optimal reconfiguration in radial distribution system

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This article was downloaded by: [National Institute of Technology - Warangal] On: 25 June 2014, At: 08:24 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Electric Power Components and Systems Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/uemp20 Optimal Reconfiguration in Radial Distribution System Using Gravitational Search Algorithm Y. Mohamed Shuaib a , M. Surya Kalavathi b & C. Christober Asir Rajan c a Department of Electrical and Electronics Engineering, Jawaharlal Nehru Technological University Hyderabad, B. S. Abdur Rahman University, Chennai, Tamilnadu, India b JNTUH College of Engineering, Hyderabad, India, Andhra Pradesh c Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry, India Published online: 24 Apr 2014. To cite this article: Y. Mohamed Shuaib, M. Surya Kalavathi & C. Christober Asir Rajan (2014) Optimal Reconfiguration in Radial Distribution System Using Gravitational Search Algorithm, Electric Power Components and Systems, 42:7, 703-715, DOI: 10.1080/15325008.2014.890971 To link to this article: http://dx.doi.org/10.1080/15325008.2014.890971 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Page 1: Optimal Reconfiguration in Radial Distribution System

This article was downloaded by: [National Institute of Technology - Warangal]On: 25 June 2014, At: 08:24Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK

Electric Power Components and SystemsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/uemp20

Optimal Reconfiguration in Radial Distribution SystemUsing Gravitational Search AlgorithmY. Mohamed Shuaiba, M. Surya Kalavathib & C. Christober Asir Rajanc

a Department of Electrical and Electronics Engineering, Jawaharlal Nehru TechnologicalUniversity Hyderabad, B. S. Abdur Rahman University, Chennai, Tamilnadu, Indiab JNTUH College of Engineering, Hyderabad, India, Andhra Pradeshc Department of Electrical and Electronics Engineering, Pondicherry Engineering College,Pondicherry, IndiaPublished online: 24 Apr 2014.

To cite this article: Y. Mohamed Shuaib, M. Surya Kalavathi & C. Christober Asir Rajan (2014) Optimal Reconfiguration inRadial Distribution System Using Gravitational Search Algorithm, Electric Power Components and Systems, 42:7, 703-715, DOI:10.1080/15325008.2014.890971

To link to this article: http://dx.doi.org/10.1080/15325008.2014.890971

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of theContent. Any opinions and views expressed in this publication are the opinions and views of the authors, andare not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon andshould be independently verified with primary sources of information. Taylor and Francis shall not be liable forany losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoeveror howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use ofthe Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Optimal Reconfiguration in Radial Distribution System

Electric Power Components and Systems, 42(7):703–715, 2014Copyright C© Taylor & Francis Group, LLCISSN: 1532-5008 print / 1532-5016 onlineDOI: 10.1080/15325008.2014.890971

Optimal Reconfiguration in Radial DistributionSystem Using Gravitational Search Algorithm

Y. Mohamed Shuaib,1 M. Surya Kalavathi,2 and C. Christober Asir Rajan3

1Department of Electrical and Electronics Engineering, Jawaharlal Nehru Technological University Hyderabad, B. S. AbdurRahman University, Chennai, Tamilnadu, India2JNTUH College of Engineering, Hyderabad, Andhra Pradesh, India3Department of Electrical and Electronics Engineering, Pondicherry Engineering College, Pondicherry, India

CONTENTS

1. Introduction

2. Load Flow

3. Mathematical Problem Statement

4. GSA

5. Test System

6. Result Analysis

7. Conclusion

References

Keywords: gravitational search algorithm, network reconfiguration, radialdistribution system, 33-bus radial distribution system, 69-bus radialdistribution system, tie Switches, I2R losses, distributed generation

Received 7 May 2013; accepted 19 January 2014

Address correspondence to C. Christober Asir Rajan, Department ofElectrical and Electronics Engineering, Pondicherry Engineering College,Pondicherry, 605 014, India. E-mail: asir [email protected] versions of one or more of the figures in the article can be found onlineat www.tandfonline.com/uemp.

Abstract—This article presents an innovative technique for solvingnetwork reconfiguration problems with an objective of minimizingnetwork I2R losses for an explicit set of loads. Amid many per-formance standards considered for optimal network reconfiguration,voltage constraint is an important one. This problem calls for deter-mining the best combination of feeders to be opened in the radial dis-tribution system so it provides optimal performance in the preferredsettings. In solving this problem, the gravitational search algorithmis used to reconfigure the radial distribution system; this algorithmpractices an optimal pattern for sustaining the radial nature of thenetwork at every stage of the solution, and it further allows proficientexploration of the solution space. The anticipated scheme minimizesthe objective function, which has been given in the problem formula-tion to reduce I2R losses in addition to balancing loads in the feeders.The solution technique involves determination of the best switchingcombinations and calculation of power loss and voltage profile. Thepracticality of the anticipated technique is validated in two distri-bution networks, where attained results are compared by means ofavailable literature. Correspondingly, it is seen from the results thatnetwork losses are reduced when voltage stability is enriched throughnetwork reconfiguration.

1. INTRODUCTION

Distribution systems are customarily designed radially, andthere are two categories of switches usually found in the systemenvisioned for both protection and configuration management.These are called closed and open switches; closed switches aretermed sectionalizing switches, and open switches are termedas tie switches. A radial distribution system (RDS) engages dif-ferent types of loads, such as industrial, commercial, domesticetc. The demand profile of these loads may possibly vary fromtime to time and will perhaps root imbalanced power flow inthe feeder, possibly leading to voltage collapse owing to lowvoltages. When there is greater I2R loss in the RDS, the voltagein the buses may violate the voltage constraint. This can affectthe quality of the power supply and the stability of the system.

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NOMENCLATUREbest(t) = best fitness at generation tFd

i (t) = total force acting on ith agentfitj(t) = fitness of jth agent at iteration tMai = active gravitational mass of ith agentMii = inertia mass of ith agentMpi = passive gravitational mass of ith agentNVB = number of buses that violate recommended volt-

age limitsPacc = real power accumulatedPi = real power load demand in bus iPi j(loss) = real power loss in line connecting ith and jth busPj = real power injection at jth bus

Qacc = reactive power accumulatedQi = reactive power load demand in bus iQ j = reactive power injection at jth busRi j = resistance in line connecting ith and jth busVi = voltage magnitude of bus iVj = voltage magnitude of jth busVL = upper limit of ith load busVmax = maximum voltage limitVmin = minimum voltage limitworst(t) = worst fitness at generation txd

i = positions of ith agent in dth dimensionδ j = phase angle at jth bus

One way to sustain the safety and reliability of the system is toreconfigure the RDS. This alteration of the network topologyis done by means of altering the status of the open and closedswitches. Certain switches can be operated remotely despitethe fact that the others are opened or closed by a lineman.When scheduling network reconfiguration, the demand profileof different consumers are considered to perceive if a particu-lar configuration is safe, is reliable, and has adequate capacityto supply all the customers. Once the feeder reconfigurationis done, overburdening of the feeder is reduced, I2R loss isminimized, and the voltage profile of the system is improved,thereby leading to voltage stability enhancement.

Venkatesh and Ranjan [1] presented a solution techniquethat used a fuzzy adaptation of evolutionary programming(FEP). This method is suitable when considering optimizationof multiple objectives. Sahoo and Prasad [2] advanced the al-teration of network topology using a fuzzy genetic approach(FGA) to maximize the voltage stability of the network. TheFGA practices an apt coding and decoding scheme for sustain-ing the radial nature of the network at every stage of geneticevolution in addition to using a fuzzy-rule-centered mutationcontroller for efficient search of the solution space. Abul’Wafa[3] described a load flow based on graph theory where the de-veloped load flow algorithm was integrated into a new heuristicsearch methodology for finding the minimum loss configurednetwork. Kashem et al. [4] proposed a branch loss-change tech-nique where they derived a loss-change formula to determinethe change of losses in the system when a branch exchangeis performed. The best branch exchange to be implementedis chosen at each successive operation that gives a maximumloss reduction without any constraints being violated.

There are many ways of handling a heuristic algorithmbased on the modification or adaptation of the algorithm. Theauthors in [5, 6] used heuristic algorithms for the reconfigu-ration problem to achieve the lowest I2R loss in the network,

but the algorithm is called heuristic until the best solution isproven to be the best. Rao et al. [7] presented a meta-heuristicharmony search algorithm (HSA) that was used concurrentlyto reconfigure and to detect optimal locations for installa-tions of distributed generation (DG) units. Nasiraghdam andJadid [8] introduced a fresh multi-objective artificial beecolony (MOABC) algorithm to explain RDS reconfigurationand hybrid (photovoltaic/wind turbine/fuel cell) energy systemsizing. MOABC outlines a potential solution for the optimiza-tion problem as a food source and the fitness value of the solu-tion as the nectar amount of the allied food source. Swarnkaret al. [9] investigated a method centered on adapted ant colonyoptimization (AACO) for the reconfiguration of RDS. AACOovercomes the drawbacks of the conventional ant colony opti-mization technique by encoding the discrete ant by means ofthe graph theory.

Savier and Das [10] discussed the impact of network recon-figuration on loss allocation based on a fuzzy multi-objectiveapproach, where loss allocation and network reconfigurationwhere considered together, in which the loss allocation is bythe quadratic loss allocation pattern and the network recon-figuration is framed using a fuzzy multi-objective problem.Kashem et al. [11] stated a geometrical approach for loss min-imization in which each loop in a network is represented as acircle, which is again derived from the relationship betweenthe change of loss due to the branch exchange and the powerflows in the branches. Abdelaziz et al. [12] projected real ant-behavior-inspired ant colony optimization implemented in thehypercube framework and a musician-behavior-inspired HSAto address the objective function. Wu et al. [13] minimizedpower loss in an RDS by network reconfiguration in the pres-ence of distributed generators, using an ant colony algorithm(ACA) to do so. Kumar and Jayabarathi [14] addressed thefeeder loss problem based on a bacterial-foraging optimizationalgorithm (BFOA). The optimization problem was considered

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Shuaib et al.: Optimal Reconfiguration in Radial Distribution System Using Gravitational Search Algorithm 705

as a non-linear problem and used to find the optimal solution.The BFOA was inspired by the social foraging behavior of Es-cherichia coli. The authors utilized this BFOA to configure anRDS to keep the load balancing so that I2R loss is minimized.Li et al. [15] recommended a tabu search (TS) approach toobtain near-optimal solutions of combinatorial optimizationproblems, which makes it appropriate to resolve the problemof RDS reconfiguration.

Gomes et al. [16] offered an approach for RDS reconfig-uration based on optimum power flow in which the branchstatuses are represented by continuous functions. Their arti-cle described a methodology that uses an optimal power flow(OPF) program based on a heuristic algorithm to solve theobjective function. Rao et al. [17] prescribed a newly devel-oped technique to find the optimal switching status of thereconfigured RDS, which was conceptualized using the musi-cal process of searching for an impeccable state of harmony;the algorithm is called the HSA. The HSA practices stochas-tic random search as an alternative to gradient search, whichremoves the necessity of derivative information. Gupta et al.[18] reduced I2R loss by creating an initial population for par-ticle swarm optimization (PSO) using a heuristic method inwhich the particles are adapted with the help of graph the-ory to generate feasible individuals. Installation costs were notconsidered in the approach. A step-by-step heuristic algorithmbased on sensitivity indexes was carried out by Rosseti et al.[19] to allocate DG with reconfiguration in electric distributionsystem to minimize energy losses.

In the light of the above progress, this article presents anoptimization technique called the gravitational search algo-rithm (GSA), which has been developed as a solution tech-nique for feeder reconfiguration. The application of the GSAfor minimization of I2R losses due to network reconfigurationis formulated as a multi-objective problem subject to opera-tional and electric constraints. The objectives considered areI2R loss reduction, voltage at buses to be kept within a spec-ified range, and persistence of network radial structure, evenafter reconfiguration in which all loads must be served. A loadflow program was developed, and the algorithm based on [20]is used to compute the power flow. It is then integrated into theGSA for determining the minimum loss RDS configuration.The distribution network presented by Baran and Wu [21] isused to demonstrate the reliability and efficacy of the proposedalgorithm.

This article is organized as follows. Section 2 describes theload flow, and Section 3 delivers the mathematical model ofthe problem. The GSA and its ability to solve the optimizationproblem are discussed in Section 4. The test system and resultanalysis are addressed in Sections 5 and 6, respectively. Finally,the article is concluded in Section 7.

2. LOAD FLOW

To accommodate the present emerging domestic, industrial,and commercial loads day by day, effective forecasting of theRDS is essential. To ensure effective planning with load trans-ferring, the load flow study of an RDS becomes of the utmostsignificant. Load flow analysis is concerned with describing theoperating state of an entire power system. Newton–Raphsonand fast decoupled load flow solution techniques are used tosolve well-behaved power systems; however, these are gener-ally unsuitable for solving load flow for RDSs because of theirlow X/R ratios of branches.

A section of the RDS has a sending-end bus (the ith bus) anda receiving-end bus (the jth bus). The line in connection withthese two sections has an impedance (Z = r + j x). The powerflow through this line can be in both directions. The power flowat the sending-end bus (Si = Pi + j Qi ) is different from thepower flow at the receiving-end bus (Sj = Pj + j Q j ).

A load flow algorithm [20] solves the power balance equa-tions at all buses and finds the corresponding voltage solution.At load buses, the load flow algorithm will solve for the busvoltage magnitude and phase angle. The known parameters ata load bus are the received real and reactive powers. Hence, aload flow must solve for the bus voltage magnitude in Eq. (1)[20] and phase angle in Eq. (2) [20]:

V 2j = −

[r P j + x Q j − V 2

i

2

]

+√(

r P j + x Q j − V 2i

2

)2

− [r2 + x2

] [P2

j + Q2j

], (1)

δ j = δi − sin−1

(x P j − r Q j

Vi Vj

). (2)

If the voltage magnitude and phase angle values are to becomputed for the receiving-end bus, the only variables neededare the receiving-end bus real and reactive power values, thesending-end bus voltage magnitude and phase angle value, andthe value of the line impedance connecting the two buses. Allvalues needed for the load bus calculations are easily attainablein practice.

2.1. Load Flow Algorithmic Steps

Step 1: Read system data structure.

Step 2: Go to slack bus.

Step 3: Initialize Pacc = 0 and Qacc = 0.

Step 4: Calculate P and Q for all buses.

Step 5: Calculate Vj and δ j for all buses using Eqs. (1) and(2).

Step 6: Determine Ploss and Qloss for all lines.

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706 Electric Power Components and Systems, Vol. 42 (2014), No. 7

Step 7: Update Pacc and Qacc using the formulas Pacc =Ploss + Pj and Qacc = Qloss + Q j .

Step 8: Go to the next bus and reprise Step 4 to 8 up until lastbus is reached.

Step 9: Check for convergence (Eq. (3)) and print the result;else, go to Step 2.

2.1.1. Convergence Criteria.

In this load flow, it is checked whether the sum of powersflowing out of the lines connected to each bus equals (or equalswithin a tolerable limit) the net power injected into that bus.Mathematically, convergence criteria for the presented loadflow are given in Eq. (3) [20]:

(PGi − P Di ) −⎡⎣∑

j

(Vi Vj Yi j cos(δi − δ j − θi j ))

⎤⎦ ≤ ε,

(QGi − Q Di ) −⎡⎣∑

j

(Vi Vj Yi j sin(δi − δ j − θi j ))

⎤⎦ ≤ ε.

(3)

3. MATHEMATICAL PROBLEM STATEMENT

3.1. Total Real and Reactive Power Loss

The real power loss in the line connecting the ith and jth busis given by

Pi j(loss) = [Pj ]2 + [Q j ]2

[Vi ]2∗ Ri j , (4)

Qi j(loss) = [Pj ]2 + [Q j ]2

[Vi ]2∗ Xi j . (5)

The total real power loss of an RDS having n buses and n – 1branches is given by

PT,loss =n∑

i=1

Pi j(loss), (6)

QT,loss =n∑

i=1

Qi j(loss), (7)

3.2. Voltage Deviation Index (VDI)

The VDI [1] is calculated using the formula

VDI =√∑NV B

i=1 (VLi − VL )2

N. (8)

To enumerate the degree of limits violation imposed onvoltages at buses in an RDS, the VDI is well-defined, where

NVB is the number of buses that violate the recommendedvoltage limits, and VL is the upper limit of the ith load bus.In the course of reconfiguration, if the state of the system hasvoltage limit violations, the anticipated solution must try tolessen the VDI. When a branch is switched on and another isswitched out in a loop, the solution space is no longer con-tinuous. The variable that defines the status of a branch as towhether it is switched in/out adopts discrete states of zero orone. Owing to the discontinuous and discrete nature of theproblem, classical techniques are rendered inappropriate, andthe practice of global search techniques is essential.

3.3. Objective Function for Network Reconfigurationin RDS

The objective is to minimize the I2R losses in an RDS, therebyenhancing the voltage profile of the system. This is attainedby finding out the best set of branches to be switched out suchthat the subsequent RDS experiences the lowest I2R loss andhas the best voltage profile.

The mathematical model of the problem can be expressedby the following expression:

minimize f =n∑

i=1

Pi j(loss) +√∑N V B

i=1 (VLi − VL )2

N,

subject to Vmin ≤ |Vi | ≤ Vmax. (9)

The first term in the Eq. (9) represents the total I2R loss inthe system, and the second term denotes the VDI.

4. GSA

This article adopts a new search algorithm—the GSA—as thesolution technique for feeder reconfiguration. This algorithmwas originally developed by Rashedi et al. [22] to addressvarious non-linear problems. Duman et al. [23] proposed theGSA to decide the optimal settings for control variables ofthe optimal power flow problem in power systems. To find theoptimum emission dispatch, optimum fuel cost, best compro-mising emission, and fuel cost, Mondal et al. [24] applied theGSA to solve the optimization problem.

In this article, the GSA is applied to minimize feeder lossesby reconfiguring the RDS. It is formulated as a real powerloss minimization problem subject to operational and electricconstraints. The GSA is based on the law of gravity and massinteractions. In this algorithm, the searcher agents are a groupof masses that act together with each other based on Newto-nian gravity and the laws of motion. The algorithm considersagents as objects consisting of different masses. Complete

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Shuaib et al.: Optimal Reconfiguration in Radial Distribution System Using Gravitational Search Algorithm 707

agents move due to the gravitational attraction force actingamong them, and the advancement of the algorithm directs themovements of all agents globally headed toward agents withheavier masses. Every agent in the GSA is specified by fourparameters: the position of the mass in the dth dimension, in-ertia mass, active gravitational mass, and passive gravitationalmass.

4.1. GSA Algorithmic Steps

Step 1: Initialization of the agents. Initialize the positions of Nnumbers of agents randomly chosen within the givensearch interval using Eq. (10):

Xi = (x1

i , . . . , xdi , . . . , xn

i

)for i = 1, 2, . . . , N .

(10)

Step 2: Fitness evolution and best fitness computation foreach agent. Perform the fitness evolution for all agentsat each iteration; also compute the best and worst fit-ness at each iteration defined for minimization prob-lems in Eqs. (11) and (12):

best(t) = minj∈{1,...,N }

fit j (t), (11)

worst(t) = maxj∈{1,...,N }

fit j (t). (12)

Step 3: Compute gravitational constant G. Compute gravita-tional constant G at iteration t using Eq. (13):

G (t) = Goe(−αt/T ). (13)

Step 4: Calculate the mass of the agents; calculate gravita-tional and inertia masses for each agent at iteration tby Eq. (11):

Mai = Mpi = Mii = Mi (i = 1, 2, . . . , N ),

mi (t) = fiti (t) − worsti (t)

best(t) − worst(t),

Mi (t) = mi (t)∑Nj=1 m j (t).

(14)

Step 5: Calculate accelerations of the agents; compute theacceleration of the ith agents at iteration t, Eq. (15):

adi (t) = Fd

i (t)

Mii (t); (15)

Fdi (t), the total force acting on the ith agent, is calcu-

lated from Eq. (16):

Fdi (t) =

∑j∈K best, j �=i

rand j Fdi j (t). (16)

Step 6: Update velocity and positions of the agents; computevelocity and position of the agents at the next iteration(t + 1) using Eq. (17):

vdi (t + 1) = randi × vd

i (t) + adi (t),

xdi (t + 1) = xd

i (t) + vdi (t + 1). (17)

Step 7: Repeat Steps 2 through 6 until iterations reach theirmaximum limit; return the best fitness computed atthe final iteration as a global fitness of the problem andthe positions of the corresponding agent at specifieddimensions as the global solution of that problem.

4.2. GSA Algorithm for Reconfiguration of RDS

An RDS can have several loops. Each loop has severalbranches. Any one of these branches forming the loops mustbe switched out such that the radial nature of the RDS ismaintained. The switching in/out of branches alters the flowof power and changes the resulting kilowatt losses and volt-age profile. The objective of the solution technique is to de-termine that combination of branches such that the resultingRDS yields the minimum kilowatt losses and the best voltageprofile.

Let vector Xi = (x1i , . . . , xd

i , . . . , xni ) (i = 1, 2, . . ., N)

refer to the combination of branches switched out in the RDSsuch that the ID number of branches switched out in the ithloop is stored in variable Xi. The GSA initially chooses NCcombinations as the starting guesses. The steps of the GSA toreconfiguration problem of RDS are given in what follows.

4.2.1. Algorithmic Steps

Step 1: Initialization. Initialize the positions of the N numberof agents, which is the different switching statusesrandomly chosen within the given search interval us-ing Eq. (10) and check for its radiality as given in[20].

Step 2: Best fitness computation for each combination ofswitches. Perform the fitness evaluation for all statusof switches at each iteration that is radial in structurefor the given systems; also compute the best and worstfitness, which is again the network configuration thatgives the least I2 > R loss and the maximum I2R lossat each iteration defined for minimization problemsin Eqs. (11) and (12).

Step 3: Attain gravitational constant G. Find gravitationalconstant G at iteration t using Eq. (13).

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708 Electric Power Components and Systems, Vol. 42 (2014), No. 7

GSA parameters 33-Bus 69-Bus

N = number of agents 2000 2500Maximum iterations 500 750α 20 20G0 100 100

TABLE 1. GSA parameters

Step 4: Estimate the mass of the agents. Calculate gravita-tional and inertia masses for each agent at iteration tby Eq. (14).

Step 5: Evaluate accelerations of the agents; compute theacceleration of the ith agent at iteration t using Eqs.(15).

Step 6: Find the velocity and the position of agents; calculatevelocity and position of agents at the (t + 1)th iterationusing Eq. (17).

Step 7: Repeat Steps 2 throught 6 until iterations reach theirmaximum limit; return the best switching combina-tion that ultimately gives the minimal I2R losses foundat the final iteration as an optimal network topologyof the problem.

4.2.2. Parameters for GSA Algorithm.

To get an optimal solution using the GSA, the parameters inTable 1 have been used to find the optimum switching statusdue to which the resulting RDS yields the minimum I2R lossand the best voltage profile.

The performance of the GSA in network reconfigurationof an RDS is estimated. Twenty independent trials have beenmade, with 2000 agents and 500 iterations per trial for the33-bus test system and 2500 agents and 750 iterations per trial

for the 69-bus test system. The α value and gravitational timeconstant G0 are set to 20 and 100, respectively, in both cases.The optimal results obtained for network reconfiguration usingthese considerations in the algorithm are tabulated in Tables 2and 3.

5. TEST SYSTEM

5.1. 33-Bus Test System

The I2R loss minimization by reconfiguration is executed on a33-bus RDS (Figure 1), and the load data are given in [17]. Thetest system consists of 33 buses, 32 lines, and 5 tie switches.The first bus is considered as the substation bus. Loads areconnected to all buses except the first bus, which is the sub-station bus. The total real power load and reactive power loadof this test system are 3715 kW and 2300 kVAR, respectively.The substation voltage is 12.66 kV.

5.2. 69-Bus Test System

To validate the proposed method, the reconfiguration processis carried out on a 69-bus RDS (Figure 2). The load and trans-mission line details were given in [10]. The test system consistsof 69 buses, 68 lines, and 5 tie switches. The total real powerload and reactive power load of this test system are 3801.89kW and 2694.1 kVAR, respectively. The substation voltage is12.66 kV.

6. RESULT ANALYSIS

6.1. Case A

The results of the 33-bus test system are given in Case A. Theprogram is coded in MATLAB software (The MathWorks,Natick, Massachusetts, USA), which is installed on an Intel R©CoreTM i5-2410M CPU @ 2.30 GHz with a setup memory of4.00 GB and a 64-bit operating system (Dell Inspiron N5110).

Final configurationTechnique Initial

configuration RGA Heuristic OPF heurisic HSA BFOA GSAAuthor Rao et al. Zhu Gomes et al. Gomes et al. Rao et al. Kumar and Proposed

[17] [28] [25] [16] [17] Jayabarathi [14] algorithmYear 2011 2002 2005 2006 2011 2012 2013

Open switches s33, s34, s35,s36, s37

s7, s9, s14,s32, s33

s7, s9, s14,s32, s37

s7, s9, s14,s32, s37

s7, s10, s14,s37, s36

s7, s9, s13,s14, s32

s7, s14, s28,s9, s32

Power loss (kW) 202.418 139.53 136.57 136.57 138.06 135.78 134.61Loss reduction

(%)— 31.07 32.53 32.53 31.793 32.92 33.49

Minimum voltage(p.u.)

0.9237 0.9315 0.9502 0.9502 0.9342 0.9589 0.9604

TABLE 2. Case A: Result analysis

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Final configurationTechnique Initial

configuration FMOA Meta-heuristic Meta-heuristic GSAAuthor Savier and Savier and Swarnkar et al. HSA Proposed

Das [10] Das [10] [6] Rao et al. [7] algorithmYear 2007 2007 2011 2013 2013

Open switches s69, s70, s71,s72, s73

— s14, s56, s61,s69, s70

s69, s18, s13,s56, s61

s14, s58, s61,s69, s70

Power loss (kW) 224.894 99.59 99.59 99.35 98.57Loss reduction (%) — 55.72 55.72 55.82 56.17Minimum voltage (p.u.) 0.9092 0.9483 0.9428 0.9428 0.9495

TABLE 3. Case B: Result analysis

Before reconfiguration, tie switches s33, s34, s35, s36, ands37 are kept open. For the given total real power load of 3715kW, the I2R loss is obtained as 202.418 kW in the base case.The minimum voltage is registered as 0.9237 p.u. at the 18thbus. The optimal network configuration for loss reduction isachieved after applying the GSA, when all tie switches s33,s34, s35, s36, and s37 are closed and sectionalizing switchess7, s14, s28, s9, and s32 are now opened. As a result, the I2Rloss is reduced to 134.6104 kW from the base case of 202.418kW, witnessing 67.808 kW of real power loss reduction. Theworst voltage is found to be 0.96044 p.u. at the 32nd bus, alsofalling within the voltage limits.

In 2005 and 2006, Gomes et al. [16, 25] carried out re-configuration of a 33-bus RDS using a heuristic algorithmand reduced the I2R loss to 136.57 kW. In 2011, Rao et al.

[17] proposed the HSA and lessened the losses to 138.05 kW.Kumar and Jayabarathi [14] suggested the BFOA in 2012 toreduce the losses to 135.78 kW. In this article, the GSA isproposed and loss reduction is 33.49%, where the percentageof loss reduction is more when compared to previous results.This proves the effectiveness of the proposed algorithm. Theresults of Case A and comparison of the proposed algorithmwith other optimization techniques are tabulated in Table 2.The optimally reconfigured structure of the RDS is drawn inFigure 3. The voltage profile of the RDS before and after re-configuration is shown in Figure 4.

6.2. Case B

The results of the 69-bus test system are given in Case B. Theprogram is coded in MATLAB software, which is installed in

FIGURE 1. Line diagram of 33-bus RDS.

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710 Electric Power Components and Systems, Vol. 42 (2014), No. 7

FIGURE 2. Line diagram of 69-bus RDS.

an Intel R© CoreTM i5-2410M CPU @ 2.30 GHz with a setupmemory of 4.00 GB and a 64-bit operating system. Beforereconfiguration, switches s69, s70, s71, s72, and s73 are open,and for the total real power load of 3801.89 kW, the I2R lossis 224.894 kW in the base case. The minimum voltage isregistered as 0.9092 p.u. at the 65th bus. The optimal networkconfiguration for loss reduction is achieved after applying theGSA, where tie switches s71, s72, and s73 are closed, andsectionalizing switches s14, s58, and s61 are now opened. Asa result, the I2R loss is reduced to 98.5718 from 224.894 kW,witnessing 126.3231 kW of real power loss reduction. Theworst voltage is found to be 0.9495 p.u. at the 61st bus.

Savier and Das in 2007 [10] carried out network reconfigu-ration using a fuzzy multi-objective approach and reduced I2Rlosses to 99.59 kW. In 2011, Swarnkar et al. [6] proposed ameta-heuristic algorithm to answer the reconfiguration prob-lem and lessen the losses to 99.59 kW. Rao et al. [7] in 2013introduced a meta-heuristic HSA to do network reconfigura-tion and decreased losses to 99.35. In this article, the GSAis proposed and the loss reduction is 56.17%, where the per-centage of loss reduction is more when compared to all resultsarrived using various algorithms; this proves the efficacy of theproposed algorithm. The results of Case B and the comparisonof the proposed algorithm with other optimization techniques

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FIGURE 3. Optimally reconfigured topology of 33-bus RDS.

are tabulated in Table 3. The optimally reconfigured structureof the RDS is drawn in Figure 5. The voltage profiles of theRDS before and after reconfiguration are shown in Figure 6.

6.3. Results Study of Network Reconfigurationin the Presence of DG Units

Kumar and Navuri [26] determined the optimum positions andsize of DG units with the objective of improving the voltageprofile and loss reduction in an RDS. The selection of can-didate buses was carried out using a loss sensitivity factor(LSF), whereas the estimation of optimal DG unit size wasby means of simulated annealing (SA). Gandomkar et al. [27]lessened distribution losses by incorporating DG units to theRDS through implementing a genetic algorithm to the TS ap-proach. The effectiveness of the GSA is verified by installingDG units in 33- and 69-bus RDSs. The scenario has been seg-

FIGURE 4. Comparison of voltage profile of 33-bus RDS.

mented into Item I and Item II. In both scenarios, DG units areinstalled after network reconfiguration.

6.3.1. Item I

The I2R loss in the 33-bus test system after reconfiguration is134.6104 kW. After the installation of DG to the reconfigurednetwork, the losses were reduced to 71.12 kW, presenting a lossreduction of 64.86%. The candidate bus locations selected forthe installation of DG units are 19, 23, and 22.

6.3.2. Item II

In the 69-bus test system, I2R loss after reconfiguration is98.57 kW. The losses were reduced to 50.25 kW after installa-tion of DG units to the reconfigured network, witnessing a lossreduction of 77.88%. The candidate bus locations selected forthe installation of DG units are 14, 40, and 48.

6.3.3. Performance of Proposed Algorithm

In 2013, Rao et al. [7] installed DG units after reconfigurationto minimize I2R loss. The authors reduced the losses in 33-and 69-bus test systems to 97.13 and 51.30 kW, respectively.

The results of the test systems in the establishment of DGafter reconfiguration and the results comparison of the pro-posed algorithm with [7] are tabulated in Table 4. The voltageprofiles of the 33- and 69-bus RDSs in the presence of a DGunit after reconfiguration are shown in Figures 7 and 8 re-spectively. The result comparison shown in Table 4 proves theefficacy of the proposed algorithm.

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FIGURE 5. Optimally reconfigured topology of 69-bus RDS.

FIGURE 6. Comparison of voltage profile of 69-bus RDS.FIGURE 7. Comparison of voltage profile of 33-bus RDS inthe presence of DG.

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Rao et al. (2013) [7], meta-heuristicHSA Proposed algorithm (GSA)

Scenario 33-Bus 69-Bus 33-Bus 69-Bus

Base case Open switches s33, s34, s35,s36, s37

s69, s70, s71,s72, s73

s33, s34, s35,s36, s37

s14, s58, s61,s69, s70

Power loss (kW) 202.67 225 202.418 224.894Minimum voltage

(p.u.)0.9131 0.9092 0.9237 0.9495

Item I (onlyreconfiguration)

Open switches s7, s14, s9,s32, s37

s69, s18, s13,s56, s61

s7, s14, s28,s9, s32

s14, s58, s61,s69, s70

Power loss (kW) 138.06 99.35 134.61 98.57Minimum voltage

(p.u.)0.9342 0.9428 0.9604 0.9495

Loss reduction (%) 31.88 55.85 33.49 56.17Item II (DG

installation afterreconfiguration)

Open switches s7, s14, s9,s32, s37

s69, s18, s13,s56, s61

s7, s14, s28,s9, s32

s14, s58, s61,s69, s70

Size of DG in kW(bus number)

269 (32)161 (31)661 (30)

1067 (61)353 (60)426 (58)

694 (19)1998 (23)1066 (22)

357 (14)139 (40)784 (48)

Power loss (kW) 97.13 51.3 71.12 50.25Minimum voltage

(p.u.)0.9479 0.9619 0.9772 0.9625

Loss reduction (%) 52.07 77.2 64.86 77.66

TABLE 4. Performance of GSA in the presence of DG

FIGURE 8. Comparison of voltage profile of 69-bus RDS inthe presence of DG.

7. CONCLUSION

This article proposes a GSA for optimal reconfiguration of anRDS to achieve the best voltage profile and minimal kilowattlosses. A VDI is established herein that computes the deviancyof load bus voltages from the recommended limits. This in-dex is minimized in the proposed algorithm to improve powerquality. The RDS reconfiguration is a discontinuous solutionspace problem with discrete zero–one variables and an objec-tive that requires the determination of the best combination offeeders in the RDS to be switched out so the resulting RDSgives the minimum kilowatt losses and the best voltage profile.

The GSA technique is found particularly suitable for solvingoptimization problems with discontinuous solution space andobjectives when the global optimum is desired. The optimalsolution in the GSA is obtained by movement of agents in thesearch space, and its direction is based on the overall forceof all other agents. Therefore, the search direction toward theoptimal solution is effective in this algorithm. The proposedmethod is tested on established 33- and 69-bus RDSs. Theresults obtained demonstrate that the GSA method optimallyreconfigures the RDS, minimizing the kilowatt losses and ob-taining the best voltage profile.

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BIOGRAPHIES

Y. Mohamed Shuaib received his B.E in electrical and elec-tronics engineering from University of Madras in 1994 andhis M.E. in power system engineering from Annamalai Uni-versity, Tamilnadu, India, in 2002. He is a research scholarin Jawaharlal Nehru Technological University, Hyderabad, In-dia, and since 2003 has been working as an assistant professor(selection grade) in the Department of Electrical and Elec-tronics Engineering, B.S. Abdur Rahman University, Chennai.His current research includes capacitor placement and recon-figuration in radial distribution networks in the presence ofdistributed generation.

M. Surya Kalavathi received her B.Tech and M.Tech from SriVenkateswara University, Tirupathi, Andhra Pradesh, India, in1988 and 1992, respectively. She obtained her doctoral degree

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from Jawaharlal Nehru Technological University, Hyderabad,and her post-doctoral from Carnegie Mellon University, USA.She is presently the professor in the Department of Electricaland Electronics Engineering at Jawaharlal Nehru Technologi-cal University Hyderabad College of Engineering, Kukatpally,Hyderabad, India. She has published 16 research papers andis presently guiding five Ph.D. scholars. Her research inter-ests include simulation studies on transients of different powersystem equipment.

C. Christober Asir Rajan was born in 1970 and received hisB.E. (distn.; electrical and electronics) and his M.E. (distn.;

power systems) from Madurai Kamaraj University, Madurai,India, in 1991 and 1996, respectively. He received his post-graduate degree in DI.S. (distn.) from Annamalai University,Chidambaram, in 1994. He received his Ph.D in power sys-tem from Anna University, Chennai, India (2001–2004). Heis currently working as an associate professor in the ElectricalEngineering Department at Pondicherry Engineering College,Pondicherry, India. He has published technical papers in inter-national and national journals and conferences. His areas ofinterest are power system optimization, operational planning,and control.

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