
85
87
89
90
91
92
99
100
103
104
105
107
110
111
112
113
116
#11
#11
#12
#1
#1
#1
#1
#1
#1
#13
#1
#14
#15
#1
#1
#1
#1
#16
#17
#1
#1
#1
#1
#18
#1
#1
#1
402.60
120.06
523.05
26.700
21.940
14.040
25.480
28.020
15.820
370.54
47.260
27.400
392.38
10.000
10.000
10.000
10.000
312.88
82.840
10.000
10.000
40.820
18.620
56.280
12.060
11.340
10.380
456.61
134.99
316.59
24.148
31.967
43.362
10.149 16.45
12.131
445.55
18.717
44.402
322.79
20.24
21.206
19.163
10.161
318.47
47.058
39.387
18.515
10.248
10.554
28.67
10.833
22.311
28.272
Cost($/hr)t 6347.2 8278.9
Losses (MW) 106.788 94.305
The comparison Results of proposed method with GA for IEEE 118-Bus in terms of the Minimum
Cost and Power Generation is shown in Table 7. Thus the cost factor for EPGA is given by 6347.2 and Power
generated is given by 106.788 MW which is seen that far better than compared with the GA whose minimum
cost is about 8278.9 which is comparatively higher than our proposed workwhich indicates our work as cost
effective one and similarly generated power is of 94.305 which is far much lesser than the framework.

 ISSN: 2088-8694
502
4.4. Result conclusion
It is clearly shown that the results obtained from our framework implying Epga has better results.
Initially, the comparison is done with Sga, Ega, Iep, Fga and Mde for justifying the. Obtained results. Similarly, in
order to verify the robustness, the proposed work is compared with Psat, Matpower.Then a brief comparison is
done with GA for justifying the betterment of process. Also, it is made damn clear, that from the above
figures and comparisons the clear knowledge and enhancement of process and importance of our proposed
method. The simulation results show that the multi objective problem is solved efficiently by using our
proposed APO with AMO algorithms than the existing methods. These make us to conclude that the
proposed research work will be a better of choice to solve optimal power flow problem with multi
objective function.
5. CONCLUSION
This article has conferred a unique HMOAPO algorithm and also the AMO algorithm to resolve the
OPF problem in electrical power systems. These algorithms are not to optimize multi objective functions at
the same time underneath the system constraints. The simulation results have verified the high performance
of each algorithms for resolution the target operate strategy within the customary IEEE 30-bus system.
Moreover, the DE algorithmic rule is employed to resolve multi-objective OPF issues with the assistance of
the fuzzy-based Pareto front methodology. It will be completed that the proposed APO algorithm-based
simulation results are competitive thereto of different recent optimization techniques. For an intensive
verification, each algorithms area unit applied to an outsized facility, i.e., the quality IEEE 118-bus system.
The simulation results have supported relevancy, potential, and effectiveness of those algorithms.
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