Distribution network expansion considering distributed generation and storage units using modified PSO algorithm

Electrical Power and Energy Systems 52 (2013) 221–230

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Distribution network expansion considering distributed generation and storage units using modified PSO algorithm M. Sedghi a,⇑, M. Aliakbar-Golkar a,1, M.-R. Haghifam b,2 a b

K.N. Toosi University of Technology, Tehran, Iran Tarbiat Modares University, Tehran, Iran

a r t i c l e

i n f o

Article history: Received 22 December 2012 Received in revised form 18 March 2013 Accepted 29 March 2013

Keywords: Distribution network planning Distributed generation Storage Reliability Modified particle swarm optimization

a b s t r a c t Multistage distribution network expansion because of load growth is a complex problem in distribution planning. The problem includes minimizing cost of objective function subject to technical constraints. The objective function consists of investment, operation and reliability costs. In this paper, HV/MV substations, main and reserve MV feeders, dispatchable DG sources and storage units are considered as possible solutions for multistage distribution expansion planning. A three-load level is used for variable load and some strategies are proposed for DG and storage units operation. A modified PSO algorithm is applied to solve the complex optimization problem. Numerical results of the case studies show the ability of the modification. Moreover, the proposed strategies improve the distribution network from both economical and reliability points of view compared with the other methods. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Optimal expansion of medium-voltage power network because of load growth is a common issue in electrical distribution network planning. The expansion planning approach determines the location, type and capacity of new equipments that should be expanded and/or added to the system. The problem consists of minimizing cost of the objective function subject to technical constraints. Additionally, the optimal system must provide acceptable customer outage profile to ensure that customer reliability requirements are satisfied. The objective function usually includes facilities installation and operation cost and the reliability cost. Distribution network expansion planning is a complex problem. However, multistage procedure of planning because of dynamic load growth makes the problem more complicated. Multistage planning approach should define not only optimal location, type and capacity of investment, but also the most appropriate times to carry out such investments. Moreover, the intricacy of the problem is increased critically as the system size becomes large. In recent years, a lot of mathematical models and algorithms have been developed for solving this problem. A comprehensive review of classical models and methods can be found in [1]. How⇑ Corresponding author. Tel.: +98 912 334 7946; fax: +98 21 88462066. E-mail addresses: [email protected] (M. Sedghi), [email protected] (M. Aliakbar-Golkar), [email protected] (M.-R. Haghifam). 1 Fax: +98 21 88462066. 2 Fax: +98 21 88004556. 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.03.041

ever, Dynamic Programming (DP), Branch Exchange (BE), Simulated Annealing (SA), Tabu Search (TS), Genetic Algorithm (GA), Ant Colony System (ACS) and Particle Swarm Optimization (PSO) are the most common modern algorithms which are used recently to solve the distribution network planning problem [2–8], and some hybrid approaches and improvements are proposed, too [9–15]. In conventional distribution expansion planning, HV/MV substations and main and reserve MV feeders installation/upgrade are considered as possible solutions. Today, new capacity options such as Distributed Generation (DG) and storage units are expanded. Due to more flexibility, DG and storage units can be implemented as possible solutions in distribution network planning. Recently several papers have considered either DG or storage units utilization in distribution network planning [16–28]. Importance of DG consideration in distribution network planning is discussed in [16–18]. In [19] analytical approaches are used for optimal placement of DG sources in radial and networked power systems with variable loads to minimize only energy loss. However, analytical approaches are not useful for more complex planning problems. In [20,21], distribution network planning considering DG sources is developed, however, load variation impact and reliability enhancement are not considered in these works. DG peak cutting benefits for distribution network planning is shown in [22] where sum of investment cost and energy loss cost is minimized. In this reference, GA is used for optimal distribution network expansion planning in a single stage. A similar study is performed in [23], meanwhile a linear program-

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Nomenclature ADG AEV AFD ALD AS ASS AST AT c1, c2 CFD

set of all DG sources set of all failure events set of all feeder sections set of all load points set of all stages set of all HV/MV substations set of all storage units set of all load levels positive constants as learning factors fix cost of feeder section installation ($/km)

C INS DG

cost function of DG source installation ($)

C INS SS

cost function of installing/upgrading HV/MV substation ($) cost function of storage unit installation ($)

C INS ST C OM ST C REP ST CESS j CF INS s CF OPR s;t

RLS

dispatched real power from the ith HV/MV substation at the jth load level in tth year of the sth stage including network losses (MW) power generation of the ith storage unit at the jth load level of the tth year of the sth stage (MW) probability of failure event at uth hour real variable that determines the relative importance of the exploitation outage time of failure event j (h) random function generating random numbers uniformly distributed within the range [0, 1] local search rate

SCAP DG;i

capacity of the ith DG source (MVA)

SCAP SS;i;s

capacity of the ith HV/MV substation at sth stage (MVA)

cost function of operation and maintenance of storage unit ($) cost function of storage replacement ($)

SCAP ST;i

capacity of the ith storage unit (MVA)

SDG i;j;s;t

electricity market price at the jth HV/MV substation ($/ MW) installation cost of the system at sth stage ($)

SFD i;j;s;t

generating power of the ith DG source at jth load level in tth year of the sth stage (MVA) power flow of the ith feeder section at jth load level in tth year of the sth stage (MVA) total power loss of the distribution network at jth load level in tth year of the sth stage (MW) dispatched appearance power from ith HV/MV substation at jth load level in tth year of the sth stage (MVA) charge/discharge power of the ith storage unit at jth load level in tth year of the sth stage (MVA) duration of the every stage (years) duration of jth load level (h) switching time (h) standard step function calculated voltage magnitude of ith load point at jth load level in tth year of the sth stage (p.u.) maximum allowed operation voltage (p.u.) minimum allowed operation voltage (p.u.) inertia weight of PSO algorithm binary decision variable associated to installation of the ith DG source at sth stage binary decision variable associated to installation of the ith main feeder section at sth stage binary decision variable associated to installation of the ith reserve feeder section at sth stage binary decision variable associated to replacement of the ith storage unit at sth stage binary decision variable associated to installing/upgrading of the ith HV/MV substation at sth stage binary decision variable associated to installation of the ith storage unit at sth stage kth component of the global best position of the ith group of particles associated to facility u kth component of the local best position of the ith group of particles associated to facility u binary variable associated to the ith load point outage due to jth failure event average failure rate of jth event

CO ECAP ST;i hi Infr Intr Li N Ng Npg

operation cost of the system during tth year of the sth stage ($) reliability (outage) cost of the system during tth year of the sth stage ($) cost function of costumer outage ($) capacity of the ith storage unit (MW h) type of the ith load point inflation rate interest rate length of the ith feeder section (km) number of all stages number of all groups in PSO algorithm number of particles in each group

NLD s

number of all load points in sth stage

NMFD s OC DG i

number of all main feeder sections in sth stage operation cost of the ith DG source including maintenance cost ($/MW) objective function ($) intermediate objective function of the sth stage ($)

CF RLB s;t

OF OFs

PSS i;j;s;t

PDG i;j

power generation of the ith DG at the jth load level (MW) PDG power generation of the ith DG at the jth load level of i;j;s;t the tth year of the sth stage (MW) PFCAP useful free capacity of the lth DG source for ith load DG;i;l point restoration (MW) PFCAP useful free capacity of the lth storage unit for ith load ST;i;l point restoration (MW) PLD i;s;t ðu þ kÞ power demand of the ith load point at the (u + k)th hour of the tth year of the sth stage (MW) PRES restored power of the ith load point by facility m (MW) m;i PRES restored power of the ith load point by all the DG DG;i sources (MW) PRES restored power of the ith load point by all the storage ST;i units (MW)

ming is applied in GA to optimize the power of DG sources. However, this linear programming is not applicable to storage units. Moreover, reliability cost is not considered in [22,23]. Some DG integration advantages for distribution network planning are presented in [24], where hybrid optimal power flow (OPF) and GA are used for multistage distribution expansion

PST i;j;s;t Pf q rj rd

PLOSS j;s;t SSS i;j;s;t SST i;j;s;t T Tj tswt U Vi,j,s,t Vmax Vmin w xDG i;s xMFD i;s xRFD i;s xRST i;s xSS i;s xST i;s xu;GB i;k xu;LB i;k xout(i, j) kj

planning. This multistage planning is suitable for the expansion of HV/MV substations, main and reserve feeders and DG units. The results show that integrating of DG sources in distribution expansion planning can improve voltage deviation, loss cost and reliability of the system. The proposed hybrid OPF/GA algorithm in [24] is appropriate for DG integrated distribution

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network planning, but the OPF algorithm executions make this method time-consuming. In [25], a dynamic programming is proposed for optimal DG allocation in distribution network planning to reduce power loss and improve the reliability. Besides time varying load is applied in the optimization and the studies are based on cost/benefit forms. The results show that the DG sources can improve not only the voltage profile, but also duration of life time of the other equipments. As a flaw, very simple test distribution networks are considered for numerical studies in [24,25]. As a result, it is not clear that the proposed methods can solve more complex distribution network planning problems efficiently. Moreover, storage units are not considered in these references. Economic analysis of electricity storage application to power system is performed in [26,27]. It is shown that using storage units only for peak cutting in distribution level is not economical with the present prices. However, the distribution network configuration and reliability indexes are not taken into account in [26,27]. In [28] DG and storage units are used only for distribution network reliability improvement and GA is used for optimal allocation and sizing of NaS batteries. The results show that using NaS storage technology can economically improve the energy not supplied index of the radial distribution network. But in this reference, any other facility such as reserve feeder is not considered for installation. In this paper, HV/MV substations, main and reserve MV feeders, dispatchable DG sources and storage units are considered as possible solutions for multistage distribution expansion planning. DG and storage batteries are optimally allocated not only for peak cutting, but also for reliability enhancement. The consuming load variation is modeled as a three-level load. To solve the combinatorial optimization problem, a Modified Particle Swarm Optimization (MPSO) is proposed. In Section 2, multistage distribution network expansion planning problem is described. Proposed operation strategies for DG and storage units are presented in Section 3. The modified PSO algorithm and numerical results are shown in Sections 4 and 5 respectively. Conclusion remarks are given in Section 6.

eter. Facilities installed in each stage have no construction cost associated with them in the next stages, but they have associated power loss and operation costs in the next stages. The operation cost consists of DG operation cost and the cost of purchased electricity at HV/MV substations. As a result, the cost of purchased electricity includes the power loss cost, too. The operation cost of storage units can be modeled by fixed operation and maintenance cost which should be calculated considering the capacity of storage units. The cost objective function of each stage should be calculated in the base year regarding the interest and inflation rate. The optimal solution may not minimize the objective function of each stage, but it should minimize the total objective function of all stages. In every stage, the optimal intermediate distribution system must supply the required loads and keep voltage magnitude of all the nodes in the acceptable boundary. Capacity constraints of the substations, feeders, DG sources and storage units cannot be exceeded. In addition the configuration of the normal-state network must be radial. As a result, the mathematical formulation can be written as follows. 2.1. Objective function

Min: OF ¼

N X OF s

ð1Þ

s¼1

where

OF s ¼



Tðs1Þ Tðs1Þþt1 T  X 1 þ Infr 1 þ Infr  CF INS þ s 1 þ Intr 1 þ Intr t¼1   OPR RLB  CF s;t þ CF s;t

ð2Þ

where

CF INS ¼ s

X

X

ðxMFD þ xRFD i;s i;s Þ  Li  C FD þ

i2AFD

xSS i;s

i2ASS

  X CAP CAP INS CAP  C INS xDG i;s  C DG ðSDG;i Þ SS SSS;i;s ; SSS;i;s1 þ i2ADG

h    i  o Xn INS OM REP CAP þ xST ECAP ECAP þ xRST i;s  C ST EST;i þ C ST i;s  C ST ST;i ST;i

2. Problem statement

i2AST

The distribution network expansion planning optimizes the location, type and installation date of new main and reserve feeders as well as the location, capacity and installation date of new DG sources, storage units and HV/MV substations, and/or the capacity increment and the upgrade date of existing HV/MV substations while minimizing the cost objective function of the network under technical constraints. The objective function includes investment cost, operation cost and reliability cost. The cost functions are calculated for the base year of study regarding the interest and inflation rate. In this paper, the reliability is included as the cost of expected Energy Not Supplied (ENS). The expected outage cost is evaluated for all load points during failure events. Outage cost of every load point is a function of the load type and interruption duration. However, each lost load point may be restored by reserve feeders, DG sources and/or storage units, regarding operation strategies. The restoration sources availability should be evaluated for every failure event. Whereas the variable load level is a function of time, the availability of restoration sources is dependent on failure occurrence time and interruption duration. Moreover, the restoration sources will be available after switching time. For multistage approach of distribution planning, at the end of each stage, an intermediate system should be determined. So each selected facility will have a construction date as a decision param-

ð3Þ CF OPR s;t ¼

(" X X j2AT

CF RLB s;t ¼

XX

) #  X  SS DG SS DG  Tj xSS xDG i;s  CEj  P i;j;s;t þ i;s  OC i  P i;j

i2ASS

ð4Þ

i2ADG

( xout ði;jÞ  kj  COðhi ;rj Þ 

" #) rj 24 X X X RES P f ðuÞ  U P LD Pm;i ðu;k; rj ;tswt Þ i;s;t ðu þ kÞ  u¼1 k¼1

i2ALD j2AEV

ð5Þ

m2ARDS

where ARDS = {RFD, DG, ST}. 2.2. Constraints

0 6 xMFD þ xRFD i;s i;s 6 1;

8i 2 AFD ;

8j 2 AT ;

8s 2 A S ;

t

¼ 1; . . . ; T CAP 0 6 xMFD  SFD i;s i;j;s;t 6 SFD;i ;

ð6Þ

8i 2 AFD ;

8j 2 AT ;

8s 2 A S ;

t ¼ 1; . . . ; T FD CAP 0 6 xRFD i;s  Si;j;s;t 6 SFD;i ;

ð7Þ

8i 2 AFD ;

8j 2 AT ;

8s 2 A S ;

t ¼ 1; . . . ; T SS CAP 0 6 xSS i;s  Si;j;s;t 6 SSS;i ;

t ¼ 1; . . . ; T

ð8Þ

8i 2 ASS ;

8j 2 A T ;

8s 2 AS ; ð9Þ

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DG CAP 0 6 xDG i;s  Si;j;s;t 6 SDG;i ;

8i 2 ADG ;

8j 2 A T ;

3.2. Storage operation strategies

8s 2 AS ;

t ¼ 1; . . . ; T 0 6 xST i;s 

ð10Þ

SST i;j;s;t

6

SCAP ST;i ;

8i 2 AST ;

8j 2 A T ;

8s 2 AS ;

t ¼ 1; . . . ; T

ð11Þ

8i 2 ALD ;

V min 6 V i;j;s;t 6 V max ;

8j 2 AT ;

8s 2 A S ;

t

¼ 1; . . . ; T NMFD ¼ NLD s s ; X

PSS i;j;s;t þ

i2ASS

ð12Þ

8s 2 A S

X

PDG i;j;s;t þ

i2ADG

ð13Þ X

PST i;j;s;t ¼

i2AST

X

LOSS PLD i;j;s;t þ P j;s;t ;

8j

i2ALD

2 AT ;

8s 2 A S ;

t ¼ 1; . . . ; T

ð14Þ C INS SS

In Eq. (3), CFD = 0 for existing feeder sections in each stage and is a discrete function.Whereas the lifetime of energy storage units is limited, replacement cost of the storage units is added to the cost objective function in Eq. (3). In this paper, the lifetime of storage units is modeled by restricted charge/discharge cycles number. If the maximum number of charge/discharge cycles of storage units is exceeded, the replacement cost is added to the objective function.Eq. (6) indicates that every feeder section may be used either as a main feeder or as a reserve feeder. The capacity of HV/MV substations can be calculated considering Eq. (14) to balance the power in distribution network. The capacity is selected among some predetermined candidate ones to satisfy Eq. (14). 3. Proposed Strategies Distribution network planning procedure should be evaluated regarding system operation. Optimal power flow may be needed for objective function calculating and constraints evaluation. In this paper, some optimal simple strategies are proposed for system operation, instead of optimal power flow computation. The strategies are proposed for DG sources and storage units operation, assuming a three-load level model for the variable loads. 3.1. DG operation strategies DG sources are allocated for both peak cutting and reliability improvement. DG sources are used to generate electrical power only in high level and normal level of load periods. As a result, DG sources are disconnected from the network in light-load periods. Moreover, DG sources may be used to restore the lost loads due to failure events. After every failure event, the failed sections are disconnected from the network using normally closed switches. Then reserve feeders are connected to the network, if they can restore the lost loads. The connection of reserve feeders is performed regarding the network configuration and feeders and HV/MV substations capacity constraints. If the reserve feeders can not restore the lost loads, DG sources are connected to the network regarding DG capacity and priority of lost loads. At first the loads which have the higher priority are connected to DG sources. Then the loads with lower priority are restored if the maximum capacity of DG is not exceeded. In the other words, the usable free capacity of DG sources is assigned to the lost loads consecutively. As a result, after switching period, the power restored by DG sources in Eq. (5) can be written as follows:

PRES DG;i ðu; k; r j ; t swt Þ ¼

X

yDG ði; lÞ  PFCAP DG;i;l

ð15Þ

l2ADG

where

yDG ði; lÞ ¼



1; if ith load is connected to the lth DG 0; otherwise

ð16Þ

Storage units can be used for either peak cutting procedure or reliability improvement or both. As the first scenario, it is assumed that storage units are inserted only for peak cutting. Then storage units are charged during light-load periods and discharged during high-load times. As a result, storage units are not connected to the network in normal-load periods. In the second scenario for reliability enhancement, similarly to DG sources, storage units are connected to the lost loads regarding the loads priority, if the reserve feeders are disable to restore the lost loads. In this scenario, storage units are discharged only during repair/replacement time of failed equipments. Because the stored energy is limited, the useful power capacity of storage units is a function of repair/replacement duration. As a result, after switching period, the power restored by storage units in Eq. (5) can be written as follows:

PRES ST;i ðu; k; r j ; t swt Þ ¼

X

yST ði; lÞ  PFCAP ST;i;l ðk; r j Þ

ð17Þ

l2AST

where

 yST ði; lÞ ¼

1; if ith load is connected to the lth storage 0; otherwise

ð18Þ

As the third scenario which is proposed in this paper, storage units are allocated to both peak cutting and reliability improvement. In normal condition of the distribution system, storage units are charged during light-load periods and discharged during highload times. However, they can restore the lost loads partly in all the periods when reserve feeders are not able to supply the energy lost. As a result, after switching period, the power restored by storage units is dependent on not only the repair/replacement duration but also the starting time of failure event, as follows:

PRES ST;i ðu; k; r j ; t swt Þ ¼

X

yST ði; lÞ  PFCAP ST;i;l ðu; k; r j Þ

ð19Þ

l2AST

where PFCAP ST;i;l is determined regarding the stored energy estimation in (u + k)th hour. The stored energy can be estimated from periodic charge/discharge curve of the storage units. This curve determines the sequential charge/discharge periods, regarding operation strategy described above. 4. Modified Particle Swarm Optimization (MPSO) Particle Swarm Optimization (PSO) is a swarm intelligence algorithm which is based on the movement of some groups of particles which share their explorations among themselves. This technique is motivated by simulation of social behavior. Each individual in PSO called particle flies in the searching space with a velocity. Assuming that the searching space is n-dimensional, the ith particle of the swarm is presented by the vector xi = (xi,1, . . ., xi,n) with a flying velocity vi = (vi,1, . . ., vi,n). The particles move in the searching space regarding their velocities. The velocity vector is updated in each iteration with respect to the best previous positions of the particles and the global best position of the swarm. More details can be found in [15]. PSO is a modern optimization algorithm, but it usually needs some improvements especially when the problem dimension increases. In this paper a modified PSO algorithm is proposed. The proposed MPSO algorithm is based on an improved hybrid TS/ PSO algorithm which is proposed in [29] for conventional distribution network expansion planning. The MPSO is adapted and applied here for modern multistage distribution expansion planning. In the proposed modified PSO algorithm for multistage planning, the population is divided into some groups of particles. The

M. Sedghi et al. / Electrical Power and Energy Systems 52 (2013) 221–230

position vector of the jth particle of the ith group is presented by xij. Each group of particles optimizes the intermediate network of one stage during iterations. So the number of groups is equal to the number of planning stages. The particles of different groups (i.e. different stages) fly consecutively. In each iteration, jth particle of the first group starts to move from its own last position, but for i > 1 the jth particle of ith group starts to move from the last position of jth particle of (i  1)th group. In ith group, objective function of each particle for ith stage is calculated using Eq. (2). The best position vector of ith group which minimizes OFs (where s = i) is presented by xLB i as a local best position. The complete solutions are obtained from serial particles positions of all groups. In each iteration, the number of new generated complete solutions is equal to the number of particles of each group. The objective function of each complete solution (i.e. OF) is calculated using Eq. (1). Then the best complete solution is found. The intermediate solution of ith group, which belongs to the best complete solution, is presented by xGB as a global best position. i In modified PSO algorithm, the best intermediate solution of ith stage (i.e. local best position), instead of the best previous position in conventional PSO, is used to update velocity vector as follows:

v uij;k ¼ w  v uij;k þ c1  rd  ðxuij;k  xu;LB i;k Þ þ c2  rd    xuij;k  xu;GB i;k

ð20Þ

where c1 < c2, i = 1, 2, . . ., Ng, j = 1, 2, . . ., Npg and u e {MFD, RFD, SS, DG, ST}. The second term in right part of Eq. (20) prevents the particles moving to ineffective regions; however, the third part leads the particles to move into the global optimum.Moreover, a new controller parameter (q) is used in MPSO to increase intensification which is needed seriously to solve large-scale optimization problems. The particles are manipulated regarding not only the velocity vector, but also the local best particles, the global best particles and the new controller parameter (q) as follows: ( xuij;k ¼

1; if

nh

i h io u;GB rd < 1=ð1 þ expðv uij;k ÞÞ ;AND ðxu;LB i;k ¼ 1Þ OR ðxi;k ¼ 1Þ OR ðq < rdÞ

0; otherwise ð21Þ

where u e {MFD, RFD, SS, DG, ST}. Additionally, to improve the PSO performance, from detailed search point of view, it is proposed to incorporate local search algorithms with the PSO algorithm. In proposed MPSO algorithm, local searches are applied in each stage separately, regarding a predefined local search rate (RLS). Accordingly, after moving a particle using PSO in sth stage, if RLS > rd, then local search is allowed to be done. Therefore, the intermediate solution related to the particle is selected as a current solution. Then some neighbor solutions of the current solution are generated randomly. The current intermediate solution of sth stage is replaced by the best neighbor solution if the neighbor solution is more adequate than the current solution, regarding objective function of the sth stage (i.e. OFs in Eq. (2)). In this paper, generating of the neighbor solutions is applied to the main feeders using an intelligent local search algorithm which is proposed in [13]. As a result, required local search size and computation time will be less. However, the neighbor generating procedure in proposed local search algorithm, for DG and storage units is as follows: Step 1: Select randomly the ith node in the sth stage. DG Step 2: If xDG i;s ¼ 0, then set xi;s ¼ 1 and go to step (4). Step 3: If (xDG ¼ 1 AND rd > 0.5), then set xDG i;s i;s ¼ 0, otherwise set ST xDG ¼ 0 and x ¼ 1. i;s i;s Step 4: Select randomly the jth node in the sth stage.

225

Fig. 1. A schematic of particle movement in MPSO algorithm.

ST Step 5: If xST j;s ¼ 0, then set xj;s ¼ 1 and STOP. Step 6: If (xST ¼ 1 AND rd > 0.5), then set xST j;s j;s ¼ 0 and STOP, ST DG otherwise set xj;s ¼ 0 and xj;s ¼ 1 and STOP.

As a result, DG and storage units can be exchanged with each other in local search algorithm to pass the probable local optimum solutions. In this paper, local search for reserve feeders is neglected. However, for all the stages except the first stage (i.e. s = 2, . . ., N), all the existing main and reserve feeders in (s  1)th stage, must be selected as either main or reserve feeders in sth stage. So there is no construction cost associated with them. The type of feeders and the capacity of DG and storage units are specified by selecting a type or capacity among some candidate ones. So each candidate type or capacity can be presented by a separate binary decision variable. The particles minimize the objective function of each stage (i.e. OFs in Eq. (2)) as a local objective function and the final objective function of all stages (i.e. OF in Eq. (1)) as a global objective function. However, the optimal solution is selected finally regarding only the global objective function. Fig. 1. shows a typical particle movement schematic in modified PSO algorithm. In this paper, the MPSO algorithm is applied to multistage distribution expansion planning in two phases. In the first phase, only main feeders are considered for optimization. The outcome of this phase is the optimal routing of main feeders in each stage to minimize the objective function of Eq. (1) subject to technical constraints. In the second phase, only other facilities (i.e. DG sources, storage units and reserve feeders) are embedded in the system for each stage to minimize the objective function in Eq. (1) subject to technical constraints and the output of the first phase. As a result, at the end of second phase, the optimal location, capacity and installation date of all equipments are determined. 5. Numerical results The proposed procedure for optimal distribution network expansion planning is applied to a 20-kV distribution system using MATLAB 7.5. The network consists of an existing 10 MVA HV/MV substation, 13 existing main feeder sections and an existing reserve feeder. 52 new load points are added to the existing network over four stages. Additionally, a new point is considered as candidate HV/MV substation which may be included by the optimal solution. The existing network configuration, new load points and candidate HV/MV substation are presented in Fig. 2. In this study, storage units are utilized for both peak cutting and reliability improvement. Therefore, storage units with high charge/ discharge cycles, such as Zn/Br batteries, are more suitable [26]. Moreover, dispatchable renewable/nonrenewable DG sources, such as fuel cells units, are considered in this study. The type of load nodes includes residential, industrial and commercial loads. Table 1 gives the costumer sector interruption cost for different load types used in the study. The loading levels and

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Fig. 2. The configuration of existing network, new load points and candidate HV/MV substation.

Table 1 Sector interruption cost for reliability cost evaluation [30]. User sector

Priority no.

Residential Industrial Commercial

3 2 1

Table 3 Technical and cost parameters.

Interruption duration (min) and cost ($/kW)

Parameter

Value

60 min

240 min

480 min

0.482 9.085 8.552

4.914 25.16 31.32

15.69 55.81 83.01

Total candidate feeders number Average peak load per node (kW) Load power factor Annual increment load rate (%) Failure rate of feeders (f/km-yr) Failure rate of HV/MV transformers (f/yr) Repair/replacement time of feeders (h) Repair/replacement time of HV/MV transformers (h) DG investment cost ($/kW) DG operation cost ($/MW h) DG operation power factor Storage investment cost ($/kW h) Unit cost of power electronic for storage ($/kW) Fixed O&M cost for storage ($/kW) Storage replacement cost ($/kW h) Storage efficiency (%) Number of charge/discharge cycles in storage life Duration of each stage (yr) Interest rate (%) Inflation rate (%) Minimum allowed operation voltage (p.u.) Maximum allowed operation voltage (p.u.)

147 525 0.9 (lag) 3 1.49 0.2 4 8 2000 50 1 225 175 20 225 75 10,000 6 10 7 0.95 1.05

Table 2 Loading levels and market price data. Load level

Percentage of peak load (%)

Time duration (h/ yr)

Market price ($/ MW h)

High Normal Low

100 70 50

2190 4380 2190

75 49 35

market price data are shown in Table 2. Two candidate types of MV feeders, two candidate sizes of DG sources (1 MVA and 2 MVA) and three candidate capacities of storage units (1.8 MW h, 2.1 MW h and 2.4 MW h) are considered in this study. Other technical and cost parameters are shown in Table 3. It should be noted that in this case study the storage units are firstly used for both peak cutting and reliability improvement. The other scenarios of storage operation strategies will be considered later. The charge/discharge curve of storage units is shown in Fig. 3. This curve may be different for various seasons of a year, regarding various market price curves in 1 year. Fig. 3 is used to estimate the stored energy of storage units for every hour of a day in this case study. The proposed MPSO algorithm is applied to the multistage distribution expansion planning in two phases with the controller parameters given in Table 4. Figs. 4 and 5 show the objective function versus computation time during execution of the first and second phase of the MPSO algorithm respectively. The configurations of the optimal networks over four stages of distribution expansion planning are shown in Figs. 6–9. Figs. 6–9 show that the new HV/MV substation should be installed at the second stage. Moreover, in this stage one new DG unit and one new storage unit should be installed. The capacities of these units are 1 MVA and 2.1 MW h, respectively. Another 1 MVA DG unit is embedded at the fourth stage. In the fourth stage,

two other 2.1 MW h storage units are inserted, too. The reserve feeders are set up to improve reliability of the system. However, in some stages they may be operated as main feeders. On the other hand, some installed main feeders may be used as reserve feeders in the next stages. Also DG sources and storage units are operated to increase the reliability in this study. Unlike the reserve feeders, DG and storage units can restore the lost loads even if the HV/MV substations fail. But storage units may not improve the reliability when they are not charged sufficiently, because of peak cutting operation strategies. Two other operation strategies described in Section 3.2, as different scenarios, are considered separately for optimal distribution expansion planning using MPSO algorithm. As the first scenario, storage units are used only for peak cutting. While in the second scenario, storage units are considered only for reliability enhancement. The results of these scenarios are compared with the main approach in Table 5. Table 5 shows that no storage unit is selected for optimal solution in scenarios 1 and 2. As a result, storage utilization is not economical if it is used only for either peak cutting or reliability improvement. However, it may be an optimal choice remarking

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the proposed operation strategy. Moreover, the optimal solution containing storage units becomes more economical and also more reliable than the other optimal solutions without storage. Since outage cost of the main approach is less than the outage cost of the other scenarios. The outage cost is assessed here using the ENS index of reliability. Unlike the optimal cost objective function, the outage cost decreases dominantly. This is important for planning a reliable distribution network planning. To verify ability of the proposed MPSO algorithm, the conventional PSO is applied to the optimization problem, too. The result compared with the proposed MPSO is presented in Table 6. Moreover, in order to test the impact of proposed local search algorithm on MPSO, the MPSO algorithm without local search is compared with the complete MPSO in Table 6. The results show the advantage of proposed MPSO algorithm. Also, the proposed local search algorithm application can improve the performance of MPSO efficiently, as the cost objective function is diminished when the proposed local search is used. 6. Conclusions

Fig. 3. Daily charge/discharge curves of storage units in two periods of year: (a) spring and summer and (b) fall and winter.

Table 4 Controller parameters of the MPSO used in case study. Controller parameter

Value

w c1 c2 q Ng Npg in 1st phase Npg in 2nd phase Local search rate for all components Local search size for main feeders Local search size for DG sources Local search size for Storage units Maximum iteration of 1st phase Maximum iteration of 2nd phase

0.9 1 5 0.998 4 10 5 0.2 15 10 20 400 100

Multistage distribution network expansion because of load growth is a complex optimization problem in distribution planning. The cost objective function should be minimized subject to technical constraints. The objective function contains the investment, operation and reliability cost. In this paper, HV/MV substations, main and reserve MV feeders, DG sources and storage units are considered to optimize the distribution system expansion over several stages. Some optimal strategies are proposed for DG sources and storage units operation considering the load variation. DG and storage units are operated not only for pick cutting but also for reliability enhancement. Simultaneously, reserve feeders are optimally utilized to improve the reliability. However, the energy of storage units is estimated hourly to determine the expected restored load. The energy estimation is performed using the sequential charge/discharge strategy. A modified PSO algorithm is proposed to solve the combinatorial optimization problem. The PSO algorithm is specifically modified for multistage distribution network expansion including DG and storage units. In order to demonstrate the ability of the proposed methodology, case studies are done on a test distribution network. The numerical results show that the proposed operation strategies for DG and storage units can reduce the optimal cost objective function. As a result, storage units’ application in

Fig. 4. Objective function versus running time of MPSO in the first phase.

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distribution planning is critically dependent on the operation strategy from economic point of view. Since the proposed strategy in-

creases the penetration of storage units in distribution network and it makes the system more reliable, too.

Fig. 5. Objective function versus running time of MPSO in the second phase.

Fig. 6. Configuration of the optimal network in the 1st stage of distribution expansion planning.

Fig. 7. Configuration of the optimal network in the 2nd stage of distribution expansion planning.

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Fig. 8. Configuration of the optimal network in the 3rd stage of distribution expansion planning.

Fig. 9. Configuration of the optimal network in the 4th stage of distribution expansion planning.

Table 5 Comparison of three strategies for storage operation in distribution expansion planning. Scenarios

First 0.9075 Second 1.0143 Proposed 0.6547

No. of all storage units embedded in optimal system

Optimal objective function (M$)

Outage cost (M$)

scenario

3

0

187.16

scenario

2

0

186.55

approach

2

3

185.49

No. of all DG units embedded in optimal system

Table 6 Comparison of the conventional PSO with proposed MPSO. Algorithms

Optimal objective function (M$)

Conventional PSO MPSO without local search MPSO with local search

203.56 186.57 185.49

The proposed modified PSO algorithm is more robust than the conventional PSO. Moreover, the proposed local search algorithm makes the MPSO more efficient. The impact of problem dimension on the proposed algorithm will be evaluated as a future work.

References [1] Khator SK. Power distribution planning: a review of models and issues. IEEE Trans Power Syst 1997;12:1151–9. [2] Ganguly S, Sahoo NC, Das D. Multi-objective planning of electrical distribution systems using dynamic programming. Elect Power Energy Syst 2013;46:65–78. [3] Aoki K, Nara K, Satoh T, Kitagawa M, Yamanaka K. New approximate optimization method for distribution system planning. IEEE Trans Power Syst 1990;5(1):126–32. [4] Parada V, Ferland JA, Arias M, Daniels K. Optimization of electrical distribution feeders using simulated annealing. IEEE Trans Power Deliv 2004;19(3):1135–41. [5] Rosado IJR, Navarro JAD. New multiobjective tabu search algorithm for fuzzy optimal planning of power distribution systems. IEEE Trans Power Syst 2006;21(1):224–33. [6] Miranda V, Ranito JV, Proença LM. Genetic algorithm in optimal multistage distribution network planning. IEEE Trans Power Syst 1994;9:1927–33. [7] Gómez JF, Khodr HM, De Oliveira PM, Ocque L, Yusta JM, Villasana R, et al. Ant colony system algorithm for the planning of primary distribution circuits. IEEE Trans Power Syst 2004;19(2):996–1004. [8] Siahkali H, Roshanfekr R. Distribution network planning using supplying area and PSO algorithms. J Iranian Assoc Elecr Elect Eng 2005;2(1):17–30. [9] Miguez E, Cidras J, Diaz-Dorado E, Garcia-Dornelas JL. An improved branchexchange algorithm for large-scale distribution network planning. IEEE Trans Power Syst 2002;17(4):931–6. [10] Mori H, Yamada Y. Two-layered neighborhood tabu search for multi-objective distribution network expansion planning. In: IEEE Int Symp Circ Syst; 2006. p. 3706–09. [11] Davalos FR, Irving MR. An efficient genetic algorithm for optimal large-scale power distribution network planning. In: IEEE Power Tech Conf, vol. 3; 2003. p. 797–801.

230

M. Sedghi et al. / Electrical Power and Energy Systems 52 (2013) 221–230

[12] Davalos FR, Irving MR. The edge-set encoding in evolutionary algorithms for power distribution network planning problem – Part I: single-objective optimization planning. In: Electr Robot Auto Mech Conf, vol. 1; 2006. p. 203–8. [13] Sedghi M, Aliakbar-Golkar M. Distribution network expansion using hybrid SA/TS algorithm. Iranian J Electr Electron Eng 2009;5(2):122–30. [14] Wang C, Wang S. The automatic routing system of urban mid-voltage distribution network based on spatial GIS. In: IEEE Int Conf Power Syst Tech; 2004. p. 1827–32. [15] Zifa L, Jianhua Z. Optimal planning of substation of locating and sizing based on GIS and adaptive mutation PSO algorithm. In: IEEE Int Conf Power Syst Tech; 2006. p. 1–5. [16] Ault GW, McDonald JR. Planning for distributed generation within distribution networks in restructured electricity markets. IEEE Power Eng Rev 2000;20(2):52–4. [17] Espie P, Ault GW, Burt GM, McDonald JR. Multiple criteria decision making techniques applied to electricity distribution system planning. IEE Proc Gen Transm Dist 2003;150(5):527–35. [18] The distribution working group of the IEEE power system planning and implementation committee. Planning for effective distribution. IEEE Power Energy Mag 2003; 1(5): 54–62. [19] Wang C, Nehrir MH. Analytical approaches for optimal placement of distributed generation sources in power systems. IEEE Trans Power Syst 2004;19(4):2068–76. [20] El-Khattam W, Hegazy YG, Salama MMA. An integrated distributed generation optimization model for distribution system planning. IEEE Trans Power Syst 2005;20(2):1158–65. [21] Haffner S, Pereira LFA, Pereira LA, Barreto LS. Multistage model for distribution expansion planning with distributed generation – Part II: numerical results. IEEE Trans Power Deliv 2008;23(2):915–23.

[22] Ouyang W, Cheng H, Zhang X, Yao L. Distribution network planning method considering distributed generation for peak cutting. Energy Convers Manage 2010;51(12):2394–401. [23] Shayeghi H, Bagheri A. Dynamic sub-transmission system expansion planning incorporating distributed generation using hybrid DCGA and LP technique. Electr Power Energy Syst 2013;48:111–22. [24] Falaghi H, Singh C, Haghifam MR, Ramezani M. DG integrated multistage distribution system expansion planning. Electr Power Energy Syst 2011;33(8):1489–97. [25] Khalesi N, Rezaei N, Haghifam M-R. DG allocation with application of dynamic programming for loss reduction and reliability improvement. Electr Power Energy Syst 2011;33:288–95. [26] Poonpun P, Jewell WT. Analysis of the cost per kilowatt hour to store electricity. IEEE Trans Energy Convers 2008;23(2):529–34. [27] Kazempour SJ, Moghadam MP. Economic viability of NaS battery plant in a competitive electricity market. In: IEEE Int Conf Clean Elect, Power; 2009. p. 453–9. [28] Naderi E, Kiaei I, Haghifam MR. NaS technology allocation for improving reliability of DG-enhanced distribution networks. In: IEEE 11th Int Conf Prob Methods Appl Power Syst; 2010. p. 148–53. [29] Aliakbar-Golkar M, Sedghi M. Improved hybrid TS/PSO algorithm for multistage distribution network expansion planning. In: 21st Int Conf Electricity Dist CIRED; 2011. p. 1–4. [30] Billinton R, Wang P. Distribution system reliability cost/worth analysis using analytical and sequential simulation techniques. IEEE Trans Power Syst 1998;13(4):1245–50.