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Optimal Deployment of Electric Vehicles’ Fast-Charging Stations

Optimal Deployment of Electric Vehicles’ Fast-Charging Stations Hindawi Journal of Advanced Transportation Volume 2023, Article ID 6103796, 14 pages https://doi.org/10.1155/2023/6103796 Research Article 1,2,3 2 4 5 Irfan Ullah , Kai Liu , Safa Bhar Layeb , Alessandro Severino , and Arshad Jamal Transportation Engineering College, Dalian Maritime University, Dalian 116026, China School of Transportation and Logistics, Dalian University of Technology, Dalian 116024, China Department of Business and Administration, ILMA University, Karachi, Pakistan LR-OASIS, National Engineering School of Tunis, University of Tunis El Manar, Tunis, Tunisia Department of Civil Engineering and Architecture, University of Catania, Catania 95123, Italy Transportation and Trafc Engineering Department, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31451, Saudi Arabia Correspondence should be addressed to Irfan Ullah; irfanktk@mail.dlut.edu.cn Received 26 August 2022; Revised 7 November 2022; Accepted 22 February 2023; Published 3 April 2023 Academic Editor: Lei Wang Copyright © 2023 Irfan Ullah et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. As climate change has become a pressing concern, promoting electric vehicles’ (EVs) usage has emerged as a popular response to the pollution caused by fossil-fuel automobiles. Locating charging stations in areas with an expanding charging infrastructure is crucial to the accessibility and future success of EVs. Nonetheless, suitable planning and deployment for EV fast-charging stations is one of the most critical determinants for large-scale EV adoption. Installing charging stations in existing fuel/gas stations in the city may be an efective way to persuade people to adopt EVs. In this paper, we aim to optimally locate a fast-charging station in an existing gas station in the real-world scenario of Aichi Prefecture, Japan. Te purpose is to locate and size fast-charging stations in such ways that drivers can get access to these charging facilities within a rational driving range while considering real-world constraints. Furthermore, we include the investment cost and the EVs users’ convenience cost. Tis problem is formulated by fve integer linear programming using a weighted set covering models. Te developed model determines where to locate charging stations as well as how many chargers should be installed in each charging station. Te experimental results demonstrate that an appropriate location scheme can be obtained using the model M . A computational experiment identifes the best infrastructure solutions for policymakers to consider in the context of growing environmental policies. diverse urban transport system [7–9]. With progressions in 1. Introduction communication and technology, a green transport system Climate change has been identifed as a major concern provides one of the most efective solutions in combating air nowadays, which is primarily produced by GHG emissions. pollution, decreasing congestion, and easing the fuel crisis Te global warming is expected to rise by more than 2 C [10, 11]. above preindustrial levels if no further steps are made to cut Green transportation is essential to address climate GHG emissions [1, 2]. In 2016, the transport sector con- change mitigation since they minimize CO and other tributed approximately 25% of worldwide emissions [3]. pollutants that are frequently used in conventional vehicles Although energy and fuel consumption signifcantly impact [12, 13]. Amongst all green transportation choices, e-bikes, the global climate change, the usage and energy production shared mobility, electric vehicles (EVs), and bus rapid transit themselves are fraught with difculties [4, 5]. In 2012, the are an intriguing option for addressing the aforementioned transport sector’s energy demand increased from 23% to challenges [14, 15]. With the call for zero-emission vehicles 28% [6]. As a result, the notion of green transport is evolving, and improved battery technologies, EVs are a solid con- which refers to an easy, efcient, safe, low polluting, and tender to replace the gasoline-driven automobile. Aside 2 Journal of Advanced Transportation practitioners. In the literature, the EVCS location issues are from contributing to energy security and sustainable envi- ronmental, EVs provide substantial benefts to users in terms categorized into two groups, namely, intracity and intercity, depending on the type of travel the charging amenities of fuel economy and cost savings [16]. Because of these reasons, the EV market has seen commercial success re- intend to support. Te intercity problem is primarily as- cently. Several state and governmental entities have also sociated with the range anxiety issue, particularly for longer established policies to encourage EV adoption, further ac- (intercity) trips, whereas intracity problems are more con- celerating the growth. Despite their benefts, EVs have not cerned with the limited accessibility of charging in- gained widespread acceptance among the public. Due to the frastructure within the boundary of metropolitan centers. In inadequate and limited charging infrastructure and the intercity problem, the charger can be installed anywhere on the highway, and this problem can solve the fow-capturing shorter driving range, EVs drivers may have range anxiety or the concern that the energy storage may run out before they refueling problem and the charger location depending on the trafc volume of origin-destination pair and EVs range get to their destination [17, 18]. In order to alleviate the drivers’ range anxiety and increase the usage of EVs, there is [26]. Te authors proposed a conceptual model to examine EVs travel throughout a long route for intercity EVs trips a need for adequate planning for charging stations to help drivers arrive safely at their destination. [25]. Te goal of their proposed model is to choose the Charging infrastructures are becoming crucial compo- battery size and charge capacity that will satisfy a particular nents for adopting EVs, connected to vehicle technology and level of service while minimizing the total social cost. efciency and the accessibility of a reliable power supply to Similarly, the authors employed a continuous facility loca- charging stations [12]. It is also tied with the increased tion approach for optimizing EVs charging station place- electricity demand in other sectors [19]. In this context, in- ment for highway corridors [27]. Teir model did not considere the cost of the battery. Considering demand frastructure issues include charging station distribution planning, electrical grid resistance, dependability, and con- uncertainty, their goal was to augment the private charging infrastructure with government-subsidized charging sumption patterns used to determine pricing and incentive policies. Performance and cost barriers are impeding the stations. In the intracity problem, the charger can be installed adoption of EVs [20]. Furthermore, travel through EVs may become unsustainable due to the limited availability of anywhere in the city. To locate EVCS in the city, the discrete charging stations [21], nonoptimal location in urban sur- network model was chosen, since stations can only be lo- roundings [22], inconsistent power fow, and amount of cated at discrete locations, such as existing service stations or energy taken from the primary electricity grid not initially parking lots [26]. Tere are two diferent methods for de- catered for this use. Tus, it is critical to identify occupation termining where charging stations should be placed. Te patterns and, consequently, such issues may be resolved by frst involves the use of classical facility location methods such as set-covering problems, with the overall goal of re- employing charging profles [23]. EVs recharge is a new type of electrical demand that is challenging to precisely estimate, ducing the number of chargers required so that all consumer can reach the charging station within a specifc time and particularly when the vehicle penetration is still low and a large data set is difcult to obtain. Another signifcant driving distance. Te second method is the multicriteria barrier to increasing EVs market share is the inconvenience decision making (MCDM) approach based on geospatial faced due to the shortage of the public charging infrastructure analysis [28]. In MCDM, individual potential location is and the limited range of batteries. Proper charging station assessed based on various criteria, including the cost of land, planning could help the motorists in this aspect. parking lots availability, and the location’s slope. Each EVs need comparatively prolonged charging times than subcategory is scored, and location decision is based on each refueling internal compaction engine vehicles (ICEVs). candidate’s cumulative score. Frade et al. (2011) attempted Tree types of charging stations are currently available, each to solve the intracity EVs' charging location problem by employing the covering model to maximize the number of having a diferent range of the charging power supply. Level- I and level-II chargers have a maximum charging power of customers served by each stations and maintaining a certain level of coverage provided by the charging station [29]. about 1.5 kW and 10 kW, respectively; however, Level-III chargers have to charge powers up to 60–150 kW because Dashora et al. (2010) suggested an early intracity EV location they need high voltage [24]. Level-III chargers are more model intending to reduce the overall cost by converting expensive to construct and can only be found in commercial parking lots to EVCS [30]. Te cost of converting a parking places. A standard EV would still require more than lot includes installing charging devices, solar shading, and 30 minutes even with a Level-III charger, which is signif- connecting these parking lots to the nearby grid stations. cantly longer than refueling ICEVs [25]. Level-I and level-II Chen et al. (2013) used a similar model to minimize the walking distance [31]. He et al. (2013) consider the in- chargers usually take several hours to charge an EV fully. As a result, an appealing alternative is placing charging stations teractions between the placement of EVCS, the operation of power networks, and the selection of route and destination at the EV driver’s house, ofce, or other locations where they are expected to stay for a long time (recreational facilities, choices [32]. Ahmad et al. (2017) developed an optimal framework for hybrid EVs based on the switching process shopping malls). Electric vehicle charging station (EVCS) planning issues from one trading place to another depending on the max- have been extensively investigated over the last decade and imum selling (i.e., discharging of EVs) and minimum continue to catch the attention of both researchers and purchasing (i.e., charging of EVs) energy cost [33]. Based on Journal of Advanced Transportation 3 deployment of solar power charging station considering these results, the aggregator paid 4.22% lesser energy cost than day-ahead while 4.65% and 9.68% lesser than DISCOM distribution network. Te outcomes are compared to the teaching-learning-based optimization and the Jaya algo- and the bilateral based trading platform. So far, existing research studies have examined the rithm; the comparison demonstrates the superiority of the performance of several optimization strategies for solving MCSO [47]. the optimal location of the EVCS problem. Various re- According to the Liao et al. (2016), range anxiety, EVCS searchers have already investigated the most efcient availability, and charging duration time are the three major placement of EVCS in distribution lines using various drawbacks for faster EV adoption [48]. Furthermore, easy computational techniques such as evolutionary algorithms access to EVCS directly infuences on EVs' penetration levels. Tis is due to the fact that ICEVs is viewed as [34], Jaya algorithm [35], particle swarm optimization (PSO) [36], and genetic algorithm (GA) [37]. Mostly, the problem a convenience purchase and the user do not prefer to plan ahead to fnd refueling stations. Consequently, fast-charging is the same, and it is based mainly on the availability of trafc fow data and the total number of EVs in the observed area. stations serve as “emergency service” amenities, and it is essential to consider consumers' behavior while locating Xiong et al. (2017) proposed the optimal location of EVCS considering distribution network and city trafc [38]. Te charging stations. Meanwhile, the fuel/gas retail industry is objective is minimizing energy not supplied while also well-established and optimized to serve vehicles, and these considering charging station costs. Zeb et al. (2020) locations are natural candidates for installing fast chargers. employed a method for the optimal deployment of the solar To address the abovementioned issues, the following con- power-based charging station considering diferent charging tributions have been made. levels with minimal losses and installation costs [39]. Te current study aims to develop a mathematical model for minimizing the total cost by optimizing the location Nevertheless, the constraints incorporated within the optimization problem vary, such as the type of EVCS, planning of charging stations, their sizing, and the number of total chargers within each charging station. Te charging courage routes, land cost, maintenance cost, fxed cost, electric grid impact, and trafc fow [40]. Shahraki et al. station opening capital cost and the user’s convenience cost (defned by station access cost) are the two essential con- (2015) proposed the application of mixed-integer linear programming (MILP) for the optimal placing of EVCS based siderations while planning for an optimal charging location. on real-world data of vehicle travel patterns [41]. Te Tis study proposes fve diferent integer linear pro- fndings indicate that an appropriate charging station gramming (ILP) models to address the problem of EVCS placement can result in signifcant improvements. Ge et al. location and sizing. Te proposed models may be grouped (2011) employed a GA for sizing and locating EVs’ charging under two main categories. First, ILP models are solely used stations using grid partitioning [42]. Te main constraints for chargers location decisions; second, ILP models consider both location and sizing decisions. Both categories are considered are charging station capacity and trafc density. An equilibrium modeling framework was proposed by He distinguished by defnite decision variables, relevant real- world constraints, and a corresponding objective function. et al. (2013) to capture the interactions between the avail- ability of charging opportunities, destination, electricity Te remainder of the paper is as follows. Section 2 details prices, and EVs route choices at regional power transmission the proposed mathematical models. Section 3 reports the and transportation networks [32]. Te paper’s objective was main results of the conducted computational experimen- to consider the constraints of power and transportation tation. Section 4 concludes and provides future research network. Dong et al. (2014) employed GA for EVCS, an avenues. activity-based technique using multitravel data [43]. Te fnding suggested that the placement of public chargers at 2. Model Formulation popular sites with some adequate infrastructure investment could considerably increase electric miles and trips. Diferent covering models (optimization models) are pro- Liu et al. (2012) used a modifed primal-dualinterior- posed. Te objective is to minimize various formulations of point algorithm to select an appropriate location for EVCS objective costs while satisfying all demands. Te suggested placement, taking environmental factors and EVs’ service models deal with the planning of EVs charging network for radius to solve the problem [44]. Tey considered cost as an a metropolitan region based solely on an existing gas station. objective function. Wang et al. (2013) employed data en- velope analysis for the EVCS problem considering the multiobjective function, power loss, EVs fow, and voltage 2.1. Assumption. Te study was based on the following main deviation [45]. Zhang et al. (2015) employed PSO for op- assumptions for simplicity: timal location planning of EVCS [36]. Te placement (i) For EV users, only daytime charging is considered. problem for fast-charging stations and public parking lots Tis appears to be convenient for a workplace in an was developed while the cost as the objective functions. Yao urban region. et al. (2014) developed a multiobjective evolutionary algo- rithm to locate fast-charging stations considering the (ii) Only fast charging stations are considered, and each multiobjective function, EV fow, cost, and energy losses charger may provide service to multiple EVs, as fast [46]. Ahmad et al. (2021) presented a modifed chicken charging is usually considered the best solution for swarm optimization (MCSO) approach for optimal gas stations. 4 Journal of Advanced Transportation (iii) Access to installed chargers within a reasonable travel distance is necessary for EV drivers. (iv) Each EV can be charged to a single charging station. 2.2. Network Planning. Identifying potential locations for future charging stations is an essential component of this research. Based on the previous research studies [49, 50], the existing gas stations in the neighborhood could be suitable places for the charging station. Google Maps is used to acquire geographic information. Table 1 contains a list of possible locations. In Figure 1, we found 18 possible charging stations. After the 18 candidates for potential lo- cations had been identifed, an adjacency graph is created in Figure 2. Based on the graph theory, a linked undirected graph G � (V, E) has been created, with V � (1, . . . ., n) indicating a set of nodes representing the feasible charging, Figure 1: Proposed EVCS location (Google Map). and E � (1, . . . , m) is the set of edges which represents the possible connections between charging stations (n � 18). Te distance between the locations is used to weight each edge (m = 54). Te Cartesian distance in each station’s neighborhood was determined and noted as d (i, j ∈ V) i,j denoted the distance between locations i and j. Table 2 provides the distance matrix. 2.3. Linear Programming Models. Diferent models might be used to optimize the installed resources. Tis section con- tains a description of these proposed models. Te location of installed stations, their size, and where to charge are all considerations made at the scope level. Users of not-yet- placed stations should charge within a reasonable radius R of an installed station. Apart from assuring a service coverage distance, these models minimize various costs while ad- hering to appropriate constraints. In this section, we look at two decision-based (location only and location and sizing) ILP models. Te frst two models focused on only location Figure 2: Te proposed graph of adjacency (Google Map). and last three models focused on both location and sizing. 2.3.1. ILP Models Considering an Only Location. Te frst x ∈ {0, 1}∀i ∈ V. (3) class of ILP models used an NP-hard set covering problem [51]. For that purpose, we defne a binary variable x for each Te objective function shown in equation (1) [19], which location i ∈ V, which takes the value 1 for an EVCS in- represents the number of stations installed, is minimized in stallation at location i; otherwise, 0. R represents a constant this model. Constraint (2) establishes the coverage radius for coverage radius that denotes the EVs user’s tolerable dis- the accessibility of EVs' users. Te constraints conditions tance while looking for a charging station. Ten, the in- shown in equation (3) indicate the binary restraints on x termediate constant is utilized. Let a (i, j ∈ V) be a binary variables. Te M model minimizes the total number of i,j constant which takes the value 1 if d ≤ V; otherwise, 0, and installed stations. It refers to minimize the total numbers of i,j d is the same as described in the preceding section. As charging station in the proposed area. Based on set covering i,j a result, the model M can be obtained as follows: 1 combinatorial optimization models [36], the M model is useful when the cost of installation is fxed from one station M : Minimize 􏽘 x , 1 i (1) to the next. For example, under normal service operation of iϵV the station network, the charger cost is somehow low relative to the opening cost. We add f (i ∈ V) a size-independent Subject to: cost of opening a charging station at each possible location i (2) 􏽘 α x ≥ 1; ∀j ∈ V, i,j i to account for the infrastructure opening cost. It is the cost of iϵV converting a gas station into EV compatible lot, specifcally Journal of Advanced Transportation 5 Table 1: Attributes of a potential location for EVCS (Google Map) [19]. Opening cost Indices (i) Type Names Coordinates Capacity (c ) (f ) $ 1 Gas station Oguchitoyota 35.322687, 136.888781 16 2210 2 Gas station Toho 35.292428, 136.909384 14 2170 3 Gas station Jeieesuesu 35.284581, 136.80638 12 1990 4 Gas station Consulate 35.189240, 136.892905 17 2150 5 Gas station Meihokogyo 35.189240, 136.886038 12 2205 6 Gas station Daiko 35.133104, 136.916251 17 1912 7 Gas station Yuni 35.08142, 137.008261 13 1890 8 Gas station Kondosh 35.112885, 137.131858 11 2150 9 Gas station Idemitsu 35.062318, 137.148337 16 2090 10 Gas station Uny 1 34.992595, 136.850333 15 2170 11 Gas station Uny 2 34.909300, 136.829734 12 1930 12 Gas station Centrair 34.885647, 136.811881 14 2010 13 Gas station Uny 3 34.893532, 136.909384 11 2075 14 Gas station Utsumi 34.762766, 136.866812 14 2113 15 Gas station Eneos 34.875618, 137.048192 19 2203 16 Gas station Casyal 34.865367, 137.321372 18 2119 17 Gas station Solato 34.865367, 137.321372 11 1999 18 Gas station Shitara 35.121872, 137.572684 12 1901 6 Journal of Advanced Transportation Table 2: Te distance among possible charging stations in (km). Indices 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 0 9.21 6.4 17.2 18.5 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 2 9.21 0 8.9 11.1 16.3 17.1 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 3 6.4 8.9 0 13.7 14.2 20.3 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 4 17.2 11.1 13.7 0 6.7 7.2 16.4 24.1 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 5 ∞ 16.3 14.2 6.7 0 9.4 20.2 29.4 32.4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 6 ∞ 17.1 20.3 7.2 9.4 0 11.5 19.5 22.9 17.4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 7 ∞ ∞ ∞ 16.4 20.2 19.5 0 12.1 13.4 17.41 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 8 ∞ ∞ ∞ 24.1 28.4 19.5 12.1 0 6.9 40 29.3 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 9 ∞ ∞ ∞ ∞ 32.4 22.9 13.4 6.9 0 28 ∞ ∞ 28.3 ∞ 21.1 26.9 31.9 39.5 10 ∞ ∞ ∞ ∞ ∞ 17.4 17.41 40 28 0 9 11.1 11.3 ∞ ∞ ∞ ∞ ∞ 11 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 29.3 ∞ 9 0 3.4 7.6 ∞ 20.9 ∞ ∞ ∞ 12 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 11.1 3.4 0 9.1 14.7 21.5 ∞ ∞ ∞ 13 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 28.3 11.3 7.6 9.1 0 14.4 11.4 ∞ ∞ ∞ 14 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 14.7 14.4 0 18.9 41.8 47.4 ∞ 15 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 21.1 ∞ ∞ 20.9 ∞ 21.5 11.4 0 24.3 30.8 ∞ 16 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 26.9 ∞ ∞ ∞ ∞ 41.8 24.3 0 6.6 36.4 17 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 31.9 ∞ ∞ ∞ ∞ 47.4 30.8 6.6 0 33.6 18 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 39.5 6.6 ∞ ∞ ∞ ∞ ∞ ∞ 33.6 0 the equipment and administrative expenditures [52]. When one hour, and s represents the entire charger service time. the accommodation capacity for all the possible locations is Te service rate is frstly introduced in the review study [53]. fxed, the size-dependent costs are constant, and then the Every location i ∈ V might be considered a possible con- model is focused on minimizing only the opening costs. As struction place for charging stations as well as the centroid of a result, the model M is formulated as follows: territory for EVs’ drivers. Here, two new decision variables are also introduced. Defning every location (i ∈ V) as M : Minimize 􏽘 f x , 2 i i (4) a non-negative integer variable n that denotes the number of iϵV total chargers installed in each location i. Defning a binary variable y , which is set to 1 if the EV from ith location i are ij Subject to: charged at jth location. As a result, the third ILP model M (5) 􏽘 α x ≥ 1; ∀j ∈ V, is as follows: i,j i iϵV M minimize 􏽘 f x + u n , 3 i i i i (8) x ∈ {0, 1}∀i ∈ V. (6) iϵV Te objective function (4) reduces and minimizes the Subject to: overall cost of all installed stations to the lowest possible (9) 􏽘 Y � 1; ∀j ∈ V, value as investigated in [52]. Constraint (5) states that i,j iϵV a minimum of 1 station on a radius R is installed for every location j (location j included), and constraint (6) expresses x ≥ Y ; ∀i, j ∈ V, (10) j i,j the variable nature. x ≤ n ≤ c x , ∀i ∈ V, (11) i i i i 2.3.2. ILP Models Considering Both Locations and Sizing. Te focus of the second ILP model is to develop suitable 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j (12) station sizes, in addition to identifying charging station iϵV locations. To begin, we assign the following numbers to individual feasible location i ∈ V, (i) a capacity c , which d Y ≤ R; ∀i, j ∈ V, (13) i,j i,j represents the maximum chargers numbers that may be installed concerning the location station capacity, (ii) price x ∈ {0, 1}; ∀i ∈ V, (14) per unit for installing a charger, represented by u , and (iii) fnally, a demand m that represents the number of EVs that n ∈ N; ∀i ∈ V, (15) can use the location i. Te maximum number of EVs served by a charger is introduced ∅, and its formulation is shown in equation (7) [19]. Y ∈ {0, 1}; ∀i, j ∈ V. (16) i,j ∅ � λ ∗ s . (7) Te objective function is shown in (8) for the M model that aims to optimize (minimize) charger installation and In the abovementioned relation, where λ implies the service rate or the number of EVs that could be charged in capital costs. Constraint (9) requires that all EVs be assigned Journal of Advanced Transportation 7 to a specifc EVCS. Constraint (10) defnes that EVs can only equations are the same as the previous model (M ). Each be charged in location j ∈ V if this site is chosen for ac- user’s preferences for station installation and access cost are commodating a charging station. Constraint (11) stipulates refected in the weights assigned to each station. Terefore, that for the chosen station, a minimum one charger must be we suggest that the preceding model can be improved by installed, with the total number of chargers not exceeding including the total construction costs of a station. Finally, the the station’s capacity. If a station is not specifed within it, no model M is introduced. chargers are deployed. Constraint (12) requires that all EV owners who prefer charging their vehicles at a selected lo- M minimizeω 􏽘 f x + u n􏼁 ω φ 􏽘 m 􏽘 d y 5 1 i i i i 2 i i,j i,j, iϵV iϵV iϵV cation should be less than the number of available service chargers. Constraint (13) denotes that the EV task from Subject to: a selected position (i ∈ V) to location (j ∈ V) is feasible if 􏽘 Y � 1; ∀j ∈ V, i,j only the provided distance between stations is less than the iϵV tolerance radius. Lastly, (14) and (15) show the integrality x ≥ Y ; ∀i, j ∈ V, j i,j constraints and constraint (16) are the non-negative integer variables n. x ≤ n ≤ c x , ∀i ∈ V, i i i i Terefore, the main focus is to minimize the charging 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j infrastructure installation costs. Following that, it is also iϵV essential to consider the access cost. More specifcally, the d Y ≤ R; ∀i, j ∈ V, travel cost was also included since EVs owners can drive i,j i,j from one location to another to fnd a suitable charging x ∈ {0, 1}; ∀i ∈ V, facility for their vehicles. Zhu et al. (2016) frst suggested this 2 n ∈ N; ∀i ∈ V, aspect in their analysis of a 60-km Beijing metropolitan region because the charging station is far from the user’s Y ∈ {0, 1}; ∀i, j ∈ V. i,j workplace [49]. Tey believe that EV drivers may walk and (20) take a cab or bus to get from one location to other. In our study, we consider only walking to get into the possible As in [54], model M corresponds to model M as 3 5 charging station. Indeed, EV users are unlikely to take a cab a particular case under the condition where ω = 1 and ω = 0 1 2 or bus from their destinations to the charging station. Te estimated cost of each walked kilometer is denoted by φ, the 3. Numerical Experiments walking cost, which is determined in equation (17) as in- vestigated in [52] After presenting the case study, the results for the base and h recommended models are discussed and compared. After (17) that, an experimental and comprehensive sensitivity analysis φ � , of the proposed ILP models was carried out to determine the s h sensitivity of the model to various cost components and also where W is the average walking speed and W is the average to other variables. Tis experiment was conducted on Intel hourly wage of an EV owner. As a result, model M is as Core I i5-8400 CPU@2.80 GHz (6CPUs) desktop with 12 GB follows: RAM. Te optimization programming language (OPL) was M minimize ω 􏽘 u n + ω φ 􏽘 m 􏽘 d y used to code the fve ILP models, and the general MIP solver 4 1 i i 2 i i,j i,j, (18) iϵV iϵV iϵV (IBM Cplex, version 12.6) was used to solve them. It is worth noting that all of the models found an optimal location in less than 30 seconds of the CPU time. Subject to: 􏽘 Y � 1; ∀j ∈ V, i,j 3.1. Parameters Setting. Using the following experiment, the iϵV cost of the deployed charger is assumed to be constant and x ≥ Y ; ∀i, j ∈ V, j i,j not dependent on the installation location. As per the previous studies, u (i ∈ V) is used as 56,000 [52, 55]. Te x ≤ n ≤ c x , ∀i ∈ V, i i i i (19) charging demand is expected to be uniformly distributed 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j between each charging station. Terefore, m (i ∈ V) is iϵV considered fxed at 13 based on [49]. Equation (7) specifes d Y ≤ R; ∀i, j ∈ V, i,j i,j a charger service rate of 3 EVs for a unit hour and a charger’s service duration of 12 hours during a day. Te average x ∈ {0, 1}; ∀i ∈ V, hourly wage W is $17/hour. It is calculated by dividing the n ∈ N; ∀i ∈ V, mean monthly wage ($3000) of an EV owner by accumulated Y ∈ {0, 1}; ∀i, j ∈ V, i,j worked hours in a month. An average walking speed is assumed to be 5 km/h [52, 56]. For M and M , models 4 5 where ω and ω are non-negative weights. Te objective equal emphasis is placed for the station and user access costs 1 2 (18) is to minimize the total weighted costs. Te remaining by setting out the ω � ω � 0.5. 1 2 8 Journal of Advanced Transportation Table 3: Te impact of the coverage radius on the results of models M and M . 1 2 Model M Model M 1 2 R (km) Number of stations Cost $ Number of stations Cost $ 0 18 37,287 18 37,287 2 18 37,287 18 37,287 4 17 35,277 17 35,277 6 17 35,277 17 35,277 8 10 20,836 10 20,436 10 9 18,666 9 18,028 12 7 14,440 7 14,025 14 7 14,180 7 13,825 16 6 11,887 6 11,767 5000 0 0 2 4 6 8 10 12 14 16 R (KM) M1 Cost ($) M2 Cost ($) Number of station Figure 3: Models M1 and M2 output variation. 3.2. Sensitivity Analysis charging stations and numbers of the charger are 5 and 16, respectively. However, based on model M , which does not 3.2.1. Coverage Radius Impact. We focused on the coverage include the station opening costs, 10 stations should be radius (R) to investigate its impact and variation on the chosen for nearly half the cost of those shown by model M . deployment of the optimal infrastructure for each ILP Te number of chargers are same for models M , M and 3 4, model’s output. Te tolerable distance R range is computed M because the charging demand is uniformly distributed. and ranged between 0 and 16 km. Table 3 represents the Moreover, in model M the high price is attributable to the 5, models M and M which simply outputs only location 1 2 user’s access cost. Te evolution of models M , M and M 3 4, 5 decisions. Te tables show the numbers of charging stations outputs is shown in Figures 4–6 and corresponding opening costs. Taking R = 1 km corre- sponds to establishing an EVCS in every available place, resulting in the number of charging stations being = 18. 3.2.2. Impact of Charging Time. EVs fast charging tech- Moreover, raising the R-value is associated with reduced nology is transforming speedily, and the current study aims opening costs and the number of locations selected. Up to to investigate the impact of charging time change on the 16 km, the numbers of charging station are 6 for both models deployed EVCS. Table 5 shows the model results for the M and M and the cost is changed because the locations are 1 2, charging time evolution and the service rate λ of the charger. not the same for both models. Te evolution of models M It is worth mentioning that the prolonged charging time and M outputs is presented in Figure 3. Furthermore, 2 increases the number of chargers; as a result, increasing Table 4 displays the ILP models result for decisions related to installation costs, which is also dependable on the number of location and sizing. Table 4 added the number of chargers. total chargers. Te 5 EVCS can be installed for M and M . 3 5 Increasing the R-value is accompanied by fewer charging Tis demonstrates that the suggested models continue to use stations; however, it also means that more chargers need to a similar EVCS placement. Even as technology progresses be installed within the charging stations. According to and decreases charging times, the established EV charging models M and M , the R-value is 16 km, and the number of scheme remain efective. 3 5 Cost ($) Number of station Journal of Advanced Transportation 9 1060000 20 940000 6 02468 10 12 14 16 R (KM) M3 Cost ($) Number of station Number of charger Figure 4: Model M output variation. 520000 20 480000 10 440000 0 0 2 4 6 8 10121416 R (KM) M4 Cost ($) Number of station Number of charger Figure 5: Model M output variation. Table 4: Te impact of the coverage radius on the results of models M , M and M . 3 4, 5 Model M Model M Model M 3 4 5 Number Number Number Number Number Number (km) Cost $ Cost $ Cost $ of stations of chargers of stations of chargers of stations of chargers 0 18 18 1,045,287 18 18 504,000 18 18 9,407,583 2 18 18 1,045,287 18 18 504,000 18 18 9,407,583 4 17 18 1,043,277 18 18 504,000 17 18 9,392,406 6 17 18 1,043,277 18 18 504,000 17 18 9,392,406 8 10 18 1,028,705 18 18 504,000 10 18 9,302,385 10 9 18 1,026,028 18 18 504,000 9 18 9,290,115 12 7 17 966,164 14 17 477,808 7 17 8,776,529 14 6 16 908,312 10 16 451,650 6 16 8,276,546 16 5 16 906,161 10 16 451,650 5 16 8,272,154 3.2.3. Efect of the EV Charger Cost. To begin, let us look at model’s outputs, both in terms of the total number of how the model’s outputs fuctuate as the unit cost of the stations and chargers to be installed, are unafected by EV’s charger is increased in the range ($42000 to $70000) the model. with an increase of 5%. Table 6 shows the numerical results. Increasing the unit cost of EV chargers, un- 3.2.4. Te Proposed EV Charging Networks. Now, we have surprisingly, increases the proposed models’ objective come up with a solution for a suitable EV charging in- costs. Following Tables 3 and 4 demonstrate that each frastructure deployment. Te proposed installation Cost ($) Cost ($) Number of station and charger Number of station and charger 10 Journal of Advanced Transportation 9600000 20 8800000 10 8000000 0 0 2 4 6 8 10 12 14 16 R (KM) M5 Cost ($) Number of station Number of charger Figure 6: Model M output variation. Table 5: Efect of the charging time on M , M and M model outputs. 3 4, 5 Model M Model M Model M Charging 3 4 5 time λ Number Number Number Number Number Number Cost $ Cost $ Cost $ of stations of chargers of stations of chargers of stations of chargers 5 12 5 5 290,162 5 5 146,483 5 5 2,728,154 10 6 5 8 458,162 6 8 229,597 5 8 4,240,154 15 4 5 13 738,162 8 13 368,007 5 13 6,754,426 20 3 5 16 906,161 10 16 451,650 5 16 8,272,154 30 2 5 23 1,298,162 10 23 650,483 5 23 11,800,154 Table 6: Efect of the EVs’ charger costs on M , M and M model outputs. 3 4, 5 Model M Model M Model M EVs’ 3 4 5 charger Number Number Number Number Number Number Cost $ Cost $ Cost $ costs of stations of chargers of stations of chargers of stations of chargers 42,000 5 16 682,161 10 16 339,650 5 16 6,256,154 44,800 5 16 726,961 10 16 362,050 5 16 6,659,354 47,600 5 16 771,761 10 16 384,450 5 16 7,062,554 50,400 5 16 816,561 10 16 406,850 5 16 7,465,754 53,200 5 16 861,361 10 16 429,250 5 16 7,868,954 56,000 5 16 906,161 10 16 451,650 5 16 8,272,154 58,800 5 16 950,961 10 16 474,050 5 16 8,675,354 61,600 5 16 995,761 10 16 496,450 5 16 9,078,554 64,400 5 16 1,040,562 10 16 518,850 5 16 9,481,754 67,200 5 16 1,085,362 10 16 541,250 5 16 9,884,954 70,000 5 16 1,130,162 10 16 563,650 5 16 10,288,154 techniques for each ILP model are shown in Figures 7–11. installation costs and EV users’ access costs. As a result, the Figure 7 shows the frst network only considered mini- convenience of both investors and EV owners is considered mizing the EVCS numbers. Figure 8 is constructed to equally. We strongly endorse these proposed locations for consider the only opening cost of EVCS. Furthermore, EVCS placement in the proposed prefecture to avoid when solely the investor’s convenience is regarded, the squandering private and public resources while main- framework shown in Figure 9 should be constructed. Te taining a suitable service level for EV users. Several pre- network depicted in Figure 10 should thus be established vious studies have been focused on EVCS in existing when the convenience of users and investors is equally parking lots, fuel stations with diferent aspects, such as important, but the station opening costs are not taken into minimizing the total cost [49, 57], minimizing access cost account, like in the case of [49]. Figure 11 depicts the most [50], EV charging demand [26], minimizing trips [58], and appropriate EVCS deployment, considering actual station minimizing the total system cost [52]. So far, the overall Cost ($) Number of station and charger Journal of Advanced Transportation 11 Figure 7: EVCS locations (model M ). Figure 8: EVCS locations (model M ). Figure 9: EVCS locations (Model M ). 3 12 Journal of Advanced Transportation Figure 10: EVCS locations (Model M ). 4. Conclusion EVs are one of the potential alternatives to transportation’s environmental and energy concerns. Due to the limited range, insufcient charging station enabling drivers to make long-distance trips is a critical step in promoting their widespread adoption. Te deployment of the optimal charging infrastructure is essential for promoting EVs. Tis study proposes an efective method for locating fast- charging stations. It is based on the optimization tech- nique of integer linear programming. Particularly, we are more concerned with ensuring that the deployed in- frastructure has a tolerable coverage radius for the EV owners. On the other hand, drivers are less willing to accept long walking distances from their destinations to charging stations. To achieve this goal, we employed fve linear integer programming based on a weighted set covering models. In spite of their apparent ease, the numerical simulations can Figure 11: EVCS locations (Model M ). assist policymakers in determining the locations and sizing of suitable EVCS while lowering investment and consumers’ fndings of this current study are extremely promising convenience costs. It is worth noting that this study has some compared to these previous studies. Te proposed ILP limitations that can be addressed in future research. EV method’s analysis was validated using several experimental users’ preferences from their home location to other designs. Finally, it is proved that the proposed ILP method charging spots are treated as a fraction, considering that the produced more accurate and precise results within the decision variables in the current models are treated as scope of its intended use. Based on these fndings, we a continuous variable. Instead of using the Cartesian dis- conclude that the ILP model is an efective method for tance, the distance matrix could be made more precise by accurately solving problems of EVCS. It is beyond the scope estimating suitable paths between all pairs of possible lo- of this study to determine how efectively the various cations, for example, average paths. Conducting an extensive approaches described will scale to issues that are very study on the estimation of EV demand and incorporating diferent from the ones analyzed. Nevertheless, the aim of consumer behavior, market anticipation, and energy con- this study is to determine appropriate locations for EV sumption in the proposed study area further consider the charging stations in Aichi Prefecture, Japan. More pre- impact of EVs’ charger deployment as well as the forecasted cisely, our concern is to ensure that the deployed in- number of EVs on the city’s electrical grid. frastructure has a tolerable coverage radius. In fact, EV drivers are hesitant to accept a long walk distance from Data Availability charging stations to their destination. Tis study provides Te data used to support the fndings of this study are an optimum infrastructure network that policymakers could adopt within the emerging environmental policy. available on request from the corresponding author. Journal of Advanced Transportation 13 [13] I. Ullah, K. Liu, T. Yamamoto, M. Zahid, and A. 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Optimal Deployment of Electric Vehicles’ Fast-Charging Stations

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10.1155/2023/6103796
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Hindawi Journal of Advanced Transportation Volume 2023, Article ID 6103796, 14 pages https://doi.org/10.1155/2023/6103796 Research Article 1,2,3 2 4 5 Irfan Ullah , Kai Liu , Safa Bhar Layeb , Alessandro Severino , and Arshad Jamal Transportation Engineering College, Dalian Maritime University, Dalian 116026, China School of Transportation and Logistics, Dalian University of Technology, Dalian 116024, China Department of Business and Administration, ILMA University, Karachi, Pakistan LR-OASIS, National Engineering School of Tunis, University of Tunis El Manar, Tunis, Tunisia Department of Civil Engineering and Architecture, University of Catania, Catania 95123, Italy Transportation and Trafc Engineering Department, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 31451, Saudi Arabia Correspondence should be addressed to Irfan Ullah; irfanktk@mail.dlut.edu.cn Received 26 August 2022; Revised 7 November 2022; Accepted 22 February 2023; Published 3 April 2023 Academic Editor: Lei Wang Copyright © 2023 Irfan Ullah et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. As climate change has become a pressing concern, promoting electric vehicles’ (EVs) usage has emerged as a popular response to the pollution caused by fossil-fuel automobiles. Locating charging stations in areas with an expanding charging infrastructure is crucial to the accessibility and future success of EVs. Nonetheless, suitable planning and deployment for EV fast-charging stations is one of the most critical determinants for large-scale EV adoption. Installing charging stations in existing fuel/gas stations in the city may be an efective way to persuade people to adopt EVs. In this paper, we aim to optimally locate a fast-charging station in an existing gas station in the real-world scenario of Aichi Prefecture, Japan. Te purpose is to locate and size fast-charging stations in such ways that drivers can get access to these charging facilities within a rational driving range while considering real-world constraints. Furthermore, we include the investment cost and the EVs users’ convenience cost. Tis problem is formulated by fve integer linear programming using a weighted set covering models. Te developed model determines where to locate charging stations as well as how many chargers should be installed in each charging station. Te experimental results demonstrate that an appropriate location scheme can be obtained using the model M . A computational experiment identifes the best infrastructure solutions for policymakers to consider in the context of growing environmental policies. diverse urban transport system [7–9]. With progressions in 1. Introduction communication and technology, a green transport system Climate change has been identifed as a major concern provides one of the most efective solutions in combating air nowadays, which is primarily produced by GHG emissions. pollution, decreasing congestion, and easing the fuel crisis Te global warming is expected to rise by more than 2 C [10, 11]. above preindustrial levels if no further steps are made to cut Green transportation is essential to address climate GHG emissions [1, 2]. In 2016, the transport sector con- change mitigation since they minimize CO and other tributed approximately 25% of worldwide emissions [3]. pollutants that are frequently used in conventional vehicles Although energy and fuel consumption signifcantly impact [12, 13]. Amongst all green transportation choices, e-bikes, the global climate change, the usage and energy production shared mobility, electric vehicles (EVs), and bus rapid transit themselves are fraught with difculties [4, 5]. In 2012, the are an intriguing option for addressing the aforementioned transport sector’s energy demand increased from 23% to challenges [14, 15]. With the call for zero-emission vehicles 28% [6]. As a result, the notion of green transport is evolving, and improved battery technologies, EVs are a solid con- which refers to an easy, efcient, safe, low polluting, and tender to replace the gasoline-driven automobile. Aside 2 Journal of Advanced Transportation practitioners. In the literature, the EVCS location issues are from contributing to energy security and sustainable envi- ronmental, EVs provide substantial benefts to users in terms categorized into two groups, namely, intracity and intercity, depending on the type of travel the charging amenities of fuel economy and cost savings [16]. Because of these reasons, the EV market has seen commercial success re- intend to support. Te intercity problem is primarily as- cently. Several state and governmental entities have also sociated with the range anxiety issue, particularly for longer established policies to encourage EV adoption, further ac- (intercity) trips, whereas intracity problems are more con- celerating the growth. Despite their benefts, EVs have not cerned with the limited accessibility of charging in- gained widespread acceptance among the public. Due to the frastructure within the boundary of metropolitan centers. In inadequate and limited charging infrastructure and the intercity problem, the charger can be installed anywhere on the highway, and this problem can solve the fow-capturing shorter driving range, EVs drivers may have range anxiety or the concern that the energy storage may run out before they refueling problem and the charger location depending on the trafc volume of origin-destination pair and EVs range get to their destination [17, 18]. In order to alleviate the drivers’ range anxiety and increase the usage of EVs, there is [26]. Te authors proposed a conceptual model to examine EVs travel throughout a long route for intercity EVs trips a need for adequate planning for charging stations to help drivers arrive safely at their destination. [25]. Te goal of their proposed model is to choose the Charging infrastructures are becoming crucial compo- battery size and charge capacity that will satisfy a particular nents for adopting EVs, connected to vehicle technology and level of service while minimizing the total social cost. efciency and the accessibility of a reliable power supply to Similarly, the authors employed a continuous facility loca- charging stations [12]. It is also tied with the increased tion approach for optimizing EVs charging station place- electricity demand in other sectors [19]. In this context, in- ment for highway corridors [27]. Teir model did not considere the cost of the battery. Considering demand frastructure issues include charging station distribution planning, electrical grid resistance, dependability, and con- uncertainty, their goal was to augment the private charging infrastructure with government-subsidized charging sumption patterns used to determine pricing and incentive policies. Performance and cost barriers are impeding the stations. In the intracity problem, the charger can be installed adoption of EVs [20]. Furthermore, travel through EVs may become unsustainable due to the limited availability of anywhere in the city. To locate EVCS in the city, the discrete charging stations [21], nonoptimal location in urban sur- network model was chosen, since stations can only be lo- roundings [22], inconsistent power fow, and amount of cated at discrete locations, such as existing service stations or energy taken from the primary electricity grid not initially parking lots [26]. Tere are two diferent methods for de- catered for this use. Tus, it is critical to identify occupation termining where charging stations should be placed. Te patterns and, consequently, such issues may be resolved by frst involves the use of classical facility location methods such as set-covering problems, with the overall goal of re- employing charging profles [23]. EVs recharge is a new type of electrical demand that is challenging to precisely estimate, ducing the number of chargers required so that all consumer can reach the charging station within a specifc time and particularly when the vehicle penetration is still low and a large data set is difcult to obtain. Another signifcant driving distance. Te second method is the multicriteria barrier to increasing EVs market share is the inconvenience decision making (MCDM) approach based on geospatial faced due to the shortage of the public charging infrastructure analysis [28]. In MCDM, individual potential location is and the limited range of batteries. Proper charging station assessed based on various criteria, including the cost of land, planning could help the motorists in this aspect. parking lots availability, and the location’s slope. Each EVs need comparatively prolonged charging times than subcategory is scored, and location decision is based on each refueling internal compaction engine vehicles (ICEVs). candidate’s cumulative score. Frade et al. (2011) attempted Tree types of charging stations are currently available, each to solve the intracity EVs' charging location problem by employing the covering model to maximize the number of having a diferent range of the charging power supply. Level- I and level-II chargers have a maximum charging power of customers served by each stations and maintaining a certain level of coverage provided by the charging station [29]. about 1.5 kW and 10 kW, respectively; however, Level-III chargers have to charge powers up to 60–150 kW because Dashora et al. (2010) suggested an early intracity EV location they need high voltage [24]. Level-III chargers are more model intending to reduce the overall cost by converting expensive to construct and can only be found in commercial parking lots to EVCS [30]. Te cost of converting a parking places. A standard EV would still require more than lot includes installing charging devices, solar shading, and 30 minutes even with a Level-III charger, which is signif- connecting these parking lots to the nearby grid stations. cantly longer than refueling ICEVs [25]. Level-I and level-II Chen et al. (2013) used a similar model to minimize the walking distance [31]. He et al. (2013) consider the in- chargers usually take several hours to charge an EV fully. As a result, an appealing alternative is placing charging stations teractions between the placement of EVCS, the operation of power networks, and the selection of route and destination at the EV driver’s house, ofce, or other locations where they are expected to stay for a long time (recreational facilities, choices [32]. Ahmad et al. (2017) developed an optimal framework for hybrid EVs based on the switching process shopping malls). Electric vehicle charging station (EVCS) planning issues from one trading place to another depending on the max- have been extensively investigated over the last decade and imum selling (i.e., discharging of EVs) and minimum continue to catch the attention of both researchers and purchasing (i.e., charging of EVs) energy cost [33]. Based on Journal of Advanced Transportation 3 deployment of solar power charging station considering these results, the aggregator paid 4.22% lesser energy cost than day-ahead while 4.65% and 9.68% lesser than DISCOM distribution network. Te outcomes are compared to the teaching-learning-based optimization and the Jaya algo- and the bilateral based trading platform. So far, existing research studies have examined the rithm; the comparison demonstrates the superiority of the performance of several optimization strategies for solving MCSO [47]. the optimal location of the EVCS problem. Various re- According to the Liao et al. (2016), range anxiety, EVCS searchers have already investigated the most efcient availability, and charging duration time are the three major placement of EVCS in distribution lines using various drawbacks for faster EV adoption [48]. Furthermore, easy computational techniques such as evolutionary algorithms access to EVCS directly infuences on EVs' penetration levels. Tis is due to the fact that ICEVs is viewed as [34], Jaya algorithm [35], particle swarm optimization (PSO) [36], and genetic algorithm (GA) [37]. Mostly, the problem a convenience purchase and the user do not prefer to plan ahead to fnd refueling stations. Consequently, fast-charging is the same, and it is based mainly on the availability of trafc fow data and the total number of EVs in the observed area. stations serve as “emergency service” amenities, and it is essential to consider consumers' behavior while locating Xiong et al. (2017) proposed the optimal location of EVCS considering distribution network and city trafc [38]. Te charging stations. Meanwhile, the fuel/gas retail industry is objective is minimizing energy not supplied while also well-established and optimized to serve vehicles, and these considering charging station costs. Zeb et al. (2020) locations are natural candidates for installing fast chargers. employed a method for the optimal deployment of the solar To address the abovementioned issues, the following con- power-based charging station considering diferent charging tributions have been made. levels with minimal losses and installation costs [39]. Te current study aims to develop a mathematical model for minimizing the total cost by optimizing the location Nevertheless, the constraints incorporated within the optimization problem vary, such as the type of EVCS, planning of charging stations, their sizing, and the number of total chargers within each charging station. Te charging courage routes, land cost, maintenance cost, fxed cost, electric grid impact, and trafc fow [40]. Shahraki et al. station opening capital cost and the user’s convenience cost (defned by station access cost) are the two essential con- (2015) proposed the application of mixed-integer linear programming (MILP) for the optimal placing of EVCS based siderations while planning for an optimal charging location. on real-world data of vehicle travel patterns [41]. Te Tis study proposes fve diferent integer linear pro- fndings indicate that an appropriate charging station gramming (ILP) models to address the problem of EVCS placement can result in signifcant improvements. Ge et al. location and sizing. Te proposed models may be grouped (2011) employed a GA for sizing and locating EVs’ charging under two main categories. First, ILP models are solely used stations using grid partitioning [42]. Te main constraints for chargers location decisions; second, ILP models consider both location and sizing decisions. Both categories are considered are charging station capacity and trafc density. An equilibrium modeling framework was proposed by He distinguished by defnite decision variables, relevant real- world constraints, and a corresponding objective function. et al. (2013) to capture the interactions between the avail- ability of charging opportunities, destination, electricity Te remainder of the paper is as follows. Section 2 details prices, and EVs route choices at regional power transmission the proposed mathematical models. Section 3 reports the and transportation networks [32]. Te paper’s objective was main results of the conducted computational experimen- to consider the constraints of power and transportation tation. Section 4 concludes and provides future research network. Dong et al. (2014) employed GA for EVCS, an avenues. activity-based technique using multitravel data [43]. Te fnding suggested that the placement of public chargers at 2. Model Formulation popular sites with some adequate infrastructure investment could considerably increase electric miles and trips. Diferent covering models (optimization models) are pro- Liu et al. (2012) used a modifed primal-dualinterior- posed. Te objective is to minimize various formulations of point algorithm to select an appropriate location for EVCS objective costs while satisfying all demands. Te suggested placement, taking environmental factors and EVs’ service models deal with the planning of EVs charging network for radius to solve the problem [44]. Tey considered cost as an a metropolitan region based solely on an existing gas station. objective function. Wang et al. (2013) employed data en- velope analysis for the EVCS problem considering the multiobjective function, power loss, EVs fow, and voltage 2.1. Assumption. Te study was based on the following main deviation [45]. Zhang et al. (2015) employed PSO for op- assumptions for simplicity: timal location planning of EVCS [36]. Te placement (i) For EV users, only daytime charging is considered. problem for fast-charging stations and public parking lots Tis appears to be convenient for a workplace in an was developed while the cost as the objective functions. Yao urban region. et al. (2014) developed a multiobjective evolutionary algo- rithm to locate fast-charging stations considering the (ii) Only fast charging stations are considered, and each multiobjective function, EV fow, cost, and energy losses charger may provide service to multiple EVs, as fast [46]. Ahmad et al. (2021) presented a modifed chicken charging is usually considered the best solution for swarm optimization (MCSO) approach for optimal gas stations. 4 Journal of Advanced Transportation (iii) Access to installed chargers within a reasonable travel distance is necessary for EV drivers. (iv) Each EV can be charged to a single charging station. 2.2. Network Planning. Identifying potential locations for future charging stations is an essential component of this research. Based on the previous research studies [49, 50], the existing gas stations in the neighborhood could be suitable places for the charging station. Google Maps is used to acquire geographic information. Table 1 contains a list of possible locations. In Figure 1, we found 18 possible charging stations. After the 18 candidates for potential lo- cations had been identifed, an adjacency graph is created in Figure 2. Based on the graph theory, a linked undirected graph G � (V, E) has been created, with V � (1, . . . ., n) indicating a set of nodes representing the feasible charging, Figure 1: Proposed EVCS location (Google Map). and E � (1, . . . , m) is the set of edges which represents the possible connections between charging stations (n � 18). Te distance between the locations is used to weight each edge (m = 54). Te Cartesian distance in each station’s neighborhood was determined and noted as d (i, j ∈ V) i,j denoted the distance between locations i and j. Table 2 provides the distance matrix. 2.3. Linear Programming Models. Diferent models might be used to optimize the installed resources. Tis section con- tains a description of these proposed models. Te location of installed stations, their size, and where to charge are all considerations made at the scope level. Users of not-yet- placed stations should charge within a reasonable radius R of an installed station. Apart from assuring a service coverage distance, these models minimize various costs while ad- hering to appropriate constraints. In this section, we look at two decision-based (location only and location and sizing) ILP models. Te frst two models focused on only location Figure 2: Te proposed graph of adjacency (Google Map). and last three models focused on both location and sizing. 2.3.1. ILP Models Considering an Only Location. Te frst x ∈ {0, 1}∀i ∈ V. (3) class of ILP models used an NP-hard set covering problem [51]. For that purpose, we defne a binary variable x for each Te objective function shown in equation (1) [19], which location i ∈ V, which takes the value 1 for an EVCS in- represents the number of stations installed, is minimized in stallation at location i; otherwise, 0. R represents a constant this model. Constraint (2) establishes the coverage radius for coverage radius that denotes the EVs user’s tolerable dis- the accessibility of EVs' users. Te constraints conditions tance while looking for a charging station. Ten, the in- shown in equation (3) indicate the binary restraints on x termediate constant is utilized. Let a (i, j ∈ V) be a binary variables. Te M model minimizes the total number of i,j constant which takes the value 1 if d ≤ V; otherwise, 0, and installed stations. It refers to minimize the total numbers of i,j d is the same as described in the preceding section. As charging station in the proposed area. Based on set covering i,j a result, the model M can be obtained as follows: 1 combinatorial optimization models [36], the M model is useful when the cost of installation is fxed from one station M : Minimize 􏽘 x , 1 i (1) to the next. For example, under normal service operation of iϵV the station network, the charger cost is somehow low relative to the opening cost. We add f (i ∈ V) a size-independent Subject to: cost of opening a charging station at each possible location i (2) 􏽘 α x ≥ 1; ∀j ∈ V, i,j i to account for the infrastructure opening cost. It is the cost of iϵV converting a gas station into EV compatible lot, specifcally Journal of Advanced Transportation 5 Table 1: Attributes of a potential location for EVCS (Google Map) [19]. Opening cost Indices (i) Type Names Coordinates Capacity (c ) (f ) $ 1 Gas station Oguchitoyota 35.322687, 136.888781 16 2210 2 Gas station Toho 35.292428, 136.909384 14 2170 3 Gas station Jeieesuesu 35.284581, 136.80638 12 1990 4 Gas station Consulate 35.189240, 136.892905 17 2150 5 Gas station Meihokogyo 35.189240, 136.886038 12 2205 6 Gas station Daiko 35.133104, 136.916251 17 1912 7 Gas station Yuni 35.08142, 137.008261 13 1890 8 Gas station Kondosh 35.112885, 137.131858 11 2150 9 Gas station Idemitsu 35.062318, 137.148337 16 2090 10 Gas station Uny 1 34.992595, 136.850333 15 2170 11 Gas station Uny 2 34.909300, 136.829734 12 1930 12 Gas station Centrair 34.885647, 136.811881 14 2010 13 Gas station Uny 3 34.893532, 136.909384 11 2075 14 Gas station Utsumi 34.762766, 136.866812 14 2113 15 Gas station Eneos 34.875618, 137.048192 19 2203 16 Gas station Casyal 34.865367, 137.321372 18 2119 17 Gas station Solato 34.865367, 137.321372 11 1999 18 Gas station Shitara 35.121872, 137.572684 12 1901 6 Journal of Advanced Transportation Table 2: Te distance among possible charging stations in (km). Indices 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 0 9.21 6.4 17.2 18.5 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 2 9.21 0 8.9 11.1 16.3 17.1 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 3 6.4 8.9 0 13.7 14.2 20.3 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 4 17.2 11.1 13.7 0 6.7 7.2 16.4 24.1 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 5 ∞ 16.3 14.2 6.7 0 9.4 20.2 29.4 32.4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 6 ∞ 17.1 20.3 7.2 9.4 0 11.5 19.5 22.9 17.4 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 7 ∞ ∞ ∞ 16.4 20.2 19.5 0 12.1 13.4 17.41 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 8 ∞ ∞ ∞ 24.1 28.4 19.5 12.1 0 6.9 40 29.3 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 9 ∞ ∞ ∞ ∞ 32.4 22.9 13.4 6.9 0 28 ∞ ∞ 28.3 ∞ 21.1 26.9 31.9 39.5 10 ∞ ∞ ∞ ∞ ∞ 17.4 17.41 40 28 0 9 11.1 11.3 ∞ ∞ ∞ ∞ ∞ 11 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 29.3 ∞ 9 0 3.4 7.6 ∞ 20.9 ∞ ∞ ∞ 12 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 11.1 3.4 0 9.1 14.7 21.5 ∞ ∞ ∞ 13 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 28.3 11.3 7.6 9.1 0 14.4 11.4 ∞ ∞ ∞ 14 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 14.7 14.4 0 18.9 41.8 47.4 ∞ 15 ∞ ∞ ∞ ∞ ∞ ∞ ∞ 21.1 ∞ ∞ 20.9 ∞ 21.5 11.4 0 24.3 30.8 ∞ 16 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 26.9 ∞ ∞ ∞ ∞ 41.8 24.3 0 6.6 36.4 17 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 31.9 ∞ ∞ ∞ ∞ 47.4 30.8 6.6 0 33.6 18 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 39.5 6.6 ∞ ∞ ∞ ∞ ∞ ∞ 33.6 0 the equipment and administrative expenditures [52]. When one hour, and s represents the entire charger service time. the accommodation capacity for all the possible locations is Te service rate is frstly introduced in the review study [53]. fxed, the size-dependent costs are constant, and then the Every location i ∈ V might be considered a possible con- model is focused on minimizing only the opening costs. As struction place for charging stations as well as the centroid of a result, the model M is formulated as follows: territory for EVs’ drivers. Here, two new decision variables are also introduced. Defning every location (i ∈ V) as M : Minimize 􏽘 f x , 2 i i (4) a non-negative integer variable n that denotes the number of iϵV total chargers installed in each location i. Defning a binary variable y , which is set to 1 if the EV from ith location i are ij Subject to: charged at jth location. As a result, the third ILP model M (5) 􏽘 α x ≥ 1; ∀j ∈ V, is as follows: i,j i iϵV M minimize 􏽘 f x + u n , 3 i i i i (8) x ∈ {0, 1}∀i ∈ V. (6) iϵV Te objective function (4) reduces and minimizes the Subject to: overall cost of all installed stations to the lowest possible (9) 􏽘 Y � 1; ∀j ∈ V, value as investigated in [52]. Constraint (5) states that i,j iϵV a minimum of 1 station on a radius R is installed for every location j (location j included), and constraint (6) expresses x ≥ Y ; ∀i, j ∈ V, (10) j i,j the variable nature. x ≤ n ≤ c x , ∀i ∈ V, (11) i i i i 2.3.2. ILP Models Considering Both Locations and Sizing. Te focus of the second ILP model is to develop suitable 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j (12) station sizes, in addition to identifying charging station iϵV locations. To begin, we assign the following numbers to individual feasible location i ∈ V, (i) a capacity c , which d Y ≤ R; ∀i, j ∈ V, (13) i,j i,j represents the maximum chargers numbers that may be installed concerning the location station capacity, (ii) price x ∈ {0, 1}; ∀i ∈ V, (14) per unit for installing a charger, represented by u , and (iii) fnally, a demand m that represents the number of EVs that n ∈ N; ∀i ∈ V, (15) can use the location i. Te maximum number of EVs served by a charger is introduced ∅, and its formulation is shown in equation (7) [19]. Y ∈ {0, 1}; ∀i, j ∈ V. (16) i,j ∅ � λ ∗ s . (7) Te objective function is shown in (8) for the M model that aims to optimize (minimize) charger installation and In the abovementioned relation, where λ implies the service rate or the number of EVs that could be charged in capital costs. Constraint (9) requires that all EVs be assigned Journal of Advanced Transportation 7 to a specifc EVCS. Constraint (10) defnes that EVs can only equations are the same as the previous model (M ). Each be charged in location j ∈ V if this site is chosen for ac- user’s preferences for station installation and access cost are commodating a charging station. Constraint (11) stipulates refected in the weights assigned to each station. Terefore, that for the chosen station, a minimum one charger must be we suggest that the preceding model can be improved by installed, with the total number of chargers not exceeding including the total construction costs of a station. Finally, the the station’s capacity. If a station is not specifed within it, no model M is introduced. chargers are deployed. Constraint (12) requires that all EV owners who prefer charging their vehicles at a selected lo- M minimizeω 􏽘 f x + u n􏼁 ω φ 􏽘 m 􏽘 d y 5 1 i i i i 2 i i,j i,j, iϵV iϵV iϵV cation should be less than the number of available service chargers. Constraint (13) denotes that the EV task from Subject to: a selected position (i ∈ V) to location (j ∈ V) is feasible if 􏽘 Y � 1; ∀j ∈ V, i,j only the provided distance between stations is less than the iϵV tolerance radius. Lastly, (14) and (15) show the integrality x ≥ Y ; ∀i, j ∈ V, j i,j constraints and constraint (16) are the non-negative integer variables n. x ≤ n ≤ c x , ∀i ∈ V, i i i i Terefore, the main focus is to minimize the charging 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j infrastructure installation costs. Following that, it is also iϵV essential to consider the access cost. More specifcally, the d Y ≤ R; ∀i, j ∈ V, travel cost was also included since EVs owners can drive i,j i,j from one location to another to fnd a suitable charging x ∈ {0, 1}; ∀i ∈ V, facility for their vehicles. Zhu et al. (2016) frst suggested this 2 n ∈ N; ∀i ∈ V, aspect in their analysis of a 60-km Beijing metropolitan region because the charging station is far from the user’s Y ∈ {0, 1}; ∀i, j ∈ V. i,j workplace [49]. Tey believe that EV drivers may walk and (20) take a cab or bus to get from one location to other. In our study, we consider only walking to get into the possible As in [54], model M corresponds to model M as 3 5 charging station. Indeed, EV users are unlikely to take a cab a particular case under the condition where ω = 1 and ω = 0 1 2 or bus from their destinations to the charging station. Te estimated cost of each walked kilometer is denoted by φ, the 3. Numerical Experiments walking cost, which is determined in equation (17) as in- vestigated in [52] After presenting the case study, the results for the base and h recommended models are discussed and compared. After (17) that, an experimental and comprehensive sensitivity analysis φ � , of the proposed ILP models was carried out to determine the s h sensitivity of the model to various cost components and also where W is the average walking speed and W is the average to other variables. Tis experiment was conducted on Intel hourly wage of an EV owner. As a result, model M is as Core I i5-8400 CPU@2.80 GHz (6CPUs) desktop with 12 GB follows: RAM. Te optimization programming language (OPL) was M minimize ω 􏽘 u n + ω φ 􏽘 m 􏽘 d y used to code the fve ILP models, and the general MIP solver 4 1 i i 2 i i,j i,j, (18) iϵV iϵV iϵV (IBM Cplex, version 12.6) was used to solve them. It is worth noting that all of the models found an optimal location in less than 30 seconds of the CPU time. Subject to: 􏽘 Y � 1; ∀j ∈ V, i,j 3.1. Parameters Setting. Using the following experiment, the iϵV cost of the deployed charger is assumed to be constant and x ≥ Y ; ∀i, j ∈ V, j i,j not dependent on the installation location. As per the previous studies, u (i ∈ V) is used as 56,000 [52, 55]. Te x ≤ n ≤ c x , ∀i ∈ V, i i i i (19) charging demand is expected to be uniformly distributed 􏽘 m y ≤ n ∅, ∀j ∈ V, i i,j j between each charging station. Terefore, m (i ∈ V) is iϵV considered fxed at 13 based on [49]. Equation (7) specifes d Y ≤ R; ∀i, j ∈ V, i,j i,j a charger service rate of 3 EVs for a unit hour and a charger’s service duration of 12 hours during a day. Te average x ∈ {0, 1}; ∀i ∈ V, hourly wage W is $17/hour. It is calculated by dividing the n ∈ N; ∀i ∈ V, mean monthly wage ($3000) of an EV owner by accumulated Y ∈ {0, 1}; ∀i, j ∈ V, i,j worked hours in a month. An average walking speed is assumed to be 5 km/h [52, 56]. For M and M , models 4 5 where ω and ω are non-negative weights. Te objective equal emphasis is placed for the station and user access costs 1 2 (18) is to minimize the total weighted costs. Te remaining by setting out the ω � ω � 0.5. 1 2 8 Journal of Advanced Transportation Table 3: Te impact of the coverage radius on the results of models M and M . 1 2 Model M Model M 1 2 R (km) Number of stations Cost $ Number of stations Cost $ 0 18 37,287 18 37,287 2 18 37,287 18 37,287 4 17 35,277 17 35,277 6 17 35,277 17 35,277 8 10 20,836 10 20,436 10 9 18,666 9 18,028 12 7 14,440 7 14,025 14 7 14,180 7 13,825 16 6 11,887 6 11,767 5000 0 0 2 4 6 8 10 12 14 16 R (KM) M1 Cost ($) M2 Cost ($) Number of station Figure 3: Models M1 and M2 output variation. 3.2. Sensitivity Analysis charging stations and numbers of the charger are 5 and 16, respectively. However, based on model M , which does not 3.2.1. Coverage Radius Impact. We focused on the coverage include the station opening costs, 10 stations should be radius (R) to investigate its impact and variation on the chosen for nearly half the cost of those shown by model M . deployment of the optimal infrastructure for each ILP Te number of chargers are same for models M , M and 3 4, model’s output. Te tolerable distance R range is computed M because the charging demand is uniformly distributed. and ranged between 0 and 16 km. Table 3 represents the Moreover, in model M the high price is attributable to the 5, models M and M which simply outputs only location 1 2 user’s access cost. Te evolution of models M , M and M 3 4, 5 decisions. Te tables show the numbers of charging stations outputs is shown in Figures 4–6 and corresponding opening costs. Taking R = 1 km corre- sponds to establishing an EVCS in every available place, resulting in the number of charging stations being = 18. 3.2.2. Impact of Charging Time. EVs fast charging tech- Moreover, raising the R-value is associated with reduced nology is transforming speedily, and the current study aims opening costs and the number of locations selected. Up to to investigate the impact of charging time change on the 16 km, the numbers of charging station are 6 for both models deployed EVCS. Table 5 shows the model results for the M and M and the cost is changed because the locations are 1 2, charging time evolution and the service rate λ of the charger. not the same for both models. Te evolution of models M It is worth mentioning that the prolonged charging time and M outputs is presented in Figure 3. Furthermore, 2 increases the number of chargers; as a result, increasing Table 4 displays the ILP models result for decisions related to installation costs, which is also dependable on the number of location and sizing. Table 4 added the number of chargers. total chargers. Te 5 EVCS can be installed for M and M . 3 5 Increasing the R-value is accompanied by fewer charging Tis demonstrates that the suggested models continue to use stations; however, it also means that more chargers need to a similar EVCS placement. Even as technology progresses be installed within the charging stations. According to and decreases charging times, the established EV charging models M and M , the R-value is 16 km, and the number of scheme remain efective. 3 5 Cost ($) Number of station Journal of Advanced Transportation 9 1060000 20 940000 6 02468 10 12 14 16 R (KM) M3 Cost ($) Number of station Number of charger Figure 4: Model M output variation. 520000 20 480000 10 440000 0 0 2 4 6 8 10121416 R (KM) M4 Cost ($) Number of station Number of charger Figure 5: Model M output variation. Table 4: Te impact of the coverage radius on the results of models M , M and M . 3 4, 5 Model M Model M Model M 3 4 5 Number Number Number Number Number Number (km) Cost $ Cost $ Cost $ of stations of chargers of stations of chargers of stations of chargers 0 18 18 1,045,287 18 18 504,000 18 18 9,407,583 2 18 18 1,045,287 18 18 504,000 18 18 9,407,583 4 17 18 1,043,277 18 18 504,000 17 18 9,392,406 6 17 18 1,043,277 18 18 504,000 17 18 9,392,406 8 10 18 1,028,705 18 18 504,000 10 18 9,302,385 10 9 18 1,026,028 18 18 504,000 9 18 9,290,115 12 7 17 966,164 14 17 477,808 7 17 8,776,529 14 6 16 908,312 10 16 451,650 6 16 8,276,546 16 5 16 906,161 10 16 451,650 5 16 8,272,154 3.2.3. Efect of the EV Charger Cost. To begin, let us look at model’s outputs, both in terms of the total number of how the model’s outputs fuctuate as the unit cost of the stations and chargers to be installed, are unafected by EV’s charger is increased in the range ($42000 to $70000) the model. with an increase of 5%. Table 6 shows the numerical results. Increasing the unit cost of EV chargers, un- 3.2.4. Te Proposed EV Charging Networks. Now, we have surprisingly, increases the proposed models’ objective come up with a solution for a suitable EV charging in- costs. Following Tables 3 and 4 demonstrate that each frastructure deployment. Te proposed installation Cost ($) Cost ($) Number of station and charger Number of station and charger 10 Journal of Advanced Transportation 9600000 20 8800000 10 8000000 0 0 2 4 6 8 10 12 14 16 R (KM) M5 Cost ($) Number of station Number of charger Figure 6: Model M output variation. Table 5: Efect of the charging time on M , M and M model outputs. 3 4, 5 Model M Model M Model M Charging 3 4 5 time λ Number Number Number Number Number Number Cost $ Cost $ Cost $ of stations of chargers of stations of chargers of stations of chargers 5 12 5 5 290,162 5 5 146,483 5 5 2,728,154 10 6 5 8 458,162 6 8 229,597 5 8 4,240,154 15 4 5 13 738,162 8 13 368,007 5 13 6,754,426 20 3 5 16 906,161 10 16 451,650 5 16 8,272,154 30 2 5 23 1,298,162 10 23 650,483 5 23 11,800,154 Table 6: Efect of the EVs’ charger costs on M , M and M model outputs. 3 4, 5 Model M Model M Model M EVs’ 3 4 5 charger Number Number Number Number Number Number Cost $ Cost $ Cost $ costs of stations of chargers of stations of chargers of stations of chargers 42,000 5 16 682,161 10 16 339,650 5 16 6,256,154 44,800 5 16 726,961 10 16 362,050 5 16 6,659,354 47,600 5 16 771,761 10 16 384,450 5 16 7,062,554 50,400 5 16 816,561 10 16 406,850 5 16 7,465,754 53,200 5 16 861,361 10 16 429,250 5 16 7,868,954 56,000 5 16 906,161 10 16 451,650 5 16 8,272,154 58,800 5 16 950,961 10 16 474,050 5 16 8,675,354 61,600 5 16 995,761 10 16 496,450 5 16 9,078,554 64,400 5 16 1,040,562 10 16 518,850 5 16 9,481,754 67,200 5 16 1,085,362 10 16 541,250 5 16 9,884,954 70,000 5 16 1,130,162 10 16 563,650 5 16 10,288,154 techniques for each ILP model are shown in Figures 7–11. installation costs and EV users’ access costs. As a result, the Figure 7 shows the frst network only considered mini- convenience of both investors and EV owners is considered mizing the EVCS numbers. Figure 8 is constructed to equally. We strongly endorse these proposed locations for consider the only opening cost of EVCS. Furthermore, EVCS placement in the proposed prefecture to avoid when solely the investor’s convenience is regarded, the squandering private and public resources while main- framework shown in Figure 9 should be constructed. Te taining a suitable service level for EV users. Several pre- network depicted in Figure 10 should thus be established vious studies have been focused on EVCS in existing when the convenience of users and investors is equally parking lots, fuel stations with diferent aspects, such as important, but the station opening costs are not taken into minimizing the total cost [49, 57], minimizing access cost account, like in the case of [49]. Figure 11 depicts the most [50], EV charging demand [26], minimizing trips [58], and appropriate EVCS deployment, considering actual station minimizing the total system cost [52]. So far, the overall Cost ($) Number of station and charger Journal of Advanced Transportation 11 Figure 7: EVCS locations (model M ). Figure 8: EVCS locations (model M ). Figure 9: EVCS locations (Model M ). 3 12 Journal of Advanced Transportation Figure 10: EVCS locations (Model M ). 4. Conclusion EVs are one of the potential alternatives to transportation’s environmental and energy concerns. Due to the limited range, insufcient charging station enabling drivers to make long-distance trips is a critical step in promoting their widespread adoption. Te deployment of the optimal charging infrastructure is essential for promoting EVs. Tis study proposes an efective method for locating fast- charging stations. It is based on the optimization tech- nique of integer linear programming. Particularly, we are more concerned with ensuring that the deployed in- frastructure has a tolerable coverage radius for the EV owners. On the other hand, drivers are less willing to accept long walking distances from their destinations to charging stations. To achieve this goal, we employed fve linear integer programming based on a weighted set covering models. In spite of their apparent ease, the numerical simulations can Figure 11: EVCS locations (Model M ). assist policymakers in determining the locations and sizing of suitable EVCS while lowering investment and consumers’ fndings of this current study are extremely promising convenience costs. It is worth noting that this study has some compared to these previous studies. Te proposed ILP limitations that can be addressed in future research. EV method’s analysis was validated using several experimental users’ preferences from their home location to other designs. Finally, it is proved that the proposed ILP method charging spots are treated as a fraction, considering that the produced more accurate and precise results within the decision variables in the current models are treated as scope of its intended use. Based on these fndings, we a continuous variable. Instead of using the Cartesian dis- conclude that the ILP model is an efective method for tance, the distance matrix could be made more precise by accurately solving problems of EVCS. It is beyond the scope estimating suitable paths between all pairs of possible lo- of this study to determine how efectively the various cations, for example, average paths. Conducting an extensive approaches described will scale to issues that are very study on the estimation of EV demand and incorporating diferent from the ones analyzed. Nevertheless, the aim of consumer behavior, market anticipation, and energy con- this study is to determine appropriate locations for EV sumption in the proposed study area further consider the charging stations in Aichi Prefecture, Japan. More pre- impact of EVs’ charger deployment as well as the forecasted cisely, our concern is to ensure that the deployed in- number of EVs on the city’s electrical grid. frastructure has a tolerable coverage radius. In fact, EV drivers are hesitant to accept a long walk distance from Data Availability charging stations to their destination. Tis study provides Te data used to support the fndings of this study are an optimum infrastructure network that policymakers could adopt within the emerging environmental policy. available on request from the corresponding author. Journal of Advanced Transportation 13 [13] I. Ullah, K. Liu, T. Yamamoto, M. Zahid, and A. 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Published: Apr 3, 2023

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