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Energy 94 (2016) 786e798

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Energy

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An aggregated model for coordinated planning and reconfiguration ofelectric distribution networks

Hamidreza Arasteh, Mohammad Sadegh Sepasian, Vahid Vahidinasab*

Department of Electrical Engineering, Abbaspour School of Engineering, Shahid Beheshti University, Tehran, Iran

a r t i c l e i n f o

Article history:Received 3 May 2015Received in revised form21 November 2015Accepted 23 November 2015Available online 18 December 2015

Keywords:Active distribution systems planningBi-level optimizationDemand response programsDistribution systems reconfiguration

* Corresponding author. Tel.: þ98 21 73932526.E-mail addresses: h_arasteh@sbu.ac.ir (H. Ara

(M.S. Sepasian), v_vahidinasab@sbu.ac.ir (V. Vahidina

http://dx.doi.org/10.1016/j.energy.2015.11.0530360-5442/© 2015 Elsevier Ltd. All rights reserved.

a b s t r a c t

This paper proposes a coordinated distribution system reconfiguration and planning model to deal withthe problem of active distribution expansion planning. DR (Demand response) programs are modeled asvirtual distributed resources to cover the effect of uncertain parameters. A bi-level optimization proce-dure is developed to solve the proposed model. At the first level, an optimization problem is solved usingPSO (particle swarm optimization) algorithm to determine the system expansion and reconfigurationplans. Next, the second level minimization problem is developed based on the sensitivity analysis. TheDR programs are taken into account in the second level problem to encounter with the problem un-certainties. Therefore, the proposed model incorporates the problem of DSR (distribution systemreconfiguration) with system expansion problem, while the presence of DR is considered to enhance theeffectiveness of the problem. The IEEE 33-bus standard test system is utilized to investigate the per-formance of the proposed model. The simulation results approve the advantages of the proposed modeland its economical profits for distribution network owners.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Distribution system expansion planning problem consists ofsizing, timing and siting of distribution facilities, while the re-strictions of the system and components are satisfied to provideforecasted load [1,2]. DEP requires a complex optimization proce-dure due to the nonlinear and combinatorial nature of the problem[3]. Various optimization algorithms are proposed for the bestallocation of limited financial resources [4]. Dynamic planning [5],graph-theory models [6], and heuristic algorithms such as simu-lated annealing, GA, EA, AC, and PSO are the examples of thesemethods [7e9]. Review of the literature shows that heuristicmethods are being used increasingly in spite of their random na-ture [10,11].

The development of distribution systems, poses new challengesand problems regarding electrification and desired reliability level[12]. Changes in the designing, planning and operation of

steh), m_sepasian@sbu.ac.irsab).

distribution networks are necessary to cope with the new chal-lenges and requirements of developing systems [12]. A hugeburden of research has investigated the planning of distributionnetworks. The following references are some of the studies in thisarea of research. Carrano et al. [13] proposed a multiobjectiveapproach to design a distribution system. The objective functionsincluded monetary cost and system failure indices includingeconomical costs of investment, maintenance, energy losses andalso failure rate costs. Venkata et al. [12] reiterated the necessity ofchanges in the designing, planning, operation and management ofdistribution networks in future power systems. They investigatedapproaches to cope with such challenges in the developed coun-tries (like the United States and the United Kingdom) and thefastest developing countries (such as China and India). Haffneret al. [2] introduced a multistage model in the planning of dis-tribution networks. The objective function was to minimize thenet present value of investment cost, as well as the operation andmaintenance costs. The constraints in Ref. [2] consisted of thefacilities' operational restrictions, voltage ranges, and logical con-straints decreasing the search space. Najafi et al. [14] utilized GA tooptimally design a large-scale distribution system. They deter-mined the location and size of substations and medium voltage

Delta:1_given nameDelta:1_surnameDelta:1_given namemailto:h_arasteh@sbu.ac.irmailto:m_sepasian@sbu.ac.irmailto:v_vahidinasab@sbu.ac.irhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.energy.2015.11.053&domain=pdfwww.sciencedirect.com/science/journal/03605442http://www.elsevier.com/locate/energyhttp://dx.doi.org/10.1016/j.energy.2015.11.053http://dx.doi.org/10.1016/j.energy.2015.11.053http://dx.doi.org/10.1016/j.energy.2015.11.053

Nomenclatures

Indicatorsy planning yearsncl network candidate linesnf network feedersT time periodsCT various types of candidate linesm bus numbers

Decision variablescncl ðyÞ integer variable that is equal to “CT” if feeder “ncl” is

reinforced with line type “CT”; otherwise, it is 0zncl ðyÞ binary variable that is equal to 1 if feeder “ncl” is

reinforced in year “y”; otherwise it is 0znf ðT ; yÞ binary variable that is equal to 1 if feeder “nf” is

selected in the time period “T” of year “y”; otherwise itis 0

pDRm ðT ; yÞ active power enabledwith DR programs at bus “m” andthe time interval “T” of year “y” [kW]

vnf ðyÞ integer variable that is equal to “CT” if the type offeeder “nf” is “CT”; otherwise it is 0

VariablesNPVC net present value of total planning costs [$]Cupg(y) network upgrading cost in year “y” [$]CLoss(y) total cost of energy losses in year “y” [$]Ctr(y) total cost of imported energy from the transmission

grid in year “y” [$]CDR(y) total DR cost in year “y” [$]CR(y) total network reliability cost in year “y” [$]plossnf ðT; yÞ active power losses of feeder “nf” in the time period “T”

of year “y” [kW]qlossnf ðT; yÞ reactive power losses of feeder “nf” in the time period

“T” of year “y” [kVAR]ptr(T,y) imported power from the transmission grid in the time

period “T” of year “y” [kW]pfnf ðT; yÞ power flow of feeder “nf” in the time period “T” of year

“y” [kW]CDRm ðT; yÞ cost of DR at bus “m” and the time period “T” of year “y”

[$/kW hour]TDRm ðT ; yÞ total enabled duration of DR at bus “m” and the time

period “T” of year “y” [hour]Vm(T,y) voltage level of bus “m” in the time period “T” of year

“y” [kV]Inf ðT ; yÞ current of feeder “nf” in the time period “T” of year “y”

[A]Psub(T,y) amount of injected active power from the distribution

substation in the time period “T” of year “y” [kW]Qsub(T,y) amount of injected reactive power from the

distribution substation in the time period “T” of year“y” [kVAR]

qDRm ðT ; yÞ reactive power enabled with DR programs at bus “m”and the time interval “T” of year “y” [kVAR]

DDRm ðyÞ total enabled duration of DR at bus “m” in year “y”

Parametersi discount rate

UCðcncl ðyÞÞ installation cost of line “CT” per kilometer [$/km]Lncl length of line “ncl” [km]Cfncl fixed cost of feeder “ncl” [$]t(T,y) duration of the time period “T” of year “y” [hour]LC(T,y) loss cost in the time period “T” of year “y” [$/kW hour]EC(T,y) cost of imported energy from the transmission grid in

the time period “T” of year “y” [$/kW hour]lðvnf ðyÞÞ failure rate of line “CT” per kilometer and per year [fail/

km year]CCLF cost of curtailed load per fault [$/kW fail]Lnf length of line “nf” [km]rpðvnf ðyÞÞaverage duration of fault on line “CT” [hour/fail]HEC energy cost per hour of fault [$/kW hour]Vmin minimum permissible voltage level [kV]Vmax maximum permissible voltage level [kV]Imaxnf ðyÞ permitted maximum current limit of feeder nf in year

“y” [A]pm(T,y) amount of active load at bus “m” in the time period “T”

of year “y” [kW]qm(T,y) amount of reactive load at bus “m” in the time period

“T” of year “y” [kVAR]DDR;maxm ðyÞ maximum enabled duration limit of DR at bus “m” in

year “y”pDR;maxm ðT ; yÞ maximum penetration level of DR at bus “m” and

the time period “T” of year “y” [kW]

SetsLcl set of all candidate linesLf set of all network feedersY set of time periodsG set of all candidate line typesJ set of planning yearsD set of system buses

AbbreviationsDSR distribution system reconfigurationDR demand responseDEP distribution expansion planningGA genetic algorithmEA evolutionary algorithmAC ant colonyPSO particle swarm optimizationTBP time-based programIBP incentive-based programMBP market-based programIEA international energy agencyMINLP mixed-integer non-linear programmingNLP non-linear programmingMILP mixed-integer linear programmingAIS artificial immune systemsDSCNO direct search continuous nonlinear optimizationOO ordinal optimizationSFLA shuffled frog leaping algorithmMPDIPA modified primal-dual interior point algorithmABC artificial bee colonyVSLA variable structure learning automataNDSGA non-dominated sorting GA

H. Arasteh et al. / Energy 94 (2016) 786e798 787

H. Arasteh et al. / Energy 94 (2016) 786e798788

feeders based on the concept of loss characteristics matrix con-cerning the constant and variable cost terms and operationalconstraints. Martins et al. [15] explored the safe, reliable andeconomic planning of distribution systems. Their objective func-tion included the costs of reliability, power losses, and importedenergy from the transmission system, as well as the investmentcosts. Esmaeeli et al. [16] proposed an MINLP problem for plan-ning distribution substations with the objective function of in-vestment, maintenance, losses and reliability costs.

Recent studies strongly focus on the role, importance, advan-tages, and difficulties of smart grids [7]. Smart grids are defined ascombination of general concepts to enhance the overall func-tionality of the electric power delivery system [17]. In fact, theyprovide suitable infrastructure to enable DR programs [17]. DR isconsidered as one of the most important elements of smart gridsenabled by end-users to motivate changes in the power con-sumption patterns [10]. Ridder et al. [18] investigated the influ-ence of DR programs in a future smart electricity system in 2020.Also the role and the importance of DR programs in smart gridsare evaluated in Ref. [19]. Aalami et al. [20] elaborated compre-hensive investigations on DR programs and their modeling. It isnoteworthy that reduction of electricity price, security enhance-ment, resolving lines congestion, decreasing the fuel dependency,and improvement of market liquidity are some of the benefits ofDR [20e23]. According to the strategic plan of IEA, DR programsare considered as the first choice in all energy policy decisions[21]. They were firstly introduced as some measures for solvingsystem deficiencies. However, the increasingly rate of these pro-grams and their success in practice made them to be regarded assome generation resources. DR programs can be classified intothree groups: TBPs, IBPs and MBPs. The details of the DR programsare provided in Ref. [10].

Future predictions of power systems are mainly focused on therole of smart grids, the penetration level of distributed resources,pollution decrement policies, and enhanced DR potential level [24].The future vision of smart grid has been investigated in Ref. [25].The backbone of smart grids concentrates on the environmentaldriven programs incorporating various clean generations, demandresponse and distributed generation for the best utilization of fa-cilities, and enhancing the customer choice [26]. Many studies arecurrently exploring the components and features of smart grids.Fig. 1 shows some of these main components and features [25,26].

Alvarez-Herault et al. [27] investigated the role of smart distri-bution systems to cope with the network challenges. Two ap-proaches are introduced in Ref. [27] to design more flexible andsmarter distribution systems: novel architecture and intelligentsystems. The main focus of this paper is on the system architectureand operational conditions.

The current trends and the future expectations together withthe barriers of constructing a smart grid are discussed in Ref. [28].The paper deals with utility barriers in the current and future po-wer systems and possible solutions. In addition, participation ofcustomers in electricity generation and consumption, automationin distribution and transmission levels, and utilization of variablegeneration units in both bulk and distributed levels are introducedas some of the future expectations.

Distribution systems have some normally close and normallyopen switches. By switching operations, the lines' power flow,power losses and voltage levels will be changed. Generally,reconfiguration is to transfer parts of loads from one feeder toanother. DSR can reduce power losses and improve the opera-tional condition of the system. Furthermore, releasing the ca-pacity of distribution networks and substations can reduce theexpansion requirements as a consequence of DSR. Hence, DSR canhave direct effect on the expansion plans by mitigating the

problem constraints. A long-term multiobjective planningframework is proposed in Ref. [29] to maximize the benefits ofDSR besides the allocation of distributed generation units. Lines'reinforcement plan, network reconfiguration and planning ofdistributed generation units are handled in Ref. [29]. A widerange of algorithms have been introduced to solve the DSRproblem. Among them, hybrid fuzzy-bees algorithm [30], hybridbig bang-big crunch algorithm [31], artificial immune networks[11], and other methods such as hyper-cube AC optimization,PSO, AIS and adaptive imperialist competitive algorithm can bementioned [32].

Considering the complexity of DEP problems, the probabilisticnature of uncertain parameters is ignored in many studies [33].However, the presence of such uncertain parameters and their ef-fects on the decision results oblige the network planners to enroll asuitable framework to model the probabilistic parameters. For thispurpose, numerous methods such as chance-constrained optimi-zation [34], decision analysis [35], robust optimization [36,37], andstochastic programming [38] algorithms have been proposed in theliterature. All these algorithms seek to find a flexible and robustsolution to cope with the problem uncertainties.

Table 1 chronologically presents some of the studies aroundthe distribution expansion planning. The details of these papersare compared together based on their main characteristicsincluding distribution voltage level, mathematical modeling,problem specifications, and optimization procedure in the last rowof the table. According to Table 1, the primary distribution systemexpansion planning in the long-term horizon is investigated in thispaper. The proposed multistage model is a mixed integer non-linear problem.

This paper proposes a novel planning framework, which in-corporates the DR, DSR, and DEP problems. The time-variablenature of load profile is considered for different energy sectors.Indeed, the reconfiguration of distribution networks is coordi-nated with the expansion planning problem, while the potentialof DR programs is integrated. The main aim of the proposedmodel is to decrease and postpone the expansion and operationcosts. It is worth mentioning that market-based DR programs aremodeled to mitigate the effect of load uncertainties. In addition, abi-level optimization algorithm is proposed to solve the intro-duced problem. The first level is a PSO-based optimizationproblem with the aim of minimizing the costs of feeders' rewir-ing, energy losses, imported energy from the transmissionnetwork, and the reliability cost. The second level is developedbased on sensitivity analysis for decreasing the effects of un-certainties with the minimum DR cost. Accordingly, the worstuncertainties regarding the load increment rates are considered.Hence, the planning problem must satisfy the system constraintseven if the worst uncertainties occur. As already mentioned,responsive loads participate in the DR contracts in the market-based mechanism. Thus, each customer will bid based on his/her willingness and potential. Thereby, it is assumed that there isno uncertainty according to the customers' behavior to partici-pate in the DR because it is actually considered in their biddingstrategy. Therefore, it is expected that responsive loads willparticipate when they are called by the DR. Moreover, the bi-leveloptimization procedure will enhance the convergence of therelatively large-scale problem. Indeed, dividing the proposedproblem into two smaller optimization problems will effectivelyhelp the convergence of the optimization tool to find the opti-mum solutions. In addition, the sensitivity analysis method doesnot reflect any convergence difficulty [39]. More details of theintroduced optimization algorithm are given in Section 2.3.Pseudo-dynamic approach is utilized for optimizing the proposedproblem in each year of the planning horizon.

Fig. 1. The main features and components of smart grids.

H. Arasteh et al. / Energy 94 (2016) 786e798 789

Briefly, the main contributions of this paper can be stated as thefollowing:

� A coordinated framework is designed between the DSR and DEPproblems considering the time-variable nature of the loadpatterns;

� A bi-level optimization procedure is applied for optimizing theproposed framework;

� The presence of market-based DR programs is modeled.

The rest of the paper is organized as follows. Section 2 dealswith the problem formulations including the objective function,problem constraints, and details of the optimization method. Sec-tion 3 is devoted to the simulation results, which are obtained usingthe IEEE 33-bus standard distribution system. Finally, conclusionremarks are elaborated in Section 4.

2. Problem modeling and formulations

In this section, the proposed multistage problem is mathemat-ically formulated. The specific feature of the proposed bi-level

problem is to coordinate the DSR and DEP problems, while thepotential of DR is taken into account.

2.1. Objective function

The main objective function consists of the following costterms:

� Upgrading cost: total investment costs to reinforce the systemlines;

� Cost of power losses: total costs corresponding to the losses of thedistribution feeders;

� Imported energy cost: total costs for purchasing electrical powerfrom the transmission grid;

� DR cost: total costs for encouraging electricity customers toparticipate in DR programs when they are called by the DR;

� Reliability cost: total costs corresponding to failure rates andrepair times.

As mentioned above, the proposed problem is solved using thebi-level optimization procedure. The first level minimizes the costsof line reinforcement, energy losses, and purchased power from the

Table 1Classification of the distribution system planning features.

References Mathematical modeling Distribution level Horizon time [year/stage] Problem specifications Optimization procedure

Uncertainty DR programs DSR

[40] MILP Primary þ Secondary 1 ILOG AMPL CPLEX System[41] MINLP Secondary 1 EA[8] MINLP Primary 10 and 20 ✓ AIS[42] NLP Primary þ Secondary 20þ DSCNO[2] MILP Primary 4 Branch and bound[14] MINLP Primary 10 GA[43] MINLP Secondary 15 TS[44] MINLP Primary þ Secondary 1e4 TS[15] MINLP Primary Horizon time ✓ GA[45] MINLP Primary 30 ✓ TRIBE PSO, OO[46] MINLP Secondary 20 VOHa

[47] MINLP Primary 4 Hybrid PSO, SFLA[5] MINLP Primary 5 ✓ GA[48] MINLP Primary 20 ✓ EA[49] MINLP Secondary (384 V) 3 MPDIPA[6] MINLP Primary 3 ABC, Comprehensive learning PSO[50] MINLP Primary 10þ (until 2024) VSLA[29] MINLP Primary 20 ✓ ✓ NDSGA[51] NLP Primary 1 ✓ GAMS (Using CONOPT solver)[52] MINLP Primary 3 PSOThis paper MINLP Primary 4 ✓ ✓ ✓ PSO þ sensitivity analysisa The best of three methods (minimum distance, minimum radial incremental distance or minimum incremental distance between each connection).

H. Arasteh et al. / Energy 94 (2016) 786e798790

transmission network, as well as the reliability cost that is formu-lated by (1). The second level corresponds to the DR cost, and issolved by the sensitivity analysis for each particle of the first levelPSO to mitigate the problem constraints under the uncertaintyenvironment. The second level optimization problem can beexplained by (2) and (3).

Min ff1g ¼(X

y

1ð1þ iÞy �

hCupgðyÞ þ CLossðyÞ þ CtrðyÞ þ CRðyÞ

i)

CupgðyÞ ¼Xncl

nUC

�cnclðyÞ

�� Lncl þ Cfncl � znclðyÞo

CLossðyÞ ¼XT

8<:

Xnf

hznf ðT ; yÞ � plossnf ðT ; yÞ � tðT ; yÞ � LCðT ; yÞ

i9=;

CtrðyÞ ¼XT

�ECðT ; yÞ � tðT ; yÞ � ptrðT ; yÞ�

CRðyÞ ¼Xnf

XT

���l�vnf ðyÞ

� tðT ; yÞ

8760

� CCLF

� Lnf � pfnf ðT ; yÞ � znf ðT ; yÞ

�

þXnf

XT

��rp�vnf ðyÞ

� l

�vnf ðyÞ

� tðT ; yÞ

8760� HEC

� Lnf � pfnf ðT ; yÞ � znf ðT ; yÞ

�

c ncl2Lcl; nf2L

f ; T2Y; y2J

(1)

Min ff2g ¼(P

y

1ð1þ iÞy � C

DRðyÞ)

CDRðyÞ ¼XT

(Xm

hCDRm ðT ; yÞ � pDRm ðT ; yÞ � TDRm ðT ; yÞ

i)

c m2D; T2Y; y2J

(2)

where,

CDRm ðT ; yÞ ¼ am � pDRm ðT ; yÞ þ bm � ð1� umÞ (3)The main objective function is to minimize f ¼ f1 þ f2.As formulated in (1), the reliability cost consists of two terms: a)

failure rates, and b) repair times.

In (3), am and bm are constant coefficients with the dimension ofð$=MW2 hourÞ and ð$=MW hourÞ, respectively, and um representsthe customers' willingness to participate in DR programs [53]. Ac-cording to [53] and as formulated in (3), when the amount of umdecreases, more costs will be needed in order to persuade thecustomer to participate in DR contracts. The introduced concept inRef. [53] is utilized in this paper to model the bidding strategy ofresponsive loads to participate in the market-based DR programs.um takes a value between 0 and 1. By increasing the value of um, thecost of DR decreases because the customer feels more tendencies toparticipate in DR [53]. Furthermore, since DR programs are

Fig. 2. The bi-level optimization procedure.

H. Arasteh et al. / Energy 94 (2016) 786e798 791

contracts that could be made for the next months or years, thecustomers' behavior to participate in DR may vary based on thecurtailment hours. It is obvious that the willingness of customerswill be decreased if they should participate in DR for more hours. Inthis paper, different values will be assumed for willingness co-efficients in correlation with the hours of curtailment.

2.2. Constraints

The mathematical formulations of the constraints are expressedat the following.

2.2.1. Radiality and connectivity of the networkDistribution systems are tree shape graphs and must be oper-

ated radially. Islanded buses should not appear for providing thesystem loads. Hence, all the nodes in a fully connected tree shapedistribution network must be connected to the root of the graph[8,41]. The presented approach in Ref. [44] is utilized in this paperto guarantee the radiality and connectivity of the network.

2.2.2. Permissible voltage levelsThe voltage levels of the distribution buses should be within the

maximum and minimum permissible thresholds as follows.

Vmin � VmðT ; yÞ � Vmax; c m2D; T2Y; y2J (4)

2.2.3. Current limitsThe maximum current limits of lines are represented by (5).

�Imaxnf ðyÞ � Inf ðT ; yÞ � Imaxnf ðyÞ; c nf2Lf ; T2Y; y2J(5)

2.2.4. Load balanceTotal injected power from the distribution substation must be

equal to the total required loads.

PsubðT ;yÞ¼Xm

pmðT ;yÞ�Xm

pDRm ðT ;yÞ

þXnf

plossnf ðT;yÞ; c T2Y; y2J; m2D; nf2Lf

(6)

QsubðT ;yÞ¼Xm

qmðT ;yÞ�Xm

qDRm ðT ;yÞ

þXnf

qlossnf ðT ;yÞ; c T2Y; y2J; m2D; nf2Lf

(7)

2.2.5. DR constraintsDR programs have limitations due to their barriers including

customer barriers, producer barriers, and structural barriers [54].These programs may encounter with some restrictions such as DRminimum and maximum duration, and DR magnitude [55] asfollows.

DDRm ðyÞ � DDR;maxm ðyÞ; c m2D; y2J (8)

pDRm ðT ; yÞ � pDR;maxm ðT ; yÞ; c m2D; T2Y; y2J (9)

2.3. Optimization tool

The bi-level optimization procedure is introduced in this paperto solve the proposed MINLP model. The first level is solved usingthe PSO algorithm, which is a population-based optimization

Fig. 3. The 33-bus distribution test system.

Table 2System specifications.

Features Values

Voltage level 12.66 [kV]Energy cost [13] 60 ($/MW hour)Discount rate 10 (%/year)Planning horizon 4 yearsPermissible voltage drop 0.05 (per-unit)Substation voltage 1.04 (per-unit)Existed feeders' initial capacity Feeder 1e2: 250 (A); other feeders: 118 (A)New candidate corridors 4-20, 10e28, 5e24, 13e32, 8e34, 26e34, 27e34, 9e35, 22e35, 12e36, 13e36, 18e37, 23e38, 24e38Forecasted load increment rate Buses 8e18: 15 (%/year); other buses: 12 (%/year)The maximum penetration level of DR 10 percent of load at responsive busesCCLF 13.7 ($/MW fail)HEC 21.7 ($/MW hour)

Table 3Customers' willingness coefficients.

The hours of participationfor each customer

Customers' willingnesscoefficients (um)

0e10 0.9510e20 0.9020e30 0.8530e40 0.840e50 0.750e60 0.6

H. Arasteh et al. / Energy 94 (2016) 786e798792

algorithm introduced by Eberhart and Kennedy [56]. It is based onthe number of particles, and inspired by the behavior of insects'swarm or birds' flock [57]. Each particle denotes a solution of theproblem. PSO has some important advantages in comparison withother heuristic methods like GA. It provides more effectivememory capacity, more diversity to search the optimum solution,and also faster search speed [58]. Swarms in the PSO algorithmconsist of the group of particles that determine the solution points

Table 4Candidate lines' specifications [13].

Lines' type Nominalcurrent (A)

ImpedanceOhm/km)

Reactance(Ohm/km)

Failure rate(fail/km yea

1 158 0.10145 0.4679 0.22 250 0.52050 0.4428 0.23 362 0.2640 0.2567 0.006254 453 0.2006 0.4026 0.2

[58]. Each particle moves in the solution space toward the bestsolution with a specific velocity, while it has memory to save itsbest previous position [56]. The ith particle velocity is assignedbased on (10).

viðjþ 1Þ ¼ viðjÞ þ r1� ðGðjÞ � xiðjÞÞ þ r2� ðPiðjÞ � xiðjÞÞ (10)

where, “j” represents the number of iterations, and vi expresses thevelocity of particle “i”. “r1” and “r2” are random variables between0 and 1. G(j) is the best solution of all particles (global best solution)until the iteration number “j”. Pi(j) is the best solution of the ithparticle (individual best position) until the iteration “j”. Further-more, xi denotes the position of the ith particle in the solutionspace. According to (10), the velocity of each particle in the PSOmethod is based on its current and previous conditions and also thepositions of other particles. The decision variables can be updatedbased on (11).

xiðjþ 1Þ ¼ xiðjÞ þ viðjþ 1Þ (11)

r)Repair time(hour/fail)

Installation cost($/km)

Replacementcost ($/km)

Fixedcost ($)

0.33 29,089.18 5188.22 3232.130.33 29,502.73 5601.78 3278.080.01 40,929.26 19,186.57 4547.700.33 27,990 7090 3110

Fig. 4. Different load patterns for residential energy sector a) in fall and winter, and b)in spring and summer.

Fig. 5. Commercial load pattern.

Table 6Different scenarios.

DR programs DSR Uncertainty

Scenario 1 (#1)Scenario 2 (#2) ✓Scenario 3 (#3) ✓ ✓Scenario 4 (#4) ✓ ✓ ✓

Table 7The net present value of distribution system planning costs (M$).

Without uncertaintyconsideration

With uncertaintyconsideration

Conventional DEP problem 2.92 (# 1) 3.25 (# 2)Proposed problem 2.19 (# 3) 2.36 (# 4)The percentage of cost reduction

by using the proposed problem25.00 27.38

H. Arasteh et al. / Energy 94 (2016) 786e798 793

The first level decision variables of this paper are line rein-forcement ðcncl ðyÞÞ and network reconfiguration plan ðznf ðT; yÞÞ.cncl ðyÞ is optimally determined for each year of the planning hori-zon, and znf ðT; yÞ is determined for each time period “T” of theplanning years. The second level of the optimization procedure isdeveloped based on the sensitivity analysis. DR specificationsðpDRm ðT ; yÞÞ are the second level decision variables that are

Table 5The combination of load points.

Load points Residential load Commercial load

1e18, 37 80 percentage 20 percentage19e22, 35 50 percentage 50 percentage23e33, 34, 36, 38 30 percentage 70 percentage

determined for each time period “T” of the planning years to facethe uncertainty effects. In the current study, uncertain parametersare the load levels in the future years. The most common sensitivityanalysis methods are the global finite difference method, thevariational method and the discrete method [59]. Here, the sensi-tivity index is defined for each responsive load point as the changesof voltage levels and power flows with respect to the changes of DRpenetration level. Considering the penalty factors for exceedingthese constraints (equations (4) and (5)), the sensitivity vector canbe defined as bellow:

SmðT ; yÞ ¼ DðPCðT; yÞÞD�pDRm ðT ; yÞ

� (12)where, Sm(T,y) is the sensitivity of constraint deviations withrespect to the amount of enabled DR at bus “m”. For each load point“m”, Sm(T,y) is a (1� S) vector inwhich “S” is the number of discretesteps of DR ðDðpDRm ðT; yÞÞÞ. Furthermore, PC(T,y) is the penalty costapplied to the constraint deviations in the time period “T” of eachyear. PC(T,y) is the summation of voltage and power flow deviationpenalty costs. Hence, DR programs are hierarchically assignedbased on their influence on the constraints. Consequently, thesecond level optimization problem is correlated with the first levelPSO, and developed to face the uncertainty conditions. At the firstlevel, system configuration is generated using the DSR variablesbased on the load levels in various time periods. Also the expansionplan is concurrently determined in this level using DEP variables.The second level of optimization procedure specifies DR specifica-tions for each generated particle of the first level PSO if they cannotsatisfy all the constraints in uncertainty conditions. Therefore, thesecond level of optimization tool utilizes sensitivity analysis todetermine the best plan for enabling DR programs (with the min-imum DR cost in order to minimize the penalty costs). Fig. 2 illus-trates the flowchart of the optimization procedure.

3. Numerical results

The IEEE 33-bus distribution test system, as depicted in Fig. 3, isutilized in this paper to investigate the simulation results. Dashedlines in Fig. 3 show the tie-lines, and colored circles illustrate theresponsive load points for DR programs. Furthermore, star-shapenodes belong to the new load points predicted to be expandedafter 3 years. These new load points are also assumed to containresponsive loads. The system specifications are given in Table 2. Thecustomers' willingness coefficients are presented in Table 3regarding the effect of DR curtailment hours. Utilities can cycle

Fig. 7. Distribution feede

Table 8The base values of cost terms.

Cost terms Base value ($)

Reinforcement 421,616Energy losses 43,517DR 78,852Imported energy 892,847Reliability 13186Total cost 1,446,357

Fig. 6. The cost terms of the proposed problem during the planning years.

H. Arasteh et al. / Energy 94 (2016) 786e798794

DR curtailments among all the responsive customers. Here, it isassumed that the utility is able to cycle the DR curtailments among100 customer groups. Hence, for instance, if the customers arepersuaded to participate in DR for 20 h throughout a year in atypical bus, the utility can manage them to have DR potential for2000 h in a year (aggregated hours of 100 different customers'responses). The 33-bus system data are extracted from Ref. [60].The candidate lines' specifications for upgrading the system arelisted in Table 4. As mentioned before, the pseudo-dynamicapproach is utilized to solve the multistage problem in each yearof the planning horizon. In the introduced test system, 75 percentof the standard load levels is assumed as the forecasted load in thefirst year. Considering 200 ($/MW hour) as the base of DR costs andthe maximum amount of DR capacity as the base of enabled DR ineach bus, the values of am and bm are assumed to be equal to 0.4 and2.5 per-unit, respectively. The amount of load prediction fault is 10percent that should be handled using the planning problem.Different load profiles are considered as shown in Figs. 4 and 5 forthe residential and commercial energy sectors, respectively. It isreasonably assumed that the residential load profile is similar toFig. 4-a in fall and winter, while it is like Fig. 4-b in spring andsummer. However, the commercial load profile is assumed to be asFig. 5 in all seasons. In many countries like Iran, such daily loadpatterns are reasonable and practical. It is assumed that each loadpoint is combined by both the residential and commercial cus-tomers. Table 5 represents the combination details of the loadpoints.

Four scenarios are taken into account for simulating andanalyzing the results as elaborated in Table 6. The net presentvalues of planning costs and the amount of cost decreases using theproposed problem are also presented in Table 7. As shown, the net

rs' upgrading plan.

Fig. 8. System configuration: a) hours 7e17 in fall and winter, and b) hours 12e15 in spring and summer.

H. Arasteh et al. / Energy 94 (2016) 786e798 795

Fig. 9. Voltage profiles: a) hours 7e17 in fall and winter, and b) hours 12e15 in spring and summer.

Table 9Total capacity of enabled DR.

Year Total DR capacity (kW)

Hours 7e17 in fall and winter Hours 12e15 in spring and summer

1 e 12.902 e e3 e 77.404 e 113.13

H. Arasteh et al. / Energy 94 (2016) 786e798796

present value of expansion cost is 2.87 (M$) in scenario 1, and theplanning cost of scenario 2 is 3.20 (M$) (11.50 percent cost incre-ment due to the presence of uncertainties). By solving the proposedproblem, the total planning costs get equal to 2.14 (M$) and 2.28(M$) in scenarios 3 and 4, respectively (6.54 percent cost incrementdue to the presence of uncertainties). It is obviously observed inTable 7 that significance decreases occur by applying the proposedproblem. Compared to the conventional DEP, the proposed activedistribution system planning will result in 25.40 percent costreduction when the parameters' uncertainties are not modeled.

Also the proposed problem shows 28.75 percent cost reduction incomparison with the conventional DEP in the presence ofuncertainties.

The expansion cost terms for the proposed problem are illus-trated in Fig. 6. It is significantly noticeable that the amplitude ofthe curves in Fig. 6 is normalized considering the maximum valueof each cost term as the base value. The base values of cost termsare shown in Table 8. According to Fig. 6, the presence of DR pro-grams and the incorporation of DSR with DEP can decrease andpostpone a major part of the expansion costs, and provide higheconomical profit for system owners.

The expansion plan for upgrading the distribution feeders isprovided in Fig. 7 (bold lines indicate the upgraded feeders). Oneshould bear in mind that the main aim of the proposed problem isto decrease all the investment and operational costs; therefore, itseeks to find a solution for decreasing the upgrading costs, whilethe optimum configuration is derived for power loss minimization.In fact, in some time periods, DSR can help the system planners topostpone and decrease the investment requirements. In other pe-riods, it is mainly employed for loss minimization. Fig. 8, forinstance, shows the system configuration during the planning years

Fig. 10. Total planning cost with respect to the DR penetration level.

H. Arasteh et al. / Energy 94 (2016) 786e798 797

for two selected time periods. Hours 7e17 in fall and winter andhours 12e15 in spring and summer are two distinct time periodsthat are selected to be explained as the examples of the outputresults. Fig. 9 depicts the voltage profiles during the planning years.It is to be noted that the minimum voltage level is considered 0.95(per-unit) that is satisfied in all time periods.

As described in the previous sections, in the proposed problem,the capacity of DR programs is considered to cover the effect of loaduncertainties. Table 9 gives the total amounts of enabled DR duringthe selected time periods.

Note that the above results are obtained when the maximumcapacity of DR is limited to 10 percent of the responsive load levels.The effect of higher DR capacity is illustrated in Fig. 10. Changes inthe total planning cost with respect to various DR potential levelsare shown in Fig. 10 using the second order approximation. Asshown, high penetration of DR can have more effect in decreasingthe planning costs.

Consequently, according to the proposed problem, systemreconfiguration should be compatible with the long-term planningpolicies to guarantee high financial profit. Hence, it can decreasethe expansion requirements, while minimizing the power losses.Furthermore, DR programs can efficiently be considered for miti-gating the effect of uncertain parameters. All the simulation resultsand analyses approve the performance and advantages of theproposed problem.

4. Conclusion

In this paper, an aggregated model is proposed to coordinatethe planning and reconfiguration of the distribution systems.The time-variable nature of the load profiles is considered fordifferent energy sectors on each bus. Moreover, the behavior ofresponsive loads is regarded by modeling their participation inDR programs. Then the bi-level optimization tool is proposed tosolve the introduced problem. The first level is based on the PSOalgorithm, and contains expansion and reconfiguration decisionvariables. The second level is correlated with the first level, andis elaborated to cope with the effect of uncertain parameters. Theperformance and validity of the proposed problem are analyzedusing the IEEE 33-bus distribution system. Simulation analysisrevealed that integrating the DSR and DR programs with the DEPproblem can decrease and postpone some parts of the expansionrequirements. Therefore, use of the proposed model can bringabout dramatic economical profit for distribution systemowners.

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An aggregated model for coordinated planning and reconfiguration of electric distribution networks1. Introduction2. Problem modeling and formulations2.1. Objective function2.2. Constraints2.2.1. Radiality and connectivity of the network2.2.2. Permissible voltage levels2.2.3. Current limits2.2.4. Load balance2.2.5. DR constraints

2.3. Optimization tool

3. Numerical results4. ConclusionReferences