Optimal Deployment of Electric Vehicles’ Fast-Charging Stations

.


Introduction
Climate change has been identifed as a major concern nowadays, which is primarily produced by GHG emissions.Te global warming is expected to rise by more than 2 °C above preindustrial levels if no further steps are made to cut GHG emissions [1,2].In 2016, the transport sector contributed approximately 25% of worldwide emissions [3].Although energy and fuel consumption signifcantly impact the global climate change, the usage and energy production themselves are fraught with difculties [4,5].In 2012, the transport sector's energy demand increased from 23% to 28% [6].As a result, the notion of green transport is evolving, which refers to an easy, efcient, safe, low polluting, and diverse urban transport system [7][8][9].With progressions in communication and technology, a green transport system provides one of the most efective solutions in combating air pollution, decreasing congestion, and easing the fuel crisis [10,11].
Green transportation is essential to address climate change mitigation since they minimize CO 2 and other pollutants that are frequently used in conventional vehicles [12,13].Amongst all green transportation choices, e-bikes, shared mobility, electric vehicles (EVs), and bus rapid transit are an intriguing option for addressing the aforementioned challenges [14,15].With the call for zero-emission vehicles and improved battery technologies, EVs are a solid contender to replace the gasoline-driven automobile.Aside from contributing to energy security and sustainable environmental, EVs provide substantial benefts to users in terms of fuel economy and cost savings [16].Because of these reasons, the EV market has seen commercial success recently.Several state and governmental entities have also established policies to encourage EV adoption, further accelerating the growth.Despite their benefts, EVs have not gained widespread acceptance among the public.Due to the inadequate and limited charging infrastructure and the shorter driving range, EVs drivers may have range anxiety or the concern that the energy storage may run out before they get to their destination [17,18].In order to alleviate the drivers' range anxiety and increase the usage of EVs, there is a need for adequate planning for charging stations to help drivers arrive safely at their destination.
Charging infrastructures are becoming crucial components for adopting EVs, connected to vehicle technology and efciency and the accessibility of a reliable power supply to charging stations [12].It is also tied with the increased electricity demand in other sectors [19].In this context, infrastructure issues include charging station distribution planning, electrical grid resistance, dependability, and consumption patterns used to determine pricing and incentive policies.Performance and cost barriers are impeding the adoption of EVs [20].Furthermore, travel through EVs may become unsustainable due to the limited availability of charging stations [21], nonoptimal location in urban surroundings [22], inconsistent power fow, and amount of energy taken from the primary electricity grid not initially catered for this use.Tus, it is critical to identify occupation patterns and, consequently, such issues may be resolved by employing charging profles [23].EVs recharge is a new type of electrical demand that is challenging to precisely estimate, particularly when the vehicle penetration is still low and a large data set is difcult to obtain.Another signifcant barrier to increasing EVs market share is the inconvenience faced due to the shortage of the public charging infrastructure and the limited range of batteries.Proper charging station planning could help the motorists in this aspect.
EVs need comparatively prolonged charging times than refueling internal compaction engine vehicles (ICEVs).Tree types of charging stations are currently available, each having a diferent range of the charging power supply.Level-I and level-II chargers have a maximum charging power of about 1.5 kW and 10 kW, respectively; however, Level-III chargers have to charge powers up to 60-150 kW because they need high voltage [24].Level-III chargers are more expensive to construct and can only be found in commercial places.A standard EV would still require more than 30 minutes even with a Level-III charger, which is signifcantly longer than refueling ICEVs [25].Level-I and level-II chargers usually take several hours to charge an EV fully.As a result, an appealing alternative is placing charging stations at the EV driver's house, ofce, or other locations where they are expected to stay for a long time (recreational facilities, shopping malls).
Electric vehicle charging station (EVCS) planning issues have been extensively investigated over the last decade and continue to catch the attention of both researchers and practitioners.In the literature, the EVCS location issues are categorized into two groups, namely, intracity and intercity, depending on the type of travel the charging amenities intend to support.Te intercity problem is primarily associated with the range anxiety issue, particularly for longer (intercity) trips, whereas intracity problems are more concerned with the limited accessibility of charging infrastructure within the boundary of metropolitan centers.In intercity problem, the charger can be installed anywhere on the highway, and this problem can solve the fow-capturing refueling problem and the charger location depending on the trafc volume of origin-destination pair and EVs range [26].Te authors proposed a conceptual model to examine EVs travel throughout a long route for intercity EVs trips [25].Te goal of their proposed model is to choose the battery size and charge capacity that will satisfy a particular level of service while minimizing the total social cost.Similarly, the authors employed a continuous facility location approach for optimizing EVs charging station placement for highway corridors [27].Teir model did not considere the cost of the battery.Considering demand uncertainty, their goal was to augment the private charging infrastructure with government-subsidized charging stations.
In the intracity problem, the charger can be installed anywhere in the city.To locate EVCS in the city, the discrete network model was chosen, since stations can only be located at discrete locations, such as existing service stations or parking lots [26].Tere are two diferent methods for determining where charging stations should be placed.Te frst involves the use of classical facility location methods such as set-covering problems, with the overall goal of reducing the number of chargers required so that all consumer can reach the charging station within a specifc time and driving distance.Te second method is the multicriteria decision making (MCDM) approach based on geospatial analysis [28].In MCDM, individual potential location is assessed based on various criteria, including the cost of land, parking lots availability, and the location's slope.Each subcategory is scored, and location decision is based on each candidate's cumulative score.Frade et al. (2011) attempted to solve the intracity EVs' charging location problem by employing the covering model to maximize the number of customers served by each stations and maintaining a certain level of coverage provided by the charging station [29].Dashora et al. (2010) suggested an early intracity EV location model intending to reduce the overall cost by converting parking lots to EVCS [30].Te cost of converting a parking lot includes installing charging devices, solar shading, and connecting these parking lots to the nearby grid stations.Chen et al. ( 2013) used a similar model to minimize the walking distance [31].He et al. (2013) consider the interactions between the placement of EVCS, the operation of power networks, and the selection of route and destination choices [32].Ahmad et al. (2017) developed an optimal framework for hybrid EVs based on the switching process from one trading place to another depending on the maximum selling (i.e., discharging of EVs) and minimum purchasing (i.e., charging of EVs) energy cost [33].Based on these results, the aggregator paid 4.22% lesser energy cost than day-ahead while 4.65% and 9.68% lesser than DISCOM and the bilateral based trading platform.So far, existing research studies have examined the performance of several optimization strategies for solving the optimal location of the EVCS problem.Various researchers have already investigated the most efcient placement of EVCS in distribution lines using various computational techniques such as evolutionary algorithms [34], Jaya algorithm [35], particle swarm optimization (PSO) [36], and genetic algorithm (GA) [37].Mostly, the problem 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.Xiong et al. (2017) proposed the optimal location of EVCS considering distribution network and city trafc [38].Te objective is minimizing energy not supplied while also considering charging station costs.Zeb et al. (2020) employed a method for the optimal deployment of the solar power-based charging station considering diferent charging levels with minimal losses and installation costs [39].
Nevertheless, the constraints incorporated within the optimization problem vary, such as the type of EVCS, courage routes, land cost, maintenance cost, fxed cost, electric grid impact, and trafc fow [40].Shahraki et al. (2015) proposed the application of mixed-integer linear programming (MILP) for the optimal placing of EVCS based on real-world data of vehicle travel patterns [41].Te fndings indicate that an appropriate charging station placement can result in signifcant improvements.Ge et al. (2011) employed a GA for sizing and locating EVs' charging stations using grid partitioning [42].Te main constraints considered are charging station capacity and trafc density.An equilibrium modeling framework was proposed by He et al. (2013) to capture the interactions between the availability of charging opportunities, destination, electricity prices, and EVs route choices at regional power transmission and transportation networks [32].Te paper's objective was to consider the constraints of power and transportation network.Dong et al. (2014) employed GA for EVCS, an activity-based technique using multitravel data [43].Te fnding suggested that the placement of public chargers at popular sites with some adequate infrastructure investment could considerably increase electric miles and trips.
Liu et al. ( 2012) used a modifed primal-dualinteriorpoint algorithm to select an appropriate location for EVCS placement, taking environmental factors and EVs' service radius to solve the problem [44].Tey considered cost as an objective function.Wang et al. (2013) employed data envelope analysis for the EVCS problem considering the multiobjective function, power loss, EVs fow, and voltage deviation [45].Zhang et al. (2015) employed PSO for optimal location planning of EVCS [36].Te placement problem for fast-charging stations and public parking lots was developed while the cost as the objective functions.Yao et al. ( 2014) developed a multiobjective evolutionary algorithm to locate fast-charging stations considering the multiobjective function, EV fow, cost, and energy losses [46].Ahmad et al. (2021) presented a modifed chicken swarm optimization (MCSO) approach for optimal deployment of solar power charging station considering distribution network.Te outcomes are compared to the teaching-learning-based optimization and the Jaya algorithm; the comparison demonstrates the superiority of the MCSO [47].
According to the Liao et al. ( 2016), range anxiety, EVCS availability, and charging duration time are the three major drawbacks for faster EV adoption [48].Furthermore, easy access to EVCS directly infuences on EVs' penetration levels.Tis is due to the fact that ICEVs is viewed as a convenience purchase and the user do not prefer to plan ahead to fnd refueling stations.Consequently, fast-charging stations serve as "emergency service" amenities, and it is essential to consider consumers' behavior while locating charging stations.Meanwhile, the fuel/gas retail industry is well-established and optimized to serve vehicles, and these locations are natural candidates for installing fast chargers.To address the abovementioned issues, the following contributions have been made.
Te current study aims to develop a mathematical model for minimizing the total cost by optimizing the location planning of charging stations, their sizing, and the number of total chargers within each charging station.Te charging station opening capital cost and the user's convenience cost (defned by station access cost) are the two essential considerations while planning for an optimal charging location.Tis study proposes fve diferent integer linear programming (ILP) models to address the problem of EVCS location and sizing.Te proposed models may be grouped under two main categories.First, ILP models are solely used for chargers location decisions; second, ILP models consider both location and sizing decisions.Both categories are distinguished by defnite decision variables, relevant realworld constraints, and a corresponding objective function.
Te remainder of the paper is as follows.Section 2 details the proposed mathematical models.Section 3 reports the main results of the conducted computational experimentation.Section 4 concludes and provides future research avenues.

Model Formulation
Diferent covering models (optimization models) are proposed.Te objective is to minimize various formulations of objective costs while satisfying all demands.Te suggested models deal with the planning of EVs charging network for a metropolitan region based solely on an existing gas station.

Assumption.
Te study was based on the following main assumptions for simplicity: (i) For EV users, only daytime charging is considered.Tis appears to be convenient for a workplace in an urban region.(ii) Only fast charging stations are considered, and each charger may provide service to multiple EVs, as fast charging is usually considered the best solution for gas stations.
(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.

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 locations 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, 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 (i, j ∈ V) denoted the distance between locations i and j.Table 2 provides the distance matrix.

Linear Programming Models.
Diferent models might be used to optimize the installed resources.Tis section contains 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-yetplaced 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 adhering 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 and last three models focused on both location and sizing.

ILP Models Considering an Only Location.
Te frst class of ILP models used an NP-hard set covering problem [51].For that purpose, we defne a binary variable x i for each location i ∈ V, which takes the value 1 for an EVCS installation at location i; otherwise, 0. R represents a constant coverage radius that denotes the EVs user's tolerable distance while looking for a charging station.Ten, the intermediate constant is utilized.Let a i,j (i, j ∈ V) be a binary constant which takes the value 1 if d i,j ≤ V; otherwise, 0, and d i,j is the same as described in the preceding section.As a result, the model M 1 can be obtained as follows: Subject to: Te objective function shown in equation (1) [19], which represents the number of stations installed, is minimized in this model.Constraint (2) establishes the coverage radius for the accessibility of EVs' users.Te constraints conditions shown in equation ( 3) indicate the binary restraints on x variables.Te M 1 model minimizes the total number of installed stations.It refers to minimize the total numbers of charging station in the proposed area.Based on set covering combinatorial optimization models [36], the M 1 model is useful when the cost of installation is fxed from one station to the next.For example, under normal service operation of the station network, the charger cost is somehow low relative to the opening cost.We add f i (i ∈ V) a size-independent cost of opening a charging station at each possible location i to account for the infrastructure opening cost.It is the cost of converting a gas station into EV compatible lot, specifcally   Journal of Advanced Transportation the equipment and administrative expenditures [52].When the accommodation capacity for all the possible locations is fxed, the size-dependent costs are constant, and then the model is focused on minimizing only the opening costs.As a result, the model M 2 is formulated as follows: Subject to: Te objective function (4) reduces and minimizes the overall cost of all installed stations to the lowest possible value as investigated in [52].Constraint (5) states that a minimum of 1 station on a radius R is installed for every location j (location j included), and constraint (6) expresses the variable nature.

ILP Models Considering Both Locations and Sizing.
Te focus of the second ILP model is to develop suitable station sizes, in addition to identifying charging station locations.To begin, we assign the following numbers to individual feasible location i ∈ V, (i) a capacity c i , which represents the maximum chargers numbers that may be installed concerning the location station capacity, (ii) price per unit for installing a charger, represented by u i , and (iii) fnally, a demand m i that represents the number of EVs that 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].
In the abovementioned relation, where λ implies the service rate or the number of EVs that could be charged in one hour, and s t represents the entire charger service time.Te service rate is frstly introduced in the review study [53].Every location i ∈ V might be considered a possible construction place for charging stations as well as the centroid of territory for EVs' drivers.Here, two new decision variables are also introduced.Defning every location (i ∈ V) as a non-negative integer variable n i that denotes the number of total chargers installed in each location i. Defning a binary variable y ij , which is set to 1 if the EV from ith location i are charged at jth location.As a result, the third ILP model M 3 is as follows: Subject to: x j ≥ Y i,j ; ∀i, j ∈ V, (10) Te objective function is shown in (8) for the M 3 model that aims to optimize (minimize) charger installation and capital costs.Constraint (9) requires that all EVs be assigned Journal of Advanced Transportation to a specifc EVCS.Constraint (10) defnes that EVs can only be charged in location j ∈ V if this site is chosen for accommodating a charging station.Constraint (11) stipulates that for the chosen station, a minimum one charger must be installed, with the total number of chargers not exceeding the station's capacity.If a station is not specifed within it, no chargers are deployed.Constraint (12) requires that all EV owners who prefer charging their vehicles at a selected location should be less than the number of available service chargers.Constraint (13) denotes that the EV task from a selected position (i ∈ V) to location (j ∈ V) is feasible if only the provided distance between stations is less than the tolerance radius.Lastly, ( 14) and ( 15) show the integrality constraints and constraint ( 16) are the non-negative integer variables n.Terefore, the main focus is to minimize the charging infrastructure installation costs.Following that, it is also essential to consider the access cost.More specifcally, the travel cost was also included since EVs owners can drive from one location to another to fnd a suitable charging facility for their vehicles.Zhu et al. (2016) frst suggested this aspect in their analysis of a 60-km 2 Beijing metropolitan region because the charging station is far from the user's workplace [49].Tey believe that EV drivers may walk and take a cab or bus to get from one location to other.In our study, we consider only walking to get into the possible charging station.Indeed, EV users are unlikely to take a cab or bus from their destinations to the charging station.Te estimated cost of each walked kilometer is denoted by φ, the walking cost, which is determined in equation ( 17) as investigated in [52] where W s is the average walking speed and W h is the average hourly wage of an EV owner.As a result, model M 4 is as follows: Subject to: where ω 1 and ω 2 are non-negative weights.Te objective ( 18) is to minimize the total weighted costs.Te remaining equations are the same as the previous model (M 3 ).Each user's preferences for station installation and access cost are refected in the weights assigned to each station.Terefore, we suggest that the preceding model can be improved by including the total construction costs of a station.Finally, the model M 5 is introduced.
Subject to: As in [54], model M 3 corresponds to model M 5 as a particular case under the condition where ω 1 = 1 and ω 2 = 0

Numerical Experiments
After presenting the case study, the results for the base and recommended models are discussed and compared.After that, an experimental and comprehensive sensitivity analysis of the proposed ILP models was carried out to determine the sensitivity of the model to various cost components and also to other variables.Tis experiment was conducted on Intel Core I i5-8400 CPU@2.80GHz (6CPUs) desktop with 12 GB RAM.Te optimization programming language (OPL) was used to code the fve ILP models, and the general MIP solver (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.

Parameters Setting.
Using the following experiment, the cost of the deployed charger is assumed to be constant and not dependent on the installation location.As per the previous studies, u i (i ∈ V) is used as 56,000 [52,55].Te charging demand is expected to be uniformly distributed between each charging station.Terefore, m i (i ∈ V) is considered fxed at 13 based on [49].Equation ( 7) specifes 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 hourly wage W h is $17/hour.It is calculated by dividing the mean monthly wage ($3000) of an EV owner by accumulated worked hours in a month.An average walking speed is assumed to be 5 km/h [52,56].For M 4 and M 5 , models equal emphasis is placed for the station and user access costs by setting out the ω 1 � ω 2 � 0.5.

Coverage Radius Impact.
We focused on the coverage radius (R) to investigate its impact and variation on the deployment of the optimal infrastructure for each ILP model's output.Te tolerable distance R range is computed and ranged between 0 and 16 km.Table 3 represents the models M 1 and M 2 which simply outputs only location decisions.Te tables show the numbers of charging stations and corresponding opening costs.Taking R = 1 km corresponds to establishing an EVCS in every available place, resulting in the number of charging stations being = 18.Moreover, raising the R-value is associated with reduced opening costs and the number of locations selected.Up to 16 km, the numbers of charging station are 6 for both models M 1 and M 2, and the cost is changed because the locations are not the same for both models.Te evolution of models M 1 and M 2 outputs is presented in Figure 3. Furthermore, Table 4 displays the ILP models result for decisions related to location and sizing.Table 4 added the number of chargers.Increasing the R-value is accompanied by fewer charging stations; however, it also means that more chargers need to be installed within the charging stations.According to models M 3 and M 5 , the R-value is 16 km, and the number of charging stations and numbers of the charger are 5 and 16, respectively.However, based on model M 4 , which does not include the station opening costs, 10 stations should be chosen for nearly half the cost of those shown by model M 3 .Te number of chargers are same for models M 3 , M 4, and M 5 because the charging demand is uniformly distributed.Moreover, in model M 5, the high price is attributable to the user's access cost.Te evolution of models M 3 , M 4, and M 5 outputs is shown in Figures 4-6 3.2.2.Impact of Charging Time.EVs fast charging technology is transforming speedily, and the current study aims to investigate the impact of charging time change on the deployed EVCS.Table 5 shows the model results for the charging time evolution and the service rate λ of the charger.It is worth mentioning that the prolonged charging time increases the number of chargers; as a result, increasing installation costs, which is also dependable on the number of total chargers.Te 5 EVCS can be installed for M 3 and M 5 .Tis demonstrates that the suggested models continue to use a similar EVCS placement.Even as technology progresses and decreases charging times, the established EV charging scheme remain efective.Figure 7 shows the frst network only considered minimizing the EVCS numbers.Figure 8 is constructed to consider the only opening cost of EVCS.Furthermore, when solely the investor's convenience is regarded, the framework shown in Figure 9 should be constructed.Te network depicted in Figure 10 should thus be established when the convenience of users and investors is equally important, but the station opening costs are not taken into account, like in the case of [49]. Figure 11 depicts the most appropriate EVCS deployment, considering actual station installation costs and EV users' access costs.As a result, the convenience of both investors and EV owners is considered equally.We strongly endorse these proposed locations for EVCS placement in the proposed prefecture to avoid squandering private and public resources while maintaining a suitable service level for EV users.Several previous studies have been focused on EVCS in existing parking lots, fuel stations with diferent aspects, such as minimizing the total cost [49,57], minimizing access cost [50], EV charging demand [26], minimizing trips [58], and minimizing the total system cost [52].So far, the overall     Journal of Advanced Transportation fndings of this current study are extremely promising compared to these previous studies.Te proposed ILP method's analysis was validated using several experimental designs.Finally, it is proved that the proposed ILP method produced more accurate and precise results within the scope of its intended use.Based on these fndings, we conclude that the ILP model is an efective method for accurately solving problems of EVCS.It is beyond the scope of this study to determine how efectively the various approaches described will scale to issues that are very diferent from the ones analyzed.Nevertheless, the aim of this study is to determine appropriate locations for EV charging stations in Aichi Prefecture, Japan.More precisely, our concern is to ensure that the deployed infrastructure has a tolerable coverage radius.In fact, EV drivers are to accept a long walk distance from charging stations to their destination.Tis study provides an optimum infrastructure network that policymakers could adopt within the emerging environmental policy.

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 fastcharging stations.It is based on the optimization technique of integer linear programming.Particularly, we are more concerned with ensuring that the deployed infrastructure 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 assist policymakers in determining the locations and sizing of suitable EVCS while lowering investment and consumers' convenience costs.It is worth noting that this study has some limitations that can be addressed in future research.EV users' preferences from their home location to other charging spots are treated as a fraction, considering that the decision variables in the current models are treated as a continuous variable.Instead of using the Cartesian distance, the distance matrix could be made more precise by estimating suitable paths between all pairs of possible locations, for example, average paths.Conducting an extensive study on the estimation of EV demand and incorporating consumer behavior, market anticipation, and energy consumption in the proposed study area further consider the impact of EVs' charger deployment as well as the forecasted number of EVs on the city's electrical grid.

Data Availability
Te data used to support the fndings of this study are available on request from the corresponding author.

Table 2 :
Te distance among possible charging stations in (km).

Table 3 :
Te impact of the coverage radius on the results of models M 1 and M 2 .

Table 4 :
Te impact of the coverage radius on the results of models M 3 , M 4, and M 5 .

Table 5 :
Efect of the charging time on M 3 , M 4, and M 5 model outputs.

Table 6 :
Efect of the EVs' charger costs on M 3 , M 4, and M 5 model outputs.