Layout evaluation for electric vehicle charging pile based on charging frequency

Abstract

This study aims to solve the problem of locating charging stations for public electric vehicles. We take into consideration the factors affecting charging station locations including mileage, electric vehicles distribution, and passenger distribution. A Non-deterministic Polynomial model aiming to minimize the total vehicle service distance is developed. We use an agent-based model to simulate the optimized charging station location based on Anylogic. Through a case study of Beijing, we test the model in five situations. The results of one situation show that the existing layout of the charging stations is unreasonable when charging frequency is sharply variant (basic model); this paper optimizes the existing location by improving the constraint for the smallest number of charging stations (improved model); compared with the basic model, the improved model has a shorter response time to passenger demand, shorter service time for passengers but more mileage for electric vehicles.

Keywords

Electric Car charging pile layout charging frequency simulation

1 Introduction

Faced with tremendous pressure from energy and the environment, people are constantly seeking clean alternative fuels to improve the deteriorating traffic emissions. Electric vehicles have gradually become the focus of attention of governments and automakers. Many cities at home and abroad are actively applying electric vehicles to urban transportation. At the same time, in the short term, electric vehicles can not completely replace ordinary fuel vehicles, which is an effective supplement to the demand for ordinary fuel vehicles, and also reflects the future development strategy. Therefore, the pattern of coexistence and common development of battery vehicles and fuel vehicles will continue to exist in the short term.

Under the current environmental and technical conditions, the core problem facing the development of electric vehicles is the selection and construction of charging pile layout. Rechargeable pile layout construction selection requirements, within a certain time range, electric vehicles are randomly distributed in a certain number of people, in areas with a large amount of traffic demand (regardless of the distance required by car search users), the purpose is based on fuel for electric vehicles situation. The layout of the charging pile is reasonably arranged such as the distance traveled by the electric vehicle and the distance of the customer. Since charging piles are scarce resources, especially in the case of an increase in population and an increase in demand for charging piles and electric vehicles, it is difficult to avoid supply and demand conflicts. In addition to the uncertainty of customer demand, the individualized needs of different levels of customers, and the matching differences between electric vehicle demand and charging pile service types, how to properly arrange charging piles is important for improving the service level of electric vehicles and improving user satisfaction significance. The convenience, economy and safety of the charging system directly influence and determine the development process of the electric vehicle. In the entire industrial chain of electric vehicle development, charging piles are undoubtedly an important part of the industrial chain and the basis for the development of the electric vehicle industry.

The problem of electric vehicle resource allocation can be attributed to the Job-shop scheduling problem, which is a classic NP problem. It is described as following: Given a collection of artifacts and a collection of machines (each artifact consists of multiple processes), scheduling is the assignment of operations to a period on the machine. The goal of the problem is to find a schedule with a minimum run length. Applying the genetic algorithm to solve the Job-shop scheduling problem requires careful design of coding methods and genetic operators. At present, most of the solutions to the scheduling problem are concentrated on mathematical programming, computer simulation, and simple rule application. These methods provide empirical help for vehicle scheduling, but any parameter changes will affect the reusability of the algorithm or simulation. However, there are many dynamic and temporary factors in car scheduling. It is difficult to cover all the factors in a single mathematical planning model. However, if these dynamic and temporary factors are not taken into account, the solution to the scheduling problem is not enough. complete. At the same time, for multi-factor and complex dynamic mathematical models, relying solely on mathematical theory to solve, not only leads to the computational process is too complicated, the calculation results are not necessarily accurate; and computer simulation can provide by considering the complex conditions and considering various complex factors.

Therefore, based on the clearing of the influence scheduling factors, this paper establishes an NP model with the minimum total running time of the vehicle as to the objective function. Under the Anylogic simulation environment, the Agent technology is used to analyze and design the electric vehicle resource allocation. The model results can be Solve the problem of car configuration to a large extent, and improve the degree of intelligent scheduling.

2 Literature review

At present, the research on the location of charging piles mainly focuses on the following five aspects: (1) traffic-based coverage problem; (2) focusing on the shortest energy path problem, and considering the total energy consumption on the path; (3) focusing on the electric vehicle path problem; (4) focusing on the location model and path model of the charging infrastructure layout; (5) locating research of charging piles.

2.1 Minimum energy loss study

Kuby and Lim [1] proposed the Flow Location Model (FRLM), which maximizes the total flow of coverage by locating a predefined number of sites in the network. The research seeks the lowest number of stations to meet all needs, rather than maximizing traffic flow coverage, which is essentially setting coverage issues. These two different types of flow-based position models were redefined by Mirhassani and Ebrazi [2] as a flexible gas station positioning problem. Huang et al. [3] allowed their passengers to pass through one or more gas stations during their journey on at least one route in their new multi-path fueling position model (MPRLM). In summary, the goals of these traffic models are minimized by network partitioning to the power loss of the charging pile, the combination of user demand loss and investment minimization, or the maximization of demand set coverage (Frade et al., 2011; Huang and Zhou, 2015) [4, 5]. It can be found that the research in this aspect provides an earlier location selection model, and has not considered the energy loss and customer demand of electric vehicles.

2.2 Charging pile layout based on energy loss

Artmeier et al. [6] focused on changes in the Shortest Path Problem (SPP), minimizing the energy required from point A to point B. Sachenbacher et al. [7] developed an energy efficient path prototype software that can be used in navigation systems. Arslan et al. [8] focused on the route selection of plug-in hybrid electric vehicles (PHEVs). A minimum cost path problem is proposed for the network of gas stations and charging piles; in addition, a heuristic algorithm for the shortest path is provided. Doppstadt et al. [9] also conducted further research on the driving problem of hybrid electric vehicles. It can be seen that these methods focus on runtime aspects, ignoring layout decisions and additional constraints that arise in the logistics environment (eg, customer time, customer needs, etc.).

2.3 Charging pile layout based on the vehicle path

Regarding the study of vehicle paths, Erdogan and Miller-Hooks [10] gave the Green Vehicle Routing Problem (GVRP) to minimize the overall distance traveled; and introduced GVRP test examples, indicating that the feasibility depends on the customer’s location. And charging piles. Barco et al. [11] proposed an electric vehicle routing problem (EVRP) that minimizes the use of energy rather than the distance traveled. Schneider et al. [7] proposed an electric vehicle routing problem with time windows (EVRP-TW), using hierarchical targets to minimize the number of vehicles and minimize the total distance traveled. By considering different types of electric vehicles, Hiermann et al. [12] extended the formula of EVRP-TW proposed by Schneider et al. The objective function minimizes the total distance traveled and the cost of acquisition for each vehicle leaving the warehouse. Bruglieri et al. [13] proposed a further solution to EVRP-TW for mathematical heuristics and variable neighborhood search branches. It can be found that this aspect of the study considers layout decisions, total distance traveled, and energy costs, but still does not impose additional constraints on customer time, customer needs, and so on.

2.4 Dual study of location and path

In addition to considering the vehicle path, the position and path model also emphasizes location selection. Dashora et al. [14] proposed a mixed-integer mathematical programming model to address the problem of charging infrastructure planning for organizations with thousands of people working in defined geographic locations, as well as parking lots that are well suited for charging pile installations. Ip et al. [15] used hierarchical clustering to determine the location of fast charging piles. This method converts road information into demand clusters, each cluster is assumed to be assigned to a fast-charging stub without explicitly giving the exact location in the cluster. A maximum coverage model proposed by Frade et al. [4] to locate a fixed number of central urban charging piles to maximize coverage requirements over a given distance, while the demand for each study area is estimated by the area. The number of vehicles is determined. Fragapane et al. [16] proposed a space-based and time-based model for determining the ownership of residential electric vehicles based on an agent decision support system in order to strategically deploy a new toll infrastructure in which the deployment of charging piles was carried out in advance. discuss. Xi et al., Nie and Mehrnaz, Yang and Sun [17 –19] also discussed the path and layout decisions. This aspect of the study illustrates recent research on standard locations and paths, providing variants and extensions to path and location issues, but not enough attention to charge usage and charge pile distribution studies.

2.5 Analysis of location problem of charging pile layout

Limited driving range and high life cycle costs have been identified as major obstacles to the large-scale marketization of electric vehicles (Huang and Zhou, 2015; Dong et al., 2014) [5, 20]. This situation is exacerbated by the lack of sufficient charging posts, especially the lack of fast charging stations for public electric vehicles that facilitate intercity travel. The evaluation of public electric vehicle layout is generally based on the distribution of supply or service to nodes in the space network, such as electric taxi charging piles (Dakak et al., 2020) [21] and electric bus charging piles (Ip et al., 2010; Momtazpour et al., 2014) [15, 22]. Multi-period or dynamic public electric vehicle facility locations have two general category models: location and location relocation models. The first type assumes that once the facility is put into use, it will not be resettled (Wesolowsky, 1973; Van Roy and Erlenkotter, 1982) [23, 24]. This type of model is ideal for capital-intensive infrastructure planning, such as refineries (Huang et al., 2010) [25]. The second category allows relocation of facilities after the migration (Wesolowsky and Truscott, 1975) [26]. Such models are particularly suitable for mobile facilities such as ambulances (Carson and Batta, 1990) and public service facilities (Gregg et al., 1988) [27, 28].

At present, in the research related to electric vehicle charging piles, in addition to continuing to pay attention to the traditional technical realization problems [29], more focus on the research of user needs specific use and layout evaluation, such as considering the problem of a communication flow (Wang et al., 2018; Wang et al., 2019; Gagarin and Corcoran, 2018) [30 –32]; user demand charging multi-target selection problem (Shi et al., 2018) [33]; user demand charging price selection problem (Lee et al., 2018) [34]; User demand for fast charging (Domínguez-Navarro et al., 2019) [35]; charging environment and charging requirements (Quddus et al., 2018) [36]; user demand shared charging problem (Loeb et al., 2018) [37]; user The problem of demand charging behavior (Li et al., 2018) [38], and the game selection problem of the user’s demand charging process (Xiong et al., 2018) [39]. Therefore, in future research on charging piles, more attention should be paid to the charging pile layout evaluation model combined with traffic flow limitation and user demand experience, to maximize the coverage of charging (Dong et al., 2019) [40]; The model of the factor, while taking into account the practical application of the model, simulation is an effective way to solve such traffic network problems (Levinson et al., 2018; Harmathy, 2018; Burinskiene, 2018) [41 –43]. In summary, the existing research on the location of charging piles mainly has the following two aspects of improvement in subject and object issues:

lack of object analysis of charging usage, charging usage can understand the appropriate charging frequency, existing research focuses on traffic flow, driving distance, path, etc., should be the duration of people’s activities, actual needs of users, for real-time Location, especially the feedback of user demand, as an important indicator for selecting the evaluation of charging pile layout;

lack of main research on the distribution of charging piles, charging pile distribution can be understood as the best site density method, existing research focuses on input, cost, coverage, etc., should optimize the construction method to estimate the minimum required for charging The level of infrastructure is designed to minimize the distance between the charging pile and the demand location. Both the charging usage and the charging pile distribution can be classified as user demand usage, that is, the charging pile layout based on the user’s demand usage.

The selection of charging piles is generally divided into two stages. The first stage is large-scale laying. (Considering the contradiction between supply and demand, the supply side usually installs charging piles when there is a clear demand, and the user needs only to charge. At the time of convenience, the demand will be reflected. Therefore, the first stage is generally the government-led charging pile layout; the second stage is the location optimization construction stage, especially the demand estimation problem (the charging pile layout needs to be adjusted according to the generated demand). Bae and Kwasinski (2012) [44] proposed similar observations on demand estimation. By applying M/M/s queuing theory and fluid dynamic traffic model, the consideration of vehicle arrival charging piles was studied, and the charging near the highway exit was estimated. demand. In recent years, many new models have been used to analyze electric vehicle layout issues, such as the best site density method, and Sathaye and Kelley (2013) [45] aim to define the best site density criteria, rather than the usual precision. Position considerations, they estimate the minimum charging infrastructure required for highway corridors by continuously optimizing the construction method, aiming to minimize the distance between the charging pile and the demand location; charging frequency analysis method, the people’s activities continue Time and its location as an important indicator for selecting the layout of charging piles, Li et al. (2017) [46] take the taxi in Beijing as an example, taking into account the location of the charging pile, the demand of each charging pile, the type of demand, and the demand. Continuity, etc., establish a simulation model for the optimization of the location of the charging pile. The model aims to provide the charging efficiency of the charging pile.

Therefore, how to objectively extract useful information and demand analysis from the use of large-scale electric vehicle users to the use of electric vehicle charging piles, and analyze the actual use requirements of electric vehicle charging piles under specific road network structure and usage habits. Therefore, it is an urgent problem to build a charging pile more reasonably.

3 Mathematical model

The unified system model makes the integration optimization analysis and design of the problem easier, and is beneficial to the optimization of the analysis algorithm. Based on the analysis basis of the previous chapter, this chapter mainly establishes the electric vehicle operation optimization model under the condition of charging pile position constraint from the aspects of automobile-user demand constraint and automobile resource use priority, which provides reference for the evaluation of charging pile layout.

Before analyzing the model, we loosen some conditions, the main purpose is to analyze the nature of the solution and whether there is a feasible solution. Table 1 gives the parameters in the layout evaluation problem.

Table 1
Parameterssetting

Serial number Variable name Variable description

1 S The amount of electricity consumed per unit distance

2 C The maximum amount of electricity that the car can store, TD

3 d _jj′ The distance between j user needs and j’ user needs

4 d _jc d _j′c Customer distance to the charging pile

5 G A large positive number

6 X _ijk Whether is the i car equipped with j user demand in the kth time, 0–1

7 Y _ikc Whether the i car accesses the charging pile in the kth time, 0-1

8 L _ik The working distance of the i car at the kth time

9 Z _ik The remaining power of the i car at the beginning of the kth time

10 e _i,k The first leg of the i car in the kth trip

Serial number	Variable name	Variable description
1	S	The amount of electricity consumed per unit distance
2	C	The maximum amount of electricity that the car can store, TD
3	d _jj′	The distance between j user needs and j’ user needs
4	d _jc d _j′c	Customer distance to the charging pile
5	G	A large positive number
6	X _ijk	Whether is the i car equipped with j user demand in the kth time, 0–1
7	Y _ikc	Whether the i car accesses the charging pile in the kth time, 0-1
8	L _ik	The working distance of the i car at the kth time
9	Z _ik	The remaining power of the i car at the beginning of the kth time
10	e _i,k	The first leg of the i car in the kth trip

Therefore, the objective function is the shortest distance traveled by a car, ie, Equations (1)–(4) $Min (\sum_{i = 1}^{n} \sum_{k = 1}^{\infty} L_{ik})$ (1) $d_{{jj}^{'}} = \sqrt{{(x_{j} - x_{j^{'}})}^{2} + {(y_{j} - y_{j^{'}})}^{2}}$ (2)

In this formula the x_j, y_j represents the coordinates of the user’s requirement j, the x_j′, y_j′ represents the coordinates of the user’s requirement. $d_{jc} = \sqrt{{(x_{j} - x_{c})}^{2} + {(y_{j} - y_{c})}^{2}}$ (3)

The x_c, y_c represents the coordinates of the charging post c. $d_{j^{'} c} = \sqrt{{(x_{j^{'}} - x_{c})}^{2} + {(y_{j^{'}} - y_{c})}^{2}}$ (4)

Model constraint

(1) Access charging pile

To ensure that the electric car does not access the charging pile, and after searching for the next user demand, it can be charged to the nearest charging pile, Equation (5): $e_{i, k} \geq (X_{i, j, k} + Y_{i, k, c} - 1) d_{jc}$ (5)

(2) Walking distance

∀i, j, k, c, When the electric car accesses the charging pile, Equation (6): $\begin{matrix} L_{i, k} \geq (X_{i, j, k} + Y_{i, k, c} - 1) d_{jc} \\ + (X_{i, j^{'}, k + 1} + Y_{i, k + 1, c} - 1) d_{j^{'} c} \end{matrix}$ (6)

The model has been searching for excellence, always looking for the maximum value, this must be $X_{i, j, k} = 1 Y_{i, k + 1, c} = 1$

When not accessing the charging pile, Equation (7): $L_{i, k + 1} \geq (X_{j, j, k} + X_{j, j^{'}, k} - 1) d_{{jj}^{'}}$ (7)

(3) No electricity cannot move

Total charging description, Equation (8): $C \sum_{c} Y_{i, k, c} + Z_{ik} \geq L_{i, k} \times S$ (8)

First distance, Equation (9): $G (1 - Y_{i, k + 1, c}) + Z_{i, k + 1} \geq S (X_{i, j, k} + Y_{i, k, c} - 1) d_{jc}$ (9)

Second distance, Equation (10): $\begin{matrix} {CY}_{i, k + 1, c} + G (1 - Y_{i, k + 1, c}) \\ \geq S (X_{i, j^{'}, k + 1} + Y_{i, k + 1, c} - 1) d_{j^{'} c} \end{matrix}$ (10)

In the case of Y_i,k+1,c = 0, ensure that the model has a solution; the optimization process, must be $Y_{i, k + 1, c} = X_{i, j^{'}, k + 1} = 1$ (4) Electricity balance

∀i, j, k, c, When the car accesses the charging pile, Equation (11): $Z_{i, k} \leq C \sum_{c} Y_{i, k, c} - S \times e_{i, k} + G (1 - \sum_{c} Y_{i, k, c})$ (11)

Because of the minimum, ∑_cY_i,k,c = 1.

When the car does not access the charging pile, Equation (12): $Z_{i, k + 1} \leq Z_{i, k} - S \times L_{i, k} + G \sum_{c} Y_{i, k, c}$ (12)

Because of the minimum, ∑_cY_i,k,c = 0

(5) User demand service

Every user needs to need to be served, Equation (13): $\sum_{i} \sum_{k} X_{i, j, k} = 1, \forall i$ (13)

Each user request can only be serviced once, Equation (14): $\sum_{j} X_{i, j, k} \leq 1, \forall i, k$ (14)

(6) Charging pile access

Each car can access up to one charging pile at the same time, Equation (15): $\sum_{c} Y_{i, k, c} \leq 1, \forall i, kv$ (15)

(7) Number of services

Guarantee the ∀i, k services are not empty, Equation (16): $\sum_{j} X_{i, j, k} \leq \sum_{j} X_{i, j, k + 1}, \forall i, k$ (16)

Considering the nature of the research problem, we will try to analyze and solve the model using simulation methods. Therefore, in the next chapter, we use the Anylogic simulation platform to build the electric vehicle agent and user demand agent respectively to analyze and optimize the layout of the existing charging pile. The Agent model proposed in this paper will analyze the factors affecting the selection of charging piles in several major aspects, such as vehicle-user demand constraints, vehicle resource usage priority, charging mode, route selection, and customer service level. The study judges the impact of these key factors on the frequency of charging pile access by changing or considering some key factors. One-way ANOVA was used to identify the impact of certain key factors on the charging pile layout.

4 Simulation model

The platform used for article modeling is the AnyLogic 6.0 University version, which uses Java as the programming language. AnyLogic 6.0 University is a modeling simulation tool from XJ Technologies. The parameters of the electric vehicle simulation model are shown in Table 2.

Table 2
Simulation setting

Object Setting Description

Initial position

Different locations inoperation

Running direction

Abscissa

electric Ordinate

car State of electric vehicle

Number of times the electric car is operated

Remaining mileage

Electric car ID

Electric car running function

Considering the mileage limitation, electric vehicles need to be charged to the charging pile frequently. The criterion for measuring the reasonableness of the charging pile layout is that the frequency of charging the electric vehicle to different locations is not much different. Electric vehicles are affected by many factors, such as position coordinates and distance, during their use. In this model, we set four rules for electric cars:

(1) class

This class defines the behavior of the car and the characteristics of the demand, including initial position coordinates, time, priority, and demand. The Coordinate class can describe the car and the requirements to fulfill the user’s demand response.

(2) Position coordinates

Electric vehicles are limited to driving in certain areas due to their own characteristics and economic requirements. Using a binary table, xc indicates the range of car’s abscissa, yc indicates the ordinate range of the car, and xc, yc are obeying uniform distribution, which is

xc = uniform(minX,maxX), yc= uniform(minY,maxY)

minX,maxXrepresents the maximum and minimum values of the abscissa direction in the region, and minY, maxY represents the maximum and minimum values of the ordinate direction in the region.

(3) Distance and shortest distance

Let there be two points (including the charging pile position point, the electric vehicle position point and the demand point position point), then calculate the distance function as

sqrt((pointX.x-pointY.x)*(pointX.x-pointY.x)

+(pointX.y-pointY.y)*(pointX.y-pointY.y))

pointX and pointY respectively represent two different nodes, and pointX.x, pointX.y, pointY.x, pointY.y respectively represent the horizontal and vertical coordinates of the node.

(4) Ability level

When an electric car is parked in a certain area, it will receive the service request information of the user. Under the limitation of the capability level, the electric car will go to the designated demand point and complete the corresponding service. Use a six-tuple to indicate the level of electric vehicle capability. $\begin{matrix} Cap - service (xloc, yloc, S_{active}, S_{travelDist}, \\ S_{leftDist}, S_{trip}) \end{matrix}$

Among them, the first two of the six-tuple represent the geographical coordinates of the electric vehicle. Here we choose to indicate the current state of the electric vehicle, including the idle state. At this time, during the busy state, it indicates the mileage of the electric vehicle; it indicates the remaining mileage of the electric vehicle; indicates the number of times the electric car is serviced. For the case of considering multiple types of electric vehicles, the last four variables in the six-tuple can be expanded. When the user needs to send demand information, the electric vehicle will respond to the needs of the user in time.

The parameters of the demand simulation model are shown in Table 6.

Table 3

Associated crawler algorithm (1)

public class Coordinate implements java.io.Serializable {

double x = 0.0;

double y = 0.0;

double time = 0.0;

double priority = 0.0;

boolean check = false;

public Coordinate(){

}

public Coordinate(double x, double y, double time, double priority, boolean check){

this.x = x;

this.y = y;

this.time = time;

this.priority = priority;

this.check = check;

}

@Override

public String toString() {

return

“x = "+x+” “+

“y = "+y+” “;

}

private static final long serialVersionUID = 1 L;

}

Table 4

Associated crawler algorithm (2)

double x;
double y;
for(int i = 0;i<eCar.size();i++)
{
x = uniform(minX,maxX);
y = uniform(minY,maxY);
eCar.get(i).setXY(x,y);

Table 5

Associated crawler algorithm (3)

double buf = 100000;

int bufj = 0;

if(findClient()! = 0)

{

for(int i = 0; i < eCar.size(); i++)

{

if(!eCar.get(i).active)

{

if(buf > sqrt((requestQueue.get(findClient()-1).x-eCar.get(i).x)*(requestQueue.get(findClient()-1).x-eCar.get(i).x)+(requestQueue.get(findClient()-1).y-eCar.get(i).y)*(requestQueue.get(findClient()-1).y-eCar.get(i).y)))

{

buf = sqrt((requestQueue.get(findClient()-1).x-eCar.get(i).x)*(requestQueue.get(findClient()-1).x-eCar.get(i).x)+(requestQueue.get(findClient()-1).y-eCar.get(i).y)*(requestQueue.get(findClient()-1).y-eCar.get(i).y));

bufj = i+1;

}

return bufj;

Table 6

Model setup

Object	Setting	Description
Demand		Demand priority
		Demand ID
		The abscissa of the demand point
		The ordinate of the demand point

When the demand is responded to, it will also be affected by some factors, such as demand priority and distance. In this model, we set three rules for requirements:

(1) Demand queuing model

Demand information is stored in queued form and served in sequential order

(2) Priority model

Demand is prioritized because of the urgency of user demand requirements.

(3) Demand status

The demand is randomly generated, and the service is completed when all the requirements of the user’s needs are responded to. So use a six-tuple to represent the demand: ${Cap}_{s} ervice (xloc, yloc, P_{number}, P_{priority}, P_{clientID})$

The first two items of the six-tuple represent the geographic coordinates of the demand point, P_number indicating the quantity of the demand; P_priority indicating the priority of the demand; and P_clientID indicating the ID of the demand. For considering multiple types of requirements, the last three variables in the six-tuple can be extended.

The model output variables mainly include statistical variables such as starting point x, starting point y, demand point x, demand point y, charging pile ID, cruising range, demand ID, demand priority, and vehicle ID, to analyze the layout of the charging pile. The model output variables mainly include starting point x, starting point y, demand location x, demand location y, charging pile, cruising range, user demand issuance time, user demand response time, user demand, user demand priority, vehicle ID, etc. Statistical variables to calculate the layout of the charging pile.

5 Simulation results analysis

In this study, we took 13 charging piles located in the center of Beijing for layout evaluation (Fig. 1) [47 –49].

Fig. 1

Current layout of charging piles.

The simulation results are shown in Figs. 2 and 3. The “green dot” represents 13 major charging piles, the “car sign” represents the running electric car, and the “house” represents the constantly generated demand point.

Fig. 2

Simulation of the initial interface (reaching the demand point through the charging pile).

Fig. 3

Simulation of the initial interface (reaching demand point directly).

The above data was solved using the Anylogic program. After iteration 100 times.

From the previous analysis, it can be found that there are many influencing factors affecting the layout of the charging pile. This chapter will optimize the current charging under the conditions of the cruising range of 600, regardless of priority and service time, and the same distribution of electric vehicles and user demand. The layout of the pile. The corresponding parameter settings are shown in Table 7.

Table 7

Model parameters

	Parameter	Remarks	Distribution (value)
user		User demand abscissa position	U(minX,maxX)
needs		User demand ordinate position	U(minY,maxY)
electric		Electric vehicle horizontal coordinate position	U(minX,maxX)
car		Electric vehicle ordinate position	U(minY,maxY)
recharge mileage		Recharge mileage	600

Combined with the analysis conclusions of the previous chapter, the mathematical model of the electric vehicle optimization process becomes, (17) and (18): $\begin{matrix} Min λ α (\sum_{c = 1}^{s} \sum_{i = 1}^{n} D_{ic} + \sum_{j = 1}^{m} \sum_{c = 1}^{s} D_{cj}) \\ X_{ijk} - λ (1 - α) (\sum_{c = 1}^{s} \sum_{i = 1}^{n} D_{ic}) X_{ijk} {ifg}_{ic} = 1 \end{matrix}$ (17) $Min λ α (\sum_{c = 1}^{s} \sum_{i = 1}^{n} D_{ic} + \sum_{j = 1}^{m} \sum_{i = 1}^{n} L_{ij}) X_{ijk} {ifg}_{ic} = 0$ (18)

Restrictions: $\sum g_{i 1} \approx \sum g_{i 2} \approx \dots \sum g_{is}$ (19) $min (s)$ (20)

(19) indicates that the optimization process will only stop when the charging frequency of each charging pile is not much different; (20) The minimum number of charging piles is required.

When α= 0.15, 10 electric vehicle initial points and 100 demand places are randomly generated, the total travel distance is 42005.47, the theoretical shortest distance is 23993.5, the bypass distance is 18011.97, and the bypass rate is 42.9%. The statistical experiment results are shown in Table 8.

Table 8

The results for α= 0.15

CS	1	2	3	4	5	6	7	8	9	10	11	12	13	Total
AF	2	1	3	5	8	5	6	4	6	14	2	6	7	69
RA(%)	3	1	4	7	12	7	9	6	9	20	3	9	10	100

When α= 0.35, 10 electric vehicle initial points and 100 demand places are randomly generated, the total travel distance is 38000.96, the theoretical shortest distance is 22584.73, the bypass distance is 15416.23, and the bypass rate is 40.6%. The statistical experiment results are shown in Table 9.

Table 9

The results for α = 0.35

S	1	2	3	4	5	6	7	8	9	10	11	12	13	Total
F	1	1	2	2	7	5	5	6	8	15	6	2	11	71
A(%)	1	1	3	3	9.9	7	7	8	11	21	8	3	15	100

When α= 0.55, 10 electric vehicle initial points and 100 demand places are randomly generated, the total travel distance is 36369.82, the theoretical shortest distance is 22823.29, the bypass distance is 13546.53, and the bypass rate is 37.2%. The statistical experiment results are shown in Table 10.

Table 10

The result for α = 0.55

CS	1	2	3	4	5	6	7	8	9	10	11	12	13	Total
AF	0	5	4	3	3	7	5	6	8	14	4	2	5	66
RA(%)	0	8	6	5	4.5	11	8	9	12	21	6	3	8	100

When α= 0.75, 10 electric vehicle initial points and 100 demand places are randomly generated, the total travel distance is 38331.24, the theoretical shortest distance is 22187.44, the bypass distance is 16143. 8, and the bypass rate is 42.1%. The statistical test results are shown in Table 11.

Table 11

The result for α = 0.75

CS	1	2	3	4	5	6	7	8	9	10	11	12	13	Total
AF	2	0	1	7	5	5	4	3	8	16	2	6	11	70
RA(%)	3	0	1	10	7	7	6	4	11	23	3	9	16	100

When α= 0.95, 10 electric vehicle initial points and 100 demand places are randomly generated, the total travel distance is 40085.88, the theoretical shortest distance is 22809.36, the bypass distance is 17276.52, and the bypass rate is 43.1%. The statistical experiment results are shown in Table 12.

Table 12

The result for α = 0.95

CS	1	2	3	4	5	6	7	8	9	10	11	12	13	Total
AF	1	1	2	8	6	5	4	3	7	14	3	13	5	72
RA(%)	1	1	3	11	8	7	6	4	10	19	4	18	7	100

A summary of the charging frequency of the charging post is shown in Fig. 4.

Fig. 4

Charging pile charging frequency.

From the above data, the following conclusions can be drawn:

Regardless of the value of α, the charging frequency of the charging piles 4, 5, 6, 9, 10, 12, 13 is relatively high. In particular, the charging post 10 has the highest entry frequency and can reach more than 20%, and the charging piles 1, 2, 3, 7, 8, 11 are used less frequently. In particular, charging stations 1, 2 and 3 have the lowest charging frequency, less than 5%. That is to say, whether the driver likes the shortest total distance or the shortest distance from the charging pile to the demanding ground, in some areas, the number of charging piles is small. The working pressure of the charging pile is relatively large, and in some areas, the number of charging piles is too dense, and the charging pile has a high idling rate. Therefore, the existing charging pile layout in Beijing is unreasonable, and the number of charging piles for charging piles 4, 5, 6, 9, 10, 12, 13 is too small. The number of charging posts in the area where the charging piles 1, 2, 3, 7, 8 and 11 are located is too large.

In theory, as α increases, the total distance traveled will decrease. The test results show that although the total running distance is decreasing when α increases, with α= 0.35, α= 0.55, α= 0.75 and α= 0.95, the total distance of operation is not large, and the bypass rate is small. The overall control fluctuates within a range of around 40%. Therefore, the effect of α on the shortest total distance is not obvious. Generally speaking, the driver is more inclined to choose the shortest path to the demanding pile.

Similarly, a similar charging pile charging frequency is obtained considering the priority and service time, as well as other conditions. Besides, we analyze the advantages of the improved Agent model from the aspects of demand response time, the average service time of users, and total running distance of the vehicle. The research results show that the improved Agent model is superior to the standard Agent model in these three aspects (Table 13).

Table 13

Comparative analysis of Agent model

Distributed	Demand response time		User demand average service time		The total running distance of the car
	Standard model	Improved model	Standard model	Improved model	Standard model	Improved model
Evenly distributed	43.3	42.3	23.2	22.4	107698.6	115088.7
	43.9	41.8	23.6	21.1	113080.5	115705.3
	44.1	39.8	23.8	19.8	111116.5	115872.2
Triangular distribution	43.8	40.7	22.3	18.6	108270.4	110664.9
	43.9	40.2	22.3	17.7	106543.3	112705.4
	43.8	41.4	22.3	18.9	108270.5	113879.1
Normal distribution	44.6	43.3	21.6	19.3	99156.4	101822.4
	44.1	43.7	21.2	19.6	98713.4	102703.4
	44.5	43.9	21.5	19.7	92975.3	104744.8

Therefore, we use endogenous variables instead of exogenous variables in the model. This paper presents statistical analysis of multiple simulation operations and charging access frequencies; more endogenous variables can be considered in the Agent-based model, which has higher accuracy and less computation time. The model proposed in the article has a shorter response time to user demand requirements, and the user needs less service time but can ensure that electric vehicles travel longer distances.

Electric vehicle charging piles are scarce resources, especially in the urban population, the contradiction between supply and demand is inevitable, coupled with the uncertainty of passenger demand and the individualized needs of passengers of different grades. At the same time, in the entire industrial chain of electric vehicle development. The convenience, economy and safety of the charging system directly influence and determine the development process of the electric vehicle. Therefore, how to reasonably arrange the rational layout of electric vehicle charging piles has great significance for improving the service level of electric vehicles and reducing production costs.

6 Conclusion

The factors in selecting the location of the electric vehicle charging pile are very complicated and have special circumstances. The article improves the reusability of the model by adopting endogenous variables such as demand priority, cruising range, electric vehicle distribution, and user demand distribution. We also developed an NP model and an agent-based model to analyze the charging frequency of the charging pile. Through case studies, it is found that the layout of charging piles in Beijing is not reasonable enough. In some areas, charging piles are too dense, and in some areas, charging piles are too sparse. With the popularity of electric vehicles, the unreasonable charging pile layout cannot meet the requirements of electric vehicles and hinder the development of the electric vehicle industry.

The main contributions of the article are as follows:

Previous studies have focused on exogenous variables such as battery size, charging capacity, charging power, and battery exchange; we focus on endogenous variables such as demand priority, cruising range, electric vehicle distribution, and demand distribution. The simulation model found that priority is not a key factor affecting the choice of charging pile position, while cruising range, electric vehicle distribution and demand distribution are the key factors affecting the position of the charging pile. Private charging piles can use the peak and valley electricity prices to provide slow charging for electric vehicles. Such charging piles are generally arranged according to actual needs; and the charging piles are distributed due to their characteristics and operating modes, such as cruising range, distribution of electric vehicles and user demand. Characteristics, etc., the reasonable degree of charging pile position plays an important role in the development of electric vehicles. The analysis of this factor helps to provide a reference for the location of urban charging piles.

One criterion for the reasonable layout proposed in the paper is that the charging frequency of different charging piles is not much different, which is different from previous studies. The position problem of the electric vehicle charging pile is as follows: a certain number of electric vehicles are randomly distributed in certain areas within a certain period of time; it is necessary to determine how to ensure the electric vehicle according to the capacity of the electric vehicle battery, the position of the charging pile and the position of the user’s demand. The maximum distance can be exercised. Due to the limitation of the cruising range, electric vehicles must access the charging post before the battery is exhausted. As a criterion for the location of a reasonable charging pile, the variance of the charging frequency for different charging piles is not large.

The article establishes an Agent-based model to analyze the charging frequency of the charging pile. Through case studies, we discuss this model in five cases, and the proposed model can be used in the development of a densely populated metropolitan electric vehicle industry.

Footnotes

Acknowledgments

This work was supported by Beijing Social Science Foundation under Grant 19JDGLA002, 18JDGLA018, MOE (Ministry of Education in China) Project of Humanities and Social Sciences under Grant 19YJC630043, and was partially supported by Beijing Logistics Informatics Research Base. We appreciate their support very much.

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Layout evaluation for electric vehicle charging pile based on charging frequency

Abstract

Keywords

1 Introduction

2 Literature review

2.1 Minimum energy loss study

2.2 Charging pile layout based on energy loss

2.3 Charging pile layout based on the vehicle path

2.4 Dual study of location and path

2.5 Analysis of location problem of charging pile layout

3 Mathematical model

Table 2 Simulation setting Object Setting Description Initial position Different locations inoperation Running direction Abscissa electric Ordinate car State of electric vehicle Number of times the electric car is operated Remaining mileage Electric car ID Electric car running function

Footnotes

Acknowledgments

References

Table 2
Simulation setting

Object Setting Description

Initial position

Different locations inoperation

Running direction

Abscissa

electric Ordinate

car State of electric vehicle

Number of times the electric car is operated

Remaining mileage

Electric car ID

Electric car running function