Location and Size Planning of Charging Parking Lots Based on EV Charging Demand Prediction and Fuzzy Bi-Objective Optimization

Abstract

The market share of electric vehicles (EVs) is growing rapidly. However, given the huge demand for parking and charging of electric vehicles, supporting facilities generally have problems such as insufficient quantity, low utilization efficiency, and mismatch between supply and demand. In this study, based on the actual EV operation data, we propose a driver travel-charging demand prediction method and a fuzzy bi-objective optimization method for location and size planning of charging parking lots (CPLs) based on existing parking facilities, aiming to reduce the charging waiting time of EV users while ensuring the maximal profit of CPL operators. First, the Monte Carlo method is used to construct a driver travel-charging behavior chain and a user spatiotemporal activity transfer model. Then, a user charging decision-making method based on fuzzy logic inference is proposed, which uses the fuzzy membership degree of influencing factors to calculate the charging probability of users at each road node. The travel and charging behavior of large-scale users are then simulated to predict the spatiotemporal distribution of charging demand. Finally, taking the predicted charging demand distribution as an input and the number of CPLs and charging parking spaces as constraints, a bi-objective optimization model for simultaneous location and size planning of CPLs is constructed, and solved using the fuzzy genetic algorithm. The results from a case study indicate that the planning scheme generated from the proposed methods not only reduces the travelling and waiting time of EV users for charging in most of the time, but also controls the upper limit of the number of charging piles to save construction costs and increase the total profit. The research results can provide theoretical support and decision-making reference for the planning of electric vehicle charging facilities and the intelligent management of charging parking lots.

1. Introduction

Nowadays, road transportation with fuel vehicles as the main body has aggravated the problems of fossil fuel resource shortage, carbon emissions and air pollution. Electric vehicles (EVs) have been considered as one of the most promising solutions to these problems [1,2]. Subsidies and related policies for EVs in China, Europe, and other countries over the past decade have led to a continuous increase in the penetration rate of EVs [3,4,5]. According to the global outlook and prediction in 2018, the number of new energy vehicles in the whole world will exceed 130 million by 2030 [6]. Compared with the fuel vehicles, the driving mileage of EVs is vulnerable to the impact of temperature and battery energy storage characteristics, which leads to electricity anxiety and increases the dependence of EVs on charging facilities [7]. Therefore, the layout of charging facilities is particularly important. Meanwhile, the construction cost, construction cycle and other issues should be considered as well.

The underdevelopment of charging infrastructure is one of the main obstacles to the popularization of EVs worldwide. Given the large parking and charging demand, there are currently insufficient charging facilities in many countries and unbalanced supply and demand in time and space; moreover, the construction period of new charging stations is long and the construction costs are high [8]. Therefore, transforming the existing traditional public parking lots into the charging parking lots (CPLs) an efficient and effective way to solve this issue. The question now is how to decide the location of these CPLs and their size. The traditional way to do so is from a macro perspective, that is, to determine the location and size of charging facilities based on some socio-economic indicators such as vehicle ownership, population, and land use. However, the results based on such an approach are often inaccurate or even wrong [9,10]. Therefore, in this study, we propose a new framework to predict the spatial–temporal distribution of EV charging demand, from the perspective of individual travel-charging behavior. More specifically, we analyze the travel and charging behavior of EV users according to their real vehicle usage data, based on which an EV charging demand prediction model is built, and it can then be used to simulate the daily travel and charging process of each vehicle. By aggregating the results of all vehicles under consideration, the spatial–temporal distribution of charging demand of all the EVs in the study area can be estimated.

Moreover, as an important urban infrastructure, the planning and reconstruction of a charging parking lot should consider both the benefit of EV drivers and the profit of CPL operators [11,12]. Therefore, in this study, we propose a fuzzy bi-objective optimization method for the location and size planning of CPLs, which takes the extra time spent by EV drivers for charging, the income of the operators due to this charging service, and the construction cost of CPLs into account. Such a method not only considers the balance between multiple objectives but also improves the model solving speed by introducing a fuzzy membership as the individual fitness function.

The rest of the paper is organized as follows: Section 2 provides a literature review on EV charging demand prediction and charging facility planning. Section 3 presents the modeling process of EV charging demand prediction. Section 4 describes the fuzzy bi-objective optimization model for the location and size planning of CPLs. A case study and the results are given in Section 5, and Section 6 summarizes the key findings from this study.

2. Literature Review

2.1. EV Charging Demand Prediction

The charging demand of electric vehicles generally refers to the sum of the charging power demand generated at a specific time and place after large-scale EVs operate and consume electricity. Previous studies have revealed that the spatial–temporal distribution of EV charging demand is mainly affected by objective factors such as vehicle types, power batteries, charging facilities, charging price, etc., and subjective factors such as user travel and charging psychology [7,13]. Based on the on-board GPS data, Ashtari [9] screened out key influencing factors that influence the charging demand of EV, involving vehicle power type, parking duration, parking type and state of charge (SOC). By exploring the correlation between charging demand and external characteristics, Gopalakrishnan [14] found that point of interest (POI) and traffic density are highly correlated with charging demand.

At present, there are three kinds of charging demand prediction methods. The first type of research method is direct estimation through external data. Dong [15] predicted the spatial–temporal distribution of EV charging demand density in London through geographic information such as POI density, population, and traffic volume. Assuming that there is an equal proportion between the charging demand and traffic flow. Shuai [16] proposed a Voronoi polygon spatial partitioning method based on charging demand clustering and two spatial econometric models, spatial lag model and spatial error model, to quantitatively analyze the influences of various elements on charging demands.

The second type of research method is driver choice prediction, which focuses on predicting which charging station will be selected by drivers for charging. Tian [17] sorted the charging stations in descending order through the two dimensions of distance and historical visit frequency and selected the top-ranked station as the charging station. Jiang [18] proposed a public charging demand prediction based on travel trajectory prediction, taking into account the supply and demand randomness of the transportation system and the heterogeneity of charging behavior of EV users.

The third type of research method is data-driven regression prediction. Data-driven models are free of many parameters and are essential to fully exploit the information contained in the data. Kuang [19] proposed a learning approach for accurate EV charging demand prediction and reasonable pricing, which enabled the integration of convolutional feature engineering, spatial–temporal dual attention mechanism and physics-informed neural network training. Ge [20] proposed a method based on improved random forest to predict the spatial–temporal distribution of EV cluster charging load.

According to the above introduction and analysis, most previous studies assume that fuel vehicles and EVs have the same travel characteristics. The electricity consumption behavior model based on resident travel survey data lacks the support of actual data. In addition, the existing prediction models do not dig deeply into the user travel behavior, resulting in high granularity in spatial distribution prediction.

2.2. Charging Facility Planning

The macro layout and service scope division of EV charging facilities are mainly realized based on spatial analysis, Voronoi diagrams and other methods. Luo [21] offered a strategic approach to EV charging network planning, emphasizing the integration of demand and supply dynamics. This method is accomplished through the utilization of continuous-time fluid queue models alongside discrete flow refueling location modeling, all in the context of innovation diffusion principles. Ip [22] proposed a two-stage model for the planning of EV charging stations. In the first stage, the cluster analysis method was employed to transform road information into charging demand clusters, and in the second stage, the optimization algorithm was utilized to determine the optimal locations for charging stations. Xi [23] built a stochastic charging model to estimate the expected number of EVs, and then used linear integer programming to conduct location and capacity determination to maximize the use of privately owned EVs.

The site selection and capacity determination of EV charging facilities need to consider multiple interests and coordinate multiple objectives. Wang [24] modeled the behavior of EV drivers from two aspects, path selection and charging behavior, to design the location and capacity of charging stations to support long-distance travel of EVs. Zeng [25] developed a metanetwork-based two-stage model for uncongested networks and a network-based bi-level model for congested networks to address the issue of charging station location. At the level of the solution algorithm, Yin [26] proposed particle swarm optimization based on deep neural network modified boundaries (DNNMBPSO) to calculate the optimal solution for charging station siting. In addition to the benefits of EV drivers, the construction cost and revenue of charging stations should also be focused on. Chen [12] established a multi-level programming model for determining the location and capacity of charging facilities. The model aims to minimize the construction costs of these facilities, as well as the travel and waiting times for EV drivers within the transportation network.

The limitation of the recent research is that it mainly focused on solving the problems of service scope division, location and size planning of new charging stations, but urban space demand is strictly limited by cost, land type and other conditions, lacking consideration of establishing planning model combining existing parking facilities and designing effective solution algorithm for this problem.

3. EV Charging Demand Prediction

In this study, the modeling framework for EV charging demand prediction consists of four parts: (i) data feature extraction, (ii) travel behavior modeling, (iii) charging behavior modeling, and (iv) charging demand distribution estimation, which is shown in Figure 1. First, data feature extraction is carried out to obtain the information of users’ travel and charging process based on their daily vehicle usage data. Next, travel behavior models and charging behavior models are established to analyze the characteristics of users’ travel and charging patterns, respectively, and construct a travel-charging behavior chain, based on which the spatial–temporal distribution of charging demand in the study area can be estimated by simulating the travel and charging behavior of all the EV drivers in this study area.

3.1. Data Feature Extraction

In this study, the usage data of 50 Roewe E50 (with a battery capacity of 22.4 kwh and a rough driving distance of 100 km in normal operating conditions) were provided by the Shanghai New Energy Vehicle Public Data Collection and Monitoring Research Center [27]. The data span from June 2015 to June 2016, with an average record duration of 214 days per vehicle.

Table 1. Recording form of original data (partial).

Vehicle ID	Acquisition Time	Accumulated Mileage	SOC	Longitude	Latitude	Status Start Time	Vehicle Status
1	5 December 2015 22:11:59	748	4	121.2073	31.2901	5 December 2015 22:11:46	3
1	5 December 2015 22:13:42	748	5	121.2073	31.2902	5 December 2015 22:11:46	3
…	…	…	…	…	…	…	…
1	6 December 2015 7:27:32	748	100	121.2073	31.2902	5 December 2015 22:11:46	3
1	6 December 2015 7:28:35	748	100	121.2073	31.2902	5 December 2015 22:11:46	3
1	6 December 2015 7:29:20	748	100	121.2118	31.2883	6 December 2015 7:28:47	1
1	6 December 2015 7:29:53	748	100	121.2154	31.2862	6 December 2015 7:28:47	1

shows an example of the original data. For each vehicle, the accumulated mileage, SOC, location, and time are recorded, with a data acquisition interval of 30~60 s. The vehicle has several statuses, and a value of 1 and 3 corresponds to normal operation and charging, respectively. Due to personal privacy protection, no information about the driver is provided.

The start and ending time of a vehicle’s travel and charging can be identified according to the change in the vehicle status shown in Table 1. Hence, the specific information of the vehicle’s travel and charging process can be extracted. One trip may be identified as multiple different trips due to driver operation errors, queuing at intersections and other reasons. In this study, the trips with an interval of less than 10 min were considered as one trip, and a charging time interval of less than 15 min was considered as one single charging behavior. In addition, the data with vacancy and abnormal recording time were discarded. In total, 15,137 trips and 8498 charging sessions were extracted.

Table 2. Travel behavior data of EV drivers (partial).

Travel ID	Vehicle ID	Departure Time	Travel Duration (min)	Driving Mileage (km)	Power Consumption (%)
630	2	25 July 2015 06:38:23	15.87	4	3
631	2	25 July 2015 12:46:45	89.40	55	58
632	2	25 July 2015 17:18:39	56.30	38	39

and

Table 3. Charging behavior data of EV drivers (partial).

Charging ID	Vehicle ID	Charging Start Time	Charging Duration (h)	SOC before Charging (%)	SOC after Charging (%)
300	3	31 August 2015 08:22:13	1.06	57	67
301	3	11 September 2015 08:58:06	6.64	18	97
302	3	14 September 2015 09:09:03	6.07	34	64

show the data extracted during travel and charging, respectively.

3.2. Travel Behavior Modeling

Based on the data, the activity–travel chain for daily commuters can be divided mainly into two types: one is from home to work and then back to home, which is recorded as an ‘H–W–H’ chain, and the other is from home to work, then to commercial leisure places, and finally back to home, which is recorded as an ‘H–W–C–H’ chain. In both types of activity–travel chain, although daily commuters always leave from their places of residence, the departure time of individual’s first trip is uncertain; moreover, although the user’s travel distance can be determined after the route selection is completed, the travel speed may vary according to different people and traffic environments, resulting in different travel times for each individual. In addition, when users arrive at the destination, their parking time is also heterogeneous and random due to travel purpose, charging demand and other factors. Therefore, we analyzed these travel behavior characteristics and estimated their probability distribution, respectively.

3.2.1. The Departure Time of the First Trip

Given the collected data, the mixed Gaussian distribution is used to fit drivers’ departure time of the first trip, and its probability density function is shown in Formula (1):

$${pdf}_T\left(x\right)=\sum _{i=1}^m{\epsilon }_i{\displaystyle \frac{1}{\sqrt{2\pi {\sigma }_i^2}}}\mathrm{e}\mathrm{x}\mathrm{p}[-{\displaystyle \frac{{(x-u_i)}^2}{2{\sigma }_i^2}}]$$

(1)

where m is the number of the Gaussian distribution used and $u_i$, ${\sigma }_i^2$, and ${\epsilon }_i$ are the mean, variance, and proportion of the Gaussian distribution i, respectively. ${\epsilon }_i\in \left(\mathrm{0,1}\right)$ and ${\sum }_i{\epsilon }_i=1$.

The fitting result is shown in Figure 2a, and the values of the corresponding parameters are as follows: m = 2, μ₁ = 12.033, μ₂ = 7.866, σ₁ = 27.206, σ₂ = 0.403, ε₁ = 0.747, and ε₂ = 0.253.

3.2.2. Travel Speed

Given the fact that the travel speed is relatively concentrated at the low-speed range, the generalized extreme value distribution is used to fit the data, and its probability density function is shown in Formula (2).

$${pdf}_V\left(x\right)={\displaystyle \frac{1}{\sigma }}\exp \left\{-{\left[1+k{\displaystyle \frac{\left(x-\mu \right)}{\sigma }}\right]}^{-{\displaystyle \frac{1}{k}}}\right\}{\left[1+k{\displaystyle \frac{\left(x-\mu \right)}{\sigma }}\right]}^{-1-{\displaystyle \frac{1}{k}}}$$

(2)

where $\mu$, $\sigma$, and $k$ are three parameters and $k\ne 0$.

The fitting result is shown in Figure 2b, and the values of the corresponding parameters are as follows: μ = 16.290, σ = 5.882, and k = 0.337.

3.2.3. Parking Duration

Based on the characteristics of data distribution, the log normal distribution is applied to fit the data of parking time. The probability density function is shown in Formula (3). By setting μ = 5.097 and σ = 1.568, the fitting result is shown in Figure 2c.

$${pdf}_P\left(x\right)=\left\{\begin{array}{c}{\displaystyle \frac{1}{x\sqrt{2\pi }\sigma }}\exp \left[-{\displaystyle \frac{1}{2{\sigma }^2}}{\left(\mathrm{l}\mathrm{n}x-\mu \right)}^2\right],x>0\\ 0,x\le 0\end{array}\right.$$

(3)

3.3. Charging Behavior Modeling

3.3.1. Energy Consumption

The travel energy consumption of EVs is mainly determined by the driving distance. The relationship between battery state of charge consumption and driving distance is shown in Formula (4).

$$\Delta SOC=E_{100}\ast (l/100)/C\ast 100\%$$

(4)

where $\Delta SOC$ is the percentage power consumption in one trip (%), $l$ is the travel mileage (km), $E_{100}$ is the vehicle power consumption per hundred kilometers (kwh/100 km), and $C$ is the battery capacity (kwh). For the Roewe E50s, its battery capacity is 22.4 kwh, and its power consumption is 20.4 kwh/100 km according to linear fitting. Regarding its charging power, the average value of 3.8 kw is utilized.

3.3.2. Charging Decision-Making

Charging decision is made by EV drivers based on the comprehensive evaluation of subsequent travel demand, current parking and charging conditions, and so on. Generally, the charging demand is divided into rigid charging demand and elastic charging demand.

Rigid charging is the charging behavior that EV drivers must carry out in order to meet the needs of travel power consumption. If the current remaining power is less than the power consumption of completing the remaining mileage to the destination, drivers must choose to charge until the battery power can meet the remaining mileage or be fully charged. On the contrary, if the remaining power can meet the demand for the next trip, the driver can choose whether to charge or not, so it is called the elastic charging demand.

For elastic charging, a fuzzy logic inference system is established to simulate driver charging decisions based on the factors such as maximum rechargeable capacity during parking ($\Delta {SOC}_{max}$) and charging price ($c\left(t\right)$). The former is related to the parking duration and the current SOC of the battery, which can be calculated using Formula (5), where $P$ is the charging power (kw) and $T$ is the parking duration (h). If the parking duration is brief, users with charging needs may still opt not to charge their vehicles. The current SOC of the battery significantly influences the amount of power that can be accepted. When the battery is nearly fully charged, users are less likely to choose to charge. Additionally, charging cost is directly influenced by the charging price. During peak hours, when electricity prices are elevated, users may opt to delay charging to reduce expenses.

$$\Delta {SOC}_{max}=\mathrm{m}\mathrm{i}\mathrm{n}(P\ast T/C\ast 100,100-SOC)$$

(5)

In the fuzzy logic inference system of elastic charging decision-making, $\Delta {SOC}_{max}$ and $c\left(t\right)$ are input variables, and the charging probability is the output variable. For $\Delta {SOC}_{max}$, three fuzzy sets are defined to express drivers’ general judgment on maximum rechargeability, which are low, medium and high. For $c\left(t\right)$, the peak–valley charge prices are considered. For the charging probability, five fuzzy sets, i.e., very low, low, medium, high, and very high, are defined to reflect drivers’ willingness to charge. Figure 3 shows the corresponding fuzzy membership functions of these input and output variables.

In combination with the actual charging behavior characteristics, six fuzzy inference rules are defined, as shown in

Table 4. Fuzzy inference rules for charging decision-making.

ID	Rule
Rule 1	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{high}\mathrm{AND}c\left(t\right)$ $==c_{valley}$ THEN charging probability == very
Rule 2	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{high}\mathrm{AND}c\left(t\right)$ $==c_{peak}$ THEN charging probability == high
Rule 3	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{medium}\mathrm{AND}c\left(t\right)$ $==c_{valley}$ THEN charging probability == high
Rule 4	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{medium}\mathrm{AND}c\left(t\right)$ $==c_{peak}$ THEN charging probability == medium
Rule 5	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{low}\mathrm{AND}c\left(t\right)$ $==c_{valley}$ THEN charging probability == low
Rule 6	$\mathrm{IF}∆{SOC}_{max}$ $==\mathrm{low}\mathrm{AND}c\left(t\right)$ $==c_{peak}$ THEN charging probability == very low

.

To sum up, after each trip, EV drivers will judge whether the current remaining power can meet the next trip. If not, they have to charge until the battery can meet the remaining mileage or full charge. Otherwise, the charging probability will be estimated according to the elastic charging decision-making system. The travel chain and the charging decision-making system constitute the final travel-charging behavior chain of EV drivers.

3.4. Spatial–Temporal Distribution of Charging Demand

Based on the travel-charging behavior chain generated from the above section, as well as the topological structure of the road network and the classification of land use types in the study area, the Monte Carlo method can be used to simulate the travel and charging behavior of individual EV drivers, based on which the spatial–temporal distribution of the charging demand in this study area can be predicted. This method is widely used in charging demand prediction and large-scale user travel simulation [28]. More specifically, for each individual EV driver, their spatial location of residence, workplace and leisure place (if any) are generated randomly according to the classification of land use types and their travel chain category, and the route of each trip is determined by applying the Logit model, based on which the travel distance can be estimated. Furthermore, the departure time of their first trip, the travel speed (or travel time) of each trip, and the park time after each trip are drawn randomly from the probability distribution functions shown in Figure 2. Thus, the overall time schedule of a driver’s one-day trips can be generated.

Meanwhile, assume that the initial SOC of all EV drivers when leaving from home every day is subject to a uniform distribution of 80~100%. When the driver arrives at a destination after one trip, it is determined whether to charge according to the current SOC, as well as the parking time and the distance to the next destination. With respect to the elastic charging, the fuzzy logic inference system introduced in the previous section is applied to make charging decisions. After the whole day trips, the driver arrives at home and charge for the trips of the next day.

In the simulation process, if the driver has charging behavior, their charging location, charging amount, charging power, charging start time, and charging duration are recorded. Finally, the charging power of all drivers is superimposed in space and time to obtain the spatial–temporal distribution characteristics of the charging demand. The overall simulation process of EV charging demand prediction based on the Markov chain Monte Carlo method is shown in Figure 4.

4. Location and Size Planning of Charging Parking Lots

4.1. Problem Description and Model Assumption

Suppose that there are M public parking lots in the study area, N of which will be transformed into CPLs. In consideration of controlling the construction cost and meeting the parking demand of fuel vehicles, the number of charging piles $C_k$ in each alternative parking lot k (k = 1, 2, …, N) should not exceed $C_k^{max}$. Taking both the benefit of EV drivers and the profit of CPL operators into account, an optimization model is established to determine the optimal location of CPLs and the optimal number of charging piles. In doing so, the following assumptions are proposed:

• All charging demand points and alternative public parking lots are located at the nodes of the road network;
• Each charging demand point will be charged at its nearest CPL;
• Drivers shall follow the shortest path in the road network from the point where the charging demand is generated to the nearest CPL;
• Drivers are driving at a constant speed v regardless of the road traffic conditions;
• Considering the capacity of CPLs, when the number of charging vehicles is greater than the number of charging piles in a CPL, the vehicles will have to wait until a charging pile is free to use.

4.2. The Objective Functions

The objectives of the aforementioned problem are twofold. First, the sum of the extra travel time and waiting time of the EVs that have charging demand should be minimized, which is denoted as Objective 1; second, the profit of the CPLs, i.e., the difference between the charging income and the cost of charging facility construction, should be maximized, which is denoted as Objective 2.

The objective function $f_1$ of Objective 1 can be expressed by Formula (6).

$$f_1=\min {\sum }_i({\displaystyle \frac{d_i}{v_i}}+W{t}_i)$$

(6)

where $d_i$ is the distance from the road node where vehicle i generates the charging demand to the nearest CPL, $v_i$ is its travel speed, and $W{t}_i$ is the waiting time of vehicle i for charging service.

As for the calculation of waiting time, real-time monitoring of each charging piles is required. To simplify the solution process, we take the calculation of vehicle queuing delay at bottleneck sections as a reference and set the time distribution curve of the number of vehicles required for charging in CPL k as ${\phi }_k\left(t\right)$. When the amount of charging demand exceeds $C_k$ in the time period $t_a$ to $t_b$, the area of the charging demand time distribution curve beyond the horizontal line $C_k$ can approximately represent the charging delay in this period, which is recorded as $D_k^{ab}$, as shown in Formula (7):

$$D_k^{ab}={\int }_{t_a}^{t_b}[{\phi }_k\left(t\right)-C_k]dt$$

(7)

The total vehicle waiting time can then be obtained approximately by summing the area of all CPL demand curves exceeding the facility capacity, as shown in Formula (8).

$${\sum }_{i}W{t}_i\approx {\sum }_k\int [{\phi }_k\left(t\right)-C_k]dt$$

(8)

The objective function $f_2$ of Objective 2 can be expressed by Formula (9).

$$f_2=\max ({\sum }_i{c}_i-{\displaystyle \frac{P_c}{T_c}}{\sum }_k{C}_k)$$

(9)

where $c_i$ is the charging cost to be paid by the i-th driver, $P_c$ is the price of a charging pile, and $T_c$ is the service life of a charging pile. Since the charging cost is calculated based on the spatial–temporal distribution of 24 h charging demand, the cost of the charging piles including the total construction price and service life of a charging pile needs to be converted into the daily consumption cost. The Objective 2 is actually to maximize the daily average profit of the charging facilities.

To calculate the value of $c_i$, it can be estimated from the number of charging vehicles at different times, and subject to the supply quantity of charging piles in the CPL, which is shown in Formula (10).

$${\sum }_i{c}_i={\sum }_k\min ({\int }_{0:00}^{24:00}{\phi }_k\left(t\right)\ast P\ast c_k\left(t\right)dt,{\int }_{0:00}^{24:00}{C}_k\ast P\ast c_k\left(t\right)dt)$$

(10)

where $c_k\left(t\right)$ is the price of timed electricity in the kth CPL and $P$ is the maximum charging power provided by each charging pile.

In summary, Objective 1 and Objective 2 have both synergistic and restrictive relationships with each other. Minimizing the charging distance for users in Objective 1 is to make CPLs located at the place where the charging demand is most concentrated within its service scale, so as to optimize the spatial layout of the charging facilities. Moreover, the goals of minimizing the waiting time of users in Objective 1 and maximizing the charging income of CPL operators in Objective 2 can be met by increasing the number of charging piles in each CPL. However, the construction cost will increase as well, which will reduce the total profit of CPL operators to a certain extent. Therefore, by satisfying both the objectives, the optimal location and size of CPLs can be determined. The established optimization model considering location and size planning is summarized in Formula (11):

$$\begin{array}{l}\left\{\begin{array}{l}\min \left({\sum }_i{\displaystyle \frac{d_i}{v_i}}+{\sum }_k^N\int [{\phi }_k\left(t\right)-C_k]dt\right)\\ \max \left({\sum }_k^N\min \left({\int }_{0:00}^{24:00}{\phi }_k\left(t\right)\ast P\ast c_k\left(t\right)dt,{\int }_{0:00}^{24:00}{C}_k\ast P\ast c_k\left(t\right)dt\right)-{\displaystyle \frac{P_c}{T_c}}{C}_k\right)\end{array}\right.\\ \mathrm{s}.\mathrm{t}.\left\{\begin{array}{l}N\le M\\ C_k\le C_k^{max},k=\mathrm{1,2},\dots ,N\end{array}\right.\end{array}$$

(11)

4.3. The Fuzzy Genetic Algorithm

For the above bi-objective programming problem, due to the existence of integral and comparative values in the objective functions, it is difficult to obtain to obtain the optimal solution using the conventional numerical optimization method, and the problem-solving efficiency is low. Therefore, in this study, we propose a fuzzy genetic algorithm (FGA) to solve the problem. More specifically, a fuzzy fitness function is established so as to provide a single standard fitness value for assessing the genetic algorithm solution of the bi-objective optimization problem. The core idea of this method is to calculate the membership degree of the optimal solution of each objective and take the minimum value of the membership degree of the optimal solution of each objective as its fitness value in Formula (12).

$$\begin{gathered} F=\min \left\{{\mu }_1\left(F_1\right),{\mu }_2\left(F_2\right)\right\} \\ {\mu }_1\left(F_1\right)=\left\{\begin{array}{c}1,F_1\le F_{1m}\\ {\displaystyle \frac{F_{1M}-F_1}{F_{1M}-F_{1m}}},{F_{1m}<F}_1<F_{1M}\\ 0,F_1\ge F_{1M}\end{array}\right. \\ {\mu }_2\left(F_2\right)=\left\{\begin{array}{c}1,F_2\ge F_{2M}\\ {\displaystyle \frac{F_{2m}-F_2}{{F_{2m}-F}_{2M}}},{F_{1m}<F}_1<F_{1M}\\ 0,F_2\le F_{2m}\end{array}\right. \end{gathered}$$

(12)

where $F$ is the fitness of a solution, $F_1$ is the solution value of the corresponding objective function $f_1$, and ${\mu }_1\left(F_1\right)$ is the membership degree of the optimal solution of Objective 1. Similarly, $F_2$ is the solution value of the corresponding objective function $f_2$, and ${\mu }_2\left(F_2\right)$ is the membership degree of the optimal solution of Objective 2. When only Objective 1 is considered, the value of the optimal solution corresponding to the objective function $f_1$ is $F_{1m}$. That is, the total travel and waiting time for charging is minimized, but the value of objective function $f_2$ corresponding to this solution, i.e., the profit of the parking lots, is not necessarily maximized, which is recorded as $F_{2m}$. Similarly, when only Objective 2 is considered, the value of the optimal solution corresponding to the objective function $f_2$ is $F_{2M}$. At this time, the profit of the parking lots is maximized, but the value of the objective function $f_1$ is not necessarily minimized, which is recorded as $F_{1M}$.

The value of the above fuzzy fitness function is between 0 and 1, with a higher value indicating a better performance in both objectives. Therefore, the main purpose of the genetic algorithm is to search for a solution achieving the highest fitness value $F$. The algorithm flow chart is shown in Figure 5, and the specific process is given as follows:

Step 1: Population initialization. Define the basic parameters of the genetic algorithm, including encoding mode, population size Q, individual size M, and maximum iteration number ${Iter}_{max}$. Here, real number coding is adopted, and the model individual solution is a vector X with a size of $2\times M$, as shown in Formula (13). The first row represents the locating solution of CPLs, and a value of 0 or 1 is used to indicate whether the corresponding public parking lot is transformed into a CPL. The second row represents the sizing solution of CPLs.

$$X=\left[\begin{array}{cccccc}{\delta }_1& {\delta }_2& \dots & {\delta }_k& \dots & {\delta }_M\\ C_1& C_2& \dots & C_k& \dots & C_M\end{array}\right]$$

(13)

where ${\sum }_{k=1}^M{\delta }_k=N$. When ${\delta }_k=0$, $C_k=0$, and when ${\delta }_k=1$, $0<0\le C_k$.

Step 2: Crossover and mutation operation. When the number of iterations does not reach the preset maximum value, crossover operation and mutation operation are performed on individual vector X. The crossover operation is divided into locating solution crossover operation and sizing solution crossover operation, as shown in Figure 6a. For the locating solution crossover operation, two columns of the decision variables are selected and exchanged their position with a probability of $P_{c1}$. For the sizing solution crossover operation, a column with the locating solution value of 1 is selected, and a linear crossover of real values is conducted with a probability of $P_{c2}$. For the mutation operation, as shown in Figure 6b, a locating variable is selected with probability $P_{m1}$ to invert it, together with its associated sizing variable. And for the sizing variable with the locating variable equaling to 1, it floats up and down to a certain extent with a probability of $P_{m2}$.

Step 3: Individual selection. Randomly generate Q feasible solutions that meet the locating and sizing constraints as the first generation of parent population P. Then, all individuals in the population are randomly matched. Each pair of individuals first carries out the locating solution crossover operation with a probability of $P_{c1}$, and then carries out the sizing solution crossover operation with a probability of $P_{c2}$. After that, all individuals in the population are selected with a probability of $P_{m1}$ and $P_{m2}$ for the locating and sizing solution mutation operation, respectively. Thus, the new population P′ with M individuals can be obtained, and the temporary population $P_{temp}=[P,P^{\prime }]$ together with the parent population P can be constituted. Thereafter, the fitness value of all individuals in $P_{temp}$ is calculated and ranked, and the top Q individuals are selected as the new population of the next generation.

Step 4: Result obtainment. Such an iteration is repeated until the number of iterations reaches ${Iter}_{max}$. Finally, in the final generation population, the individuals with the highest fitness value are found to reach the optimal solution of the problem.

5. A Case Study

5.1. The Simulation Scenario

Taking the Nguyen–Dupuis road network as the simulation scenario, which has 13 nodes and 19 two-way road sections, assume that nodes 1, 4, 5 and 12 are residential sites, nodes 2, 3, 8 and 13 are working sites, and nodes 6, 7, 9, 10 and 11 are commercial leisure sites (see Figure 7). The distances between two adjacent nodes are given in

Table 5. Distance of the road section in the Nguyen–Dupuis road network.

Road Section	Node	Distance (km)	Road Section	Node	Distance (km)
1	1–5	11.2	11	6–7	8
2	1–12	13.6	12	6–10	20.8
3	2–8	14.4	13	6–12	11.2
4	2–11	14.4	14	7–8	8
5	3–11	12.8	15	7–11	14.4
6	3–13	17.6	16	8–12	22.4
7	4–5	14.4	17	9–10	10
8	4–9	19.2	18	9–13	14.4
9	5–6	4.8	19	10–11	10
10	5–9	14.4

.

Suppose that there are 2000 EVs in this study area, and the H–W–H and H–W–C–H travel chains each account for 50%. The proportion of drivers living in nodes 1, 4, 5 and 12 is 0.4, 0.3, 0.2 and 0.1, respectively. The probability matrix of drivers transferring from residential node to working node and from working node to commercial leisure node is shown in Formulas (14) and (15).

Now, suppose that there are five public parking lots located at the five commercial leisure sites, and it is decided to transform two of them into CPLs so as to meet the increasing charging demand of these EVs. The question now is how to choose the appropriate location of these two CPLs and the optimal number of charging piles in each CPL.

$$\begin{array}{cc}& \begin{array}{cccc}2& 3& 8& 13\end{array}\\ \begin{array}{c}1\\ 4\\ 5\\ 12\end{array}& \left[\begin{array}{cccc}0.4& 0.3& 0.2& 0.1\\ 0.1& 0.3& 0.2& 0.4\\ 0.2& 0.4& 0.1& 0.3\\ 0.3& 0.2& 0.4& 0.1\end{array}\right]\end{array}$$

(14)

$$\begin{array}{cc}& \begin{array}{ccccc}6& 7& 9& 10& 11\end{array}\\ \begin{array}{c}2\\ 3\\ 8\\ 13\end{array}& \left[\begin{array}{ccccc}0.3& 0.2& 0.2& 0.1& 0.2\\ 0.4& 0.2& 0.1& 0.2& 0.1\\ 0.3& 0.2& 0.1& 0.3& 0.1\\ 0.2& 0.2& 0.3& 0.1& 0.2\end{array}\right]\end{array}$$

(15)

5.2. Results

5.2.1. Spatial–Temporal Distribution of EV Charging Demand

Based on the charging demand prediction model introduced in Section 3, 3673 charging demands with a total of 42,511 kwh are generated from the simulated travel-charging behavior of these 2000 EVs during a working day. Figure 8a shows that there are two peak values in the total charging power. The highest peak happens at 21:00 pm with a value of 5232.6 kw, and the second peak occurs at 10:27 am with a value of 4316.8 kw. A maximum of 1377 vehicles (68.9%) are charging at the same time.

In terms of the spatial distribution, the charging demand load curves of different land use types are shown in Figure 8b. In the residential area, the charging load gradually accumulates from about 16:00 pm to the peak of 21:00 pm, and continues until 4:43 am, accounting for 59.8% of the total charging demand. The work area acts as the first charging place of the travel-charging behavior chain of the EV drivers, and the charging time in this area lasts from 6:36 am to 15:32 pm, completing 35.7% of the total charging demand. Such a result is in line with the basic spatial–temporal rule of EV drivers’ travel and charging behavior.

Considering the commercial leisure area, in which the five public parking lots are located, it is the parking place for the EV users with the “H–W–C–H” travel chain. As can be seen from Figure 8b, the charging demand in this area lasts from about 16 pm to 22 pm, with the peak value at 18:50 pm, and 164 vehicles are charging at this moment. Furthermore, the temporal distribution of the charging demand at each node is shown in Figure 9. The numbers of charging requirements at these five nodes (i.e., nodes 6, 7, 9, 10, and 11) are 99, 73, 70, 74 and 73, respectively. It can be seen from (15) that compared with the other four commercial leisure nodes, node 6 undertakes more EV drivers, so its charging demand is also significantly higher than the other four nodes, while those four nodes have similar charging demands.

5.2.2. Sensitivity Analysis of EV Charging Demand

Based on the above simulation conditions, the traffic factors and power consumption factors that affect the charging demand are integrated, and charging demand prediction model variables such as user scale, departure time of the first trip, parking duration, battery capacity and charging power, respectively, fluctuate by 10%. The changes in key indicators such as total charging demand, peak time and peak power of users in non-residential nodes were studied to conduct sensitivity analysis of influencing factors. The results are shown in

Table 6. Sensitivity analysis results of influencing factors of charging demand.

Non-Residential Area		Total Demand (MWh)	Amplitude of Change %	Peak Time	Variation (min)	Peak Power (kw)	Amplitude of Change %
Original parameter		17.081		10:27		4316.8
User scale	+10%	18.713	9.554 **	10:27	0	4743.8	9.892 **
	−10%	15.455	−9.519 **	10:27	0	3906.4	−9.507 **
Departure time of the first trip	+10%	17.122	0.240	10:46	+19 *	4031.8	−6.602 **
	−10%	16.772	−1.809 *	9:59	−28 **	4297.8	−0.440
Travel speed	+10%	17.067	−0.082	10:21	−6	4301.6	−0.352
	−10%	17.060	−0.123	10:50	+23 **	4199.0	−2.729 *
Parking duration	+10%	17.306	1.317 *	10:22	−5	4290.2	−0.616
	−10%	16.972	−0.638	10:28	+1	4373.8	1.320 *
Battery capacity	+10%	15.508	−9.209 **	10:26	−1	3959.6	−8.275 **
	−10%	18.422	7.851 **	10:26	−1	4727.2	9.507 **
Charging power	+10%	15.745	−7.822 **	10:26	−1	4145.8	−3.961 *
	−10%	18.654	9.209 **	10:32	+5	4434.6	2.729 *
Power consumption per 100 km	+10%	19.876	16.363 ***	10:36	+9	4791.8	11.004 ***
	−10%	13.998	−18.049 ***	10:26	−1	3750.6	−13.116 ***

*—The change amplitude is more than 1% or the change amount is more than 10min; **—The change amplitude is more than 5% or the change amount is more than 20min; ***—The change amplitude is more than 10%.

.

When the user scale increases by 10%, the total charging demand and peak power of the user in the non-residential area will increase by close to the corresponding proportion, and vice versa. However, the change in user size has no effect on the peak time of charging demand load. In terms of user travel behavior, changes in the departure time of the first trip and travel speed may have little impact on the total charging demand or peak power in non-residential areas. It can be found that the user behavior variable mainly affects the time when the charging load peak occurs. For the departure time of the first trip, the peak time of the charging power of the user is correspondingly advanced or delayed with its advance and delay. The increase in travel speed will advance the charging peak in non-residential areas; the slower travel speed will significantly delay the peak charging time. The extension of parking duration will lead to slightly earlier charging peak times in non-residential areas, caused by users’ increased willingness to charge and more concentrated choice of charging. The total charging demand also increases, but the peak charging power decreases due to the extension of the overall parking and charging duration. The change caused by shorter parking duration is the opposite to the change caused by longer parking duration.

The increase in power consumption per 100 km will lead to faster power consumption of users, so the total charging demand of users and charging peak power are correspondingly increased, and vice versa. In addition, the increase in power consumption per 100 km will also affect the peak time of the charging load, which is due to the increase in power consumption leading to an increase in charging demand, which leads to an increase in the number of users charging and, thus, charging time, thus delaying the charging peak time. However, the reduction in power consumption per 100 km has little effect on peak charging power times. When the battery capacity is increased by 10%, the total charging demand and peak power of users will decrease, and the peak time of demand load will remain almost unchanged. This is because when the battery capacity rises, the proportion of electricity consumed per trip will decrease accordingly, so that the battery SOC is maintained at a relatively higher state, and the user has less charging demand, so the charging demand in the middle destination of the travel chain is reduced, and more is transferred to charging after going home. When the battery capacity is reduced, the situation is completely the opposite, because the proportion of power consumption of the user will increase. Finally, the increase in charging power can shorten the charging duration, and the ratio of users to concentrate on charging at a certain time is reduced, so that the peak power of charging load in each region is reduced to a certain extent, and the total charging demand of users is also reduced correspondingly, but it has almost no impact on the peak time. On the contrary, the reduction in charging power will lead to an increase in the total charging demand and the peak power of the user, and the charging peak time will be slightly delayed.

5.2.3. Fuzzy Bi-Objective Optimization

Set the genetic algorithm population size to 100, the maximum number of iterations to 100, and each feasible solution to a vector of $2\times 5$. Given the charging demand distribution of five public parking lots, we apply the optimization models presented in Section 4. First, the single Objective 1 is considered, and the optimal solution is $X_1=\left[\begin{array}{cc}1& 0\\ 89& 0\end{array}\begin{array}{cc}0& 1\\ 0& 92\end{array}\begin{array}{c}0\\ 0\end{array}\right]$, i.e., nodes 6 and 10 are selected as the locations of 2 CPLs, and 89 and 92 charging piles should be installed at these two nodes, respectively. The value of the objective functions $f_1$ and $f_2$, i.e., $F_{1m}$ and $F_{2m}$, is 3356.7 min and CNY 1021.9, respectively, and the spatial–temporal distribution results of the number of charging vehicles in the CPL are shown in Figure 10. Next, Objective 2 is individually considered, the optimal solution is $X_2=\left[\begin{array}{cc}0& 1\\ 0& 5\end{array}\begin{array}{cc}0& 1\\ 0& 20\end{array}\begin{array}{c}0\\ 0\end{array}\right]$, i.e., nodes 7 and 10 are selected as the locations of 2 CPLs, and 5 and 20 charging piles should be installed at these 2 nodes, respectively. In this case, the value of $F_{1m}$ and $F_{2m}$ is 25,089 min and CNY 1150.1, respectively, the results are shown in the Figure 11. Since Objective 2 only takes the profit of CPL operators into account and ignores the time cost of EV users, the number of charging piles in this scheme is low. Now, if both Objective 1 and Objective 2 are considered, the optimal solution is $X=\left[\begin{array}{cc}1& 0\\ 37& 0\end{array}\begin{array}{cc}0& 1\\ 0& 45\end{array}\begin{array}{c}0\\ 0\end{array}\right]$. That is, nodes 6 and 10 are selected as the locations of 2 CPLs, and 37 and 45 charging piles should be installed at these 2 nodes, respectively. The value of $F_{1m}$ and $F_{2m}$ is 11,277 min and CNY 1103.3, respectively, and the final fitness is 0.6346, which can better meet the two optimization objectives at the same time. As can be seen, the result of $X$ increases the profit of the CPL operators by 7.97% compared with the result of $X_1$. Compared with the result of $X_2$, the profit of the CPL operators only decreases by 4.07%, but the EV driver’s extra time for charging decreases by 55.05%; the results are shown in the Figure 12. Thus, such a scheme not only reduces the travelling and waiting time of EV users for charging in most of the time but also controls the upper limit of the number of charging piles to save construction costs and expand total profit. It is a reasonable result and can be used as the optimal scheme for CPL location and size planning of this case study.

6. Discussion and Conclusions

This paper analyzes travel and charging behaviors of EV drivers according to the operation data of EVs, establishes a charging demand prediction model for EVs, and then obtains the spatial–temporal distribution of charging demand in the study area. Based on the predicted charging demand spatial–temporal distribution, a fuzzy bi-objective optimization model is built from the perspective of time cost and CPL profit so as to determine the optimal location of CPLs and the number of charging piles.

Compared with the previous studies, the method proposed in this paper is more accurate in predicting the charging demand spatial–temporal distribution of EVs. The travel characteristics extracted based on EVs operation data make the constructed travel-charging behavior chain more able to reflect the travel and charging behavior of actual EV drivers. In addition, the fuzzy elastic charging decision-making method further improves the accuracy of predicting the charging demand spatial–temporal distribution.

The transformation scheme of adding charging piles to some existing public parking lots reduces the construction cost and lowers the waiting time for charging. In terms of CPL location and size planning, the multi-objective optimization method can provide more appropriate results than the single-objective optimization method, and the fuzzy bi-objective optimization algorithm avoids the problems of the traditional algorithm, such as long solving time and high subjectivity of weight.

To sum up, aiming at the problem of insufficient charging facilities, this paper proposes a new planning method to renovate the public parking lot combined with predicting the spatial–temporal distribution of charging demand based on real travel data. The specific contributions are as follows:

• This paper proposes a transformation scheme of adding charging piles to some existing public parking lots, so as to curtail the construction period, reduce the construction cost and lower the waiting time for charging;
• A charging demand prediction model considering user travel behavior is constructed by using EV travel data of large sample size to predict charging demand spatial–temporal distribution that accurately considers the road network nodes;
• According to the influencing factors of EV charging and historical charging data, a fuzzy inference system for elastic charging decision is proposed, which can truly reflect the charging decision-making process under the influence of different residual power and external factors;
• The optimization model considers both drivers time cost and charging station profit. According to the calculation method of vehicle queuing delay, a method is proposed to calculate the waiting time of charging queuing vehicles;
• The model proposed in this study considers the location and size planning of charging facilities at the same time, and the fuzzy bi-objective membership is used as the individual fitness function to speed up the solution.

Although the research method proposed in this paper achieves promising results in the planning of charging pile locations (CPLs) and their scale, further research is necessary to enhance the robustness and applicability of the method. Future research should consider the following directions: complex and realistic EV user travel scenarios: (1) incorporate more complex and realistic travel scenarios of EV users, including variations in travel patterns due to seasonal changes, special events, and different geographical regions. (2) Latest and diverse datasets: utilize the latest and diverse datasets to improve the accuracy and relevance of charging demand forecasting models. (3) Impact on the grid: investigate the impact of charging loads on the power grid, including grid dispatch, vehicle-to-grid (V2G) capabilities, and the integration of renewable energy sources. This will aid in developing strategies for grid stability and efficient energy management. (4) Traffic conditions: analyze the impact of road network traffic conditions on the time required for electric vehicles to reach charging stations, enabling more precise planning of CPL locations. (5) Multi-objective optimization improvements: further enhance the multi-objective optimization algorithm to reduce solution time and explore advanced optimization technologies and machine learning methods. By addressing these issues, future research can build on the foundation laid by this study and contribute to more efficient and user-centered EV charging infrastructure planning.