duration based reconfiguration of electric distribution networks using dynamic programming and...

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Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm Mohammad-Hossein Shariatkhah a , Mahmoud-Reza Haghifam a,, Javad Salehi a , Albert Moser b a Department of Electrical Engineering, Tarbiat Modares University, Tehran, PO Box 14115-111, Iran b IAEW, Aachen Technical University (RWTH), 52056 Aachen, Germany article info Article history: Received 29 August 2011 Received in revised form 15 December 2011 Accepted 18 December 2011 Available online 23 April 2012 Keywords: Distribution network Reconfiguration Dynamic programming Harmony search algorithm Graph theory abstract Feeder reconfiguration is one of the most important tasks for loss reduction and reliability improvement in distribution networks. Most of studies so far have investigated reconfiguration problem as a static problem considering fixed level of loads. This assumptions lead to suboptimal solution because of time-varying nature of loads in distribution networks. The switching operation should be cost effective and the reconfiguration scheme should balance the benefits in system loss reduction and reliability improvement against the costs of switching. Moreover, this is a dynamic problem and switching opera- tions of time intervals over a year are not independent. This paper presents a method to determine annual feeder reconfiguration scheme considering switching costs and time-varying variables such as load profiles. In the first stage of the proposed method, to obtain effective configurations, optimal config- uration for each day of year is determined independently using harmony search algorithm (HSA) and graph theory. After determination of effective configurations for the network, in the second stage, year is divided into multi equal periods and considering loss cost, interruption cost and also switching cost from a configuration to another configuration, dynamic programming algorithm (DPA) is used to find the optimum annual reconfiguration scheme. The proposed method has been tested on 95-bus distribu- tion network and the obtained results denote that to have an optimum solution it is necessary to compare operation costs dynamically. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Failure statistics reveal that distribution networks constitute the greatest risk to the uninterrupted supply of power. Moreover, distribution networks have the major portion of power system losses. Therefore, reliability improvement and loss reduction of these networks are necessary. Distribution network reconfigura- tion is one of the traditional methods implemented for these purposes exploiting normally opened and normally closed switches. Lots of researches have been conducted for distribution net- works reconfiguration so far. Marilyn presented the idea of distri- bution network reconfiguration for the first time in 1975 [1]. He presented a linear model for distribution network reconfiguration and solved it using discrete branch and bound method. In this method, initially all normally open switches are considered to be closed and subsequently normally closed switches which lead to loss reduction are opened. In [2] one proper normally open switch is selected and is assumed to be closed, then in the obtained loop, normally closed switches are opened respectively to find critical switch which leads to the most power loss reduction. This proce- dure is repeated for all of normally open switches until finding optimum feeder configuration. Disadvantage of this method is that the obtained solution is dependent on the primary configuration. In [3] Shirmohammadi has extended Merilyn Beck’s method. In this method first all normally open switches are closed and using load flow in created meshed network, switch which minimum current flow across is opened, this procedure is repeated until new radial configurations found. In [4] unlike previous methods, first all switches are opened and in each stage switch which closing of it leads to minimum increase in cost function is selected. Cost function in each stage is equal to proportion of increased loss to connected load in that stage. In [5] branch exchange method has been implemented for distribution network reconfiguration. Graph theory is used for reconfiguration of distribution networks in [6]. In this method distribution network is considered as a graph and each sub graph of the main graph which has a tree structure can be con- sidered as a network configuration. In this method starting with a feasible configuration, all tree based configurations are obtained using graph theory and after comparing cost of each configuration, optimal solution is achieved. Advantage of this method is finding global optimal solutions but its disadvantage is that this method cannot be implemented in large distribution networks. 0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijepes.2011.12.014 Corresponding author. Tel./fax: +98 21 82884347. E-mail address: [email protected] (M.-R. Haghifam). Electrical Power and Energy Systems 41 (2012) 1–10 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

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Page 1: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Electrical Power and Energy Systems 41 (2012) 1–10

Contents lists available at SciVerse ScienceDirect

Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Duration based reconfiguration of electric distribution networks usingdynamic programming and harmony search algorithm

Mohammad-Hossein Shariatkhah a, Mahmoud-Reza Haghifam a,⇑, Javad Salehi a, Albert Moser b

a Department of Electrical Engineering, Tarbiat Modares University, Tehran, PO Box 14115-111, Iranb IAEW, Aachen Technical University (RWTH), 52056 Aachen, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 29 August 2011Received in revised form 15 December 2011Accepted 18 December 2011Available online 23 April 2012

Keywords:Distribution networkReconfigurationDynamic programmingHarmony search algorithmGraph theory

0142-0615/$ - see front matter � 2012 Elsevier Ltd. Adoi:10.1016/j.ijepes.2011.12.014

⇑ Corresponding author. Tel./fax: +98 21 82884347E-mail address: [email protected] (M.-R. Ha

Feeder reconfiguration is one of the most important tasks for loss reduction and reliability improvementin distribution networks. Most of studies so far have investigated reconfiguration problem as a staticproblem considering fixed level of loads. This assumptions lead to suboptimal solution because oftime-varying nature of loads in distribution networks. The switching operation should be cost effectiveand the reconfiguration scheme should balance the benefits in system loss reduction and reliabilityimprovement against the costs of switching. Moreover, this is a dynamic problem and switching opera-tions of time intervals over a year are not independent. This paper presents a method to determineannual feeder reconfiguration scheme considering switching costs and time-varying variables such asload profiles. In the first stage of the proposed method, to obtain effective configurations, optimal config-uration for each day of year is determined independently using harmony search algorithm (HSA) andgraph theory. After determination of effective configurations for the network, in the second stage, yearis divided into multi equal periods and considering loss cost, interruption cost and also switching costfrom a configuration to another configuration, dynamic programming algorithm (DPA) is used to findthe optimum annual reconfiguration scheme. The proposed method has been tested on 95-bus distribu-tion network and the obtained results denote that to have an optimum solution it is necessary to compareoperation costs dynamically.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Failure statistics reveal that distribution networks constitutethe greatest risk to the uninterrupted supply of power. Moreover,distribution networks have the major portion of power systemlosses. Therefore, reliability improvement and loss reduction ofthese networks are necessary. Distribution network reconfigura-tion is one of the traditional methods implemented for thesepurposes exploiting normally opened and normally closedswitches.

Lots of researches have been conducted for distribution net-works reconfiguration so far. Marilyn presented the idea of distri-bution network reconfiguration for the first time in 1975 [1]. Hepresented a linear model for distribution network reconfigurationand solved it using discrete branch and bound method. In thismethod, initially all normally open switches are considered to beclosed and subsequently normally closed switches which lead toloss reduction are opened. In [2] one proper normally open switchis selected and is assumed to be closed, then in the obtained loop,normally closed switches are opened respectively to find critical

ll rights reserved.

.ghifam).

switch which leads to the most power loss reduction. This proce-dure is repeated for all of normally open switches until findingoptimum feeder configuration. Disadvantage of this method is thatthe obtained solution is dependent on the primary configuration.In [3] Shirmohammadi has extended Merilyn Beck’s method. Inthis method first all normally open switches are closed and usingload flow in created meshed network, switch which minimumcurrent flow across is opened, this procedure is repeated untilnew radial configurations found. In [4] unlike previous methods,first all switches are opened and in each stage switch which closingof it leads to minimum increase in cost function is selected. Costfunction in each stage is equal to proportion of increased loss toconnected load in that stage. In [5] branch exchange method hasbeen implemented for distribution network reconfiguration. Graphtheory is used for reconfiguration of distribution networks in [6]. Inthis method distribution network is considered as a graph and eachsub graph of the main graph which has a tree structure can be con-sidered as a network configuration. In this method starting with afeasible configuration, all tree based configurations are obtainedusing graph theory and after comparing cost of each configuration,optimal solution is achieved. Advantage of this method is findingglobal optimal solutions but its disadvantage is that this methodcannot be implemented in large distribution networks.

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2 M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10

In last decades intelligent search methods have been imple-mented for network reconfiguration problem widely. In [7] distri-bution network reconfiguration problem has been investigatedusing simulated annealing method. In [8,9] genetic algorithmhas been implemented for reconfiguration of distribution net-works. In [10] particle swarm optimization (PSO) method hasbeen implemented for reconfiguration problem considering dis-tributed generators; the feasibility of the proposed approach iscompared with other evolutionary methods such as geneticalgorithm (GA), tabu search (TS) over a realistic distribution testsystem. In [11] a new hybrid evolutionary (EA) algorithm basedon the combination of the honey bee mating optimization(HBMO) and the Discrete Particle Swarm Optimization (DPSO),called DPSO–HBMO, is implemented to solve a multi objectiveand non-differentiable distribution feeder reconfiguration prob-lem. Ref. [12] introduces an ant colony search algorithm (ACSA)to solve the optimal network reconfiguration problem for powerloss reduction. In [13] ant colony optimization method is used forreconfiguration of distribution networks with distributed genera-tion. Using interval analysis technique, Ref. [14] presented amethodology to deal with uncertainties in reliability inputs,electrical parameters and load data in the reconfiguration prob-lem. In [15] the feeder reconfiguration problem is formulatedas non-linear optimization problem and bacterial foraging opti-mization algorithm (BFOA) is used to find optimal configurationwith minimum loss. In [16], non-dominated sorting geneticalgorithm (NSGA) is used to solve reconfiguration problem withthe objective of operation cost minimization in restructuredenvironment.

Most of presented methods so far have implemented reconfigu-ration methods for fixed level of power demand whereas thisassumptions lead to suboptimal solution because of time-varyingnature of loads in distribution networks. In Ref. [17] networkreconfiguration and capacitor allocation are implemented for lossreduction using mixed integer nonlinear programming (MINLP)method. The proposed method considers the daily load curve rep-resented by a given number of load levels; however, it does notconsider switching costs. Ref. [18], is one of the few researcheswhich considers time-varying nature of loads and switching costsduring reconfiguration process. The objective function consists ofloss cost, outage cost and switching costs. In this method annualload curve is divided into multi periods load levels and the feederconfiguration of each load level is optimized using BPSO method.Disadvantage of this method is that configuration of each load levelis achieved based on load profile in that period and switching costfrom configuration in previous period network. Therefore, onlynetwork configuration in the previous period is considered indetermination of one period and configurations of other periodsare not considered. Whiles, one switching have impact on reliabil-ity and loss costs of multiple periods, so it is not optimal to com-pare the switching cost only with reliability and loss cost of theprevious period.

In this paper, a novel method has been presented to deter-mine the annual feeder reconfiguration scheme of a network con-sidering variable load profile. In order to achieve an optimalsolution, the costs of system loss, customer interruption andswitching, are compared dynamically to determine economicaltime and situation for a switching operation. The proposed meth-od is implemented on 95-bus distribution systems and theobtained results are presented to show the effectiveness of theproposed method.

This paper is organized as follows: Sections 2 and 3 are dedi-cated to the problem formulation and description of the proposedmethod respectively. Section 4 presents the results obtained withthe test system and finally conclusions about the results are dis-cussed in Section 5.

2. Problem formulation

Metering devices are usually being installed in distribution net-works to monitor and control the system. Using the data of feeder/substation loading, three models can be established to demonstrateload varying of residential, commercial and industrial customersover a year. Each of these models includes 8760 elements. Basedon the type of customers and annual average loading, using Eq.(1), annual load profile of each customer will be obtained:

Loadmc ðd; tÞ ¼

Xm2R;C;I

Loadavec �Wmðd; tÞ ð1Þ

where Loadmc ðd; tÞ and Wm(d, t) are the estimated load of customer c

and the load weighting for day d, time t, respectively. Loadavec de-

notes the average customer load for a customer c. Moreover, m isthe type of the customer and can be residential, commercial orindustrial.

Since load profile and energy loss varies with time, for calcula-tion of loss cost over a day or period based on load curves, it is nec-essary to use a load flow solution and compute loss for each hour ofthe period. Therefore the cost of energy loss over a period can beexpressed as:

CLOSS ¼XND

d¼1

X24

t¼1

XNl

l¼1

Cenergyðd; tÞ � Rl � I2l ðd; tÞ ð2Þ

where CLOSS is the cost of energy losses, Cenergy(d, t) represents theenergy cost ($/KW h) and can be assumed time-varying in differenthours of period, Nl is the number of distribution network lines, NDrepresents number of days in each time period. Moreover Rl and Il

are line resistance and line current, respectively.Similar to loss cost formulation customer interruption cost var-

ies with time too. To determine this cost, it should be computedthat when a feeder is interrupted with a probability, which cus-tomers will be interrupted, with which duration and how muchis the cost of the interruption for interrupted customers. Thereforethe customer interruption cost over a period is calculated as fol-lows [18]:

CCI ¼XND

d¼1

X24

t¼1

XNl

i¼1

kiðdÞli

XNload

j¼1

Cjðd; tÞLjðd; tÞ !

ð3Þ

where CCI represents customer interruption cost over a period, ki isoutage rate (failure/km) and can be assumed variable with time, li islength of line i, Nload is the number of interrupted customers due tointerruption in line i and should be determined for each new config-uration, Lj represents the load of customer j and also Cj is the inter-ruption cost ($/kW) of load j. Note that interruption cost ofresidential, commercial and industrial customers are different andalso can be assumed time-varying.

It is assumed that there is a breaker at the beginning of eachfeeder and when a fault occurs, it operates. So Nload is equal tothe number of all customers that are supplied from a feeder, whichincludes line i. Graph theory is implemented to determine Nloadfor all lines of each new configuration.

In this paper a year is divided into several periods and costs ofswitching operation between these periods are considered in theobjective function. If the number of time intervals in a year is NT,the total annual switching cost is calculated by:

TCSW ¼XNT�1

s¼1

CSWs ð4Þ

CSWs ¼ SW � NSWx;y ð5Þ

where TCSW represents total switching operation cost over a year.Moreover, CSWs and NSWx,y represent switching cost and total num-

Page 3: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Fig. 1. Voltage penalty functions used to compute fitness function [19].

Fig. 2. Current penalty functions used to compute fitness function [19].

M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10 3

ber of switching operations from configuration x in sth time periodto configuration y in s + 1th time period, respectively.

The voltage magnitude at each bus and current magnitude ateach branch are two constraints of this problem which are ex-pressed as follows:

Vmin 6 Vi 6 Vmax ð6Þ

jIij 6 Imax ð7Þ

where Vmin and Vmax are the minimum and maximum allowablevoltage magnitudes and Imax is maximum current magnitude,

Fig. 3. Flowchart of the

respectively. A penalty function is defined for each of these con-straints to restrict them in the allowable level in obtained results.Therefore if f(x) is the obtained objective function for a configura-tion without considering these constraints, fitness function of theconfiguration can be calculated as follows:

FtnsFun ¼ Fpenalty;V � Fpenalty;I � f ðxÞ ð8Þ

where Fpenalty,V and Fpenalty,I represent total penalty function for volt-age and current constraints violation, respectively. These penaltyfunctions are calculated as below [19].

Fpenalty;V ¼YND

d¼1

Y24

t¼1

YNb

i¼1

f ipenalty;v ð9Þ

Fpenalty;I ¼YND

d¼1

Y24

t¼1

YNl

i¼1

f ipenalty;i ð10Þ

Nb and Nl are the number of buses and lines respectively. Voltagepenalty function for bus i is drawn in Fig. 1. A similar function is alsoused for current of all lines, as shown in Fig. 2.

3. Proposed method

The proposed method for dynamic reconfiguration of distribu-tion networks is presented in this section. The presented methodadopt dynamic programming algorithm (DPA) for distribution fee-der scheduling. To run a DPA it is necessary to determine severalcandidate states in each period. In this problem each state is a con-figuration. As there are many feasible configurations for a distribu-tion network so it is necessary to find several effectiveconfiguration of a network.

Considering the flowchart shown in Fig. 3, the proposed algo-rithm contains two main parts. In the first part, a year is divided

proposed method.

Page 4: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Fig. 4. Procedure of finding effective configurations.

4 M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10

into 365 daily time periods and using harmony search algorithm(HSA) and graph theory, optimal configuration is obtained for eachday without considering interaction between periods. Objectivefunction used in HSA consists of loss and customer interruptioncosts. As optimal configurations are obtained for all levels of loadprofile over a year, so many effective configurations are obtainedfor the network. In the second part, a year is divided into multiequal periods, then considering loss and customer interruptioncosts and also switching cost, DPA finds annual feeder configura-tion scheduling using effective configurations. Details of men-tioned parts of the proposed method are investigated in continue.

3.1. Finding effective configurations using harmony search and graphtheory

For reconfiguration of distribution feeder dynamically, if thereare m periods and n feasible configurations for each period, there

Fig. 5. Forward dynamic pr

will be nm possible annual feeder scheduling scheme which one ofthese schemes is the best (least cost) annual reconfigurationscheme. This means it is a complex problem to find optimal dy-namic reconfiguration scheme especially in large distribution net-works. For solving this problem we have proposed a novelapproach in this paper which uses DPA method for distributionnetwork reconfiguration. DPA method uses effective configura-tions of a network based on annual load curve and determinesannual reconfiguration scheme considering switching cost be-tween periods. To find effective configurations, a year is dividedinto 365 daily periods and optimal configuration is obtained foreach period without considering interaction between periods,using HSA as a novel meta-heuristic method and graph theory.Note that a year can be divided into periods with arbitrary length,but shorter time intervals leads to finding more effective config-urations; considering more load level, the solution method willbe more accurate.

ogramming algorithm.

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M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10 5

In most of traditional optimization methods which have beenused for reconfiguration, a matrix of switches status X =[x1,x2, ...,xD] represents a configuration of network. xi can take 0or 1 value as open and close switches respectively and D denotestotal number of switches [13]. Since during optimization processin HSA, X takes random integer values (0 or 1), there will be a lotof infeasible configuration in each population which do not haveradial configuration. To decrease possibility of generating infeasi-ble configurations, in some previous researches, number of nor-mally open switches (number of 0) is limited to the number ofloops in initial network. Since this technique needs to add a con-straint or loop to optimization process, it will increase size of over-all optimization process. In this paper we have used matrix ofnormally opened switches x0 ¼ ðx01; x02; :::; x0NÞ to denote a configura-tion, in which x0i represent switch number and N denotes the num-ber of loops in original network. In other words, just normally openswitches are used for network representation in optimization pro-cess. To find loops of initial network, one of normally openswitches in the network is closed and a loop is created conse-quently. For finding branches of this loop all normally closedswitches of the network are opened respectively. If opening of anormally closed switch create radial configuration, that switch be-longs to the first loop of the initial network. This procedure is re-peated for all normally open switches of initial network.Obtained results indicate that using this technique takes less exe-cution time than that of the above procedure. Note that geneticbased methods also have disadvantage of generating infeasibleconfigurations due to mutation and crossover operators but wehave solved this problem based on HSA method and using graphtheory. Procedure of finding effective configurations is shown inFig. 4.

According to configuration matrix, it is obvious that most of dai-ly configurations are similar due to similarity in load level. Forexample first and second days’ configurations are similar in abovematrix. Considering non-repetitive configurations of this matrix,effective configurations are achieved and used in second part ofthe proposed method to find annual dynamic configuration of dis-tribution network.

Procedure of finding each day’s configuration using HSA is pre-sented in the following steps [20–24].

Step (1) Initialize the optimization problem and algorithmparameters. In this step the optimization problem is specifiedas follows:

Minimize f ðxÞ ¼ CLOSSþ CCI ð11Þ

where f(x) denotes the objective function. Furthermore, CLOSS andCCI represent loss and customer interruption costs for a day(ND = 1), respectively as expressed in Eqs. (2) and (3), x is a candi-date solution consists of N decision variables (xi). (xi) should besmaller or equal to the number of network lines. In addition, HSAparameters that are required to solve the desired optimizationproblem are specified in this step. These parameters are the har-mony memory size (HMS) or the number of solution vectors, har-mony memory considering rate (HMCR), pitch adjusting rate(PAR) and termination criterion (maximum number of searches).HMCR and PAR are parameters that are used to improve the solu-tion vector (both are defined in step 3).

Step (2) Initialize the harmony memory (HM): In this step, theharmony memory matrix (HM), shown in Eq. (11), is filled withas many randomly generated solution vectors as HMS. Thenusing graph theory, each vector is checked if the configurationassociated with that vector is a tree or not. Details of this pro-cess were discussed previously. If the configuration is not a treethe vector will be filled with new random values. If all HM vec-tors are tree go to step 3.

HM ¼

x1

x2

..

.

xHMS

266664

377775 ð12Þ

Step (3) Fitness function calculation: In order to calculate lossand interruption costs for each vector, a forward–backwardload flow method is used to compute bus voltages and line cur-rents for all hours of the day. As expressed in Eqs. (9) and (10),penalty functions are used if voltage and current constraints arenot satisfied and fitness function is calculated for each vectorusing Eq. (11). Afterward, HM matrix is sorted by the valuesof the fitness function.Step (4) Improvise a new harmony from the HM: A newharmony vector x0 ¼ ðx01; x02; . . . ; x0NÞ; is generated from the HM,based on memory considerations, pitch adjustments, andrandomization. For instance, the value of the first decision var-iable ðx01Þ for the new vector can be chosen from any value inthe specified HM range x1

1 � xHMS1 or randomly. Values of the

other decision variables x0i can be chosen in the same way.Two operators are used in HSA optimization method. The firstoperator is HMCR that indicates the probability of choosing avalue from values stored in the HM, and (1 � HMCR) indicatesprobability of choosing a feasible value which this value is notnecessarily stored in the HM. For example, HMCR of 0.9 indi-cates that the HSA will choose the decision variable value fromvalues stored in the HM with the probability of 90% or from theentire possible range with probability of 10%. This is similar tothe reason why genetic algorithms use a mutation rate in theselection process. Second operator of HSA optimization methodis PAR. PAR indicates the probability of adjustment for the pitchchosen from the HM and value of (1 � PAR) indicates the

probability of doing nothing. For example,

Yes with probability PARNo with probability ð1� PARÞ

�PAR of 0.3 indicates that

the algorithm will choose a neighboring value, with 30% HMCRprobability. The HMCR and PAR parameters, introduced in theHSA, help the algorithm find globally and locally improved solu-tions, respectively.Step (5) Update the HM: Initial and generated HM vectors aresorted by the objective function value and new HM will includebest harmony vectors of initial and generated HM vectors.Step (6) Repeat steps 4 and 5 until the termination criterion issatisfied. Mentioned procedure is executed for each day of thestudy period and after creation of configuration matrix(Fig. 4), effective configurations are determined.

After determination of effective configurations DPA is used forfinding annual feeder scheduling considering switching cost be-tween time intervals which its details are presented in the nextsection.

3.2. Dynamic programming algorithm

As mentioned in Section 3.1, after obtaining effective configura-tions, DPA is used to find annual reconfiguration scheme consider-ing switching cost. Assume a year is divided into n equal periodsand the optimal configuration of a network should be determinedover each of those periods dynamically, considering switchingcosts between periods. If there are m effective configurations fora network (m states in each period of DPA) and n periods there willbe about mn possible paths for feeder scheduling in a year. Withoutusing DPA it is needed to investigate all of paths simultaneously tofind minimum cost path. Since DPA has several advantages such as

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6 M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10

dimension reduction of problems it can be used for solving thisproblem. To find annual reconfiguration scheme using DPA, theobjective function is calculated as follows:

Minimize f ðxÞ ¼ CLOSSþ CCI þ TCSW ð13Þ

The objective function that is used in DPA (Eq. (13)) is similar tothe objective function that was used in HSA, but in Eq. (13), T CSWis added which represents total switching operation costs. Anotherdifference of Eq. (13) with Eq. (11) is that in Eq. (11), ND representsone day (ND = 1) but in Eq. (13) each period consists of more thanone day and loss and customer interruption costs should be calcu-lated for all days of each period.

Flowchart of DPA method is shown in Fig. 5. Study period is di-vided into n intervals which each interval has ND days. Before run-ning a DPA, it is needed to calculate loss and interruption costs ofeach state (each configuration during each time interval). More-over, it is required to calculate the transition cost between eachtwo states (switching operations cost between a configuration xto a configuration y). Here Eqs. (2) and (3) are used to calculate lossand interruption costs for all m effective configurations duringeach of n time intervals and Eq. (5) is used to calculate switchingoperations cost between each binary compound of all m effectiveconfigurations.

As discussed previously, there are m candidate states (feasibleconfigurations for a network) in each period with different lossand customer interruption costs, therefore, DPA should balancethe benefits in system reliability and loss against the costs ofswitching and determine optimum reconfiguration scheme for ayear. Starting from the first period, in each stage DPA determinethe path with minimum cost to arrive at each state of a period

Fig. 6. Real 95-busses distr

and other non-optimal paths are removed. So in the next stage,for the next time period, the path with minimum cost to arriveat each state is determined based on costs calculated in the previ-ous period and this procedure is repeated until finding least costpath between first and last interval. The recursive algorithm tocalculate the minimum cost is:

Fcos tðK; IÞ ¼ min½Pcos tðK; IÞ þ Scos tðK � 1; L : K; IÞ þ Fcos tðK � 1; LÞ�ð14Þ

where Fcost(K, I) is the least total cost to arrive at state (K, I) andPcost(K, I) is operation costs (loss and interruption costs) during state(K, I). Moreover Scost(K � 1, L:K, I) is transition (switching) cost fromstate (K � 1,L) to state (K,I). State (k,I) is the Ith configuration in per-iod K. For the forward DPA, a strategy is defined as the path fromone state to a state at the next period [25].

4. Numerical results

The proposed method has been tested on real 95-busses distri-bution network (Fig. 6), to exhibit the time-varying effects in an-nual feeder switching planning. The cost of electricity is assumedto be $6.5625 cents per kW h, the average customer interruptioncost for 1 h is assumed to be $0.482, $9.085, and $8.552 per kWfor residential, industrial, and commercial customers, respectively.Furthermore, the cost of one switching is assumed $203 which isone-twentieth of a new switch installation cost [18]. The proposedmethod has been simulated by MATLAB software with an execu-tion time of 6 h in a personal computer with 2.8 GHz CPU, 4 GBRAM. Daily and average annual load profiles of a distribution fee-der in Iran have been used as a pattern for residential, commercial

ibution network [18].

Page 7: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Fig. 7. Load profiles of a distribution feeder in Iran have been used in this paper as a pattern: Daily load profiles for a typical residential consumer.

Fig. 8. Load profiles of a distribution feeder in Iran have been used in this paper as a pattern: Annual average peak load for three typical commercial, residential and industrialconsumers.

M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10 7

and industrial consumers. Figs. 7 and 8 show daily load profiles fora typical residential consumer and annual average peak load forthree typical commercial, residential and industrial consumersduring 52 weeks of a year, respectively.

In this network, busses number 7–20, 30–34, 42–45, 67–70, 85–88 are considered as residential consumers, busses number 35–41,46–66, 77–84 are considered as commercial consumers and bussesnumber 2–6, 11–14, 21–29, 71–76, 89–95 are considered to beindustrial consumers.

Initial network (Fig. 6) loops are obtained using discussed pro-cedure in Section 3.1. These loops are as follows:

Loop1: 77–70–69–68–1–2–3–4–104–88Loop2: 16–17–18–19–80–67–66–61–103–92Loop3: 20–21–22–36–37–38–39–81–93–97Loop4: 27–28–29–30–53–54–83–95–101Loop5: 31–32–53–54–71–75–76–83–87–101Loop6: 5–6–7–40–41–42–43–78–89–98Loop7: 23–24–25–26–44–45–46–47–48–49–82–94–99Loop8: 56–57–58–59–60–61–62–63–64–65–86–102–103Loop9: 8–9–10–11–12–13–14–15–79–90–91Loop10: 33–34–35–50–51–52–84–96–100

Loop11: 53–54–55–72–73–74–85–101

For finding annual reconfiguration scheme for this network, ayear is divided into 365 days and configuration of each day is ob-tained using HSA. Since most of days in a year have approximatelysame load level, therefore most of obtained configurations aresimilar and dissimilar configurations are marked as effective con-figurations. In this test network 69 non-similar effective configura-tions are obtained and results are shown in Table 1. Each effectiveconfiguration is shown by its normally open switches.

Considering Table 1, there are 69 effective configurations basedon annual load curve. After derivation of feasible configurations,study period is divided to arbitrary m periods and considering nfeasible configurations annual feeder scheduling scheme is ob-tained using DPA. In this paper it is assumed that each time inter-val of DPA is a week. So there will be 52 weekly periods. Loss andcustomer interruption costs are calculated for each of these 69 con-figurations during all 52 weekly intervals. Moreover, switchingcosts between these 69 configurations are calculated. Finally,DPA is used for finding annual reconfiguration scheme consideringswitching cost between each week. The results will be as Table 2and Fig. 9.

Page 8: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Table 1Effective configurations, disregarding switching cost.

Configuration Opened switches Configuration Opened switches

1 4–13–19–30–35–49–55–76–78–81–86 36 4–19–32–39–49–51–60–78–79–83–852 4–15–18–30–32–39–43–52–55–60–82 37 4–19–32–42–49–51–79–81–83–85–863 4–15–19–22–30–43–49–59–73–84–87 38 4–19–39–43–49–51–55–79–83–86–874 4–15–19–22–32–43–49–60–83–84–85 39 4–26–32–60–74–78–79–80–81–83–845 4–15–19–27–32–42–55–60–81–82–84 40 4–29–32–35–43–49–55–65–79–80–816 4–15–19–27–32–49–55–64–78–81–84 41 4–30–32–35–39–43–49–55–60–79–807 4–15–19–28–37–49–55–78–84–86–87 42 4–30–39–49–52–55–60–78–79–80–878 4–15–19–29–34–38–55–60–78–82–87 43 7–15–19–22–32–49–65–77–83–84–859 4–15–19–30–31–43–52–81–82–85–86 44 14–19–22–29–43–49–60–77–84–85–87

10 4–15–19–30–35–49–55–78–81–86–87 45 14–19–30–32–39–43–49–55–65–77–8411 4–15–19–30–38–43–49–55–65–84–87 46 14–19–39–76–77–78–82–83–84–85–8612 4–15–19–30–39–43–49–55–60–83–84 47 14–30–32–39–59–70–78–80–82–84–8513 4–15–19–30–39–43–49–55–60–84–87 48 15–18–30–31–39–49–60–74–77–78–8414 4–15–19–30–39–43–55–82–84–86–87 49 15–19–26–29–32–35–65–77–78–81–8515 4–15–19–30–39–49–55–60–78–83–84 50 15–19–26–29–35–39–55–65–77–78–8716 4–15–19–30–43–49–55–60–81–83–84 51 15–19–26–30–42–52–55–65–77–81–8717 4–15–19–30–49–55–60–78–81–83–84 52 15–19–29–32–35–43–49–64–74–77–8118 4–15–19–32–39–43–49–55–60–83–84 53 15–19–30–34–49–55–77–78–81–86–8719 4–15–19–32–43–49–55–60–81–83–84 54 15–19–30–35–39–43–49–55–64–77–8720 4–15–19–39–43–49–55–60–83–84–87 55 15–19–30–39–43–55–60–77–82–83–8421 4–15–19–39–43–55–60–82–83–84–87 56 15–19–30–39–43–55–60–77–82–84–8722 4–15–22–28–32–49–55–78–80–84–86 57 15–19–30–43–55–60–77–81–82–84–8723 4–15–30–32–39–43–49–55–60–80–84 58 15–19–30–55–60–77–78–81–82–84–8724 4–15–30–39–43–49–55–80–84–86–87 59 15–19–31–42–52–60–73–77–81–82–8325 4–15–30–39–49–55–78–80–84–86–87 60 15–19–32–43–77–81–82–83–84–85–8626 4–18–30–35–43–49–55–65–79–81–87 61 15–19–32–77–78–81–82–83–84–85–8627 4–19–22–29–31–43–49–60–79–84–85 62 15–30–31–43–49–60–74–77–80–81–8428 4–19–22–30–33–49–65–78–79–85–87 63 19–22–28–31–49–52–65–77–78–79–8529 4–19–22–49–52–60–74–78–79–83–87 64 19–28–31–43–65–72–77–79–81–82–8430 4–19–29–32–38–55–78–79–82–84–86 65 19–29–39–49–65–77–78–79–84–85–8731 4–19–29–39–42–49–52–55–60–79–87 66 19–30–32–34–39–49–60–77–78–79–8532 4–19–30–31–49–54–65–78–79–81–84 67 19–30–38–43–48–60–74–77–79–84–8733 4–19–30–35–39–43–49–55–59–79–87 68 19–37–43–49–52–72–77–79–83–86–8734 4–19–30–35–55–63–78–79–81–82–87 69 30–35–39–48–60–77–78–79–80–85–8735 4–19–30–39–41–49–74–79–84–86–87

Table 2Feeder scheduling of all periods using dynamic programming algorithm.

Weeks Opened switches Interruption cost ($) Loss cost ($)

1–10 15–19–30–43–55–60–77–81–82–84–87 246709.5 194226.911 4–15–19–30–49–55–60–78–81–83–84 111301.1 69189.9312 4–15–19–30–39–43–49–55–60–83–84 128904.5 98941.2813 15–19–30–55–60–77–78–81–82–84–87 167034.7 107860.214–15 15–19–30–43–55–60–77–81–82–84–87 86207.61 49474.3216–17 15–19–30–39–43–55–60–77–82–84–87 68304.37 54028.9818 4–15–19–30–39–43–49–55–60–83–84 215945.6 106630.419 4–15–19–39–43–49–55–60–83–84–87 183016.9 122585.420–21 4–15–19–30–39–43–49–55–60–84–87 156203.6 94946.5422–23 4–15–19–30–39–49–55–60–78–83–84 310359 184227.224–52 15–19–30–39–43–55–60–77–82–84–87 510345.3 341892.5

8 M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10

To illustrate the optimal annual feeder reconfiguration scheme,results of Table 2 are drawn in Fig. 9. In this figure, EC representeach of 69 effective configurations obtained from Table 1. More-over, cost of switching (CSW) from a configuration to another con-figuration represents the transition cost from one state to anotherstate.

The proposed method repeated without considering switchingcost between time intervals and results are shown in Table 3.

Comparing results with and without considering switching costbetween time intervals, it is obvious that number of switchingoperations is decreased in the case of considering switching costwith respect to the situation that switching cost is ignored in opti-mization process.

Table 4 shows annual total costs using different reconfigurationmethods. For the configuration shown in Fig. 6, the total annualcost is $3691,062. Considering one reconfiguration for a whole yearand neglecting the switching cost, the annual cost is reduced to

$3686,316. Comparing the obtained results from second and thirdrows of Table 4 denotes that it is necessary to compare operationcosts consists of system loss, switching costs and reliability costsdynamically to have an optimum solution. As it can be seen multi-ple reconfigurations without considering the switching cost inoptimization process results total cost of $3637,259. This meansif we do not consider switching operation cost in the optimizationprocess, number of switching operations during a year (Table 3)will be increased comparing the case switching operation cost isconsidered in optimization process (Table 2).

5. Conclusion

Network reconfiguration is one of most important tasks for lossreduction and also reliability improvement in distribution net-works. A lot of researches have been conducted in this area in pre-vious decades but time varying nature of load level has been

Page 9: Duration based reconfiguration of electric distribution networks using dynamic programming and harmony search algorithm

Fig. 9. Optimal annual feeder reconfiguration scheme determined by DPA.

Table 3Annual reconfiguration scheme, disregarding switching cost.

Weeks Opened switches Weeks Opened switches

1 15–19–30–39–43–55–60–77–82–84–87

28 15–19–30–39–43–55–60–77–82–84–87

2 15–19–30–43–55–60–77–81–82–84–87

29 15–19–32–43–77–81–82–83–84–85–86

3–4 15–19–32–43–77–81–82–83–84–85–86

30 15–19–30–43–55–60–77–81–82–84–87

5–7 15–19–30–43–55–60–77–81–82–84–87

31 15–19–30–39–43–55–60–77–82–84–87

8 15–19–32–43–77–81–82–83–84–85–86

32–33 15–19–30–43–55–60–77–81–82–84–87

9 15–19–30–43–55–60–77–81–82–84–87

34–35 15–19–30–39–43–55–60–77–82–84–87

10–11 15–19–32–43–77–81–82–83–84–85–86

36 4–15–30–39–43–49–55–80–84–86–87

12 4–15–19–30–39–43–49–55–60–83–84

37–38 15–19–30–43–55–60–77–81–82–84–87

13 15–19–32–77–78–81–82–83–84–85–86

39–40 15–19–30–39–43–55–60–77–82–84–87

14–15 15–19–30–43–55–60–77–81–82–84–87

41 15–19–30–43–55–60–77–81–82–84–87

16–17 15–19–30–39–43–55–60–77–82–84–87

42–43 15–19–30–39–43–55–60–77–82–84–87

18 4–15–19–30–39–43–49–55–60–83–84

44–45 15–19–30–43–55–60–77–81–82–84–87

19 4–15–19–39–43–49–55–60–83–84–87

46 15–19–30–39–43–55–60–77–82–84–87

20 4–15–19–39–43–55–60–82–83–84–87

47 4–15–19–30–39–43–55–82–84–86–87

21 15–19–32–43–77–81–82–83–84–85–86

48 15–19–30–43–55–60–77–81–82–84–87

22 4–15–19–30–49–55–60–78–81–83–84

49 15–19–32–77–78–81–82–83–84–85–86

23 4–15–19–30–39–49–55– 50 4–15–19–30–39–43–55–

Table 3 (continued)

Weeks Opened switches Weeks Opened switches

60–78–83–84 82–84–86–8724 15–19–30–43–55–60–77–

81–82–84–8751 15–19–30–39–43–55–60–

77–82–84–8725 15–19–32–43–77–81–82–

83–84–85–8652 15–19–30–43–55–60–77–

81–82–84–8726–27 15–19–30–43–55–60–77–

81–82–84–87

Table 4Different configuration methods comparison.

Configuration method Losscosts andinterruptioncosts

Switchingcosts

Totalcosts

Base configuration 3691,062 No Sw. 3691,062One reconfiguration from base

configuration3686,316 No Sw. 3686,316

Multiple reconfigurations withoutconsidering the switching cost

3606,200 31,059 3637,259

Multiple reconfigurations by DPA 3608,300 4060 3612,360

M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10 9

ignored in most of these researches. In other words, reconfigura-tion optimization process based on fixed load level leads to suboptimal solutions. Furthermore switching operations cost whichhave considerable effect on reconfiguration scheme have beenignored in previous researches. In this paper a novel method hasbeen presented for annual reconfiguration in distribution networks

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10 M.-H. Shariatkhah et al. / Electrical Power and Energy Systems 41 (2012) 1–10

considering annual load level and switching costs. This methoduses HSA method as a meta-heuristic approach to find effectiveconfigurations considering load profile and DPA uses theseconfigurations to find annual configuration considering switchingcost between time intervals. Obtained results indicate consider-able difference between traditional methods and the proposedmethod.

References

[1] Merlin A, Back H. Search for a minimum-loss operating spanning treeconfiguration for an urban power distribution system. In: Proc Of 5th powersystems comp conf, September 1–5, 1975.

[2] Civanlar S, Grainger JJ, Yin H, Lee SSH. Distribution feeder reconfiguration forloss reduction. Power Deliver IEEE Trans 1988;3:1217–23.

[3] Shirmohammadi D, Hong HW. Reconfiguration of electric distributionnetworks for resistive line losses reduction. Power Deliver IEEE Trans1989;4:1492–8.

[4] DcDermott TE, Drezga I, Broadwater RP. A heuristic nonlinear constructivemethod for distribution system reconfiguration. Power Syst IEEE Trans1999;14:478–83.

[5] Baran ME, Wu FF. Network reconfiguration in distribution systems for lossreduction and load balancing. Power Deliver IEEE Trans 1989;4:1401–7.

[6] Morton AB, Mareels IMY. An efficient brute-force solution to the networkreconfiguration problem. Power Deliver IEEE Trans 2000;15:996–1000.

[7] Chiang HD, Jean-Jumeau R. Optimal network reconfigurations in distributionsystems I. A new formulation and a solution methodology. Power Deliver IEEETrans 1990;5:1902–9.

[8] Nara K, Shiose A, Kitagawa M, Ishihara T. Implementation of genetic algorithmfor distribution systems loss minimum re-configuration. Power Syst IEEE Trans1992;7:1044–51.

[9] Zhu JZ. Optimal reconfiguration of electrical distribution network using therefined genetic algorithm. Electric Power Syst Res 2002;62:37–42.

[10] Olamaei J, Niknam T, Gharehpetian G. Application of particle swarmoptimization for distribution feeder reconfiguration considering distributedgenerators. Appl Math Comput 2008;201:575–86.

[11] Niknam T. An efficient hybrid evolutionary algorithm based on PSO and HBMOalgorithms for multi-objective distribution feeder reconfiguration. EnergyConvers Manage 2009;50:2074–82.

[12] Su CT, Chang CF, Chiou JP. Distribution network reconfiguration for lossreduction by ant colony search algorithm. Electric Power Syst Res2005;75:190–9.

[13] Yuan-Kang W, Ching-Yin L, Le-Chang L, Shao-Hong T. Study of reconfigurationfor the distribution system with distributed generators. Power Deliver IEEETrans 2010;25:1678–85.

[14] Zhang P, Li W, Wang S. Reliability-oriented distribution networkreconfiguration considering uncertainties of data by interval analysis. Int JElectric Power Amp Energy Syst 2012;34:138–44.

[15] Sathish Kumar K, Jayabarathi T. Power system reconfiguration and lossminimization for an distribution systems using bacterial foraging optimizationalgorithm. Int J Electric Power Amp Energy Syst 2010.

[16] Chandramohan S, Atturulu N, Devi RPK, Venkatesh B. Operating costminimization of a radial distribution system in a deregulated electricitymarket through reconfiguration using NSGA method. Int J Electric Power AmpEnergy Syst 2010;32:126–32.

[17] de Oliveira LW, Carneiro Jr S, de Oliveira EJ, Pereira JLR, Silva Jr IC, Costa JS.Optimal reconfiguration and capacitor allocation in radial distribution systemsfor energy losses minimization. Int J Electric Power Amp Energy Syst2010;32:840–8.

[18] Shih-An Y, Chan-Nan L. Distribution feeder scheduling considering variableload profile and outage costs. Power Syst IEEE Trans 2009;24:652–60.

[19] Masoum MAS, Ladjevardi M, Jafarian A, Fuchs EF. Optimal placement,replacement and sizing of capacitor banks in distorted distribution networksby genetic algorithms. IEEE Trans Power Deliver 2004;19:1794–801.

[20] Khorram E, Jaberipour M. Harmony search algorithm for solving combinedheat and power economic dispatch problems. Energy Convers Manage2011;52:1550–4.

[21] Vasebi A, Fesanghary M, Bathaee SMT. Combined heat and power economicdispatch by harmony search algorithm. Int J Electric Power Energy Syst2007;29:713–9.

[22] Geem ZW, Kim JH, Loganathan GV. A new heuristic optimization algorithm:harmony search. Simulation 2001;76:60–8.

[23] Afkousi-Paqaleh M, Rashidinejad M, Pourakbari-Kasmaei M. Animplementation of harmony search algorithm to unit commitment problem.Electric Eng 2010;92:215–25.

[24] Khazali AH, Kalantar M. Optimal reactive power dispatch based on harmonysearch algorithm. Int J Electric Power Amp Energy Syst 2011;33:684–92.

[25] Wood AJ, Wollenberg BF. Power generation operation and control. 2nded. Addison Wesley; 1996.