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Multi-Objective Optimization of Electric Vehicle Fast Charging Stations with SPEA-II
9th IFAC symposium on Control of Power and Energy Systems Indian Institute of Technology 9th IFAC symposium on Control of Power and Energy Systems Indian Institute of Technology December 9-11, 2015. Delhi, Indiaof Power and Energy Systems 9th IFAC symposium on Control Indian Institute of Technology Available online at www.sciencedirect.com December 9-11, 2015. Delhi, India Indian Institute of Technology December 9-11, 2015. Delhi, India December 9-11, 2015. Delhi, India
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IFAC-PapersOnLine 48-30 (2015) 535–540 Multi-Objective Multi-Objective Optimization Optimization of of Electric Electric Vehicle Vehicle Fast Fast Charging Charging Stations Stations with with Multi-Objective Optimization of Electric Vehicle Fast Charging Stations with SPEA-II SPEA-II Multi-Objective Optimization of Electric Vehicle Fast Charging Stations with SPEA-II SPEA-II
Ruifeng Shi*, Kwang Y. Lee** Ruifeng Shi*, Kwang Y. Lee** Ruifeng Shi*, Kwang Y. Lee** RuifengEngineering, Shi*, Kwang Y. Lee** *School of Control and Computer North China Electric Power University, *School of Control and Computer Engineering, North China Electric Power University, China, (e-mail: [email protected]). *School of ControlBeijing, and Computer Engineering, North China Electric Power University, Beijing, China, (e-mail: [email protected]). *School ofofControl andand Computer Engineering, North China Electric Power University, **Department Electrical Computer Engineering, Baylor University, TX 76798 USA (e-mail: Beijing, China, (e-mail: [email protected]). **Department of Electrical and China, Computer Engineering, Baylor University, TX 76798 USA (e-mail: Beijing, (e-mail: [email protected]). [email protected]) **Department of Electrical and Computer Engineering, Baylor University, TX 76798 USA (e-mail: [email protected]) **Department of Electrical and Computer Engineering, Baylor University, TX 76798 USA (e-mail: [email protected]) [email protected]) Abstract: During the past two decades, electrification of the transportation sector is gradually becoming Abstract: During the past two decades, electrification of the transportation sector is gradually becoming a global trend due the to the benefits from electric vehicle (EV).sector Although EV charging post Abstract: During pastenvironmental two decades, electrification of the transportation is gradually becoming a global trend due the to the environmental benefits from electric vehicle (EV).sector Although EV charging post Abstract: During past two decades, electrification of the transportation is gradually becoming plays as a primary energy supply, public EV Fast Charging Station (FCS) is definitely an important aplays global trend due toenergy the environmental benefits fromCharging electric vehicle (EV). Although EV charging post as a primary supply, public EV Fast Station (FCS) is definitely an important aplays globalenergy trend due toenergy the environmental benefits from electric vehicle (EV). Although EV charging post backup supply system to the EV customers in Charging case of urgent need. Based current existing FCS a primary public EV Fast Station (FCS) is on definitely important backupas energy supply systemsupply, to the EV customers in Charging case of urgent need. Based on current an existing FCS plays as a primary energy supply, public EV Fast Station (FCS) is definitely an important system and the prediction of the EV charging need in the future, this paper proposes a multi-objective EV backup energy system to EV the EV customers of urgent on acurrent existing FCS system and the supply prediction of the charging need in in case the future, thisneed. paper Based proposes multi-objective EV backup energy supply system to EV the EV customers in case of urgent need. Based on acurrent existing FCS layout re-planning optimization problem, which simultaneously takes the economic issue andFCS the system and the prediction of the charging need in the future, this paper proposes multi-objective EV FCS layout re-planning optimization problem, which simultaneously takes the economic issue and the system and the prediction of consideration. the EV charging in the the future, this paper proposes a multi-objective EV customers’ satisfaction into Toneed solve problem a popular multi-objective evolutionary FCS layout re-planning optimization problem, which simultaneously takes the economic issue and the customers’ satisfaction into consideration. To solve the problem a popular multi-objective evolutionary FCS layoutStrengthen re-planning optimization problem, whichthesimultaneously takes multi-objective the in economic issue and the algorithm, Pareto Evolutionary Algorithm-II (SPEA-II), is employed this study. Numerical customers’ satisfaction into consideration. To solve problem a popular evolutionary algorithm, Strengthen Pareto Evolutionary Algorithm-II (SPEA-II), is employed in this study. Numerical customers’ satisfaction into consideration. To solve the problem a popular multi-objective evolutionary case studies shows that the SPEA-II can successfully address the balance between different objectives algorithm, Pareto Evolutionary Algorithm-IIaddress (SPEA-II), is employed in this study. Numerical case studiesStrengthen shows that the SPEA-II can successfully the balance between different objectives algorithm, Pareto Evolutionary Algorithm-II (SPEA-II), is employed in this study. Numerical during the Strengthen re-planning FCS procedure bysuccessfully contrast toaddress that of the a single-objective optimization method case studies shows that the SPEA-II can balance between different objectives during the re-planning FCS procedure by contrast to that of a single-objective optimization method case studies shows that the SPEA-II can successfully address the balance between different objectives (Improved Genetic Algorithm). during the Genetic re-planning FCS procedure by contrast to that of a single-objective optimization method (Improved Algorithm). during the Genetic re-planning FCS procedure by contrast to that of a single-objective optimization method (Improved Algorithm). © 2015, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. AllSPEA-II. rights reserved. Keywords: Electric Vehicle;Federation Charging Station Planning; Multi-objective Optimization; (Improved Genetic Algorithm). Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. but simply regarding them as constraints. This may cause but simply regarding them as constraints. This may cause overlapping construction under FCS re-planning scenario. 1. INTRODUCTION but simply regarding them as the constraints. This may cause overlapping construction under the FCS re-planning scenario. 1. INTRODUCTION but simply regarding them as constraints. This may cause overlapping construction under the FCS re-planning scenario. 1. INTRODUCTION This paper isconstruction organized asunder follows: An EV FCS Re-Planning Transportation Electrification becomes a trend during the overlapping the FCS re-planning scenario. 1. INTRODUCTION paper is organized as follows: An EV FCS Re-Planning Transportation Electrification becomes a trend during the This (EVFCS-RP) is proposed Section II, Re-Planning and a wellpast two decades, due to the development clean, efficient This paper is organized as follows:in EV FCS Transportation Electrification becomes a of trend during the model model (EVFCS-RP) is proposed inAn Section II, Re-Planning and a wellpast two decades, due to the development of clean, efficient This paper is organized as follows: An EV FCS known multi-objective evolutionary algorithm, SPEA-II, is Transportation Electrification becomes a trend during the and economical electric vehicle (EV) industry. Besides USA model (EVFCS-RP) is evolutionary proposed in Section II, SPEA-II, and a wellpast economical two decades, due tovehicle the development of clean, efficient known multi-objective algorithm, is and electric (EV) industry. Besides USA model (EVFCS-RP) is proposed in Section II, and a wellintroduced to solve the EVFCS-RP problem in Section III. past two decades, due to the development of clean, efficient and UK, many countries, such as Dutch, Poland, China and known multi-objective evolutionary algorithm, SPEA-II, is and economical electric vehicle (EV) industry. Besides USA introduced to solve the EVFCS-RP problem in Section III. and UK, many countries, such as Dutch, Poland, China and known multi-objective evolutionary algorithm, is and electric vehicle (EV) industry. Besides USA IV to verifies the method proposed Iran, havemany madecountries, their own EVas industry development introduced solvethe theeffectiveness EVFCS-RP of problem in SPEA-II, Section III. and economical UK, such Dutch, Poland, Chinaplans and Section Section IV verifies the effectiveness of the method proposed Iran, have made their own EV industry development plans introduced to solvethe theeffectiveness EVFCS-RP of problem in Section III. with a case study. and UK, many countries, such as Dutch, Poland, and Section (Hatton 2009, Benysek 2012, Liindustry 2011). development The EVChina charging IV verifies the method proposed Iran, have made their own EV plans with a case study. the effectiveness of the method proposed (Hatton 2009, 2012, 2011). development The EV charging IV verifies Iran, madeBenysek their own EVLi plans Section stationhave layout planning researchers with a case study. (Hatton 2009, Benysek 2012, Liindustry 2011).employ The EVoperations charging station layout planning researchers employ operations (Hatton 2009, 2012, Li 2011). The EVoperations charging research, game Benysek theory, graph theory, and modern heuristic with a case study. station layout planning researchers employ 2. ELECTRIC VEHICLE FAST CHARGING STATION research, game theory, graph theory, and modernoperations heuristic station layout planning employ optimization techniques to researchers solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE FAST CHARGING STATION research, game theory, graph theory, and modern heuristic RE-PLANNING (EVFCS-RP) optimization techniques to solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE MODEL FAST CHARGING STATION research, theory, graph theory, and modern heuristic Feng 2012,game Jiatechniques 2012, Mehar 2013, Jin 2013). RE-PLANNING (EVFCS-RP) optimization to solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE MODEL FAST CHARGING STATION Feng 2012, Jia 2012, Mehar 2013, Jin 2013). RE-PLANNING MODEL (EVFCS-RP) optimization techniques to solve the problem (Zhou 2011, The EVFCS-RP problemMODEL is a (EVFCS-RP) typical combinatorial Feng EV 2012, Jiacharging 2012, Mehar 2013, Jin 2013). RE-PLANNING The fast station (FCS) problem has invoked The EVFCS-RP problem is a typical combinatorial Feng EV 2012, Jiacharging 2012, Mehar 2013, Jin 2013). optimization problem, which isshould not onlycombinatorial consider to The fast station (FCS) problem has invoked The EVFCS-RP problem a typical great attentions during the past decade. Kim andhas his colleges problem, which isshould not onlycombinatorial consider to The EV fast charging station (FCS) problem invoked optimization The EVFCS-RP problem a issues, typical seeking the optimality of economic but consider also should great attentions during the past decade. Kim and his colleges optimization problem, which should not only to The EV fast charging station (FCS) problem has invoked studied the EV FCS location problem in high ways (Kim seeking the optimality of economic issues, but also should great attentions during the past problem decade. Kim and his colleges optimization problem, which not only consider to pursues for the satisfaction of should EV customers with efficient studied the EV FCS location in high ways (Kim seeking the optimality of economic issues, but also should great during the past problem decade. Kim andstudying his colleges 2013),attentions many focused the pursues for the satisfaction of EV customers with efficient studied the EVother FCS researchers location in on high ways (Kim seeking the optimality of economic issues, but also should services. In order to obtain a well-balanced solution, a multi2013), many other researchers focused on studying the pursues the satisfaction EV customers with efficient studied of theEVEV FCS location problem high ways 2013, (Kim impact FCS network to the poweringrid (Crosier services. for In order to obtain a of well-balanced solution, a multi2013), many other researchers on studying the pursues the satisfaction of EV customers with efficient objectivefor EVFCS-RP mathematical model solution, is formulated in impact of EV FCS network to the focused power grid (Crosier 2013, services. In order to obtain a well-balanced a multi2013), many other researchers focused on studying the Xu 2013, Zhang 2013). Although EV Charging Post serves as objective EVFCS-RP mathematical model is formulated in impact of EV FCS network to the power grid (Crosier 2013, services. In order to obtain a well-balanced solution, a multithis paper. Xu 2013, Zhang 2013). Although EV Charging Post serves as objective EVFCS-RP mathematical model is formulated in impact of Zhang EV FCS network to FCS theEV power grid (Crosier 2013, aXu primary energy supply, EV isCharging definitely a necessary this paper. 2013, 2013). Although Post serves as objective EVFCS-RP mathematical model is formulated in aXuprimary energy2013). supply, EV FCS isCharging definitelyPost a necessary 2013,choice Zhang Although EV serves as this paper. refilling to supply, EV customers in isthe case of urgent need arefilling primary energy EV FCS definitely a necessary this choice to EV customers in the case of urgent need 2.1 paper. Assumptions a(Etezadi-Amoli primarychoice energy supply, EV FCS definitely ainvestment necessary 2010). Besides, the economical refilling to EV customers in isthe case of urgent need 2.1 Assumptions (Etezadi-Amoli 2010). Besides, the economical investment 2.1 Assumptions refilling choice to EV of customers in the case of isurgent need Several and the operation cost an EV charging station also taken (Etezadi-Amoli 2010). Besides, the economical investment assumptions are taken in the study. 2.1 Assumptions and the operation cost of an EV charging station is also taken Several assumptions are taken in the study. (Etezadi-Amoli 2010). the economical investment into study (Li 2011, Schroeder Only very is recently, the and the operation cost ofBesides, an EV2012). charging station also taken Several assumptions are taken in the study. into study (Li 2011, Schroeder 2012). Only very recently, the 1) Distribution of theare EV charging investigated in and the operation cost charging of an EV charging station also taken multi-objective EV station siting problem is Several into study (Li 2011, Only very is recently, assumptions in thedemand study. is Distribution of the EVtaken charging demand is investigated in multi-objective EV Schroeder charging 2012). station siting problem the is 1) advance to find of thethe candidate locations for potential EV FCSs, into study (Li 2011, Schroeder Only verythe recently, the optimized systematically (Yao 2012). 2014) although objectives 1) Distribution EV charging demand is investigated in multi-objective EV charging station siting problem is advance to find of thethe candidate locations for potential EV FCSs, optimized systematically (Yao 2014) although theproblem objectives 1) Distribution EV charging demand is investigated in which helps to avoid violating the construction safety and multi-objective EV charging station siting is are focused more on technical aspect than on customers’ advance to find the candidate locations for potential EV FCSs, optimized systematically (Yao 2014) although the objectives which helps to the avoid violating the construction safety and are focused more on technical aspect than on customers’ advance to find candidate locations for potential EV FCSs, environmental laws. optimized systematically (Yao 2014) although the objectives satisfaction. helps tolaws. avoid violating the construction safety and are focused more on technical aspect than on customers’ which environmental satisfaction. helps tolaws. avoid violating the construction safety and are focused more on technical aspect than on customers’ which environmental satisfaction. The charging demands in each candidate location is Current research publication shows that most researchers 2) environmental laws. satisfaction. The charging demands in each candidate location is Current research publication shows that most researchers 2) proportional to the total number EVscandidate in that area.location is focus on solving the EV FCS planning problem without The charging demands in of Current shows that most researchers proportional to the total number ofeach EVscandidate in that area. focus onresearch solving publication the EV FCS planning problem without 2) 2) The charging demands in each Current research publication shows that most researchers much consideration on the existing FCS system expansion, focus on solving the EV FCS planning problem without proportional to the total number of EVs in that area.location is much consideration on the existing FCS system expansion, focus on solving the planning problem without proportional to the total number of EVs in that area. much consideration on EV the FCS existing FCS system expansion, much consideration Copyright © 2015 IFAC on the existing FCS system expansion, 535 Copyright 2015 IFAC 535Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Copyright 2015 responsibility IFAC 535Control. Peer review©under of International Federation of Automatic Copyright © 2015 IFAC 535 10.1016/j.ifacol.2015.12.435
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3) EV users are assumed to charge their vehicles in a fixed (optimal) charging station.
c p : the charging pole decay factor, usually set as 5%. b) Customers’ Cost: f 2
2.2 Multi-objective Mathematical EVFCS-RP Model
The customer costs include two parts, one part is the electricity payment for charging; the other part is the driving cost from the customers’ home to the corresponding FCS, which can be formulated as
1) Optimization Objectives: Three objectives are taken into consideration: minimal FCSs’ cost and the customers’ cost; maximal charging poles’ utility.
max
f 2 Fc v, t tT vV
a) FCSs’ Cost: f1
ct C1, j1dv, j1 v, j1, t
The FCSs’ cost can be estimated with two parts, one part is the fixed investment of constructing new FCSs and reinforcing existing FCSs; the other part is the daily operation cost of FCSs, which can be formulated as
min f1
C F n F 1, j1
i , new
j1
o, new
j1J 1
C F n F 2, j 2
i , rein
j 2,2
o , rein
j 2J 2
tT vV j1J 1
ct dv , j 2 v, j 2, t where, T : the planning horizon; V : the predicted EV set in the study; ct : the per unit driving cost on the way to FCS;
n j1
n F n j 2,2
o , old
j 2,1
(1)
j 2J 2
d (v, j ) : the distance of EV v to FCS j ;
v, j, t : the status of v charging at FCS j at time t ,
where, J 1 : the location set of potential new FCSs; J 2 : the location set of current existing FCSs; C1, j1 : 0/1 decision variable to construct a new FCS;
satisfying the constraint
C
v, j1, t
1, j1
j1J 1
v, j, t 0,1 , j1, j 2
th
n j1 : new charging poles to be constructed in j1 FCS;
And, Fc
n j 2,1 : current existing charging poles in j 2th FCS;
Fi , new : investment cost of a new constructed FCS;
Fo, new : operation cost of a new constructed FCS;
c) Charging Poles Utility: f 3
Fo, rein : operation cost of a reinforced FCS.
The ECP objective well explains the effectiveness of the utility of the FCS layout planning scheme, which can be defined as
These economic objectives can be estimated as j1J 1
Fi , rein
C n 2, j 2
j 2,2
j 2J 2
Fo, new Fo, rein
Qc en2j1
(2)
Qc en2j 2,2
(3)
C F c n 1, j1
i
j1J 1
i , new
p
Qc
j1
max
(4)
C2, j 2 i Fi,rein cp n j 2,2Qc
(5)
c n
(6)
p
Qc
j 2,1
f3
t T
C1, j1 i, j1, t
j1J 1 i{n j1 } C1, j1n j1 j1J 1 t T
i, j 2, t
j 2J 2 i{n j 2,1 n j 2,2 }
C2, j 2 n j 2,2 n j 2,1 j 2J 2
(10) where, i, j, t denotes the working status of charging pole i of
j 2J 2
Fo,old
(9)
L denotes the average running mileage of an EV between two charging gap.
Fo,old : operation cost of an old existing FCS;
j1
denotes the charging cost of EV v in time t ,
Where, c denotes the charging price per miles;
Fi , rein : investment cost to reinforce an existing FCS;
1, j1
(8)
Fc c L
n j 2,2 : charging poles to be reinforced in j 2th FCS;
C W n
v, j 2, t 1
j 2J 2
C2, j 2 : 0/1 decision variable to reinforce an existing FCS;
Fi , new
(7)
tT vV j 2J 2
FCS j at time t , i, j, t {0,1} ; it is assigned as 1 when
j 2J 2
the charging pole is working at time t, otherwise set as 0.
where, W : the basic investment of a FCS; Qc : the net price of buying an EV charging pole; e : the mounting cost and other corresponding facility costs for charging poles in an EV FCS. i : the coefficient of operation cost by contrast to its construction investment cost, usually set as 10%;
2) Constraints: a) Charging FCS Selection Constraint: EV customers in charging demand location i is required to refuel at one fixed FCS, as defined by,
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C
1, j1
jJ1
Ruifeng Shi et al. / IFAC-PapersOnLine 48-30 (2015) 535–540
X ij C2, j 2 X ij 1,
iD
the dominated solutions in the Pt and At to the At 1 until the
(11)
jJ 2
size of At 1 is equal to N . Step 3: if t T , output the external file At 1 as the final Pareto set, stop the search process; otherwise, turn to Step 4. Step 4: select individuals from At 1 into the mating pool with substituted binary championship rule. Step 5: implement crossover and mutation operator to the individuals of mating pool and population Pt 1 , let t t 1 , turn to Step 2.
where,
X ij 0,1 denotes the allocation 0/1 choice variable; it is assigned as 1 if EV customers in demand location i are allocated to refuel their EV at FCS j , otherwise it is assigned as 0; D denotes the subset of EVs with charging demands. b) Limits on Charging Poles Number at the FCS: FCSs for newly constructed and for reinforced stations should satisfy the limit on the number of charging poles, as defined respectively by
Nmin N j Nmax , j J1
(12)
Ncur N j Nmax , j J 2
(13)
The flowchart of SPEA-II algorithm is described in Fig. 1. Begin Initialize P(0), A(0) Calculate the fitness of P(t), A(t)
where, N min : the minimum charging poles number in a FCS;
Update A(t+1)
N cur : the number of current existing charging poles in the FCS; N max : the maximum charging poles number in a FCS.
t >T? NO
Selection Crossover
c) Distance between FCSs:
YES
Output A(t+1) as final Pareto set
t=t+1
In order to obtain a well pre-distributed potential EV FCSs, a minimum distance between each pair of FCSs is employed to guarantee the performance, as defined by,
Dij Dmin , i J1 , j J1 J 2
537
End
Mutation
Fig.1. the flowchart of SPEA-II algorithm.
(14)
3.2 Implementation of SPEA-II to the EVFCS-RP Problem
where, Dij : the distance between stations i and j ;
Since the EVFCS-RP model includes three kind of variables, C1, j1 / C2, j 2 , X ij and n j1 / n j 2,2 , and all of them are
Dmin : the minimum distance requirement.
discrete integer variables. We propose a hybrid chromosome coding strategy to express the solution of EVFCS-RP with regards to satisfying its constraints. Corresponding crossover and mutation evolutionary operators are proposed to match the coding strategy.
3. IMPLEMENTING SPEA-II TO EVFCS-RP PROBLEM Compared with traditional optimization methods, multiobjective evolutionary algorithms, such as Non-dominated Sorting Genetic Algorithm-II (NSGA-II) (Deb 2002), Strengthen Pareto Evolutionary Algorithm-II (SPEA-II) (Zitzler 2001), have been widely adopted in many industrial optimization applications (Ngatchou 2008). In this study, SPEA-II is employed as an optimizer to solve the EVFCS-RP problem based on a new chromosome coding strategy.
a) Chromosome Coding Strategy: A hybrid chromosome encoding strategy is proposed in this paper (Fig. 2). Chromosome Coding Strategy for EVFCS-RP Location 1
……
Location 2
Location l_max
3.1 SPEA-II Algorithm Description Potential location index: Either existing EV FCS Or potential new EV FCS
The basic flowchart of SPEA-II algorithm includes the following steps: Step 0: create an initial population P0 , population size as N ,
0/1
N/E
n_CP
0/1 decision variable 0: Set up FCS in the location 1: Give up FCS in the location
and a null external file A0 , and set generation count as t 0 . Step 1: calculate the individual fitness of population Pt and
N/E type variable N: New FCS to be constructed E: Existing FCS to be reinforced
external file At .
Step 2: define At 1 xi | xi Pt At ; if the archived
Size of the FCS n: Charging poles’number in the FCS
Pareto solutions size of At 1 is over the maximum limit N , cut the size to N ; but if the size of At 1 is less than N , join
Fig. 2. Chromosome of SPEA-II for EVCS-RP problem.
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Selection strategy: roulette wheel selection.
genetic algorithm, IGA (Jin 2013), is also employed for comparison study.
Crossover operator: In order to guarantee the feasibility and effectiveness of the offsprings derived by crossover operator, substring crossover strategy proposed by Park (Park 2000) is employed in this study.
The coordinates of EV charging demands are distributed as shown in Table 1, and the coordinates of current existing FCSs and potential newly constructed FCSs are shown in Table 2.
b) Evolutionary Operators:
Mutation operator: A simple point variation mutation operator is taken to avoid local optimality. c) Fitness Evaluation (Zitzler 2001): Obtain the values of the three objective functions with (1), (7) and (10) and calculate its strength S (i) ,
S i | { j | xi Pt At , xi
x j }|
(15)
The original fitness R(i) of individual i is equal to the sum of strengths of all individuals dominated by it (Yao 2014).
R i
x j Pt At , x j
S j
(16)
xi
Fig. 4. Potential new EV FCS sites in Futian District.
The k-proximity method is employed to calculate the density value D(i) for individual i (Ngatchou 2008).
1 D i k i 2
Table 1. Demand coordinates & EV refuel amount. Demand index 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(17)
where, ik is the distance in the objective space between an individual i and the k th adjacent individuals to i ,
k N N , where N is the population size, and N is maximum archived Pareto set limit. Finally, the fitness F (i ) is calculated as
F i R i D i
(18)
4. CASE STUDY 4.1 Problem Description In order to verify the effectiveness of the method proposed in this paper, a FCS re-planning case study that comes from Shenzhen City, Southern East China, is employed for demonstration.
X
Y
0.7 0.6 1.6 1.0 1.4 2.3 2.7 3.3 3.7 4.0 4.9 5.9 8.5 6.6 7.9
1.8 0.7 0.4 1.3 2.1 0.4 1.9 0.2 1.6 3.3 1.4 3.9 4.3 0.4 2.4
EV amount 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
Demand index 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
X
Y
5.3 8.2 7.2 7.5 4.7 6.3 6.3 7.5 9.2 10.3 10.7 10.7 9.8 10.2 8.9
4.8 0.3 4.6 4.0 3.3 2.1 4.1 1.9 1.4 4.5 3.0 3.5 1.0 2.8 3.5
EV amount 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
Table 2. Coordinates of FCS sites candidate locations. Coordinate index 1 2 3 4 5 6 7 8 9 10 11 12 13
There are 11 existing EV FCSs within the Futian District before the re-planning. Considering the feasibility and availability of the land space for constructing new FCSs, the areas near the schools, shopping malls, and parks are first taken into consideration. After a brief investigation, 11 new sites near the schools, 6 new sites near the shopping malls, and 3 new sites near the parks are selected for potential new EV FCS candidates (the total of 20 new potential FCS sites and 11 existing FCSs are shown in Fig. 3, where purple points represents the existing FCSs and green points represents the potential FCS sites). It is assumed that the total EV numbers in Futian District as 1,200. In order to verify the effectiveness of employing SPEA-II to solve the EVFCS-RP problem, a single-objective improved 538
X
Y
2.0 0.6 1.1 4.5 6.1 5.9 6.6 8.3 8.5 9.9 10.3 1.8 2.7
0.7 1.4 1.5 4.1 1.1 2.3 4.5 4.6 2.9 4.4 3.5 3.7 2.2
Coordinate index 17 18 19 20 21 22 23 24 25 26 27 28 29
X
Y
5.5 7.5 7.9 8.2 10.4 10.5 2.9 6.9 5.0 9.6 9.2 6.2 5.6
0.1 0.0 2.5 1.8 2.3 1.0 1.6 1.9 1.7 1.4 2.7 4.2 2.9
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3.3 4.9 7.3
0.0 5.0 3.8
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30 31
6.9 11.3
539
b) Algorithm Stability Analysis
3.0 2.1
In order to further test the stability of the SPEA-II, M-index is employed for demonstration. The M-index is an index to measure the gap between the Pareto solutions searched by one algorithm and the theoretical Pareto solution set of the problem, which is mathematically defined as,
4.2 Parameters Setting In the case study, the parameters are set as follows: a) Model Parameters Setting:
M ( A) :
Basic investment of a FCS: W $300,000 ; Price of buying an EV charging pole: Qc $10,000 ; Mounting cost and
1 A
min a x
x Xp
a A
(19)
Where, A is the Pareto set, A represents the solution number of set A .
other facility costs of an EV charging pole: e $3000 . Annual operation cost of a FCS: i 0.1 , c p 0.05 .
Table 4 shows the 20 M-index obtained by SPEA-II operated independently. The M-index result shows that, the average of the deviation between the Pareto solution set obtained by SPEA-II and the theoretical optimal Pareto set is within 10, which is a respectively small deflection from the global theoretical Pareto solutions. Thus, the SPEA-II is expected to find a stable good Pareto solution set when it is employed to solve the EVFCS-RP problems.
Driving cost to FCS: ct $0.06 / mile ; road equivalent length factor (city road): λ 1.2 ; Charging price c $0.04 / mile ; FCS busy period ratio: 0.9 ; the planning horizon T 24 365 hours. Besides, it is also assumed that an EV battery storage capacity can obtain 80%~90% energy within 15~20 minutes, so the charging time is set as 15 minutes. The minimum and maximum number of charging poles: Nmin 2 , Nmax 12 ; the minimum distance between FCSs: Dmin 0.3 mile.
Table 4. M-index of SPEA-II for EVFCS-RP case study.
b) Algorithms’ Parameters Setting: SPEA-II:
index
1
2
3
4
5
6
7
8
9
10
M(A)
4.55
8.79
1.65
9.67
8.25
2.86
0.38
3.25
1.63
8.92
index
11
12
13
14
15
16
17
18
19
20
M(A)
2.71
9.93
9.65
0.67
4.26
3.78
0.36
0.95
2.70
9.89
c) Decision Making
Population size: PopSize 300 ; archived population size:
PopArch 20 ; maximum generation: Genmax 200 ; crossover probability: pc 0.6 ; mutation probability: pm 0.08 . IGA: Population size (refers to reference (Jin 2013)): PopSize 300 ; maximum generation: Genmax 200 ; crossover probability: pc 0.8 ; mutation probability: pm 0.08 .
In a real application scenario, a Decision Maker (DM) needs to choose a final decision solution from the Pareto set, one can employ the multi-objective decision method to select a final satisfied solution [18], such as TOPSIS. In this study, the TOPSIS method is employed with the preference weights of objectives f1, f2 and f3 as 0.7, 0.2 and 0.1, respectively. The final optimal solution is chosen as Pareto solution 2 (Table. 3), which represents the real planning scheme as Fig. 4.
4.3 Results and Analysis a) Comparison with Single-objective Optimization After running the SPEA-II and IGA independently 20 times with all parameters as set above, a set of Pareto solutions and an optimal solution are obtained by the two algorithms, in which IGA aims at minimizing the f1 . Table 3 lists three typical Pareto solutions of SPEA-II and the optimal solution of IGA, from which it can be seen that SPEA-II can obtain better balanced solution by contrast to the single-objective IGA optimization with regards to the EV customers’ cost and the facility utilization ratio. Table 3. Typical solutions by SPEA-II and IGA Pareto solution1
SPEA-II Pareto solution 2
Pareto solution 3
IGA Optimal solution
1.876
1.864
1.823
1.820
f2(10 $)
0.392
0.401
0.410
0.586
f3(%)
62.2
63.7
61.4
64.1
objectives f1(106$) 6
Fig. 4. The optimal FCS plan obtained by SPEA-II & TOPSIS.
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5. CONCLUSIONS The electric vehicle (EV) fast charging station (FCS) replanning (RP) problem is a typical mixed 0-1 integer combinatorial optimization problem. A multi-objective EVFCS-RP problem is formulated mathematically in this paper, and an improved SPEA-II algorithm is developed to solve the problem. Case study shows that the proposed method can handle the multi-objective optimization problem well with good stability performance, and can provide the Pareto solutions for a decision maker. REFERENCES Benysek, G. and Jarnut, M. (2012). Electric vehicle charging infrastructure in Poland. Renewable and Sustainable Energy Reviews, 16(1), 320-328. Chankong, V., and Haimes, Y. Y. (2008). Multiobjective Decision Making: Theory and Methodology, Dover Publications. Crosier, R. and Wang S. (2013). Modeling the closed-loop interaction between the grid and a multifunctional electric vehicle charging station integrated with an active power filter. In Proceedings of 2013 IEEE International Conference on Electric Vehicle Conference (IEVC-2013), Santa Clara, CA, 1-7. Deb, K., Pratap, A., Agarwal S., and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. Etezadi-Amoli, M., Choma, K., and Stefani, J. (2010). Rapidcharge electric-vehicle stations, IEEE Transactions on Power Delivery, 25(3), 1883-1887. Feng, L., Ge, S., Liu, H., Wang, L., and Feng, Y. (2012). The planning of charging stations on the urban trunk road. In Proceedings of 2012 IEEE International Conference on Innovative Smart Grid Technologies - Asia (ISGT Asia), Tianjin, 1-4. Hatton, C. E., Beella, S. K., Brezet, J. C., and Wijnia, Y.C. (2009). Charging station for urban settings: the design of a product platform for electric vehicle infrastructure in Dutch cities, World Electric Vehicle Journal, (3), 1-13. Jia, L., Hu, Z., Song, Y., and Luo, Z. (2012). Optimal siting and sizing of electric vehicle charging stations. In Proceedings of 2012 IEEE International Conference on Electric Vehicle Conference (IEVC-2012), Greenville, SC, 1-6. Jin, M. J., Shi R. F., Zhang, N., and Zhang, L. (2013). Study on Multi-Level Layout Planning of Electric Vehicle Charging Stations Based on an Improved Genetic Algorithm. International Journal of Smart Grid and Clean Energy, 2(2), 277-282. Kim, S., Jung, H., Hwang, J., Lee, S., and Song, K. (2013). A study on the construction of EV charging infrastructures in highway rest area. In Proceedings of 2013 IEEE Fourth International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), Istanbul, 396-400. Li, Z. and Ouyang, M. G. (2011). The pricing of charging for electric vehicles in China-Dilemma and solution. Energy, 36, 5765-5778. 540
Mehar S. and Senouci, S. M. (2013). An optimization location scheme for electric charging stations. In Proceedings of 2013 International Conference on Smart Communications in Network Technologies (SaCoNeT). Paris, 6, 17-19. Ngatchou, P. N., Zarei, A., Fox, W. L. J., and El-Sharkawi, M. A. (2008). Pareto Multiobjective Optimization. In Lee, K. Y. and El-Sharkawi, M. A. of Editors, Modern Heuristic Optimization Techniques with Applications to Power Systems, IEEE Press, Wiley: New York. Park, J. B., Park, Y. M., Won, J. R. and Lee, K. Y. (2000). An improved genetic algorithm for generation expansion planning, IEEE Transactions on Power Systems, 15(3), 916-922. Schroeder A. and Traber, T. (2012) The economics of fast charging infrastructure for electric vehicles. Energy Policy, 43, 136-144. Xu, H., Miao, S., Zhang, C., and Shi, D. (2013). Optimal placement of charging infrastructures for large-scale integration of pure electric vehicles into grid. International Journal of Electrical Power & Energy Systems, 53, 159-165. Yao, W., Zhao, J., Wen, F., Dong, Z., Xue, Y., Xu, Y., and Meng, K. (2014). A multi-objective collaborative planning strategy for integrated power distribution and electric vehicle charging systems. IEEE Transactions on Power Systems, 29(4), 1811-1821. Zhang, L., Brown, T. and Samuelsen S. (2013). Evaluation of charging infrastructure requirements and operating costs for plug-in electric vehicles. Journal of Power Sources, 240, 515-524. Zhou, H. and Li, H. (2011). Optimization model of electric vehicle charging station sitting based on game theory. Science Technology and Industry, 11(2), 51-54. Zitzler, E. L., Laumanns, M., and Thiele, L. (2001). SPEA-II: Improving the Strength Pareto Evolutionary Algorithm. Technical report TIK-Report 103, Swiss Federal Institute of Technology.
ScienceDirect
IFAC-PapersOnLine 48-30 (2015) 535–540 Multi-Objective Multi-Objective Optimization Optimization of of Electric Electric Vehicle Vehicle Fast Fast Charging Charging Stations Stations with with Multi-Objective Optimization of Electric Vehicle Fast Charging Stations with SPEA-II SPEA-II Multi-Objective Optimization of Electric Vehicle Fast Charging Stations with SPEA-II SPEA-II
Ruifeng Shi*, Kwang Y. Lee** Ruifeng Shi*, Kwang Y. Lee** Ruifeng Shi*, Kwang Y. Lee** RuifengEngineering, Shi*, Kwang Y. Lee** *School of Control and Computer North China Electric Power University, *School of Control and Computer Engineering, North China Electric Power University, China, (e-mail: [email protected]). *School of ControlBeijing, and Computer Engineering, North China Electric Power University, Beijing, China, (e-mail: [email protected]). *School ofofControl andand Computer Engineering, North China Electric Power University, **Department Electrical Computer Engineering, Baylor University, TX 76798 USA (e-mail: Beijing, China, (e-mail: [email protected]). **Department of Electrical and China, Computer Engineering, Baylor University, TX 76798 USA (e-mail: Beijing, (e-mail: [email protected]). [email protected]) **Department of Electrical and Computer Engineering, Baylor University, TX 76798 USA (e-mail: [email protected]) **Department of Electrical and Computer Engineering, Baylor University, TX 76798 USA (e-mail: [email protected]) [email protected]) Abstract: During the past two decades, electrification of the transportation sector is gradually becoming Abstract: During the past two decades, electrification of the transportation sector is gradually becoming a global trend due the to the benefits from electric vehicle (EV).sector Although EV charging post Abstract: During pastenvironmental two decades, electrification of the transportation is gradually becoming a global trend due the to the environmental benefits from electric vehicle (EV).sector Although EV charging post Abstract: During past two decades, electrification of the transportation is gradually becoming plays as a primary energy supply, public EV Fast Charging Station (FCS) is definitely an important aplays global trend due toenergy the environmental benefits fromCharging electric vehicle (EV). Although EV charging post as a primary supply, public EV Fast Station (FCS) is definitely an important aplays globalenergy trend due toenergy the environmental benefits from electric vehicle (EV). Although EV charging post backup supply system to the EV customers in Charging case of urgent need. Based current existing FCS a primary public EV Fast Station (FCS) is on definitely important backupas energy supply systemsupply, to the EV customers in Charging case of urgent need. Based on current an existing FCS plays as a primary energy supply, public EV Fast Station (FCS) is definitely an important system and the prediction of the EV charging need in the future, this paper proposes a multi-objective EV backup energy system to EV the EV customers of urgent on acurrent existing FCS system and the supply prediction of the charging need in in case the future, thisneed. paper Based proposes multi-objective EV backup energy supply system to EV the EV customers in case of urgent need. Based on acurrent existing FCS layout re-planning optimization problem, which simultaneously takes the economic issue andFCS the system and the prediction of the charging need in the future, this paper proposes multi-objective EV FCS layout re-planning optimization problem, which simultaneously takes the economic issue and the system and the prediction of consideration. the EV charging in the the future, this paper proposes a multi-objective EV customers’ satisfaction into Toneed solve problem a popular multi-objective evolutionary FCS layout re-planning optimization problem, which simultaneously takes the economic issue and the customers’ satisfaction into consideration. To solve the problem a popular multi-objective evolutionary FCS layoutStrengthen re-planning optimization problem, whichthesimultaneously takes multi-objective the in economic issue and the algorithm, Pareto Evolutionary Algorithm-II (SPEA-II), is employed this study. Numerical customers’ satisfaction into consideration. To solve problem a popular evolutionary algorithm, Strengthen Pareto Evolutionary Algorithm-II (SPEA-II), is employed in this study. Numerical customers’ satisfaction into consideration. To solve the problem a popular multi-objective evolutionary case studies shows that the SPEA-II can successfully address the balance between different objectives algorithm, Pareto Evolutionary Algorithm-IIaddress (SPEA-II), is employed in this study. Numerical case studiesStrengthen shows that the SPEA-II can successfully the balance between different objectives algorithm, Pareto Evolutionary Algorithm-II (SPEA-II), is employed in this study. Numerical during the Strengthen re-planning FCS procedure bysuccessfully contrast toaddress that of the a single-objective optimization method case studies shows that the SPEA-II can balance between different objectives during the re-planning FCS procedure by contrast to that of a single-objective optimization method case studies shows that the SPEA-II can successfully address the balance between different objectives (Improved Genetic Algorithm). during the Genetic re-planning FCS procedure by contrast to that of a single-objective optimization method (Improved Algorithm). during the Genetic re-planning FCS procedure by contrast to that of a single-objective optimization method (Improved Algorithm). © 2015, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. AllSPEA-II. rights reserved. Keywords: Electric Vehicle;Federation Charging Station Planning; Multi-objective Optimization; (Improved Genetic Algorithm). Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. Keywords: Electric Vehicle; Charging Station Planning; Multi-objective Optimization; SPEA-II. but simply regarding them as constraints. This may cause but simply regarding them as constraints. This may cause overlapping construction under FCS re-planning scenario. 1. INTRODUCTION but simply regarding them as the constraints. This may cause overlapping construction under the FCS re-planning scenario. 1. INTRODUCTION but simply regarding them as constraints. This may cause overlapping construction under the FCS re-planning scenario. 1. INTRODUCTION This paper isconstruction organized asunder follows: An EV FCS Re-Planning Transportation Electrification becomes a trend during the overlapping the FCS re-planning scenario. 1. INTRODUCTION paper is organized as follows: An EV FCS Re-Planning Transportation Electrification becomes a trend during the This (EVFCS-RP) is proposed Section II, Re-Planning and a wellpast two decades, due to the development clean, efficient This paper is organized as follows:in EV FCS Transportation Electrification becomes a of trend during the model model (EVFCS-RP) is proposed inAn Section II, Re-Planning and a wellpast two decades, due to the development of clean, efficient This paper is organized as follows: An EV FCS known multi-objective evolutionary algorithm, SPEA-II, is Transportation Electrification becomes a trend during the and economical electric vehicle (EV) industry. Besides USA model (EVFCS-RP) is evolutionary proposed in Section II, SPEA-II, and a wellpast economical two decades, due tovehicle the development of clean, efficient known multi-objective algorithm, is and electric (EV) industry. Besides USA model (EVFCS-RP) is proposed in Section II, and a wellintroduced to solve the EVFCS-RP problem in Section III. past two decades, due to the development of clean, efficient and UK, many countries, such as Dutch, Poland, China and known multi-objective evolutionary algorithm, SPEA-II, is and economical electric vehicle (EV) industry. Besides USA introduced to solve the EVFCS-RP problem in Section III. and UK, many countries, such as Dutch, Poland, China and known multi-objective evolutionary algorithm, is and electric vehicle (EV) industry. Besides USA IV to verifies the method proposed Iran, havemany madecountries, their own EVas industry development introduced solvethe theeffectiveness EVFCS-RP of problem in SPEA-II, Section III. and economical UK, such Dutch, Poland, Chinaplans and Section Section IV verifies the effectiveness of the method proposed Iran, have made their own EV industry development plans introduced to solvethe theeffectiveness EVFCS-RP of problem in Section III. with a case study. and UK, many countries, such as Dutch, Poland, and Section (Hatton 2009, Benysek 2012, Liindustry 2011). development The EVChina charging IV verifies the method proposed Iran, have made their own EV plans with a case study. the effectiveness of the method proposed (Hatton 2009, 2012, 2011). development The EV charging IV verifies Iran, madeBenysek their own EVLi plans Section stationhave layout planning researchers with a case study. (Hatton 2009, Benysek 2012, Liindustry 2011).employ The EVoperations charging station layout planning researchers employ operations (Hatton 2009, 2012, Li 2011). The EVoperations charging research, game Benysek theory, graph theory, and modern heuristic with a case study. station layout planning researchers employ 2. ELECTRIC VEHICLE FAST CHARGING STATION research, game theory, graph theory, and modernoperations heuristic station layout planning employ optimization techniques to researchers solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE FAST CHARGING STATION research, game theory, graph theory, and modern heuristic RE-PLANNING (EVFCS-RP) optimization techniques to solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE MODEL FAST CHARGING STATION research, theory, graph theory, and modern heuristic Feng 2012,game Jiatechniques 2012, Mehar 2013, Jin 2013). RE-PLANNING (EVFCS-RP) optimization to solve the problem (Zhou 2011, 2. ELECTRIC VEHICLE MODEL FAST CHARGING STATION Feng 2012, Jia 2012, Mehar 2013, Jin 2013). RE-PLANNING MODEL (EVFCS-RP) optimization techniques to solve the problem (Zhou 2011, The EVFCS-RP problemMODEL is a (EVFCS-RP) typical combinatorial Feng EV 2012, Jiacharging 2012, Mehar 2013, Jin 2013). RE-PLANNING The fast station (FCS) problem has invoked The EVFCS-RP problem is a typical combinatorial Feng EV 2012, Jiacharging 2012, Mehar 2013, Jin 2013). optimization problem, which isshould not onlycombinatorial consider to The fast station (FCS) problem has invoked The EVFCS-RP problem a typical great attentions during the past decade. Kim andhas his colleges problem, which isshould not onlycombinatorial consider to The EV fast charging station (FCS) problem invoked optimization The EVFCS-RP problem a issues, typical seeking the optimality of economic but consider also should great attentions during the past decade. Kim and his colleges optimization problem, which should not only to The EV fast charging station (FCS) problem has invoked studied the EV FCS location problem in high ways (Kim seeking the optimality of economic issues, but also should great attentions during the past problem decade. Kim and his colleges optimization problem, which not only consider to pursues for the satisfaction of should EV customers with efficient studied the EV FCS location in high ways (Kim seeking the optimality of economic issues, but also should great during the past problem decade. Kim andstudying his colleges 2013),attentions many focused the pursues for the satisfaction of EV customers with efficient studied the EVother FCS researchers location in on high ways (Kim seeking the optimality of economic issues, but also should services. In order to obtain a well-balanced solution, a multi2013), many other researchers focused on studying the pursues the satisfaction EV customers with efficient studied of theEVEV FCS location problem high ways 2013, (Kim impact FCS network to the poweringrid (Crosier services. for In order to obtain a of well-balanced solution, a multi2013), many other researchers on studying the pursues the satisfaction of EV customers with efficient objectivefor EVFCS-RP mathematical model solution, is formulated in impact of EV FCS network to the focused power grid (Crosier 2013, services. In order to obtain a well-balanced a multi2013), many other researchers focused on studying the Xu 2013, Zhang 2013). Although EV Charging Post serves as objective EVFCS-RP mathematical model is formulated in impact of EV FCS network to the power grid (Crosier 2013, services. In order to obtain a well-balanced solution, a multithis paper. Xu 2013, Zhang 2013). Although EV Charging Post serves as objective EVFCS-RP mathematical model is formulated in impact of Zhang EV FCS network to FCS theEV power grid (Crosier 2013, aXu primary energy supply, EV isCharging definitely a necessary this paper. 2013, 2013). Although Post serves as objective EVFCS-RP mathematical model is formulated in aXuprimary energy2013). supply, EV FCS isCharging definitelyPost a necessary 2013,choice Zhang Although EV serves as this paper. refilling to supply, EV customers in isthe case of urgent need arefilling primary energy EV FCS definitely a necessary this choice to EV customers in the case of urgent need 2.1 paper. Assumptions a(Etezadi-Amoli primarychoice energy supply, EV FCS definitely ainvestment necessary 2010). Besides, the economical refilling to EV customers in isthe case of urgent need 2.1 Assumptions (Etezadi-Amoli 2010). Besides, the economical investment 2.1 Assumptions refilling choice to EV of customers in the case of isurgent need Several and the operation cost an EV charging station also taken (Etezadi-Amoli 2010). Besides, the economical investment assumptions are taken in the study. 2.1 Assumptions and the operation cost of an EV charging station is also taken Several assumptions are taken in the study. (Etezadi-Amoli 2010). the economical investment into study (Li 2011, Schroeder Only very is recently, the and the operation cost ofBesides, an EV2012). charging station also taken Several assumptions are taken in the study. into study (Li 2011, Schroeder 2012). Only very recently, the 1) Distribution of theare EV charging investigated in and the operation cost charging of an EV charging station also taken multi-objective EV station siting problem is Several into study (Li 2011, Only very is recently, assumptions in thedemand study. is Distribution of the EVtaken charging demand is investigated in multi-objective EV Schroeder charging 2012). station siting problem the is 1) advance to find of thethe candidate locations for potential EV FCSs, into study (Li 2011, Schroeder Only verythe recently, the optimized systematically (Yao 2012). 2014) although objectives 1) Distribution EV charging demand is investigated in multi-objective EV charging station siting problem is advance to find of thethe candidate locations for potential EV FCSs, optimized systematically (Yao 2014) although theproblem objectives 1) Distribution EV charging demand is investigated in which helps to avoid violating the construction safety and multi-objective EV charging station siting is are focused more on technical aspect than on customers’ advance to find the candidate locations for potential EV FCSs, optimized systematically (Yao 2014) although the objectives which helps to the avoid violating the construction safety and are focused more on technical aspect than on customers’ advance to find candidate locations for potential EV FCSs, environmental laws. optimized systematically (Yao 2014) although the objectives satisfaction. helps tolaws. avoid violating the construction safety and are focused more on technical aspect than on customers’ which environmental satisfaction. helps tolaws. avoid violating the construction safety and are focused more on technical aspect than on customers’ which environmental satisfaction. The charging demands in each candidate location is Current research publication shows that most researchers 2) environmental laws. satisfaction. The charging demands in each candidate location is Current research publication shows that most researchers 2) proportional to the total number EVscandidate in that area.location is focus on solving the EV FCS planning problem without The charging demands in of Current shows that most researchers proportional to the total number ofeach EVscandidate in that area. focus onresearch solving publication the EV FCS planning problem without 2) 2) The charging demands in each Current research publication shows that most researchers much consideration on the existing FCS system expansion, focus on solving the EV FCS planning problem without proportional to the total number of EVs in that area.location is much consideration on the existing FCS system expansion, focus on solving the planning problem without proportional to the total number of EVs in that area. much consideration on EV the FCS existing FCS system expansion, much consideration Copyright © 2015 IFAC on the existing FCS system expansion, 535 Copyright 2015 IFAC 535Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Copyright 2015 responsibility IFAC 535Control. Peer review©under of International Federation of Automatic Copyright © 2015 IFAC 535 10.1016/j.ifacol.2015.12.435
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3) EV users are assumed to charge their vehicles in a fixed (optimal) charging station.
c p : the charging pole decay factor, usually set as 5%. b) Customers’ Cost: f 2
2.2 Multi-objective Mathematical EVFCS-RP Model
The customer costs include two parts, one part is the electricity payment for charging; the other part is the driving cost from the customers’ home to the corresponding FCS, which can be formulated as
1) Optimization Objectives: Three objectives are taken into consideration: minimal FCSs’ cost and the customers’ cost; maximal charging poles’ utility.
max
f 2 Fc v, t tT vV
a) FCSs’ Cost: f1
ct C1, j1dv, j1 v, j1, t
The FCSs’ cost can be estimated with two parts, one part is the fixed investment of constructing new FCSs and reinforcing existing FCSs; the other part is the daily operation cost of FCSs, which can be formulated as
min f1
C F n F 1, j1
i , new
j1
o, new
j1J 1
C F n F 2, j 2
i , rein
j 2,2
o , rein
j 2J 2
tT vV j1J 1
ct dv , j 2 v, j 2, t where, T : the planning horizon; V : the predicted EV set in the study; ct : the per unit driving cost on the way to FCS;
n j1
n F n j 2,2
o , old
j 2,1
(1)
j 2J 2
d (v, j ) : the distance of EV v to FCS j ;
v, j, t : the status of v charging at FCS j at time t ,
where, J 1 : the location set of potential new FCSs; J 2 : the location set of current existing FCSs; C1, j1 : 0/1 decision variable to construct a new FCS;
satisfying the constraint
C
v, j1, t
1, j1
j1J 1
v, j, t 0,1 , j1, j 2
th
n j1 : new charging poles to be constructed in j1 FCS;
And, Fc
n j 2,1 : current existing charging poles in j 2th FCS;
Fi , new : investment cost of a new constructed FCS;
Fo, new : operation cost of a new constructed FCS;
c) Charging Poles Utility: f 3
Fo, rein : operation cost of a reinforced FCS.
The ECP objective well explains the effectiveness of the utility of the FCS layout planning scheme, which can be defined as
These economic objectives can be estimated as j1J 1
Fi , rein
C n 2, j 2
j 2,2
j 2J 2
Fo, new Fo, rein
Qc en2j1
(2)
Qc en2j 2,2
(3)
C F c n 1, j1
i
j1J 1
i , new
p
Qc
j1
max
(4)
C2, j 2 i Fi,rein cp n j 2,2Qc
(5)
c n
(6)
p
Qc
j 2,1
f3
t T
C1, j1 i, j1, t
j1J 1 i{n j1 } C1, j1n j1 j1J 1 t T
i, j 2, t
j 2J 2 i{n j 2,1 n j 2,2 }
C2, j 2 n j 2,2 n j 2,1 j 2J 2
(10) where, i, j, t denotes the working status of charging pole i of
j 2J 2
Fo,old
(9)
L denotes the average running mileage of an EV between two charging gap.
Fo,old : operation cost of an old existing FCS;
j1
denotes the charging cost of EV v in time t ,
Where, c denotes the charging price per miles;
Fi , rein : investment cost to reinforce an existing FCS;
1, j1
(8)
Fc c L
n j 2,2 : charging poles to be reinforced in j 2th FCS;
C W n
v, j 2, t 1
j 2J 2
C2, j 2 : 0/1 decision variable to reinforce an existing FCS;
Fi , new
(7)
tT vV j 2J 2
FCS j at time t , i, j, t {0,1} ; it is assigned as 1 when
j 2J 2
the charging pole is working at time t, otherwise set as 0.
where, W : the basic investment of a FCS; Qc : the net price of buying an EV charging pole; e : the mounting cost and other corresponding facility costs for charging poles in an EV FCS. i : the coefficient of operation cost by contrast to its construction investment cost, usually set as 10%;
2) Constraints: a) Charging FCS Selection Constraint: EV customers in charging demand location i is required to refuel at one fixed FCS, as defined by,
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C
1, j1
jJ1
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X ij C2, j 2 X ij 1,
iD
the dominated solutions in the Pt and At to the At 1 until the
(11)
jJ 2
size of At 1 is equal to N . Step 3: if t T , output the external file At 1 as the final Pareto set, stop the search process; otherwise, turn to Step 4. Step 4: select individuals from At 1 into the mating pool with substituted binary championship rule. Step 5: implement crossover and mutation operator to the individuals of mating pool and population Pt 1 , let t t 1 , turn to Step 2.
where,
X ij 0,1 denotes the allocation 0/1 choice variable; it is assigned as 1 if EV customers in demand location i are allocated to refuel their EV at FCS j , otherwise it is assigned as 0; D denotes the subset of EVs with charging demands. b) Limits on Charging Poles Number at the FCS: FCSs for newly constructed and for reinforced stations should satisfy the limit on the number of charging poles, as defined respectively by
Nmin N j Nmax , j J1
(12)
Ncur N j Nmax , j J 2
(13)
The flowchart of SPEA-II algorithm is described in Fig. 1. Begin Initialize P(0), A(0) Calculate the fitness of P(t), A(t)
where, N min : the minimum charging poles number in a FCS;
Update A(t+1)
N cur : the number of current existing charging poles in the FCS; N max : the maximum charging poles number in a FCS.
t >T? NO
Selection Crossover
c) Distance between FCSs:
YES
Output A(t+1) as final Pareto set
t=t+1
In order to obtain a well pre-distributed potential EV FCSs, a minimum distance between each pair of FCSs is employed to guarantee the performance, as defined by,
Dij Dmin , i J1 , j J1 J 2
537
End
Mutation
Fig.1. the flowchart of SPEA-II algorithm.
(14)
3.2 Implementation of SPEA-II to the EVFCS-RP Problem
where, Dij : the distance between stations i and j ;
Since the EVFCS-RP model includes three kind of variables, C1, j1 / C2, j 2 , X ij and n j1 / n j 2,2 , and all of them are
Dmin : the minimum distance requirement.
discrete integer variables. We propose a hybrid chromosome coding strategy to express the solution of EVFCS-RP with regards to satisfying its constraints. Corresponding crossover and mutation evolutionary operators are proposed to match the coding strategy.
3. IMPLEMENTING SPEA-II TO EVFCS-RP PROBLEM Compared with traditional optimization methods, multiobjective evolutionary algorithms, such as Non-dominated Sorting Genetic Algorithm-II (NSGA-II) (Deb 2002), Strengthen Pareto Evolutionary Algorithm-II (SPEA-II) (Zitzler 2001), have been widely adopted in many industrial optimization applications (Ngatchou 2008). In this study, SPEA-II is employed as an optimizer to solve the EVFCS-RP problem based on a new chromosome coding strategy.
a) Chromosome Coding Strategy: A hybrid chromosome encoding strategy is proposed in this paper (Fig. 2). Chromosome Coding Strategy for EVFCS-RP Location 1
……
Location 2
Location l_max
3.1 SPEA-II Algorithm Description Potential location index: Either existing EV FCS Or potential new EV FCS
The basic flowchart of SPEA-II algorithm includes the following steps: Step 0: create an initial population P0 , population size as N ,
0/1
N/E
n_CP
0/1 decision variable 0: Set up FCS in the location 1: Give up FCS in the location
and a null external file A0 , and set generation count as t 0 . Step 1: calculate the individual fitness of population Pt and
N/E type variable N: New FCS to be constructed E: Existing FCS to be reinforced
external file At .
Step 2: define At 1 xi | xi Pt At ; if the archived
Size of the FCS n: Charging poles’number in the FCS
Pareto solutions size of At 1 is over the maximum limit N , cut the size to N ; but if the size of At 1 is less than N , join
Fig. 2. Chromosome of SPEA-II for EVCS-RP problem.
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Selection strategy: roulette wheel selection.
genetic algorithm, IGA (Jin 2013), is also employed for comparison study.
Crossover operator: In order to guarantee the feasibility and effectiveness of the offsprings derived by crossover operator, substring crossover strategy proposed by Park (Park 2000) is employed in this study.
The coordinates of EV charging demands are distributed as shown in Table 1, and the coordinates of current existing FCSs and potential newly constructed FCSs are shown in Table 2.
b) Evolutionary Operators:
Mutation operator: A simple point variation mutation operator is taken to avoid local optimality. c) Fitness Evaluation (Zitzler 2001): Obtain the values of the three objective functions with (1), (7) and (10) and calculate its strength S (i) ,
S i | { j | xi Pt At , xi
x j }|
(15)
The original fitness R(i) of individual i is equal to the sum of strengths of all individuals dominated by it (Yao 2014).
R i
x j Pt At , x j
S j
(16)
xi
Fig. 4. Potential new EV FCS sites in Futian District.
The k-proximity method is employed to calculate the density value D(i) for individual i (Ngatchou 2008).
1 D i k i 2
Table 1. Demand coordinates & EV refuel amount. Demand index 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(17)
where, ik is the distance in the objective space between an individual i and the k th adjacent individuals to i ,
k N N , where N is the population size, and N is maximum archived Pareto set limit. Finally, the fitness F (i ) is calculated as
F i R i D i
(18)
4. CASE STUDY 4.1 Problem Description In order to verify the effectiveness of the method proposed in this paper, a FCS re-planning case study that comes from Shenzhen City, Southern East China, is employed for demonstration.
X
Y
0.7 0.6 1.6 1.0 1.4 2.3 2.7 3.3 3.7 4.0 4.9 5.9 8.5 6.6 7.9
1.8 0.7 0.4 1.3 2.1 0.4 1.9 0.2 1.6 3.3 1.4 3.9 4.3 0.4 2.4
EV amount 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
Demand index 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
X
Y
5.3 8.2 7.2 7.5 4.7 6.3 6.3 7.5 9.2 10.3 10.7 10.7 9.8 10.2 8.9
4.8 0.3 4.6 4.0 3.3 2.1 4.1 1.9 1.4 4.5 3.0 3.5 1.0 2.8 3.5
EV amount 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40
Table 2. Coordinates of FCS sites candidate locations. Coordinate index 1 2 3 4 5 6 7 8 9 10 11 12 13
There are 11 existing EV FCSs within the Futian District before the re-planning. Considering the feasibility and availability of the land space for constructing new FCSs, the areas near the schools, shopping malls, and parks are first taken into consideration. After a brief investigation, 11 new sites near the schools, 6 new sites near the shopping malls, and 3 new sites near the parks are selected for potential new EV FCS candidates (the total of 20 new potential FCS sites and 11 existing FCSs are shown in Fig. 3, where purple points represents the existing FCSs and green points represents the potential FCS sites). It is assumed that the total EV numbers in Futian District as 1,200. In order to verify the effectiveness of employing SPEA-II to solve the EVFCS-RP problem, a single-objective improved 538
X
Y
2.0 0.6 1.1 4.5 6.1 5.9 6.6 8.3 8.5 9.9 10.3 1.8 2.7
0.7 1.4 1.5 4.1 1.1 2.3 4.5 4.6 2.9 4.4 3.5 3.7 2.2
Coordinate index 17 18 19 20 21 22 23 24 25 26 27 28 29
X
Y
5.5 7.5 7.9 8.2 10.4 10.5 2.9 6.9 5.0 9.6 9.2 6.2 5.6
0.1 0.0 2.5 1.8 2.3 1.0 1.6 1.9 1.7 1.4 2.7 4.2 2.9
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3.3 4.9 7.3
0.0 5.0 3.8
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30 31
6.9 11.3
539
b) Algorithm Stability Analysis
3.0 2.1
In order to further test the stability of the SPEA-II, M-index is employed for demonstration. The M-index is an index to measure the gap between the Pareto solutions searched by one algorithm and the theoretical Pareto solution set of the problem, which is mathematically defined as,
4.2 Parameters Setting In the case study, the parameters are set as follows: a) Model Parameters Setting:
M ( A) :
Basic investment of a FCS: W $300,000 ; Price of buying an EV charging pole: Qc $10,000 ; Mounting cost and
1 A
min a x
x Xp
a A
(19)
Where, A is the Pareto set, A represents the solution number of set A .
other facility costs of an EV charging pole: e $3000 . Annual operation cost of a FCS: i 0.1 , c p 0.05 .
Table 4 shows the 20 M-index obtained by SPEA-II operated independently. The M-index result shows that, the average of the deviation between the Pareto solution set obtained by SPEA-II and the theoretical optimal Pareto set is within 10, which is a respectively small deflection from the global theoretical Pareto solutions. Thus, the SPEA-II is expected to find a stable good Pareto solution set when it is employed to solve the EVFCS-RP problems.
Driving cost to FCS: ct $0.06 / mile ; road equivalent length factor (city road): λ 1.2 ; Charging price c $0.04 / mile ; FCS busy period ratio: 0.9 ; the planning horizon T 24 365 hours. Besides, it is also assumed that an EV battery storage capacity can obtain 80%~90% energy within 15~20 minutes, so the charging time is set as 15 minutes. The minimum and maximum number of charging poles: Nmin 2 , Nmax 12 ; the minimum distance between FCSs: Dmin 0.3 mile.
Table 4. M-index of SPEA-II for EVFCS-RP case study.
b) Algorithms’ Parameters Setting: SPEA-II:
index
1
2
3
4
5
6
7
8
9
10
M(A)
4.55
8.79
1.65
9.67
8.25
2.86
0.38
3.25
1.63
8.92
index
11
12
13
14
15
16
17
18
19
20
M(A)
2.71
9.93
9.65
0.67
4.26
3.78
0.36
0.95
2.70
9.89
c) Decision Making
Population size: PopSize 300 ; archived population size:
PopArch 20 ; maximum generation: Genmax 200 ; crossover probability: pc 0.6 ; mutation probability: pm 0.08 . IGA: Population size (refers to reference (Jin 2013)): PopSize 300 ; maximum generation: Genmax 200 ; crossover probability: pc 0.8 ; mutation probability: pm 0.08 .
In a real application scenario, a Decision Maker (DM) needs to choose a final decision solution from the Pareto set, one can employ the multi-objective decision method to select a final satisfied solution [18], such as TOPSIS. In this study, the TOPSIS method is employed with the preference weights of objectives f1, f2 and f3 as 0.7, 0.2 and 0.1, respectively. The final optimal solution is chosen as Pareto solution 2 (Table. 3), which represents the real planning scheme as Fig. 4.
4.3 Results and Analysis a) Comparison with Single-objective Optimization After running the SPEA-II and IGA independently 20 times with all parameters as set above, a set of Pareto solutions and an optimal solution are obtained by the two algorithms, in which IGA aims at minimizing the f1 . Table 3 lists three typical Pareto solutions of SPEA-II and the optimal solution of IGA, from which it can be seen that SPEA-II can obtain better balanced solution by contrast to the single-objective IGA optimization with regards to the EV customers’ cost and the facility utilization ratio. Table 3. Typical solutions by SPEA-II and IGA Pareto solution1
SPEA-II Pareto solution 2
Pareto solution 3
IGA Optimal solution
1.876
1.864
1.823
1.820
f2(10 $)
0.392
0.401
0.410
0.586
f3(%)
62.2
63.7
61.4
64.1
objectives f1(106$) 6
Fig. 4. The optimal FCS plan obtained by SPEA-II & TOPSIS.
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5. CONCLUSIONS The electric vehicle (EV) fast charging station (FCS) replanning (RP) problem is a typical mixed 0-1 integer combinatorial optimization problem. A multi-objective EVFCS-RP problem is formulated mathematically in this paper, and an improved SPEA-II algorithm is developed to solve the problem. Case study shows that the proposed method can handle the multi-objective optimization problem well with good stability performance, and can provide the Pareto solutions for a decision maker. REFERENCES Benysek, G. and Jarnut, M. (2012). Electric vehicle charging infrastructure in Poland. Renewable and Sustainable Energy Reviews, 16(1), 320-328. Chankong, V., and Haimes, Y. Y. (2008). Multiobjective Decision Making: Theory and Methodology, Dover Publications. Crosier, R. and Wang S. (2013). Modeling the closed-loop interaction between the grid and a multifunctional electric vehicle charging station integrated with an active power filter. In Proceedings of 2013 IEEE International Conference on Electric Vehicle Conference (IEVC-2013), Santa Clara, CA, 1-7. Deb, K., Pratap, A., Agarwal S., and Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGAII. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. Etezadi-Amoli, M., Choma, K., and Stefani, J. (2010). Rapidcharge electric-vehicle stations, IEEE Transactions on Power Delivery, 25(3), 1883-1887. Feng, L., Ge, S., Liu, H., Wang, L., and Feng, Y. (2012). The planning of charging stations on the urban trunk road. In Proceedings of 2012 IEEE International Conference on Innovative Smart Grid Technologies - Asia (ISGT Asia), Tianjin, 1-4. Hatton, C. E., Beella, S. K., Brezet, J. C., and Wijnia, Y.C. (2009). Charging station for urban settings: the design of a product platform for electric vehicle infrastructure in Dutch cities, World Electric Vehicle Journal, (3), 1-13. Jia, L., Hu, Z., Song, Y., and Luo, Z. (2012). Optimal siting and sizing of electric vehicle charging stations. In Proceedings of 2012 IEEE International Conference on Electric Vehicle Conference (IEVC-2012), Greenville, SC, 1-6. Jin, M. J., Shi R. F., Zhang, N., and Zhang, L. (2013). Study on Multi-Level Layout Planning of Electric Vehicle Charging Stations Based on an Improved Genetic Algorithm. International Journal of Smart Grid and Clean Energy, 2(2), 277-282. Kim, S., Jung, H., Hwang, J., Lee, S., and Song, K. (2013). A study on the construction of EV charging infrastructures in highway rest area. In Proceedings of 2013 IEEE Fourth International Conference on Power Engineering, Energy and Electrical Drives (POWERENG), Istanbul, 396-400. Li, Z. and Ouyang, M. G. (2011). The pricing of charging for electric vehicles in China-Dilemma and solution. Energy, 36, 5765-5778. 540
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