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A Tabu Search Approach to Distribution NetworkReconfiguration for Loss ReductionK. K. LI a , T. S. CHUNG b , G. J. CHEN c & G. Q. TANG da Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon,Hong Kongb Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon,Hong Kongc Nari-relays Electric Co., Ltd., Nanjing, People's Republic of Chinad Department of Electrical Engineering, Southeast University, Nanjing, People's Republic ofChinaPublished online: 24 Jun 2010.

To cite this article: K. K. LI , T. S. CHUNG , G. J. CHEN & G. Q. TANG (2004) A Tabu Search Approach to Distribution NetworkReconfiguration for Loss Reduction, Electric Power Components and Systems, 32:6, 571-585, DOI: 10.1080/15325000490228414

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Electric Power Components and Systems, 32:571–585, 2004Copyright c© Taylor & Francis Inc.ISSN: 1532-5008 print/1532-5016 onlineDOI: 10.1080/15325000490228414

A Tabu Search Approach to Distribution NetworkReconfiguration for Loss Reduction

K. K. LIT. S. CHUNGDepartment of Electrical EngineeringThe Hong Kong Polytechnic UniversityKowloon, Hong Kong

G. J. CHENNari-relays Electric Co., Ltd.Nanjing, People’s Republic of China

G. Q. TANGDepartment of Electrical EngineeringSoutheast UniversityNanjing, People’s Republic of China

Distribution network reconfiguration for loss minimization is a complex, large-scale combinatorial optimization problem. A new efficient and robust algorithmfor the reconfiguration of distribution networks in order to reduce the powerenergy losses under normal operating conditions is presented in this article. Thedeveloped algorithm is based on a tabu search (TS) approach, which is a recentmember in the family of modern heuristic methods. Tabu search is used forefficiently obtaining the near-optimal solutions of combinatorial optimizationproblems, which makes it suitable to solve the problem of distribution networkreconfiguration. The components of proposed TS-based method and effectiveschemes, which aim at speeding up the solution methodology, are also presented.To demonstrate the validity and effectiveness of the proposed method, three testsystems with different sizes are studied. The numerical results reveal that theproposed method is promising.

Keywords distribution network reconfiguration, heuristic optimizationtechnique, loss reduction, tabu search

Manuscript received in final form on 10 March 2003.The authors would like to acknowledge the Hong Kong Polytechnic University for the

research grant support for this research project.Address correspondence to K. K. Li, Department of Electrical Engineering, The Hong

Kong Polytechnic University, Kowloon, Hong Kong. E-mail: gilbert.kk.li@polyu.edu.hk

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1. Introduction

It was reported in [1] that about 5 to 13% of the total power system generation isdissipated in the form of line loss at the distribution level. Hence, it is of great benefitto investigate methods for reducing line losses in distribution systems. Generally,five methods of loss reduction in distribution systems are available:

• Capacitor installation;• Reconductoring;• Introduction of higher voltage levels;• Load balancing;• Reconfiguration.

As analyzed in [2], capacitor installation, reconductoring and introduction ofhigher voltage levels are seldom used as ways of loss reduction due to the economyand reliability considerations. Network reconfiguration is thought to be an effectivemethod that can make use of existing equipment to reduce distribution feeder lossesand improve system security.

In a distribution system, each feeder has a different mixture of commercial,residential and industrial type loads. These load types have different daily loadpatterns, which make the peak loads of feeders occur at different times. In normaloperating conditions, part of loads can be transferred from heavily loaded feedersto relatively less heavily loaded feeders by network reconfiguration, which aims atminimizing the resistive line losses as well as improving the voltage profile alongfeeders.

Distribution feeders contain a number of switches that are normally closed andswitches that are normally open. When the operating conditions change, networkreconfiguration is performed by the opening/closing of these network switches toreduce the line losses under the constraints of transformer capacity, feeder thermalcapacity, voltage drop and radiality of the network. Therefore, the problem ofnetwork reconfiguration is to determine the status of these network switches sothat the reduction of line losses in distribution systems is maximized. Basically, itis a mixed-integer, non-linear combinatorial optimization problem.

In past decades, the topic of distribution network reconfiguration for lossreduction is a very active field for researchers, and many solution methods havebeen proposed. These methods can be classified into three groups: those basedupon a blend of heuristics and optimization techniques [3–8], those making use ofheuristics alone [9–12], and modern heuristic methods [13–19], including simulatedannealing (SA) [13–16], genetic algorithms (GAs) [17], evolutionary programming(EP) [18] and artificial neural network (ANN) [19]. Among them, the heuristicmethods offer solutions in minimum times, but the final network configurationsfrom them are often restricted to local optimization. The methods are based upona combination of heuristics and optimization techniques offer more accurate systemmodels. Compared to heuristic methods, they give more accurate solutions, butneed longer solution times. Modern heuristic methods, while different from thosetraditional methods, are extremely suitable for solving large-scale combinatorialoptimization problems. The existing applications of those modern heuristic methodsin distribution network configuration also show that they are very promising.

In this article, a new efficient and robust method based on tabu search tech-nique, which is a recent member in the family of modern heuristic methods, is

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proposed to solve the problem of network reconfiguration in distribution systemsin order to reduce the resistive line losses under normal operating conditions. Tabusearch is a heuristic optimization technique used for efficiently obtaining the near-optimal solutions of combinatorial optimization problems. Until now, tabu searchhas achieved impressive progress in extensive fields. In recent years, it has been suc-cessfully applied in solving power system problems, such as hydro-thermal schedul-ing [20], thermal unit maintenance scheduling [21], alarm processing [22], faultsection estimation [23], and trouble call analysis [24]. The components of proposedTS-based method are designed in detail in this article. To speed up the solutionmethodology, effective schemes have also been developed, which can always main-tain each neighborhood solution in radial network format which is the major con-straint in distribution network reconfiguration. To demonstrate the validity andeffectiveness of the proposed method, three test systems with different sizes arestudied. The numerical results are also given in this article, which reveal that theproposed method is promising.

The article is organized as follows: First, the problem of distribution networkreconfiguration is illustrated and formulated as a non-linear, mixed-integer pro-gramming problem. Secondly, the new TS-based method for distribution networkreconfiguration is described in detail. Finally, three test systems with different sizesare studied. The numerical results are also given, which demonstrate the proposedmethod is feasible and effective.

2. Mathematical Description of the Distribution NetworkReconfiguration Problem

Generally, there are two types of switches in distribution systems: tie switch andsectionalizing switch. As shown in Figure 1 [10], switches in dotted branches 15,21 and 26 are tie switches, and switches in other continuous branches are sec-tionalizing switches. The tie switches are normally open and the sectionalizingswitches are normally closed. When the operating conditions has been changed,

Figure 1. An example distribution system.

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feeder reconfiguration is performed by the opening/closing of these two types ofswitches to reduce resistive line losses. That is, a tie switch may be closed for thepurpose of transferring loads to different feeders, and, at the same time, a section-alizing switch should be opened to maintain the radial structure of the distributionnetwork. For example, in Figure 1, when the loads of feeder II become heavy undernormal operating conditions, the tie switch 15 may be closed to transfer the loadat bus 11 from feeder II to feeder I and at the same time the sectionalizing switch19 must be opened to maintain the radial structure of the network.

The problem of network reconfiguration in this article is to identify which tieswitches should be closed and which sectionalizing switches should be opened sothat the resultant network has minimum resistive line losses. The problem can beformulated as follows:

Minimize: Ploss =∑

i∈Fc

riP 2i +Q2i

Vi(1)

where

ri is the resistance of feeder i;Pi is the active power of feeder i;Qi is the reactive power of feeder i;Vi is the voltage of feeder i;Fc is the feeder set in which all feeders are closed in the network.

Subject to:

1. Conservation of power flow;

AP = D (2)

where

A is the node-arc incidence matrix;P is the vector of feeder power flow;D is the vector of load demand.

2. Power capacity constraints;

Pi ≤ PMaxi (3)

for i ∈ T ∪ Fc; where T is the set of transformers.3. Voltage drop constraints

Vi ≥ Vmin (4)

for i = 1, . . . N (N is the number of nodes).4. Radial configuration constraints.

It can be seen that distribution network reconfiguration for loss reduction isa non-linear, mixed-integer programming problem. In this article, a tabu searchmethod is adopted to solve this problem.

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3. Tabu Search

Tabu search was originally proposed in 1977 by Fred Glover as an optimizationtool to solve non-linear covering problem [25]. Recently it has been extensivelyapplied in many areas and proved to be very effective in solving many combinatorialoptimization problems. The successful applications of TS in solving power systemproblems have also been reported [20–24].

TS is a general meta-heuristic optimization technique that has been revealedto be effective in solving combinatorial optimization problems by exploiting certainforms of flexible memory to keep a search from being trapped in local optima. Thefundamental concepts underlying TS are neighborhood and tenure. Generally, TSstarts from an initial solution that is chosen randomly or generated from existingheuristic methods. By applying the operator move, a subset of neighbors that canbe reached directly from current sub-optimal solution is generated. Among theseneighbors, the one that improves most of the evaluation function is chosen as thenew best. If there are no improving moves, it means the current solution is a localoptima. To prevent the search strategy from becoming trapped in local optima, atable of length tenure (which is called tabu list), containing the most recent movesis created and updated with each iteration of the neighborhood search. The movesin tabu list must be avoided in the exploration of a neighbor because they couldbring the algorithm back to a region of the search space that has been visited. Thisprocedure is repeated until the stopping criterion is satisfied.

4. Application of Tabu Search to Distribution NetworkReconfiguration Problem

The flow chart of the proposed TS-based algorithm for distribution network recon-figuration is shown in Figure 2 and described as follows:

1. Choose current operating network as an initial solution Sinitial and calculatethe evaluation function of Sinitial . Let the current solution vector Scurrent =Sinitial and the best solution vector Sbest = Sinitial . Initialize the tabu listT and the aspiration function A. Set the iteration counter I = 0.

2. If I is equal to pre-specified maximum permitted iteration number Imax,then output Sbest as the final result and stop. Otherwise, set I = I +1, andgo to step 3.

3. Select a trial radial solution from the neighborhood of Scurrent by theoperator move, which will be defined later, and calculate the evaluationfunction f(S) of the corresponding solution S. Repeat the process until thespecified neighborhood sampling number Nmax has been reached.

4. If Sbest is not better than the best trial solution that has the minimumevaluation function value, then assign this best trial solution to Sbest andupdate the aspiration function A. Otherwise, go to step 5.

5. Scurrent is updated to the best trial solution that has the minimum evalua-tion function value as evaluated in step 3 if the corresponding move is notin the tabu list or its aspiration level is attained. Then, include the movein the tabu list and update the tabu list T . Go to step 2. If the best trialsolution corresponds to a tabu move and its aspiration level is not attained,then check the next trial solution, and repeat this step.

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Figure 2. The mainframe of the TS-based algorithm for distribution network reconfigu-ration.

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Variable Expression Design

In applying modern heuristic methods, such as SA and GA to solve the problem ofdistribution network reconfiguration, it is very important to choose a good variableexpression. This is also true for the TS-based distribution network reconfigurationproblem. An initial attempt is to choose all feeders with switches as a set of variablesto represent the solution of the problem. With such a variable expression, eachelement of the solution vector represents one feeder with a switch. The value 0 and1 of one element in the solution vector denote that the status of correspondingswitch in the feeder is open and closed, respectively. It was found that such avariable expression is often not efficient because the extremely large number ofunfeasible non-radial solutions appearing at each generation will lead to a longcomputing time before reaching an optimal solution. A good variable expressiondesign, which can restrict each trial solution to be radial networks in distributionnetwork reconfiguration, is very important to improve the efficiency of searchprocess.

In this article, an upward-node expression, which has been developed in solvingthe problem of restorative planning of power system in [26], is adopted. As weknow, in a radial distribution system, each load node or transportation node hasonly one upward-node though it may have several downward-nodes. The upward-node expression chooses the upward-nodes of all load points as the variables of theproblem. That is, a vector of trial solution denotes the upward-nodes of all loadpoints. Here, the upward-node of load point refers to the node, from which the loadpoint is fed. By using the upward-node expression, the three-feeder distributionnetwork in Figure 1 can be expressed with Table 1.

Although this expression cannot always guarantee that the solution is a radialnetwork, it favors the solution with a larger probability to be a radial network.In this article, an effective scheme is integrated into the upward-node expression,which can restrict each trial solution to be radial networks.

Move and Neighborhood Design

TS is a restricted neighborhood search technique. Each trial solution is generatedfrom the current sub-optimal solution by the operation move. These trial solutions

Table 1The variable expression of the network in Figure 1

using upward-node expression

Node Upward-node Node Upward-nodenumber number number number

4 1 11 95 4 12 96 4 13 37 6 14 138 2 15 139 8 16 1510 8

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Figure 3. Flowchart of the single move.

form a subset of neighbors of current solution. In this article, the process of singlemove is described as Figure 3. Where

Kmax represents the total number of variables.Nmax represents the specified neighborhood sampling number.Node (K) represents the node whose upward-node is the kth element in the variable

expression. For example, in Table 1, the 8th element of variable expression is 9and the corresponding node is 11, so Node (8) = 11.

BN(K) represents the number of branches in current solution which connect toNode (K). For example, BN(8) = 1 because only node 9 is connected withnode 11.

BNmax(K) represents the maximum possible number of branches in the networkthat can connect to Node (K). For example, BNmax(8) = 2 because node 5and 9 can be connected with node 11.

In Figure 3, the process of checking the radiality of trial solutions is shown inFigure 4. In Figure 4, U(K) represents the upward-node of Node (K), that is, the

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Figure 4. Flowchart of checking the radiality.

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kth element in the variable expression. First of all, set A is defined in which feederswill be placed. Each feeder in set A has a “sending node” and a “receiving node.”The “sending node” is the source node, which feeds the “receiving node.” Beforechecking the radiality of a scheme, all branches in which no switches are associatedwith are added to set A. The rest of the feeders are then added to set A one byone through a recursive process. After one feeder has been added to set A, thecorresponding Flag(K) is set to 1 and N = N +1 where N is the number of feederswhich have been added to set A. T is used to indicate how many feeders are addedto set A in one iteration (K varied from 0 to Kmax). If T = 0 after one iteration,it means that no more feeders can be added to set A. If the upward-node in thefeeder is a source node, the feeder can be added to set A. As defined before, the“receiving node” receives power flow from the corresponding “sending node.” If theupward-node in one feeder has appeared in the “receiving nodes” of set A, it is asource node and according to our criterion, the feeder is allowed to be added to setA. Besides, if the upward-node in one feeder is a substation node, the feeder is alsoallowed to be added to set A since substation node is undoubtedly a source node.

Evaluation Function Design

In order to select the best solution among Nmax neighborhood sampling solutionsgenerated in each iteration, an evaluation function f(S) is defined to evaluate eachsolution. Although each trial solution will guarantee the formation of a radial net-work, it does not guarantee that they are all feasible solutions because some ofthem may violate other constraints. These constraints include transformer capac-ity constraints, feeder thermal capacity constraints, and voltage drop constraints.Obviously when a trial solution is an unfeasible solution, it cannot be evaluated bythe loss function Ploss defined in equation (1), so three other functions as f1(S),f2(S) and f3(S) are defined.

The evaluation function f(S) = f1(S) when transformer capacity constraints areviolated.

The evaluation function f(S) = f2(S) when feeder capacity constraints are vio-lated.

The evaluation function f(S) = f3(S) when voltage drop constraints are violated.The evaluation function f(S) = Ploss when no constraints are violated.

Generally, f1(S) > f2(S) > f3(S) > Pmaxloss is always guaranteed; where Pmaxlossrepresents the maximum line losses.

Tabu List

To prevent the algorithm from moving back to a region of the search space thathas been formerly visited in search process, a tabu list in which the reverse movesof performed moves are stored is created. These moves in the tabu list are called astabu moves, which are forbidden to be implemented in forming a trial solution fora given period (defined by a tabu tenure). By enforcing tabu moves, the tabu listcan avoid cycling and help the search process to escape from the local optima.

The dimension of the tabu list is called the tabu list size. In this article, thetabu list size is determined experientially and the tabu list is updated after each

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iteration [22]. That is, after each iteration, the new move is added to the tabu list,and an old move may be removed if it has been remained in the tabu list for Tmaxiterations. Tmax is called the tabu tenure, which is an important parameter of TS.

Aspiration Function

These are rules that override tabu restrictions; that is, if a certain move is forbiddenby tabu restrictions, then the aspiration level, when attained, can make this moveallowable. The definition of aspiration function is favorable for allowing a worthymove to be released from the tabu list. In this article, aspiration function is definedas the minimum evaluation function value found so far. If a tabu move fromthe current solution Scurrent can generate a trial solution, which is better thanaspiration function, then the aspiration level for the tabu move is attained and thetabu move can be overridden.

5. Simuation Results

The proposed method has been programmed with Microsoft Visual C++ and testedon a PC. Three test systems with different sizes have been chosen to test theproposed TS-based method for distribution network reconfiguration. The selectionof the control parameters Imax, Nmax, and Tmax in the proposed method is mainlybased on trial and error and experience. The value of Nmax and Tmax are oftenselected to be less than the number of variables. And the selection of Imax dependson the accuracy of final solutions. The larger the parameter Imax, the more accurateis the final solution. The value of Imax chosen should satisfy the specified range oferror.

The first example, the data from reference [9] is a three-bus system with3 feeders and 13 load demands, as shown in Figure 1. It is assumed that threenormally open tie switches are associated with branches 15, 21, and 26; 13 normallyclosed sectionalizing switches are associated with all other branches. Feeder sectionimpedance, system load data, and bus voltages can be found in [9]. The maximumiteration number Imax, the specified neighborhood sampling number Nmax and thetabu tenure Tmax are chosen as 5, 10 and 5, respectively. The optimal networkconfiguration is obtained, that is: the switches associated with branches 15 and 21are closed and the switches associated with branches 17 and 19 are opened. Thisresult is identical to the result obtained by using the method proposed by [9].Table 2 shows the results of example one using the proposed method.

Table 2Results of example one using the proposed method

Initial Reconfiguration by using ReconfigurationExample one network the proposed method result of [9]

Tie switches 15, 21, 26 17, 19, 26 17, 19, 26Loss (kW) 511.4 466.1 466.1Reduction rate 8.858% 8.858%Iteration time (s) 0.035

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Figure 5. Test system with 32 load demands.

The second example comes from reference [10], and consists of 32 load demands,as shown in Figure 5. Five tie switches exist between nodes (20, 33), (14, 34),(21, 35), (32, 36), and (28, 37), which are normally open. Sectionalizing switchesare also assumed to be associated with all other branches. The system data canbe obtained from [10]. The control parameters Imax, Nmax and Tmax are chosen as10, 10, and 10, respectively based on the experience obtained after running severalsimulations. The final optimal network configuration obtained is: close the switchesassociated with branches 33, 34, 35, and 36, and open the switches associated withbranches 7, 9, 14, and 32. The results of example two using the proposed methodare shown in Table 3 and compared with the results from [3] and [7]. It can be seenthat the result obtained from the proposed method is the same as that from [7] andbetter than that from [3]. Although the running time of the other two methods isunknown, the running time of the proposed method is very fast (0.043 s).

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Table 3Results of example two using the proposed method

After reconfiguration

Initial ProposedExample two network method Method in [3] Method in [7]

Tie switches 33, 34, 35, 7, 9, 14, 7, 10, 14, 7, 9, 14,36, 37 32, 37 32, 37 32, 37

Loss (kW) 196.5 136.355 137.142 136.355Reduction rate 30.61% 30.21% 30.61%Iteration time (s) 0.043

The data of the third example comes from reference [13, 14], and is composedof 69 load demands, as shown in Figure 6. Five tie switches exist between nodes(11, 43), (13, 21), (15, 46), (27, 65), and (50, 59), which are normally open.Sectionalizing switches are also assumed to be associated with all other branches.The control parameters, Imax, Nmax, and Tmax are chosen as 15, 10, and 10,respectively in a similar manner as example one and two. The optimal networkconfiguration is obtained in normal load: close the switches associated with branches(15, 46), (50, 59), and (27, 65), and open the switches associated with branches(14, 15), (55, 56), and (61, 62). This result is also identical to the results obtainedby using the method proposed by [13] and [14]. Table 4 shows the results of examplethree using the proposed method.

From the three examples shown above, we can say that the results fromthe proposed method are optimal. It is performing very well in convergence (theiteration number is not more than 15 in all cases) and only needs a short time toget the final results (the time is not more than 0.2 s even for example three), whichshows that it is very efficient and promising for practical applications.

Figure 6. Test system with 69 load demands.

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Table 4Results of example three using the proposed method

Reconfiguration Reconfigurationby using the result of

Example three Initial network proposed method [13] and [14]

Tie switches 70, 71, 72, 73, 74 15, 56, 62, 70, 71 15, 56, 62, 70, 71Loss (kW) 20.88 9.43 9.43Reduction rate 54.84% 54.84%Iteration time (s) 0.189

6. Conclusions

In this article, a new and efficient Tabu search method has been presented tosolve the problem of optimal distribution network reconfiguration for loss reduction,which is formulated as a non-linear, mixed-integer programming problem. The novelvariable “upward-node expression” approach is adopted and an effective schemeis integrated to restrict each trial solution in radial networks format. The othercomponents of the proposed Tabu search based method, including neighborhooddesign, evaluation function design, tabu list etc., are described in detail. Theproposed method has been tested on three example systems with different networksizes. Results show that the proposed Tabu search based method is feasible, efficientand promising for practical applications.

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