International Journal of Trend in Research and Development, Volume 3(6), ISSN 2394-9333
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Multi-Objective Optimal Power Flow using Fuzzy
Supported Ant Lion Algorithm
1
J. Radha, 2S. Subramanian, 3S. Ganesan and 4M. Abirami
1,3,4
Assistant Professor, 2Professor
1,2,3,4
Department of Electrical Engineering, Annamalai University, Annamalai Nagar, Tamil Nadu, India
Abstract— The purpose of this paper is to solve a multiobjective electric power dispatch problem, which is a multiple
non-commensurable objective problem, minimizes operating
cost, adhering pollution norms, low transmission loss and no
violations on voltage levels subject to various constraints.
Improved control settings such as generator powers, bus
voltage magnitudes, transformer taps and shunt capacitor
settings for individual and simultaneous minimization of
objectives are obtained by as new algorithm called Ant Lion
Optimization (ALO). Fuzzy based approach is used to extract
the best compromise solution from the trade off front. The best
solution records of IEEE-30 bus, IEEE-118 bus and New
England power systems are updated in this work. To further
demonstrate the efficiency and effectiveness of the ALO based
OPF, it has been compared with other state of the art
evolutionary algorithms on this domain. Comprehensive
simulation results with various case studies show a great
potential for application of ALO in multi-objective OPF
problems.
Various heuristic and bio inspired algorithms such as
Differential Evolution (DE) [1], Evolving Ant Direction
Differential Evolution (EADDE) [2], Gravitational Search
Algorithm (GSA) [3], improved harmony search [4], fuzzy
evolutionary and swarm optimization [5], mixed-binary
evolutionary Particle Swarm Optimization (PSO) [6],
improved Teaching Learning Based Optimization (TLBO)
using Levy mutation strategy (LTLBO) [7], PSO with an aging
leader and challengers [8], Artificial Bee Colony (ABC) with
quantum theory [9], improved Group Search Optimization
(GSO) [10], chaotic Krill Herd Algorithm (KHA) [11],
Adaptive Genetic Algorithm (AGA) with adjusting population
size [12], Black-Hole-Based Optimization (BHBO) [13],
Improved Electromagnetism-like Mechanism (IEM) [14], Gbest guided ABC (GABC) [15], hybrid Modified Imperialist
Competitive Algorithm–Teaching Learning Algorithm
(MICA-TLA) [16], hybrid Shuffle Frog Leaping AlgorithmSimulated Annealing (SFLA-SA) [17] and Artificial Bee
Colony (ABC) [18] have been applied to solve the multi
objective OPF problem.
Keywords—Ant Lion Optimizer; Emission; Multi-Objective
Optimal Power Flow; Voltage Stability; Quadratic Cost
The above methods solve the OPF problem by taking into
consideration of minimization of objectives individually i.e.,
one objective is minimized at a time and the values of other
objectives at that instant is noted. Nevertheless, it is not
worthwhile in many cases to optimize a single objective
function, since a power planning designer needs to arrive to a
grit handling contrasting and, in some circumstances,
conflicting design objectives. At this juncture, the application
of a multi-objective optimization algorithm stands out as the
only appropriate way to optimally set the control variables at
the same time, to consider a wide range of objective functions.
Compared with single objective optimization techniques, the
multi-objective ones are advantageous, because they are able
to generate a solution including various trade-offs among
different individual objectives and this facilitates the operators
to select the best final solution. This motivates the researchers
to handle the objectives individually and simultaneously to
reach the exact solution. In this regard, the optimization
techniques, Biogeography Based Optimization (BBO) [19],
GSA [20], KHA [21], hybrid PSOGSA [22], Adaptive GSO
(AGSO) [23], Adaptive Biogeography based Predator-Prey
Optimization (ABPPO) [24], TLBO [25], Improved Colliding
Bodies Optimization (ICBO) [26], Backtracking Search
Algorithm (BSA) [27], Differential Search Algorithm (DSA)
[28] and MICA-TLA [16] have been used and Pareto set have
been developed by means of weighing factors. Unfortunately,
the weighted sum method requires multiple runs to reach the
solution and this method cannot be employed in problems
having a non-convex Pareto-optimal front.
I. INTRODUCTION
Optimal Power Flow (OPF) is one of the special tools to
optimally analyze, monitor and control different aspects of
power system. Since 1962, OPF has attracted worldwide
attention for its significant influence on secure and economic
operations of power systems. The goal of OPF is to find the
optimal settings of a given power system network that
optimize a certain objective function while satisfying its power
flow equations, system security and equipment operating
limits. Different control variables (continuous and discrete) are
manipulated to achieve an optimal setting based on problem
formulation. The traditional objectives of OPF are
minimization of fuel cost, active power losses, bus voltage
deviation, emission of generating units, number of control
actions and load shedding. Previous research primarily
pertained to the single objective optimization of OPF
objectives. It is also realistic to use multi-objective functions
model as the goal of OPF formulation.
A. Classical and Evolutionary Methods for OPF
Earlier OPF solution methods are based on optimization
methods such as non-linear programming, quadratic
programming, Newton‘s method based solution of optimality,
linear programming, interior point methods and linear
programming.
It should be emphasized that all these approaches, are
based on gradients and derivatives that are not able to
determine the global optimum. In the recent years, many
intelligent optimization methods have been developed to
overcome the issues and limitations of the classical methods.
These methods are population based and are developed by
inspiring evolutionary process, nature and biological
behaviours of species.
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Due to the hassle involved in weighting method, fuzzy
based approach has been developed to solve multi-objective
optimization problem. Enhanced Genetic AlgorithmDecoupled Quadratic Load Flow (EGA-DQLF) [29], MultiObjective Harmony Search (MOHS) [30], multi-objective
variants of ABC and TLBO algorithm [31], Grey Wolf
Optimizer (GWO) [32], DE [32], Improved PSO (IPSO) [33],
Forced Initialised DE (FIDE) [34], Improved Strength Pareto
Evolutionary Algorithm (SPEA2) [35], Quasi-Oppositional
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TLBO (QOTLBO) [36], hybrid Modified PSO-SFLA (MPSOSFLA) [37], Modified SFLA (MSFLA) [38], glowworm
swarm optimization [39], Modified TLBO (MTLBO) [40], and
Modified ABC (MABC) [41] have been applied to solve the
issue that has both discrete and continuous variables.
B. Why ALO?
From a problem solving perspective, it is difficult to
formulate a universal optimization algorithm that could solve
all the problems. According to this, Seyedali Mirjalili et al.,
developed a new meta-heuristic algorithm, namely, the Ant
Lion Optimization (ALO) algorithm [42] and it has been
successfully applied to power system optimization problems
(short-term wind integrated hydrothermal power generation
scheduling). The ALO algorithm mimics hunting mechanism
of ant lions in nature [42]. The advantages of ALO such as
high rate of local optima avoidance, guarantee of exploration
of search space, requiring few parameters to adjust and
gradient-free attracts the authors to implement it to solve OPF
problem. In this work, it is intend to cover the objectives such
as cost, emission, transmission losses and L-index with
equality and inequality constraints and ALO has been
implemented to solve the issue. Having formulated as multiobjective optimization problem, Pareto solution has been
obtained through fuzzy mechanism.
Concisely, the main contributions of this article are
summarized as follows:
i. We proposed an OPF model that consists of four
important operational objectives such as fuel cost, pollutant
emission, transmission loss and voltage stability index.
ii. Fuzzy decision making mechanism is incorporated in
ALO and is used to solve MO-OPF problem for the first time
in literature.
iii. The Best Compromise Solution (BCS) is obtained for
the proposed OPF model over the recent report.and not as an
independent document. Please do not revise any of the current
designations.
D. Paper Organisation
The rest of the paper is organized as follows. The
framework of the proposed multi-objective OPF model is
given in section II. Section III gives a brief introduction about
ALO algorithm and the implementation of the proposed
technique to the MO-OPF problem. Simulation results are
presented in Section IV, and these results are compared to
other methods, that were used for solving the OPF problem.
Finally, the conclusion is presented in Section V.
II. OPF MODEL
The OPF problem is a non-linear, non-convex optimization
problem which determines the optimal control variables for
minimizing certain objectives subject to several equality and
inequality constraints.
Minimize, Fi(x,u)
OPF
The control variable u can be expressed as (uT):
[ PG 2 ,...,PGNG, VG1,...,VGNG, T1,...,TNT , Qc1,...,QcNC ] (5)
A. Cost Effective Objective
This objective is to minimize the total fuel cost of the
system that is represented as follows:
NG
FT   (ai PGi 2  bi PGi  ci )
(6)
i 1
B. Environmental Objective
The representation of emission function of SO2 and NOx
which is expressed in ton/h is:
NG
E   i   i PGi   i PGi 2   i exp( i PGi )
(7)
i 1
C. Transmission Loss
The objective function to minimize the real power
transmission line losses (PL) in the system can be stated as:
NL
PL   g k (Vi 2  V j 2  2ViV j cos( i   j ))
(8)
k 1
C. Contributions of the Paper
The Multi-Objective
formulated as follows:
xT  [ PG1, VL1,...,VLNPQ, QG1,...,QGNG, S L1,...,S LNL ] (4)
(MO-OPF)
i=1,2……….Nobj
problem
is
(1)
The formulation of objective function with four objectives
can be represented as,
Fi(x) = Min [F, E, PL, Lindex]
Subject to, g(x,u)=0; h(x,u) ≤ 0
The state variable x is expressed as:
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(2)
(3)
D. L-index Minimization
In order to enhance the voltage stability of the system, the
voltage stability indicator (Lindex) should be minimized.
NG
L j  1   F ji
i 1
Vi
Vj
(9)
Lindex =Lmax= max {Lj, j=1,2,....,NL} (10)
E. Constraints
The equality constraints are distinctive load flow equations
which can be stated using (11)-(12).
PGi  PDi  Vi
NB
V j (Gij cos  ij  Bij sin  ij )  0, iN PQ (11)
j 1
QGi  QDi  Vi
NB
V j (Gij cos  ij  Bij sin  ij )  0, iNB (12)
j 1
The inequality constraints characterize the system operating
limits which are mentioned using (13)-(19).
(13)
VGimin  VGi  VGimax , i  1, ........,NG
PGimin  PGi  PGimax ,
min
max
QGi
 QGi  QGi
,
min
max
Ti  Ti  Ti ,
Qcimin  Qci  Qcimax ,
VLimin  VLi  VLimax ,
S Li 
max
S Li
,
i  1, ........,NG
(14)
i  1, ........,NG
(15)
i  1, ........,NT
(16)
i  1, ........,NC
(17)
i  1, ........,NPQ
(18)
i  1, ........,NL
(19)
(13)-(15) represents generator constraints and the
transformer, Shunt VAR settings are restricted by their upper
and lower limits as in (16)-(17) respectively. The security
constraints are included in (18)-(19).
III. FUZZY SUPPORTED ALO
A. ALO in Brief
Inspired by the foraging behavior of ant lion‘s larvae,
Seyedali Mirjalili has proposed a mathematical model to
design an optimization algorithm known as Ant Lion
Optimization (ALO). The ALO algorithm impersonates
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interface between ant lions and ants in the trap. Five main
steps of hunting prey in ALO [42] are the random walk of ants,
building traps, entrapment of ants in traps, catching preys and
rebuilding traps.
In the first step of ALO, to model the interactions between
ant lions and ants in the trap, ants are necessitated to move
over the search space and ant lions are consented to hunt them
and become fitter using traps. A random walk is chosen for
modeling ants‘ movement, since, during the search for food,
the ants move stochastically in nature. The assumption
considered in ALO is that ―The random walks of ants are
affected by ant lion‘s traps‖ [42]. In building traps phase, a
roulette wheel operator is used to select the ant lions based on
their fitness during optimization. This mechanism offers high
possibilities to the fitter ant lions for grasping ants. To prevent
the trapped ants from escaping the radius of ants‘s random
walks, hyper-sphere is reduced adaptively. In the final stage of
hunting behavior, when an ant reaches the bottom of the pit it
is caught in the ant lion‘s jaw. Then, the ant lion pulls the ant
inside the sand and consumes its body. In ALO, it is assumed
that every ant randomly walks around a selected ant lion and
the elite.
B. Decision Making with Multi-Objective Solution
The OPF problem is formulated as a multi-objective
search, aiming at searching for a set of control variable settings
that are comparatively ‗equally good‘ for multiple objectives.
In order to select a suitable representative solution for the
multiple objectives, Pareto-optimality concept is used. To
evaluate the solutions on the Pareto front, a membership
function [42] is utilized. Therefore, the ith objective value of
solution p is normalized using:
 ip
1
if Fi  F imin

 F max -F

i
i
  max
if F imin  Fi
-Fi min
 Fi

if Fi  F imax
0


F imax
(20)
Nobj
M Nobj
i 1
p 1 i 1
(22)
ALi, j  x min
 rand * ( x max
- x min
j
j
j )
(23)
Step 4: Run Newton-Raphson load flow and calculate the
objective functions for all ants and ant lions subject to
constraints.
Step 5: Frame J(x) using the computed objective function
values as:
(24)
J ( x)  [ F1 ( x) F2 ( x)
F3 ( x)
F4 ( x)]
Step 6: Formulate fuzzy membership function using (20) for all
objective function values.
Step 7: Compute the values of p for each search agent using
(21), the value having maximum value of p is the BCS (elite).
Step 8: For every ant select an ant lion using Roulette wheel.
Step 9: Update the minimum (rk) and maximum (mk) bounds of
variables using,
r
(25)
rk  k
C
m
(26)
mk  k
C
Step 10: Generate a random walk and normalize it.
Step 11: Update the position of ant and compute the objective
functions for all ants.
Step 12: Calculate membership function for all ants and find
the BCS.
Step 13: Update elite, if an ant lion becomes fitter than the
elite.
Step 14: Termination criterion: If the iteration value exceeds
the maximum number of iterations, print the optimal results,
otherwise goto Step 8.
“Fig. 1,” depicts the flowchart for the implementation of
FSALO algorithm for solving MO-OPF problem.
IV. SIMULATION RESULTS AND ANALYSIS
The normalized membership function is computed by,
 p  (   ip) /(   ip)
Ai, j  x min
 rand * ( x max
- x min
j
j
j )
(21)
The solution p with the largest membership function p is
considered as the best representative solution.
C. Implementation of FSALO to MO-OPF
The fuzzy set theory is introduced for multi-objective
optimization using ALO and is made possible with simple
modifications in Steps 5-7 and 12. The implemented procedure
of the Fuzzy Supported ALO (FSALO) algorithm for solving
MO-OPF problem can be summarized as follows:
In order to illustrate the effectiveness of the proposed
methodology, four benchmark systems such as IEEE-30 bus,
New England 39 bus and IEEE-118 bus systems are
considered. The proposed methodology has been implemented
in Matlab7.9 programming language and executed on Intel(R)
core(TM) i3 CPU 3 GHz with 3 GB RAM. The following
control parameters have been chosen for the ALO to obtain the
optimal results: PS=50 and Itermax=500. The following four
cases are studied to analyze the efficacy of the proposed
approach:
Case 1: All the objectives are optimized individually
(FT, E, PL, Lindex)
Case 2: Bi-objective optimization (FT and PL, FT and Lindex, PL
and Lindex, FT and E, PL and E, Lindex and E)
Step 1: Initialize the system data including maximum and
minimum values of control variables such as power outputs of
generating units, voltages, transformer taps and shunt
capacitors.
Case 3: Tri-objective optimization (FT, PL and Lindex, FT, PL and
E, FT, E and Lindex, E, PL and Lindex)
Step 2: Initialize ALO variables such as number of search
agents (ants and ant lions) (Ps) and maximum number of
iterations (Itermax).
To demonstrate the proposed OPF model in ALO
algorithm, the objectives such as total fuel cost, total emission,
transmission loss and L-index are minimized individually in
Case 1. Table I shows the optimal settings of control variables
obtained after single objective optimization. Further two, three
and four objectives optimizations are carried out by the
FSALO algorithm in cases 2, 3 and 4 respectively.
Step 3: Generate the initial population: Obtain the initial
population matrix of ants (Ai,j), ant lions (ALi,j) according to the
number of ants, ant lions and dimension of the OPF problem
(number of control variables) (Nd) using (22) - (23) as,
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Case 4: Tetra-objective optimization (FT, PL, Lindex, E)
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PG11
PG13
V1
V2
V5
V8
V11
V13
T11
T12
T15
T36
Qc10
Qc12
Qc15
Qc17
Qc20
Qc21
Qc23
Qc24
Qc29
START
Initialize system data, number of ants, ant
lions and maximum number of iterations
sesearchagents
Initialize the population of ants and ant
lions according to (22) - (23)
Compute the value of objective function for each
ant & ant lion subject to constraints
Form J(x) for each ant and ant lion
Formulate fuzzy membership function for all
fitness values and determine elite
k=1
Select an ant lion for every ant
using Roulette wheel
Case 1: In this case, all the objective functions are optimized
individually using ALO and the best value of FT, obtained
using ALO is found to be 798.6718 $/h and the corresponding
control variables settings are shown in Table I. Obtained result
from the proposed ALO for this test system are shown in Table
II and compared with the results of 40 other solution methods.
It is seen that the ALO outperforms other methods reported in
the literature.
Update minimum and maximum
bounds of variables
Create a random walk, normalize it and
update the position of ant
Calculate the objective function values,
Form J(x) and Formulate fuzzy membership
values for all objectives
k= k+1
In the view of economy and security operation of power
plant, Emission (E), transmission losses (PL) and Lindex should
also be regard as objectives in the OPF problem. Therefore, the
three objectives E, PL and Lindex are added in our proposed
model. The best values of E, PL and Lindex found using ALO are
0.20479 ton/h, 2.795 MW and 0.0953 respectively which are
lesser than the results obtained using different techniques
reported in the literature. Table III shows the capability of
ALO for getting best values of E, PL and Lindex when compared
with various algorithms applied to solve the OPF problem and
the optimal control settings for the variables acquired using
ALO are given in Table I.
YES
Is
Ant lion fitter than
elite?
Update the
position of elite
NO
Retain the position of elite
NO
Is k≧Itermax?
YES
Print the results
STOP
a.
Fig. 1. Flowchart for implementation of ALO to OPF problem.
A. Test System 1: IEEE-30 Bus System
To authenticate the performance of the proposed algorithm,
a standard IEEE 30 bus system comprising of 6 generating
units at buses 1, 2, 5, 8, 11 and 13, 4 transformers with offnominal tap ratio in the lines 6–9, 6–10, 4–12 and 27–28 and
reactive power injection at the buses 10, 12, 15, 17, 20, 21, 23,
24 and 29 is considered. The test system data are adopted from
[3, 40].
Table 1: Optimal Control Settings Obtained Using Alo – Ieee30 Bus System – Case 1
Control
variables
PG1
PG2
PG5
PG8
13.0663
30
22.5758
29.8510
13.2438
40
13.9669
39.9213
1.1
1.1000
1.1000
1.1
1.09
1.0973
1.0900
1.1
1.06
1.0900
1.0352
1.1
1.0584
1.0992
1.0800
1.1
1.07
1.0431
0.9765
1.1
1.07
1.0800
1.0396
1.1
1.1
1.0020
1.1000
0.9909
0.9208
1.0791
0.9392
0.9740
1.0765
1.0962
1.1000
0.9682
1.0173
1.0334
1.0574
0.9808
3.5873
5.0000
1.1770
5.0000
3.0691
5.0000
5.0000
5.0000
4.6059
4.3601
1.9008
4.5499
3.0701
5.0000
2.2973
5.0000
5
4.4947
3.4300
5.0000
5
5.0000
2.4233
5.0000
2.2871
4.5101
4.6311
5.0000
3.1504
5.0000
1.2573
5.0000
3.2
3.1509
1.5064
3.7288
PGi in MW; Vi in p.u; T in p.u.; Qc in p.u.
Case 2: This case presents the results obtained after biobjective optimization of objectives such as FT and PL, FT and
Lindex, PL and Lindex, FT and E, PL and E, Lindex and E. Obtained
control settings from the ALO for this test case are presented
in Table IV and the results are compared with earlier reports.
The values of FT and PL obtained using ALO are 822.3986 $/h
and 5.2449 MW respectively.
Table 2: Comparison Of Results For Total Fuel Cost
Minimization – IEEE-30 Bus System – Case 1
Methods
Gradient method [13]
SFLA [38]
Modified DE [38]
MSFLA [39]
PSO-Fuzzy [29]
GSO [23]
Stochastic GA [23]
EGA [13]
MTLBO [40]
Cost
($/h)
804.853
802.509
802.376
802.287
802.19
802.188
803.7
802.06
801.892
E(ton/h)
NR
0.3720
NR
0.3723
NR
NR
NR
NR
0.3665
PL(MW)
NR
NR
9.459
9.6991
10.083
NR
NR
L-index
NR
NR
NR
NR
0.12256
NR
NR
NR
NR
NR
NR
Hybrid SFLA-SA [17]
801.79
NR
NR
NR
FT
E
Lindex
PL
AGSO [23]
801.75
NR
NR
NR
179.189
3
49.1102
18.0293
19.2931
64.053
3
67.500
6
50
35
165.478
293
29.8831
28.8279
27.4782
51.5040
79.9299
49.9888
35.0000
HMPSO-SFLA [37]
801.75
NR
9.54
NR
PSO [28]
GWO [32]
800.41
801.41
NR
NR
NR
9.3
NR
NR
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NR
NR
DE [32]
MICA [16]
MICA-TLA [16]
ABC [18]
GABC [15]
DSA [28]
BHBO [13]
801.23
801.079
801.048
800.66
800.440
800.388
799.921
NR
NR
0.20482
NR
0.36672
NR
9.22
9.1923
9.1895
9.0328
NR
8.9819
8.6793
AGA [12]
799.844
NR
8.9166
NR
EGA-DQLF [29]
799.56
NR
8.697
0.111
8.7558
8.615
NR
8.6591
8.63
8.63
8.6543
8.6260
8.62457
8.48
8.615
8.61
8.6132
NR
NR
8.94
8.38604
8.532
NR
0.1226
NR
0.1176
NR
0.1277
0.1273
0.1159
0.1164
NR
0.11796
0.1197
0.1261
NR
0.1265
NR
0.1307
0.1076
LTLBO [7]
DE [1]
LCA [14]
IEM [14]
BBO [19]
FIDE [34]
BSA [27]
TLBO [25]
Hybrid PSOGSA [22]
GSO [39]
ABPPO [24]
EADDE [2]
ICBO [26]
IGA [21]
KHA [21]
MADE [40]
GSA [3]
ALO
799.436
0.3672
799.289
NR
799.197
NR
799.182
NR
799.111
NR
799.082
NR
799.076
0.3671
799.071
NR
799.070
NR
799.06
NR
799.056
NR
799.054
NR
799.035
NR
800.805
NR
799.031
NR
798.73
NR
798.675
NR
0.3722
798.672
NR - Not Reported
NR
NR
0.1381
NR
0.12624
0.1302
The percentage increase in values of cost and loss with respect
to case 1 are 2.89% and 46.71% respectively. When FT, Lindex
and PL, Lindex are considered to optimize simultaneously, BCS
obtained using ALO are 0.05%, 2.66% and 6.4% and 8.89%
respectively higher than the single objective optimized values.
It is evident from Table VI that the result obtained by the
proposed approach is least against other approaches which
shows the capability of FSALO for getting the best BCS when
compared with other techniques that are reported in the
literature.
Table 3: Comparison of Results – IEEE-30 Bus System
Cost
E (ton/h)
($/h)
Emission minimization
BSA [27]
835.0199
0.2425
SFLA [38]
960.1911
0.2063
GSO [23]
NR
0.206
AGSO [23]
NR
0.2059
DSA [28]
944.4086
0.2058
IPSO [33]
954.248
0.2058
MSFLA [38]
951.5106
0.2056
HMPSO-SFLA [38]
NR
0.2052
TLBO [40]
947.4392
0.20503
MTLBO [40]
945.1965
0.20493
ABC [18]
944.4391
0.20483
944.0706
ALO
0.20479
Transmission loss minimization
IPSO [33]
941.672
0.20807
BHBO [13]
924.1365
NR
PSO-Fuzzy [29]
956.45
NR
GWO [32]
968.38
NR
DE [32]
968.23
NR
EGA-DQLF [29]
967.86
NR
ABC [18]
967.6810
0.20727
DSA [28]
967.6493
0.20826
MOHS [36]
964.5121
NR
TLBO [36]
967.0371
NR
QOTLBO [36]
967.0371
NR
IEM [14]
967.1147
NR
ABPPO [24]
966.4081
NR
Methods
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PL
(MW)
Lindex
5.0526
NR
NR
NR
3.24373
5.362
NR
NR
NR
NR
3.247
3.164
0.1266
NR
NR
NR
0.12734
0.1131
NR
NR
NR
NR
0.1402
0.1425
5.0732
3.7545
3.6294
3.41
3.38
3.2008
3.1078
3.0945
2.9678
2.8834
2.8834
2.8699
2.867
0.1294
0.1371
0.1286
NR
NR
0.12178
0.1386
0.12604
0.1154
0.1262
0.1262
0.1156
0.11611
FIDE [34]
ALO
ABC [18]
DSA [28]
FIDE [34]
Hybrid PSOGSA [22]
DE [1]
TLBO [25]
IEM [14]
ABPPO [24]
TLBO [36]
PSO-Fuzzy [29]
EGA-DQLF [29]
IPSO [33]
MOHS [36]
QOTLBO [36]
KHA [21]
ALO
967.0002
NR
966.2086
0.2073
L-index minimization
801.6650
0.3643
967.4718
NR
915.2172
NR
801.22928
NR
807.5272
NR
805.0087
NR
799.8349
NR
877.3579
NR
912.5914
NR
837.06
NR
898.817
NR
866.11393
0.24709
895.6223
NR
844.1237
NR
919.6706
NR
806.639
0.3333
NR - Not Reported
2.8535
2.795
0.1262
0.1346
9.2954
3.4217
3.626
9.26567
10.3142
8.42603
8.9477
4.679
3.7474
8.8209
6.092
14.001
4.3244
7.2826
NR
5.2622
0.1379
0.1244
0.1243
0.12393
0.1219
0.11671
0.1144
0.11388
0.1003
0.11055
0.10402
0.1037
0.1006
0.0994
0.09754
0.0953
Along with these combinations of bi-objectives, the stated
approach deliberates on concurrent optimization of FT and E,
PL and E, Lindex and E. The FSALO attains BCS values of
867.5875 $/h and 0.2247 ton/h, 2.9804 MW and 0.2054 ton/h,
0.1049 and 0.2269 ton/h while considering simultaneous
minimization of FT and E, PL and E, Lindex and E respectively.
It is worthwhile to note that the bi-objective optimization of PL
and E, Lindex and E using FSALO yields better results as
compared to IPSO [33].
Table 4: Optimal Control Settings Obtained Using ALO –
IEEE-30 Bus System – Case 2
Control
variable
PG1
PG2
PG5
PG8
PG11
PG13
V1
V2
V5
V8
V11
V13
T11
T12
T15
T36
Qc10
Qc12
Qc15
Qc17
Qc20
Qc21
Qc23
Qc24
Qc29
PL , E
Lindex,
E
130.25
168.39
91.34
97.575
65.12
46
81
2
96
11
50.459
49.347
60.433
68.03
66
4
6
79
57
18.261
21.183
31.233
49.10
50
5
7
2
25
33.405
19.145
34.12
35
35
8
0
11
29.209
15.650
23.01
30
30
6
8
67
17.290
21.02
35.580
27.058
40
9
75
101
1.1
1.1
1.1
1.1
1.07
1.053
1.0882
1.1
1.07
1.0662
8
1.020
1.027
1.07
1.0651
1.05
4
5
1.018
1.044
1.09
1.1
1.0607
1
2
1.038
1.0744
1.07
1.05
1.07
2
1.030
1.028
1.0946
1.07
1.0554
8
6
1.084
1.079
1.0217
1.1
1.1
2
2
0.931
1.056
1.0271
1.1
0.9239
3
2
0.997
1.078
1.0214
1.0867
1.0283
8
7
1.061
0.9764
1.0472
1.0436
0.9
6
2.482
4.6358
1.1834
5.0
5.0000
6
0.140
3.501
2.8891
4.7607
2.6750
1
2
1.941
3.290
4.4853
3.956
1.0000
9
8
2.652
3.5895
2.368
5.0
4.7870
2
4.525
2.193
5
5
5.0000
0
3
2.468
2.703
5
5
5.0000
1
8
1.639
2.285
4.4293
4.0953
2.0000
1
2
4.784
0.029
2.5373
5
2.6240
4
5
2.790
4.753
1.9212
5
4.0000
PGi in MW; Vi in p.u; 6T in p.u.; Qc in p.u. 6
101.3
294
52.68
67
50.00
00
28.79
92
28.66
43
26.96
91
1.1
1.1
1.078
3
1.056
9
1.05
0.991
4
1.1
1.1
1.046
5
0.923
3
1.292
4
2.000
0
2.416
7
0.754
8
0.101
3
4.161
1
3.311
1
2.277
5
1.737
1
FT, PL
FT ,
Lindex
PL ,
Lindex
FT, E
Table 5: Optimal Control Settings obtained using ALO –
IEEE-30 Bus System
Control
variable
PG1
PG2
PG5
PG8
PG11
PG13
V1
Tri-objective optimization
FT, PL,
FT, PL,
FT, E,
E, PL,
Lindex
E
Lindex
Lindex
159.950
94.629
115.04
91.846
28.5401
79.249
44.002
72.610
3
3
76
8
37.4583
29.169
38.227
48.103
7
17.0711
34.956
32
34.638
6
9
9
19.1151
27.787
21.337
21.231
4
3
26.8822
24.777
39.998
22.127
7
3
8
1.1
1.1
1.1
1.1
5
6
6
Tetraobjective
optimization
109.1106
79.2819
44.2315
30.5712
15.5443
12.1947
1.1
90
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V2
V5
V8
V11
V13
T11
T12
T15
T36
Qc10
Qc12
Qc15
Qc17
Qc20
Qc21
Qc23
Qc24
Qc29
1.086
1.0771
1.0083
1.0794
1.06
1.05
1.1
1.06
1.0497
1.0389
0.9666
1.0723
1.0769
1.09
1.1
1.0188
1.0585
1.0692
1.08
1.0244
1.0399
0.9986
1.0229
1.0023
0.9218
1.0483
1.0337
1.0142
1.0091
0.9
1.0050
1.0104
1.0842
1.1
1.0305
1.0758
0.7696
5.0
3.1491
4.3422
1.4911
3.9231
1.9716
3.4159
2.4902
4.9495
5.0
4.9607
0.8842
0.5740
0.8312
4.0087
0.5773
5.0
5.0
5.0000
4.1422
4.0948
5.0
2.9583
3.5606
0.7832
5.0
2.3273
3.7278
0.9801
5.0
3.0504
2.5456
1.0531
3.4632
1.7635
PGi in MW; Vi in p.u; T in p.u.; Qc in p.u.
869.9272 $/h, 7.1695 MW, 0.2328 ton/h and 868.1073 $/h,
0.2404 ton/h, 0.1175 respectively. The corresponding optimal
control settings are provided in Table V. The three
dimensional Pareto solutions with projection views of threeobjective optimization problem are depicted in Fig. 2. When E,
PL and Lindex are considered as tri-objectives, the increase in E,
PL and Lindex level with respect to case 1 are found to be 9.94%,
60.96% and 19.17% respectively.
1.09
1.06
1.0548
1.05
1.05
1.1
1.0412
1.1
1.0959
3.471
2.6054
4.176
5.0
5.0
5.0
4.0
5.0
2.0304
Table 6: Comparison of Results for Multi-Objective
Optimization – IEEE-30 Bus System
Objectives
Methods
FT
E
PL
Bi-objective optimization
NR
822.87
5.61
EGA-DQLF [29]
3
NR
847.011
5.66
PSO-Fuzzy [29]
58
MOEAD/DRA
NR
827.717
5.26
[31]
MOTLA/D [31]
NR
826.446
5.30
FT, PL
74
MOABC/D( [31]
NR
827.636
5.24
ABPPO [24]
NR
51
822.769
5.45
PSOGSA [22]
3
NR
2
822.406
5.46
FIDE [34]
820.880
31
NR
826
5.59
2
0.2645
49
FSALO
822.398
5.24
6
49
NR
NR
802.06
EGA-DQLF [29]
NR
NR
809.79
PSO-Fuzzy [29]
MOEAD/DRA
NR
NR
799.111
[31]
MOTLA/D [31]
NR
NR
799.116
MOABC/D [31]
NR
NR
799.064
FT, Lindex
KHA [21]
NR
3.40
801.863
62
ABPPO [24]
3
NR
8.61
799.069
9
PSOGSA [22]
6
NR
9.27
801.229
FIDE [34]
NR
8.60
799.691
2
2
ICBO [26]
NR
8.64
799.327
65
7
BSA [27]
NR
8.49
800.334
04
0
0.3414
7.61
FSALO
799.044
61
3
NR
NR
3.15
EGA-DQLF [29]
81
NR
NR
5.57
PSO-Fuzzy [29]
79
NR
NR
PL, Lindex
IPSO [33]
7.91
3
960.321
NR
ABPPO [24]
2.98
9
9
892.348
0.2245
FSALO
2.98
8
62
872.853
0.2249
NR
SFLA [38]
3
0.2247
NR
FT, E
MSFLA [38]
867.713
6.42
FSALO
867.587
0.2247
31
5
0.2066
5.16
IPSO [33]
NR
PL, E
2
939.109
FSALO
0.2054
2.98
4
04
NR
0.2286
IPSO [33]
NR
Lindex, E
894.331
8.01
FSALO
0.2269
7
31
Tri-Objective optimization
NR
5.69
EGA-DQLF [29]
844.5
FT, PL,
NR
7.22
PSO-Fuzzy [29]
836.96
Lindex
07
0.3171
FSALO
828.298
5.61
5
71
FT, PL, E
869.927
0.2328
7.16
2
95
FT, E, Lindex
7.21
868.107
0.2404
FSALO
34
3
E, PL, Lindex
903.559
0.2274
7.15
8 NR - Not Reported
91
FT in ($/h); E in (ton/h); PLin MW;
Lindex
NR
NR
NR
NR
NR
NR
NR
NR
0.1158
0.1056
0.1146
(a)
(b)
0.1287
0.1287
0.1288
0.1092
0.1148
1
0.12
0.1249
39
0.1252
0.1259
0.0979
0.1049
0.1140
0.1073
0.1140
8
0.1046
NR
NR
0.1174
NR
0.1332
0.1051
0.1049
0.1084
0.1091
0
0.1067
0.1391
0.1175
0.1179
Case 3: During tri-objective minimization of FT, PL and Lindex,
the BCS value acquired using FSALO algorithm is 828.2985
$/h, 5.6171 MW and 0.1067 respectively. The BCS values
reported so far in the literature are given in Table VI. It can be
deduced from the results that the FSALO performs better in
finding the FT, PL and Lindex optimally. The tri-objective
optimization of FT, PL, E and FT, E, Lindex yields BCS values of
IJTRD | Nov-Dec 2016
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Case 4: In the literature, few attempts have been made at
simultaneous optimization of four objectives which always
exist in real-time power system operations. Herein, the
proposed algorithm has been employed to optimize
simultaneously all the considered objectives (FT, E, PL and
Lindex) and the BCS obtained is 878.2416 $/h, 0.2514 ton/h,
7.5342 MW and 0.1204. The corresponding control settings
are given in Table V and the percentage increase level in the
values of objectives with respect to case 1 are 9.06, 18.54, 62.9
and 20.85 respectively.
(c)
(d)
Fig. 2. Pareto optimal front for three objectives – IEEE 30 bus system:
(a) Cost, Loss and L-index, (b) Cost, Loss and Emission, (c) Cost, emission
and L-index (d) Emission, Loss and L-index
B. Test System 2: New England 39 Bus System
To demonstrate the practical application of the proposed
approach, New England 39 bus system consisting of 10
generating units interconnected with 46 branches of a
transmission network is considered. The bus data and the
branch data are taken from [35].
Case 1: During individual optimization of objectives, the
best value of cost obtained using ALO is 350660 $/h which is
comparatively less by 0.04% than SPEA2 [35]. The settings of
the control variables for the results obtained using ALO is
given in Table VII. The best values of E and Lindex are found to
be 317.9566 ton/h and 0.1593 respectively (Table VIII) and
when compared to SPEA2, the percentage of reduction in E is
0.09.
Case 2: In the bi-objective optimization process, the trade off
values between FT and E, FT and Lindex, E and Lindex are found
to be 351700 $ /h and 9983.1 ton/h, 358700 $ /h and 0.1739,
8842 ton/h and 0.1729 respectively.
91
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Table 7: Optimal Control Settings obtained using ALO – New England 39 System
Control
variables
PG30
PG31
PG32
PG33
PG34
PG35
PG36
PG37
PG38
PG39
V30
V31
V32
V33
V34
V35
V36
V37
V38
V39
T12-11
T12-13
T6-31
T10-32
T19-33
T20-34
T22-35
T23-36
T25-37
T2-30
T29-38
T19-20
Single objective
optimization
FT
168.32
16
311.62
16
455.05
67
307.47
42
742.39
15
773.65
09
900.03
10
857.25
05
485.10
00
499.10
20
1.0016
0.94
1.006
0.9818
0.94
1.06
0.9671
1.0225
0.9683
0.9471
0.907
0.9
0.9024
0.9293
0.9466
1.0156
1.0984
0.9
0.9629
1.0923
1.0912
1.1
E
472.04
48
547.03
22
584.11
00
591.20
00
591.01
00
600.30
10
557.00
10
560.00
00
494.00
10
503.30
00
1.0185
1.0087
0.9737
0.9612
1.0131
0.9746
0.94
1.0121
1.0195
1.06
1.1
1.0709
0.9881
1.1
1.0496
1.0433
0.9021
1.0679
1.0424
1.1
0.9294
0.9659
Bi-objective optimization
Lindex
FT , E
FT, Lindex
137.000
49.9083
250.1800
0
300.000
300.801
435.0100
0
3
404.524
551.089
444.2000
4
0
300.000
598.968
681.5400
0
1
700.000
570.168
686.9300
0
2
781.153
605.435
510.0800
2
4
889.242
718.148
684.7200
9
5
893.881
814.811
514.0900
0
0
583.721
551.300
540.4000
7
4
597.568
508.344
498.1000
6
3
0.9677
1.0078
0.9677
1.0225
0.96
1.0497
1.0057
0.968
1.0058
0.94
1.0443
0.94
1.0044
0.9797
1.0044
0.94
1.0448
0.94
1.0165
1.0453
1.05
1.06
1.0464
1.06
0.9727
0.9560
0.9551
0.9743
0.9808
0.9586
0.98
0.9322
0.98
0.9
1.0580
0.9
0.9
1.0669
0.9
0.9
1.0163
0.9
0.9
0.9000
0.9
1.0628
0.9605
1.0606
0.98
1.0899
0.98
0.9668
0.9380
0.9664
0.9499
1.0684
0.9487
0.9598
1.0775
0.9597
0.97
0.9245
0.9698
0.9292
0.9000
0.9266
PGi in MW; Vi in p.u; T in p.u.
It is clear from the BCS values, that the proposed approach
is superior and preserves the diversity of the non-dominated
solutions over the trade-off front.
Case 3: The tradeoff curve in three facet for the 20 generated
Pareto optimal solutions of the FSALO algorithm is depicted
in Fig. 3 which clearly shows the relationships among FT, E
and Lindex. The increase in FT, E and Lindex are 2.75%, 97.52%
and 11.01% respectively with respect to case 1.
E, Lindex
109.5579
326.4515
445.6551
460.3871
761.6523
733.1450
800.0000
700.0000
600.0000
563.1512
0.9665
1.0225
1.0059
0.94
1.0052
0.94
1.05
1.06
0.9552
0.9587
0.9792
0.9
0.9
0.9
0.9
1.0791
0.9794
0.9676
0.9479
0.96
0.9697
0.9286
Tri-objective
optimization
FT, E, Lindex
303.2200
300.0000
405.2526
395.7044
703.0631
653.5961
798.0000
800.0000
548.9265
523.6173
0.9572
1.05
1.0057
0.94
1.0055
0.94
1.0362
1.06
0.99
0.9542
0.9743
0.9
0.9
0.9
0.9
1.0648
0.9765
0.9666
0.9441
0.9599
0.9698
0.9286
C. Test System 3: IEEE-118 Bus System
The aim of this example is to demonstrate the effectiveness
of the proposed method for the large scale IEEE-118 [42] bus
system which consist of 54 thermal units, 64 loads, 9
transformer settings and 12 shunt capacitor var injections. The
total system demand is 4242 MW and base MVA is assumed
as 100. The chosen objectives such as FT, E, PL and Lindex are
minimized in the multi-objective frame and the obtained
values are 47768 $ /h, 3465.2 ton//h, 103.77 MW and 0.1176
respectively. It can be inferred from Table IX, that the results
obtained using FSALO outperforms the results by MABC
[42]. The proposed ALO takes execution time of about 280 s
for the chosen complex large scale system.
Table 9: Comparison of Results for Tetra Objective
Optimization – IEEE-118 Bus System
Methods
MABC [45]
ALO
Fig. 3. Pareto optimal front – New England 39 bus system : Case 3
Table 8: Comparison of Results – New ENgland 39 Bus
System
Objective
FT
E
Lindex
Cost
E
($/h)
(ton/h)
Single objective optimization
SPEA2 [35] 350810
76814
76638
ALO
350660
SPEA2 [35] 396590
318.083
396220
ALO
317.9566
372310
91132
ALO
Methods
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L-index
NR
0.1867
NR
0.1926
0.1593
FT ($/h)
47823
47768
E (ton/h)
3502.2
3465.2
PL(MW)
120.31
103.77
Lindex
NR
0.1176
D. Solution Quality
From Tables II, III, IV and VIII it is clear that the minimum
values of FT, E, PL and Lindex for all the considered test systems
are best and less compared to that reported in literature
emphasizing its better solution quality. Further, for IEEE-118
and New England test systems, ALO exhibited better
performance when compared with other algorithms. As the
best values in ALO are better as compared to other
approaches, it only indicates its ability to reach global minima
in a consistent manner and its better convergence
characteristics. Due to limitations of space, the convergence
and robustness characteristics are not provided in the article.
The computational time taken for all the test systems is less
92
International Journal of Trend in Research and Development, Volume 3(6), ISSN 2394-9333
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which indicates that the time taken by the proposed approach
does not increase greatly as the system size increases.
Generally, the test on a large scale system requires long
computation time to converge and large memory requirement.
These two major obstacles are overcome by ALO in solving
OPF problems. Succinctly, considering all the results for study
with different dimensions and constraints it can be concluded
that ALO yields better optimal solutions with less
computational effort in terms of cost, emission, transmission
loss and L-index than the previously reported results.
CONCLUSIONS
The major focus of this paper is to present the application
of ALO to optimal P-Q dispatch in power system. The
realistic OPF is complicated because of multiple objectives
and hardly, very few reports in the literature have been made
with four objectives. The algorithm has been tested and
examined with different objectives such as fuel cost, emission,
loss and L-index for standard IEEE-30, IEEE-118 and New
England power systems. Detailed case studies are presented to
demonstrate the application of the proposed scheme. The
Pareto based approach have the advantage of including
multiple criteria without the need of introducing weights. Case
studies with single objective, bi-objective, tri-objective and
four objectives are performed to check the performance,
accuracy, robustness in comparison with the other reports in
the literature. The advantages of the exploitation of ALO for
MO-OPF are as follows:
 The search mechanism of ALO works well for unknown,
challenging search space that helps to identify the optimal
real/reactive power settings.
 As there is no relation between search agents and the
fitness functions in the updating process of ALO, this
facility avoids trapping in local optima and explores the
best solution for MO-OPF problems.
Following the results of the proposed approach many
interesting topics such as incorporation of multi-objective
framework in reserve constrained dynamic OPF problem are
worth investigating in future research work.
List Of Abbreviations And Acronyms
Fi
ith objective function
g,h
Equality and inequality constraints
x, u
Vector of dependent and control variables
VG, VL Generator and load voltages
PG, QG Real and reactive power of generators
Qc
Reactive power injections
T
Transformer tap settings
SL
Transmission line loading
NG
Number of generator buses
NL
Number of transmission lines
NB
Number of buses
NPQ
Number of load buses
NT
Number of regulating transformers
NC
Number of VAR compensators
ai,bi,ci Cost coefficients of ith generator
αi,βi,γi,εi,λi Emission coefficients of ith unit
gk
Conductance of transmission line k
V, δ
Voltage magnitudes, phase angles of buses
Fji
Partial inversion of Ybus matrix
PDi, QDi Real and reactive power demand at ith bus
Gij
Transfer conductance between i and jth bus
Bij
Susceptance of the line between i and j bus
rand
Random values in the range (0,1)
ximax, ximin Upper and lower bounds of control variables
IJTRD | Nov-Dec 2016
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Fimin, Fimax Minimum and maximum value of ith objective
function among all non-dominated solutions
M
Total number of non-dominated solutions
Nobj
Number of objective functions
Itermax
Maximum number of iterations
C
Ratio that relates current iteration, Itermax
BBO
Biogeography Based Optimization
MOEAD Multi-Objective Evolutionary Algorithm
/DRA
based on Decomposition with Dynamical
Resource Allocation
MOTLA/D Multi-Objective Teaching-Learning Algorithm
based on Decomposition
MOABC/D Multi-Objective ABC Algorithm based on
Decomposition
Acknowledgment
The authors gratefully acknowledge the authorities of
Annamalai University, Annamalai Nagar, Tamilnadu, India,
for providing facilities to carry out this research work.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
A.A.A. El Ela, M.A. Abido, and S.R. Spea, ―Optimal power flow using
differential evolution algorithm,‖ Electric Power Systems Research, Vol.
80, pp. 878-885, January 2010.
K. Vaisakh, and L.R. Srinivas, ―Evolving ant direction differential
evolution for opf with non-smooth fuel cost functions,‖ Engineering
Applications of Artificial Intelligence, Vol. 24, pp. 426- 436, April
2011.
S. Duman, U. Guvene, Y. Sonmez, and N. Yorukeren, ―Optimal power
flow using gravitational search algorithm,‖ Energy Conversion and
Management, Vol. 59, pp. 86–95, March 2012.
N. Sinsuphan, U. Leeton, and T. Kulworawanichpong, ―Optimal power
flow solution using improved harmony search method,‖ Applied Soft
Computing, Vol. 13, pp. 2364-2374, February 2013.
D.K. Sanjeev Kumar, and Chaturvedi, ―Optimal power flow solution
using fuzzy evolutionary and swarm optimization,‖ Electrical Power and
Energy Systems, Vol. 47, pp. 416–423, January 2013.
V.H.Hinojosa, and R. Araya, ―Modeling a Mixed-integer-binary smallpopulation evolutionary particle swarm algorithm for solving the
optimal power flow problem in electric power systems,‖ Applied Soft
Computing, Vol. 13, pp. 3839-3852, June 2013.
M. Ghasemi, S. Ghavidel, M. Gitizadeh, and E. Akbari, ―An improved
teaching–learning-based optimization algorithm using levy mutation
strategy for non-smooth optimal power flow,‖ Electrical Power and
Energy Systems, Vol. 65, pp. 375-384, February 2015.
R. P. Singh, V.Mukherjee, and S.P. Ghoshal, ―Particle swarm
optimization with an aging leader and challengers algorithm for the
solution of optimal power flow problem,‖ Applied Soft Computing, Vol.
40, pp. 161-177, March 2016.
X. Yuan, P. Wang, Y. Yuan, Y. Huang, and X. Zhang, ―A new quantum
inspired chaotic artificial bee colony algorithm for optimal power flow
problem,‖ Energy Conversion and Management, Vol. 100, pp. 1-9, April
2015.
Y. Tan, C. Li, Y. Cao, K. Y. Lee, L. Li, S. Tang, and L. Zhou,
―Improved group search optimization method for optimal power flow
problem considering valve point loading effects,‖ Neurocomputing, Vol.
148, pp. 229-239, 2015.
A. Mukherjee, and V. Mukherjee, ―solution of optimal power flow using
chaotic krill herd algorithm,‖ Chaos, Solitons & Fractals, Vol. 78, pp.
10-21, September 2015.
A.F. Attia, Y.A.AL-Turki, and A.M. Abusorrah, ―Optimal power flow
using adapted genetic algorithm with adjusting population size,‖ Electric
Power Components and Systems, Vol. 40, pp. 1285-1299, August 2012.
H. R. E. H. Bouchekara, ―Optimal power flow using black-hole-based
optimization approach,‖ Applied Soft Computing, Vol. 24, pp. 879-888,
August 2014.
H. R. E. H. Bouchekara, M.A. Abido, and A.E. Chaib,
―Optimal power flow using an
improved
electromagnetism-like
mechanism method,‖ Electric Power Components and Systems, Vol. 44,
pp. 434- 449, January 2016.
H.
T.
Jadhav,
and
P.
D
Bamane,
―Temperature
dependent optimal power flow using g-best guided artificial bee colony
algorithm,‖ Electrical Power and Energy Systems, Vol. 77, pp. 77-90,
May 2016.
M. Ghasemi, S.Ghavidel, S.Rahmani, A. Roosta, and H. Falah, ―A novel
hybrid algorithm of imperialist competitive algorithm and teaching
learning algorithm for optimal power flow problem with non-smooth
93
International Journal of Trend in Research and Development, Volume 3(6), ISSN 2394-9333
www.ijtrd.com
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
cost functions,‖ Engineering Applications of Artificial Intelligence, Vol.
29, pp. 54-69, March 2014.
T. Niknam, M.R. Narimani, and R. Azizipanah-Abarghooee, ―A new
hybrid algorithm for optimal power flow considering prohibited zones
and valve point effect,‖ Energy Conversion and Management, Vol. 58,
pp. 197-206, February 2012.
M. Rezaei Adaryani and A. Karami, ―Artificial bee colony algorithm for
solving multi-objective optimal power flow problem,‖ Electrical Power
and Energy Systems, Vol. 53, pp. 219–230, April 2013.
A. Bhattacharya, and P.K. Chattopadhyay, ―Application of
biogeography based optimization to solve different optimal power flow
problems,‖ IET Generation Transmission and Distribution, Vol.5, pp.
70-80, January 2011.
A. Bhattacharya, and P.K. Roy, ―Solution of multiobjective optimal
power flow using gravitational search algorithm,‖ IET Generation
Transmission and Distribution, Vol. 6, pp. 751-763, February 2012.
P.K. Roy, and Chandan Paul, ―Optimal power flow using krill herd
algorithm,‖ International Transactions on Electrical Energy Systems,
Vol.25, pp. 1397-1419, August 2015.
Jordan Radosavljevic, Dardan Klimenta, Miroljub Jevtic, and Nebojsa
Arsic, ―Optimal power flow using a hybrid optimization algorithm of
particle swarm optimization and gravitational search algorithm,‖ Electric
Power Components and Systems, Vol. 43, pp. 1958-1970, August 2015.
N. Daryani, Mehrdad Tarafdar Hagh, and Saeed Teimourzadeh,
―Adaptive group search optimization algorithm for multi-objective
optimal power flow problem,‖ Applied Soft Computing, Vol. 38, pp.
1012-1024, January 2016.
A.A. Christy, P. Ajay, and D. Vimal Raj, ―Adaptive biogeography based
predator–prey
optimization
technique
for optimal power flow,‖
Electrical Power and Energy System, Vol. 62, pp. 344-352, May 2014.
H. R. E. H. Bouchekara, M.A. Abido, and M. Boucherma, ―Optimal
power flow using teaching learning based optimization technique,‖
Electric Power System Research, Vol. 114, pp. 49-59, May 2014.
H. R. E. H. Bouchekara, A. E. Chaib, M. A. Abido, R. A. El-sehiemy,
―Optimal power flow using an improved colliding bodies optimization
algorithm,‖ Applied Soft Computing, Vol. 42, pp. 119-13, January 2016.
A.E. Chaib, H. R. E. H. Bouchekara, R. Mehasni, and M.A. Abido,
―Optimal power flow with emission and non-smooth cost functions
using backtracking search optimization algorithm,‖ Electrical Power and
Energy Systems, Vol. 81, pp. 64-77, February 2016.
K. Abaci, and V. Yamacli, ―Differential search algorithm for solving
multi- objective optimal power flow problem,‖ Electrical Power and
Energy Systems, Vol. 79, pp. 1-10, January 2016.
M.S. Kumari, and S. Maheswarapu, ―Enhanced genetic algorithm based
computation technique for multi-objective optimal power flow solution,‖
Electrical Power and Energy System, Vol. 32, pp. 736–742, January
2010.
S. Sivasubramani, and K.S. Swarup, ―Multi-objective harmony search
algorithm for optimal power flow problem,‖ Electrical Power and
Energy Systems, 33, pp. 745–752, February 2011.
M. A. Medina, S. Das, C. A. C. Coello, and J. M. Ramírez,
―Decomposition-based modern metaheuristic algorithms for multiobjective optimal power flow – A comparative study,‖ Engineering
Applications of Artificial Intelligence, Vol. 32, pp. 10-20, July 2014.
A.A. El-Fergany, and H.M. Hasanien, ―Single and multi-objective
optimal power flow using grey wolf optimizer and differential evolution
algorithms,‖ Electric Power Components and Systems, Vol. 43, pp.
1548-1559, July 2015.
T. Niknam, M.R. Narimani, J. Aghaei, and R. A. Abarghooee,
―Improved particle swarm optimization for multi-objective optimal
power flow considering the cost, loss, emission and voltage stability
index,‖ IET Generation, Transmission and Distribution, Vol. 6, pp. 515527, June 2012.
A.M. Shaheen, R.A. El-Sehiemy, and S.M. Farrag, ―Solving multiobjective optimal power flow problem via forced initialised differential
evolution algorithm,‖ IET Generation, Transmission and Distribution,
Vol. 10, pp. 1634-1647, October 2015.
H. B Aribia, Nizar Derbel, and Hsan Hadj Abdallah. ―The active–
reactive complete dispatch of an electrical network,‖ Electrical Power
and Energy Systems, Vol. 44, pp. 236–248, January 2013.
B. Mandal, and P.K. Roy, ―Multi-objective Optimal power flow using
quasi-oppositional teaching learning based optimization,‖ Applied Soft
Computing, Vol. 21, pp. 590-606, August 2014.
M.R. Narimani, R. Azizipanah-Abarghooee, B. Zoghdar-MoghadamShahrekohne, and K. Gholami, ―A novel approach to multi-objective
optimal power flow by a new hybrid optimization algorithm considering
generator constraints and multi-fuel type,‖ Energy, Vol. 49, pp. 119136, January 2013.
T. Niknam, M.R. Narimani, M. Jabbari, and A.R. Malekpour, ―A
modified shuffle frog leaping algorithm for multi-objective optimal
power flow,‖ Energy, Vol. 36, pp. 6420-6432, October 2011.
IJTRD | Nov-Dec 2016
Available [email protected]
[39] S.S. Reddy, and C.S. Rathnam, ―Optimal power flow using glowworm
swarm optimization,‖ Electrical Power and Energy Systems, Vol. 80, pp.
128-139, January 2016.
[40] A. S. Haghighi, A. R. Seifi and T. Niknam, ―A modified teachinglearning based optimization for multi-objective optimal power flow
problem,‖ Energy Conversion and Management, Vol. 77, pp. 597–607,
January 2014.
[41] A. Khorsandi, S.H Hosseinian, and A. Ghazanfari, ―Modified artificial
bee colony algorithm based on fuzzy multi – objective technique for
optimal power flow problem,‖ Electric Power Systems Research, Vol.
95, pp. 206-213, February 2013.
[42] S. Mirjalili, ―The ant lion optimizer,‖ Advances in Engineering
Software, Vol. 83, pp. 80-98, January 2015.
94