Location of Electric Vehicle Charging Piles Based on Set Coverage Model

: Electric vehicles are rapidly popping up in the market as a new alternative to fossil fuels, in order to reduce carbon emissions in urban areas. However, the improper placement of charging piles has impeded the development of electric vehicles. In this paper, 12 indicators from 4 categories, namely economy, environment, cost, and service quality are selected to form an index system for evaluating the location of electric vehicle charging piles. The entropy weight-TOPSIS method is also applied for the same purpose. On the basis of the evaluation, this paper proposes a set coverage model and adopts a greedy heuristic algorithm to ﬁnd out the optimal location of charging piles. Finally, the paper veriﬁes the reasonability and feasibility of this model by studying the existing location of electric vehicle charging piles in northeast China. The evaluation is based on the Liaoning Province Electric Vehicle Big Data Supervision Platform, which has data that are ofﬁcial and scientiﬁcally based. The set coverage model proposed, based on the evaluation, is a new solution to ﬁnding out the optimal location of electric vehicle charging piles across China. This study aims to provide a theoretical basis for the development of this new energy industry.


Introduction
In this new era, it is necessary to promote a green and low-carbon life. With policy dividend and technology advancement, China's electric vehicle industry is booming with remarkable results achieved. As of January 2020, more than 3.85 million electric vehicles have been manufactured and 531,000 public charging piles have been installed in China [1]. Northeast China is a region where the development of electric vehicles has set off to a good start. In this region, the task of controlling haze is still demanding, and much infrastructure development is underway. Therefore, there exists the need for environmental protection, energy conservation, and emissions reduction, unleashing the development potential of new industries to revitalize the region and upgrade its industrial structure. Since the industrial revolution, fossil energy has been the main source of energy for propelling cars. Although this has contributed much to the economy and brought convenience to people's lives, it has led to a cascade of environmental problems, due to combustion. The electric vehicle is more eco-friendly compared to traditional cars, as it is the electricity stored in the battery pack that propels the vehicle, without producing exhaust gases. For this reason, developing electric vehicles has become a key national strategy, especially in cities facing daunting tasks to control haze. Against such a backdrop, it is imperative to install more charging piles in order to meet the demand for charging electric vehicles.
However, critical issues have presented themselves: some electric vehicles currently have nowhere to charge, or charging piles in some places are left unused. The improper with the least charging stations and the lowest cost. They combined a greedy algorithm and an entropy power method to work out the solution of this model.
From what is discussed above, it can be seen that most of the existing studies focus more or less on the location of electric vehicle charging piles. But few use an index system to evaluate the location systematically, which is exactly the focus of the government and the market. Therefore, this paper evaluates the location of charging piles in northeast China from four aspects: economy, environment, cost, and service quality. Combining the entropy weight method and TOPSIS method, this paper evaluates the location of charging piles based on the set coverage model while considering the situation of each province. The rationality and feasibility of this model are verified. The data used by this paper are sourced from the Liaoning Province Electric Vehicle Big Data Supervision Platform, which is official but not released. This paper also studies the proper location of charging piles using a scientifically based model to make the choosing of location more targeted and reasonable.

The Index System for Evaluating the Location of Electric Vehicle Charging Piles
The charging pile is the supporting facility for electric vehicles. It is composed of a body, an electrical module, a metering module, and so on. Currently, there are three modes for charging electric vehicles: quick charging, slow charging, and battery swapping. The slow charging mode is the most widely used. According to surveys, 90% of vehicles are charged this way, while those with quick charging is less than 10%.

Building the Index System for Evaluating the Location of Charging Piles
On the basis of previous studies, this paper summarizes several factors influencing the location of electric vehicle charging piles. To be objective and reasonable, while considering data availability, 12 indicators are selected from four categories, including economy, environment, cost, and service quality. These indicators constitute the index system for evaluating the location of electric vehicle charging piles. According to personal experience, more indicators are added: C 1 , C 2 , C 10 . The index system is shown in Table 1.  [14] and so on Note: Indicators C 1 , C 2 , and C 10 are added according to personal experience.
The index system developed in this paper includes both quantitative and qualitative indicators, among which nine indicators from economy, environment and service quality, and the land price under the cost factor are quantitative, while the construction cost and the operation cost under the cost factor are qualitative, because it is difficult to weigh them by number. The questionnaire is used to evaluate quantitative factors. The result of the study can provide a theoretical basis for choosing the location of charging piles.

Entropy Method
There are many evaluation methods, such as the hierarchical analysis, the gray correlation method, and the data envelopment method, etc. The entropy weight method, which is objective, works by calculating the entropy weight of each indicator through the information entropy, and on this basis, ranking the weight of all indicators to obtain a more objective weight for each indicator [2]. After the weight of indicator is determined, the TOPSIS method is applied to solve the problem of the multi-objective decision. The evaluation on the location of charging piles is made in an objective way to avoid errors caused by subjective assumption. The result of which sheds light on finding out the optimal location for electric vehicle charging piles.
(1) Develop the original evaluation index matrix. The original matrix forms evaluation schemes and n indicators as follows: In the formula: a ij is the jth indicator value of the ith evaluation scheme.
(2) Standardize the data in the matrix with the following equation. For positive indicators: For negative indicators: (3) Normalize matrix A.
The normalized matrix A* is obtained: (4) Calculate the information entropy.
Among them, 0 ≤ w j ≤ 1, m ∑ i=1 w j = 1, w j represents the weight coefficient of indicator j, and 1 − H j represents the difference coefficient of indicator j.

TOPSIS Method
The TOPSIS method, also known as the Technique for Order of Preference by Similarity to Ideal Solution, is a common, multi-criteria decision analysis method for finite solutions, which mainly relies on the "ideal solution" and "negative ideal solution" of the decision problem to do the ranking and choose the optimal solution. TOPSIS needs to be processed in a weighted, normalized decision matrix. As indicators have different dimensions, it is necessary to normalize the original data.
(1) Develop the normalized decision matrix Z = (Z ij ) m×n : Develop the weighted normalized decision matrix V, element V ij = W j Z ij , where w j represents the weight coefficient of indicator j.
(2) Determine the ideal solution and the negative ideal solution.
The larger the value of element V ij in the decision matrix V, the better the scheme is. Ideal solution: Negative ideal solution: (3) Calculate the distance from each scheme to the ideal S i + and the distance from each scheme to the negative ideal S i − .
(4) Calculate the relative proximity of each scheme.
Rank the result by relative proximity. The larger the value of C i , the better the overall performance.

An Optimal Model for Choosing the Location of Charging Piles Based on Location Evaluation
Choosing the location by coverage is one of the three typical models for choosing the location. This was first put forward by Toregas and other scholars. This model is mainly used to choose the location for emergency service facilities, which requires the widest coverage with the least number of service facilities [43].

Model Overview
The set coverage model functions by distributing discrete points. When the demand points are given, a set of service points can be determined to meet the demand and cover all demand points with the least number of service store areas. The model is often applied to logistics distribution centers, express delivery outlets, gas stations, emergency centers, and electric vehicle charging piles. M refers to the set of candidate points, M = {1, 2, · · · , m}; N is the set of demand points, N = {1, 2, · · · , n} (By researching map information and related literature, the crowd flow center is selected and N is taken as the demand point for charging piles); x i represents whether to set up a charging pile at point i, and when: The charging pile is located at point i 0, The charging pile is not located at point i (14) r ij is the distance from candidate point i to demand point j, R is the warning distance that the electric vehicle can run with the electricity left, and y ij represents whether point j is within the range of point i. x i is the node, y ij is 1 when it is selected, and 0 when it isn't. To be specific, if the distance between the vehicle and candidate point j is smaller than that between the vehicle and demand point i, y ij is 1, otherwise it is 0.
The objective function is as follows (The objective function of the set coverage model refers to the number of demand points covered within the alarm-driving distance of the candidate points, so that the construction cost is minimized):

Model Solution
First, demand points and candidate points of electric vehicle charging piles are determined according to the distribution of existing charging piles in each district. Since the set coverage model is an NP-hard problem with polynomial complexity, this paper, based on the 0-1 programming model and following the greedy algorithm, has obtained the optimal solution on MATLAB software.

Background
City S is located in the south of Northeast China, and at the center of the Northeast Asian Economic Circle and the Bohai Rim Economic Circle. It is a comprehensive hub connecting the Yangtze River Delta, the Pearl River Delta, and Beijing-Tianjin-Hebei District to Northeast China. In 2020, the total gross domestic product (GDP) of city S reached 657.16 billion yuan, up 0.8% from the previous year. In the innovation-driven era, with electric-driven vehicles the main focus of national strategy, the new path to developing the electric vehicle industry in a fast, efficient, healthy, and sustainable way lies in properly placing charging stations and other infrastructure within overall planning.

Evaluation on the Location of Charging Piles
First, demand points of this paper are located in ten districts of city S. (1). Data collection and processing. After collecting the data for each indicator, we analyzed the economic, environmental, cost, and service quality factors. The initial data for different indicators were obtained from the statistical yearbook, the Bureau of Natural Resources, the Bureau of Statistics, and the Liaoning Province Electric Vehicle Big Data Supervision Platform, as shown in Table 2. As the data about the construction cost and the operation cost were limited, they went through processing. The questionnaire was used with the value of data made between 0 and 1. The land price, construction cost, operation cost, utilization rate, and charging price were negative indicators. After the questionnaire was analyzed, we developed the Table 3 showing indicators. (2). Calculate the information entropy and the weight of various indicators. The information entropy and weight of the 12 indicators were calculated following Formulas (1)-(7), as shown in Table 4. Table 4. The information entropy and the weight of each indicator.  (3). Calculate the distance between positive and negative ideal solutions. The distances between the 10 districts and the positive and negative ideal solutions were calculated following Formulas (8)- (13), as shown in Table 5. (4). Calculate the proximity. The proximity of the 10 districts in City S was calculated following Formula (13), as shown in Table 6. (5). The location evaluation results. The proximity of the 10 districts of S city was calculated, as shown in Figure 1. The proximity was in the following sequence from highest to lowest: district 1, district 2, district 4, district 10, district 3, district 7, district 5, district 8, district 6, and district 9.
World Electr. Veh. J. 2022, 13, x FOR PEER REVIEW 9 of 16 (4). Calculate the proximity. The proximity of the 10 districts in City S was calculated following Formula (13), as shown in Table 6. (5). The location evaluation results. The proximity of the 10 districts of S city was calculated, as shown in Figure 1. The proximity was in the following sequence from highest to lowest: district 1, district 2, district 4, district 10, district 3, district 7, district 5, district 8, district 6, and district 9.

Optimal Location for Charging Piles
According to the district's urgency to choose the location for charging piles, the paper selected the top three districts from the location evaluation results: district 1, district 2, and district 4, to find the optimal location, which would be significant to the overall planning of the location for charging piles.
(1). Current distribution of charging piles. We know the location of electric vehicle charging piles in district 1, 2, and 4 from the China Liaoning Province Electric Vehicle Big Data Supervision Platform. The latitude and longitude of 10 candidate points are shown in Table 7.

Optimal Location for Charging Piles
According to the district's urgency to choose the location for charging piles, the paper selected the top three districts from the location evaluation results: district 1, district 2, and district 4, to find the optimal location, which would be significant to the overall planning of the location for charging piles.
(1). Current distribution of charging piles. We know the location of electric vehicle charging piles in district 1, 2, and 4 from the China Liaoning Province Electric Vehicle Big Data Supervision Platform. The latitude and longitude of 10 candidate points are shown in Table 7. By checking the map and reviewing relevant literature, we chose 16 places with high traffic as demand points for charging piles, as shown in Table 8. The distance between the location of the candidate points and the demand points can be seen in Figure 2. (2). Analyzing the Set Coverage Model. From relevant literature, it is known that an electric vehicle can drive no more than 3 km after a power-off warning is sent out. Therefore, the maximum driving distance was set to 3 km. Based on this, we further analyzed the candidate points in Figure 2 and ob- (2). Analyzing the Set Coverage Model. From relevant literature, it is known that an electric vehicle can drive no more than 3 km after a power-off warning is sent out. Therefore, the maximum driving distance was set to 3 km. Based on this, we further analyzed the candidate points in Figure 2 and obtained the demand points covered within the radius of 3 km for each candidate point, as shown in Table 9.
Note: There is no coverage demand point within the radius of 3 km for candidate points Y 9 and Y 16 .
According to the constraint in Equation (17) and the coverage areas in Table 9, we can obtain the constraint function: The constraint function was worked out according to Formulas (16) and (17), and obtained the least number of candidate points that could cover all demand points. Given that there was much calculation to be done, we ran the greedy heuristic algorithm on Python software. The final results are shown in Table 10. From the results in Table 10, it can be seen that: a. Taking into account the location of the existing charging piles, there were 16 demand points for electric vehicle charging piles.
After checking the map and reviewing relevant literature, this paper found it necessary to place 16 electric vehicle charging piles in such crowded places as the commercial center, residential areas, and industrial areas. Through model analysis, it was found that 11 demand points, namely Y 1 , Y 2 , Y 3 , Y 4 , Y 5 , Y 7 , Y 9 , Y 10 , Y 13 , Y 15 and Y 16 , could meet the existing charging demand. But some electric vehicle owners still had no place to charge their cars. To solve this problem, this paper tried to find out the optimal location for charging piles for the above-mentioned high traffic places.
b. Through some calculation, the study found that the current location for some charging piles might be improper. So, their location awaited adjustment.
A total of 12 electric vehicle charging piles were built in the three selected districts of city S. Among them, 7 were in district 1, distributed in Y 1~Y7 ; 3 were in district 2, distributed in Y 8 , Y 9 and Y 10 ; and 2 were in district 4, distributed in Y 11 and Y 12 . According to the set coverage model, and considering that the maximum driving distance of an electric vehicle after a power-off warning was sent out was 3 km, the following charging piles were found to meet the above basic conditions: X 3 , X 4 and X 6 in district 1, X 8 and X 9 in district 2, and X 11 in district 4. The rest could not meet the needs of the vehicle owners. To reduce the operation cost and improve the efficiency of the charging piles, X 1 , X 2 , X 5 , X 7 , X 10 , X 12 were suspended for use.
c. To meet the demand for charging, five new charging piles need to be placed. Based on the greedy heuristic algorithm, to meet the charging demand of electric vehicle owners, new charging piles should be placed for Y 6 and Y 8 in district 1 of city S and Y 11 , Y 12 and Y 14 in district 2.
The analysis on the location of charging piles through the set coverage model should focus on improving the utilization rate. To cover all demand points, 11 out of 28 candidate points were selected in this paper: X 3 , X 4 , X 6 , X 8 , X 9 , X 11 , Y 6 , Y 8 , Y 11 , Y 12 , Y 14 . In district 1, X 3 , X 4 , and X 6 were kept while Y 6 and Y 8 were newly built. In district 2, X 8 and X 9 remained in use while Y 11 , Y 12 , and Y 14 were newly built. In district 4, only X 11 was left. These charging piles could cover all demand points without overlap or inadequacy.

Conclusions
Based on previous studies on electric vehicles and their charging facilities in China, this paper studies the location of electric vehicle charging piles by developing the entropy-TOPSIS model and the set coverage model. City S in Liaoning Province is studied to verify the feasibility of the model with data sourced from the Liaoning Province Electric Vehicle Big Data Supervision Platform.
Major achievements of this paper are as follows.
(1) The location of electric vehicle charging piles should be reasonable and feasible. It is the trend of the era to develop electric vehicles and new energy to reduce urban carbon emissions. However, after studying the current situation of charging facilities and problems related to electric vehicles, it is found that some electric vehicles have nowhere to charge, or that charging piles in some places are left unused. Therefore, the improper location of charging piles impedes the development of electric vehicles.
(2) This paper develops a reasonable and scientifically based index system for evaluating the location of charging piles. As many factors influence the choice of location, this paper focuses on economic factors, environmental factors, cost factors, and service quality factors, and uses the entropy weight-TOPSIS method to evaluate the location. Compared to other approaches, this method is more objective, with simple calculations. Using existing data, it can obtain scientific evaluation results to meet the need of choosing the optimal location for electric vehicle charging piles.
(3) According to the traffic and land conditions, this paper proposes the optimal location of charging piles by developing a set coverage model with city S as an example. An objective function is set up with known constraints to find out the optimal candidate points that cover demand points. The greedy heuristic algorithm is used to work out the solution. It is found that the optimal way of placing charging piles is to keep six existing ones and add five new ones, which can cover all demand points without overlap or inadequacy.

Data Availability Statement:
The data presented in this study is available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.