Scenario-based planning of fast charging stations considering network reconfiguration using cooperative coevolutionary approach

Journal of Energy Storage 23 (2019) 544–557

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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est

Scenario-based planning of fast charging stations considering network reconfiguration using cooperative coevolutionary approach

T

Afshin Pahlavanhoseini , Mohammad Sadegh Sepasian ⁎

Department of Electrical Engineering, Shahid Beheshti University, A.C., Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Fast charging station Cooperative Coevolutionary approach Uncertainty Network reconfiguration

In recent years, plug-in electric vehicles (PEVs) have attracted a great deal of attention because of environmental issues. For large-scale integration of PEVs, appropriate siting and sizing of PEV charging stations are essential. In this paper, a framework for simultaneous fast charging stations (FCSs) planning and distribution network reconfiguration is proposed. The distribution network reconfiguration is effectively used to optimize objective functions. The objective function considered is defined as the sum of the initial investment and energy loss costs subject to different distribution system constraints. In the model, a scenario-based approach is used for taking into account uncertainties of traditional electric load, FCS load, and electricity price. To reduce the computational burden of the problem, a scenario reduction technique is utilized. A cooperative coevolutionary genetic algorithm (CCGA) is employed to solve the problem. The FCSs locations and the network switches are coded separately, and they evolve cooperatively as two different species, i.e., the location species and the switch species. Furthermore, an efficient technique called Dijkstra's algorithm is used to calculate FCSs sizes in which the nearest FCS to PEVs is determined based on their driving distance from FCSs on their path to their destination. Finally, the performance and the effectiveness of the proposed method are demonstrated by numerical results. More specifically, use of the proposed scenario-based approach yields to a more accurate solution than deterministic method. In addition, usage of network reconfiguration in FCSs planning both reduces the total costs and improves the voltage profile.

1. Introduction In recent years, plug-in electric vehicles (PEVs) have been used as an appropriate tool for transportation thanks to their fewer adverse impacts on the environment [1,2]. In many countries, there is a plan to increase the PEV ownership. PEVs, owing to the less driving range compared with internal combustion engine vehicles, need to get recharged during the trip at fast charging stations (FCSs) [1]. Appropriate planning of FCSs is important to enable large-scale PEV deployment where the FCS investment will continuingly grow to meet the increasing PEV charging demand [1]. Efficient, convenient, and economic FCSs can enhance the people willingness to buy PEVs and promote the industry development [2]. The FCSs site selection is important in the whole life cycle, which has a major impact on the service quality and efficiency of FCSs [2]. In addition, it has a significant influence on environmental, social, and economic factors. The impacts of EV charging on the distribution network have been documented in [3–6]. Optimal planning of charging stations can improve the voltage profile, reduce network loss, and yield economic benefits for distribution

⁎

company [7–9]. Therefore, it is necessary to use proper methods for FCSs planning [10,11]. Recently, there has been increasing interest in the optimal planning of FCSs [10–33]. Table 1 presents the summary of the main works in the context of FCSs planning problem in chronological order. In some studies, single-objective optimization techniques have been used [10,12–16,18,21–27] to find the optimum value of the decision variables, while in others multi-objective optimization methods have been applied [2,11,17,20]. In previous works, different objectives have been considered, including minimization of the FCSs deployment cost [11,12,14,15,18,21–27], loss reduction [11,13–15,17,20,21,25-27], maximization of the captured traffic flow by FCSs [11], voltage profile improvement [20,21], and waiting time in FCSs [10]. In some more recent studies, simultaneous planning of distribution network and electrical vehicle charging systems has been studied in which the distribution network expansion costs have been considered [11,18,19]. Different methods have been utilized to solve the FCSs planning problem, including genetic algorithm (GA) [13,15], modified differential evolution [14], particle swarm optimization (PSO) [16], genetic

Corresponding author. E-mail address: [email protected] (A. Pahlavanhoseini).

https://doi.org/10.1016/j.est.2019.04.024 Received 12 December 2018; Received in revised form 24 April 2019; Accepted 24 April 2019 Available online 01 May 2019 2352-152X/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 23 (2019) 544–557

A. Pahlavanhoseini and M.S. Sepasian

Nomenclature

Loss cost Capital cost of a set of fast charging facilities Location sensitive cost of FCS at bus k Fixed investment cost of FCS at bus k Charging demand of kth FCS at hour h EkFCS Total consumed energy in kth FCS during a day Pid, se, d, h, sc Load of bus i at the scth scenario of hour h in day d of season se excluding the load of FCSs. Pig, se, d, h, sc Generated power at bus i at the scth scenario of hour h in day d of season se PseLoss Total power loss of network at the scth scenario of hour h , d, h, sc in day d of season se Gij, Bij Real part and imaginary part of the nodal admittance matrix Vj, se, d, h, sc Voltage amplitude of buses i,j at the scth scenario of hour h in day d of season se ij, se, d, h, sc Phase angle deviation of branch ij at the scth scenario of hour h in day d of season se Vimin, Vimax Minimum and maximum bounds of voltage amplitude at bus i Sijmax Apparent power capacity of feeder ij W allowed Maximum allowed waiting time N FCS The number of FCSs N CL The number of candidate locations Nk Size of the kth FCS (the number of charging plugs in the kth FCS) N max Maximum size of FCS N min Minimum size of FCS N NOS The number of normally open switches N Loop The number of loops in the network N Branch The number of branches in the network N Bus The number of buses in the network uk Binary decision variable for the kth FCS

f loss c CHF ckLS ckF

Original set of scenarios Set of scenarios chosen in scenario reduction procedure b Set of network buses f Set of feeders FCS Set of candidate locations for fast charging stations (FCSs) SE Set of seasons (spring, summer, autumn, winter) D Set of days (weekday, weekend) H Set of time intervals (24 h) RH Occupation rate of charging facilities of the kth FCS at k,h , k hour h and in the rush hour RH Mean arrival rate of PEVs in the kth FCS at hour h and in k, h , k the rush hour WkRH Average waiting time for charging service in the kth FCS during the rush hour µ Mean service rate of FCSs fhtrip Trip ratio in hour h fktrip Traffic flow captured by the kth FCS in hour h ,h CD Overall daily charging demand (times/day) Percentage of EVs which are recharged at home Choosing ratio of FCSs LLF Load level factor (the ratio of load to its peak value) ¯ h Load level factor and its average at hour h LLFh, LLF Pk, h, n The probability that there are n PEVs undergoing charging service in the kth FCS at hour h Pk0, h , Pk0, RH The probability of being no PEV undergoing charging service in the kth FCS at hour h and in the rush hour Probse, d, h, sc Probability of the scth scenario of hour h in day d of season se EPse, d, h, sc Electricity price at the scth scenario of hour h in day d of season se f inv Investment cost J

s

templates in the planning model to deal with uncertain operational states. In the present paper, we present a scenario-based planning method which addresses the uncertainties of the conventional load levels, FCSs load levels, and the electricity price. The results indicate that consideration of the abovementioned uncertainties can influence the solution and thus should be carefully considered in FCSs planning studies. The traffic and the geography of the area have been considered and studied in some previous works in the planning of parking lots [13,25–27] and FCSs [12,20,23,28–33]. In this regard [12], has determined the optimal locations of charging stations considering service radius using a two-level screening method. Then, according to the related costs, optimal sizing of charging stations has been found via a modified primal-dual interior point algorithm. Reference [20] has considered the distribution and traffic network topologies as well as the EV owner’s driving behaviour with a multi-objective charging station planning method proposed. In this work, the cross-entropy method has been used to solve the multi-objective planning problem. Also [23], adopted a method for FCS planning on a round freeway. The authors used the Origin-Destination (OD) analysis to model the spatial and temporal transportation behaviours [28] has proposed a location model for charging stations based the characteristics of people travel behaviours. Reference [29] has proposed an optimal allocation model for EV charging stations to maximize the social welfare associated with the coupled distribution and traffic transportation network. Further [30], has analysed the optimal placement of CSs to achieve maximum coverage at minimum cost. In this work, the authors considered a graph of all possible locations of CSs and obtained the optimal subgraph of this graph with complete coverage of all areas in the network. In addition [31], presented CS placement problem with the aim of easy access to a

algorithm based improved particle swarm optimization (GAIPSO) [21], quantum-inspired simulated annealing algorithm (QSA) [25,26] and quantum annealing (QA) [27]. In addition, in [11], a multi-objective evolution algorithm, called the decomposition based multi-objective evolution algorithm (MOEA/D), has been used to find the non-dominate solutions. In [19], non-dominated sorting genetic algorithm (NSGA-II) has been applied to solve the problem. Considering the optimal Pareto non-dominated solutions sets, a satisfying fuzzy method has been used to select the best solution. Further [17], considered objective functions of the distribution company and municipal transportation organization, obtaining the optimal solution using the bargaining theory. Having reviewed the previous works (Table 1), it is observed that FCSs planning has been often solved by deterministic approaches. Only a few recent works [13,14,17,23,24,27] have focused on modelling the uncertainties associated with the uncertain variables, while some of these uncertainties are important in the FCS planning. In this regard [23], has utilized the Monte Carlo simulation (MCS) to obtain the spatial-temporal distribution of the EVs charging demand considering the uncertainties related to battery characteristics and transportation behaviours. As the traffic flow and traditional loads are uncertain over the planning horizon, a set of potential future scenarios have been forecasted in [24]. In this work, some scenarios for base load templates and traffic flow profiles have been generated. Then, a two-stage stochastic programming model is used for FCSs planning. Furthermore [14], has included the adoption cost in the objective functions to consider the uncertainties such as EVs’ penetration rate and the charging habits of EV drivers. In this paper, to simulate the uncertain growth rate of EVs and construct the scenarios randomly, MCS approach has been used. Also [17], considered different scenarios generated by load profile 545

546

✓ ✓ ✓ ✓ ✓ ✓ ✓

✓ ✓

✓ ✓

✓

✓

✓ ✓

✓

✓

✓ ✓

✓ ✓ ✓ ✓

✓ ✓ ✓

✓ ✓ ✓ ✓ ✓

MINLP

✓

MILP

NLP

Singleobjective

Multiobjective

Mathematical model

Objective function model

✓ ✓ ✓ ✓

✓

✓ ✓ ✓

✓ ✓ ✓ ✓ ✓ ✓

FCS

✓

✓

✓ ✓

✓

parking lot

Charging system

✓

Electricity price

Uncertainty

✓

✓

✓ ✓

✓

✓

FCS load

1

Solution methods (Table 1): Modified Primal-Dual Interior-Point Algorithm (MPDIPA). 2 Cross-entropy. 3 Modified Differential Evolution. 4 GA. 5 Decomposition based multi-objective evolution algorithm (MOEA/D). 6 TOPSIS, a technique for order of preference by similarity to ideal solution. 7 Quantum annealing (QA). 8 Voronoi diagram together with particle swarm optimization algorithm. 9 An enumeration method. 10 Shared Nearest Neighbor (SNN) Clustering algorithm. 11 Quantum-inspired simulated annealing algorithm (QSA). 12 Genetic Algorithm based Improved Particle Swarm Optimization (GAIPSO). 13 Quantum-inspired simulated annealing algorithm and genetic algorithm. 14 CPLEX. 15 CPLEX. 16 OCEAN-C (Optimizing eleCtric vEhicle chArging statioN placement with Continuous variables). 17 CCGA.

*

[12] [20] [14] [15] [11] [2] [27] [16] [17] [23] [25] [21] [26] [24] [22] [10] This paper

Reference

Table 1 Important works in the scope of FCS planning.

✓

✓

✓

Conventional load

✓

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

✓

Charging system investment

Objective functions

✓

✓ ✓ ✓

✓

✓

✓ ✓ ✓ ✓ ✓

Loss

✓

✓

Voltage profile

✓ ✓

✓

✓

✓

Traffic

✓

✓

✓

✓

✓

✓

Waiting time in queue

✓

Reconfiguration

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Solution method

A. Pahlavanhoseini and M.S. Sepasian

Journal of Energy Storage 23 (2019) 544–557

Journal of Energy Storage 23 (2019) 544–557

A. Pahlavanhoseini and M.S. Sepasian

CS within EVs driving range. Further [32], studied the impact of the CSs placement on power grid considering traffic flow of EVs. This paper analysed the strategic interactions among service providers such as power grid operator, EV owner, and CS owner using a Bayesian game framework. It is obvious that consideration of the driving distance between the PEVs and FCSs can significantly facilitate obtaining a better solution [33] assumed that EVs go to the nearest FCS to get recharged. The authors considered a straight-line distance between EVs and FCSs. Meanwhile, EVs normally do not choose the CS with a less straight-line distance as compared to the FCS with a shorter driving distance. To develop the method in [33], we consider the driving distance of EVs to get to FCS. We assume that the EVs go to the nearest FCS in their origindestination path. Indeed, they go to the FCS whose sum of their driving distance from their origin to that FCS and the distance from that FCS to their destination is minimum. Here, Dijkstra's algorithm is used for determining the size of FCSs based on the EV origin- destination data and the driving distance between the PEVs and FCSs. In addition, to the best of the authors’ knowledge, the previous works have not used any approach to decrease the effect of FCSs loads on the network to obtain a better value of the objective function. In this paper, the network reconfiguration is considered as a tool to improve the objective function of the distribution company. There are two types of switches in the distribution networks: normally open switches (tie switches) and normally closed switches (sectionalizing switches). Distribution network reconfiguration is the process of determining the topology of distribution network by selecting the open/closed status of tie and sectionalizing switches [34]. Note that the operational constraints of the distribution network especially maintaining the radial structure of the distribution network should be satisfied. In previous studies, the main objective of the reconfiguration has been reducing the active power losses [35–38]. In addition, reconfiguration has been used for other objectives such as decreasing voltage deviation [39], improving reliability indices [40], and load balancing [41]. Previous works have employed different methods such as optimum flow pattern [37], neural network [38], PSO [40], and expert systems [42], to solve the reconfiguration problem. In the present work, reconfiguration of the distribution network is used to optimize the objective function of the distribution company in the FCSs planning. Numerical results of this paper demonstrate that considering network reconfiguration in FCSs planning can largely improve investment efficiency. Utilizing network reconfiguration not only leads to less total costs but also improves the voltage profile.

The FCSs planning problem considering network reconfiguration is solved using the cooperative coevolutionary genetic algorithm (CCGA). The coevolutionary computation has been developed from evolutionary algorithms (EAs). It has been used to simulate the electricity market [43–45], to determine the equilibrium of noncooperative game [46] as well as the market equilibrium [47], etc. CCGA, which is a type of coevolutionary algorithms, has the following characteristics [48,49]: 1 A complete solution is composed of more than one sub-component. Each sub-component is represented by one species. 2 An individual is combined with the individuals of other species to form a complete solution. Then it can be evaluated. 3 Each species evolves using a standard GA. In the present work, the effectiveness of applying CCGA in solving the FCSs planning problem considering the network reconfiguration is investigated. The main contributions of this paper, compared to the similar works, can be listed as follows:

• A scenario-based method is proposed for FCSs planning to address • • •

future uncertainties, namely the conventional load levels, FCSs load, and electricity price. The FCS planning is done considering network reconfiguration possibility. In other words, the model determines the locations and sizes of FCSs and the status of switches (open/close), simultaneously. The effectiveness of CCGA in the study of FCS planning, when network reconfiguration is possible, is investigated in which the FCSs locations and the network switches are coded separately, and they evolve cooperatively as two different species. A novel method is proposed to calculate the FCSs sizes based on the origin-destination (OD) matrix of traffic network where Dijkstra's algorithm is used for calculating the distance between PEVs and FCSs.

2. Problem definition and formulation This paper presents a method for scenario-based planning of FCSs considering network reconfiguration, in which different uncertainties related to the FCSs and conventional loads as well as electricity price are considered. Here, the problem is solved from DISCO point of view. Specifically, the locations and sizes of FCSs as well as the status of

Fig. 1. Framework of FCS planning method. 547

Journal of Energy Storage 23 (2019) 544–557

A. Pahlavanhoseini and M.S. Sepasian

2.1. Uncertainty modelling There are several uncertainty handling methods to deal with uncertain parameters such as probabilistic, possibilistic, and hybrid possibilistic-probabilistic approaches, information gap decision theory, robust optimization, and interval analysis [51]. Each of these methods has its own advantages and disadvantages and is used in different problems. In this regard [51], has presented a complete review of these methods. The probabilistic approach is used when the input parameters of the problem are random variables and the probability density functions (PDFs) of these parameters are known. In the possibilistic method, the input parameters are described by a membership function (MF). Hybrid possibilistic-probabilistic approaches are used when both random and possibilistic parameters are considered. In the information gap decision theory, PDF or MF is not available for problem parameters. On the other hand, in the robust optimization technique and interval analysis, the representation of input parameters is performed by intervals. The robust optimization is extremely difficult to use in nonlinear models. Further, the interval analysis is too conservative. Therefore, in this paper, based on the abovementioned explanations and the complete information presented in [51], a scenario-based decision making, which belongs to the probabilistic approach, is used to handle the uncertainty of parameters. The FCSs load depends on different factors such as number of PEVs being charged, charger type, battery state-of-charge (SOC) and capacity, charging start time, and charging duration [52]. Since these factors are uncertain, the overall load of FCS is uncertain too. In addition to FCS load, there are other uncertain parameters in the network which affect the FCS planning. Considering these uncertainties can lead to a more effective solution. Among these uncertainties, the uncertainty of electricity price and conventional load (electrical load except FCS load) are considered. Fig. 2. Load curve of the network and related uncertainty model.

2.1.1. Uncertainty modelling of conventional load The load demand is one of the uncertain parameters in planning problems. Eight scenarios (weekday and weekend of 4 seasons) have been considered. It is assumed that the load demand follows a normal distribution around its expected values in different hours as demonstrated in Fig. 2 [53–55]. Each normal distribution is divided into 7 states [55]. The probability of each state is depicted in Fig. 2. Reference [55] has presented a detailed description about the probability of each state. Taking 8 scenarios into account for modelling uncertainties associated to weekday/weekend and different seasons as well as 7 states of normal distribution, for each hour we have totally 8 × 7 = 56 different scenarios.

switches (open/close) are determined, such that the objective function of DISCO is optimized. In the proposed model, although the traffic data is considered and we have calculated the FCSs sizes based on OD matrix of traffic network, we have not considered any objective function related to traffic issues. Indeed, we have considered a constraint based on which the average waiting time for charging service should be within the predefined threshold. Considering DISCO and traffic objective functions and multi-objective modelling of the problem is one of our future works. Fig. 1 presents the framework of FCS planning method. The input data includes the followings in the studied area:

• Traffic network and its OD matrix during rush hour. Note that OD • • • •

matrix values show the number of trips between pairs of zones in a geographic region within a specific time period [50]. Penetration rate of PEVs for the planning horizon. Maximum limit for average waiting time in queue for charging service. Candidate locations for FCSs installation. Electric load and electricity price data.

2.1.2. Uncertainty modelling of FCS load It is assumed that the arrival time of PEVs to FCSs and service time in FCSs can be modelled by Poisson distribution and negative exponential distribution, respectively [11,56]. Furthermore, PEVs are charged based on the first-come first-served (FCFS) rule. Therefore, the M/M/s theory can be used [11]. The M/M/s queue is a queueing model which describes a system with three properties: -Poisson process determines the arrival -There are s identical servers in the system -The service time follows a negative exponential distribution [11].

First, by knowing the traffic network data during the rush hour and penetration rate of PEVs, the spatial and temporal distribution of PEVs is determined. Then, considering FCSs candidate location, the spatial and temporal distribution of PEVs arrivals is determined. Thereafter, using distribution of PEVs arrivals, electric load, and electricity price data, uncertainty modelling is developed. Finally, based on previous stage information and maximum allowed waiting time in FCSs queue, the outputs (the FCSs sizes and locations as well as the status of the network switches) are determined.

¯ h + x) (LLFh = LLF Based on the M/M/s queuing system, the probability that there are n PEVs in the kth FCS at hour h is calculated by Eq. (1). This equation is used for generating the scenarios for the FCSs electrical load.

548

Journal of Energy Storage 23 (2019) 544–557

A. Pahlavanhoseini and M.S. Sepasian

Pk0, h n! Pk0, h

Pk, h, n =

Nk ! Nk 1

Pk0, h =

(Nk

k,h )

n if

(Nk ) Nk (

k,h )

(Nk

i

k,h )

i=1

n if

+

i!

functions in charging station planning. The proposed model is similar to the model developed in [11]. However, we have made some modifications for calculating the energy loss cost. Therefore, in this paper, the objective function is defined as follows: Objective:

0 < n < Nk Nk

n

(Nk

k,h )

Nk ! (1

(1) Nk

1

(2)

Where, f Inv and f loss are the investment and energy loss costs, respectively. Each term of the above equation is explained as follows:

is the probability that there are no PEVs undergoing charging in the kth FCS at hour h. Also, k, h is the occupation rate of charging facilities of the kth FCS at hour h which is calculated by:

Pk0, h

k,h

=

(8)

minf = f Inv + f loss

k, h )

2.3.1. Investment cost Since the size and location of FCSs can directly impact the investment cost, they are added to the objective function and defined as follows:

k,h

(3)

Nk µ

µ is the mean service rate of FCSs. FCSk, h represents the mean arrival rate of PEVs in the kth FCS at hour, h.

f Inv =

2.1.3. Uncertainty modelling of electricity price The electricity price is assumed to follow the demand level factor [53,57]. Therefore, it is assumed that the price level factor follows a normal distribution around its expected value similar to load level factor illustrated in Fig. 2.

2.2.1. Scenario generation As stated earlier, the uncertainty of conventional load, FCS load, and electricity price are considered. One specific realization of these three uncertainties at hour h is represented by the following vector:

1

k

FCS

uk (c CHFNk + ckLS Nk + ckF )

(9)

2.3.2. Energy loss cost The power demand of FCSs can change the power loss of the distribution system. The energy loss cost of the system can be calculated by Eq. (10).

(4)

f loss =

FCS D Pse Pse Where, =[P1,Dse, d,h, sc P2,Dse, d, h, sc… P DBus ], = , d, h, sc , d, h, sc N , se, d, h, sc FCS FCS [P1,FCS P … P EP EP EP ], =[ se, d, h, sc se, d,1, sc se, d,2, sc…EPse, d,24, sc ] se, d, h, sc 2, se, d, h, sc N FCS, se, d, h, sc

se SE d D h H sc

s

probse, d, h, sc . EPse, d, h, sc . PseLoss , d, h, sc

(10)

is the total power loss of network at the scth In this equation, scenario of hour h in day d of season se, which is calculated by Eq. (11).

represent the load of buses excluding the load of FCSs, the electrical load of FCSs, and electricity price at the scth scenario of hour h in day d of season se. The probability of each scenario of hour h in day d of season se is calculated by: EP probse, d, h, sc = (probseD, d, h, sc )(probseFCS , d, h, sc )( probse, d, h, sc )

(1 + )n

FCS

FCS

The first factor is the capital recovery factor. and nFCS represent the interest rate and lifespan of FCS respectively. Investment cost consists of fixed and variable costs of FCS construction. More specifically, c CHF , insensitive to location, is the capital cost of charging facilities like charging machines, transformers, cables, and so on; ckLS denotes the location sensitive costs such as cost of land required for installing FCS. These two costs are proportional to the size of FCSs. The last cost, ckF , irrelevant to the size of FCSs, refers to fixed costs.

2.2. Combined states model

se, d, h, sc ] Sse, d, h, sc = [PseD, d, h, sc PseFCS , d, h, sc EP

(1 + )n

PseLoss , d, h, sc

PseLoss , d, h, sc = f

ij

gij (Vi2, se, d, h, sc + V 2j, se, d, h, sc

2Vi, se, d, h, sc Vj, se, d, h, sc cos

ij, se, d, h, sc )

(5)

(11)

EP In Eq. (5), probseD, d, h, sc , probseFCS , d, h, sc , and probse, d, h, sc are the occurrence se, d, h, sc EP probability of PseD, d, h, sc , PseFCS , an d, respectively. , d, h, sc

In Eq. (11), denotes the set of network feeders, Vi, se, d, h, sc and Vj, se, d, h, sc are voltage magnitudes of bus i and j at the scth scenario of hour h in day d of season se, gij represents conductance of feeder ij, and ij, se, d, h, sc is the phase angle deviation of branch ij at the scth scenario of hour h in day d of season se. f

2.2.2. Scenario reduction Since the quantity of scenarios is too large, a scenario reduction method [58] is used to represent the original set with a smaller set, as follows: Step 1: Calculate the distance between each pair of scenarios d (sc,sc ). Step 2: Obtain the first scenario as follows:

sc1 = arg s

minJ

sc

=

s

The following constraints guarantee a secure optimal power flow as well as radial structure of the network for hour h and scenario sc:

Pig, se, d, h, sc = Pid, se, d, h, sc + PiFCS , se, d, h, sc + Vi, se, d, h, sc

Probsc d (sc,sc ) sc

= {sc1 } ,

J

=

J

{scn} ,

J

=

J

+ Bij sin

(6)

s

s

Vj, se, d, h, sc (Gij cos

s

as below:

ij, se, d, h, sc )

b,

i

ij, se, d, h, sc

b

j

J

Step 3: Select the next scenario which is added to s

2.4. Constraints

se

SE ,

d

D,

h

H,

sc

s

(12)

(7)

Qig, se, d, h, sc

Step 4: If the number of new scenarios is equal to a predefined value, continue; otherwise go to step 2. Step 5: Add the probability of each non-selected scenario to its closet scenario in the selected set.

=

Qid, se, d, h, sc

+

QiFCS , se, d, h, sc

+ Vi, se, d, h, sc

Vj, se, d, h, sc (Gij sin

Bij cos b,

i

ij, se, d, h, sc

b

j ij, se, d, h, sc )

se

SE ,

d

D,

h

H,

sc

s

(13)

2.3. Objective function

Vimin i

The cost of investment and energy losses is one of the main objective 549

b,

se

SE ,

Vi, se, d, h, sc d

D,

Vimax h

H,

sc

s

(14)

Journal of Energy Storage 23 (2019) 544–557

A. Pahlavanhoseini and M.S. Sepasian

Sijmax

|Sij, se, d, h, sc| b,

i

se

SE ,

N Loop = N Branch uk

d

D,

h

H,

(15)

s

sc

(16)

N Bus + 1

1

(17)

FCS

k

Nk WkRH

<

WkRH =

(18)

FCS

uk k

W allowedk (Nk RH k

(19)

FCS

RH Nk k )

Nk ! (1

k, RH P0 RH 2 k, RH k )

k

FCS

(20)

Eqs. (12) and (13) represent the power flow constraints of the system. Eq. (14) limits the bus voltages to specific upper and lower limitations. Eq. (15) determines the limitations on the apparent power flow. The radial structure of the network is guaranteed by constraint (16). In this paper, the main closed loops of the system are employed to control the radial structure of the network. Note that each main loop consists of a tie switch and the corresponding sectionalizing switches that form a loop. To preserve a radial network structure when a tie switch is closed, only one sectionalizing switch is opened in each loop. Eq. (17) guaranties that at least one FCS should be installed. Eq. (18) denotes the constraint for number of charging plugs in each FCS. Eq. (19) represents that during the rush hour the average waiting time for charging service should be within the predefined value. Eq. (20) shows how to calculate WkRH based on Little’s law in the queuing theory [11].The mean arrival rate of PEVs in the kth FCS during the rush hour ( kRH ) can be calculated as [11]: RH k

= max

= CD (1

Fig. 3. a) Location gene, b) switch gene.

parts: 1 The evolution of the location species 2 The evolution of the switch species. When an individual in the location species is evaluated, an individual from the switch species needs to be chosen randomly and combined with the individual from the location species to achieve the complete solution. To solve the problem, three types of variables should be determined: the location of each FCS, the size of FCS in each location, and the status of switches. The status of switches and FCSs locations are determined by CCGA, and the FCSs sizes are calculated by Dijkstra’s algorithm. The location gene and the switch gene are illustrated in Fig. 3. The location genes are in binary form. Each location gene contains values of zero or one representing installation status of FCSs, i.e. if kth gene value equals to one, FCS will be installed in the kth candidate location. Each switch gene represents the switches which should be open. When the switches which should be open are determined, the status of the other switches are automatically determined. The number of open switches equals to N NOS = N Branch N Bus + 1. Therefore, each switch gene has N Branch N Bus + 1 value. Note that the values of switch genes are integer numbers which are chosen between 1 and the maximum number of switches in the network. Furthermore, the combination of switches is acceptable only if the network is radial. In the present paper, a blend crossover operator has been employed. The offspring is randomly generated by this operator as follows [47]:

k,h | k,h

)( )

fktrip ,h

f htrip f trip h H h

k

trip

FCS f k , h

,

h H,

k

FCS

(21) 3. Solution method 3.1. Cooperative coevolutionary genetic algorithm (CCGA) In biology, coevolution happens when two or more species influence each other's evolution. Coevolutionary computation is an area in the evolutionary computation which is developed from traditional evolutionary algorithms (EAs). It simulates the coevolutionary mechanism in nature. Coevolutionary computation belongs to agent-based simulation techniques. The species in nature are simulated by agents. Different species interact with each other and coevolve which result in the evolution of ecosystem. Reference [59] has explained the framework of coevolutionary computation: There are two types of coevolutionary algorithms: cooperative and competitive. In the cooperative algorithms, individuals are rewarded when they interact and perform well with other individuals and punished when they work poorly together. However, in competitive algorithms, individuals are rewarded at the expense of individuals with whom they interact [59]. Our work investigates the effectiveness of using CCGA in solving FCSs planning problem considering network reconfiguration. The proposed approach is described below. The FCSs locations and open switches are coded separately, and they evolve cooperatively as two different species, i.e., the location species and the switch species. The chromosome contains two types of genes: the location gene and the switch gene. The location gene describes the FCS locations, and the switch gene defines the open switches in the network. As the location variables and the open switches are set to be two different species, the evolution process is divided into two

[x i

(yi

x i ), yi + (yi

x i )]

(22)

Where, x i and yi ، x i < yi represent the decision variable values of the parent solutions which are selected from the best solutions and τ is a random number between 0 and 1. In this paper, for balancing exploitation and exploration of the search space, = 0.5 has been chosen [47]. A dynamical non-uniform mutation operator is employed in order to reduce the divergence caused by the use of a random mutation operator, which is defined as follows [47]:

x i' =

xi + xi

(t , Ub (t , Lb

x i ) if = 1 x i ) if = 0

(23)

Where, x i and x i are the chosen and obtained values in the mutation operator, respectively, and t is the number of generations. The function (t , y ) yields a value within the interval [0, y]. As t increases, the value of this function approaches zero. This feature causes the mutation operator to search the space uniformly in the initial generations and locally at the next generations. The function Δ is defined as follows:

(t , y ) = y (1

(1

t) T

)

(24)

Where, T is the maximum number of generations, represents a random number in the interval [0,1], and denotes a system 550

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A. Pahlavanhoseini and M.S. Sepasian

Table 2 Description of Dijkstra’s algorithm. Input: A bidirected graph G with weights c : E (G ) + and a vertex s V (G ) Output: Shortest paths and their lengths from s to all v V (G ) . All d (v ) and p (v ) for all v V (G ) are calculated, where d (v ) is the length of a shortest s v -path together with the edge (p (v ), v ) . If v is not reachable from s then d (v ) = and p (v ) is undefined. 1

2 3 4

5

Set the followings: d (v ) = for v (V (G ) {s}) d (s ) = 0 R= ; Find a vertex v (V (G ) R) such that d (v ) = mind (w ), w (V (G ) {v } ; Set: R = R For all w (V (G ) R) such that , (v, w ) E (G ) do: If l (w ) > l (v ) + c ((v, w )) then Set l (w ) = l (v ) + c ((v , w )) and p (w ) = v ; end if end for If R V (G ) then go to line 2 end if

R) ;

parameter. This parameter determines the degree of dependency on the generation number. 3.2. Dijkstra’s algorithm Finding the shortest path between two nodes in a directed or undirected graph is one of the best-known optimization problems. The shortest path problem is to find the shortest path and the minimum distance between two nodes in a directed or undirected graph with a conservative weight. Here, conservative means that there is no path

Fig. 5. Proposed algorithm for solving the problem.

with a negative total weight [60]. Dijkstra’s algorithm proposes a method to find the shortest path between two nodes. The Dijkstra’s algorithm is briefly described in Table 2 [60]. Normally, PEVs drivers go to the nearest FCS to get recharged [16]. Here, Dijkstra’s algorithm is used to determine FCSs sizes based on OD matrix of traffic network. Indeed, it is utilized to determine which FCS is the nearest one to PEVs on their path from origin to destination. 3.3. Solution process The FCSs planning problem considering network reconfiguration is a mixed integer nonlinear optimization problem. The CCGA proposed in Section 3.1 is used to solve this problem. The whole solution process is shown by the flowchart in Fig. 4 which is described in detail in Fig. 5. The steps of the proposed algorithm are expressed as follows: Step 1: Initialize the location and switch species. Step 2: Evolve the location species. Step 3: Calculate the driving distance between PEVs and FCSs on their paths to destination by Dijkstra’s algorithm. Step 4: Determine which FCS is the nearest one to PEVs on their paths to destination. Step 5: Determine the number of PEVs which are recharged in each FCS.

Fig. 4. Flowchart of the solution process. 551

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Fig. 6. Initial configuration of the 33-bus distribution system.

Fig. 7. Sioux-Falls network.

Step 6: Knowing the number of PEVs that get recharged in each FCS, determine FCSs sizes considering allowed waiting time in FCSs queues. Step 7: Generate scenarios for FCS load, conventional load, and electricity price for each hour. Step 8: Reduce the number of scenarios to a predefined value. Step 9: Evolve the switch species.

Step 10: For each chromosome, check the constraints. If there is any constraint violation, consider a penalty for the objective function. Update the best solution. Step 11: Check the termination condition. If the termination condition is false, go to Step 2; otherwise, go to Step 12. Step 12: Output the results.

552

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Fig. 8. Trip ratio during 24 h.

Fig. 9. The topology of 33 bus distribution system and Sioux-Falls traffic network. Table 3 Investment cost of FCS.

Table 5 CCGA parameters.

Candidate FCSs

1

2

3

4

5

Parameters

Description

Bus number Traffic node

cCHF [10 4 USD ]

5 12 8.0

10 3 8.0

20 10 8.0

25 15 8.0

32 18 8.0

ciF [10 4 USD ]

40

42

32

36

38

Initial population Mutation Crossover Number of generations Population size (location gene) Population size (switch gene) Mutation probability Crossover probability

Randomly initialized population Non-uniform mutation Blend crossover 70 20 40 0.3 0.8 0.5 1

ciLS [10 4 USD ]

4.0

4.2

3.2

3.6

4.0

Table 4 Electricity tariffs during a day. Time of day

Price (USD/kWh)

Peak (14-20) Mid-peak (7-14 and 20-22) Off-peak (other times)

0.5 0.2 0.15

4. Simulation results 4.1. 33-bus distribution system The IEEE 33 bus system [61], as shown in Fig. 6, is used to demonstrate the efficiency of the proposed method. The voltage level of 553

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Table 6 Summary of the final results with and without network reconfiguration. Method

Proposed method without reconfiguration

Proposed method with reconfiguration

Optimal buses Optimal sizes Open switches

5 20 25 7 8 11 S33, S34, S35, S36, S37

5 20 25 7 8 11 S7, S9, S14, S36, S37

Table 7 Cost comparisons between the scenarios with and without network reconfiguration. Method

Cost (105USD )

Proposed method without reconfiguration Proposed method with reconfiguration Difference (105 USD ) Difference (%)

Investment

Loss

Total

4.09 4.09 0

2.99 1.95 1.04

7.08 6.04 1.04

0

34.78

14.69

Fig. 11. The trend of convergence of the presented method.

network can be found in [62]. The trip ratio during 24 h is shown in Fig. 8. The penetration rate of PEVs and the percentage of PEVs which are recharged at home ( ) are set to 0.3 and 20% [11], respectively. The percentage of the remaining PEVs recharged in FCSs ( ) is set to 20% [11]. The coupled relationship between distribution and transportation systems is illustrated in Fig. 9. It is assumed that candidate locations for FCSs are where an electrical bus and a traffic node are in the same place [11]. Therefore, nodes 5, 10, 20, 25 and 32 are chosen as the candidate buses for installing FCS (see Fig. 9). However, any other node can be chosen as a candid for FCSs. Furthermore, the investment costs of FCSs are given in Table 3 [11]. According to IEC 61851-1 standard, charge level 3 is chosen for FCS. The capacity of batteries is 20 kW h and the charging power of each facility is 44 kW based on IEC 61851 standard. Three rates of time of use (TOU) tariffs, including peak, mid-peak, and off-peak, are used as shown in Table 4 [14]. In addition, the parameters of the CCGA utilized for solving the problem are provided in Table 5. To investigate the effect of network reconfiguration in FCSs planning, the results of two scenarios (with and without reconfiguration) are compared. Tables 6 and 7 present the comparison between final results and costs of these two scenarios respectively. As can be seen in Table 7, considering the possibility of reconfiguration, the loss cost and consequently the overall cost decrease considerably. As shown in Table 7, when reconfiguration is feasible, the loss and total cost diminish by 34.78% and 14.69%, respectively. The voltage profiles for the test system with and without network reconfiguration are shown in Fig. 10. It shows that use of reconfiguration in the planning of FCSs improves the voltage profile. With network reconfiguration, the minimum voltage has raised from 0.9079 p.u. to 0.9305 p.u. When network reconfiguration is used the voltage drops are managed. This happens by changing the status of switches resulting in changes in feeders’ lengths and currents. In the next section the effectiveness of the proposed probabilistic approach is examined. For this purpose, the cost of the solutions of the proposed method and deterministic method are calculated and compared for the base case in which all scenarios are considered and no scenario reduction is done. Indeed, we calculate the objective function in the base case once for the proposed method solution and another time for the deterministic method solution and compare these two values. If in the base case, the cost of our proposed approach solution is less than that of the deterministic method solution, it suggests that our method works correctly. This comparison is shown in Table 8. As can be seen in this table, our proposed method outperforms the deterministic method. In addition, when the uncertainties are considered, the optimum solution of the problem is different from that of the deterministic

Fig. 10. Voltage magnitude at each bus in the 33-node test system for the best solution. Table 8 Comparison of final results of the proposed and deterministic methods. Method

Deterministic

Proposed method

Optimal buses Optimal sizes Open switches

10 20 25 8 10 8 S7, S9, S13, S32, S37 6.89

5 20 25 7 8 11 S7, S9, S14, S36, S37 6.04

Cost (105USD )

Table 9 CCGA performance analysis. Maximum generation

Mean (105USD )

Relative variance

50 70 90

6.1013 6.0593 6.0486

9.93 E-04 1.03 E-04 3.84 E-05

this distribution system is 12.66 kV. Other specifications of this distribution system can be found in [61]. This network is supplied by the substation at bus 1. For traffic network, Sioux-Falls network is chosen. This network has 24 zones, 24 nodes, and 76 links (see Fig. 7). Each node denotes an intersection between links. The information of this 554

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Fig. 12. IEEE 69-bus distribution system.

stability for solving the method presented for FCS planning. To achieve this, the average and relative variances of optimum objective function value from a definite number of implemented runs are used. The presented method is implemented 10 times for three different values of number of generations with the results listed in Table 9. As can be seen, the mean value of optimum objective function values is improved when the number of generations increases. Additionally, as the number of generations grows, the variance declines. Indeed, as the number of generations increases, the optimality and stability of the proposed algorithm improve. Fig. 11 indicates the trend of convergence of the presented method. As can be seen, the proposed method has a suitable convergence speed.

Table 10 The FCS investment cost at different points. Candidate FCSs

1

2

3

4

5

6

7

cCHF [10 4 USD ]

Bus number

14 8.0

30 8.0

37 8.0

40 8.0

49 8.0

57 8.0

65 8.0

ciF [10 4 USD ]

40.0

35.0

50.0

30.0

45.0

30.0

35.0

ciLS [10 4 USD ]

4

3.5

4.5

2.5

4

3

3.5

Table 11 Summary of the final solution (case 2). Bus number

14

30

FCS size Open switches Cost (105 USD )

0 6 s12 10.38

37 s14

9

s58

40

49

11

7

57 s63

11

65 s69

4.3. Extended case study (69-bus distribution system)

0

The proposed method of FCS planning has been applied to a larger distribution system (see Fig. 12 [63]). The voltage of this network is 12.66 kV. More details can be found in [63]. Furthermore, the candidate buses and the construction costs of FCSs in each location are presented in Table 10 [11]. For traffic network, the 25-node transportation is chosen [64]. Other parameter settings are determined in a similar way as employed in case 1. Table 11 reports the results of this case. As can be seen FCSs should be installed in buses 30, 37, 40, 49, and 57. The FCSs sizes are 6, 9, 11, 7, and 11, respectively. In addition the open switches are s12, s14, s58, s63, and s69.

method. This indicates the importance of consideration of uncertainties; when the mentioned uncertainties are not considered, the obtained solution is not necessarily optimum. It is obvious that for proper planning, the obtained results must be as accurate as possible. In the deterministic method, for each hour, only a probable scenario is considered. Consequently, the deterministic model cannot lead to a proper response. On the contrary, in the stochastic method, the entire spectrum of all the parameters having uncertainty is covered. It can be concluded that considering uncertainties related to mentioned parameters leads to a vast range of probable scenarios where the results are more suitable and reliable.

5. Conclusion This paper presents a method to determine the optimal location and size of the FCSs to minimize the entire cost of FCSs investment and energy loss. The problem is solved using a mixed integer non-linear programming formulation. The proposed approach considers the different uncertainties related to the conventional load and FCS demand as

4.2. CCGA performance analysis The CCGA performance is investigated in terms of optimality and 555

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well as electricity price. The problem is solved by a scenario-based method using CCGA algorithm. Since the number of scenarios is considerable, a scenario reduction method is used to decrease the calculations. The simulation results demonstrate that the proposed model can be used as a proper scheme for the FCSs planning. In addition, using network reconfiguration in FCS planning both reduces the loss cost and improves the voltage profile.

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