Reduction
IJDI-ERET of
INTERNATIONAL JOURNAL OF DARSHAN INSTITUTE ON
ENGINEERING RESEARCH & EMERGING TECHNOLOGIES
Vol. 4, No. 1, 2015
www.ijdieret.in
Real Power Loss by Enhanced Krill Herd Algorithm
Mr. K. Lenin1*, Dr. B. Ravindhranath Reddy2, Dr. M. Suryakalavathi3
1
Research scholar, Jawaharlal Nehru Technological University Kukatpally, Hyderabad 500 085, India
Executive Engineer, Jawaharlal Nehru Technological University Kukatpally, Hyderabad 500 085, India
Professor3, 3Jawaharlal Nehru Technological University Kukatpally, Hyderabad 500 085, India
2
Abstract
Reactive power optimization problem play a major role in operation and control of power system. In this research a new
natural inspired algorithm called Enhanced Krill Herd algorithm is utilized to solve the reactive power problem. Krill Herd
algorithm is based on herd behavior of Krill individuals. The minimum distance of each individual Krill from food and from
utmost concentration of the herd are considered as the main assignment for the Krill movement. The location of every krill in
time period is dependent on persuaded movement of other Krill’s, foraging movement and physical dissemination. in this paper
krill herd algorithm is enhanced by integrating with chaos theory and the logistic chaotic mapping is used in physical
dissemination. Thus the Enhanced Krill Herd algorithm (EKHA) is used to solve the reactive power problem and the validity of
the algorithm has been tested in standard IEEE 57 and 118 bus test systems. Simulation study shows the better performance of
the proposed algorithm.
Key words: Reactive Power, Transmission loss, Krill herd, chaos theory, nature inspired algorithm.
1. Introduction
The key objective of reactive power dispatch problem is to
reduce the real power loss and to keep the voltage profiles
within the specified limits .Various algorithms utilized to
solve the reactive power problem.O.Alsac et al [1]
successfully solved optimal load flow with steady state
security.
K.Lenin,
B.Ravindhranath
Reddy
and
M.SuryaKalavathi has successfully solved the reactive
power problem by Ant Colony
Search Algorithm [2],
Spatial Extended Particle Swarm Optimization [3],
Attractive and Repulsive Particle Swarm Optimization [4],
Intelligent Water Drop Algorithm [5], Fish School Search
Algorithm [6], Improved Teaching Learning Based
Optimization [7], League Championship Algorithm [8],
Harmony Search
Algorithm[9], Restarted Simulated
Annealing Particle Swarm Optimization [10], Adaptive
bacterial foraging oriented particle swarm optimization
algorithm [11], Improved Great Deluge Algorithm [12],
Improved Cuckoo Search Algorithm [13], Hybrid – Invasive
Weed Optimization Particle Swarm Optimization [14],
Water Cycle Algorithm[15],Grand salmon run algorithm
*
Corresponding Author: e-mail:[email protected], Tel-+919879493705
ISSN 2320-7590
 2015 Darshan Institute of Engg. & Tech., All rights reserved
[16], Dolphin Echolocation Algorithm[17], Black Hole
Algorithm[18], Improved Bees Algorithm [19], New
charged system Search[20], Fusion of Flower Pollination
Algorithm with Particle Swarm Optimization[21], Improved
Bat Algorithm[22], Hybrid Eagle Strategy Flower
Pollination Algorithm[23],
Bumble
Bees
Mating
Optimization[24], Mine Blast Algorithm[25], Improved
Spider Algorithm [26], Improved seeker optimization
algorithm [27], Kudu Herd Algorithm[28],Double GlowWorms Swarm Co-Evolution Optimization Algorithm[29],
Brain Storm Optimization Algorithm[30], Crossbreed Spiral
Dynamics Bacterial Chemotaxis Algorithm[31], Improved
Biogeography algorithm[32], Simulating Annealing Based
Krill Herd Algorithm[33], Atmosphere Clouds Model
Algorithm[34], Adaptive Cat Swarm Optimization[35],
Hybrid - Genetic Algorithm and Hooke-Jeeves Method[36],
Cuckoo Search Algorithm with Powell Search[37],
Improved Evolutionary Algorithm[38], Termite Colony
Optimization[39].This paper proposes a new nature inspired
algorithm called Enhancedkrill algorithm (EKHA) is used to
solve the optimal reactive power dispatch problem. This
method is based on the imitation of the herd of the krill
swarms [40] in response to specific biological and
environmental processes. In this paper, chaotic system [41]
is replaced with capricious numbers for different parameters
of krill algorithm. Using this method, speed and
International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
accurateness of responses will be augmented and possibility
of avoiding local optimized points will be provided. The
proposed algorithm EKHA been evaluated in standard IEEE
57 bus test system & the simulation results shows that our
proposed approach outperforms all reported algorithms in
minimization of real power loss .
1. Problem formulation
Upper and lower bounds on the transformers tap ratios:
The objective of the reactive power dispatch is to
minimize the active power loss in the transmission network,
which can be described as follows:
Where N is the total number of buses, NT is the total number
of Transformers; Nc is the total number of shunt reactive
compensators.
F = PL =
or
F = PL =
k∈Nbr
i∈Ng
g k Vi2 + Vj2 − 2Vi Vj cosθij
Pgi − Pd = Pgslack +
Ng
i≠slack
Pgi − Pd
Timin ≤ Ti ≤ Timax , i ∈ NT
Upper and lower bounds on the compensators reactive
powers:
Qmin
≤ Q c ≤ Qmax
, i ∈ NC
c
C
3. Krill herd algorithm
(2)
Krill is one of the finest-studied classes of marine animal.
The krill herds are aggregations with no similar direction of
existing on time scales of hours to days and space scales of
10 s to 100 s of meters. One of the key characteristics of this
specie is its ability to form large swarms. The KH algorithm
replicates the systematic activities of krill. When predators,
such as seals, penguins or seabirds, attack krill, they get rid
of individual krill. This results in dropping the krill
concentration. The composition of the krill herd after
predation depends on many parameters. The herding of the
krill individuals is a multi-objective process including two
main goals: (1) escalating krill concentration, and (2)
attainment food. In the present study, this procedure is taken
into account to plan a new metaheuristic algorithm for
solving global optimization problems. Thickness-dependent
hold of krill (increasing concentration) and finding food
(areas of high food concentration) are used as objectives
which finally lead the krill to herd around the global minima.
In this procedure, an individual krill moves toward the best
solution when it searches for the highest concentration and
food. They are i. progress induced by other krill individuals;
ii. Foraging activity; and iii.Random dissemination. The krill
individuals try to maintain a high concentration and shift due
to their mutual effects [42]. The course of motion induced,
𝛼𝑖 , is estimated from the local swarm concentration (local
effect), a target swarm concentration (target effect), and a
repulsive swarm concentration (repulsive effect) . For a krill
individual, this movement can be defined as:
VD is the voltage deviation given by:
Npq
i=1
Vi − 1
(4)
B. Equality Constraint
The equality constraint of the ORPD problem is represented
by the power balance equation, where the total power
generation must cover the total power demand and the power
losses:
PG = PD + PL
(5)
This equation is solved by running Newton Raphson load
flow method, by calculating the active power of slack bus to
determine active power loss.
C. Inequality Constraints
The inequality constraints reflect the limits on components
in the power system as well as the limits created to ensure
system security. Upper and lower bounds on the active
power of slack bus, and reactive power of generators:
max
min
Pgslack
≤ Pgslack ≤ Pgslack
Qmin
≤ Q gi ≤ Qmax
, i ∈ Ng
gi
gi
𝑁𝑖𝑛𝑒𝑤 = 𝑁 𝑚𝑎𝑥 𝛼𝑖 + 𝜔𝑛 𝑁𝑖𝑜𝑙𝑑
(11)
Where
𝑡𝑎𝑟𝑔𝑒𝑡
𝛼𝑖 = 𝛼𝑖𝑙𝑜𝑐𝑎𝑙 + 𝛼𝑖
(12)
max
And N
is the greatest induced speed, 𝜔𝑛 is the inertia
weight of the motion induced in the range [0, 1], 𝑁𝑖𝑜𝑙𝑑 is the
last motion induced, 𝛼𝑖𝑙𝑜𝑐𝑎𝑙 is the local effect provided by
𝑡𝑎𝑟𝑔𝑒𝑡
the neighbours and 𝛼𝑖
is the target direction effect
provided by the best krill individual according to the
measured values of the maximum induced speed.
The consequence of the neighbours in a krill movement
individual is determined as follows:
(6)
(7)
Upper and lower bounds on the bus voltage magnitudes:
Vimin ≤ Vi ≤ Vimax , i ∈ N
(10)
(1)
where gk : is the conductance of branch between nodes i and
j, Nbr: is the total number of transmission lines in power
systems. Pd: is the total active power demand, Pgi: is the
generator active power of unit i, and Pgsalck: is the
generator active power of slack bus.
A. Voltage profile improvement
For minimizing the voltage deviation in PQ buses, the
objective function becomes:
F = PL + ωv × VD
(3)
where ωv: is a weighting factor of voltage deviation.
VD =
(9)
(8)
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International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
𝛼𝑖𝑙𝑜𝑐𝑎𝑙 =
𝑋𝑖,𝑗 =
𝑁𝑁
𝑗 =1 𝐾𝑖𝑗
𝑋 𝑗 −𝑋 𝑖
𝑋𝑖𝑗
consequence of the best fitness of the ith krill so far
according to the measured values of the foraging speed.
(13)
(14)
𝑋 𝑗 −𝑋 𝑖 +𝜀
The centre of food for each iteration is formulated as:
𝐾𝑖 −𝐾𝑗
𝐾𝑖,𝑗 = 𝑤𝑜𝑟𝑠 𝑡 𝑏𝑒𝑠𝑡
(15)
𝐾
−𝐾
best
worst
where K
and K
are the best and the worst fitness
values of the krill individuals so far; Ki represents the fitness
or the objective function value of the ith krill individual; Kj
is the fitness of jth (j = 1,2,. . .,NN) neighbour; X represents
the associated positions; and NN is the quantity of the
neighbours. For avoiding the singularities, a small positive
number,𝜀, is added to the denominator.
𝑋
1
5𝑁
𝑁
𝑗 =1
𝑋𝑖 − 𝑋𝑗
𝑓𝑜𝑜𝑑
𝛽𝑖
= 𝐶 𝑏𝑒𝑠𝑡 𝐾𝑖,𝑏𝑒𝑠𝑡 𝑋𝑖,𝑏𝑒𝑠𝑡
𝐶 𝑓𝑜𝑜𝑑 = 2 1 −
(16)
𝐼
𝐼𝑚𝑎𝑥
(22)
𝐼
(23)
𝐼𝑚𝑎𝑥
The food attraction is defined to possibly draw the krill
swarm to the global optima. Based on this definition, the
krill individuals normally flock around the global optima
after some iteration. This can be considered as an efficient
global optimization strategy which helps recuperating the
globalist of the KH algorithm. The consequence of the best
fitness of the ith krill individual is also handled using the
following equation:
𝛽𝑖𝑏𝑒𝑠𝑡 = 𝐾𝑖,𝑖𝑏𝑒𝑠𝑡 𝑋𝑖.𝑖𝑏𝑒𝑠𝑡
(17)
(24)
Where 𝐾𝑖.𝑖𝑏𝑒𝑠𝑡 is the best previously visited position of the
ith krill individual.
Where, Cbest is the effective coefficient of the krill individual
with the best fitness to the ith krill individual. This
𝑡𝑎𝑟𝑔𝑒𝑡
coefficient is defined since 𝛼𝑖
leads the solution to the
global optima and it should be more successful than other
krill individuals such as neighbours. Herein, the value of
Cbestis defined as:
𝐶 𝑏𝑒𝑠𝑡 = 2 𝑟𝑎𝑛𝑑 +
= 𝐶 𝑓𝑜𝑜𝑑 𝐾𝑖,𝑓𝑜𝑜𝑑 𝑋𝑖,𝑓𝑜𝑜𝑑
Since the effect of food in the krill herding decreases during
the time, the food coefficient is determined as:
The consequence of the individual krill with the best fitness
on the ith individual krill is taken into account by using the
formula
𝑡𝑎𝑟𝑔𝑒𝑡
(21)
Where Cfood is the food coefficient.
Where 𝑑𝑠,𝑖 the sensing distance for the ith krill is individual
and N is the number of the krill individuals. The factor 5 in
the denominator is empirically obtained. Using Eq. (16), if
the distance of two krill individuals is less than the definite
sensing distance, they are neighbours.
𝛼𝑖
=
𝑁 1
𝑖=1 𝐾 𝑋 𝑖
𝑖
𝑁 1
𝑖=1𝐾
𝑖
Therefore, the food attraction for the ith krill individual can
be determined as follows:
The sensing distance for each krill individual can be
determined by using the following formula for each
iteration:
𝑑𝑠,𝑖 =
𝑓𝑜𝑜𝑑
The physical dissemination of the krill individuals is
considered to be an arbitrary process. This motion can be
articulated in terms of a maximum dissemination speed and
an arbitrary directional vector. It can be formulated as
follows:
𝐷𝑖 = 𝐷𝑚𝑎𝑥 𝛿
(18)
(25)
Where rand is a arbitrary value between 0 and 1 and it is for
enhancing searching, I is the actual iteration number and I max
is the maximum number of iterations.
The Foraging motion can be expressed for the ith krill
individual as follows:
Where Dmax is the maximum diffusion speed, and 𝛿 is the
random directional vector and its arrays are arbitrary values
between -1 and 1. This term linearly decreases the arbitrary
speed with the time and works on the basis of a geometrical
annealing schedule:
𝐹𝑖 = 𝑉𝑓 𝛽𝑖 + 𝜔𝑓 𝐹𝑖𝑜𝑙𝑑
(19)
𝐷𝑖 = 𝐷𝑚𝑎𝑥 1 −
Where
𝑓𝑜𝑜𝑑
𝛽𝑖 = 𝛽𝑖
+ 𝛽𝑖𝑏𝑒𝑠𝑡
(20)
𝐼
𝐼𝑚𝑎𝑥
𝛿
(26)
The physical dissemination performs a arbitrary search in
the projected method. Using different effective parameters
of the motion during the time, the position vector of a krill
individual during the interval t to t + ∆𝑡 is given by the
following equation
And Vf is the foraging speed, 𝜔𝑓 is the inertia weight of the
foraging motion in the range [0, 1], is the last foraging
𝑓𝑜𝑜𝑑
motion, 𝛽𝑖
is the food attractive and 𝛽𝑖𝑏𝑒𝑠𝑡 is the
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International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
𝑑𝑋 𝑖
(27)
c.
It should be noted that ∆𝑡 is one of the important constants
and should be cautiously set according to the optimization
problem. This is because this parameter works as a range
factor of the speed vector. ∆𝑡 Completely depends on the
explore space and it seems it can be simply obtained from
the following formula:
d.
𝑋𝑖 𝑡 + ∆𝑡 = 𝑋𝑖 𝑡 + ∆𝑡
∆𝑡 = 𝐶𝑡
𝑁𝑉
𝑗 =1
𝑑𝑡
𝑈𝐵𝑗 − 𝐿𝐵𝑗
e.
f.
(28)
g.
Where NV is the total number of variables, 𝐿𝐵𝑗 and 𝑈𝐵𝑗
are lower and upper bounds of the jth variables (j = 1,2,. .
.,NV),respectively. Therefore, the complete of their
subtraction shows the explore space. It is empirically found
that 𝐶𝑡 is a constant number between [0, 2]. It is also obvious
that low values of 𝐶𝑡 let the krill individuals to search the
space cautiously.
h.
4. Chaotic Krill Algorithm
Chaos is a trend that is known as a development in
constrained amplitude which has occurred in a definite
vibrant non-linear system. Any such movement is much akin
to the arbitrary process. This movement is susceptible
towards the primary conditions which are sometimes called
the butterfly consequence to designate the unpredictability.
The chaotic portrait has particular virtues such as ergodic,
the strength of being semi incidental, sensitivity to the
primary conditions and sincerity. A chaotic system by using
these particular conditions can be a qualified technique to
keep the variance in the problems. In this algorithm instead
of using arbitrary variables in the incidental physical
dissemination, chaotic variables are utilized. While the
logistic portrait is more general in chaos theory, we make
employ of that in this paper so that we cover a wider and
fitting environment around the krill and have a wider variety
to entrée more points in the scope.
Taking into account of elevated sensitivity of the chaotic
functions in the direction of the primary conditions we could
create a broad diversity in these sequences so that no
recurred elements are secluded through the population which
are optimized themselves or are close to the optimized
points. The united Krill algorithm and Chaos theory is
called the EKHA which in it the physical dissemination is
allocated by a chaotic portrait. In order to produce a logistic
chaotic portrait in this paper we utilize a polynomial
quadratic portrait which is mentioned below:
To perk up the performance of the algorithm, genetic
reproduction mechanisms are integrated into the algorithm.
a. Crossover
The binomial method performs crossover on each of the d
components or parameters. By generating a uniformly
distributed random number between 0 and 1, the mth
component of Xi ,Xi,m, is manipulated as:
𝑋𝑖,𝑚 =
𝑋𝑟,𝑚 𝑟𝑎𝑛𝑑 𝑖,𝑚 <𝐶𝑟
𝑋𝑖,𝑚 𝑒𝑙𝑠𝑒
𝐶𝑟 = 0.2𝐾𝑖,𝑏𝑒𝑠𝑡
(29)
(30)
Where r ∈ {1, 2,. ..,N}. Using this novel crossover
probability, the crossover probability for the global best is
equal to zero and it increase with decreasing the fitness.
b. Mutation
The mutation process used here is formulated as:
𝑋𝑖,𝑚 =
𝑋𝑔𝑏𝑒𝑠 ,𝑚 + 𝜇 𝑋𝑝,𝑚 − 𝑋𝑞,𝑚 𝑟𝑎𝑛𝑑𝑖,𝑚 < 𝑀𝑢
𝑋𝑖,𝑚
𝑒𝑙𝑠𝑒
(31)
𝑀𝑢 = 0.05 𝐾𝑖,𝑏𝑒𝑠𝑡
(32)
𝑥 𝑖 + 1 = 𝜇𝑥 𝑖 ∙ 1 − 𝑥 𝑖 ,
𝑥 𝑖 𝑜 0,1 , 𝑖 = 1~𝑛
Where p, q ∈{1, 2, .,K} and l is a number between 0 and 1.
It should be noted in 𝐾𝑖,𝑏𝑒𝑠𝑡 the nominator is Ki-Kbest
b.
(33)
𝑥 𝑖 in this equation is the magnitude of the 𝑥 in the “𝑖” th
step, and is known control parameter for the system. If 𝜇 is
between 3 and 4 it reveals the chaotic behaviour of the
function. In this paper is 𝜇 assumed to be equal to 4.
Krill herd Algorithm
a.
Fitness evaluation: assessment of each krill
individual according to its location.
Motion computation:
Motion induced by the presence of other
individuals,
Foraging activity
Physical dissemination
Implementing the genetic operators
Updating: updating the krill individual location in
the explore space.
Repeating: go to step fitness evaluation until the
stop criteria is reached.
End
Define the simple limits and determination of
algorithm constraint
Initialization: arbitrarily generate the initial
population in the explore space.
Enhanced Krill Herd algorithm for solving optimal
reactive power dispatch problem.
10
International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
a.
b.
c.
d.
e.
f.
g.
h.
Define the simple limits and determination of
algorithm limitation
Initialization: arbitrarily generate the initial
population in the explore space.
Fitness evaluation: assessment of each krill
individual according to its location.
Motion computation:
Motion induced by the existence of other
individuals,
Foraging activity,
Physical dissemination based on chaotic portrait
apply the genetic operators
Updating: updating the krill individual location in
the explore space.
Repeating: go to step fitness assessment until the
stop criteria is reached.
End
Table 1: Variables Limits For IEEE-57 Bus Power System
(P.U.)
REACTIVE POWER GENERATION LIMITS
1
2
3
6
8
9
12
QGMIN
-1.2
2
-.012
0.3
-.01
0.2
-0.04
0.22
-1.1
2
-0.01
0.03
-0.1
1.43
QGMAX
VOLTAGE AND TAP SETTING LIMITS
VGMIN
VGMAX
VPQMIN
VPQMAX
TKMIN
TKMAX
0.7
1.0
0.92
1.05
0.4
1.1
SHUNT CAPACITOR LIMITS
BUS NO
QCMIN
QCMAX
5. Simulationstudy
18
0
10
25
0
5.3
53
0
6.0
Table 2: control variables obtained after optimization by
EKHA method for IEEE-57 bus system (p.u.).
Control
EKHA
Variables
V1
1.1
V2
1.079
V3
1.069
V6
1.050
V8
1.074
V9
1.049
V12
1.059
Qc18
0.0832
Qc25
0.323
Qc53
0.0617
T4-18
1.015
T21-20
1.069
T24-25
0.968
T24-26
0.938
T7-29
1.090
T34-32
0.949
T11-41
1.011
T15-45
1.068
T14-46
0.931
T10-51
1.049
T13-49
1.069
T11-43
0.910
T40-56
0.909
T39-57
0.969
T9-55
0.983
At first projected EKHA algorithm is tested in standard
IEEE-57 bus power system. The IEEE 57-bus system data
consists of 80 branches, seven generator-buses and 17
branches under load tap setting transformer branches. The
probable reactive power compensation buses are 18, 25 and
53. Bus 2, 3, 6, 8, 9 and 12 are PV buses and bus 1 is
selected as slack-bus. In this case, the explore space has 27
dimensions, i.e., the seven generator voltages, 17
transformer taps, and three capacitor banks. The system
variable limits are given in Table 1. The primary conditions
for the IEEE-57 bus power system are given as follows:
Pload= 12.310 p.u. Qload = 3.242 p.u.
The total initial generations and power losses are obtained as
follows:
𝑃𝐺 = 12.6834 p.u.
BUS NO
𝑄𝐺 = 3.3468 p.u.
Ploss= 0.26381 p.u. Qloss = -1.2159 p.u.
Table II shows the various system control variables i.e.
generator bus voltages, shunt capacitances and transformer
tap settings obtained after EKHA based optimization which
are within their tolerable limits. In Table III, a comparison of
optimum results obtained from projected EKHA with other
optimization methods for reactive power problem mentioned
in literature for IEEE-57 bus power system is given. These
results point out the forcefulness of projected EKHA
approach for providing better optimal solution in case of
IEEE-57 bus system.
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International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
Table 3: comparative optimization results for IEEE-57 bus
power system (p.u.)
S.No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Optimization
Algorithm
NLP [43]
CGA [43]
AGA [43]
PSO-w [43]
PSO-cf [43]
CLPSO [43]
SPSO-07[43]
L-DE [43]
L-SACP-DE
[43]
L-SaDE [43]
SOA [43]
LM [44]
MBEP1 [44]
MBEP2 [44]
BES100 [44]
BES200 [44]
Proposed
EKHA
Best
Solution
0.25902
0.25244
0.24564
0.24270
0.24280
0.24515
0.24430
0.27812
0.27915
Worst
Solution
0.30854
0.27507
0.26671
0.26152
0.26032
0.24780
0.25457
0.41909
0.36978
Average
Solution
0.27858
0.26293
0.25127
0.24725
0.24698
0.24673
0.24752
0.33177
0.31032
0.24267
0.24265
0.2484
0.2474
0.2482
0.2438
0.3417
0.22285
0.24391
0.24280
0.2922
0.2848
0.283
0.263
0.2486
0.23791
0.24311
0.24270
0.2641
0.2643
0.2592
0.2541
0.2443
0.23190
6. Conclusion
In this paper a novel approach EKHA algorithm has been
sucessfully solved optimal reactive power problem and the
algorithm has been validated by testing in standard IEEE 57
and 118 test systems .Performance comparisons with wellknown population-based algorithms gives encouraging
results. EKHA emerges to find good solutions when
compared to that of other algorithms. The simulation study
presented in previous section prove the ability of EKHA
approach to arrive at near global optimal solution.real power
loss has been considerably reduced and voltage profile are
well within the limits.
References
1.
2.
Secondly EKHA has been tested in standard IEEE 118-bus
test system [45] .The system has 54 generator buses, 64 load
buses, 186 branches and 9 of them are with the tap setting
transformers. The line and bus data and their limits are given
in [www.ee.washington.edu/trsearch/pstca]. The limits of
voltage on generator buses are 0.95-1.1 per-unit., and on
load buses are 0.95-1.05 per-unit. The limit of transformer
rate is 0.9-1.1, with the changes step of 0.025. The
limitations of reactive power source are listed in Table 4,
with the change step of 0.01.
3.
4.
Table 4: Limitation of reactive power sources
BUS
5
34 37 44 45
46
48
QCMAX
0
14 0
10 10
10
15
QCMIN -40 0 -25 0
0
0
0
BUS
74 79 82 83 105 107 110
QCMAX 12 20 20 10 20
6
6
QCMIN
0
0
0
0
0
0
0
5.
6.
In this case, the number of population is increased to 120 to
explore the larger solution space. The total number of
generation times is set to 200. The statistical comparison
results of 50 trial runs have been list in Table 5 and the
results clearly show the better performance of proposed
algorithm.
Table 5:Comparison of simulation results in 118-bus system
Active power
loss (p.u)
BBO
[46]
min
max
Average
128.77
132.64
130.21
ILSBBO/
strategy1
[46]
126.98
137.34
130.37
ILSBBO/
strategy1
[46]
124.78
132.39
129.22
7.
Proposed
EKHA
121.01
130.98
124.91
12
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Harmony Search (HS) Algorithm for Solving
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International Journal of Electronics and Electrical
Engineering ,Vol. 1, No. 4, pp270-274 December,
2013, ISSN 2301-380X.
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,
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Problem”, Pinnacle Engineering & Technology ,
Volume 2013, Article ID pet_104, pp 1-6 ,2013.
ISSN: 2360-9516
K.Lenin,
B.Ravindranath
Reddy
,
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oriented particle swarm optimization algorithm for
solving optimal reactive power dispatch problem”
International Journal of Energy and Power
Engineering 2014; 3(1):pp 1-6, ISSN: 2326-960X.
K.
Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi, “An Improved Great Deluge
Algorithm (IGDA) for Solving Optimal Reactive
Power Dispatch Problem” International Journal of
Electronics and Electrical Engineering ,Vol. 2, No.
4, pp321-326 December, 2014, ISSN 2301-380X.
K.Lenin,B.RavindranathReddy,M.SuryaKalavathi,“
Improved Cuckoo Search Algorithm for Solving
Optimal Reactive Power Dispatch Problem”
International Journal of Research in Electronics and
Communication Technology, Vol. 1, Issue 1, pp 2024 Jan – March 2014, ISSN 2348 - 9065 .
K.Lenin,B.RavindranathReddy,
M.SuryaKalavathi,“Hybrid – Invasive Weed
Optimization Particle Swarm Optimization
Algorithm For Solving Optimal Reactive Power
Dispatch Problem” International Journal of
Research in Electronics and Communication
Technology,Vol. 1, Issue 1, pp 45-50 Jan - March,
2014, ISSN 2348 - 9065 .
15. K.Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi,“Water Cycle Algorithm For
Solving Optimal Reactive Power Dispatch
Problem” Scientia Research Library, Journal of
Engineering And Technology Research, 2014, 2
(2):1-11, ISSN 2348-0424, USA CODEN:
JETRB4.
16. K.Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi,“Grand salmon run algorithm for
solving optimal reactive power dispatch problem”
International Journal of Energy and Power
Engineering, 2014; 3(2):pp77-82, ISSN: 2326960X.
17. K.Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi,“Dolphin
Echolocation
Algorithm for Solving Optimal Reactive Power
Dispatch Problem” International Journal of
Computer (2014) Volume 12, No 1, pp 1-15 ISSN
2307-4531.
18. K.Lenin, B.Ravindranath Reddy, M.SuryaKalavathi
“Black Hole Algorithm for Solving Optimal
Reactive Power Dispatch Problem” International
Journal of Research in Management, Science &
Technology (E-ISSN: 2321-3264) Vol. 2, No. 1, pp
10-15, April 2014.
19. K.Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi, “Dwindling of real power loss
by using Improved Bees Algorithm” International
Journal of Recent Research in Electrical and
Electronics Engineering , Vol. 1, Issue 1, pp: (3442), Month: April - June 2014. ISSN 2349-7815.
20. K.
Lenin,
B.Ravindranath
Reddy,
M.SuryaKalavathi, “A New charged system Search
for Solving Optimal Reactive Power Dispatch
Problem” International Journal of Computer
(2014) Volume 14, No 1, pp 22-40, ISSN 23074531.
21. K.Lenin,B.RavindhranathReddy,“Reduction of real
power loss by using Fusion of Flower Pollination
Algorithm with Particle Swarm Optimization”
Journal of the Institute of Industrial Applications
Engineers ,Vol.2, No.3, pp.97–103, (2014.7.25),
ISSN:2187-8811.
22. K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“ Reduction of Real Power Loss by using Improved
Bat Algorithm” International Journal of Research in
Electrical and Electronics Technology ,Volume 1 Issue 2, June 2014, pp 23-29,ISSN 2349-2074.
13
International Journal of Darshan Institute on Engineering Research and Emerging Technology
Vol. 4, No. 1, 2015, pp. 07-15
23. K.Lenin,B.RavindhranathReddy,“Hybrid
Eagle
Strategy Flower Pollination Algorithm for Solving
Optimal Reactive Power Dispatch Problem”
International Journal of Electrical Energy, Vol. 2,
No. 3, September 2014, Engineering and
Technology Publishing ,pp 221-225,ISSN 23013656.
24. K.Lenin,B.RavindhranathReddy, “Bumble Bees
Mating Optimization (BBMO) Algorithm for
Solving Optimal Reactive Power Dispatch
Problem” International Journal of Electronics and
Electrical Engineering, Vol. 3, No. 4, August
2015,pp269-273, ISSN 2301-380X.
25. K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Abatement of Real Power Loss by Using Mine
Blast Algorithm” International Journal of Research
in Electronics and Communication Technology,
Vol.1, Issue 3,2014,pp7-13. ISSN: 2348 – 9065.
26. K.Lenin,B.RavindhranathReddy,“ImprovedSpider
Algorithm for Solving Optimal Reactive Power
Dispatch Problem” International Journal of Recent
Research in Interdisciplinary Sciences ,Vol. 1, Issue
1, pp: (35-46), Month: April - June 2014, ISSN
2350- 1049.
27. K.Lenin,B.RavindhranathReddy,“Improvedseekero
ptimization algorithm-based on artificial bee colony
algorithm for solving optimal reactive power
dispatch problem” American Journal of Energy and
Power Engineering ,2014; 1(3): pp 34-42.
28. K.Lenin,B.Ravindhranath
Reddy,
M.SuryaKalavathi “Reduction of real power loss by
using Kudu Herd Algorithm” International Journal
of Electrical and Electronic Science 2014; 1(2):pp
18-23.
29. K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Reduction of Real Power Loss by Using Double
Glow-Worms Swarm Co-Evolution Optimization
Algorithm Based Levy Flights” International
Journal of Novel Research in Electrical and
Mechanical Engineering ,Vol. 1, Issue 1, pp: (112), Month: September-October 2014 .
30. K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Brain Storm Optimization Algorithm for Solving
Optimal Reactive Power Dispatch Problem”
International Journal of Research in Electronics and
Communication
Technology,
Vol.1,
Issue
3,2014,pp25-30, ISSN: 2348 – 9065.
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Voltages and Reduction of Real Power Loss in
32.
33.
34.
35.
36.
37.
38.
39.
14
Power System by Using Crossbreed Spiral
Dynamics Bacterial Chemotaxis Algorithm”,
Journal of Automation and Control Engineering,
Vol. 3, No. 3, pp. 233-236, June, 2015,ISSN:23013702.
K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Abatement of Real Power Loss by Using
Improved Biogeography algorithm”, International
Journal of Novel Research in Electronics and
Communication, Vol. 1, Issue 1, pp: (1-9), Month:
September-October 2014.
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“Reduction of Active Power Loss and Improvement
of Voltage Profile Index by Using Simulating
Annealing Based Krill Herd Algorithm”,
International Journal of Novel Research in
Electronics and Communication, Vol. 1, Issue 1,
pp: (10-21), Month: September-October 2014.
K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Atmosphere Clouds Model Algorithm For Solving
Optimal Reactive Power Dispatch Problem”,
Indonesian Journal of Electrical Engineering and
Informatics ,Vol. 2, No. 2, June 2014, pp.
76~85,ISSN: 2089-3272.
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of
Active Power Loss by Using Adaptive Cat Swarm
Optimization”, Indonesian Journal of Electrical
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and
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No.3,September 2014, pp. 111~118 ,ISSN: 20893272.
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of
Real Power Loss by Hybrid - Genetic Algorithm
and
Hooke-Jeeves
Method”,
Columbia
International Publishing, International Journal of
Computational Intelligence and Pattern Recognition
(2014), Vol. 1 No. 1 pp. 77-88.
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Power Loss and preservation of Voltage Stability
by Hybridization of Cuckoo Search Algorithm with
Powell Search”, International Journal Of Energy,
Volume 8, 2014,pp71-75, ISSN: 1998-4316.
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of
Real Power Loss by Improved Evolutionary
Algorithm”, International Institute for Science,
Technology and Education- journal of Control
Theory and Informatics, Vol.4, No.9, 2014,pp4349,ISSN: 2225-0492.
K.Lenin,B.RavindhranathReddy,M.SuryaKalavathi,
“Termite Colony Optimization Algorithm For
International Journal of Darshan Institute on Engineering Research and Emerging Technology
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K.Lenin has received his B.E., Degree, electrical and electronics engineering in 1999 from university of madras, Chennai, India
and M.E., Degree in power systems in 2000 from Annamalai University, TamilNadu, India. Presently pursuing Ph.D., degree at
JNTU, Hyderabad,India.
Bhumanapally . RavindhranathReddy, Born on 3rd September, 1969. Got his B.Tech in Electrical & Electronics Engineering
from the J.N.T.U. College of Engg.,Anantapur in the year 1991. Completed his M.Tech in Energy Systems in IPGSR of
J.N.T.University Hyderabad in the year 1997. Obtained his doctoral degree from JNTUA,Anantapur University in the field of
Electrical Power Systems. Published 12 Research Papers and presently guiding 6 Ph.D. Scholars. He was specialized in Power
Systems, High Voltage Engineering and Control Systems. His research interests include Simulation studies on Transients of
different power system equipment.
M. Surya Kalavathi has received her B.Tech. Electrical and Electronics Engineering from SVU, Andhra Pradesh, India and
M.Tech, power system operation and control from SVU, Andhra Pradesh, India. she received her Phd. Degree from JNTU,
hyderabad and Post doc. From CMU – USA. Currently she is Professor and Head of the electrical and electronics engineering
department in JNTU, Hyderabad, India and she has Published 16 Research Papers and presently guiding 5 Ph.D. Scholars. She has
specialised in Power Systems, High Voltage Engineering and Control Systems. Her research interests include Simulation studies on
Transients of different power system equipment. She has 18 years of experience. She has invited for various lectures in institutes.
15