Optimal Planning of EVCS Considering Renewable Energy Uncertainty via Improved Thermal Exchange Optimizer: A Practical Case Study in China

Abstract

With the rapid development of distributed energy and electric vehicles (EVs), the limited hosting capacity of distribution networks has severely impacted their economic dispatch and safe operation. To address these challenges, in this work, an optimal planning model considering the uncertainty of wind and solar power output is proposed, aiming to determine the location and capacity of electric vehicle charging stations (EVCSs). The model seeks to minimize the total costs, voltage fluctuations, and network losses, subject to constraints such as EV user satisfaction and grid company satisfaction. A multi-objective heat exchange optimization algorithm under Gaussian mutation (MOTEO-GM) is employed to validate the model on an extended IEEE-33 bus system and a real-world case in the University Town area of Chenggong District, Kunming City. Simulation results indicate that, in the test system, voltage fluctuations and system power losses are decreased by 43.05% and 37.47%, respectively, significantly enhancing the economic operation of the distribution grid.

1. Introduction

As environmental sustainability and energy shortages become increasingly pressing issues, new energy technologies have experienced rapid development. A large number of distribution generations (DGs) have been integrated into the power grid, which has not only increased the structural complexity of power systems but also turned site selection and capacity planning into a challenging problem. Conventional loads are easily influenced by human behavior, exhibiting temporal variability and randomness. Wind power and photovoltaic distributed power sources, whose output is affected by wind speed and sunlight intensity, also exhibit strong uncertainty and seasonality. Neglecting these characteristics can severely compromise the accuracy of distribution grid planning. With continuous technological progress and government promotion of electric vehicles (EVs), the penetration of EVs into the load profile has been increasing annually, exerting an irreversible influence on distribution networks. Therefore, a rational solution is urgently required to respond to this emerging challenge. EV charging loads are also influenced by human habits and exhibit temporal characteristics, which has led to growing interest in the optimal planning of electric vehicle charging stations (EVCSs).

In recent years, many domestic and international scholars have conducted extensive research on the site selection and capacity optimization of EVCS. Ref. [1] proposed a three-tier framework to enhance EVCS flexibility through distribution network design and developed incentive mechanisms for EVCSs within coupled power and transportation networks. These mechanisms aim to achieve dynamic equilibrium by maximizing profits and ensuring operational safety. That study only considered grid satisfaction conditions, such as construction costs, voltage fluctuations, and network losses, during periods of low renewable energy output; the charging loads for systems A and B were reduced by 11.01 MW and 7.88 MW, respectively, effectively improving grid satisfaction. However, this does not deeply consider user satisfaction. Ref. [2] introduced a novel strategy for determining the optimal location of EVCSs, greatly helping the EV and distribution industries improve system reliability and efficiency; active power losses decreased by 78.4% year-on-year, total voltage deviation decreased by 86.1% year-on-year, and total operating costs were optimized by 78.4%, effectively meeting grid satisfaction requirements. However, this still only considers grid satisfaction and does not consider user satisfaction. Ref. [3] optimized and evaluated photovoltaic–wind–battery/EV charging station systems, primarily aiming to minimize total net present value costs and power supply interruption probability. When load, irradiance, and wind speed each increase by 30%, costs increase by 1.63%, 0.48%, and 0.60%, respectively. Similarly, the study considers grid satisfaction metrics like grid costs and power outage probability, yet it neglects user satisfaction. This one-sided focus on grid satisfaction without considering user satisfaction can lead to numerous issues. Ref. [4] proposed a novel planning framework to determine the optimal location, capacity, and type of electric vehicle charging stations within multi-energy systems. Comprehensive planning for all energy resources achieves cost savings by addressing cost issues, including both user satisfaction and grid satisfaction. In Cases 3 and 4, compared to Case 1, line losses decreased by 15% due to V2G injecting active power into the grid, effectively enhancing grid user satisfaction. However, that study solely focuses on grid satisfaction costs without considering safety dimensions like voltage fluctuations and network losses. This research overly prioritizes cost reduction at the expense of safety, representing a flawed and undesirable approach. Ref. [5] found that increasing EV utilization requires fast-charging systems, which may overload the grid and necessitate costly additional installations and equipment. To address this, Ref. [5] focused on grid satisfaction without examining user satisfaction. This research is clearly too narrow and should incorporate user satisfaction considerations. Both Refs. [6,7] addressed uncertainty analysis for wind and solar power, but neither conducted in-depth uncertainty studies on their output. In Ref. [6], voltage fluctuations and system network losses decreased by 36.73% and 35.41%, respectively, effectively enhancing the stability and economic efficiency of the distribution network. However, Ref. [7] aimed to maximize technical, financial, and social benefits while considering grid satisfaction. When distributed generation and distribution static compensators are deployed concurrently, voltage distribution is significantly improved, with power losses reduced by 36% and 40% in the 33-node and 108-node systems, respectively. Although investment costs increase, energy loss costs and emission costs are substantially reduced. Energy loss costs and emission costs decrease by 35% and 27% in the 33-node system, and by 15% and 20% in the 108-node system, yet because it makes no mention of user satisfaction, this research is clearly incomplete.

First, this work comprehensively considers the uncertainty of wind turbine and photovoltaic output caused by environmental variability, as well as the volatility of demand loads. Wind speed, solar irradiance, and load demand are modeled in a time-series framework. Second, based on Monte Carlo random simulation, a time-series model of EV charging load is established and combined with a wind–solar–load model to generate multi-dimensional distributed power source planning scenarios [8,9,10,11]. Refs. [8,9,10,11] do not discuss wind and solar uncertainty. It is only mentioned in passing, and no specific research has been conducted. This study fills the gap in research on wind and solar uncertainty. To improve computational efficiency, clustering algorithms such as fuzzy kernel clustering are used to cluster complex multi-dimensional scenarios, yielding representative, typical operational scenarios. Then, an optimal EVCS planning model is formulated based on the coupled wind–solar–load system, with objectives including the minimization of total construction cost, user waiting time, voltage deviation, and network losses. The model comprehensively considers the interests of three key stakeholders, namely, investors, EV users, and grid operators, to achieve a balanced, win–win planning outcome [12,13,14,15,16,17,18]. In Refs. [12,13,14,15,16,17,18], user satisfaction and grid satisfaction were only considered individually, without comprehensively balancing the relationship between the two. Therefore, this study is able to reflect the relationship between the interests of the two parties.

Currently, the optimal planning for EVCSs remains primarily focused on construction costs and user satisfaction, with most studies considering only basic load forecasts limited to EV demand. Research on the uncertainty of wind and solar power under high penetration rates and the impact of EVCSs on distribution grids is still at an early stage. To address this issue, this paper couples wind and solar power generation output models with EV load, thereby establishing a three-level planning framework that integrates the wind, solar, and load dimensions. Based on the aforementioned model, an optimal planning method for EVCS is proposed that accounts for the uncertainty of wind and solar power generation, as well as EV load.

Finally, the opposition-based particle swarm optimization with multi-objective heat exchange optimization algorithm under Gaussian mutation (MOTEO-GM) is applied to the extended IEEE-33 node system to validate the model’s effectiveness. Subsequently, the entire planning framework is implemented in a real-world case study involving EVCS deployment at the University Town of Chenggong District, Kunming City. Its performance is compared with other optimization algorithms, including the multi-objective artificial lemming algorithm (MOALA), the multi-objective hawkfish optimization algorithm (MOHFOA), the multi-objective mayfly algorithm (MOMA), multi-objective particle swarm optimization (MOPSO), and the non-dominated sorting genetic algorithm III (NSGA-III). The results demonstrate the superior effectiveness of the proposed EVCS siting and planning model in accounting for wind and solar uncertainty, as well as the high applicability of the MOTEO-GM algorithm to EVCS planning problems.

The remainder of this paper is structured as follows:

Section 2 introduces the wind and solar power output models and the electric vehicle load model, and combines them. Section 3 introduces a planning model for electric vehicle charging stations with voltage fluctuations and network losses as objective functions; Section 4 describes the main algorithm of this paper, based on a multi-objective heat exchange algorithm model under Gaussian mutation; Section 5 validates the above model using an extended IEEE-33 node network and applies it to an actual case study in a district of Kunming City, Yunnan Province, demonstrating the effectiveness of the algorithm.

2. Uncertainty of Wind Power Output and Establishment of Electric Vehicle Load Models

2.1. Overall Framework

The overall framework of this study is shown in Figure 1 [6]. It mainly includes three parts: (1) the establishment of wind and solar power output and EV load models; (2) the optimal planning of an EVCS; (3) the solution to multi-objective models.

2.2. Consideration of Scenarios with Uncertain Wind and Solar Power Output

2.2.1. Wind Power Output Model

The wind power output model is closely related to the magnitude of natural wind speed. At the same time, the location of wind farms and wind fields is also closely related to the establishment of wind farms. Based on existing research, a two-parameter Weibull distribution can be used to simulate changes in wind speed, whose probability density function is expressed as follows [19]:

$$f(v_{l,t},s_{l,t},c_{l,t})={\displaystyle \frac{s_{l,t}}{c_{l,t}}}{({\displaystyle \frac{v_{l,t}}{c_{l,t}}})}^{s_{l,t}-1}{\mathrm{e}}^{(-{({\displaystyle \frac{v_{l,t}}{c_{l,t}}})}^{s_{l,t}})}$$

(1)

where $v_{l,t}$ represents the wind speed at the wind turbine at location $l$ at time $t$; $c_{l,t}$ is the shape parameter of the wind turbine at location $l$ at time $t$; and $s_{l,t}$ denotes the scale parameter of the wind turbine at location $l$ at time $t$. The specific distribution diagram is shown in Figure 2.

In this work, considering that wind power is controlled at constant power, the relationship between wind power output and wind speed at a given location can be approximately represented by the following function:

$$P_l^{\mathrm{WTG}}=\left\{\begin{array}{l}0,0\le v_l\le v_l^0,\\ P_l^{\mathrm{WTG}}{\displaystyle \frac{v_l-v_l^0}{v_l^1-v_l^0}},v_l^0<v_l<v_l^1,\\ P_l^{\mathrm{WTG}},v_l^1\le v_l\le v_l^2\\ 0,v_l^2\le v_l\end{array}\right.$$

(2)

where $P_l^{\mathrm{WTG}}$ represents the rated capacity of the representative office’s wind farm. $v_l^0$, $v_l^1$, and $v_l^2$ are the cut-in wind speed, rated wind speed, and cut-out wind speed, respectively.

2.2.2. Photovoltaic Power Output Model

The variability of photovoltaic power output is influenced by multiple factors, including environmental conditions, geographical location, and material properties. Different environmental conditions result in varying levels of solar radiation, and different geographical locations experience significant differences in sunlight duration. Moreover, photovoltaic panels made from different materials or based on different technologies can generate different levels of electricity under identical irradiation conditions. However, in this work, only the primary factor that affects photovoltaic power output is considered, i.e., the variation in sunlight intensity throughout the day. Typically, the beta distribution is employed to describe the variation in sunlight intensity over a 24 h period. The specific expression is as follows [20,21,22]:

$$f\left(I_{l,t}\right)={\displaystyle \frac{\Gamma ({\alpha }_{l,t}+{\beta }_{l,t})}{\Gamma ({\alpha }_{l,t})+\Gamma ({\beta }_{l,t})}}{\left({\displaystyle \frac{I_{l,t}}{I_{l,\max }}}\right)}^{{\alpha }_{l,t}-1}{\left(1-{\displaystyle \frac{I_{l,t}}{I_{l,\max }}}\right)}^{{\beta }_{l,t}-1}$$

(3)

where $I_{l,t}$ and $I_{l,\max }$ represent the light intensity at position $l$ and its maximum value; Similarly, ${\alpha }_{l,t}$ and ${\beta }_{l,t}$ denote the two parameters of the beta distribution at position and time, respectively. The specific distribution diagram is shown in Figure 3.

The expression for photovoltaic output is

$$P_l^{\mathrm{PV}}=\left\{\begin{array}{l}{P}_l^{\mathrm{pvn}}{\displaystyle \frac{I_l^2}{I_l^{\mathrm{stc}}{R}_l^{\mathrm{c}}}}, I_l<R_l^{\mathrm{c}}\\ P_l^{\mathrm{pvn}}{\displaystyle \frac{I_w}{I_l^{\mathrm{stc}}}}, I_l\ge R_l^{\mathrm{c}}\end{array}\right.$$

(4)

where $P_l^{\mathrm{pvn}}$ represents the rated output of the photovoltaic panel at the representative office; $I_l$ and $I_l^{\mathrm{stc}}$ denote the actual and test conditions of the photovoltaic module at the representative office, respectively; $R_l^{\mathrm{c}}$ is the light irradiation point at the representative office.

2.3. Electric Vehicle Load Model

2.3.1. EV Daily Mileage Distribution Function and Distribution Chart

The daily mileage follows a log-normal distribution, $S~\log -N({\mu }_{\mathrm{a}}, {\delta }_a^2)$, whose probability density function is described by

$$N_a(s)={\displaystyle \frac{1}{s{\delta }_a\sqrt{2\pi }}}{\mathrm{e}}^{-{\displaystyle \frac{(\ln s-{\mu }_a{)}^2}{2{\delta }_a^2}}}$$

(5)

where $s$ represents the daily mileage, with units of minutes; ${\mu }_a$ and ${\delta }_a$ denote the mean and standard deviation of the daily mileage; and ${\mu }_a$ = 3.3 and ${\delta }_a$ = 0.88 [6]. The daily mileage probability distribution chart for EVs can be obtained from Equation (5), as shown in Figure 4 [6].

2.3.2. EV Initial Driving Distribution Function and Its Distribution Chart

The distribution of EV departure times is easily influenced by factors such as travel plans, holidays, morning and evening rush hours, and weather changes. To simplify the model and ensure its rationality, this study excludes the impact of such sudden or irregular events and instead focuses solely on regular daily travel patterns [23,24]. The departure behavior of EVs, which aligns with typical daily commuting patterns, can be modeled using a bimodal distribution function, whose probability density function is defined as follows:

$$P_s(t)={\displaystyle \frac{1}{{\delta }_{s,1}\sqrt{2\pi }}}{e}^{-\frac{(t-{\mu }_{s,1})}{2{\delta }_{s,1}^2}}+{\displaystyle \frac{1}{{\delta }_{s,2}\sqrt{2\pi }}}{e}^{-\frac{(t-{\mu }_{s,2})}{2{\delta }_{s,2}^2}}$$

(6)

where t represents travel time in minutes; ${\mu }_{s,1}$, ${\delta }_{s,1}$ and ${\mu }_{s,2}$, ${\delta }_{s,2}$ denote the mean and standard deviation of the first and second peaks, respectively. The values of these parameters in this work are ${\mu }_{s,1}$ = 8, ${\delta }_{s,1}$ = 3, ${\mu }_{s,2}$ = 18, and ${\delta }_{s,2}$ = 2.25 [6].

2.4. EV Initial Charge State

State of charge (SOC) has a significant impact on both user charging time and the charging demand of EVs. Therefore, this study incorporates the effect of SOC into the planning model. Since SOC values are inherently variable and not fixed, SOC is modeled as a random variable. Its probability density function is given as follows:

$$\chi \left({\mathrm{SOC}}^{\mathrm{EV}}\right)={\displaystyle \frac{1}{{\delta }_{\mathrm{SOC}}\sqrt{2\pi }}}{\mathrm{e}}^{\frac{-\left({\mathrm{SOC}}^{\mathrm{EV}}-{\mu }_{\mathrm{SOC}}\right)}{2{\delta }_{\mathrm{SOC}}^2}}$$

(7)

where ${\mathrm{SOC}}^{\mathrm{EV}}$ is the initial SOC of the EV, and ${\mu }_{\mathrm{SOC}}$ denotes the average SOC, and ${\delta }_{\mathrm{SOC}}$ is the standard deviation of SOC. The values of ${\mu }_{\mathrm{SOC}}$ and ${\delta }_{\mathrm{SOC}}$ are set as 0.3 and 0.15, respectively [6].

2.5. User Waiting Time Model

EV users arriving at a charging station must queue on a first-come, first-served basis. If no charging pile is available upon arrival, the vehicle must enter a waiting queue for charging [25].

The EV user waiting time is calculated by

$$S(i)=\left\{\begin{array}{l}0,T\left(\omega \right)\le \min (Q)\\ \min (Q)-T(\omega ),T(\omega )\ge \min (Q)\end{array}\right.$$

(8)

where $T(\omega )$ represents the time when the EV arrives at the nearest EVCS, and $\min (Q)$ denotes the time required to complete charging at a charging pile within the station.

2.6. Method for Constructing Typical Scenarios

Based on the probability density functions representing the uncertainty of wind and solar power output, as well as the EV load forecasting model described above, this study applies fuzzy kernel clustering to data collected from a district in Kunming to divide the year into four representative scenarios: spring, summer, autumn, and winter. Each scenario reflects distinct wind and solar power generation characteristics. The detailed scenario generation process is as follows [26,27]:

(1) Collect historical wind and solar power output data and EV charging demand data from a specific district in Kunming City; then, perform data cleaning and normalization.

(2) Select a specific Kernel-Based Fuzzy C-Means Clustering (KFCM) method.

(3) Define representative scenarios based on output characteristics, labeling the four clusters as spring, summer, autumn, and winter scenarios.

(4) Use the four seasonal scenarios and the aforementioned solar and wind power output profiles for subsequent load model establishment.

KFCM is an improvement and extension of the traditional Fuzzy C-Means (FCM) algorithm. Its core mechanism involves mapping linearly inseparable data from the original low-dimensional space to a high-dimensional feature space via kernel functions, thereby enabling linearly separable clustering in the high-dimensional domain. This addresses the limitations of traditional FCM, which struggles with clustering nonlinear data and is susceptible to noise interference. Essentially, it employs the “Kernel Trick” to circumvent direct computations in high dimensions while preserving the flexible partitioning characteristics of fuzzy clustering.

The clustering principle of the KFCM algorithm in the feature space is intended to minimize the sum of the weighted squared distances between samples and cluster centers, which is described as follows:

$$J_m(\mathbf{U},v)={\displaystyle \sum _{i=1}^c{\displaystyle \sum _{k=1}^n{u}_{ik}^m}}{‖\Phi (x_k)-\Phi (v_i)‖}^2$$

(9)

where $m>1$ is a constant; $c$ and $n$ represent the number of clusters and the number of samples, respectively; $x_k$ is the $k$th sample; $v_i$ is the center of the $i$th cluster; $u_{ik}^m(i=1,2,\dots ,c;k=1,2,\dots n)$ is the membership function of the $k$th sample in the $i$th cluster, meeting $0\le u_{ik}^m\le 1$ and $0<{\displaystyle \sum _{k=1}^n{u}_{ik}<n}$; and $\mathrm{U}$ is the membership matrix, $\mathbf{U}=\left\{u_{ik}\right\}$.

Expanding Equation (9), we obtain

$${‖\Phi \left(x_k\right)-\Phi \left(v_i\right)‖}^2=\Phi {\left(x_k\right)}^{\mathrm{T}}\Phi \left(x_k\right)+\Phi {\left(v_i\right)}^{\mathrm{T}}\Phi \left(v_i\right)-2\sum _{i=1}^c\Phi {\left(x_k\right)}^{\mathrm{T}}\Phi \left(v_i\right)$$

(10)

We define the kernel function, $K\left(x,y\right)=\Phi {\left(x\right)}^T\Phi \left(y\right)$, and perform the kernel substitution; then,

$$\Phi \left(x_k\right)-\Phi {\left(v_i\right)}^2=K\left(x_k,x_k\right)+K\left(v_i,v_i\right)-2K\left(x_k,v_i\right)$$

(11)

Substituting Equation (10) into Equation (9), we obtain

$$u_{ik}={\displaystyle \frac{{\left(1/\left(K\left(x_k,x_k\right)+K\left(v_i,v_i\right)-2K\left(x_k,v_i\right)\right)\right)}^{1/\left(m-1\right)}}{{\displaystyle \sum _{j=1}^c}{\left(1/\left(K\left(x_k,x_k\right)+K\left(v_j,v_j\right)-2K\left(x_k,v_j\right)\right)\right)}^{1/\left(m-1\right)}}}$$

(12)

where if $K(x_k,v_i)$ is the Gaussian kernel function, then $\tilde{K}(x_k,v_i)=K(x_k,v_i)$.

From Equation (11), it can be concluded that $v_i$ still belongs to the input space, but KFCM introduces $\tilde{K}(x_k,v_i)$ weighted coefficients to the cluster centers, thereby giving reasonable weight values to noise points and outliers.

In this study, we employed a Windows 11 Professional 64-bit operating system with an Intel^® Core^TM i5-14600K processor (3.50 GHz) running on an x64 architecture. The manufacturer is Intel, and the city and location of purchase are Shanghai, China. Solutions were computed using MATLAB R2024b. The resulting output profiles for each scenario are shown in Figure 5. The steps of clustering are detailed in

Table A1. The clustering process of wind power and photovoltaic output under KFCM.

Step1: →Input dataset, $x$. Set the number of clusters, $c$; fuzzifier, $m$; kernel function parameters; maximum iterations, $\max \_iter$

Step2: →Initialize membership matrix U randomly (ensure ${\displaystyle \sum _{k=1}^n{u}_{ik}=1}$ for all $i$). Compute initial kernel matrix, $K$, using selected kernel.

Step3: While iteration < $\max \_iter$ do

Step4: ----For each cluster $k$ = 1 to $n$ do

Step5: --------Calculate the sum of weighted memberships, ${\displaystyle \sum _{i=1}^c{u}_{ik}^m}$

Step6: --------Update the cluster center $v_i$ using the kernel-based formula

Step7: ----End For

Step8: ----For each sample $x_k$ and each cluster $i$ do

Step9: --------Compute the high-dimensional distance ${‖\Phi (x_k)-\Phi (v_i)‖}^2$, using the kernel function for RBF kernel)

Step10: -------Update the membership $u_{ik}$

Step11: ---End For

Step12: ---Calculate the error

Step13: End While

Step14: Assign each sample to the cluster with the highest membership to get the clustering result.

Step15: Return the clustering result and cluster centers.

of Appendix B, and the clustering results are presented in

Table A2. Seasonal output based on KFCM clustering.

Time	Spring		Summer		Autumn		Winter
	Photovoltaic	Wind Power	Photovoltaic	Wind Power	Photovoltaic	Wind Power	Photovoltaic	Wind Power
1:00	0	0.129	0	0.112	0	0.072	0	0.075
2:00	0	0.114	0	0.119	0	0.048	0	0.057
3:00	0	0.117	0	0.084	0	0.065	0	0.056
4:00	0	0.095	0	0.102	0	0.054	0	0.082
5:00	0	0.116	0	0.086	0	0.055	0	0.072
6:00	0	0.137	0	0.064	0	0.042	0	0.062
7:00	0	0.125	0.035	0.087	0.001	0.044	0	0.047
8:00	0.032	0.104	0.262	0.064	0.133	0.049	0.057	0.048
9:00	0.682	0.09	0.684	0.071	0.686	0.043	0.673	0.06
10:00	0.71	0.105	0.692	0.086	0.71	0.042	0.681	0.076
11:00	1.068	0.236	1.187	0.133	1.068	0.066	0.94	0.123
12:00	1.317	0.284	1.345	0.149	1.296	0.073	1.059	0.195
13:00	1.287	0.293	1.468	0.162	1.394	0.094	1.123	0.281
14:00	1.23	0.34	1.5	0.181	1.311	0.117	1.187	0.413
15:00	1.23	0.33	1.5	0.153	1.311	0.189	1.187	0.362
16:00	0.886	0.33	1.12	0.184	0.854	0.204	0.844	0.339
17:00	0.643	0.421	0.754	0.205	0.615	0.152	0.531	0.251
18:00	0.383	0.372	0.441	0.18	0.405	0.138	0.183	0.259
19:00	0.069	0.342	0.179	0.179	0.159	0.11	0.046	0.135
20:00	0	0.247	0.023	0.108	0.002	0.09	0	0.096
21:00	0	0.239	0	0.122	0	0.064	0	0.152
22:00	0	0.204	0	0.144	0	0.059	0	0.121
23:00	0	0.154	0	0.12	0	0.063	0	0.09
0:00	0	0.147	0	0.058	0	0.065	0	0.05

of Appendix B.

3. EVCS Site Selection and Capacity Planning Optimization Model

3.1. Objective Function

3.1.1. EVCS Investment and Construction Costs

This work considers the investment and construction costs of EVCS in the planning process. To achieve more cost-effective site selection and capacity planning, it is essential to account for the comprehensive cost structure [28,29,30].

The comprehensive costs of EVCS combined with a battery energy storage system (BESS) are as follows:

$$C_1=M_1+M_2+M_3$$

(13)

where $C_1$ represents the total cost of the EVCS and BESS system, i.e., the overall construction cost of the charging station; $M_1$ denotes the annualized total cost of the EVCS investment and construction; $M_2$ is the full life cycle cost of the BESS investment and construction; $M_3$ represents the cost of power loss.

$$M_1={\displaystyle \sum _{i=1}^{n_{\mathrm{EVCS}}}(C_i^{\mathrm{la}}+C_i^{\mathrm{co}}+C_i^{\mathrm{om}})}\times {\displaystyle \frac{{\theta }_0{(1+{\theta }_0)}^x}{{(1+{\theta }_0)}^x-1}}$$

(14)

where ${\theta }_0$ represents the average discount rate; $x$ denotes the operating period; $n_{\mathrm{EVCS}}$ means the number of EVCS; and $C_i^{\mathrm{la}}$, $C_i^{\mathrm{co}}$, and $C_i^{\mathrm{om}}$ represent the land purchase cost, construction cost, and operating and maintenance costs, respectively.

$$C_i^{\mathrm{la}}=C_j\times n_i^{\mathrm{char}}\times \left[(1+\alpha )\times A_{\mathrm{car}}+A_e\right]$$

(15)

where $C_j$ represents the unit land price in different regions. The regions are classified based on land use characteristics, and the corresponding guideline prices vary accordingly. These prices are affected by factors such as proximity to the city center and the post-development land use type, making this value variable. $n_i^{\mathrm{char}}$ represents the number of charging stations within the ith charging station; $\alpha$ represents the ratio coefficient of the parking space area after the conversion of the building and other areas; $A_{\mathrm{car}}$ and $A_e$ denote the parking space area and the equipment area, respectively.

$$C_i^{\mathrm{bu}}=C_{\mathrm{f}i}+n_i^{\mathrm{char}}\times C_{\mathrm{bu}}+\gamma \times Cap{a}_i^{\mathrm{EVCS}}$$

(16)

where $C_{\mathrm{fi}}$ represents the fixed cost of the charging station; $C_{\mathrm{bu}}$ means the purchase cost; $Cap{a}_i^{\mathrm{EVCS}}$ denotes the capacity; and $\gamma$ represents the investment coefficient related to capacity.

$$C_i^{\mathrm{op}}=\beta \times Cap{a}_i^{\mathrm{EVCS}}$$

(17)

where $\beta$ represents the operation and maintenance coefficient related to charging station capacity.

$$M_2=\left[{\displaystyle \frac{e}{{(1+e)}^{y_B}}}+e\right]\times {\displaystyle \sum _{\lambda }^{n_{\mathrm{bess}}}(T{C}_{\lambda }+O{P}_{\lambda }+R{C}_{\lambda }+D{C}_{\lambda })}$$

(18)

where $y_B$ represents the service life of the BESS; $n_{\mathrm{bess}}$ denotes the number of BESS units; $e$ is the BESS discount rate; $TC$, $OP$, $RC$, and $DC$ mean the total investment cost, operational and maintenance cost, replacement cost, and disposal and recycling cost, respectively.

$$T{C}_{\lambda }={\psi }_{\mathrm{bat}}\times C{\mathrm{apa}}_{\lambda }^{\mathrm{bess}}+{\psi }_{\mathrm{inv}}\times P_{B,\lambda }$$

(19)

where ${\psi }_{\mathrm{bat}}$ and ${\psi }_{\mathrm{inv}}$ represent the costs of the storage battery and inverter.

$$O{P}_{\lambda }=({\mu }_{\mathrm{op}, \mathrm{bat}}\times {\psi }_{\mathrm{bat}}\times C{\mathrm{apa}}_{\lambda }^{\mathrm{bess}})+({\mu }_{\mathrm{op}, \mathrm{inv}}\times {\psi }_{\mathrm{inv}}\times P_{B,\lambda })$$

(20)

where ${\mu }_{\mathrm{op},\mathrm{bat}}$ and ${\mu }_{\mathrm{op},\mathrm{inv}}$ denote the ratio of OP to battery investment costs and the proportion of inverter investment costs, respectively.

$$R{C}_{\lambda }={{\displaystyle \sum _{n=1}^{n_{ct}}\left(\frac{1-\theta }{1+e}\right)}}^{n\times T_{\mathrm{bat}}}\times ({\psi }_{\mathrm{bat}}\times Cap{a}_{\lambda }^{\mathrm{bess}}+{\psi }_{\mathrm{inv}}\times P_{B,\lambda })$$

(21)

where $n_{ct}$ represents the number of times the BESS is replaced; $T_{\mathrm{bat}}$ is the replacement cycle of the BESS; and $\theta$ represents the annual reduction rate of the BESS cost.

$$D{C}_{\lambda }={\displaystyle \sum _{n=1}^{n_{ct}}\frac{\upsilon }{{(1+e)}^{n\times T_{\mathrm{bat}}}}}\times ({\psi }_{\mathrm{bat}}\times Cap{a}_{\lambda }^{\mathrm{bess}}+{\psi }_{\mathrm{inv}}\times P_{B,\lambda })$$

(22)

where $\upsilon$ is the recovery coefficient of the battery and inverter.

$$M_3={\Omega }_p{\displaystyle {\int }_0^{8760}\left[P_{\mathrm{los}2}(t)-P_{\mathrm{los}1}(t)\right]}dt$$

(23)

where ${\Omega }_p$ is the conversion coefficient between power loss and loss cost; $P_{\mathrm{los}1}$ and $P_{\mathrm{los}2}$ denote the active power loss in the distribution network before connecting to the charging station and BESS and the active power loss after connecting to the charging station and BESS, respectively.

3.1.2. Waiting Time Costs

When EV users arrive at a charging station, if no charging piles are available, they must wait in a queue according to the first-come, first-served principle. Users who arrive earlier will begin charging earlier. Later-arriving EV users incur a waiting time equal to the sum of the previous user’s charging time and waiting time. During this period, users experience waiting-related costs, referred to as user waiting time costs. These costs consist of both the time spent traveling to the charging station and the time spent waiting in line and can be calculated as follows [31,32,33]:

$$C_2={\displaystyle \frac{1}{n_{\mathrm{EV}}}}{\displaystyle \sum _{j=1}^{m_{\mathrm{EVCS}}}{\displaystyle \sum _{i=1}^{n_{\mathrm{EV}}}(\frac{d_{\mathrm{EV},i}^j}{v}+W_j(i)}})$$

(24)

where $n_{\mathrm{EV}}$ represents the number of EVs; $d_{\mathrm{EV},i}^j$ denotes the shortest distance from the ith vehicle to the jth EVCS; $v$ is the average driving speed; and $W(i)$ signifies the waiting time of the ith vehicle at the jth EVCS.

3.1.3. Voltage Fluctuations

The constraints for voltage fluctuations are as follows:

$$C_3={\displaystyle \sum _{i=1}^{N_{\mathrm{node}}}{\displaystyle \sum _j^T\left|V_{ij}-\stackrel{-}{V_i}\right|}}$$

(25)

where $N_{node}$ represents the number of nodes; $T$ represents time; $V_{ij}$ denotes the voltage of the node i at time j; and $\stackrel{-}{V}$ represents the average voltage of node during the period [1–T].

3.2. Constraints

3.2.1. Charging Station Distance Constraints

In order to prevent EVCSs from being built too far apart or too close together, which would reduce user satisfaction in the former case and lead to a waste of resources in the latter, it is necessary to impose a distance constraint:

$$R_{\mathrm{EVCS}}\le D_{\mathrm{EVCS}}\le 2R_{\mathrm{EVCS} }$$

(26)

where $R_{\mathrm{EVCS}}$ represents the charging radius of the charging station, and $D_{\mathrm{EVCS}}$ denotes the distance between two charging stations.

$$E{Q}_{\mathrm{RE}}^{\mathrm{EVCS}}\le {\displaystyle \sum _{i=1}^{n_{\mathrm{EVCS}}}(Cap{a}_i^{\mathrm{EVCS}}\times T_{\max })}$$

(27)

3.2.2. Charging Station Capacity Constraints

The constraints for charging stations are as follows:

$$E{Q}_{\mathrm{RE}}^{\mathrm{EVCS}}=\max \left\{E{Q}_{\mathrm{RE}}^{\mathrm{char}}\right\}$$

(28)

where $E{Q}_{\mathrm{RE}}^{\mathrm{EVCS}}$ is the maximum charging demand in this area, and $T_{\max }$ represents the maximum service time of the charging station.

3.2.3. Node Voltage Constraints

The constraints for voltage nodes are as follows:

$$V_{\mathrm{EVCS},n}^{\min }\le V_{\mathrm{EVCS},n}\le V_{\mathrm{EVCS},n}^{\max }$$

(29)

where $V_{\mathrm{EVCS},n}^{\min }$ and $V_{\mathrm{EVCS},n}^{m\mathrm{ax}}$ represent the voltage threshold after the node is connected to the EVCS.

$$\left\{\begin{array}{l}{\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{P}_n-P_{\mathrm{loss}}={\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{P}_{\mathrm{load},n}-}{\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{P}_{\mathrm{EVCS},n}}}\\ {\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{Q}_n-Q_{\mathrm{loss}}={\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{Q}_{\mathrm{load},n}-}{\displaystyle \sum _{n=1}^{n_{\mathrm{node}}}{Q}_{\mathrm{EVCS},n}}}\end{array}\right.$$

(30)

where $P_n$ and $Q_n$ represent the active and reactive power injected by the node; $P_{\mathrm{loss}}$ represents the total active power loss of the system; $Q_{\mathrm{loss}}$ denotes the total reactive power loss of the system; $P_{\mathrm{load},n}$ and $Q_{\mathrm{load},n}$ are the active and reactive loads of the node; and $P_{\mathrm{EVCS},n}$ and $Q_{\mathrm{EVCS},n}$ are the active and reactive power output of the node, n, after connecting to the EVCS.

3.2.4. SOC Constraints for BESS

The charging and discharging of energy storage systems occur within a specific power range.

$$SO{C}_{\min }^{\mathrm{bess}}\le SO{C}_{\kappa }^{\mathrm{bess}}\le SO{C}_{\max }^{\mathrm{bess}}$$

(31)

where $SO{C}_{\kappa }^{\mathrm{bess}}$ represents the SOC of BESS.

3.2.5. BESS Charging and Discharging Power Constraints

The constraints are as follows:

$$\left\{\begin{array}{l}0\le P_{{\mathrm{in},\mathrm{B}}_{\epsilon }}\le P_{{\mathrm{in},\mathrm{B}}_{\epsilon }}^{\mathrm{rat}}\\ 0\le P_{{\mathrm{out},\mathrm{B}}_{\epsilon }}\le P_{{\mathrm{out},\mathrm{B}}_{\epsilon }}^{\mathrm{rat}}\end{array}\right.$$

(32)

where $P_{\mathrm{in}{.\mathrm{B}}_{\epsilon }}^{\mathrm{rat}}$ and $P_{\mathrm{out}{.\mathrm{B}}_{\epsilon }}^{\mathrm{rat}}$ represent the rated power of the BESS.

4. Model Solving Based on MOTEO-GM

4.1. MOTEO Algorithm

Thermal exchange optimization (TEO) is a novel optimization algorithm based on Newton’s cooling law, characterized by fast convergence and strong optimization capabilities. MOTEO extends the TEO algorithm to the field of multi-objective optimization. Its core challenge lies in the fact that the solution to a multi-objective problem is no longer a single scalar value but rather a set of Pareto optimal solutions. Therefore, MOTEO requires introducing multi-objective processing strategies on top of the original TEO mechanism. While retaining TEO’s physical update mechanism, the MOTEO algorithm shifts its core comparison criterion from “scalar value comparison” to “Pareto dominance comparison.” It also incorporates external archiving and a diversity maintenance mechanism based on crowding distance. The transition from TEO to MOTEO fundamentally represents a paradigm shift from scalar optimization to vector optimization. MOTEO performs well in solving multi-objective problems, delivering a series of balanced trade-off solutions. However, its efficiency typically falls below TEO due to additional computational overhead (domination checks, archive maintenance). The MOTEO algorithm introduces a thermally meaningful energy exchange mechanism, where its energy transfer model effectively guides particles toward the Pareto front, achieving fast convergence. By combining Pareto dominance and diversity preservation strategies, it can simultaneously optimize multiple conflicting objectives and obtain a uniformly distributed set of non-inferior solutions. However, the standard MOTEO algorithm still exhibits certain deficiencies. Therefore, this work introduces several enhancement mechanisms, such as Gaussian mutation, crowded distance, and roulette wheel selection, to improve its overall performance. These mechanisms enhance the performance of the standard MOTEO algorithm from three key perspectives: local search or perturbation, solution set distribution control, and parent selection strategy. This enables the algorithm to obtain high-quality solution sets that are closer to the true Pareto frontier, more uniformly distributed, and have a broader range when solving complex multi-objective optimization problems. The initial population size in this algorithm is 300, with the fitness function minimizing construction costs, voltage fluctuations, and network losses. The specific solution process is illustrated in Figure 6 [34]. To prove the effectiveness of the added mechanism, this paper conducted tests on the mechanism’s analytical functions and instance test functions. For details, please refer to Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6, Figure A7, Figure A8, Figure A9 and Figure A10 in Appendix A.

4.2. Solving the Model Based on Gaussian Mutation

Gaussian mutation is a commonly used perturbation strategy in evolutionary algorithms such as genetic algorithms and particle swarm optimization. It is typically employed to perform local fine-grained searches in the solution space or to escape local optima. Gaussian mutation generates new solutions by adding a random perturbation that follows a normal distribution to the current solution, as follows:

$$x_{\mathrm{new}}=x_{\mathrm{old}}+N(0,{\sigma }^2)$$

(33)

where $N(0,{\delta }^2)$ represents a Gaussian random function with a mean of 0 and a variance of ${\delta }^2$, in which $\delta$ controls the variation intensity and typically decreases with each iteration.

The crowding distance measures an individual’s sparsity on the Pareto front. The larger the value, the more isolated the individual is, and the more it should be prioritized for retention. After sorting each objective function, m, in ascending order, the crowding distance for each individual is calculated as follows:

$$d_i^m={\displaystyle \frac{f_{i+1}^m-f_{i-1}^m}{f_{\max }^m-f_{\min }^m}}$$

(34)

where $f_{i+1}^m$ and $f_{i-1}^m$ represent the adjacent target values, and $f_{\max }^m$ and $f_{\min }^m$ denote the maximum and minimum target values, respectively.

The total congestion distance is expressed as

$$d_i={\displaystyle \sum _{m=1}^M{d}_i^m}$$

(35)

Roulette wheel selection is used to determine the selection probability of individuals based on their crowding distance. Individuals with larger crowding distances—i.e., those located in sparser regions of the solution space—are assigned higher probabilities of being selected as leaders.

Probability calculation:

$$p_i={\displaystyle \frac{d_i}{{\displaystyle {\sum }_{j=1}^N{d}_j}}}$$

(36)

Cumulative probability:

$$q_i={\displaystyle \sum _{j=1}^i{p}_j}$$

(37)

Crowding distance quantifies sparsity, and roulette-based selection of leaders based on sparsity jointly maintains the uniformity and diversity of the Pareto frontier.

The solution procedure of the MOTEO-GM-based joint sitting and sizing model for electric vehicle charging stations integrated with BESS is illustrated in Figure 7.

5. Case Study

Kunming, the provincial capital of Yunnan Province in China, is located between 102°10′ and 103°40′ east longitude and 24°23′ and 26°33′ north latitude. As of 2024, it has a permanent population of 8.687 million and serves as an important gateway for China’s opening-up to South Asia and Southeast Asia, as well as a front-line hub for the Belt and Road Initiative. In this work, the University Town in Chenggong District, Kunming City, Yunnan Province, will be used as a practical case study. Figure 8, below, shows the specific location of the University Town in Kunming City. It is noted that the simulation results are limited to an actual case study.

5.1. Test Model

First, prior to conducting the model testing, we make the following declarations regarding the model parameters: (1) the number of electric vehicles is set at 2000; (2) both the EV and EVCS considered are of the BYD series; (3) the BESS is installed within the EVCS, so the installation locations of the BESS and EVCS are the same; (4) the charging station operates in fast-charging mode.

To verify the effectiveness of the proposed model, preliminary testing is conducted on the expanded IEEE-33 bus system. Wind power generation units with a capacity of 0.45 MW are installed in buses 21 and 24, while photovoltaic generation units with a capacity of 1.5 MW are configured in buses 17 and 31. The specific configuration diagram is shown in Figure 9 [6]. The numbers 1 to 33 in the Figure 9 respectively represent 33 nodes.

Before conducting model testing, this study provides detailed descriptions of the model structure and system parameters, as shown in

Table 1. System parameters.

Parameters	Value	Parameters	Value
Installed capacity of wind turbines	0.45 MW	SOC range [6]	0.2–0.9
Installed photovoltaic capacity	1.5 MW	Number of Monte Carlo simulations	100
BESS capacity range	0–4 MWh	BESS power range	(−1.2) MW–1.2 MW
Number of EVs	2000

,

Table 2. Comparison of algorithm parameters.

Algorithm	Parameters	Value
Shared parameters	Maximum number of iterations	300
	Population size	100
	Size of Pareto solution set	100
NSGA-III	Number of intervals	10
	Crossover percentage	0.5
MOTEO-GM	Cross-probability	0.7
	Mutation rate	0.4
	Mutation probability	0.02
	Individual learning factors	1.1
	Social learning factor	2.2
MOPSO	Deletion selection pressure	2
	Inertia weight damping rate	0.99
	Inertia weight	0.5
MOMA	Random flight coefficient	0.77
	Random flight damping ratio	0.99
	Distance perception coefficient	2
MOHFOA	Expansion rate	0.05
	Leadership selection	1.8
MOALA	Migration rate	0.6
	Suicide rate	0.6
	Fertility rate	0.1

and

Table 3. Basic parameters of EV [6].

Parameter Symbols	Meaning	Value
$C{\mathrm{ar}}_{\mathrm{capa}}/(\mathrm{kW}\cdot \mathrm{h})$	EV battery capacity	80
$C{\mathrm{ar}}_{\mathrm{char}}/(\mathrm{kW}\cdot {\mathrm{h}}^{-1})$	EV charging power	120
$C{\mathrm{ar}}_{\mathrm{loss}}/(\mathrm{kW}\cdot \mathrm{h}\cdot {\mathrm{km}}^{-1})$	EV energy consumption	0.2
$C{\mathrm{ar}}_{\mathrm{need}}$	Need to charge SOC	0.3
$C{\mathrm{ar}}_{\min }$	Minimum SOC	0.1
$C{\mathrm{ar}}_{\max }$	Maximum SOC	0.9
$v/(\mathrm{km}\cdot {\mathrm{h}}^{-1})$	Average speed	35

.

Based on the establishment of the above model and the setting of model parameters, the simulation results obtained using the IEEE-33 bus system are shown in

Table 4. IEEE-33 node simulation test results.

	Cost (CNY 1000)	System Network Loss (MWh)	Voltage Fluctuation (p.u)
MOALA	7729.139	4.8862	0.7932
MOHFOA	5097.80	3.5126	0.5759
NSGA-III	5347.48	3.0713	0.4818
MOPSO	4749.10	3.1638	0.5218
MOMA	4978.28	3.2022	0.4917
MOTEO-GM	5454.11	3.0551	0.4517

. From the results, it can be observed that the total cost of the MOTEO-GM-based planning scheme for electric vehicle charging stations is CNY 5,454,110, which is 13.64% higher than the lowest-cost solution provided by the MOPSO algorithm (CNY 4,749,100). Although the cost of MOTEO-GM is slightly inferior to other algorithms in this study, the cost in the power grid is less important than voltage fluctuations and network losses that affect the safe operation and economic dispatch of the power system network. MOTEO-GM achieves significant improvements in both voltage fluctuations and network losses compared to other algorithms. Specifically, network losses are reduced by 37.47%, 13.02%, 3.44%, 4.60%, and 0.52% compared to MOALA, MOHFOA, MOPSO, MOMA, and NSGA-III, respectively. Similarly, voltage fluctuations are reduced by 43.05%, 21.57%, 13.43%, 8.13%, and 6.24% compared to MOALA, MOHFOA, MOPSO, MOMA, and NSGA-III, respectively. Based on the above analysis, MOTEO-GM demonstrates certain advantages and strong applicability in this model.

In Figure 10, the voltage fluctuations of each algorithm are respectively presented. It can be concluded that the voltage fluctuation of MOTEO-GM is the smallest, which proves the effectiveness of MOTEO-GM in this paper.

Table 5. EVCS capacity configuration table under IEEE-33 node.

	Algorithm		MOALA	MOHFOA	MOMA	MOPSO	MOTEO-GM	NSGA-III
Charging Station
Charging station #1		EVCS capacity (kWh)	632.8559	499.6351	360.0720	894.2439	360	360
		Location (node)	11	2	2	2	19	20
		Number of charging stations	10	5	4	8	3	3
Charging station #2		EVCS capacity (kWh)	470.5486	437.8286	484.8423	366.4698	360	360
		Location (node)	1	19	5	19	20	5
		Number of charging stations	6	4	5	4	3	3
Charging station #3		EVCS capacity (kWh)	669.8371	989.4701	553.7209	363.7630	440.2740	465.1220
		Location (node)	17	27	21	20	5	17
		Number of charging stations	6	9	5	4	4	4
Charging station #4		EVCS capacity (kWh)	616.9071	947.8585	836.2983	649.0001	979.6140	767.9872
		Location (node)	13	25	3	25	3	3
		Number of charging stations	9	8	7	6	9	7
Charging station #5		EVCS capacity (kWh)	423.4923	438.4271	360.3348	665.0405	839.6769	839.6769
		Location (node)	28	20	20	23	22	20
		Number of charging stations	9	4	4	5	7	7
Charging station #6		EVCS capacity (kWh)	652.8598	654.5450	724.8534	818.9534	458.4150	458.4149
		Location (node)	17	21	19	3	2	17
		Number of charging stations	7	7	7	5	4	4

shows the locations, capacities, and numbers of charging stations accommodated by six EVCS under various optimization algorithms.

Furthermore, to demonstrate that incorporating Gaussian mutation and roulette wheel selection into this study can significantly improve the algorithm’s shortcomings, this paper selected mu—the most critical parameter in Gaussian mutation—as the variable. Sensitivity analysis was conducted using cost as the observed value, with the results shown in Figure 11.

5.2. Planning of the Actual Area

To further validate the effectiveness and practical applicability of the proposed model, it is applied to the University Town in Chenggong District, Kunming City, Yunnan Province, to conduct optimal planning for EVCSs in the area, based on the aforementioned test model. To demonstrate the impact of EV charging on the power grid, and since obtaining actual grid topology data is unfeasible, this paper assumes each region constitutes a grid node [35]. The specific system parameters can be found in

Table A3. Based on the improved IEEE-69 node simulation system parameters.

Node Number	Node Type	Active Power	Reactive Power	Electrical Conductivity	Capacitance	Section Number of Cross-Section	Voltage Amplitude	Voltage Phase Angle	Reference Voltage	Loss Allocation Number	Voltage Limit	Voltage Lower Limit
1	3	0	0	0	0	1	1	0	12.66	1	1	1
2	1	0	0	0	0	1	0.999966497	−0.001227666	12.66	1	1.1	0.9
3	1	0	0	0	0	1	0.999932994	−0.002455415	12.66	1	1.1	0.9
4	1	0	0	0	0	1	0.999839452	−0.005886544	12.66	1	1.1	0.9
5	1	0	0	0	0	1	0.999020282	−0.018507242	12.66	1	1.1	0.9
6	1	0.0026	0.0022	0	0	1	0.990085012	0.049326521	12.66	1	1.1	0.9
7	1	0.0404	0.03	0	0	1	0.980793218	0.121065807	12.66	1	1.1	0.9
8	1	0.075	0.054	0	0	1	0.978577191	0.13827704	12.66	1	1.1	0.9
9	1	0.03	0.022	0	0	1	0.977443724	0.147095216	12.66	1	1.1	0.9
10	1	0.028	0.019	0	0	1	0.972443492	0.231898885	12.66	1	1.1	0.9
11	1	0.145	0.104	0	0	1	0.971341968	0.250706633	12.66	1	1.1	0.9
12	1	0.145	0.104	0	0	1	0.968180409	0.3035534	12.66	1	1.1	0.9
13	1	0.008	0.0055	0	0	1	0.965254673	0.350039842	12.66	1	1.1	0.9
14	1	0.008	0.0055	0	0	1	0.962362972	0.396922206	12.66	1	1.1	0.9
15	1	0	0	0	0	1	0.959492912	0.442861898	12.66	1	1.1	0.9
16	1	0.0455	0.03	0	0	1	0.958959606	0.451423951	12.66	1	1.1	0.9
17	1	0.06	0.035	0	0	1	0.958079017	0.46557271	12.66	1	1.1	0.9
18	1	0.06	0.035	0	0	1	0.958070106	0.465718512	12.66	1	1.1	0.9
19	1	0	0	0	0	1	0.95760504	0.474247655	12.66	1	1.1	0.9
20	1	0.001	0.0006	0	0	1	0.957306587	0.47977782	12.66	1	1.1	0.9
21	1	0.114	0.081	0	0	1	0.956824374	0.488651852	12.66	1	1.1	0.9
22	1	0.0053	0.0035	0	0	1	0.956817471	0.488779545	12.66	1	1.1	0.9
23	1	0	0	0	0	1	0.956745624	0.490114457	12.66	1	1.1	0.9
24	1	0.028	0.02	0	0	1	0.95658924	0.493020527	12.66	1	1.1	0.9
25	1	0	0	0	0	1	0.956420157	0.496164372	12.66	1	1.1	0.9
26	1	0.014	0.01	0	0	1	0.956350406	0.497461619	12.66	1	1.1	0.9
27	1	0.014	0.01	0	0	1	0.956330854	0.497825596	12.66	1	1.1	0.9
28	1	0.026	0.0186	0	0	1	0.999926086	−0.002706277	12.66	1	1.1	0.9
29	1	0.026	0.0186	0	0	1	0.999854392	−0.005306859	12.66	1	1.1	0.9
30	1	0	0	0	0	1	0.999733267	−0.003181042	12.66	1	1.1	0.9
31	1	0	0	0	0	1	0.999711893	−0.002805761	12.66	1	1.1	0.9
32	1	0	0	0	0	1	0.999605025	−0.000929117	12.66	1	1.1	0.9
33	1	0.014	0.01	0	0	1	0.999348825	0.00349713	12.66	1	1.1	0.9
34	1	0.0195	0.014	0	0	1	0.99901333	0.009350378	12.66	1	1.1	0.9
35	1	0.006	0.004	0	0	1	0.998945917	0.01041506	12.66	1	1.1	0.9
36	1	0.026	0.0186	0	0	1	0.999919185	−0.002969196	12.66	1	1.1	0.9
37	1	0.026	0.0186	0	0	1	0.999747353	−0.00937513	12.66	1	1.1	0.9
38	1	0	0	0	0	1	0.999588856	−0.011791768	12.66	1	1.1	0.9
39	1	0.024	0.017	0	0	1	0.999543104	−0.012489114	12.66	1	1.1	0.9
40	1	0.024	0.017	0	0	1	0.999540889	−0.012523227	12.66	1	1.1	0.9
41	1	0.0012	0.001	0	0	1	0.998843384	−0.023504257	12.66	1	1.1	0.9
42	1	0	0	0	0	1	0.998551048	−0.028141779	12.66	1	1.1	0.9
43	1	0.006	0.0043	0	0	1	0.998512427	−0.028751789	12.66	1	1.1	0.9
44	1	0	0	0	0	1	0.998504106	−0.02890436	12.66	1	1.1	0.9
45	1	0.0392	0.0263	0	0	1	0.99840562	−0.030710284	12.66	1	1.1	0.9
46	1	0.0392	0.0263	0	0	1	0.998405202	−0.030718665	12.66	1	1.1	0.9
47	1	0	0	0	0	1	0.999789366	−0.007699078	12.66	1	1.1	0.9
48	1	0.079	0.0564	0	0	1	0.998543487	−0.052531491	12.66	1	1.1	0.9
49	1	0.3847	0.2745	0	0	1	0.994698618	−0.191631031	12.66	1	1.1	0.9
50	1	0.3847	0.2745	0	0	1	0.994153654	−0.211441054	12.66	1	1.1	0.9
51	1	0.0405	0.0283	0	0	1	0.978541748	0.138572287	12.66	1	1.1	0.9
52	1	0.0036	0.0027	0	0	1	0.978532166	0.138753628	12.66	1	1.1	0.9
53	1	0.0043	0.0035	0	0	1	0.974657359	0.169020609	12.66	1	1.1	0.9
54	1	0.0264	0.019	0	0	1	0.971414412	0.19463532	12.66	1	1.1	0.9
55	1	0.024	0.0172	0	0	1	0.966940947	0.230222883	12.66	1	1.1	0.9
56	1	0	0	0	0	1	0.962572345	0.265180456	12.66	1	1.1	0.9
57	1	0	0	0	0	1	0.940098457	0.661744946	12.66	1	1.1	0.9
58	1	0	0	0	0	1	0.929038861	0.864303071	12.66	1	1.1	0.9
59	1	0.1	0.072	0	0	1	0.92476117	0.945280836	12.66	1	1.1	0.9
60	1	0	0	0	0	1	0.919736665	1.049778681	12.66	1	1.1	0.9
61	1	1.244	0.888	0	0	1	0.912339563	1.118831179	12.66	1	1.1	0.9
62	1	0.032	0.023	0	0	1	0.912049951	1.121553655	12.66	1	1.1	0.9
63	1	0	0	0	0	1	0.911662223	1.125196596	12.66	1	1.1	0.9
64	1	0.227	0.162	0	0	1	0.909762018	1.143057298	12.66	1	1.1	0.9
65	1	0.059	0.042	0	0	1	0.909187714	1.148433818	12.66	1	1.1	0.9
66	1	0.018	0.013	0	0	1	0.971285235	0.251855337	12.66	1	1.1	0.9
67	1	0.018	0.013	0	0	1	0.971284575	0.251868941	12.66	1	1.1	0.9
68	1	0.028	0.02	0	0	1	0.967850456	0.309615229	12.66	1	1.1	0.9
69	1	0.028	0.02	0	0	1	0.967849401	0.309634005	12.66	1	1.1	0.9

of Appendix B. An improved 69-node grid model was re-established for simulation testing. This method has been thoroughly validated in domestic research, as detailed in Ref. [6]. The corresponding distribution network structure is shown in Figure 12 [6].

It shows a transformation of the road area into a distribution network node structure in the Figure 12. Eventually, an actual case test was conducted using the improved 69-node model.

This section first predicts the traffic flow in the region, incorporates the predicted traffic flow into the charging demand calculation model, and derives the charging demand distribution across each time segment of the day, as shown in Figure 13.

Based on the aforementioned model, following the simulation process, the graph of the IEEE-33 bus system is transformed into the road network topology structure shown in Figure 9. Similarly, different wind and solar generation systems with varying outputs are connected to different nodes to construct a planning diagram that closely aligns with real-life scenarios. Similar to the IEEE-33 bus system, 0.45 MW wind power generation systems are configured at nodes 16 and 67, and 1.5 MW photovoltaic power generation systems are configured at nodes 56 and 33. The planning result diagram is shown in Figure 14.

The charging and discharging power and SOC changes in the BESS at each charging station under the MOTEO optimization results are illustrated in Figure 13.

Figure 15 shows the charging and discharging power and SOC changes of each BESS within a day. It can be seen that all 10 BESS units operate continuously throughout the day, with their SOC levels maintained between 20% and 90%, which is beneficial for ensuring both the operational lifespan and safety of the BESS units.

6. Conclusions

This study first establishes an uncertainty model for wind and solar power output and then applies the Monte Carlo method to predict traffic flow in the University Town of Chenggong District, Kunming City, while simulating the corresponding EV charging demand. Finally, wind and solar power outputs are integrated with EV loads. This study aims to maximize the satisfaction of three stakeholders, i.e., EVCS developers, EV users, and power grid companies, by establishing an optimal planning model for EVCS that accounts for wind and solar power uncertainty. The MOTEO-GM algorithm is then applied for validation and tested on both an expanded IEEE-33 bus system and a real-world case study in Chenggong District, Kunming City, Yunnan Province, China. The simulation results show that, although the proposed planning scheme incurs slightly higher costs, it achieves significant reductions in network losses and voltage fluctuations, thereby enabling more economical dispatch and stable operation of the distribution network. This study provides a solid foundation for future EVCS planning research. Future work may explore the integration of demand response strategies and coordinated scheduling mechanisms to further enhance the effectiveness of EVCS planning. In this study, we only considered EVs as loads and did not account for their V2G (vehicle-to-grid) scheduling capabilities as distributed energy storage. This will be another direction for our research. At the same time, the classical Weibull/beta distribution is used in this paper, and the LSTM method, which is currently more popular, is not used. In the next study, it will be our key research direction. At the same time, the classical Weibull/beta distribution is used in this paper, and the LSTM method, which is currently more popular, is not used. In the next research, it will be our key research direction.