tabu search algorithm distribution system reconfiguration using a modified tabu search algorithm

8/13/2019 Tabu search algorithm Distribution system reconfiguration using a modified Tabu Search algorithm

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Electric Power Systems Research 80 (2010) 943953

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Electric Power Systems Research

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Distribution system reconguration using a modied Tabu Search algorithm

A.Y. Abdelaziz , F.M. Mohamed, S.F. Mekhamer, M.A.L. BadrElectrical Power and Machines Department, Faculty of Engineering, Ain Shams University, 1 Elsarayat Street, Abdo Basha Square Abbassia, Cairo, Egypt

a r t i c l e i n f o

Article history:Received 31 March 2008Received in revised form 30 October 2009Accepted 3 January 2010Available online 20 January 2010

Keywords:Distribution system recongurationPower loss reductionModied Tabu Search

a b s t r a c t

This article presents an efcient meta-heuristic method for reconguration of distribution systems. Amodied Tabu Search (MTS) algorithm is used to recongure distribution systems so that active powerlosses are globally minimized with turning on/off sectionalizing switches. TS algorithm is introduced

with some modications such as using a tabu list with variable size according to the system size. Also,a random multiplicative move is used in the search process to diversify the search toward unexploredregions. The Kirchhoff algebraic method is adopted to check the radial topology of the system. A salientfeature of the MTS method is that it can quickly provide a global optimal or near-optimal solution to thenetwork reconguration problem. To verify theeffectiveness of theproposed approach,the effectof loadvariation is taken into consideration and comparative studies are conducted on three test systems withrather encouraging results. The obtained results, using the proposed MTS approach, are compared withthat obtained using other approaches in the previous work.

2010 Elsevier B.V. All rights reserved.

1. Introduction

The subject of minimizing distribution systems losses hasgained a great deal of attention due to the high cost of electri-cal energy and therefore, much of current research on distributionautomation has focused on the minimum-loss conguration prob-lem. There are many alternatives available for reducing losses atthe distribution level: reconguration, capacitor installation, loadbalancing, and introduction of higher voltage levels. This researchfocuses on the reconguration alternative.

Network reconguration is the process of changing the topol-ogy of distribution systems by altering the open/closed statusof switches. Because there are many candidate-switching com-binations in the distribution system, network reconguration isa complicated combinatorial, non-differentiable constrained opti-mization problem. Two types of switches are used in primarydistribution systems. There are normally closed switches (section-alizing switches) and normally open switches (tie switches). Thosetwo types of switches are designed for both protection and con-guration management. The change in network conguration isachieved by opening or closing of these two types of switches insuch a way that the radiality of the network is maintained.

The reconguration algorithms can be classied by the solutionmethods that they employ: those based upon a blend of heuristicsand optimization methods, those making use of heuristics alone,

Corresponding author. Tel.: +20 101372930.E-mail addresses: [email protected] , [email protected]

(A.Y. Abdelaziz).

and those using some from of articial intelligence (AI). Numerousresearchers advocate the use of a blend of heuristics and optimiza-tion techniques. The blend of the two types of technique permitsthe problem to retain a certain degree of accuracy, while assuringconvergence and an acceptable solution time.

InRef. [1] , a branch exchange method thatconsidered the onoff conditions of the sectionalizing switches in discrete numbers wasdeveloped [1] . Since themethod is based on heuristics, it is noteasyto take a systematic way to evaluate an optimal solution.

Two different methods with varying degree of accuracy toapproximate power ow in systems were proposed in Ref. [2] . Thesearch method has an acceptableconvergencecharacteristic. How-ever, it can get stuck in local minimum. The method is very timeconsuming due to the complicated combinations in large-scale sys-tems.

An expert system for feeder reconguration, based upon exten-sions of the rules of Ref. [1] was presented in Ref. [3], with thepotential of handling realistic operating constrains. The approachtaken is set up a decision tree to represent the various switch-ing operations available. This strategy is efcient for trees that arenot too large. However, as a search tree becomes larger, a greatamount of time can be spent searching for the optimal solution. Toguarantee an optimal solution an exhaustive tree search should beused.

A linear programming method using transportation techniquesanda new heuristic search method forcomparison with previouslydeveloped heuristic techniques which are based on an optimalload ow analysis were presented in Ref. [4] . This study indicatesthat linear programming, in the form of transportation algorithms,is not suitable for application to feeder reconguration since the

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944 A.Y. Abdelaziz et al. / Electric Power Systems Research 80 (2010) 943953

power loss function is not linear whilst heuristic approaches,although not optimal, can provide substantial saving if properlyformulated.

Based on partitioning the distribution network into groups of load buses, the line section losses between the groups of nodes areminimized [5] . By dividing the distribution network into groups of busses, the combinatorial nature of the reconguration problem isovercome, while simultaneously minimizing losses.

In recent years, meta-heuristic methods have been studied forsolving combinatorial optimization problems to obtain an opti-mal solution of global minimum. Typical meta-heuristic methodsinclude Simulated Annealing (SA), Genetic Algorithm (GA), andTabu Search (TS).

A two-stage solution methodology based on a modied simu-lated annealing technique for solving the reconguration problemof distribution systems was proposed in Ref. [6] . In Ref. [7] , a mod-ied SA technique for network reconguration for loss reductionin distribution systems was presented. An efcient perturba-tion scheme and an initialization procedure determining a betterstarting temperature for the simulated annealing approach wereproposed. This method can get a solution better than that obtainedusing the method presented in Ref. [5]. This solution algorithmgives a near-optimal solution but this method does not work sowell in the case of load variation.

A GA based method for feeder reconguration was proposed inRef. [8] . Strings which represent switch status, a tness functionconsisting of total system losses, and penalty values of volt-age drop limit and current capacity limit were formed. Sampleresults demonstrate that, although the minimal loss solutions wereobtained, solution time was prohibitive.

An articial neural network based method for feeder recong-uration was presented in Ref. [9]. However, such technique canencounter difculties, such as getting trapped in local minima,increased computational complexity, and not being applicable tocertain objectivefunctions. This ledto theneed of developing a newclass of solution methods that can overcome these shortcomings.

A parallel Tabu Search (PTS) based method for feeder recong-

uration has been proposed in Ref. [10] . PTS introduces two parallelschemes. One is the decomposition of the neighborhood with par-allel processors to reduce computational efforts. The other is themultiplicity of the tabu length to improve the solution accuracy.PTS algorithm gives results better than results obtained by SA, par-allelSimulatedAnnealing(PSA), GA,and parallel Genetic Algorithm(PGA).InRef. [11] , a TSalgorithmforsolvingthe problem ofnetworkrecongurationin distributionsystems in order to reducethe resis-tive line losses under normal operating conditions was presented.A method for checking system radiality based on an upward-nodeexpression, which has been developed in solving the problem of restorative planning of power systemwas proposed. In Ref. [12] , anefcienthybrid algorithmof SA andTS method for feederrecongu-ration to improve the computation time and convergence property

was proposed. In Ref. [13] , a modied Tabu Search (MTS) basedalgorithmfor reconguration of distribution systems has been pro-posed. The TS algorithm was introduced with some modicationssuch as using a tabu list with variable size to prevent cycling andto escape from local minimum. Also, a constrained multiplicativemove wasused in thesearch process to diversifythe searchprocesstoward unexplored regions.

Zhang et al. [14] presented an Improved Tabu Search (ITS)algorithm for loss-minimization reconguration in large-scale dis-tribution systems. In ITS algorithm, mutation operation, a mainoperator used in genetic algorithm, is introduced to weaken thedependence of global search ability on tabu length. In addition,the candidate neighborhood, which only contains several optimalswitch exchanges in each tie switch associated loop network, is

designed to improve local search efciency and to save a large

Fig. 1. 16-Node distribution system.

amount of computing time. The ITS algorithm in Ref. [14] wasapplied to the 119-node system and gave an optimal solution.

In this article, an enlarged version of Ref. [13] is introduced tosolve the reconguration problem.The proposedmethod is appliedto large-scale networks to show the effectiveness of the modiedTabu Search algorithm. In comparison with Ref. [14] in which themutation operation of GA is used to weaken the dependence of

global search ability on tabu length, on the other side, we use adynamic tabu list with variable size according to the system sizeand a multiplicative move is applied to diversify the search processand improve the local search efciency of Tabu Search to reach theglobalsolution. Also, theeffect of variationof load is taken into con-sideration to show the capability of the proposed algorithm (MTS)to work at different load levels.

To verify the effectiveness of the proposed method, compar-ative studies are conducted on three test systems with ratherencouraging results. The proposed method is applied to a 16-nodesystem, a 69-node system, and a 119-node system. The results,obtained using the proposed MTS approach, are compared with

Fig. 2. Flow chart of Tabu Search algorithm.


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A.Y. Abdelaziz et al. / Electric Power Systems Research 80 (2010) 943953 945

Fig. 3. Flow chart for checking system radiality.

results obtained using other modern techniques to examine theperformance of the proposed approach.

2. Problem formulation

Generally, there are two types of switches in distribution sys-tems: tie switch and sectionalizing switch. As shown in Fig. 1,switches in dotted branches connecting nodes(1014), (511), and(716) are tie switches, and switches in other continuous branchesare sectionalizing switches. The tie switches are normally open

and the sectionalizing switches are normally closed. When theoperating conditions have been changed, feeder reconguration isperformed by the opening/closing of these two types of switchesto reduce resistive line losses.

That is,a tieswitch may be closedfor thepurpose of transferringloads to different feeders, and, at the same time, a sectionalizingswitchshould be openedto maintain theradial structureof thedis-tribution network. For example, in Fig. 1, when the loads of feeder2 become heavy under normal operating conditions, the tie switchconnecting nodes (511) may be closed to transfer the load at node11fromfeeder 2 tofeeder1 and atthe sametimethe sectionalizingswitch connecting nodes (911) must be opened to maintain theradial structure of the network.

The objective of the reconguration is to minimize the dis-

tribution losses with turning on/off sectionalizing switches. The

reconguration problem has the following constrains:

1. Power ow equations.2. Upper and lower bounds of nodal voltages.3. Upper and lower bounds of line currents.4. Feasible conditions in terms of network topology.

Mathematically, the problem can be formulated as follows:Cost function:

Min Z =L

i= 1

r i P 2i + Q

2i

V 2i(1)

Subject to:

g ( x) = 0 (2)

V mini < V i < V maxi (3)

I mini < I i < I maxi (4)

det( A) = 1 or 1 radial system (5)

det( A) = 0 not radial (6)

where Z : objective function (kW); L: no. of branches; P i: active

power loss at sending endof branch i; Q i: reactive power at sending


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Fig. 4. Optimal conguration of the 16-node system.

end of branch i; V i: voltage at sending end of branch i; I i: line cur-rent at branch i; g ( x): power ow equations; V mini : lower voltagelimit (taken to be 0.9 p.u); V maxi : upper voltage limit (taken to be1 p.u); I mini : lower current limit; I

maxi : upper current limit; A: bus

incidence matrix; r i: resistance of branch i.

3. Tabu Search

Tabu Search is one of the modern heuristic search methodsfor combinatorial optimization problems, based on neighborhoodsearch with local optimaavoidance, which modelshuman memoryprocesses. Tabu Search was initially proposed by Glover and manyother authors have applied similar ideas to various classical prob-lems [15,16] . Tabu Search (TS) canbe considered as a neighborhoodsearch method which is more elaborate than the descent method.

Like any local search method (LS), TS needs three basic compo-nents: a conguration structure, a neighborhood function denedon the conguration structure, and neighborhood examinationmechanism. The rst component denes the search space of S of the application, the second associates with each point of the searchspace which is a subset of S, while the third one prescribes the wayof going from one conguration to another.

3.1. Conguration space

Conguration space is the set of allowed congurations overwhich the optimal system conguration is to be searched for Ref.[6] . In the present case, it is considered that the distribution systemunder study has a number of nodes and corresponding sectionaliz-ing and tie switches. The open/closed status of each sectionalizingswitch and tie switch determines the network conguration of thesystem. Hence the conguration space = 1 2 , where 1 isthe set of sectionalizing switches and 2 is the set of tie switches.

3.2. Tabu list

Thetabu list is another importantconcept in Tabu Search. Whenthe move is accepted, the move and its reverse are recorded in the

tabu list. When the move is recorded in tabu list, it is not allowedto visit or use this move again but this restriction can be violatedunder Aspiration Criterion as describedbelow. The basic role of thetabu list is to identify cycling and escape from local minimum. Thedimension of the tabu list is updated every iteration according tothe problem size.

Fig. 5. Voltage prole before and after reconguration for the 16-node system.

Fig. 6. 69-Node distribution system.


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Table 116-Node system results.

System Power loss Voltage prole (p.u.) Tie lines

Before reconguration 511.43 kW V max = 1V min = 0.9693

(511), (1014), (716)

After reconguration using proposed MTS 466.1kW V max = 1V min = 0.9694

(810), (911), (716)

After reconguration using (TS+SA) [18] 466.1kW V max = 1V min = 0.9694

(810), (911), (716)

After reconguration using ACSA [20] 466.1kW V max = 1V min = 0.9694 (810), (911), (716)

Table 269-Node system results (normal load).

System type Power loss Voltage prole (p.u.) Tie lines

Normally loaded feeder Before reconguration 20.89 kW V max = 1 1070

V min = 0.9724 12201490

3848

2654After reconguration using proposed MTS algorithm 9.4kW V max = 1 1070

V min = 0.982 1220131444455051

After reconguration using SA [6] 9.4kW V max = 1 1070V min = 0.982 1220

131445465051


131444455051

Table 369-Node system results (heavy load).


Heavily loaded feeder Before reconguration 30.36 kW V max = 1 1070

V min = 0.9669 1220149038482654

After reconguration using proposed MTS algorithm 13.66kW V max = 1 1070V min = 0.978 1220

131447485051


131445465051


131444455051


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Table 469-Node system results (light load).


Lightly loaded feeder Before reconguration 5.09 kW V max = 1 1070

V min = 0.9865 1220149038482654

After reconguration using proposed MTS algorithm 2.32kW V max = 1 1070V min = 0.9913 1220

131444455051


18191819424342435051


13144445

5051

3.3. Aspiration criterion

If the evaluation objective function value of a trail solution issmaller than that of the current best solution, this move can be

Fig. 7. Optimal conguration of 69-node distribution system (normal load).


accepted,eventhoughtthemoveis listedin thetabulist. This meansthat if solution is get trapped in local minimum, a non-improvedsolution is accepted conguration with power loss greater thanthe current value to diversify the solution to unexplored regionssearching for the optimal solution.

4. Solution mechanism

As stated in the previous sections, the network recongurationproblem is equivalent to the problem of nding an optimal radial

conguration such that the loss is minimized. In this section, thegeneral algorithm of the Tabu Search method is adapted to solvethe network reconguration problem. Detailed discussions of eachstep in implementing the Tabu Search and the transition from cur-rent solution (conguration) to another one through neighborhoodgeneration (perturbation mechanism) are as in the following sec-tions.

4.1. The Tabu Search algorithm for distribution systemreconguration

The solution algorithm for distribution system recongurationis described in the following steps:

Step 1: Input data and initialize parameters, initialize the currentsolution X 0 , the optimal solution X opt = X 0 .

Step 2: Generate a new conguration by the proposed topology-based perturbation mechanism explained in Section 4.2.If this transition is tabu or does not satisfy aspiration cri-terion, the previous conguration is restored and a newconguration is generated. Store the radial congurationof the system in tabu list.

Step 3: Run a load ow program, based on NewtonRaphsonmethod, for each conguration in tabu list to check thefeasibility. Calculate power loss for each conguration andthen determine the conguration with minimum power

loss and acceptable voltage prole.


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Fig. 9. Optimal conguration of 69-node distribution system (heavy load).


Step 4: If the new power loss is less than the current solution,then accept this perturbation and set current power lossto be equal new power loss, otherwise restore the previousreconguration and undo this conguration.

Step 5: Check stopping criterion (a specied number of iterationsis assigned based on system size): if satised, go to step 6,else go to step 2.

Step 6: End.

A owchartof a typical Tabu Searchalgorithm is shown in Fig.2 .


4.2. Perturbation mechanism

New system conguration is generatedviaa perturbation mech-anism. It is considered in this article that the system under studyis a single-substation multiple-feeder model. Three types of movescan be used to implement the perturbation mechanism.

4.2.1. Add/subtract move (single move)

1. Close a tie line t k from the set 2 by using random number gen-erator. This will create a loop in the normally radial network, sayLk .

Fig. 11. Optimal conguration of 69-node distribution system (light load).


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Fig. 13. Initial conguration of the 119-node test system.

2. Sequentially perform a branch exchange between this tie lineand all sectionalizing switches in 1 . At each branch exchangeprocess check, if det( A)=+1 or 1, then the system is radial,accept this branch exchange and store this sectionalizing switchin Lk , otherwise the system is not radial or radial, but some loadsare disconnected from the network.

3. Open a sectionalizing switch from the set 1 , chosen from Lk ,which will lead to minimum losses. This will restore thenetworkinto radial structure. The line opened by this operation becomes

a tie line and will replace t k in 2 .

4.2.2. Multiplicative move

1. Close a few tie lines from the set 2 by using random numbergenerator. This will create loops in the normally radial network.

2. Perform branch exchange and check if the system is radial or notas mentioned in the previous section.

3. Open a corresponding number of sectionalizing switches fromtheset 1 chosen from each loop. This operation will restore thesystem intoradialstructure. Theselines opened by thisoperationbecome tie lines.

Fig. 14. Optimal conguration of the 119-node test system.


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4.2.3. Constrained multiplicative move

1. Randomly choose a number n of tie lines to be closed subjectto the constraint n < nmax , where nmax is the total number of tielines in the system.

2. Sequentially close the n tie lines. This will create loops in thenormally radial network.

3. After each closing operation, open a corresponding number of sectionalizing switches from the set 1 chosen from each of the

loops. This will restore the system into radial structure.

The last type of move is used exclusively for the case that thenumber of switch-on/switch-off operations is constrained.

4.3. Variable expression design

In applying modern heuristic methods, such as SA and GA tosolvethe problem of distribution network reconguration,it is veryimportant to choose a good variable expression. This is also truefor the TS-based distribution network reconguration problem. Aninitial attempt is to choose all feeders with switches as a set of variablesto representthe solution of theproblem. With such a vari-able expression, each element of the solution vector represents onefeeder with a switch. The value 0 or 1 of one element in the solu-tion vector denotes that the status of corresponding switch in thefeeder is open or closed, respectively. It was found that such a vari-able expression is often not efcient because the extremely largenumber of unfeasiblenon-radial solutionsappearingat eachgener-ation will lead to a long computing time before reaching an optimalsolution.A good variable expression design, which canrestricteachtrial solution to be radial networks in distribution network recon-guration, is very important to improve the efciency of searchprocess.

In this section, we propose to apply the Kirchhoff algebraicmethod based on the bus incidence matrix for checking the radi-ality of trial solutions [17] . A graph may be described in terms of aconnectionor incidence matrix. Of particular interest is the branch-

to-node incidence matrix , which has one row for each branchandone column for each node with an entry a ij in row i and column jaccording to the following rules:

a ij = 0 if branch i is not connected to node j (7)

a ij = 1 if branch i is directed away from node j (8)

a ij = 1 if branch i is directed toward node j (9)

These rules formalizefor a network theprocedure used to setup thecoefcient of . In network calculation, a reference node must bechosen. Thecolumn corresponding to thereference node is omittedfrom and the resultant matrix is denoted by A . If the number of branches is equal to the number of nodes then, by applying the

previous rules a square branch-to-node matrix is obtained. Thenon-reference nodes of a network are often called independentnodes or buses, and when we say thatthe network has N buses, thismeans that there are N independent nodes not including the refer-ence node. The A matrix has the rowcolumn dimension B N forany network with B branches and N nodes excluding the referencenode. By assuming, that there is a branch between this referencenode and the root of the network; this will lead to a square matrixif the initial structure of the network is radial. The new proposedmethod is based on the value of the det( A). It is found that, if thedet( A) is equal to1 or 1,thenthe systemis radial. Else if the det( A)is equal to zero, this means that either the system is not radial orgroup of loads are disconnected from service. The ow chart of thechecking system radiality algorithm is shown in Fig. 3.

The advantages of using the previous method are:

It reduces the computation time. It restrictseach trial solution to be radialnetworksin distribution

network reconguration. It can be used to determine the branches of the loop formed by

closing a tie line.

5. The application of TS to solve the distribution systemreconguration problem

The proposed algorithm has been implemented into a softwarepackage in MATLAB 6.5, executed on a Pentium III 700-MHz PCwith 128-MB RAM, and applied to several distribution systems. Inthis section several numericalresults arepresentedto illustrate theperformance of the proposed solution algorithm.

5.1. 16-Node system

The rst test system is the three-feeder distribution systemstudied by Civanlar et al. [1] . The schematic structure of the testsystem is shown in Fig. 1 with the system data contained in Ref.[1] . The test system is a hypothetical 23 kV with three feeders, 13normally closed sectionalizing switches, and three normally opentie switches. The load of the system is assumed to be constant.This particular system is purposely introduced because its opti-mal solution can be easily determined by enumerating all possiblecongurations.

The initial system real power loss was 511.43 kW. By applyingthe proposed MTS technique, the nal power loss is 466.1 kW. It isshown from the simulation results listed in Table 1 that the powerloss after reconguration is reduced by 8.85% of its initial value.These results are identical to the results obtained by the methodsproposed in Refs. [18,19] . The optimal conguration of the systemis shown in Fig. 4.

Fig. 5 shows the voltage prole improvement achieved by theproposed feeder reconguration algorithm. As shown, most of thenodevoltageshave beenimprovedafter feeder reconguration.Theminimum voltage before reconguration was 0.9693 p.u. and afterreconguration the minimum node voltage is raised to 0.9694 p.u.

For this system the control parameters are chosen as follows:n = 2 and nmax = 3. The execution time of the developed program isabout 5 s and this time is suitable for practical applications.

5.2. 69-Node system

The test system is a hypothetical 12.66kV system with 69 nodeand 7 laterals. The system data is given in Ref. [6] . The schematicdiagram of the test system is shown in Fig. 6.

To evaluate the performance of the proposed MTS method, theoptimal structures for various load levels reported in Ref. [6] arelisted in Tables 24 f or comparison.

5.2.1. Case 1: normal loadThe system real and reactive load demands of each node are

used without any change. The initial system real power loss was20.88kW. By applying theproposedMTS algorithm, thenal powerloss is 9.4kW. It is shown from the simulation results listed inTable 2 that the power loss after reconguration is reduced by55% of its initial value. These results are identical to the resultsobtained by the methods proposed in Refs. [6,7] . The optimal con-guration is shown in Fig. 7. For 69-node system, under normalloading conditions, the control parameters are chosen as follow:n = 3 and nmax = 5. The execution time of the developed program isabout 25min. which is suitable for practical applications.

Fig. 8 shows the voltage prole improvement achieved by theproposed feeder reconguration algorithm. As shown, most of the

nodevoltageshave beenimprovedafter feeder reconguration.The


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Table 5119-Node system results.

Init ial structure Branchexchange [2] TS [20] Improved TS [14] Proposed MTS

Tie lines 48 27 45 44 45 44 45 44 45 4417 27 17 27 27 26 27 26 27 26

8 24 23 24 22 23 23 24 23 2456 45 53 52 54 53 54 53 54 5365 51 51 50 51 50 65 51 65 5138 65 64 65 64 65 61 62 61 62

9 42 41 42 41 42 41 42 41 4261 100 61 100 61 100 95 100 95 10076 95 76 77 76 77 77 78 77 7891 78 74 75 74 75 74 75 74 75

103 80 79 80 80 79 101 102 101 102113 86 85 86 85 86 86 113 86 113110 89 89 110 89 110 89 110 89 110115 123 114 115 114 115 114 115 114 115

25 36 35 36 33 34 35 36 35 36

Power loss (kW) 1294.3 885.56 884.163 865.865 865.865Min. voltage (p.u.) 0.866 0.9321 0.9321 0.9321 0.9321Lowest voltage node 116 116 116 116 116

minimum node voltage before reconguration was equal to 0.9724p.u. and after reconguration; it is raised to 0.98 p.u.

5.2.2. Case 2: heavy loadThe system real and reactive load demands of each node are

multiplied by a constant equal to 1.2 to construct a heavy load sys-tem. The initial system real power loss was 30.36 kW. By applyingthe proposed MTS algorithm, the nal power loss is 13.66 kW. It isshown from the simulation results listed in Table 3 that the powerloss after reconguration is reduced by 55% of its initial value. Theoptimal conguration is shown in Fig. 9 . These results are identicalto the results obtained by the method proposed in Ref. [7] and arebetter that the results obtained by the method proposed in Ref. [6] .

Fig. 10 shows the voltage prole improvement achieved by theproposed feeder reconguration algorithm. As shown, most of thenodevoltageshave beenimprovedafter feederreconguration.The

minimum node voltage before reconguration was equal to 0.9669p.u. and after reconguration; it is raised to 0.978 p.u.

5.2.3. Case 3: light loadThe system real and reactive load demands of each node are

multiplied by a constant equal to 0.5 to construct a light load sys-tem. The initial system real power loss was 5.09kW. By applyingthe proposed MTS algorithm, the nal power loss is 2.32 kW. It isshown from the simulation results listed in Table 4 that the powerloss after reconguration is reduced by 54.42% of its initial value.The optimal conguration is shown in Fig. 11 . These results areidentical to the results obtained by the method proposed in Ref. [7]and are better than the results obtained by the method proposedin Ref. [6] .

Fig. 12 shows the voltage prole improvement achieved by theproposed feeder reconguration algorithm. As shown, most of thenodevoltageshave beenimprovedafter feederreconguration.Theminimum node voltage before reconguration was equal to 0.9865p.u. and after reconguration; it is raised to 0.9913 p.u.

5.3. 119-Node system

The test system is a hypothetical 11kV with 118 sectionalizingswitches, 119 node, and 15tie lines. The systemdata is given in Ref.[18] . The schematic diagram of the test system is shown in Fig. 13.The total power loads are 22,709.7kW and 17,041.1 kV Ar.

The initial system real power loss was 1294.3 kW. By applyingthe proposed MTS technique, the nal power loss is 865.86 kW.

The optimal conguration is shown in Fig. 14. It is shown from the

Table 6Cost function statistics for the 119-node system.

Best cost function Average cost function Worst cost function865.865 kW 870 kW 884 kW


simulation results listed in Table 5 that the power loss after recon-guration is reduced by 33.1% of its initial value. These results areidentical to the results obtained by the method proposed by Zhanget al. [14] and are better than the results obtained by the meth-ods proposed in Refs. [2,20] . For the 119-node system the controlparameters are chosen as follow: n =13 and nmax = 15. The execu-

tion time of the developed program is about 5h.The obtained results using the proposed MTS algorithm havebeen reached after 10 trails. Table 6 shows the statistics of the costfunction in the simulation results.

Fig. 15 shows the voltage prole improvement achieved by theproposed feeder reconguration algorithm. As shown, most of thenodevoltageshave beenimprovedafter feeder reconguration.Theminimum node voltage was equal to 0.866 p.u. and after recong-uration; it is raised to 0.9323 p.u.

6. Conclusion

This article has proposed MTS-based method for recongura-tion of distribution systems. TS algorithm is introduced with some

modications such as using a tabu list with variable size to pre-


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vent cycling andto escape from local minimum. Also, a constrainedmultiplicative move is used in the search process to diversify thesearch process toward unexplored regions. The simulation resultshave shown that TS algorithm is better than SA in terms of solu-tion accuracy because TS has a deterministic optimization, whileSA is considered as a stochastic optimization technique. Therefore,SA may fail to reach the optimal solution. For the 16-node systemin comparison with Refs. [18,19] same results are obtained. For the69-node system in comparison with Ref. [6] equal in power lossand in voltage prole, but in case of load variation the proposedmethod has results better than the results obtained using methodsin Ref. [6] . For the 119-node system the results obtained are iden-tical to the results obtained by the ITS method proposed by Zhanget al. [14] and are better that the results obtained by the methodproposed in Refs. [2,20] .

It can be concluded that the proposed MTS algorithm is bet-ter than SA, branch exchange, and TS in large-scale distributionsystems. Also, in comparison with the results obtained using ITS,same results are obtained. Therefore, it can be concluded that TSwith some modications can give results identical to the resultsobtained using hybrid algorithm of TS and GA. The validity andeffectiveness of the proposed MTS algorithm is well proved by thesample test systems. The execution time of the developed softwareis acceptable for practical applications. A new application based onthe value of det( A) is used to check, whether the system is radial ornot is also presented.

References

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[2] M.E. Baran, F.F. Wu, Network reconguration in distribution systems for lossreductionand loadbalancing,IEEE Transactionson Power Delivery4 (April (2))(1989) 14011407.

[3] T. Taylor,D. Lubkeman, Implementation of heuristicsearchstrategiesfor distri-bution feeder reconguration, IEEE Transactions on Power Delivery 5 (January(1)) (1990) 239246.

[4] T.P. Wagner, A.Y. Chikhani, R. Hackam, Feeder reconguration for loss reduc-tion: an application of distribution automation, IEEE Transactions on PowerDelivery 6 (October (4)) (1991) 19221931.

[5] R.J.Sar, M.M.A. Salama,A.Y. Chikhani,Distributionsystemreconguration forloss reduction: an algorithm based on partitioning theory, IEEE Transactionson Power Systems 11 (February (1)) (1996) 504510.

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[7] H.-C. Chang, C.-C. Kuo, Network reconguration in distribution systems usingsimulated annealing, Electric Power Systems Research 29 (May (3)) (1994)227238.

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Power Systems 7 (August (3)) (1992) 10441051.[9] H. Kim, Y. Ko, K. Jung, Articial neural network based feeder recongurationfor lossreduction in distribution systems,IEEE Transactionson Power Delivery8 (July (3)) (1993) 13561366.

[10] H. Mori, Y. Ogita, A parallel tabu search method for reconguration of distri-bution systems, in: Proceedings of the 2000 IEEE Power Engineering SocietySummer Meeting, vol. 1, 2000, pp. 7378.

[11] K.K. Li, T.S. Chung, G.J. Chen, G.Q. Tang, A tabu search approach to distributionnetwork reconguration for loss reduction, Electric Power Components andSystems 32 (June (6)) (2004) 571585.

[12] Y.-J. Jeon, J.-C. Kim, Application of simulatedannealing and tabusearch for lossminimization in distribution systems, Electric Power and Energy Systems 26(January (1)) (2004) 918.

[13] S.F. Mekhamer, A.Y. Abdelaziz, F.M. Mohammed, M.A.L. Badr, A new intel-ligent optimization technique for distribution systems reconguration, in:Proceedings of the Twelfth International Middle-East Power Systems Confer-enceMEPCON2008, South Valley University, Egypt, March, 2008, pp.397401.

[14] D. Zhang, Z. Fu, L. Zhang, An improved TS algorithm for loss-minimum recon-gurationin large-scale distribution systems,ElectricPower SystemsResearch77 (2007) 685694.

[15] F. Glover, Tabu search, Part II, ORSA Journal on Computing 1 (Summer (3))(1989) 190206.

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[17] P. Wright, On minimum spanning trees and determinants, Mathematics Mag-azine 73 (February (1)) (2000) 2128.

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tabu search algorithm distribution system reconfiguration using a modified tabu search algorithm

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