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Optimal siting and sizing of distribution system operator owned EV parking lots
Applied Energy 179 (2016) 1176–1184
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Optimal siting and sizing of distribution system operator owned EV parking lots Mohammad Amin Kazemi a,⇑, Mostafa Sedighizadeh a, Mohammad Javad Mirzaei b, Omid Homaee b a b
Department of Electrical Engineering, Shahid Beheshti University, Iran Department of Electrical Engineering, Iran University of Science and Technology, Iran
h i g h l i g h t s An approach to determine the optimal number, location and capacity of EV parking lots. Investigation of ‘‘EV owners’ welfare” and the effect of this term. Investigation of the growth percentage of the EVs as a probabilistic parameter.
a r t i c l e
i n f o
Article history: Received 3 March 2016 Received in revised form 22 June 2016 Accepted 26 June 2016
Keywords: EV parking lot Growth rate of EVs Welfare of the EV owners K-means clustering method Probabilistic model
a b s t r a c t In this paper, a new approach is presented to determine the optimal number, location and capacity of each Electric Vehicle (EV) parking lot to maximize the profit of electrical distribution companies. In the proposed approach, while considering the term of ‘‘EV owners’ welfare”, the effect of this term on optimal location and capacity of the EV parking lots is also investigated. Moreover, the expected growth percentage of the EVs in the upcoming years is presented as a probabilistic parameter. The way of affecting the planning of the parking lots is analyzed. Also, an approach has been presented based on K-means clustering method to estimate the number of EVs approaching for a parking lot which can lead to a more accurate prediction of the costs and incomes of establishing a parking lot. The presented approach is performed on the 69 node radial distribution system and the results are analyzed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Concurrent with the increment of penetration of EVs, the distribution system operators are obliged to improve the system and to provide equipment and facilities needed for charging EVs [1]. On the other hand, economic and environmental stability [2] and providing electrical energy with high level of reliability for consumers by means of implementing the programs of vehicle to grid (V2G) and grid to vehicle (G2V) [3], are the most important advantages of EV parking lots. Parking lots are established in an area so that an EV owner could spend an hour or more while his/her vehicle is charged /discharged [4]. Hence, parking lots are known as one of the most important urban infrastructures [5]. Efforts always have been made in order to improve the social welfare by adding the number of parking lots as increasing the number of parking lots will make it easier for the EV owners to get to parking lots. In order to achieve all of the
⇑ Corresponding author. E-mail address: [email protected] (M.A. Kazemi). http://dx.doi.org/10.1016/j.apenergy.2016.06.125 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.
advantages mentioned above, determining the optimal location and capacity of the parking lots in distribution systems is very important [6]. On the other hand, EVs distribution and network loss are critical items in determining the location of a parking lot. The parking lot capacity affects on parking lot development cost and the number of EVs that should be charged in the parking lot to make it economically feasible. These issues show that parking lot siting and sizing is a complex problem that needs to be addressed fully in both electric grid and EV aspects [7]. Therefore, in recent years, many studies have been carried out on optimal siting and sizing of the EV parking lots. Some of the most important conducted works and vital challenges about this issue are investigated as follows.
1.1. Literature review In [8] it has been emphasized that parking lot locations will be determined based on the estimated regional charging demand and their distances to the nearest power transmission stations. A planning model for determining the optimal location and capacity of
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
the EV parking lots has been presented in [9] where the vehicle flow information and the road network structure are considered. It is shown that the road system and the flow of traffic could directly affect the sites of the charging stations. They could also indirectly affect the capacity of the parking lots. A multiobjective planning model is also presented to locate EV charging stations considering distribution of charging demands, charging consumers’ behavior and municipal planning [10]. In [11] a multi-objective planning method to determine the optimal location and size of EV parking lots has been presented, which maximized the EV traffic flow considering constraint of battery capacity. In [12], in addition to emphasize the use of probabilistic approach for EVs’ modeling, the capacity of batteries, the distance covered by EVs and the duration of traveling are considered as probabilistic parameters. The allocation of parking lots is implemented to decrease the power losses. It is shown that the optimal allocation of the charging station will decrease the improper effects on the system caused by charging so many EVs. This deduction is according to the random patterns of charging EVs including the arrival time, duration of presence and power of the charging [13]. In addition, in [14] optimal allocation of EV parking lots is determined based on load and generation models of parking lots. Also, a multi-objective scheduling model has been presented to improve the voltage profile, increase the state of reliability and decrease the costs. The technical aspects of determining the optimal capacities of parking lots have been investigated in [15], and it is shown that the optimal location of the parking lots is very sensitive to the number of EVs and the way of charging them. Whereas, in the present paper in addition to the technical aspects, the economic challenges of the parking lots’ planning issue are also considered. Also, in [16] a dynamic traffic network method is used to determine the optimal location and capacity of the parking lots considering the minimization of the charging costs and investments. Additionally, in [17] a multi-objective approach is presented to determine the optimal location and capacity of parking lots in distribution systems. Also a suitable energy scheduling of the system resources was suggested. In [18] a multi-criteria decision-making (MCDM) approach considering environmental, economic and social criteria has been presented to determine the optimal location and capacity of the parking lots. Also, it is shown that the social criteria such as harmonization of EV parking lots with the development planning of urban road networks and power grid, traffic convenience, service capability and impact on people’s lives are paid more attention from decision makers than economic criteria. In [19], although optimal sizing of the EV parking lots is implemented considering the maximization of the profit of parking lots and the income due to the decrease of power loss and improving the reliability, the location of the parking lots is already determined. While in the present paper, determining the optimal location and capacity of the EV parking lots is carried simultaneously. Planning horizon length of a one year period is considered in [19]. However, in the present paper according to the lifetime of parking lots, same as [20], 10 year planning horizon length is considered. In addition, in [19], the initial state of charge of the EVs is considered only as specified discrete amounts, while based on the charging and discharging scheduling used in this paper the initial state of charging the EVs at their arrival time can be any amount less than the maximum capacity of the battery. In [21], a mixed-integer non-linear (MINL) optimization approach has been presented to determine the optimal location and capacity of the parking lots. Proposed approach includes factors such as the parking development costs, electric grid loss, electric vehicle energy loss as well as the location of urban roads.
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Also, in [22], a method has been proposed to determine the optimal locations and capacities of the EV parking lots. In this method, to maximize the profit, some economic factors have been considered. These economic factors are the income from the power exchange between the system and the parking lot, the income from improving the reliability of the system, the cost of investment of establishing parking lots and connecting them to the buses of the system, maintenance costs, the costs of the purchased energy from the energy market, the cost of the amortization of the batteries and the charging cost discount for the encouragement of the EV owners approaching for the parking lot. The maintenance cost of the equipment which includes the repair cost has been modeled according to the number of working parking lots in [22]. Whereas in the present paper, similar to [20], these costs are divided into two parts: the maintenance costs which are associated with the capacity of the parking lot and the costs which are related to the number of approaching EVs to the parking lots. Furthermore, in [20], the amortization of the batteries is considered as one of the payments that the EV owners should make. However, in the present paper, with the opportunity of making money for the EV owners due to charging in the low-price periods and discharging in the high-price periods, EV owners will not be charged for amortization of the batteries. A complete analysis is done on effect of the behavior of the EV owners and land price on the location, capacity and gaining profit from establishing parking lots. It is demonstrated that the land price is one of the most important parameters in determining the optimal location and capacity of the parking lots [20]. Also, an initiative scheduling method of EVs charging and discharging, considering the maximization of the profit of the EV owners, is presented which not only has a simple mechanism but also its runtime is very short. Additionally, in [20], the growth percentage of the EVs in the upcoming years is considered as one of the deterministic parameters. In the present paper, due to the uncertainty in estimation of the number of EVs in the future, this parameter is considered as a probabilistic variable. This study is the subsequent phase of [20]. 1.2. Contribution Although many predictions are made about the penetration level of the EVs in the future, there has not been any comprehensive examination about the effect of the growth percentage of the EVs on the optimal determination of number, location and capacity of the EV parking lots. Also, increasing the welfare of the EV owners in the time of using the parking lots and its effect on the planning issue of the parking lots has not been investigated so far. On the other hand, according to the completion of the restructuring in power systems and the privatization of the distribution system companies, the main goal of the electrical distribution companies is to earn the maximum profit. Therefore, the optimal determination of location and capacity of EV parking lots seems necessary in order to maximize the profit of the electrical distribution companies. Furthermore, presenting a method for a more accurate estimation of the number of EVs approaching for each parking lot can result in a more accurate prediction of the costs and the incomes of establishing parking lots in distribution systems. In this paper an effort has been made to discuss and investigate all of the above mentioned issues. Most important challenges in the problem of parking lots planning are mentioned bellow: – The EV owners’ welfare is one of the important issues that should be considered in distribution system planning. What would the effect be if we consider this term in long-term planning of the parking lots?
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– It is obvious that the growth rate of EVs in the future can affect the long-term planning of the parking lots. Because we are not sure about the amount of the growth rate of EVs in the future, how should this parameter be considered? How much can the correct prediction of this parameter help making better decisions to invest in establishing parking lots? – The amount of the income and costs of each parking lot is directly a function of the number of approaching EVs for the parking lot. As EVs might have different choices for approaching to different parking lots, what mechanism should be used to estimate the number of EVs approaching for a parking lot? – One of the purposes of the distribution companies by establishing parking lots is to gain the most possible amount of profit. What kind of planning model can be suggested that can simultaneously consider the EV owners welfare and maximize the profit for the distribution network operator? The contributions of this paper are organized in order to answer mentioned challenges. Hence, the paper’s main contributions are fourfold. (1) Studying the effects of growth percentage of the EVs on the optimal location and capacity of EV parking lots and the profits from establishing EV parking lots. (2) As the availability of the EV parking lots is important for the EV owners in different places of the city considering the time saving, in this paper, the effect of considering the welfare of the EV owners on the optimal location and capacity of EV parking lots has been investigated. (3) Estimating the number of approaching EVs to each parking lot by bordering the zones of the distribution system by using k-means clustering method in order to more accurate estimation of the costs and incomes from establishing parking lots during the study period. (4) Presenting a new model in order to determine the optimal location and capacity of the parking lots considering maximization of the profit of electrical distribution companies.
could be modeled as a random variable under long-normal probability density function (PDF) as found by [20]. According to the explanations above, the method of the modeling of the EV owners’ behavior has been completely explained in our previous work [20]. 2.1. Objective function: maximizing the profit of the distribution system operator Our purpose in this paper is to determine the optimal number, location and capacity of EV parking lots to maximize the profit of the distribution system operator. The optimal number of parking lots is the number of the parking lots needed in order to maximize the profit of the distribution system operator. Also, optimal locations of parking lots are places in the network, where if parking lots are established, the profit of the distribution system operator will be maximized. Moreover, optimal capacities of parking lots are the capacities of parking lots which the profit of the distribution system operator will be maximized. It should be noted that the network constraints should be considered for optimal number, locations and capacities of parking lots as well. Therefore, the proposed objective function has been presented as follows:
f 1 þ CO2 þ CO3 Þ f 1 ð CO ProfDSO ¼ ReDSO CoDSO ¼ RE
where ProfDSO , ReDSO and CoDSO are the total profit, the total revenue and the total cost of the distribution system operator, respectively. f 1 Þ and total Total revenue of DSO has been formed in the term ð RE f 1, the cost of DSO has been formed in the sum of three terms CO CO2 and CO3 . f 1 shown in (2), represents the expected value of The term RE income from selling energy to customers and also the electric vehicles charging process in the parking lots. Because of the energy delivery to the customers and providing them with charging and discharging equipment, definite percentage of profit will be devoted to the distribution system operator. In fact, the amount of payments to the distribution system operator is determined according to the exchanged energy and the price of electricity at the time of these exchanges.
1.3. Paper organization The remainder of this paper is organized as follows. In Section 2, the problem formulation of determining the optimal location and the capacity of EV parking lots is presented in three parts: introducing the objective function, charging and discharging scheduling and the problem constraints. Numerical studies and the analysis of the results are discussed in Section 3. Finally, the conclusion is given in Section 4.
2. Formulation In this section, the problem formulation of determining the optimal location and the capacity of EV parking lots is presented in three parts: introducing the objective function, charging and discharging scheduling and defining the problem constraints. The first parameter that should be modeled is the distance that an EV covers. The log-normal distribution would be an appropriate choice to model this parameter [20]. Therefore, this probability distribution function is used to determine the optimal location and capacity of the EV parking lots [20]. The second and the third parameters that should be modeled are the arrival time and the departure time of the EVs. These parameters are modeled by a Gaussian distribution function because this function is the most homogenous to the driving pattern viewpoint. The fourth parameter is the battery’s initial state of charge (SOC). This parameter
ð1Þ
f1 ¼ RE
Ny N ll X XX j t ðCFÞ j Pricet Pi;j t Dt c ð1 þ b1 Þ j¼1
i2Xc t¼1
Nv Ny Nll X XX X j K;t k;t ðCFÞ j X k;t þ EV RaCH Dt CH Pricet ð1 þ b2 Þ p
j¼1
ð2Þ
p2Xp t¼1 k¼1
where Ny is the planning horizon length (year), Nll is the number of K;t is load levels, Npv is the number of EVs in the pth parking lot, RaCH the charging rate of the kth vehicle in the tth load level, and Xp and Xc are the set of parking lots and the set of the customers whom the distribution system provide their consumption loads,
respectively. Also, X k;t EV is a binary variable which shows the status of charging or not charging the kth vehicle in the tth load level and P i;j t is consumption power of the ith customer in the jth year j
and in the tth load level. In addition, Pricet represents the price of purchased electricity from the system in the jth year and the tth load level, Dt k;t CH is the charging duration of the kth vehicle in the tth load level, b1 and b2 are respectively the considered percentages of the profit of the distribution system operator for delivering energy to the customers and providing electric vehicles with charging and discharging equipment [20] and CF is the present value factor. f 1 , depends on the The second part of the objective function, CO cost of discharging EVs and buying electricity from substations which is presented in (3).
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g1 ¼ CO
Ny Nll X XX j j ðCFÞ j Pt;s Pricet Dttc j¼1
where N z;0 Varea is the number of vehicles in the zth zone at the time of establishing the parking lots, czj is the growth percentage of the
s0 2Xs t¼1
i;z
p
Nv Ny N ll X X XX j k;t k;t þ ðCFÞ j Y k;t EV RaDCH Dt DCH Pricet j¼1
ð3Þ
p2Xp t¼1 k¼1
where Xs is the set of substations, Rak;t DCH is the discharging rate of j is the amount of power the kth vehicle in the tth load level and P t;s purchased from the sth substation in the jth year and the tth load k;t level. Also, Dt DCH is the discharging duration of the kth vehicle in k;t the tth load level and Y EV is a binary variable which shows the status of discharging or not discharging the kth vehicle in the tth load level. It should be noted that maximizing the profit of the distribution system operator should not prevent the maximization of the profit of the EV owners. In other words, the profit of the distribution system operator is in the shadow of the maximization of the profit of EV owners and their financial expectations. Therefore, scheduling the charging and discharging of EVs to maximize the profit of the EV owners is necessary. The details related to this scheduling will be discussed in Section 2.2. Obtained optimal powers of charging and discharging resulted from this part are used in calculating g1 . g1 and CO RE
The third part of the objective function is associated with the needed investment for establishing a parking lot including the first term, the cost of buying land, and the second term, the cost regarding construction, and also buying charging and discharging equipment shown in (4). Nz Nz X X z z z CO2 ¼ Spark Pricel þ Pricec C park z¼1
ð4Þ
i;z kj
P 1i;j N v ¼
k¼1
dk;z
" # Ny Nz Nz X X X j z j j j;z CO3 ¼ ðCFÞ Prm C park þ Prr Nv area z¼1
ð5Þ
PNz 1 z ¼ 1 PNvi;j dk;z k¼1 z–i
!
ð7Þ
where N i;j v is the number of vehicles in the jth year and ith zone in which the parking lot does not have enough capacity calculated by (8).
1 1 ! C C BB X Ny Y C C BB Nz i;0 i C BB Ni:j czj C NVarea v ¼ BB C C park C A A @@i ¼ 1 j¼0 00
ð8Þ
i–z k;z
Also, d , the distance of the kth vehicle from the determined bus for establishing parking lot in the zth zone, is calculated by (9). k;z
where Nz is the number of zones, is the capacity of the established parking lot in the zth zone and Pricec is the cost of establishing parking lot and purchasing charging and discharging equipment z for each EV parking lot, Pricel is the price of each square meter of z is the area needed for establishing land in the zth zone and Spark parking lot in the zth zone in term of square meters which is a function of the capacity of the parking lot and the architecture features of the construction such as the number of floors. The fourth part of the objective function, CO3, contains the costs of repair and maintenance of parking lots during the operation shown in (5). As can be seen, these costs contain two parts. The first part is cost of the parking lots maintenance as snow removal depended on the capacity of the parking lot. The second part is cost of the repair for parking lots such as the cost of equipment depreciation associated with the number of arriving EVs [20].
d
¼ jLk Lz j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxk xz Þ2 þ ðyk yz Þ2
ð9Þ
where Lk and Lz are the location of the kth vehicle and the location of the determined bus for establishing parking lot in the zth zone, respectively. The set of the geographic areas, in which if a parking lot is established, all of the vehicles in those areas will approach for, is defined as a zone. In this paper, K-means clustering method [23] is used, to classify the distribution system to different zones and determine the border of the zones. Genetic Algorithm [24] is also used to determine the optimal location and capacity of EV parking lots, as in [19,25]. Moreover, the probabilistic model of an EV is considered based on the point estimate method [26]. It should be noted that although the power loss in the distribution system is not directly in the formulation, it is considered indirectly because when the profit is maximized, the power loss is minimized. 2.2. The EVs charging and discharging scheduling
z¼1
where Pr mj is the annual cost of the maintenance of the parking lot for each vehicle in the jth year, Pr rj is the annual cost of the repair for each vehicle and Nj;z Varea is the number of vehicles that arrive at the parking lot in the jth year and the zth zone calculated by (6). In fact, N j;z Varea is the sum of the vehicles from the zth zone and some of the vehicles of other zones in which the parking lots do not have enough capacity to accept all the vehicles of those zones. 20
i;z
with the distance of the vehicle from the parking lot. Therefore, kj is calculated by (7).
z¼1 z C park
j¼1
vehicles in the zth zone and the jth year, and kj represents the percentage of the vehicles that if there is no empty capacity in the parking lot at the ith zone, will approach for the parking lot in the zth zone. It is obvious that the owners of electric vehicles prefer to refer to the nearest parking lot. Therefore, the probability of arrival of excess vehicles of each zone which does not have enough parking lot capacity to the parking lots of other zones has a reverse relation
000
1
1
11
3
! BBB !C 6B C CC 7 Ny Ny Nz Y Y C 6B z;0 BBB X C C 7 i;z C j;z i i;0 B BB C CC z 7 N Varea ¼ min 6 cij þ B czj C N Varea C C park C kj CC;C park 7 6BN Varea BBB A 4@ @@@i ¼ 1 A AA 5 j¼0 j¼0 i–z
ð6Þ
One of the purposes of the EV owners approaching for a parking lot is minimizing the payments. Therefore, the objective function for minimizing the costs of the EV owners is presented in (10). It is obvious that because of the independence of the EV owners from each other, this function should be minimized for each electric vehicle independently.
t kd 1 k;t Min w ¼ m Prkt Pkt Dtk;t gCH X EV þ Y k;t EV ;
gDCH
t¼t ka
8k 2 Xv ;
P > 0; state of charge p < 0;
ð10Þ
state of discharge
where gCH and gDCH are the efficiency of charging and discharging, respectively.
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Besides the minimization of the objective function presented in (10), the following constraints should be met: – The batteries of the electric vehicles cannot be charging and discharging, simultaneously [27]. k;t k;t k;t X k;t EV þ Y EV 6 1; X EV ; Y EV 2 f0; 1g
tk
j X 1 Dt k;t P kt gCH X k;t Y k;t P sockmax EV þ g EV DCH
tk
socka
j X 1 P sockmin þ Dtk;t Pkt gCH X k;t Y k;t EV þ g EV
8tj 2 ft a þ 1; . . . ; td g ð12Þ where SOC ka is the initial state of charge of the kth vehicle. Also, SOC kmin and SOC kmax are the minimum and the maximum possible state of charge of the battery of the kth electric vehicle, respectively. – The sum of charging and discharging powers during the presence of each vehicle in the parking lot equals the difference between the desired final state of charge by the EV owner and the initial state of charge of the vehicle. k
t¼t d X Dtk;t Pkt P sockd socka
ð13Þ
t¼t ka
where SOC kd is the desired final state of charge of the kth vehicle, and is calculated according to (14) [20].
sockd ¼ minð½ld þ rd :Nd :Enk ; sockmax Þ
ð14Þ
where Enk is the amount of energy that the kth electric vehicle needs to cover 1 km. – The injected power or the absorbed power by each vehicle in each time interval has to be in a specific range.
( Pmin 6
8k 2 Xv ;
Pkt
6 Pmax )
Pkt P P min
P kt P Pmax 8t ¼ f1; 2; . . . ; Nll g
where Nbus is the number of all buses and V is the voltage of the bth bus in the tth load level. Also, vmin and vmax are the minimum and the maximum permitted voltages of the buses, respectively. – The capacity of each parking lot for accepting electric vehicles is limited [20]. As there are limitations such as the needed space and the costs of establishing a parking lot, the capacity of each parking lot is limited. z z C park 6 C park;max
DCH
t¼t ka
ð17Þ b,t
– The state of charge of the vehicles in all the time intervals should be between a minimum and a maximum quantity [28].
t¼t ka
lðV b;t Þ þ w rðV b;t Þ 6 v max ; b ¼ 1; 2; . . . ; Nbus ; t ¼ 1; . . . ; Nll lðV b;t Þ w rðV b;t Þ P v min ; b ¼ 1; 2; . . . ; Nbus ; t ¼ 1; . . . ; Nll
ð11Þ
8 k 2 Xv ; 8 t ¼ f1; 2; . . . ; Nll g
socka
is, the more the probability of being in the permitted limit of voltage and current are. – The voltages of buses should be in the permitted limit [20].
ð15Þ
where P min and P max are the minimum and the maximum power that can be exchanged between electric vehicles and the parking lot in each time interval, respectively. Because of similarity with the standard form of linear programming (LP) method, the problem is solved by LP method [29] as [28].
ð18Þ
z where C park;max is the maximum possible capacity for establishing a parking lot in the zth zone. The distribution system operator profit can be only increased in a way that it will not result in EV owners’ welfare reduction below a specific limit, (this limit is determined by the political and economic indicators of each district, by international standards or legislative organs). In order to increase the convenience of the owners of the EVs, the maximum distance of each vehicle from the nearest parking lot should be less than a specific amount.
jLk Ln j 6 Dmax ;
8k 2 Xv
ð19Þ
where Ln is the location of the nearest parking lot to the kth vehicle and Dmax is the maximum permitted distance of the vehicles from the nearest parking lot. The flowchart shown in Fig. 1 demonstrates the procedure of the proposed approach of determining the optimal location and capacity of the EV parking lots, briefly. As is observed, after receiving the input data of the problem, initial responses containing the optimal location and capacity of the parking lots are produced. The acceptability of this response is verified by the satisfaction of the constraint of the maximum permitted distance. In the next step, based on these suggested locations, bordering the distribution system and determining the percentage of the approaching EVs to parking lots from other zones is done by using k-means clustering method. Then, based on these suggested locations, the probabilistic scheduling of charging and discharging the EVs is carried using point estimate method (PEM) probabilistic approach. Linear programming is also implemented and the optimal amounts of charging and discharging powers are calculated. In the next step, the objective function related to the optimization of the profit of the distribution system companies, considering the constraints of the problem, is calculated. To make sure about the satisfaction of the constraints related to the voltages of the buses and the currents of the lines, distribution load flow program is implemented and finally the optimal responses of the proposed approach are extracted.
2.3. Constraints of Parking Lots Planning Problem – The current of each line should be in the permitted limit. For each load level of t, the constraint of line current is considered as bellow [30].
lðIl;t Þ þ w rðIl;t Þ 6 Ilmax ; l 2 X1 ; t ¼ 1; . . . ; Nll
ð16Þ
where Ilmax is the nominal value of the lth line, Il,k is the current of the lth line in the tth load level, Xl is the set of distribution system lines and w is a constant factor that in this paper as [20], is assumed 3. Therefore, with the probability of more than 99%, line currents will be in the permitted limit. In [20] it is proved that the more w
3. Numerical studies and discussion In this paper, in order to verify the effectiveness of the proposed model, the proposed approach has been performed on a 69 node radial system shown in Fig. 2. Also, the figure shows the distribution of EVs in the first year. System and load data are presented in [31]. In this study, as [20], the planning horizon length is 10 years and the annual interest and inflation rates are assumed 5% and 4% respectively. The mutation rate and the crossover rate have been chosen as 0.2 and 0.6 respectively.
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
Start
Define Input Data
Genetic Algorithm Generating initial solution including capacity and location of EVs parking lots
Is maximum permitted distance criteria satisfied?
No
Yes Determining the way of distributing EVs in the zones where parking lots are located
Determining the borders of the zones by K-means clustering method
Calculating the number of initial EVs in each zone based on the bordering
Designating the percentage of the EVs which approach for each zone
Objective function evaluation Point estimate method Cost minimization of charge and discharge Running the LP program to calculate the amounts of charging and discharging powers
Profit maximization of the distribution system operator
Calculating the objective function using expected and standard deviation values Implementation of load flow using the forward-backward sweep method
Is the stopping criterion satisfied? No Yes Display outputs results such as optimal capacity and location of EVs parking lots, revenues, costs and Profit from the construction of parking lots
End Fig. 1. Flowchart of the proposed approach.
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Number of EVs
1182
75 50 25
Fig. 2. 69 node radial system and distribution of the EVs in the understudy region.
A comparison between the results of the presented approach in [20] and the proposed approach presented in this paper is shown in Table 1. The growth percentage of the EVs is the same in both approaches (10%). At first, the optimal location and capacity of the EV parking lots are determined by the approach presented in [20]. Then amounts of the terms of the costs and incomes are calculated by the knowledge of these locations and capacities. As can be seen, the total profit of establishing parking lots for the electrical distribution companies in this situation, in comparison with that of Ref. [20] has increased. It shows the efficacy of the proposed approach compared to that of the previous presented approaches. Table 2, illustrates the effects of the expected value of the growth percentage of the EVs on the incomes, costs and profits of establishing EVs parking lots. As can be seen, by increasing the growth percentage of EVs, both the incomes and costs of establishing parking lots increase continually. If the growth amount of EVs reaches to a verge limit (verge limit is the limit that if the growth of EVs transcend that, the distribution system will need to establish more parking lots), the rate of increasing of the cost will be more than that of the incomes. This issue will lead to declination of the profit of the electrical distribution companies. As is observed, by increasing the expected value of growth percentage from 2.5 to 10, the total profit increases continually, but by increasing 20% in the number of EVs, because of the need for increasing in the number of the parking lots, costs will face a huge increase and finally, the total profit will be decreased. Also, increasing the expected value of the percentage growth of the EVs from 20% to 30% will lead to an increase of the profits and if the growth percentage grows to 40%, because of the need of establishing new parking lots, the total profit will be decreased. Even it is possible that the growth rate of the costs
makes it impossible for the electrical distribution companies to get to the profit they expect or even recover their own investments. In this condition, naturally there will not be any motivation for further investment in establishing new EV parking lots. Thus, predicting the growth rate of the EVs in the upcoming years is vital to electrical distribution companies. In order to show the importance of the EVs growth percentage accuracy, in this section, the EVs growth percentage is not considered as a probabilistic parameter in the optimal determination of capacity and location of EV parking lots. If the growth percentage of the EVs with the error of 10% is predicted as 5%, in fact, the growth percentage will be between 4.5% and 5.5% and the distribution system can determine the optimal location and capacity of the parking lots based on the amounts which are mentioned above. It is obvious that the more the chosen growth percentage is, the more the risk of the distribution system company will be. In the worst case, the scheduling of the parking lots is based on growth of 5.5% and the real percentage is 4.5%. In fact, there will be more parking lots than the required amounts, and because of the over design, the profit of the distribution system company will decrease as much as 0.7 million dollars. Also, if the real growth percentage is 5/5%, in this case, the maximum profit will be devoted to the distribution system company. On the other hand, the growth percentage of 14 is a critical point because with a little increasing in it, the distribution system will need more parking lots. If the predicted interval for the growth percentage of the EVs with the error of 2%, contains this critical point, in the worst case, the scheduling of the parking lots is based on growth of 14.28% and the real percentage is 13.72%. It can lead to a 1.2 million dollars decreasing in the total profit of the distribution system which is more in compared to the previous case. As can be seen, even by increasing the accuracy compared with that of the previous case (2% instead
Table 1 Comparing the proposed approach and the approach presented in [20]. Results
Method Presented approach in Ref. [20] 29 1537
44 1493
Proposed approach
Optimal location of parking lots Optimal capacity of parking lots f 1 (m$) RE
3 1411 139.97
53 1404
68 821
4 1276 147.73
f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
51.76
57.96
43.78 0.259 44.17
41.13 0.261 48.38
31 1283
44 1449
51 1184
57 1421
1183
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184 Table 2 Investigating the impacts of electric vehicles growth. Percentage of vehicles growth (%)
2.5
5
7
10
20
30
40
60
f 1 (m$) RE f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
135.13
138.42
143.62
148.48
163.84
179.64
201.74
244.98
53.60
54.53
56.077
58.19
64.91
70.21
79.145
94.73
42.04 0.247 39.24
43.73 0.251 39.9
45.88 0.261 41.4
47.22 0.269 42.8
56.14 0.293 42.5
57.01 0.325 52.1
70.19 0.365 52.04
79.48 0.416 67.35
of 10%), the total profit will be reduced further. Thus, if the growth percentage of the EVs is close to the critical point, the error can lead to decreasing the profit of the distribution system company with more slopes. Therefore, the accurate prediction of the growth percentage of EVs, particularly near the critical point, is vital to the distribution system company in order to reach the maximum profit. Another considerable point is that by increasing the number of established parking lots in distribution systems, the profit of the distribution system operator will not necessarily increases. The effect of different growth percentages of EVs on the optimal location and capacity of the parking lots is shown in Table 3. As is evident from Table 3, by increasing the growth rate of the EVs from 10% to 20%, the number of parking lots in need, will increase from 6 to 7 in order to maintain the welfare of the EV owners. Also, increasing the number of EVs from 30% to 40% will lead to the increasing the parking lots from 7 to 8. As a matter of fact, the presented results in Table 3 also emphasizes that the reason for increasing costs and decreasing profits in Table 2 is
Table 3 Investigating the impacts of electric vehicles growth on parking lot capacity and location.
increasing of the number of the EV parking lots. Furthermore, the sum of the capacities of the established parking lots in the distribution system increases by increasing the number of EVs. Thus, the growth rate of EVs affects the locations, number, capacities and the profit of establishing parking lots. Table 4 shows the comparison of the optimal locations and capacities, incomes, costs and total profits of establishing parking lots in two scenarios with and without considering the welfare of the EVs owners. As can be seen, by considering the constraint of the maximum permitted distance of EVs from the nearest parking lot in order to increase the welfare of the EVs owners, the number of EV parking lots has increased from 4 to 6. Also, it is observed that the incomes and costs of the power exchange are the same in the two scenarios. The reason is that the sum of the capacities parking lots is equal in both scenarios, and also the price of electric energy in all parking lots (in one year and equal load level), is equal. Nevertheless, it is observed that the profit of establishing parking lots in the second scenario, because of increasing in costs of construction of new parking lots, has been decreased. The reason is that the excess parking lots are established in the zones, in which the price of land is high. Thus increasing the welfare of the EV owners will lead to decreasing the profit of the electrical distribution companies. Indeed, it should be noted that the task of the distribution system operator is to improve the facilities of the system, to increase the welfare of the customers and the EV owners. However the maximization of the income of the distribution system operator should not overshadow the welfare of the EV owners.
Percentage of vehicles growth (%)
Optimal location of parking lots
2.5
4 1022
26 798
44 1407
51 1134
57 864
69 937
– –
– –
5
4 1057
26 811
44 1448
51 1147
57 891
69 958
– –
– –
4. Conclusion
7
4 1076
26 833
44 1469
51 1171
57 911
69 972
– –
– –
10
3 848
20 942
32 1319
40 934
65 1131
67 1439
– –
– –
20
4 859
24 1392
34 786
46 891
48 1042
55 1270
69 974
– –
30
4 903
24 1471
34 887
46 957
48 1162
55 1333
69 1102
– –
40
3 1141
14 1322
23 1211
32 1047
37 872
49 920
51 735
62 1168
60
3 1307
14 1482
23 1391
32 1119
37 937
49 1145
51 913
62 1324
In this paper, a new approach is presented to determine the optimal location and capacity of EV parking lots in distribution systems. Considering the constraint of the maximum amount of permitted distance from the nearest parking lot in order to increase the welfare of the EV owners will lead to increasing the number of parking lots and as a result, this will decrease the profit of the distribution system companies. Since the efforts are made to improve the facilities of the distribution systems and the welfare of the EV owners is one of the main priorities of distribution systems, state of the welfare of the EV owners should always be considered even if it leads to decreasing the profit of the distribution system companies.
Optimal capacity of parking lots
Table 4 Consideration of welfare of electric vehicles owners. Results
Scenario 1: without considering the welfare of the EVs owners
Scenario 2: with considering the welfare of the EVs owners
Optimal location of parking lots Optimal capacity of parking lots f 1 (m$) RE
4 1719 146.03
4 1074 146.03
f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
57.12
57.12
40.78 0.261 47.869
46.55 0.265 42.095
59 1491
44 1725
69 1489
26 833
44 1467
51 1171
57 911
69 968
1184
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
Furthermore, it is observed that by increasing the growth percentage of the EVs, as a result of increasing the number of EVs and capacities of the established parking lots in the distribution system, the profit of the distribution system operator will not necessarily increase. It is possible that the amount of increasing of the growth percentage of the EVs leads to the need of establishing more parking lots in the distribution system, whilst the price of establishing parking lots is higher. Thus, the rate of increasing the costs will be more than that of the incomes and this will lead to decreasing the profit of establishing parking lots. If the intervals of the prediction of the growth percentage of EVs contain critical points, the amount of profit deduction will be more compared to the situation in which these intervals contain none of these critical points. Thus, deciding about establishing parking lots in this situation is very sensitive due to the high risks it has. In fact, if the predicted growth percentage is more than the real amount, because of excessive initial investment, the profit will decrease. Therefore, the more the difference in between the predicted amount and the real amount is, the less the profit will be. Also, if the predicted growth percentage is less than the real amount, we can say that the distribution system operator would not be able to gain all of possible amount of profit. In other words, a part of the profit will be lost. In this state, the more the difference in between the predicted amount and the real amount is, the more the loss of the profit will be. So, decreasing the error of prediction of the expected amount of the growth percentage of EVs in the upcoming years is a vital factor which leads to better decision making for the electrical distribution company for their possible investment in order to establish new parking lots. With the variation in the growth percentage of the EVs, the optimal location, capacity and number of the EV parking lots will vary. The sum of the capacities of the established parking lots in the distribution system will sequentially increase by increasing the growth percentage of the EVs, but it is possible that the optimal number and locations of the parking lots do not change and stay constant. However, the more increment of the growth percentage of the EVs will lead to establishment of more parking lots and change their locations. References [1] Su, Chun-Lien, et al. Optimal electric vehicle charging stations placement in distribution systems. In: Industrial electronics society, IECON 2013-39th annual conference of the IEEE. [2] Hajimiragha AH, Canizares CA, Fowler MW, Moazeni S, Elkamel A. A robust optimization approach for planning the transition to plug-in hybrid electric vehicles. IEEE Trans Power Syst 2011;26:2264–74. [3] Bunyamin Y, Uzunoglu M. A double-layer smart charging strategy of electric vehicles taking routing and charge scheduling into account. Appl Energy 2016;167:407–19. [4] Nansai K, Tohno S, Kono M, Kasahara M, Moriguchi Y. Life-cycle analysis of charging infrastructure for electric vehicles. Appl Energy 2001;70:251–65. [5] Wang, wu Zheng, Tan Zhenxia, Xu Hui. Location model and algorithm of public parking facilities. 2008 international conference on intelligent computation technology and automation (ICICTA), vol. 1. IEEE; 2008. [6] Sadeghi-Barzani P, Rajabi-Ghahnavieh A, Kazemi-Karegar H. Optimal fast charging station placing and sizing. Appl Energy 2014;125:289–99. [7] Diaz-Chavez R, Woods J, San Román TG, Momber I, Abbad MR, Sánchez Miralles Á. Regulatory framework and business models for charging plug-in electric vehicles: infrastructure, agents, and commercial relationships. Energy Policy 2011;39:6360–75.
[8] Liu J. Electric vehicle charging infrastructure assignment and power grid impacts assessment in Beijing. Energy Policy 2012;51:544–57. [9] Ge S, Feng L, Liu H, Wang L. ‘‘The planning of electric vehicle charging stations in the urban area”. In: 2nd international conference on electronic & mechanical engineering and information technology, (Yichang, China), September 2011. p. 2726–30. [10] Hengsong Wang, Qi Huang, Changhua Zhang, Aihua Xia. A novel approach for the layout of electric vehicle charging station. International conference on apperceiving computing and intelligence analysis (ICACIA), 17–19 December 2010, 2010. [11] Wang GB, Xu Z, Wen FS, Wong KP. Traffic-constrained multiobjective planning of electric-vehicle charging stations. IEEE Trans Power Deliv 2013;28:2363–72. [12] Bioki MMH, Jahromi MZ, Rashidinejad M. A combinatorial artificial intelligence real-time solution to the unit commitment problem incorporating V2G. Electr Eng 2012:1–15. [13] Su CL, Leou RC, Yang JC, Lu CN. ‘‘Optimal electric vehicle charging stations placement in distribution systems”. In: Proceedings of the 39th annual conference of the IEEE industrial electronics society, Vienna, Austria, 10–13 November 2013. p. 10–3. [14] Aghaebrahimi MR, Ghasemipour MM, Sedghi A. Probabilistic optimal placement of EV parking considering different operation strategies. Mediterranean electrotechnical conference (MELECON), 2014 17th IEEE. IEEE; 2014. [15] Amini MH, Islam A. Allocation of electric vehicles’ parking lots in distribution network. In: Proc IEEE PES innovative smart grid technologies conf (ISGT). p. 1–5. [16] Ren Y, Shi L, Zhang Q, Han W, Huang S. Optimal distribution and scale of charging stations for electric vehicles. Autom Electr Power Syst 2011;35 (14):53–7 [in Chinese]. [17] El-Zonkoly Amany, dos Santos Coelho Leandro. Optimal allocation, sizing of PHEV parking lots in distribution system. Int J Electr Power Energy Syst 2015;67:472–7. [18] Guo Sen, Zhao Huiru. Optimal site selection of electric vehicle charging station by using fuzzy TOPSIS based on sustainability perspective. Appl Energy 2015;158:390–402. [19] Moradijoz M, Parsa Moghaddam M, Haghifam MR, Alishahi E. A multiobjective optimization problem for allocating parking lots in a distribution network. Int J Electr Power Energy Syst 2013;46:115–22. [20] Mirzaei MJ, Kazemi A, Homaee O. A probabilistic approach to determine optimal capacity and location of electric vehicles parking lots in distribution networks. In: IEEE transactions on industrial informatics [accepted]. http:// dx.doi.org/10.1109/TII.2015.2482919. [21] Sadeghi-Barzani Payam, Rajabi-Ghahnavieh Abbas, Kazemi-Karegar Hosein. Optimal fast charging station placing and sizing. Appl Energy 2014;125:289–99. [22] Rahmani-Andebili Mehdi, Venayagamoorthy Ganesh K. SmartPark placement and operation for improving system reliability and market participation. Electr Power Syst Res 2015;123:21–30. [23] Florez JM, Angarita JC, Plata GO. K-means algorithm and mixture distributions for locating faults in power systems. Electr Power Syst Res 2009:714–21. [24] Vose MD. The simple genetic algorithm. Foundation and theory. Cambridge, MA: MIT Press; 1999. [25] Su CL, Leou RC, Yang JC, Lu CN. Optimal electric vehicle charging stations placement in distribution systems. In: Proceedings of the 39th annual conference of the IEEE industrial electronics society, Vienna, Austria, 10–13 November 2013. p. 10–3. [26] Malekpour AR, Niknam T. A probabilistic multi-objective daily Volt/Var control at distribution networks including renewable energy sources. J Energy 2011;36:3477–88. [27] Amirioun MH, Kazemi A. A new model based on optimal scheduling of combined energy exchange modes for aggregation of electric vehicles in a residential complex. Energy 2014;69:186–98. [28] Clement-Nyns K, Haesen E, Driesen J. The impact of vehicle-to-grid on the distribution grid. Electr Power Syst Res 2011;81(1):185–92. [29] Candès E, Tao T. Decoding by linear programming. IEEE Trans Inf Theory 2005;51(12):4203–15. [30] Carpinelli G, Noce C, Proto D, Russo A, Varilone P. Single objective probabilistic optimal allocation of capacitors in unbalanced distribution systems. Electr Power Syst Res 2012;87:47–572. [31] Venkatesh B, Ranjan R. Fuzzy EP algorithm and dynamic data structure for optimal capacitor allocation in radial distribution systems. IEE Proceedings – Gener Trans Distrib 2006;153(1):80–8.
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Optimal siting and sizing of distribution system operator owned EV parking lots Mohammad Amin Kazemi a,⇑, Mostafa Sedighizadeh a, Mohammad Javad Mirzaei b, Omid Homaee b a b
Department of Electrical Engineering, Shahid Beheshti University, Iran Department of Electrical Engineering, Iran University of Science and Technology, Iran
h i g h l i g h t s An approach to determine the optimal number, location and capacity of EV parking lots. Investigation of ‘‘EV owners’ welfare” and the effect of this term. Investigation of the growth percentage of the EVs as a probabilistic parameter.
a r t i c l e
i n f o
Article history: Received 3 March 2016 Received in revised form 22 June 2016 Accepted 26 June 2016
Keywords: EV parking lot Growth rate of EVs Welfare of the EV owners K-means clustering method Probabilistic model
a b s t r a c t In this paper, a new approach is presented to determine the optimal number, location and capacity of each Electric Vehicle (EV) parking lot to maximize the profit of electrical distribution companies. In the proposed approach, while considering the term of ‘‘EV owners’ welfare”, the effect of this term on optimal location and capacity of the EV parking lots is also investigated. Moreover, the expected growth percentage of the EVs in the upcoming years is presented as a probabilistic parameter. The way of affecting the planning of the parking lots is analyzed. Also, an approach has been presented based on K-means clustering method to estimate the number of EVs approaching for a parking lot which can lead to a more accurate prediction of the costs and incomes of establishing a parking lot. The presented approach is performed on the 69 node radial distribution system and the results are analyzed. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Concurrent with the increment of penetration of EVs, the distribution system operators are obliged to improve the system and to provide equipment and facilities needed for charging EVs [1]. On the other hand, economic and environmental stability [2] and providing electrical energy with high level of reliability for consumers by means of implementing the programs of vehicle to grid (V2G) and grid to vehicle (G2V) [3], are the most important advantages of EV parking lots. Parking lots are established in an area so that an EV owner could spend an hour or more while his/her vehicle is charged /discharged [4]. Hence, parking lots are known as one of the most important urban infrastructures [5]. Efforts always have been made in order to improve the social welfare by adding the number of parking lots as increasing the number of parking lots will make it easier for the EV owners to get to parking lots. In order to achieve all of the
⇑ Corresponding author. E-mail address: [email protected] (M.A. Kazemi). http://dx.doi.org/10.1016/j.apenergy.2016.06.125 0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.
advantages mentioned above, determining the optimal location and capacity of the parking lots in distribution systems is very important [6]. On the other hand, EVs distribution and network loss are critical items in determining the location of a parking lot. The parking lot capacity affects on parking lot development cost and the number of EVs that should be charged in the parking lot to make it economically feasible. These issues show that parking lot siting and sizing is a complex problem that needs to be addressed fully in both electric grid and EV aspects [7]. Therefore, in recent years, many studies have been carried out on optimal siting and sizing of the EV parking lots. Some of the most important conducted works and vital challenges about this issue are investigated as follows.
1.1. Literature review In [8] it has been emphasized that parking lot locations will be determined based on the estimated regional charging demand and their distances to the nearest power transmission stations. A planning model for determining the optimal location and capacity of
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
the EV parking lots has been presented in [9] where the vehicle flow information and the road network structure are considered. It is shown that the road system and the flow of traffic could directly affect the sites of the charging stations. They could also indirectly affect the capacity of the parking lots. A multiobjective planning model is also presented to locate EV charging stations considering distribution of charging demands, charging consumers’ behavior and municipal planning [10]. In [11] a multi-objective planning method to determine the optimal location and size of EV parking lots has been presented, which maximized the EV traffic flow considering constraint of battery capacity. In [12], in addition to emphasize the use of probabilistic approach for EVs’ modeling, the capacity of batteries, the distance covered by EVs and the duration of traveling are considered as probabilistic parameters. The allocation of parking lots is implemented to decrease the power losses. It is shown that the optimal allocation of the charging station will decrease the improper effects on the system caused by charging so many EVs. This deduction is according to the random patterns of charging EVs including the arrival time, duration of presence and power of the charging [13]. In addition, in [14] optimal allocation of EV parking lots is determined based on load and generation models of parking lots. Also, a multi-objective scheduling model has been presented to improve the voltage profile, increase the state of reliability and decrease the costs. The technical aspects of determining the optimal capacities of parking lots have been investigated in [15], and it is shown that the optimal location of the parking lots is very sensitive to the number of EVs and the way of charging them. Whereas, in the present paper in addition to the technical aspects, the economic challenges of the parking lots’ planning issue are also considered. Also, in [16] a dynamic traffic network method is used to determine the optimal location and capacity of the parking lots considering the minimization of the charging costs and investments. Additionally, in [17] a multi-objective approach is presented to determine the optimal location and capacity of parking lots in distribution systems. Also a suitable energy scheduling of the system resources was suggested. In [18] a multi-criteria decision-making (MCDM) approach considering environmental, economic and social criteria has been presented to determine the optimal location and capacity of the parking lots. Also, it is shown that the social criteria such as harmonization of EV parking lots with the development planning of urban road networks and power grid, traffic convenience, service capability and impact on people’s lives are paid more attention from decision makers than economic criteria. In [19], although optimal sizing of the EV parking lots is implemented considering the maximization of the profit of parking lots and the income due to the decrease of power loss and improving the reliability, the location of the parking lots is already determined. While in the present paper, determining the optimal location and capacity of the EV parking lots is carried simultaneously. Planning horizon length of a one year period is considered in [19]. However, in the present paper according to the lifetime of parking lots, same as [20], 10 year planning horizon length is considered. In addition, in [19], the initial state of charge of the EVs is considered only as specified discrete amounts, while based on the charging and discharging scheduling used in this paper the initial state of charging the EVs at their arrival time can be any amount less than the maximum capacity of the battery. In [21], a mixed-integer non-linear (MINL) optimization approach has been presented to determine the optimal location and capacity of the parking lots. Proposed approach includes factors such as the parking development costs, electric grid loss, electric vehicle energy loss as well as the location of urban roads.
1177
Also, in [22], a method has been proposed to determine the optimal locations and capacities of the EV parking lots. In this method, to maximize the profit, some economic factors have been considered. These economic factors are the income from the power exchange between the system and the parking lot, the income from improving the reliability of the system, the cost of investment of establishing parking lots and connecting them to the buses of the system, maintenance costs, the costs of the purchased energy from the energy market, the cost of the amortization of the batteries and the charging cost discount for the encouragement of the EV owners approaching for the parking lot. The maintenance cost of the equipment which includes the repair cost has been modeled according to the number of working parking lots in [22]. Whereas in the present paper, similar to [20], these costs are divided into two parts: the maintenance costs which are associated with the capacity of the parking lot and the costs which are related to the number of approaching EVs to the parking lots. Furthermore, in [20], the amortization of the batteries is considered as one of the payments that the EV owners should make. However, in the present paper, with the opportunity of making money for the EV owners due to charging in the low-price periods and discharging in the high-price periods, EV owners will not be charged for amortization of the batteries. A complete analysis is done on effect of the behavior of the EV owners and land price on the location, capacity and gaining profit from establishing parking lots. It is demonstrated that the land price is one of the most important parameters in determining the optimal location and capacity of the parking lots [20]. Also, an initiative scheduling method of EVs charging and discharging, considering the maximization of the profit of the EV owners, is presented which not only has a simple mechanism but also its runtime is very short. Additionally, in [20], the growth percentage of the EVs in the upcoming years is considered as one of the deterministic parameters. In the present paper, due to the uncertainty in estimation of the number of EVs in the future, this parameter is considered as a probabilistic variable. This study is the subsequent phase of [20]. 1.2. Contribution Although many predictions are made about the penetration level of the EVs in the future, there has not been any comprehensive examination about the effect of the growth percentage of the EVs on the optimal determination of number, location and capacity of the EV parking lots. Also, increasing the welfare of the EV owners in the time of using the parking lots and its effect on the planning issue of the parking lots has not been investigated so far. On the other hand, according to the completion of the restructuring in power systems and the privatization of the distribution system companies, the main goal of the electrical distribution companies is to earn the maximum profit. Therefore, the optimal determination of location and capacity of EV parking lots seems necessary in order to maximize the profit of the electrical distribution companies. Furthermore, presenting a method for a more accurate estimation of the number of EVs approaching for each parking lot can result in a more accurate prediction of the costs and the incomes of establishing parking lots in distribution systems. In this paper an effort has been made to discuss and investigate all of the above mentioned issues. Most important challenges in the problem of parking lots planning are mentioned bellow: – The EV owners’ welfare is one of the important issues that should be considered in distribution system planning. What would the effect be if we consider this term in long-term planning of the parking lots?
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– It is obvious that the growth rate of EVs in the future can affect the long-term planning of the parking lots. Because we are not sure about the amount of the growth rate of EVs in the future, how should this parameter be considered? How much can the correct prediction of this parameter help making better decisions to invest in establishing parking lots? – The amount of the income and costs of each parking lot is directly a function of the number of approaching EVs for the parking lot. As EVs might have different choices for approaching to different parking lots, what mechanism should be used to estimate the number of EVs approaching for a parking lot? – One of the purposes of the distribution companies by establishing parking lots is to gain the most possible amount of profit. What kind of planning model can be suggested that can simultaneously consider the EV owners welfare and maximize the profit for the distribution network operator? The contributions of this paper are organized in order to answer mentioned challenges. Hence, the paper’s main contributions are fourfold. (1) Studying the effects of growth percentage of the EVs on the optimal location and capacity of EV parking lots and the profits from establishing EV parking lots. (2) As the availability of the EV parking lots is important for the EV owners in different places of the city considering the time saving, in this paper, the effect of considering the welfare of the EV owners on the optimal location and capacity of EV parking lots has been investigated. (3) Estimating the number of approaching EVs to each parking lot by bordering the zones of the distribution system by using k-means clustering method in order to more accurate estimation of the costs and incomes from establishing parking lots during the study period. (4) Presenting a new model in order to determine the optimal location and capacity of the parking lots considering maximization of the profit of electrical distribution companies.
could be modeled as a random variable under long-normal probability density function (PDF) as found by [20]. According to the explanations above, the method of the modeling of the EV owners’ behavior has been completely explained in our previous work [20]. 2.1. Objective function: maximizing the profit of the distribution system operator Our purpose in this paper is to determine the optimal number, location and capacity of EV parking lots to maximize the profit of the distribution system operator. The optimal number of parking lots is the number of the parking lots needed in order to maximize the profit of the distribution system operator. Also, optimal locations of parking lots are places in the network, where if parking lots are established, the profit of the distribution system operator will be maximized. Moreover, optimal capacities of parking lots are the capacities of parking lots which the profit of the distribution system operator will be maximized. It should be noted that the network constraints should be considered for optimal number, locations and capacities of parking lots as well. Therefore, the proposed objective function has been presented as follows:
f 1 þ CO2 þ CO3 Þ f 1 ð CO ProfDSO ¼ ReDSO CoDSO ¼ RE
where ProfDSO , ReDSO and CoDSO are the total profit, the total revenue and the total cost of the distribution system operator, respectively. f 1 Þ and total Total revenue of DSO has been formed in the term ð RE f 1, the cost of DSO has been formed in the sum of three terms CO CO2 and CO3 . f 1 shown in (2), represents the expected value of The term RE income from selling energy to customers and also the electric vehicles charging process in the parking lots. Because of the energy delivery to the customers and providing them with charging and discharging equipment, definite percentage of profit will be devoted to the distribution system operator. In fact, the amount of payments to the distribution system operator is determined according to the exchanged energy and the price of electricity at the time of these exchanges.
1.3. Paper organization The remainder of this paper is organized as follows. In Section 2, the problem formulation of determining the optimal location and the capacity of EV parking lots is presented in three parts: introducing the objective function, charging and discharging scheduling and the problem constraints. Numerical studies and the analysis of the results are discussed in Section 3. Finally, the conclusion is given in Section 4.
2. Formulation In this section, the problem formulation of determining the optimal location and the capacity of EV parking lots is presented in three parts: introducing the objective function, charging and discharging scheduling and defining the problem constraints. The first parameter that should be modeled is the distance that an EV covers. The log-normal distribution would be an appropriate choice to model this parameter [20]. Therefore, this probability distribution function is used to determine the optimal location and capacity of the EV parking lots [20]. The second and the third parameters that should be modeled are the arrival time and the departure time of the EVs. These parameters are modeled by a Gaussian distribution function because this function is the most homogenous to the driving pattern viewpoint. The fourth parameter is the battery’s initial state of charge (SOC). This parameter
ð1Þ
f1 ¼ RE
Ny N ll X XX j t ðCFÞ j Pricet Pi;j t Dt c ð1 þ b1 Þ j¼1
i2Xc t¼1
Nv Ny Nll X XX X j K;t k;t ðCFÞ j X k;t þ EV RaCH Dt CH Pricet ð1 þ b2 Þ p
j¼1
ð2Þ
p2Xp t¼1 k¼1
where Ny is the planning horizon length (year), Nll is the number of K;t is load levels, Npv is the number of EVs in the pth parking lot, RaCH the charging rate of the kth vehicle in the tth load level, and Xp and Xc are the set of parking lots and the set of the customers whom the distribution system provide their consumption loads,
respectively. Also, X k;t EV is a binary variable which shows the status of charging or not charging the kth vehicle in the tth load level and P i;j t is consumption power of the ith customer in the jth year j
and in the tth load level. In addition, Pricet represents the price of purchased electricity from the system in the jth year and the tth load level, Dt k;t CH is the charging duration of the kth vehicle in the tth load level, b1 and b2 are respectively the considered percentages of the profit of the distribution system operator for delivering energy to the customers and providing electric vehicles with charging and discharging equipment [20] and CF is the present value factor. f 1 , depends on the The second part of the objective function, CO cost of discharging EVs and buying electricity from substations which is presented in (3).
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g1 ¼ CO
Ny Nll X XX j j ðCFÞ j Pt;s Pricet Dttc j¼1
where N z;0 Varea is the number of vehicles in the zth zone at the time of establishing the parking lots, czj is the growth percentage of the
s0 2Xs t¼1
i;z
p
Nv Ny N ll X X XX j k;t k;t þ ðCFÞ j Y k;t EV RaDCH Dt DCH Pricet j¼1
ð3Þ
p2Xp t¼1 k¼1
where Xs is the set of substations, Rak;t DCH is the discharging rate of j is the amount of power the kth vehicle in the tth load level and P t;s purchased from the sth substation in the jth year and the tth load k;t level. Also, Dt DCH is the discharging duration of the kth vehicle in k;t the tth load level and Y EV is a binary variable which shows the status of discharging or not discharging the kth vehicle in the tth load level. It should be noted that maximizing the profit of the distribution system operator should not prevent the maximization of the profit of the EV owners. In other words, the profit of the distribution system operator is in the shadow of the maximization of the profit of EV owners and their financial expectations. Therefore, scheduling the charging and discharging of EVs to maximize the profit of the EV owners is necessary. The details related to this scheduling will be discussed in Section 2.2. Obtained optimal powers of charging and discharging resulted from this part are used in calculating g1 . g1 and CO RE
The third part of the objective function is associated with the needed investment for establishing a parking lot including the first term, the cost of buying land, and the second term, the cost regarding construction, and also buying charging and discharging equipment shown in (4). Nz Nz X X z z z CO2 ¼ Spark Pricel þ Pricec C park z¼1
ð4Þ
i;z kj
P 1i;j N v ¼
k¼1
dk;z
" # Ny Nz Nz X X X j z j j j;z CO3 ¼ ðCFÞ Prm C park þ Prr Nv area z¼1
ð5Þ
PNz 1 z ¼ 1 PNvi;j dk;z k¼1 z–i
!
ð7Þ
where N i;j v is the number of vehicles in the jth year and ith zone in which the parking lot does not have enough capacity calculated by (8).
1 1 ! C C BB X Ny Y C C BB Nz i;0 i C BB Ni:j czj C NVarea v ¼ BB C C park C A A @@i ¼ 1 j¼0 00
ð8Þ
i–z k;z
Also, d , the distance of the kth vehicle from the determined bus for establishing parking lot in the zth zone, is calculated by (9). k;z
where Nz is the number of zones, is the capacity of the established parking lot in the zth zone and Pricec is the cost of establishing parking lot and purchasing charging and discharging equipment z for each EV parking lot, Pricel is the price of each square meter of z is the area needed for establishing land in the zth zone and Spark parking lot in the zth zone in term of square meters which is a function of the capacity of the parking lot and the architecture features of the construction such as the number of floors. The fourth part of the objective function, CO3, contains the costs of repair and maintenance of parking lots during the operation shown in (5). As can be seen, these costs contain two parts. The first part is cost of the parking lots maintenance as snow removal depended on the capacity of the parking lot. The second part is cost of the repair for parking lots such as the cost of equipment depreciation associated with the number of arriving EVs [20].
d
¼ jLk Lz j ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðxk xz Þ2 þ ðyk yz Þ2
ð9Þ
where Lk and Lz are the location of the kth vehicle and the location of the determined bus for establishing parking lot in the zth zone, respectively. The set of the geographic areas, in which if a parking lot is established, all of the vehicles in those areas will approach for, is defined as a zone. In this paper, K-means clustering method [23] is used, to classify the distribution system to different zones and determine the border of the zones. Genetic Algorithm [24] is also used to determine the optimal location and capacity of EV parking lots, as in [19,25]. Moreover, the probabilistic model of an EV is considered based on the point estimate method [26]. It should be noted that although the power loss in the distribution system is not directly in the formulation, it is considered indirectly because when the profit is maximized, the power loss is minimized. 2.2. The EVs charging and discharging scheduling
z¼1
where Pr mj is the annual cost of the maintenance of the parking lot for each vehicle in the jth year, Pr rj is the annual cost of the repair for each vehicle and Nj;z Varea is the number of vehicles that arrive at the parking lot in the jth year and the zth zone calculated by (6). In fact, N j;z Varea is the sum of the vehicles from the zth zone and some of the vehicles of other zones in which the parking lots do not have enough capacity to accept all the vehicles of those zones. 20
i;z
with the distance of the vehicle from the parking lot. Therefore, kj is calculated by (7).
z¼1 z C park
j¼1
vehicles in the zth zone and the jth year, and kj represents the percentage of the vehicles that if there is no empty capacity in the parking lot at the ith zone, will approach for the parking lot in the zth zone. It is obvious that the owners of electric vehicles prefer to refer to the nearest parking lot. Therefore, the probability of arrival of excess vehicles of each zone which does not have enough parking lot capacity to the parking lots of other zones has a reverse relation
000
1
1
11
3
! BBB !C 6B C CC 7 Ny Ny Nz Y Y C 6B z;0 BBB X C C 7 i;z C j;z i i;0 B BB C CC z 7 N Varea ¼ min 6 cij þ B czj C N Varea C C park C kj CC;C park 7 6BN Varea BBB A 4@ @@@i ¼ 1 A AA 5 j¼0 j¼0 i–z
ð6Þ
One of the purposes of the EV owners approaching for a parking lot is minimizing the payments. Therefore, the objective function for minimizing the costs of the EV owners is presented in (10). It is obvious that because of the independence of the EV owners from each other, this function should be minimized for each electric vehicle independently.
t kd 1 k;t Min w ¼ m Prkt Pkt Dtk;t gCH X EV þ Y k;t EV ;
gDCH
t¼t ka
8k 2 Xv ;
P > 0; state of charge p < 0;
ð10Þ
state of discharge
where gCH and gDCH are the efficiency of charging and discharging, respectively.
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Besides the minimization of the objective function presented in (10), the following constraints should be met: – The batteries of the electric vehicles cannot be charging and discharging, simultaneously [27]. k;t k;t k;t X k;t EV þ Y EV 6 1; X EV ; Y EV 2 f0; 1g
tk
j X 1 Dt k;t P kt gCH X k;t Y k;t P sockmax EV þ g EV DCH
tk
socka
j X 1 P sockmin þ Dtk;t Pkt gCH X k;t Y k;t EV þ g EV
8tj 2 ft a þ 1; . . . ; td g ð12Þ where SOC ka is the initial state of charge of the kth vehicle. Also, SOC kmin and SOC kmax are the minimum and the maximum possible state of charge of the battery of the kth electric vehicle, respectively. – The sum of charging and discharging powers during the presence of each vehicle in the parking lot equals the difference between the desired final state of charge by the EV owner and the initial state of charge of the vehicle. k
t¼t d X Dtk;t Pkt P sockd socka
ð13Þ
t¼t ka
where SOC kd is the desired final state of charge of the kth vehicle, and is calculated according to (14) [20].
sockd ¼ minð½ld þ rd :Nd :Enk ; sockmax Þ
ð14Þ
where Enk is the amount of energy that the kth electric vehicle needs to cover 1 km. – The injected power or the absorbed power by each vehicle in each time interval has to be in a specific range.
( Pmin 6
8k 2 Xv ;
Pkt
6 Pmax )
Pkt P P min
P kt P Pmax 8t ¼ f1; 2; . . . ; Nll g
where Nbus is the number of all buses and V is the voltage of the bth bus in the tth load level. Also, vmin and vmax are the minimum and the maximum permitted voltages of the buses, respectively. – The capacity of each parking lot for accepting electric vehicles is limited [20]. As there are limitations such as the needed space and the costs of establishing a parking lot, the capacity of each parking lot is limited. z z C park 6 C park;max
DCH
t¼t ka
ð17Þ b,t
– The state of charge of the vehicles in all the time intervals should be between a minimum and a maximum quantity [28].
t¼t ka
lðV b;t Þ þ w rðV b;t Þ 6 v max ; b ¼ 1; 2; . . . ; Nbus ; t ¼ 1; . . . ; Nll lðV b;t Þ w rðV b;t Þ P v min ; b ¼ 1; 2; . . . ; Nbus ; t ¼ 1; . . . ; Nll
ð11Þ
8 k 2 Xv ; 8 t ¼ f1; 2; . . . ; Nll g
socka
is, the more the probability of being in the permitted limit of voltage and current are. – The voltages of buses should be in the permitted limit [20].
ð15Þ
where P min and P max are the minimum and the maximum power that can be exchanged between electric vehicles and the parking lot in each time interval, respectively. Because of similarity with the standard form of linear programming (LP) method, the problem is solved by LP method [29] as [28].
ð18Þ
z where C park;max is the maximum possible capacity for establishing a parking lot in the zth zone. The distribution system operator profit can be only increased in a way that it will not result in EV owners’ welfare reduction below a specific limit, (this limit is determined by the political and economic indicators of each district, by international standards or legislative organs). In order to increase the convenience of the owners of the EVs, the maximum distance of each vehicle from the nearest parking lot should be less than a specific amount.
jLk Ln j 6 Dmax ;
8k 2 Xv
ð19Þ
where Ln is the location of the nearest parking lot to the kth vehicle and Dmax is the maximum permitted distance of the vehicles from the nearest parking lot. The flowchart shown in Fig. 1 demonstrates the procedure of the proposed approach of determining the optimal location and capacity of the EV parking lots, briefly. As is observed, after receiving the input data of the problem, initial responses containing the optimal location and capacity of the parking lots are produced. The acceptability of this response is verified by the satisfaction of the constraint of the maximum permitted distance. In the next step, based on these suggested locations, bordering the distribution system and determining the percentage of the approaching EVs to parking lots from other zones is done by using k-means clustering method. Then, based on these suggested locations, the probabilistic scheduling of charging and discharging the EVs is carried using point estimate method (PEM) probabilistic approach. Linear programming is also implemented and the optimal amounts of charging and discharging powers are calculated. In the next step, the objective function related to the optimization of the profit of the distribution system companies, considering the constraints of the problem, is calculated. To make sure about the satisfaction of the constraints related to the voltages of the buses and the currents of the lines, distribution load flow program is implemented and finally the optimal responses of the proposed approach are extracted.
2.3. Constraints of Parking Lots Planning Problem – The current of each line should be in the permitted limit. For each load level of t, the constraint of line current is considered as bellow [30].
lðIl;t Þ þ w rðIl;t Þ 6 Ilmax ; l 2 X1 ; t ¼ 1; . . . ; Nll
ð16Þ
where Ilmax is the nominal value of the lth line, Il,k is the current of the lth line in the tth load level, Xl is the set of distribution system lines and w is a constant factor that in this paper as [20], is assumed 3. Therefore, with the probability of more than 99%, line currents will be in the permitted limit. In [20] it is proved that the more w
3. Numerical studies and discussion In this paper, in order to verify the effectiveness of the proposed model, the proposed approach has been performed on a 69 node radial system shown in Fig. 2. Also, the figure shows the distribution of EVs in the first year. System and load data are presented in [31]. In this study, as [20], the planning horizon length is 10 years and the annual interest and inflation rates are assumed 5% and 4% respectively. The mutation rate and the crossover rate have been chosen as 0.2 and 0.6 respectively.
M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
Start
Define Input Data
Genetic Algorithm Generating initial solution including capacity and location of EVs parking lots
Is maximum permitted distance criteria satisfied?
No
Yes Determining the way of distributing EVs in the zones where parking lots are located
Determining the borders of the zones by K-means clustering method
Calculating the number of initial EVs in each zone based on the bordering
Designating the percentage of the EVs which approach for each zone
Objective function evaluation Point estimate method Cost minimization of charge and discharge Running the LP program to calculate the amounts of charging and discharging powers
Profit maximization of the distribution system operator
Calculating the objective function using expected and standard deviation values Implementation of load flow using the forward-backward sweep method
Is the stopping criterion satisfied? No Yes Display outputs results such as optimal capacity and location of EVs parking lots, revenues, costs and Profit from the construction of parking lots
End Fig. 1. Flowchart of the proposed approach.
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M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
Number of EVs
1182
75 50 25
Fig. 2. 69 node radial system and distribution of the EVs in the understudy region.
A comparison between the results of the presented approach in [20] and the proposed approach presented in this paper is shown in Table 1. The growth percentage of the EVs is the same in both approaches (10%). At first, the optimal location and capacity of the EV parking lots are determined by the approach presented in [20]. Then amounts of the terms of the costs and incomes are calculated by the knowledge of these locations and capacities. As can be seen, the total profit of establishing parking lots for the electrical distribution companies in this situation, in comparison with that of Ref. [20] has increased. It shows the efficacy of the proposed approach compared to that of the previous presented approaches. Table 2, illustrates the effects of the expected value of the growth percentage of the EVs on the incomes, costs and profits of establishing EVs parking lots. As can be seen, by increasing the growth percentage of EVs, both the incomes and costs of establishing parking lots increase continually. If the growth amount of EVs reaches to a verge limit (verge limit is the limit that if the growth of EVs transcend that, the distribution system will need to establish more parking lots), the rate of increasing of the cost will be more than that of the incomes. This issue will lead to declination of the profit of the electrical distribution companies. As is observed, by increasing the expected value of growth percentage from 2.5 to 10, the total profit increases continually, but by increasing 20% in the number of EVs, because of the need for increasing in the number of the parking lots, costs will face a huge increase and finally, the total profit will be decreased. Also, increasing the expected value of the percentage growth of the EVs from 20% to 30% will lead to an increase of the profits and if the growth percentage grows to 40%, because of the need of establishing new parking lots, the total profit will be decreased. Even it is possible that the growth rate of the costs
makes it impossible for the electrical distribution companies to get to the profit they expect or even recover their own investments. In this condition, naturally there will not be any motivation for further investment in establishing new EV parking lots. Thus, predicting the growth rate of the EVs in the upcoming years is vital to electrical distribution companies. In order to show the importance of the EVs growth percentage accuracy, in this section, the EVs growth percentage is not considered as a probabilistic parameter in the optimal determination of capacity and location of EV parking lots. If the growth percentage of the EVs with the error of 10% is predicted as 5%, in fact, the growth percentage will be between 4.5% and 5.5% and the distribution system can determine the optimal location and capacity of the parking lots based on the amounts which are mentioned above. It is obvious that the more the chosen growth percentage is, the more the risk of the distribution system company will be. In the worst case, the scheduling of the parking lots is based on growth of 5.5% and the real percentage is 4.5%. In fact, there will be more parking lots than the required amounts, and because of the over design, the profit of the distribution system company will decrease as much as 0.7 million dollars. Also, if the real growth percentage is 5/5%, in this case, the maximum profit will be devoted to the distribution system company. On the other hand, the growth percentage of 14 is a critical point because with a little increasing in it, the distribution system will need more parking lots. If the predicted interval for the growth percentage of the EVs with the error of 2%, contains this critical point, in the worst case, the scheduling of the parking lots is based on growth of 14.28% and the real percentage is 13.72%. It can lead to a 1.2 million dollars decreasing in the total profit of the distribution system which is more in compared to the previous case. As can be seen, even by increasing the accuracy compared with that of the previous case (2% instead
Table 1 Comparing the proposed approach and the approach presented in [20]. Results
Method Presented approach in Ref. [20] 29 1537
44 1493
Proposed approach
Optimal location of parking lots Optimal capacity of parking lots f 1 (m$) RE
3 1411 139.97
53 1404
68 821
4 1276 147.73
f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
51.76
57.96
43.78 0.259 44.17
41.13 0.261 48.38
31 1283
44 1449
51 1184
57 1421
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M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184 Table 2 Investigating the impacts of electric vehicles growth. Percentage of vehicles growth (%)
2.5
5
7
10
20
30
40
60
f 1 (m$) RE f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
135.13
138.42
143.62
148.48
163.84
179.64
201.74
244.98
53.60
54.53
56.077
58.19
64.91
70.21
79.145
94.73
42.04 0.247 39.24
43.73 0.251 39.9
45.88 0.261 41.4
47.22 0.269 42.8
56.14 0.293 42.5
57.01 0.325 52.1
70.19 0.365 52.04
79.48 0.416 67.35
of 10%), the total profit will be reduced further. Thus, if the growth percentage of the EVs is close to the critical point, the error can lead to decreasing the profit of the distribution system company with more slopes. Therefore, the accurate prediction of the growth percentage of EVs, particularly near the critical point, is vital to the distribution system company in order to reach the maximum profit. Another considerable point is that by increasing the number of established parking lots in distribution systems, the profit of the distribution system operator will not necessarily increases. The effect of different growth percentages of EVs on the optimal location and capacity of the parking lots is shown in Table 3. As is evident from Table 3, by increasing the growth rate of the EVs from 10% to 20%, the number of parking lots in need, will increase from 6 to 7 in order to maintain the welfare of the EV owners. Also, increasing the number of EVs from 30% to 40% will lead to the increasing the parking lots from 7 to 8. As a matter of fact, the presented results in Table 3 also emphasizes that the reason for increasing costs and decreasing profits in Table 2 is
Table 3 Investigating the impacts of electric vehicles growth on parking lot capacity and location.
increasing of the number of the EV parking lots. Furthermore, the sum of the capacities of the established parking lots in the distribution system increases by increasing the number of EVs. Thus, the growth rate of EVs affects the locations, number, capacities and the profit of establishing parking lots. Table 4 shows the comparison of the optimal locations and capacities, incomes, costs and total profits of establishing parking lots in two scenarios with and without considering the welfare of the EVs owners. As can be seen, by considering the constraint of the maximum permitted distance of EVs from the nearest parking lot in order to increase the welfare of the EVs owners, the number of EV parking lots has increased from 4 to 6. Also, it is observed that the incomes and costs of the power exchange are the same in the two scenarios. The reason is that the sum of the capacities parking lots is equal in both scenarios, and also the price of electric energy in all parking lots (in one year and equal load level), is equal. Nevertheless, it is observed that the profit of establishing parking lots in the second scenario, because of increasing in costs of construction of new parking lots, has been decreased. The reason is that the excess parking lots are established in the zones, in which the price of land is high. Thus increasing the welfare of the EV owners will lead to decreasing the profit of the electrical distribution companies. Indeed, it should be noted that the task of the distribution system operator is to improve the facilities of the system, to increase the welfare of the customers and the EV owners. However the maximization of the income of the distribution system operator should not overshadow the welfare of the EV owners.
Percentage of vehicles growth (%)
Optimal location of parking lots
2.5
4 1022
26 798
44 1407
51 1134
57 864
69 937
– –
– –
5
4 1057
26 811
44 1448
51 1147
57 891
69 958
– –
– –
4. Conclusion
7
4 1076
26 833
44 1469
51 1171
57 911
69 972
– –
– –
10
3 848
20 942
32 1319
40 934
65 1131
67 1439
– –
– –
20
4 859
24 1392
34 786
46 891
48 1042
55 1270
69 974
– –
30
4 903
24 1471
34 887
46 957
48 1162
55 1333
69 1102
– –
40
3 1141
14 1322
23 1211
32 1047
37 872
49 920
51 735
62 1168
60
3 1307
14 1482
23 1391
32 1119
37 937
49 1145
51 913
62 1324
In this paper, a new approach is presented to determine the optimal location and capacity of EV parking lots in distribution systems. Considering the constraint of the maximum amount of permitted distance from the nearest parking lot in order to increase the welfare of the EV owners will lead to increasing the number of parking lots and as a result, this will decrease the profit of the distribution system companies. Since the efforts are made to improve the facilities of the distribution systems and the welfare of the EV owners is one of the main priorities of distribution systems, state of the welfare of the EV owners should always be considered even if it leads to decreasing the profit of the distribution system companies.
Optimal capacity of parking lots
Table 4 Consideration of welfare of electric vehicles owners. Results
Scenario 1: without considering the welfare of the EVs owners
Scenario 2: with considering the welfare of the EVs owners
Optimal location of parking lots Optimal capacity of parking lots f 1 (m$) RE
4 1719 146.03
4 1074 146.03
f 1 (m$) CO CO2 (m$) CO3 (m$) Total profit (m$)
57.12
57.12
40.78 0.261 47.869
46.55 0.265 42.095
59 1491
44 1725
69 1489
26 833
44 1467
51 1171
57 911
69 968
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M.A. Kazemi et al. / Applied Energy 179 (2016) 1176–1184
Furthermore, it is observed that by increasing the growth percentage of the EVs, as a result of increasing the number of EVs and capacities of the established parking lots in the distribution system, the profit of the distribution system operator will not necessarily increase. It is possible that the amount of increasing of the growth percentage of the EVs leads to the need of establishing more parking lots in the distribution system, whilst the price of establishing parking lots is higher. Thus, the rate of increasing the costs will be more than that of the incomes and this will lead to decreasing the profit of establishing parking lots. If the intervals of the prediction of the growth percentage of EVs contain critical points, the amount of profit deduction will be more compared to the situation in which these intervals contain none of these critical points. Thus, deciding about establishing parking lots in this situation is very sensitive due to the high risks it has. In fact, if the predicted growth percentage is more than the real amount, because of excessive initial investment, the profit will decrease. Therefore, the more the difference in between the predicted amount and the real amount is, the less the profit will be. Also, if the predicted growth percentage is less than the real amount, we can say that the distribution system operator would not be able to gain all of possible amount of profit. In other words, a part of the profit will be lost. In this state, the more the difference in between the predicted amount and the real amount is, the more the loss of the profit will be. So, decreasing the error of prediction of the expected amount of the growth percentage of EVs in the upcoming years is a vital factor which leads to better decision making for the electrical distribution company for their possible investment in order to establish new parking lots. With the variation in the growth percentage of the EVs, the optimal location, capacity and number of the EV parking lots will vary. The sum of the capacities of the established parking lots in the distribution system will sequentially increase by increasing the growth percentage of the EVs, but it is possible that the optimal number and locations of the parking lots do not change and stay constant. However, the more increment of the growth percentage of the EVs will lead to establishment of more parking lots and change their locations. References [1] Su, Chun-Lien, et al. Optimal electric vehicle charging stations placement in distribution systems. In: Industrial electronics society, IECON 2013-39th annual conference of the IEEE. [2] Hajimiragha AH, Canizares CA, Fowler MW, Moazeni S, Elkamel A. A robust optimization approach for planning the transition to plug-in hybrid electric vehicles. IEEE Trans Power Syst 2011;26:2264–74. [3] Bunyamin Y, Uzunoglu M. A double-layer smart charging strategy of electric vehicles taking routing and charge scheduling into account. Appl Energy 2016;167:407–19. [4] Nansai K, Tohno S, Kono M, Kasahara M, Moriguchi Y. Life-cycle analysis of charging infrastructure for electric vehicles. Appl Energy 2001;70:251–65. [5] Wang, wu Zheng, Tan Zhenxia, Xu Hui. Location model and algorithm of public parking facilities. 2008 international conference on intelligent computation technology and automation (ICICTA), vol. 1. IEEE; 2008. [6] Sadeghi-Barzani P, Rajabi-Ghahnavieh A, Kazemi-Karegar H. Optimal fast charging station placing and sizing. Appl Energy 2014;125:289–99. [7] Diaz-Chavez R, Woods J, San Román TG, Momber I, Abbad MR, Sánchez Miralles Á. Regulatory framework and business models for charging plug-in electric vehicles: infrastructure, agents, and commercial relationships. Energy Policy 2011;39:6360–75.
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