G Model ARTICLE IN PRESS - متلبی€¦ · water distribution networks is addressed using HSA incorpo-rated particle swarm algorithm (PSO) and the result outcomes are better than

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ARTICLE IN PRESSG ModelSOC 3714 1–22

Applied Soft Computing xxx (2016) xxx–xxx

Contents lists available at ScienceDirect

Applied Soft Computing

j ourna l h o mepage: www.elsev ier .com/ locate /asoc

ntegrated approach of network reconfiguration with distributedeneration and shunt capacitors placement for power lossinimization in radial distribution networks

. Muthukumar (Assistant Professor) a,∗, S. Jayalalitha (Associate Dean) b

EEE/SEEE, SASTRA University, Tirumalaisamudram, Thanjavur, Tamilnadu, IndiaEIE/SEEE, SASTRA University, Tirumalaisamudram, Thanjavur, Tamilnadu, India

r t i c l e i n f o

rticle history:eceived 5 January 2016eceived in revised form 15 July 2016ccepted 17 July 2016vailable online xxx

eywords:adial distribution network (RDN)article artificial bee colony algorithmPABC)

a b s t r a c t

This article presents the significance of efficient hybrid heuristic search algorithm(HS-PABC) based onHarmony search algorithm (HSA) and particle artificial bee colony algorithm (PABC) in the context ofdistribution network reconfiguration along with optimal allocation of distributed generators and shuntcapacitors. The premature and slow convergence over multi model fitness landscape is the main limitationin standard HSA. In the proposed hybrid algorithm the harmony memory vector of HSA are intelligentlyenhanced through PABC algorithm during the optimization process to reach the optimal solution withinthe search space. In hybrid approach, the exploration ability of HSA and the exploitation ability of PABCalgorithm are integrated to blend the potency of both algorithms. The box plot and Wilcoxon rank sumtest are used to show the quality of the solution obtained by hybrid HS-PABC with respect to HSA.The

istributed generator (DG)hunt capacitorsarmony search algorithm (HSA)

computational results prove the integrated approach of the network reconfiguration problem along withoptimal placement and sizing of DG units and shunt capacitors as an efficient approach towards theobjective. The results obtained on 69 and 118 node network by proposed method and the standard HSAreveals the powerfulness of the proposed approach which guarantees to achieve global optimal solutionwith less iteration.

© 2016 Elsevier B.V. All rights reserved.

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. Introduction

The locality of electrical energy generation is far away from theonsumer loads connected with lengthy feeder lines leads to addi-ional power loss in the transmission and distribution network.ower loss reduction is achieved by reconfiguring the existing net-ork topology and by installing fixed/switched shunt capacitor

anks and distributed generation units (DG) in close proximity tohe consumer loads in transmission and distribution networks. Thellocation of such sources has numerous advantages such as post-onement for investing new transmission and distribution networkonstruction, reduction in power loss, bus voltage profile enhance-ent. Prior to the implementation of loss reduction techniques in

he distribution network; there is a necessary to investigate their

Please cite this article in press as: M. K., J. S., Integrated approand shunt capacitors placement for power loss minimization inhttp://dx.doi.org/10.1016/j.asoc.2016.07.031

onsequence, such as power loss, bus voltage magnitude, harmonicistortion and system voltage stability. A suitable planning method

∗ Corresponding author.E-mail address: [email protected] (M. K.).

ttp://dx.doi.org/10.1016/j.asoc.2016.07.031568-4946/© 2016 Elsevier B.V. All rights reserved.

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must be implemented to get the benefits of integrating the DG unitsand shunt capacitors into the distribution networks.

The network reconfiguration of the RDN is the method of chang-ing the topological structure of the network by opening and closingof sectionalizing and tie switches to achieve optimal topology withminimum power loss. During the reconfiguration process, the sys-tem radiality should be maintained with all loads connected to thenetwork. In recent years, a noticeable research work has been car-ried out for loss reduction using network reconfiguration problem.Since there are numerous candidate switching combinations to findthe optimal topology of the network, the reconfiguration prob-lem is modeled as combinatorial, non-differentiable, constrainedoptimization problem. The discrete nature of sectionalizing and tieswitches along with radiality constraints avert the application ofclassical optimization methodologies. So there has been a growinginterest in various population based heuristic search algorithmssuch as Artificial Immune (AIS) Systems [1], Modified particleswarm optimization [2], Binary group search optimization [3],

ach of network reconfiguration with distributed generation radial distribution networks, Appl. Soft Comput. J. (2016),

Adapted ant colony [4], Fireworks algorithm [5], Harmony search[6] algorithm. A fuzzy multi objective network reconfigurationmethodology for radial distribution systems has been proposed in

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dx.doi.org/10.1016/j.asoc.2016.07.031

http://www.sciencedirect.com/science/journal/15684946

www.elsevier.com/locate/asoc

mailto:[email protected]

dx.doi.org/10.1016/j.asoc.2016.07.031

ARTICLE ING ModelASOC 3714 1–22

2 M. K., J. S. / Applied Soft Compu

Nomenclature

QDGi Reactive power injection of ith DG unit

p.f DGmax Maximum allowable power factor of DG unit

p.f DGmin Minimum allowable power factor of DG unit

p.f DGi Power factor of ith DG unit

nbus Total number of nodes in the RDNnb Total branches in the RDNnc Total number of capacitors to be installed in RDNIi,i + 1 Current flow between ith branch and i + 1th branchIi,i + 1max Allowable maximum permissible current at branch

i + 1IBmax(i) Maximum allowable branch current

IWcompBmax(i) Branch current flow in ith branch with compensa-

tionPw/comp

loss(i,i+1) Real ower loss in the branch between nodes i andi + 1 with DG units, shunt capacitor

Pw/compTloss

Total power loss in the RDN with DG units, shuntcapacitor

|Vi| Bus voltage magnitude of ith busVspec

min Specified lower bound of bus voltage of the RDNVspec

max Specified upper bound of bus voltage of RDNPDG

max Maximum size of DG unit in kilowattsPDG

min Minimum size of DG unit in kilowattsQcL Sum of total reactive demand of the RDNQcj Reactive power injection by the jth shunt capacitor

[uaprfcautmimotfiut[op

csmslptsttohA

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PiDG Size of ith DG unit in kilowatts

7]. Tabu search approach has been proposed for network reconfig-ration in [8–10]. Mathematical illustration of radiality constraintsssociated with the radial distribution network reconfigurationroblem has been addressed in [11]. Optimal network reconfigu-ation along with the placement of distribution generation unitsor power loss minimization has been proposed in [12,13]. Asompared with classical optimization techniques, meta-heuristiclgorithms are capable to achieve a near optimal solution for DGnits and shunt capacitors sizing and placement problem in dis-ribution networks. Artificial Bee Colony (ABC) algorithm which

imics the foraging nature of honey bees swarm has been proposedn [14] to find the best possible sizing of static capacitors. Various

odels and methods applied for the optimal DG allocation, impactf dispatchable and non-dispatchable type DG units integration inhe modern distribution system, current and future trends in thiseld has been addressed in [15,16]. Analytical approach based DGnits sizing and its optimal operating power factor for differentypes of DG unit’s for power loss reduction has been addressed in17]. An analytical approach for simultaneous allocation and sizingf DG units and shunt capacitor to achieve power loss reduction isroposed in [18].

In [19] a heuristic algorithm, mimicking the improvisation pro-ess of musical instruments to get a pleasant harmonious melodyo called harmony search algorithm (HSA) is proposed. The perfor-ance of the developed algorithm is demonstrated with a traveling

alesman problem and minimum-cost pipe network design prob-em. In [20] an improved harmony search algorithm (IHSA) isroposed which intelligently generates new solution vector forhe best solution and convergence of HSA. HSA is a stochasticearch procedure which does not need any derivative informationo solve the complex combinatorial optimization problem. In [21]


he discrete search strategy of HSA is utilized for structural sizeptimization problem with discrete design variables. In [22,23] aybrid heuristic search approach is proposed which makes use ofBC algorithm and its variants to enhance the solution vector in the

PRESSting xxx (2016) xxx–xxx

HS algorithm and the simulation results are compared with the har-mony search algorithm (HSA), improved harmony search algorithm(IHSA), global harmony search algorithm (GHSA) and self adaptiveglobal harmony search (SGHS) algorithm. The parameters of hybridalgorithm and its impact has been studied with uniform designexperiments optimization problems. In [24,25] the optimal designof water distribution networks is addressed using HSA incorpo-rated particle swarm algorithm (PSO) and the result outcomes arebetter than the genetic algorithm, simulated annealing and Tabusearch technique. In [26] a self-adaptive global best harmony searchalgorithm (SGHS) is proposed which utilize a new harmony mem-ory enhancement strategy by dynamic adaptation of HMCR andPAR, distance bandwidth (BW) as learning mechanism to balancethe exploration and exploitation ability. In [27] a hybrid heuris-tic algorithm is proposed which makes use of sequential quadraticprogramming technique (HSA-SQL) to accelerate the local searchability and to get better accuracy in HSA solutions. To exhibitthe effectiveness and sturdiness of the proposed hybrid HSA-SQLalgorithm, various benchmark engineering optimization problemsare taken into consideration. The intelligent honey bee foragingbehavior of bee swarm is utilized in [28–30] to obtain the optimalsolution in multi-dimensional numerical optimization problems.The simulation results outperform the results obtained with theother meta-heuristic algorithms such as a particle swarm opti-mization algorithm, differential evolution algorithm and geneticalgorithms. In calculus based methods, the optimal solution isobtained by using derivatives which is suitable only for continuous-valued functions rather than discrete-valued functions. In [31,32]a new HS algorithm is proposed for solving engineering optimiza-tion problems with continuous as well as discrete design variables.In [33,34] the overview of the recent applications of HSA, whichuses a ‘probabilistic-gradient’ to select the neighboring values ofdecision variables is addressed. It is an efficient meta-heuristicoptimization tool for practitioners to solve complex optimizationparadigms such as construction, telecommunications, engineering,health and energy, and robotics. The HSA provides probabilistic-gradient based search to get the local or global optimal solutioninstead of mathematical gradient as in conventional optimizationtechniques. In [35–38] a HSA based optimal solution is obtained forcomplex optimization problems like scheduling of multiple damsystems, broadcast scheduling in packet radio networks, estima-tion of the success of companies and vehicle routing. In [39] a hybridgrouping HSA is proposed for the multiple-type access node loca-tion problem to determine the optimum location. In [40] a hybridapproach is used to deploy 24-h medical emergency resources bycombining the HSA with the grouping encoding concept to repairinfeasible solutions. In [41] a multi-objective harmony search forurban road network reconfiguration problem to offer near-optimalsolution to improve the vehicles mobility is proposed. In [42] aquasi-oppositional harmony search algorithm is proposed to inves-tigate the optimal controller gains to enhance the performance ofAutomatic Generation Control (AGC) of the power system. A newhybrid PSO algorithm has been addressed in [43] to augment theexploration and exploitation capability by introducing the globaldimension selection strategy using HSA and validated with the PSOvariants, and other meta-heuristic algorithms. In [44] a new self-adaptive HS-PSO search algorithm is proposed with an effectiveinitialization scheme by utilizing the PSO algorithm to improve thesolution quality of the initial harmony memory in the HSA. A newself-adaptive adjusting method for control parameters PAR and BWis designed to accelerate the convergence rate and solution accu-racy of the proposed algorithm. The poor exploitation ability of the


ABC algorithm makes an issue of slow convergence in solving non-linear and constrained optimization nature of engineering designproblems. To overcome these insufficiencies, a modified version ofthe ABC algorithm is suggested in [45–49] by incorporating adap-

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Nb = Nbus − 1

where Nb is the number of branches, Nbus is the number of nodesin the RDN.

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ARTICLESOC 3714 1–22

M. K., J. S. / Applied Soft C

ive inertia weights and acceleration coefficient parameters of PSOlgorithms.

The combined approach of network reconfiguration problemlong with the placement of distributed generators and shuntapacitors is complex combinatorial problems which involves dis-rete (status of sectionalizing and tie switches) and continuousontrol variables (size of DG units and shunt capacitors). To find theptimal topology all the feasible radial topologies of the networkre to be evaluated. Tracing such optimal topology is computa-ionally expensive and NP- hard in nature. Solving such type ofard optimization problems using meta-heuristic techniques will

ead to premature convergence and local optima. Improper bal-nce between intensification and diversification to find the optimalolution is the major issue in meta-heuristic techniques. This neces-itates the hybridization of meta-heuristics which makes use ofomplementary characteristic of different optimization strategieso get the improved solution.

In this article, hybridization of HSA with PSO embedded artificialee colony algorithm (HS-PABC) has been proposed and utilizedo provide the optimal network reconfiguration problem alongith the placement of DG units and shunt capacitors to realizeinimization of real power loss at distinct load levels. In hybrid,S-PABC approach, the global searching ability (exploration) ofSA and the local searching (exploitation) ability of PABC are inte-rated to harmoniously enhance the HS algorithm performance. Inhis way, the strength of local searching ability of standard HSA ismproved to find out the best solution quickly and ride over theocal optima. In this work, different test scenarios are considered

ith an aim to enumerate the benefits of RDN through graph theoryased network reconfiguration along with the allocation of shuntapacitors and DG units. Simulation results point out that the pro-osed hybrid HS-PABC algorithm is proficient than standard HSAlgorithm.

This article is structured as: In Section 2 the formulation of theroblem and graph theory based network reconfiguration is dis-ussed. Outline of standard HS algorithm and the proposed hybridS-PABC algorithm is summarized in Section 3. In Section 4, simu-

ation results and discussion are presented. In Section 5 conclusionsf the work are presented.

. Problem formulation

A multi objective optimization model has been proposed whichncludes technical factors such as real power loss reduction, lineoading reduction and voltage profile improvement. The multibjective proposition is considered simultaneously using weight-

ng factors for obtaining maximum benefits as in Eq. (1). All theerformance indices are given equal weightage.

in.fitness = W1(RPLRI) + W2(MBCCLI) + W3(VDI) (1)

here∑3

i=1wi = 1.0 �wi� [0,1] .A set of performance improvement indices is described mathe-

atically as stated below to enumerate the technical benefits.

.1. Real power loss reduction index (RPLRI)

The objective of real power loss reduction index is to quan-ify the power loss reduction in the distribution network. The realower loss reduction index (RPLRI) is defined as the ratio betweenhe real power loss of the network with and without DG units and


hunt capacitor compensation as in Eq. (2),

PLRI = (plosswcomp

plosswocomp ) (2)

PRESSting xxx (2016) xxx–xxx 3

2.2. Maximum branch current capacity limit index (MBCCLI)

This index is used to reflect the improvement in reserve capacitylimit of the feeder lines. It is the ratio of current flow through thefeeder lines after compensation and the maximum current carryinglimit of that feeder branch as in Eq. (3),

MBCCLI = max(IBwcomp

(i)

IBmax(i)) (3)

2.3. Voltage deviation index (VDI)

The optimal network reconfiguration along with DG units andshunt capacitor placement provides the reduction in bus voltagedeviation. The bus voltage deviation index (VDI) can be defined asin Eq. (4)

VDI = max(V1 − Vi

V1)∀i = 1, 2, .....nbus whereV1

is taken as 1.0p.u (4)

2.4. Constraints associated with the objective function

The nominal bus voltage limit, thermal limit of the feeder lines,maximum real and reactive power injection by the DG units andshunt capacitors, radial structure of the distribution network areconsidered as constraints in Eqs. (5)–(10).

|Vspecmin

| ≤ |Vi| ≤ |Vspecmax | (5)

0.9 ≤ |Vi| ≤ 1.1 i = 1, 2, ....Nbus

|Ii,i+1| ≤ |Ii,i+1max|, i = 1, 2, ....Nb

(6)

∑nc

j=1Qcj ≤ 1.0

∑nl

j=1QcL (7)

The DG units are modeled as controllable synchronous machinebased biomass plants with active and reactive power injectioncapabilities at an operating power factor of 0.85 lagging [17]. Thereal power output (kW) range of DG units sizing is selected as10–50% of the total active power demand of the RDN.

PDGmin ≤ PDG

i ≤ PDGmax (8)

where PDGmin = 0.1

n∑i=2

PDGi and PDG

Max = 0.5n∑

i=2

PDGi

QDGi = PDG

i tan(cos−1(p.f)) (9)

p.fDGmax ≥ p.fDG

i ≥ p.fDGmin (10)

Radiality constraints:


2.5. Spanning tree approach for network reconfiguration

A directed graph representation of the radial distribution net-work is utilized to form the adjacency matrix (AM) with ‘1’s and

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0’s representing the presence and absence of direct edge betweenodes. The node isolation is identified by determining the columnsf the adjacency matrix with only zeros except the root node and inegree of each node is limited to one by determining the columnsith only one nonzero element. The formation of the loop dur-

ng reconfiguration process is identified using MATLAB functionraphisdag (AM).

In this proposed work, the graph data structure is used to con-truct the RDN as spanning tree. The vertices representing theodes of RDN connected with edges (branches) are used to formhe directed graph. The load flow algorithm developed is basedn the formation of BIBC and BCBV matrices [50]. The BIBC matrixelates the bus current injection with branch current where as BCBV

atrix relates the branch current with bus voltage which repre-ents the line impedance of the RDN. In each switching operation,he adjacency matrix and BCBV matrix are changed in accordanceith the change in the system structure. The depth-first search

DFS) discovery order is utilized for traversing the graph fromach node. Based on the discovery order from each node, the cor-esponding BIBC matrix is generated by assigning ‘1′ to discoveraths.

The hypothetical 6 node RDN with sectionalizing and tie switchs shown in Fig. 1(a). The adjacency matrix representation is shownn Eq. (18). Let E be a set of direct edges {(1,2),(2,3),(3,4),(4,5),(3,6)}.ach element in the adjacency matrix AMij = 1 if (i,j)C-- E and AMij = 0

f (i,j) /∈ E. The adjacency matrix before closing the tie switch isormulated as in Eq. (11).

M = [

0

00000

1

00000

0

10000

0

01000

0

00100

0

01000

] (11)

ig. 1(b) represents the directed graph generated using adjacencyatrix represented in (11). The RDN structure modification is

btained by closing the tie switch between the node 5 & 6 andpening the sectionalizing switch between the node 4 and 5 andhe corresponding modified adjacency matrix obtained is shownn Eq. (12). Fig. 1(c) represents the directed graph generated usingdjacency matrix represented in Eq. (12) for the modified structuref the RDN.

M = [

0

00000

1

00000

0

10000

0

01000

0

00001

0

01000

] (12)

The steps involved in solving the optimal network reconfigura-ion problem of RDN are lined as follows:

Step 1: Generate the adjacency matrix (AM) of the given RDNith ‘1’ and ‘0’ representing the presence and absence of direct edge

etween the nodes.


Step2: Generate the directed graph using function, bio-graphbg) from the adjacency matrix (AM).

Step 3: Traverse the directed graph in depth first search (DFS)rder using function traverse (bg, S) where S = 1,2. . ..n to obtain dis-overy vector. The power flow path matrix [i.e., BIBC] is formed bylling ‘1’ in position (i,j) where ith row corresponds to each value of

and jth column corresponds to each element in discovery vectorith respect to S.


Step 4: Obtain the branch current [BC] by multiplying BIBCmatrix obtained from step 3 with bus current injection [I]

[BC] = [BIBC ∗ I] (13)

Step 5: The distribution load flow matrix (DLF) is obtained bymultiplying BCBV and BIBC matrices which relates the bus currentinjection and bus voltages and it is expressed as,

�V = [BCBV] ∗ [BIBC] ∗ [I] = [DLF ∗ I] (14)

The bus current injection in i + 1th node at kth iteration can beobtained as follows,

Iki+1 =

√P2

i+1 + Q2i+1

|Vi|2(15)

The change in bus voltage at i + 1th node at k + 1th iteration can beobtained as follows,

�VK+1i+1 = [DLF ∗ IKi+1] (16)

VK+1I+1 = V0 + �VK+1

I+1 (17)

In this similar fashion, the bus voltages are updated during iter-ative steps. The iterative steps are terminated once the requiredtolerance limit is reached.

3. Evolutionary algorithms

3.1. Overview of harmony search algorithm

Harmony search algorithm (HSA) was proposed by Geem et al.[19]. The HSA algorithm requires fewer mathematical calcula-tions and it does not require any derivative information due to itsstochastic searching nature. Various advantages of HS algorithmare (a) it does not require differential gradients, thus it can be suit-able for discontinuous as well as continuous functions; (b) it canhave the capability to handle discrete as well as continuous deci-sion variables [32]; (c) it does not require initial value setting forthe decision variables.

HMCR, PAR and BW are considered as tuning parameters inHSA. The computational procedures of HSA are a) random initial-ization of decision variables in the harmony memory vector (HMV)b) Improvisation of HMV values by updating the solutions by mem-ory consideration c) pitch adjustment and random re-initializationprocess. Repeat the improvisation process in the HMV until thetermination criteria.

Updating of harmony memory vector is described below.


(18)HM is pitch adjusted or modified slightly with a probability of

PAR as,

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ARTICLE IN PRESSG ModelASOC 3714 1–22

M. K., J. S. / Applied Soft Computing xxx (2016) xxx–xxx 5

hypoth

(w

3a

tmttbtttprt

ts

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Fig. 1. (a) Example hypothetical 6 node RDN with directed graph of the

19)where “BW” represents a random distance bandwidth. In thisay the HMV is improved iteratively.

.2. PSO embedded artificial bee colony algorithm (PABClgorithm)

Particle swarm optimization (PSO) is one of the recent stochas-ic algorithm based on the idea of swarm intelligence of social

odels such as bird flocking, fish schooling [50]. In PSO, simul-aneous co-existence of multiple candidate solutions flies withinhe problem search space. Each particle adjusts its flying positionased on its own experience as well as the best flying position ofhe neighboring particles to reach the optimal solution point. Inhis way each particle retains its best position (Pbest—local searchhrough its own experience) and its neighboring particle’s best


osition (Gbest—global search through neighboring particles expe-ience) during the search process to find the optimal solution withinhe search space of the problem.

The PSO algorithm has three steps: The algorithm process startshe initialization of randomly distributed populations within theearch solution space. Then at each iteration, the velocities and

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etical RDN (b) before closing of tie switch (c) after closing of tie switch.

positions of each particle is updated using velocity and positionequations expressed as below,

Vt+1i

= ω.Vti + C1rand(1)(Pbestti − Xtid) + C2rand(2)(Gbest

ti − Xtid) (20)

Xt+1i

= (Xti

+ Vt+1i

), i = 1, 2, ......., N, d=1,2,......, D (21)

where “N” is the total number of particles; D is the dimension ofthe search space. Vt

isymbolize the velocity of the ith particle at

the tth iteration;Xtid

is the ith particle position at the tth iteration.The term “�” indicate the inertia weight which provides a balancebetween exploration and exploitation. The C1 and C2 are positivesocial weight parameters, which has control over the preeminenceand neighboring particle’s position on the current one. “Pbest” imi-tates the previous best position of the particle and “Gbest” knownas global best position which provides the best “Pbest” amongst allthe Pbest position; rand(1) and rand(2) are the random real value inthe range of [0,1].


Karaboga and Basturk [28] proposed artificial bee colony algo-rithm (ABC) from the foraging nature of honey bee swarm to solvethe constrained optimization problems. The ABC algorithm con-sists of the following groups; employed bee, onlooker bee and scout

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bee phase best fitness probability, the new food source position

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ee. The role of employed bees is to search for the food source andhare the information to the onlooker bees; based on the better foodource information shared from the employed bees, the onlookerurther searches the better food source neighboring around theelected food source. If any food source is found abandoned, theew food source is randomly searched by the scout bees.

Let us suppose the solution space of the optimization problems D—dimensional. The algorithm is initiated with randomly gen-rated population and it can be represented as Xj = (Xj1, Xj2,. . ..jD) where j D {1,2,. . ..,SN). SN is the size of the food source. Then

he employed bee’s could modify the solution in its memory byandomly selecting a neighboring food source position using theollowing Eq. (22),

t+1j

= (Xtj + rand(1)(Xtj − Xtk) (22)

here K D {1,2,. . .. . .,SN) is chosen randomly with j /= K; rand (1)s a random number within the range of [−1,1].

In onlooker bee phase, the onlooker bees start searching theolution around the best food source provided by the employedees using Eq. (22) based on the probability value “Pj” as in Eq. (23)

Pj = fitnessj∑HMSj=1 fitnessj

(23)

itnessj is the fitness value of jth the solution. The fitness of eacholution is computed by Eq. (24) as,

itnessj = [1/(1 + min.fitness)] (24)

During this improvisation process, if any food source foundbandoned after a predetermined number of cycles (called as limit)t is replaced with new random food source by the scout bee usinghe following Eq. (25).

t+1j

= (Xmax + rand(0, 1)(Xmax − Xmin) (25)

here Xmax, Xmin are the maximum and minimum bound of theood source position.

If the new candidate food source position has better quality (fit-ess function) than the previous one, then such candidate foodource is retained by replacing the older one. Repeat the above stepsntil the optimal solution is obtained.

The standard ABC algorithm encounters the problem in explo-ation and exploitation ability when handling high dimensionalptimization problems. The solution search space is explored andxploited by the employee and onlooker bees using Eq. (22) isuperior in terms of tracing diverged solution (well explorationbility) but fails to exploit within the search space. Greedy selec-ion method on the bee’s trajectories will lead the ABC algorithmo trap into local optima. In this work, to cope with this problem,he intensification and diversification capability of ABC algorithms balanced by integrating the PSO into the ABC algorithm. Themproved ABC algorithm (PABC) updates the bee’s position by mak-ng use of Eq. (26). The inertia weight and acceleration constants arencorporated into the employed bee phase of the ABC algorithm tomprove the searching capability of the bees. These capabilities alle-iate the premature convergence and avoidance of the local optiman standard ABC algorithm.

.3. Proposed hybrid HS-PABC algorithm

It is a common practice to combine different search procedure tovercome the deficiencies of the individual heuristic optimization


lgorithms in order to provide a robust optimization technique.tandard HSA is incompetent in local search ability [27] and itncounters the problem of slow convergence, traps in local optimalolution over multi model fitness landscape. The local searching


capability of the HSA has been enhanced by crossbreeding the HSAwith other optimization algorithms [22].

It is evident that in the HS algorithm the harmony memory (HM)plays a vital part which decides the algorithm performance. In thiswork, to augment the solution accuracy of the standard HSA, theparticle ABC algorithm is integrated and a new HS-PABC has beenproposed. In hybrid HS-PABC algorithm, the HMV in the HSA istaken as the initial food source by the PABC algorithm to producea diverse range of potentially optimal solutions while at the sameinstant it intensify its search in the vicinity of optimal solution. Newimprovised HMV values are used as initial values by the PABC algo-rithm to search for optimal solution. If the locally optimized vectorproduced by the PABC algorithm has better fitness value than thosein the HMV, they will be retained in the HM. The harmony vec-tor (HMV) in the HSA is improved by utilizing the potency of bothheuristic algorithms to get the best solution. Besides this hybridalgorithm requires the tuning of the control parameters such asHarmony Memory Size (HMS), Pitch Adjustment Rate (PAR), Har-mony Memory Consideration Rate (HMCR) and Maximum CycleNumber (MCN). The flowchart of the proposed hybrid HS- PABCalgorithm is presented in Fig. 2.

The computational procedure of the proposed hybrid HS-PABCalgorithm is detailed as follows,

Step 1: Initialize the parameters of HS-PABC algorithm; HMS,PAR, HMCR, MCN.

Step 2: Initialize the Harmony Memory Vector (HMV) with ran-dom population

Step 3: Cycle = Cycle + 1Step 4: Employed bee phase initiation: Random populations

generated in the HMV is improvised by using Eq. (26) to updatethe bee’s position.

Xjknew = [�Xjk + C1�jk(Xbest

k − Xjk) + C2�jk(Xnk − Xjk)] (26)

where Xjknew is the new feasible solution on its preceding solution

Xjk. The term “�” indicate the inertia weight utilized to modify thecurrent position of bees with respect to its prior one. To exploreglobal search at initial stage of the search, the inertia weight isdeclined linearly from 0.9 to 0.4 as suggested in [51] to exploreglobal search initially. The C1 and C2 are positive social weightparameter values chosen as 2.05 [51]. Xbest reflects the finest foodsource amongst the population. Xnk is the random neighbor valueof the population and �jk is the random value in the range of[0,1]. After the estimate of each candidate food source position, thegreedy selection procedure is applied among the solution obtainedthrough step 2 and 4. The onlooker bees utilize the nectar infor-mation shared from the employed bees and select the food sourcebased on the probability value accompanied with that food sourcePj from Eq. (27).

Pj = fitnessj∑HMSj=1 fitnessj

(27)

The fitness value of jth solution is taken as fitnessj. The fitnessof each solution is computed by Eq. (28) as,

Fitnessj = [1/(1 + min.fitness)] (28)

“min.fitness” is obtained through the BFS based power flow solution


Xjknew in the vicinity of food source Xj,k

old is determined by usingEq. (29)

Xjknew = {Xj,k

old + u(Xj,kold − Xn,k)} (29)

495

496

497

dx.doi.org/10.1016/j.asoc.2016.07.031



sed hy

Dwrlv

498

499

500

501

502

503

504505

Fig. 2. Flowchart of propo

where n D {1,2,. . ..CS} and k D {1,2,. . .. D} are random indices; is the total number of parameters in the optimization problem


hich decides the dimension of the problem; n /= j; ‘u’ signifies aandom number produced which lies between [−1,1]. If the calcu-ated value of the candidate food position Xjk

new using Eq. (25) mayiolate the predefined boundary, resetting scheme is employed,

brid HS-PABC algorithm.

which put the violating boundary values to the adjoining boundarylimit value, i.e.,


Xjknew = Xjmin, ifXjk

new ≤ Xjmin

Xjknew = Xjmax, ifXjk

new ≥ Xjmax

506

507

dx.doi.org/10.1016/j.asoc.2016.07.031

ING ModelA

8 ompu

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pt

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Scenario 2: Optimal allocation and sizing of DG unitsScenario 3: Simultaneous allocation (location and sizing) of DG

units and shunt capacitors

508

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After the estimation of each candidate food source position, thereedy selection method is adopted.

Step 6: Scout bee phase initiation: If any abandoned solution isresent, it is swapped with a new arbitrary solution generated byhe scout bee phase using Eq. (30).

jknew = min(Xk

j) + rand(0, 1)[max(Xkj) − min(Xk

j)] (30)

Step 7: Retain the best solution obtained so far in HMVStep 8: Improvise the populations (decision variables) in the

MV by HMCR, PAR and Random selection steps in the HS algo-ithm.

Step 9: Evaluate new HMV and check new HMV is better thanxisting HMV. If so, update HMV

Step 10: Cycle = Cycle + 1Step 11: Check if the stopping criterion is met. i.e., total number

f MCN is reached.Step 12: If not, go to step 4 and reiterate from step 4 until

ycle = MCN

.4. The pseudo code of proposed hybrid HS-PABC algorithm

Step 1: Initialize the parameters: Machine cycle (MCN), Har-ony memory size (HMS), Harmony memory consideration rate

HMCR) and Pitch Adjustment Rate (PAR)Step 2: Initialize HMS.For i = 1 to HMS doFor j = 1 to D do

Xij = lbj + rand ()*(ubj − lbj)Step 2.1: Calculate fitness value.

F(xi) = Evaluate(xi)Step 3: Start Cycle = 1



Step 6: IF f(Xjnew) > f(Xj), update the HM as Xj = Xi

new

Step 7: Retain the best solution in the HMV.Step 8: Next Cycle = Cycle + 1Step 9: IF Cycle number < MCN, goto step 4; else stop the itera-

tive procedure

4. Numerical results and discussions

This article proposes an efficient hybrid heuristic search algo-rithm for the enhancement of distribution network performance byimplementing the four test scenarios with an objective of optimiz-ing the multi objective performance improvement indices such aspower loss reduction, bus voltage deviation and branch current ofthe RDN. The backward/forward sweep based power flow method(BFS) is utilized to find the load flow solution [50]. The proposedhybrid optimization algorithm is applied on 69 and 118 node radialtest networks on a Matlab7.7.0 platform. For both the test net-works, substation voltage is taken as 1.0 p.u. The four test scenariosat seven discrete load levels are,

Scenario 1: Optimal allocation (location and sizing) of shuntcapacitors


dx.doi.org/10.1016/j.asoc.2016.07.031



Table 1Average load duration schedule of a day.Q8

Time duration % load level No of hours/day No of hours/year

6 a.m.–7 a.m. 40 1 3657 a.m.–8 a.m. 50 1 3658 a.m.–9 a.m. 60 1 3659 a.m.–1 p.m. 80 4 14601p.m.–2 p.m. 70 1 3652 p.m.–5 p.m. 100 3 10955 p.m.–6 p.m. 90 1 3656 p.m.–9 p.m. 80 3 10959 p.m.–12 a.m. 60 3 1095

a

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Cap

acit

or(k

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@n

ode

(67)

Cap

acit

or(k

VA

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@n

ode

(23)

Cap

acit

or(k

VA

R)

@n

ode

(61)

DG

1(k

W)

@

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(kW

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@

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e(6

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G3

(kW

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G

(kW

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@

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apac

itor

(kV

AR

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(kW

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@

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apac

itor

(kV

AR

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@n

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(19)

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118.

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558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

591

592

593

594

595

596

597

598

599

600

601

602

603

604

605

606

12 a.m.–6 a.m. 40 6 2190Total annual hours 8760

Scenario 4: Simultaneous optimal network reconfigurationlong with DG units and shunt capacitor compensation

The daily load schedule for the RDN is modeled for 24 h timenterval of the day and it is assumed to be repetitive for 365 dayso get the annual load schedule. The average daily load intervalchedule is depicted in Table 1. There are seven discrete load levelsarying from 40% to 100% as shown in Fig. 3. The DG unit’s injections considered as a negative PQ load with real and reactive powernjection capability with 0.85 lagging as an operating power factor.he status of sectionalizing and tie switches, location and size ofG unit and shunt capacitors are taken as the decision variables.he maximum penetration limit of DG unit is limited to 50% of theotal system real power demand.

.1. Simulation results of 69 node RDN

To test the effectiveness of the proposed hybrid HS-PABC algo-ithm a medium scale 69 node radial distribution network isonsidered with the real power load demand of 3802.1 kW andeactive power load demand of 2694.5 kVAR. This test system has3 line segments with five tie switches. The tie switches are num-ered from 69 to 73 and the sectionalizing switches are numberedrom 1 to 68.The active and reactive power loss at nominal load levels 224.97 kW and 102.15 kVAR respectively. The system operates

ith the nominal bus voltage magnitude of 12.66 kV with 100 MVAase. Minimum bus voltage magnitude of 0.9092 p.u. is observed at5th node. The test network data are obtained from [7].

The simulation results obtained with proposed hybrid algo-ithm and standard HSA for scenarios I–IV is summarized inables 2 and 3. The real power loss reduction obtained with HSA andybrid HS-PABC algorithm is summarized in Table 4. From Table 4,

t is observed that at 40% load level the base case loss of 32.50 kWs reduced to 21.65 kW, 10.54 kW, 11.09 kW and 7.07 kW withespect to the scenarios I–IV using hybrid approach. At mediumoad level (70%), the power loss reduction is from 104.52 kW to8.91 kW, 32.99 kW, 35.37 kW and 21.72 kW. At nominal load level100%) the power loss reduction is from 224.96 kW to 145.68 kW,9.08 kW, 73.11 kW and 48.62 kW. The bus voltage profile withhe scenarios I–IV at 100% load level is depicted in Fig. 4. It cane seen that, the proposed hybrid algorithm provides a significant

mprovement of minimum bus voltage profile with scenario-IV asompared with other scenarios. Fig. 5 depicts the optimal reconfig-ration topology and directed graph representation of 69 node RDNlong with DG units and shunt capacitor placement (Scenario-IV)t 100% load level. It is observed that scenario-IV provides bet-er loss reduction with improved bus voltage profile at all loadevel as compared with scenario-III. Since the power flow path is

Please cite this article in press as: M. K., J. S., Integrated approach of network reconfiguration with distributed generationand shunt capacitors placement for power loss minimization in radial distribution networks, Appl. Soft Comput. J. (2016),http://dx.doi.org/10.1016/j.asoc.2016.07.031

ptimized in scenario IV by retaining the DG and shunt capacitorocation obtained in scenario-III (@ node 19 for capacitor locationnd @ node 60 for DG unit location) better power loss reduction ischieved. Table 5 shows the minimum bus voltage profile obtained Ta

ble

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40

50

60

70

80

90

100

dx.doi.org/10.1016/j.asoc.2016.07.031


10 M. K., J. S. / Applied Soft Computing xxx (2016) xxx–xxx

Fig. 3. Daily load schedule.

0.9

0.92

0.94

0.96

0.98

1

1 6 11 16 21 26 31 36 41 46 51 56 61 66

Bus V

olta

ge (p

.u)

Bus Number

Base Case Ca pac itor Placeme ntDG Uni ts PlacementSimulta neous DG un its + Capa cito r Placeme ntSimulta neous recon f + DG un its + capa citors

Fig. 4. Bus voltage profile of 69 node RDN with different scenarios with hybrid HS-PABC algorithm at 100% load level.

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ith standard HSA and hybrid HS-PABC algorithm. The results pre-ented in Tables 4 and 5 reflect the efficiency of the proposed hybridlgorithm over standard HSA with respect to loss reduction andoltage profile improvement in all load levels.

The active power loss in each branch of the RDN with the sce-arios I–IV at 100% load level is depicted in Fig. 6. The reduction

n total real power loss of the RDN with scenario-IV at 40%, 70%nd 100% load level using hybrid HS-PABC algorithm is depicted inig. 7. It is revealed that scenario-IV offers more loss reduction withnhanced bus voltage profile as compared with other scenarios.

.2. Simulation results of 118 node RDN

To show the suitability of the proposed hybrid approach on largecale RDN it is applied on 118 node balanced three phase radial dis-ribution network. The system operates under 11 kV voltage level at00 MVA base with active load demand of 22709.7 kW and reactive

oad demand of 17041.1 kVAR respectively. The active and reac-ive power loss before compensation is 1298.1 kW and 978.74 kVAR


espectively. The line and load data are obtained from [8]. This testetwork consists of 118 nodes with 117 sectionalizing switchesnormally closed) and fifteen tie switches (normally open). The tiewitches are numbered from 118 to 132.

Simulation results obtained using HS and hybrid HS-PABC algo-rithm at different load level of the network along with the candidatenodes for the placement of DG units and shunt capacitors are pre-sented in Tables 6–11. The real power loss reduction obtainedwith HSA and hybrid HS-PABC algorithms with four test scenar-ios are summarized in Table 12. From Table 12, it is observedthat loss reduction realized using proposed hybrid algorithm atlight load level (40%) is from 187.17 kW (base case) to 126.13 kW,59.59 kW, 66.75 kW and 54.91 kW with respect to the scenariosI–IV. At medium load level (70%), the power loss reduction is from602.18 kW to 399.78 kW, 185.32 kW, 209.21 kW and 163.91 kWwith respect to the scenarios I–IV. At nominal load level (100%) thepower loss reduction is from 1298.09 kW to 847.75 kW, 384.65 kW,435.62 kW and 340.12 kW with respect to the scenarios I–IV. Itis observed that scenario-IV provides better loss reduction withimproved bus voltage profile at all load level as compared withother scenarios. Fig. 8 depicts the optimal reconfiguration topol-ogy and directed graph representation of 118 node RDN along withDG units and shunt capacitor placement (Scenario-IV) at 100% load


level.Table 13 shows the minimum bus voltage profile with differ-

ent scenarios obtained with standard HSA and hybrid HS-PABCalgorithms. It can be inferred from the results presented in

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650

dx.doi.org/10.1016/j.asoc.2016.07.031



Fig. 5. Directed graph representation of optimal topology of 69 Node RDN (Scenario-IV at 100% load level).

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651

652

653

654

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665

666

ables 12 and 13, that the proposed hybrid algorithm provides bet-er loss reduction with improved bus voltage profile as comparedith the standard HSA (with scenarios I–IV) at all load levels. The

us voltage profile with the scenarios I–IV at 100% load level isepicted in Fig. 9. It can be seen that, the proposed hybrid algorithmrovides a significant improvement of minimum bus voltage profile

n scenario-IV as compared with other scenarios. The active power


oss in each branch of the RDN with the scenarios I–IV at 100% loadevel is depicted in Fig. 10.The reduction in total real power loss ofhe RDN with scenario-IV at 40%, 70% and 100% load levels usingybrid HS-PABC algorithm is depicted in Fig. 11. It can be inferred

that the combined approach of optimal network reconfigurationproblem along with DG units and shunt capacitors compensation(Scenario-IV) yields more loss reduction with improved bus voltageprofile as compared with other scenarios.

4.3. Parameter settings


An empirical study is performed to determine the impact ofcontrol parameters towards the solution quality of the hybrid HS-PABC algorithm. To demonstrate the effects of single parameterchange on the fitness function for 69-node RDN, 12 different cases

667

668

669

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dx.doi.org/10.1016/j.asoc.2016.07.031




Fig. 6. Variation of power loss at each line of 69 node RDN with different scenarios with hybrid HS-PABC algorithm at 100% load level.

0

50

100

150

200

250

40%70%100%

224.96

104.52

32.548.62

21.727.07

Pow

er l

oss

(k

W)

% load le vel

Base Case Scenario-I Scenario-II Scenario-III Scenario-IV

Fig. 7. Power loss reduction in 69 node RDN with different scenarios with hybrid HS-PABC algorithm at 100% load level.

Fig. 8. Directed graph representation of optimal reconfiguration topology of 118 node RDN (Scenario-IV at 100% load level).

dx.doi.org/10.1016/j.asoc.2016.07.031



0.85

0.9

0.95

1

1.05

1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116Bu

s Vol

tage

(p.u

)

Bus NumberBase Case Capacitor Placement DG units Placement Simultaneous DG units + capacitor placementSimultaneous reconf + DG units + capacitors placement

Fig. 9. Bus voltage profile of 118 node RDN with different scenarios (100% load level).

Fig. 10. Variation of real power loss at each line of 118 node RDN with different scenarios (100% load level).

0

500

1000

1500

%04%07%001

1298.09

602.18

187.17340.12

163.91 54.91

Po

wer

lo

ss (

kW

)

% Load level

Base Case Scenario-I Scenario-II Scenario-III Scenario-IV

Fig. 11. Real power loss reduction in 118 node RDN with different scenarios (100% load level).

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the empirical study, the parameters chosen for 69 node network

671

672

673

674

675

676

677

678

679

680

681

682

683

684

685

re tested as shown in Table 14. Each case is tested over 50 runsn three stages. In stage 1–3, HMCR, HMS, PAR and MCN are var-ed respectively, and other parameters are kept constant. If theMCR value selection is too low, the algorithm behaves like aure random search which leads to slow convergence. If the HMCRalue is higher, all the harmonies in the HM are utilized, the other


armonies are not well explored and this may lead to local opti-al solution. As shown in Table 14, large and small HMCR values

ead to a decrease in the solution quality. The pitch adjustmentPAR) is used to produce new solution around the existing best

solution. Selection of low PAR will limit the exploration and itcan lead to slow convergence. Higher PAR selection will lead thesolution to scatter around some potential optima similar to ran-dom search. The selection of larger and smaller values of HMS willdecrease the efficiency of the algorithm as seen in Table 14. From


are HMS = 20, HMCR = 0.9, PAR = 0.3, MCN = 15. Similarly for 118node RDN the control parameter values are selected as HMS = 50,MCN = 50, HMCR = 0.9, PAR = 0.3.

686

687

688

dx.doi.org/10.1016/j.asoc.2016.07.031

Please cite

this

article in

press

as: M

. K

., J.

S., In

tegrated ap

proach

of n

etwork

reconfi

guration

with

distribu

ted gen

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d

shu

nt

cap

acitors

placem

ent

for

p

ower

loss

m

inim

ization

in

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istribution

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etworks,

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Table 3Simulation results of 69 node RDN at different load levels obtained with HSA.

%Load level Fixed/SwitchedCapacitor

Scenario-I Scenario-II Scenario-III Scenario-IV

Capacitor(kVAR) @node (67)



DG1 (kW)@ node (63)

DG2 (kW)@ node (61)

DG3 (kW)@ node (64)

DG (kW) @node (60)


DG (kW) @node (60)


Optimaltopology(openswitches)

40 Fixed 200 100 450 11.13 244.83 121 380.22 200 294.15 350 4-13-70-63-57

50 Switched 50 50 200 121.29 246 107.15 425.24 100 396 150 69-11-70-62-52

60 Switched 50 – 100 138.57 316.32 120.03 555.12 50 500.76 100 7-12-70-63-53

70 Switched 100 – 150 71.94 387.32 205.66 661.02 50 592.08 100 69-14-70-61-55

80 Switched 50 – 350 128.07 450.29 171.28 734.72 100 699.1 50 69-13-70-62-55

90 Switched – – – 133.97 503.13 207.74 823.75 – 791.7 100 7-11-70-62-58

100 Switched – – 100 104.06 538.30 227.03 900.02 – 878.9 300 69-12-70-63-57

Table 4Reduction in real power loss with different scenarios using HSA and hybrid HS – PABC.

%Load level Real Power loss (kW)

Before Compensation Scenario-ICapacitors @ node:(67),(23),(61)

Scenario-IIDG units @ node(63),(61),(64)

Scenario-IIIDG unit @ node(60)Capacitor @ node (19)

Scenario-IVReconfiguration alongwith DG @ node (60)Capacitor @ node (19)

HSA HS-PABC HSA HS-PABC HSA HS-PABC HSA HS-PABC

40 32.50 21.65 21.65 10.65 10.54 11.07 11.09 9.204 7.0750 51.59 34.41 34.26 16.64 16.61 19.92 17.53 13.16 11.4960 75.51 49.88 49.88 24.81 24.13 26.41 25.98 19.68 15.7170 104.52 68.91 68.91 32.99 32.99 35.37 35.37 23.57 21.7280 138.88 93.96 93.89 44.22 43.66 48.59 47.12 29.55 28.5090 178.92 117.44 117.58 56.23 55.41 61.52 59.98 43.87 36.48100 224.96 146.11 145.68 77.25 69.08 77.65 73.11 51.41 48.62

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nt

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acitors

placem

ent

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p

ower

loss

m

inim

ization

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istribution

n

etworks,

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pp

l.

Soft

Com

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(2016),h

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K.,

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pplied Soft

Computing

xxx (2016)

xxx–xxx

15

Table 5Minimum bus voltage magnitude with different scenarios using HSA and hybrid HS-PABC.

%Load level Minimum bus Voltage (p.u) @(Node)

Before compensation Scenario-I Scenario-II Scenario-III Scenario-IV

HSA @65 HS-PABC @ (65) HSA @ (65) HS-PABC @ (65) HSA @ (65) HS-PABC @ (65) HSA @63 HS-PABC @63

40 0.9656@18 0.9732 0.9739 0.9835 0.9836 0.9816 0.9815 0.9878 0.987850 0.9566@18 0.9675 0.9675 0.9792 0.9792 0.9750 0.9768 0.9849 0.986660 0.9474@18 0.9604 0.9604 0.9752 0.9755 0.9716 0.9720 0.9826 0.984870 0.9382@18 0.9539 0.9539 0.9711 0.9711 0.9673 0.9673 0.9816 0.982180 0.9287@18 0.9500 0.9500 0.9658 0.9670 0.9617 0.9620 0.9776 0.977990 0.9191@18 0.9409 0.9412 0.9616 0.9628 0.9563 0.9571 0.9738 0.9778100 0.9091@18 0.9330 0.9326 0.9538 0.9583 0.9504 0.9526 0.9733 0.9749

Table 6Optimal results obtained with hybrid HS-PABC algorithm—Scenario- I & II.

Load level Fixed/Switched Capacitor Scenario-I Scenario-II

Qc1 @(86) Qc2 @(82) Qc3 @(111) Qc4 @(49) Qc5 @(32) Qc6 @(107) Qc7 @(71) Qc8 @(96) DG1 @ (109) DG2 @(52) DG3 @(70)

40 Fixed 350 300 600 800 750 500 700 400 1315.43 1118.27 1195.4350 Switched 100 100 100 200 200 150 250 150 1646.62 1402.83 1498.1260 Switched 100 50 200 200 200 100 200 100 1978.76 1689.54 1802.4270 Switched 100 100 100 200 200 150 200 100 2311.87 1978.46 2108.3680 Switched 100 100 200 200 200 100 250 150 2646.42 2267.10 2415.1190 Switched 50 100 100 300 – 150 250 100 2980.41 2563.56 2726.37100 Switched – – 150 100 – – 200 50 3224.02 2757.83 2964.16

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nt

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acitors

placem

ent

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ower

loss

m

inim

ization

in

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istribution

n

etworks,

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pp

l.

Soft

Com

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t.

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(2016),h

ttp://d

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AR

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odelA

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3714 1–22

16

M.

K.,

J. S.

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pplied Soft

Computing

xxx (2016)

xxx–xxx

Table 7Optimal results obtained with hybrid HS-PABC algorithm—Scenario-III.

%Load level Fixed/Switched Capacitor Scenario-III

Qc1 Node (32) Qc2 Node (50) Qc3 Node (15) Qc4 Node (93) Qc5 Node (103) DG (kW)@ Node (71) DG (kW) @ Node (110)

40 Fixed 800 850 250 400 550 1147.65 1166.0450 Switched 200 250 100 50 150 1435.09 1458.1860 Switched 200 250 50 100 100 1727.78 1747.5670 Switched 250 300 50 100 150 2018.77 2041.4180 Switched 250 250 100 100 150 2315.09 2334.4790 Switched 250 250 50 100 150 2608.78 2629.85100 Switched 200 250 50 100 100 2904.64 2924.14

Table 8Optimal results obtained with hybrid HS-PABC algorithm—Scenario-IV.

%Load level Type of capacitor Scenario-IV

Fixed/Switched Capacitor size in kVAR Optimal DG units sizing in kW Optimal topology (Open Switches)

@ Node (32) @ Node (50) @ Node (15) @ Node (93) @ Node (103) @ Node (71) @ Node (110)

40 Fixed 750 750 300 250 550 1366.76 1594.45 25-23-39-42-34-60-51-125-126-96-127-107-79-130-12150 Switched 350 100 150 200 450 1527.37 1453.32 25-22-38-42-34-59-51-125-126-98-86-107-82-130-12160 Switched 250 200 – 150 – 1750.64 2090.32 25-22-38-42-34-61-50-125-126-97-87-131-80-130-12170 Switched 400 – 50 50 50 2252.65 2457.30 26-23-38-42-34-59-50-125-126-97-86-131-80-130-12180 Switched 200 300 150 – 100 2404.66 2769.04 26-22-39-42-34-59-50-125-126-97-86-131-80-130-12190 Switched – 350 – 150 250 2562.01 3146.19 25-23-39-42-34-60-51-125-126-97-86-131-80-130-121100 Switched – – 200 150 50 1366.76 1594.45 25-23-39-42-34-60-51-125-126-97-127-131-80-130-121

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acitors

placem

ent

for

p

ower

loss

m

inim

ization

in

radial

d

istribution

n

etworks,

A

pp

l.

Soft

Com

pu

t.

J.

(2016),h

ttp://d

x.doi.org/10.1016/j.asoc.2016.07.031

AR

TIC

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IN P

RE

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G M

odelA

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3714 1–22

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K.,

J. S.

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pplied Soft

Computing

xxx (2016)

xxx–xxx

17

Table 9Optimal results obtained with HSA—Scenario-I & II.

Load level Fixed/Switched Capacitor Scenario-I Scenario-II

Qc1 @ (86) Qc2 @ (82) Qc3 @ (111) Qc4 @ (49) Qc5 @ (32) Qc6 @ (107) Qc7 @ (71) Qc8 @ (96) DG1 @ (109) DG2 @ (52) DG3 @ (70)

40 Fixed 300 300 650 1050 1000 450 750 350 1323.79 1276.49 1229.8250 Switched 100 50 150 50 550 150 250 200 1843.42 1654.55 1458.5060 Switched 150 150 100 200 50 150 150 100 2586.35 1686.08 1804.4970 Switched – 100 150 50 50 150 200 100 2515.81 1282.55 2108.8380 Switched – 150 150 100 50 150 250 150 2646.66 2269.03 2715.2990 Switched – 150 100 100 50 150 250 100 2998.59 2666.05 2821.19100 Switched – 700 50 100 50 150 100 – 3222.79 2759.82 2962.21

Table 10Optimal results obtained with HSA—Scenario-III.

%Load level Fixed/Switched Capacitor Scenario-III

Qc1 @Node (32) Qc2 @Node (50) Qc3 @Node (15) Qc4 @Node (93) Qc5 @Node (103) DG (kW) @ Node (71) DG (kW) @ Node (110)

40 Fixed 700 850 250 350 500 1143.54 1463.3350 Switched 250 250 100 150 150 1132.03 1758.5560 Switched 200 250 50 50 150 1525.89 1846.7370 Switched 200 300 50 50 150 1909.97 2231.7080 Switched 250 250 100 – 100 2119.18 2333.5690 Switched 250 250 50 250 100 2127.67 2632.98100 Switched 350 200 – 100 600 2936.47 3172.35

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acitors

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ower

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inim

ization

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istribution

n

etworks,

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pp

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Soft

Com

pu

t.

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(2016),h

ttp://d

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AR

TIC

LE

IN P

RE

SS

G M

odelA

SOC

3714 1–22

18

M.

K.,

J. S.

/ A

pplied Soft

Computing

xxx (2016)

xxx–xxx

Table 11Optimal results obtained with HSA—Scenario-IV.

%Load level Type of capacitor Scenario-IV

Fixed/Switched Capacitor size in kVAR Optimal DG units sizingin kW Optimal topology (Open Switches)

@ Node (32) @ Node (50) @ Node (15) @ Node (93) @ Node (103) @ Node (71) @ Node (110)

40 Fixed 50 1000 100 550 350 1322.98 1226.79 119-20-124-42-34-61-52-125-126-96-86-131-82-130-12150 Switched 1700 550 300 150 250 1715.63 1540.30 25-22-124-42-33-58-50-125-126-98-86-131-81-130-12160 Switched 150 50 50 50 100 1911.94 2605.31 26-20-124-43-34-59-53-125-126-128-86-106-80-130-12170 Switched 50 50 50 50 50 1802.79 2662.57 26-23-39-44-33-59-50-125-126-97-87-104-81-130-12180 Switched – – 50 – – 2074.84 2930.43 25-22-38-43-33-59-50-125-126-97-74-131-80-130-12190 Switched 450 50 – – – 1795.53 3475.60 25-21-38-45-33-58-52-57-126-98-74- 131-79-130-121100 Switched 750 100 – – 600 2103.25 3984.31 25-21-39-44-34-59-52-125-70-128-127-131-80-130-121

Table 12Reduction in real power loss with scenarios: I–IV using HSA and hybrid HS-PABC.

%Load level Real Power loss (kW)

Before Compensation Scenario-ICapacitorsat node: (86),(82),(111),(49),(32),(107),(71),(96)

Scenario-IIDG units at node(109),(52),(70)

Scenario-IIIDG at node (71),(110)Capacitors at node(32),(50),(15),(93),(103)

Scenario-IVReconfiguration alongwith DG at node(71),(110)Capacitors at node(32),(50),(15),(93),(103)

HSA HS-PABC HSA HS-PABC HSA HS-PABC HSA HS-PABC

40 187.17 128.07 126.13 60.25 59.59 69.33 66.75 61.57 54.9150 297.14 200.12 199.52 96.15 93.59 110.95 105.03 99.53 86.7860 434.97 290.52 290.44 144.48 135.46 154.03 152.27 135.16 118.5170 602.18 400.06 399.78 197.31 185.32 210.83 209.21 179.83 163.9180 800.46 529.08 528.82 246.15 243.31 277.10 275.19 226.10 212.1190 1031.72 678.89 677.84 310.25 309.57 358.85 350.70 320.82 268.64100 1298.09 853.35 847.75 385.89 384.65 438.19 435.62 380.21 340.12

dx.doi.org/10.1016/j.asoc.2016.07.031


M. K., J. S. / Applied Soft Compu

Table 13Minimum bus voltage magnitude with scenarios: I–IV using HSA and hybrid HS-PABC.

%Load level Minimum bus Voltage (p.u) @(Node)

Beforecompensation@ (78)

Scenario-I Scenario-II

HSA @ (78) HS-PABC @ (78) HSA @ (47) H

40 0.9513 0.9658 0.9662 0.9844 050 0.9385 0.9581 0.9582 0.9803 060 0.9253 0.9487 0.9486 0.9763 070 0.9117 0.9396 0.9397 0.9713 080 0.8978 0.9312 0.9315 0.9682 090 0.8835 0.9226 0.9228 0.9641 0100 0.8687 0.9122 0.9127 0.9598 0

Table 14Impact of hybrid HS-PABC algorithm parameter variations on the fitness functionQ9(Scenario-IV) at 100% load level.

Stage Parameter settings Fitness

HMS HMCR PAR MCN

1 5 0.3 0.3 5 0.376405 0.3 0.3 10 0.354245 0.3 0.3 15 0.35324

2 5 0.3 0.3 15 0.353245 0.3 0.4 15 0.360585 0.3 0.5 15 0.35789

3 5 0.3 0.3 15 0.383245 0.7 0.3 15 0.357465 0.95 0.3 15 0.37668

4a

1

TS

TS

689

690

691

692

693

694

695

696

697

698

699

700

701

702

703

704

4 2 0.9 0.3 15 0.3775720 0.9 0.3 15 0.3440430 0.9 0.3 15 0.36862

.4. Robustness and convergence rate of hybrid HS-PABC and HS


lgorithm

The formulated optimization problem (Scenarios-I–IV with00% load level) is solved 50 times repeatedly with random popula-

able 15tatistical study to test the robustness of the HS and hybrid HS −PABC algorithm with 50

Scenarios Max.fitness Min.fitness Mean fitness

HSA HS-PABC HSA HS-PABC HSA

I 0.525175272 0.515918944 0.515953 0.5158 0.517805366II 0.37432 0.370575 0.3703 0.36998 0.371701

III 0.381935 0.368598 0.3473269 0.347311 0.368063

IV 0.385383465 0.384051451 0.3457147 0.344045 0.368376043

able 16tatistical study to test the robustness of the HS and hybrid HS-PABC algorithm with 50 i

Scenarios Max.fitness Min.fitness Mean fitness

HSA HS-PABC HSA HS-PABC HSA

I 0.38792539 0.379718752 0.3811177 0.37960 0.38356404

II 0.186545315 0.180605777 0.180605 0.18060 0.183937826III 0.202517727 0.188078869 0.188329 0.188075 0.197148549IV 0.198168189 0.166000427 0.1630003 0.14670 0.180038661


Scenario-III Scenario-IV

S-PABC @ (47) HSA @ (55) HS-PABC HSA HS-PABC @ (51)

.9844 0.9821 0.9824@55 0.9857@97 0.9884

.9803 0.9784 0.9784@55 0.9846@51 0.9842

.9763 0.9744 0.9744@55 0.9796@43 0.9811

.9722 0.9713 0.9713@55 0.9774@51 0.9764

.9682 0.9674 0.9675@55 0.9732@51 0.9728

.9642 0.9635 0.9635@47 0.9629@58 0.9725

.9599 0.9589 0.9593@47 0.9655@ 99 0.9684

tion seeds. Both the algorithms are allowed to run over generationwith the same initial population. The robustness of hybrid approachover standard HSA is depicted in Tables 15 and 16. Scenarios-I–IVat 100% load level is considered to visualize the convergence plotof fitness function using HSA and hybrid HS-PABC algorithm asshown in Figs. 12 and 14(a–d). Undoubtedly Figs. 12 and 14(a–d)demonstrates the effectiveness of hybrid HS-PABC algorithm overHSA with stable and improved performance in terms of solu-tion accuracy and fast convergence to reach the optimal solutionin all the scenarios. This is because of high probability of bestsolutions updated in HMV by integrating PABC algorithm withHSA.

Table 17Statistical study using Wilcoxon signed rank sum test.

Algorithms Scenario 69 node RDN 118 node RDNP-Value P-Value

HS-PABC vsHSA

I 1.415656224849e-009 1.415656224849e-009II 1.415656224849e-009 1.390302548729e-009


independent runs at 100% load level – 69 node RDN.

Median Std deviation

HS-PABC HSA HS-PABC HSA HS-PABC

0.515901409 0.5176626 0.5158997 0.001751687 4.14644E-060.370158 0.371478 0.370096 0.000884 0.0001620.352237 0.36821 0.352933 0.008454 0.005464

0.353342188 0.370414 0.351459 0.010975562 0.009082648

ndependent runs at 100% load level –118 node RDN.

Median Std deviation

HS-PABC HSA HS-PABC HSA HS-PABC

0.379684188 0.3831836 0.3796802 0.001672306 9.68724E-06 0.18060575 0.1840858 0.1806057 0.001740765 7.13674E-09 0.18807596 0.1976716 0.18807568 0.003243615 7.62759E-07

0.153444577 0.1814853 0.1531285 0.009251209 0.004382506

III 1.795360263143e-007 1.415656224849e-009IV 1.651603235538e-005 1.991413222361e-009

dx.doi.org/10.1016/j.asoc.2016.07.031




(a)

(b)

(c)

0 50 10 0 15 0 200 25 0 30 0 350 400 45 0 500 550 60 00.51 5

0.516

0.51 7

0.51 8

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0.52

0.52 1

0.522

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Fitness

( O

bje

ctive function)

Conver gence plot of fitness fun ction with HSA and Hybrid HS -PABC algo rithms ( Scenario-I)

HSA- Cap Placenment

Hybrid HS -PABC -Cap Placement

0 50 100 150 200 250 300 350 400 450 500 550 6000.37

0.371

0.372

0.373

0.374

0.375

0.376

Iterations

Fitness

(O

bje

ctive functions)

Conver gence plot of fitness fun ction with HSA and Hybrid HS -PABC algo rithms ( Sce nario-II )

HSA- DG Placement

Hybrid HS -PABC- DG Placement

0 50 100 150 200 250 300 350 400 450 500 550 6000.346

0.348

0.35

0.352

0.354

0.356

0.358

0.36

Convergence plot of fitness function with HSA and Hybrid HS -PABC algo rithms ( Sce nario- III)

Fit

ness

( O

bje

cti

ve f

un

cti

on

)

Iterations

HSA- DG + Capacitor Place ment

Hybrid HS -PABC - DG + Capacitor Place ment

(d)

0 50 100 15 0 200 250 300 350 400 450 500 550 6000.34

0.34 5

0.35

0.35 5

0.36

0.36 5

0.37

0.37 5

0.38

0.38 5

0.39

Convergence plot of fitness function with HSA and Hy brid HS -PABC algorithms ( Scenario-IV)

Iterations

Fitness

( O

bje

cti

ve functi

on)

HSA- Rec on + DG+Capa citor placement

Hybrid HS -PABC- Recon+ DG+ Capacitor placement

Fig. 12. (a–d) Convergence plot of fitness function with HS and hybrid HS-PABCalgorithms (Scenario- I–IV)—100% load level-69 node RDN.

(a)

(b)

(c)

0 500 10 00 1500 2000 2500 3000 3500 400 0 45 00 50000.37 8

0.38

0.38 2

0.38 4

0.38 6

0.38 8

0.39

0.39 2

Iterations

Fit

nes

s (

Ob

ject

ive

fun

ctio

n)

Convergence plot of fitness function with HS and hybrid HS-PABC algorithms ( Scenario-I)

HSA- Capacitor placement

Hybrid HS-PABC- Capacitor Placement

0 50 0 1000 1500 200 0 250 0 300 0 350 0 40 00 45 00 50 000.18

0.18 2

0.18 4

0.18 6

0.18 8

0.19

0.19 2

0.19 4Convergence plot of fitness fun ction with HS and hybrid HS-PABC algo rithms ( Sce nario-II)

Iterations

Fit

ness

( o

bje

cti

ve f

un

cti

on

)

HSA - DG Placement

Hybrid HS- PABC- DG Placement

0 50 0 100 0 150 0 200 0 250 0 30 00 35 00 4000 4500 500 00.18

0.19

0.2

0.21

0.22

0.23

Iter ations

Fit

ness

( O

bje

cti

ve f

uncti

on)

Conver gence plot of fitness fun ction with HSA and hybrid HS- PABC algo rithms ( Sce nario-III )

Hybrid HS-PABC DG + Capacitor Placement

HSA- DG + Ca pacitor Placement

(d)

0 30 0 600 90 0 120 0 15 00 180 0 21 00 240 0 27 00 3000 330 0 3600 390 0 42 00 450 0 48 00 50 000.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

Iter ations

Fit

ness

( O

bje

cti

ve f

un

cti

on

)

Convergence plot of fitness fun ction with HS and hybrid HS-PABC algorithms (Sce nario-IV)

Hybr id HS-PABC- Recon+ DG+ Capacitors

HSA - Rec on+ DG+ Capacitors

Fig. 14. (a–d) Convergence plot of fitness function with HSA and Hybrid HS-PABCalgorithm (Scenario- I–IV)—100% load level-118 node RDN.

(a) (b)

0.51

0.512

0.514

0.516

0.518

0.52

0.522

0.524

0.526

HS-PABC HSA

Fitn

ess

Algori thm

Scenario-I -69 node RDN

0.367

0.368

0.369

0.37

0.371

0.372

0.373

0.374

0.375

HS-PABC HSA

Fit

nes

s

Algori thm

Scenario-II - 69 nod e RDN

(c) (d)

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

HS-PABC HSA

Fit

nes

s

Algorithm

Scenario-III - 69 node RDN

0.32

0.33

0.34

0.35

0.36

0.37

0.38

0.39

HS-PABC HSA

Fit

nes

s

Algorithm

Scenario-IV - 69 node RDN

Fig. 13. (a–d) Box plot for the results of HS-PABC and HS algorithms—Scenarios I–IV for 69 node RDN.

dx.doi.org/10.1016/j.asoc.2016.07.031


M. K., J. S. / Applied Soft Compu

(a) (b

0.3740.3760.378

0.380.3820.3840.3860.388

0.39

HS-PABC HSA

Fit

nes

s

Algorithm

Scenario-I 118 node RDN

(c ) (d

0.18

0.183

0.186

0.189

0.192

0.195

0.198

0.201

0.204

HS-PABC HSA

Fit

nes

s

Algori thm

Scenario-III 118 node RDN

and H

4

qH

4dsiqoHo

4ptsd

HP

HH

snmsHwwbewm

Q7

705

706

707

708

709

710

711

712

713

714

715

716

717

718

719

720

721

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723

724

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729

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731

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733

734

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736

737

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749

750

751

752

753

754

755

756

757

758

759

760

761

762

763

764

765

766

767

768

Fig. 15. (a–d) Box plot for the results of HS-PABC

.4.1. Statistical analysisThe box plot and Wilcoxon rank sum test is used to show the

uality of the solution obtained by hybrid HS-PABC with respect toSA.

.4.1.1. Box-plot. Repeatedly 50 runs are performed to visualize theistribution of the samples in HS-PABC and HS algorithms with fourcenarios in box plot format as shown in Figs. 13 and 15(a–d). Its observed that the distribution of data based on minimum, firstuartile, median, third quartile, and maximum are close to eachther in proposed hybrid HS-PABC algorithm when compared withSA. The results in box plots reveal the robustness and superiorityf the proposed hybrid HS-PABC over standard HS algorithm.

.4.1.2. Wilcoxon rank sum test. Wilcoxon rank sum test is a non-arametric test utilized to show the statistical comparison betweenhe proposed hybrid HS-PABC and HS algorithm. This test assumeselection of different random samples with continuous probabilityistribution. The following hypotheses are tested.

0. The probability distributions of fitness values obtained by HS-ABC and HSA are identical.

1. Distribution of the fitness values differ between HS-PABC andSA

Wilcoxon rank sum test results are termed p-values (observedignificance level). When p-values less than or equal to level of sig-ificance (� = 5%), we reject the null hypothesis. The approximationethod is used to calculate the p-values and the results are pre-

ented in Table 17 to illustrate the efficiency of proposed hybrid


S-PABC algorithm over standard HS algorithm. For both the RDNsith scenario-IV, all the p-values are less than 0.05 (refer Table 17)hich signifies the choice of selecting alternative hypothesis. It can

e concluded that these test implies a significant statistical differ-nce between the HS-PABC and standard HS algorithm. Thereforee can come to the conclusion that the proposed HS-PABC canaintain superior performance than the standard HSA.

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)

0.176

0.178

0.18

0.182

0.184

0.186

0.188

HS-PAB C HSA

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nes

s

Algorithm

Scenario-II 118 node RDN

)

0.12

0.14

0.16

0.18

0.2

0.22

0.24

HS-PABC HSA

Fit

nes

s

Algori thm

Scenario-IV - 118 node RDN

S algorithms—Scenarios I–IV for 118 node RDN.

5. Conclusion

This article presents a hybrid HS-PABC algorithm basedapproach for network reconfiguration problem along with optimallocation and sizing of DG units and shunt capacitors for optimalplanning of distribution networks. Different test scenarios are sim-ulated on 69 and 118 node distribution network at varying loadconditions. The hybrid HS-PABC algorithm offers a promising andpreferable performance in terms of power loss reduction, improvedbus voltage profile than standard HSA at all discrete load levels.From the simulation results, it is inferred that integrated approachof network reconfiguration problem with the simultaneous instal-lation of DG units and shunt capacitors is an efficient approachtowards more loss reduction with the enhanced bus voltage profileas compared with individual loss reduction approaches. A statisticalanalysis is performed using 50 independent trials for each approachon the test system. To measure and prove the quality of the solu-tions obtained by proposed approach, box plot and Wilcoxon ranksum test are performed. The HS-PABC is a co-evolutionary algo-rithm that runs in parallel to accomplish the optimal solution inhigh-dimensional optimization problems. The simulation resultsconfirm the capability of proposed HS-PABC algorithm to reachthe optimal solution with faster convergence rate than standardHS algorithm. Finally, this work provides interesting basis forcombining promising aspects of different evolutionary algorithmtechniques into a new hybrid meta-heuristic algorithm that showssignificant performance.

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G Model ARTICLE IN PRESS - متلبی€¦ · water distribution networks is addressed using HSA incorpo-rated particle swarm algorithm (PSO) and the result outcomes are better than