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Electric Power Systems Research 80 (2010) 943–953

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Electric Power Systems Research

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istribution system reconfiguration using a modified Tabu Search algorithm

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

r t i c l e i n f o

rticle history:eceived 31 March 2008eceived in revised form 30 October 2009ccepted 3 January 2010vailable online 20 January 2010

a b s t r a c t

This article presents an efficient meta-heuristic method for reconfiguration of distribution systems. Amodified Tabu Search (MTS) algorithm is used to reconfigure distribution systems so that active powerlosses are globally minimized with turning on/off sectionalizing switches. TS algorithm is introducedwith some modifications such as using a tabu list with variable size according to the system size. Also,

eywords:istribution system reconfigurationower loss reductionodified Tabu Search

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 reconfiguration problem. To verify the effectiveness of the proposed approach, the effect of 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 with

appr
that obtained using other
. Introduction

The subject of minimizing distribution systems losses hasained a great deal of attention due to the high cost of electri-al energy and therefore, much of current research on distributionutomation has focused on the minimum-loss configuration prob-em. There are many alternatives available for reducing losses athe distribution level: reconfiguration, capacitor installation, loadalancing, and introduction of higher voltage levels. This researchocuses on the reconfiguration alternative.

Network reconfiguration is the process of changing the topol-gy of distribution systems by altering the open/closed statusf switches. Because there are many candidate-switching com-inations in the distribution system, network reconfiguration iscomplicated combinatorial, non-differentiable constrained opti-ization problem. Two types of switches are used in primary

istribution systems. There are normally closed switches (section-lizing switches) and normally open switches (tie switches). Thosewo types of switches are designed for both protection and con-guration management. The change in network configuration ischieved by opening or closing of these two types of switches in
uch a way that the ‘radiality’ of the network is maintained.
The reconfiguration algorithms can be classified by the solutionethods that they employ: those based upon a blend of heuristics

nd optimization methods, those making use of heuristics alone,

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

A.Y. Abdelaziz).

378-7796/$ – see front matter © 2010 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2010.01.001

oaches in the previous work.© 2010 Elsevier B.V. All rights reserved.

and those using some from of artificial 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.

In Ref. [1], a branch exchange method that considered the on–offconditions of the sectionalizing switches in discrete numbers wasdeveloped [1]. Since the method is based on heuristics, it is not easyto take a systematic way to evaluate an optimal solution.

Two different methods with varying degree of accuracy toapproximate power flow in systems were proposed in Ref. [2]. Thesearch method has an acceptable convergence characteristic. 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 reconfiguration, 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 efficient 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 techniques
and a new heuristic search method for comparison with previouslydeveloped heuristic techniques which are based on an optimalload flow analysis were presented in Ref. [4]. This study indicatesthat linear programming, in the form of transportation algorithms,is not suitable for application to feeder reconfiguration since the
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9 r Systems Research 80 (2010) 943–953

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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

44 A.Y. Abdelaziz et al. / Electric Powe

ower loss function is not linear whilst heuristic approaches,lthough not optimal, can provide substantial saving if properlyormulated.

Based on partitioning the distribution network into groups ofoad buses, the line section losses between the groups of nodes are

inimized [5]. By dividing the distribution network into groups ofusses, the combinatorial nature of the reconfiguration problem isvercome, while simultaneously minimizing losses.

In recent years, meta-heuristic methods have been studied forolving combinatorial optimization problems to obtain an opti-al solution of global minimum. Typical meta-heuristic methods

nclude Simulated Annealing (SA), Genetic Algorithm (GA), andabu Search (TS).

A two-stage solution methodology based on a modified simu-ated annealing technique for solving the reconfiguration problemf distribution systems was proposed in Ref. [6]. In Ref. [7], a mod-fied SA technique for network reconfiguration for loss reductionn distribution systems was presented. An efficient perturba-ion scheme and an initialization procedure determining a bettertarting temperature for the simulated annealing approach wereroposed. This method can get a solution better than that obtainedsing the method presented in Ref. [5]. This solution algorithmives a near-optimal solution but this method does not work soell in the case of load variation.

A GA based method for feeder reconfiguration was proposed inef. [8]. Strings which represent switch status, a fitness functiononsisting of total system losses, and penalty values of volt-ge drop limit and current capacity limit were formed. Sampleesults demonstrate that, although the minimal loss solutions werebtained, solution time was prohibitive.

An artificial neural network based method for feeder reconfig-ration was presented in Ref. [9]. However, such technique canncounter difficulties, such as getting trapped in local minima,ncreased computational complexity, and not being applicable toertain objective functions. This led to the need of developing a newlass of solution methods that can overcome these shortcomings.

A parallel Tabu Search (PTS) based method for feeder reconfig-ration has been proposed in Ref. [10]. PTS introduces two parallelchemes. One is the decomposition of the neighborhood with par-llel processors to reduce computational efforts. The other is theultiplicity of the tabu length to improve the solution accuracy.

TS algorithm gives results better than results obtained by SA, par-llel Simulated Annealing (PSA), GA, and parallel Genetic AlgorithmPGA). In Ref. [11], a TS algorithm for solving the problem of networkeconfiguration in distribution systems in order to reduce the resis-ive line losses under normal operating conditions was presented.

method for checking system radiality based on an upward-nodexpression, which has been developed in solving the problem ofestorative planning of power system was proposed. In Ref. [12], anfficient hybrid algorithm of SA and TS method for feeder reconfigu-ation to improve the computation time and convergence propertyas proposed. In Ref. [13], a modified Tabu Search (MTS) based

lgorithm for reconfiguration of distribution systems has been pro-osed. The TS algorithm was introduced with some modificationsuch as using a tabu list with variable size to prevent cycling ando escape from local minimum. Also, a constrained multiplicative

ove was used in the search process to diversify the search processoward unexplored regions.

Zhang et al. [14] presented an Improved Tabu Search (ITS)lgorithm for loss-minimization reconfiguration in large-scale dis-ribution systems. In ITS algorithm, mutation operation, a main
perator used in genetic algorithm, is introduced to weaken theependence of global search ability on tabu length. In addition,he candidate neighborhood, which only contains several optimalwitch exchanges in each tie switch associated loop network, isesigned to improve local search efficiency 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 reconfiguration problem. The proposed method is appliedto large-scale networks to show the effectiveness of the modifiedTabu Search algorithm. In comparison with Ref. [14] in which themutation operation of GA is used to weaken the dependence ofglobal 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 efficiency of Tabu Search to reach theglobal solution. Also, the effect of variation of 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-

Fig. 2. Flow chart of Tabu Search algorithm.

A.Y. Abdelaziz et al. / Electric Power Systems Research 80 (2010) 943–953 945

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Fig. 3. Flow chart for

esults obtained using other modern techniques to examine theerformance of the proposed approach.

. Problem formulation

Generally, there are two types of switches in distribution sys-ems: tie switch and sectionalizing switch. As shown in Fig. 1,witches in dotted branches connecting nodes (10–14), (5–11), and7–16) are tie switches, and switches in other continuous branchesre sectionalizing switches. The tie switches are normally opennd the sectionalizing switches are normally closed. When theperating conditions have been changed, feeder reconfiguration iserformed by the opening/closing of these two types of switcheso reduce resistive line losses.

That is, a tie switch may be closed for the purpose of transferringoads to different feeders, and, at the same time, a sectionalizingwitch should be opened to maintain the radial structure of the dis-ribution network. For example, in Fig. 1, when the loads of feederbecome heavy under normal operating conditions, the tie switch

onnecting nodes (5–11) may be closed to transfer the load at node
1 from feeder 2 to feeder 1 and at the same time the sectionalizingwitch connecting nodes (9–11) must be opened to maintain theadial structure of the network.
The objective of the reconfiguration is to minimize the dis-ribution losses with turning on/off sectionalizing switches. The

ing system radiality.

reconfiguration problem has the following constrains:

1. Power flow 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

ri

P2i

+ Q 2i

V2i

(1)

Subject to:

g(x) = 0 (2)

Vmini < Vi < Vmax

i (3)

Imini < Ii < Imax

i (4)

det(A) = 1 or − 1 radial system (5)

det(A) = 0 not radial (6)

where Z: objective function (kW); L: no. of branches; Pi: activepower loss at sending end of branch i; Qi: reactive power at sending

946 A.Y. Abdelaziz et al. / Electric Power Syst

erl1i

3

fspols

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

nd of branch i; Vi: voltage at sending end of branch i; Ii: line cur-ent at branch i; g(x): power flow equations; Vmin

i: lower voltage

imit (taken to be 0.9 p.u); Vmaxi

: upper voltage limit (taken to bep.u); Imin

i: lower current limit; Imax

i: upper current limit; A: bus

ncidence matrix; ri: resistance of branch i.

. Tabu Search

Tabu Search is one of the modern heuristic search methodsor combinatorial optimization problems, based on neighborhood
earch with local optima avoidance, which models human memoryrocesses. Tabu Search was initially proposed by Glover and manyther authors have applied similar ideas to various classical prob-ems [15,16]. Tabu Search (TS) can be considered as a neighborhoodearch method which is more elaborate than the descent method.
Fig. 5. Voltage profile before and after reco

Fig. 6. 69-Node distri

ems Research 80 (2010) 943–953

Like any local search method (LS), TS needs three basic compo-nents: a configuration structure, a neighborhood function definedon the configuration structure, and neighborhood examinationmechanism. The first component defines the search space of S ofthe 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 configuration to another.

3.1. Configuration space

Configuration space is the set of allowed configurations overwhich the optimal system configuration 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 configuration of thesystem. Hence the configuration space ˝ = ˝1 ∪ ˝2, where ˝1 isthe set of sectionalizing switches and ˝2 is the set of tie switches.

3.2. Tabu list

The tabu list is another important concept in Tabu Search. Whenthe move is accepted, the move and its reverse are recorded in thetabu list. When the move is recorded in tabu list, it is not allowed
to visit or use this move again but this restriction can be violatedunder Aspiration Criterion as described below. 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.
nfiguration for the 16-node system.

bution system.


Table 116-Node system results.

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

Before reconfiguration 511.43 kW Vmax = 1Vmin = 0.9693

(5–11), (10–14), (7–16)

After reconfiguration using proposed MTS 466.1 kW Vmax = 1Vmin = 0.9694

(8–10), (9–11), (7–16)

After reconfiguration using (TS+SA) [18] 466.1 kW Vmax = 1Vmin = 0.9694

(8–10), (9–11), (7–16)

After reconfiguration using ACSA [20] 466.1 kW Vmax = 1Vmin = 0.9694

(8–10), (9–11), (7–16)

Table 269-Node system results (normal load).

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

Normally loaded feederBefore reconfiguration 20.89 kW Vmax = 1 10–70

Vmin = 0.9724 12–2014–90

38–4826–54

After reconfiguration using proposed MTS algorithm 9.4 kW Vmax = 1 10–70Vmin = 0.982 12–20

13–1444–4550–51

After reconfiguration using SA [6] 9.4 kW Vmax = 1 10–70Vmin = 0.982 12–20

13–1445–4650–51


13–1444–4550–51

Table 369-Node system results (heavy load).


Heavily loaded feederBefore reconfiguration 30.36 kW Vmax = 1 10–70

Vmin = 0.9669 12–2014–9038–4826–54


13–1447–4850–51


13–1445–4650–51


13–1444–4550–51

948 A.Y. Abdelaziz et al. / Electric Power Systems Research 80 (2010) 943–953

Table 469-Node system results (light load).


Lightly loaded feederBefore reconfiguration 5.09 kW Vmax = 1 10–70

Vmin = 0.9865 12–2014–9038–4826–54


13–1444–4550–51


18–1918–1942–4342–4350–51

After reconfiguration using SA [7] 2.32 kW Vmax = 1 10–70

3

s

F

.3. Aspiration criterion

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

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

ig. 8. Voltage profile before and after reconfiguration for the 69-node system.

Vmin = 0.9913 12–2013–1444–4550–51

accepted, even thought the move is listed in the tabu list. This meansthat if solution is get trapped in local minimum, a non-improvedsolution is accepted – configuration 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 reconfigurationproblem is equivalent to the problem of finding an optimal radialconfiguration such that the loss is minimized. In this section, thegeneral algorithm of the Tabu Search method is adapted to solvethe network reconfiguration problem. Detailed discussions of eachstep in implementing the Tabu Search and the transition from cur-rent solution (configuration) to another one through neighborhoodgeneration (perturbation mechanism) are as in the following sec-tions.

4.1. The Tabu Search algorithm for distribution systemreconfiguration

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

Step 1: Input data and initialize parameters, initialize the currentsolution X0, the optimal solution Xopt = X0.

Step 2: Generate a new configuration 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 configuration is restored and a newconfiguration is generated. Store the radial configurationof the system in tabu list.
Step 3: Run a load flow program, based on Newton–Raphsonmethod, for each configuration in tabu list to check thefeasibility. Calculate power loss for each configuration andthen determine the configuration with minimum powerloss and acceptable voltage profile.


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

F

S

S

S 4.2.1. Add/subtract move (single move)

1. Close a tie line tk from the set ˝2 by using random number gen-

ig. 10. Voltage profile before and after reconfiguration for the 69-node system.

tep 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 previousreconfiguration and undo this configuration.

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

tep 6: End.

A flow chart of a typical Tabu Search algorithm is shown in Fig. 2.

Fig. 11. Optimal configuration of 69-nod

Fig. 12. Voltage profile before and after reconfiguration for the 69-node system.

4.2. Perturbation mechanism

New system configuration is generated via a 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.

erator. This will create a loop in the normally radial network, sayLk.

e distribution system (light load).


on of t

2

3

Fig. 13. Initial configurati

. 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.

. Open a sectionalizing switch from the set ˝1, chosen from Lk,which will lead to minimum losses. This will restore the networkinto radial structure. The line opened by this operation becomesa tie line and will replace tk in ˝2.

Fig. 14. Optimal configuration of

he 119-node test system.

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 from
the set ˝1 chosen from each loop. This operation will restore thesystem into radial structure. These lines opened by this operationbecome tie lines.
the 119-node test system.

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.2.3. Constrained multiplicative move

. 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.

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

. After each closing operation, open a corresponding number ofsectionalizing switches from the set ˝1 chosen from each of theloops. This will restore the system into radial structure.

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

.3. Variable expression design

In applying modern heuristic methods, such as SA and GA toolve the problem of distribution network reconfiguration, it is verymportant to choose a good variable expression. This is also trueor the TS-based distribution network reconfiguration problem. Annitial attempt is to choose all feeders with switches as a set ofariables to represent the solution of the problem. With such a vari-ble expression, each element of the solution vector represents oneeeder with a switch. The value 0 or 1 of one element in the solu-ion vector denotes that the status of corresponding switch in theeeder is open or closed, respectively. It was found that such a vari-ble expression is often not efficient because the extremely largeumber of unfeasible non-radial solutions appearing at each gener-tion will lead to a long computing time before reaching an optimalolution. A good variable expression design, which can restrict eachrial solution to be radial networks in distribution network recon-guration, is very important to improve the efficiency of searchrocess.

In this section, we propose to apply the Kirchhoff algebraicethod based on the bus incidence matrix Â for checking the radi-

lity of trial solutions [17]. A graph may be described in terms of aonnection or incidence matrix. Of particular interest is the branch-o-node incidence matrix Â, which has one row for each branch andne column for each node with an entry aij in row i and column jccording to the following rules:

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

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

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

hese rules formalize for a network the procedure used to set up theoefficient of Â. In network calculation, a reference node must behosen. The column corresponding to the reference node is omittedrom Â and the resultant matrix is denoted by A. If the number ofranches is equal to the number of nodes then, by applying therevious rules a square branch-to-node matrix is obtained. Theon-reference nodes of a network are often called independentodes or buses, and when we say that the network has N buses, thiseans that there are N independent nodes not including the refer-

nce node. The A matrix has the row–column dimension B × N forny network with B branches and N nodes excluding the referenceode. By assuming, that there is a branch between this referenceode and the root of the network; this will lead to a square matrix

f the initial structure of the network is radial. The new proposedethod is based on the value of the det(A). It is found that, if the

et(A) is equal to 1 or −1, then the system is radial. Else if the det(A)s equal to zero, this means that either the system is not radial orroup of loads are disconnected from service. The flow chart of thehecking system radiality algorithm is shown in Fig. 3.

The advantages of using the previous method are:

ems Research 80 (2010) 943–953 951

• It reduces the computation time.• It restricts each trial solution to be radial networks in distribution

network reconfiguration.• 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 systemreconfiguration 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 numerical results are presented to illustrate theperformance of the proposed solution algorithm.

5.1. 16-Node system

The first 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 possibleconfigurations.

The initial system real power loss was 511.43 kW. By applyingthe proposed MTS technique, the final power loss is 466.1 kW. It isshown from the simulation results listed in Table 1 that the powerloss after reconfiguration 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 configuration of the systemis shown in Fig. 4.

Fig. 5 shows the voltage profile improvement achieved by theproposed feeder reconfiguration algorithm. As shown, most of thenode voltages have been improved after feeder reconfiguration. Theminimum voltage before reconfiguration was 0.9693 p.u. and afterreconfiguration 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 12.66 kV 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 2–4 for 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 was20.88 kW. By applying the proposed MTS algorithm, the final powerloss is 9.4 kW. It is shown from the simulation results listed inTable 2 that the power loss after reconfiguration 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-figuration 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 25 min. which is suitable for practical applications.
Fig. 8 shows the voltage profile improvement achieved by theproposed feeder reconfiguration algorithm. As shown, most of thenode voltages have been improved after feeder reconfiguration. The


Table 5119-Node system results.

Initial structure Branch exchange[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

884.163 865.865 865.8650.9321 0.9321 0.9321

116 116 116

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

Best cost function Average cost function Worst cost function

865.865 kW 870 kW 884 kW

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

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

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

ultiplied by a constant equal to 1.2 to construct a heavy load sys-em. The initial system real power loss was 30.36 kW. By applyinghe proposed MTS algorithm, the final power loss is 13.66 kW. It ishown from the simulation results listed in Table 3 that the poweross after reconfiguration is reduced by 55% of its initial value. Theptimal configuration is shown in Fig. 9. These results are identicalo the results obtained by the method proposed in Ref. [7] and areetter that the results obtained by the method proposed in Ref. [6].

Fig. 10 shows the voltage profile improvement achieved by theroposed feeder reconfiguration algorithm. As shown, most of theode voltages have been improved after feeder reconfiguration. Theinimum node voltage before reconfiguration was equal to 0.9669

.u. and after reconfiguration; it is raised to 0.978 p.u.

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

ultiplied by a constant equal to 0.5 to construct a light load sys-em. The initial system real power loss was 5.09 kW. By applyinghe proposed MTS algorithm, the final power loss is 2.32 kW. It ishown from the simulation results listed in Table 4 that the poweross after reconfiguration is reduced by 54.42% of its initial value.he optimal configuration is shown in Fig. 11. These results aredentical to the results obtained by the method proposed in Ref. [7]nd are better than the results obtained by the method proposedn Ref. [6].

Fig. 12 shows the voltage profile improvement achieved by theroposed feeder reconfiguration algorithm. As shown, most of theode voltages have been improved after feeder reconfiguration. Theinimum node voltage before reconfiguration was equal to 0.9865

.u. and after reconfiguration; it is raised to 0.9913 p.u.

.3. 119-Node system

The test system is a hypothetical 11 kV with 118 sectionalizingwitches, 119 node, and 15 tie lines. The system data is given in Ref.
18]. The schematic diagram of the test system is shown in Fig. 13.he total power loads are 22,709.7 kW and 17,041.1 kV Ar.
The initial system real power loss was 1294.3 kW. By applyinghe proposed MTS technique, the final power loss is 865.86 kW.he optimal configuration is shown in Fig. 14. It is shown from the

Fig. 15. Voltage profile before and after reconfiguration for the 119-node system.

simulation results listed in Table 5 that the power loss after recon-figuration 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 5 h.

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 profile improvement achieved by theproposed feeder reconfiguration algorithm. As shown, most of thenode voltages have been improved after feeder reconfiguration. Theminimum node voltage was equal to 0.866 p.u. and after reconfig-uration; it is raised to 0.9323 p.u.

6. Conclusion

This article has proposed MTS-based method for reconfigura-tion of distribution systems. TS algorithm is introduced with somemodifications such as using a tabu list with variable size to pre-

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[19] C.-T. Su, C.-F. Chang, J.-P. Chiou, Distribution network reconfiguration for lossreduction by ant colony search algorithm, Electric Power Systems Research 75(2005) 190–199.

A.Y. Abdelaziz et al. / Electric Powe

ent cycling and to escape from local minimum. Also, a constrainedultiplicative move is used in the search process to diversify the

earch process toward unexplored regions. The simulation resultsave shown that TS algorithm is better than SA in terms of solu-ion accuracy because TS has a deterministic optimization, whileA is considered as a stochastic optimization technique. Therefore,A may fail to reach the optimal solution. For the 16-node systemn comparison with Refs. [18,19] same results are obtained. For the9-node system in comparison with Ref. [6] equal in power lossnd in voltage profile, but in case of load variation the proposedethod has results better than the results obtained using methods

n Ref. [6]. For the 119-node system the results obtained are iden-ical to the results obtained by the ITS method proposed by Zhangt al. [14] and are better that the results obtained by the methodroposed in Refs. [2,20].

It can be concluded that the proposed MTS algorithm is bet-er than SA, branch exchange, and TS in large-scale distributionystems. Also, in comparison with the results obtained using ITS,ame results are obtained. Therefore, it can be concluded that TSith some modifications can give results identical to the results

btained using hybrid algorithm of TS and GA. The validity andffectiveness of the proposed MTS algorithm is well proved by theample test systems. The execution time of the developed softwares acceptable for practical applications. A new application based onhe value of det(A) is used to check, whether the system is radial orot is also presented.

eferences

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