Charging Station Siting and Capacity Determination Based on a Generalized Least-Cost Model of Traffic Distribution

Abstract

With the popularization of electric vehicles and the continuous expansion of the electric vehicle market, the construction and management of charging facilities for electric vehicles have become important issues in research and practice. In some remote areas, the charging stations are idle due to low traffic flow, resulting in a waste of resources. Areas with high traffic flow may have fewer charging stations, resulting in long queues and road congestion. The purpose of this study is to optimize the location of charging stations and the number of charging piles in the stations based on the distribution of traffic flow, and to construct a bi-level programming model by analyzing the distribution of traffic flow. The upper-level planning model is the user-balanced flow allocation model, which is solved to obtain the optimal traffic flow allocation of the road network, and the output of the upper-level planning model is used as the input of the lower-layer model. The lower-level planning model is a generalized minimum cost model with driving time, charging waiting time, charging time, and the cost of electricity consumed to reach the destination of the trip as objective functions. In this study, an empirical simulation is conducted on the road network of Hefei City, Anhui Province, utilizing three algorithms—GA, GWO, and PSO—for optimization and sensitivity analysis. The optimized results are compared with the existing charging station deployment scheme in the road network to demonstrate the effectiveness of the proposed methodology.

1. Introduction

With the rapid growth of the number of fuel vehicles, the environmental problems caused by the combustion of fossil fuels are becoming increasingly serious. The transportation industry, as the world’s second-largest source of carbon emissions, has a significant impact on the environment. The electrification of transportation is considered an effective measure to achieve energy conservation and emission reduction [1]. As the energy supply for electric vehicles (EVs), the location and capacity determination of public charging stations (CSs) are of great significance [2]. Reasonable site planning for electric vehicle charging stations (EVCSs) is beneficial for improving the utilization rate of charging facilities and investment returns.

In recent years, the establishment of models for site selection optimization problems has shown diversified development. Among them, the single-layer static model laid the foundation first. By integrating the objective function and constraints at the same level, this model greatly reduces the computational complexity and can quickly generate interpretable site selection schemes [3,4]. On the other hand, the model has low data requirements and can easily expand grid constraints or space constraints, which is especially suitable for large-scale scenarios with clear demand distribution and rapid decision-making, providing efficient support for urban planning [5,6,7]. For example, He et al. [8] constructed the first population-vehicle-coupled demand forecasting model by analyzing the spatiotemporal characteristics of the plug-in hybrid electric vehicle (PHEV) travel chain. As the complexity of the problem escalates, the dual-level planning framework has gradually become a key tool for solving the dynamic game from system planners to user groups. The bi-level programming model explicitly divides decision-making into upper and lower levels, where the upper level decision is the input parameter for the lower-level problem and the lower-level decision is the input for the upper-level objective function. This accurately simulates the decision-making sequence and dependency relationships in reality [9]. In practice, Yang et al. [10] further coupled the transportation network and distribution network, introducing dynamic electricity price decision variables in the upper level to reveal the relationship between demand price elasticity and system revenue. In order to avoid the distortion of the essence of single-layer models and the problem of high model complexity, it is necessary to establish effective models for the hierarchical decision-making structures that exist in reality and improve the robustness of the models. Therefore, we choose the bi-level programming model as the method to solve this problem.

There is a closely interdependent and mutually shaping symbiotic relationship between the solving algorithm and the bi-level programming model. The complex structure of the bi-level programming model poses a serious challenge to algorithm design. Some heuristic algorithms that simulate natural systems, such as genetic algorithms and simulated annealing algorithms, solve the NP-Hard problem by combining randomness with directed search [11,12,13]. However, such algorithms perform poorly in high-dimensional, dynamic, and real-time scenarios. On the contrary, swarm intelligence optimization algorithms replace individual evolution with distributed collaboration, which has a significant effect on solving such complex models [14]. For example, Cui et al. [15] proposed adaptive mutation PSO, which solves the problem of high-dimensional decision space oscillation by dynamically adjusting inertia weights and the random Gaussian mutation mechanism. To break through the trap of local optima, PSO hybrid frameworks have rapidly developed [16,17]. In practice, Amirteimoori et al. [18] integrated the PSO-GA dual population strategy to significantly improve robustness under demand random fluctuations. However, PSO faces problems such as dimensionality disaster and delayed response to dynamic spatiotemporal demands in ultra-large-scale networks. In response to this issue, the Grey Wolf Optimization (GWO) algorithm retains suboptimal solution information through the collaboration of three levels of leadership, fundamentally avoiding these risks and thus becoming the preferred algorithm for this study [19].

This article first studies the mathematical properties of the location selection problem for charging stations, and a bi-level programming model is constructed by analyzing the distribution of traffic flow. The upper-level planning model is a user equilibrium flow allocation model, while the lower-level planning model is a generalized minimum cost model with driving time, charging waiting time, charging time, and the electricity cost consumed to reach the destination as objective functions. The road network in Hefei, Anhui Province, is selected as a case study. The condition of the city’s power grid load is not considered for the time being, and then the model is calculated through GA, GWO, and PSO, while comparing the existing charging stations in the original road network for analysis. The results show that the model proposed in this article can improve the utilization rate of charging stations and the investment return of charging piles. A flowchart of the study is shown in Figure 1.

2. Methods

2.1. Problem Statement

Under the strong promotion of government policies, the number of electric vehicle users is growing rapidly, and the demand for charging facilities is also increasing. Although the number of charging stations has begun to take shape, but compared to the huge number of new energy vehicles, the existing charging infrastructure still lags far behind market demand. In addition, the lack of actual usage data and traffic distribution related data of electric vehicles in the initial stage of charging infrastructure construction. This has led to an unreasonable distribution of some electric vehicle charging stations, and the number of charging piles does not match the actual charging demand, resulting in idle charging stations in some remote areas and causing a waste of resources. The unreasonable distribution of charging piles and low charging efficiency have become a huge challenge for the industry. Figure 2 illustrates the problem in hot areas due to the small number of charging posts.

2.2. Model Building

The transportation network is represented by $G=(N,A)$, The mathematical symbols involved in the model are shown in Appendix A.

2.2.1. Upper-Level Planning Model

The traffic management department mainly considers macro-level issues such as the operational efficiency of the entire urban transportation system and traffic congestion. Therefore, the bi-level programming model mainly establishes the objective function based on the traffic efficiency of the entire road network. In order to maximize the traffic efficiency of the road network, the objective function can be set to minimize the travel time of electric vehicles in the entire road network; that is, the objective function is

$$\min Z={\displaystyle \sum _{a\in A}{\displaystyle {\int }_0^{x_a}{t}_a\left(w\right)}}dw$$

(1)

where $t_a\left(x\right)$ can be expressed using the formula of the Bureau of Public Roads (BPR) in the United States:

$$t_a=t_a^0\left[1+0.15{\left({\displaystyle \frac{x_a}{L_a}}\right)}^4\right]$$

(2)

Constraints:

$$s.t.\left\{\begin{array}{l}{q}^{rs}={\displaystyle \sum _{k\in K_{rs}}{f}_k^{rs}}\\ x_a={\displaystyle \sum _{r\in R}{\displaystyle \sum _{s\in S}{\displaystyle \sum _{k\in K_{rs}}{f}_k^{rs}{\delta }_{ak}^{rs}}}}\\ f_k^{rs}\ge 0,\forall r,s,k\\ x_a\ge 0,a\in A\end{array}\right.$$

(3)

where $q^{rs}={\displaystyle \sum _{k\in K_{rs}}{f}_k^{rs}}$ represents the conservation relationship between path flow and OD demand, $x_a={\displaystyle \sum _{r\in R}{\displaystyle \sum _{s\in S}{\displaystyle \sum _{k\in K_{rs}}{f}_k^{rs}{\delta }_{ak}^{rs}}}}$ constrains the relationship between path flow and road segment flow, and $f_k^{rs}\ge 0,\forall r,s,k$ and $x_a\ge 0,a\in A$ restricts the non-negativity of path flow and road segment flow.

2.2.2. Lower-Layer Planning Model

The lower-layer planning model is chosen to construct a generalized minimum cost model from the personal perspective of electric vehicle users. Its goal is to minimize the cost of user travel.

The generalized minimum travel cost from the perspective of electric vehicle users includes driving time, charging waiting time, charging time, and the electricity cost consumed to reach the destination. The objective function is

$$\min N={\displaystyle \sum _{a\in A}\left[\left(t_a+\left(T_c+W_{qj}\right)\cdot {\psi }_j\cdot {\phi }_j\right)\cdot U+P_E{t}_a\cdot \eta \right]}$$

(4)

Based on existing literature research, lower-level planning is approached from the user’s perspective. When an electric vehicle travels at a constant speed, its energy consumption is the lowest, corresponding to the lowest electricity cost. When an electric vehicle is moving at a constant speed on a flat road, it travels at a constant speed on a level road. The two forces acting in the horizontal direction, namely, the traction force and the friction force, are balanced with each other; that is, the traction force is equal to the friction force. When the traction force remains constant, the power of the engine and the work carried out by the electric vehicle at the destination can be calculated based on the driving speed of the electric vehicle. The constraint conditions are as follows.

① User arrival rate

Due to insufficient charging station resources and long charging times for individual vehicles, electric vehicles may face queuing problems when arriving at charging stations, directly affecting service efficiency. Therefore, when establishing a charging station location model, it is advisable to avoid excessively long queuing times as much as possible. Assuming there is a charging station on section $a$, and there are $y$ independent paths from starting point $O$ to point $j$, and each path consists of g sections connected in series, the arrival probability calculation rule is as follows:

$${\lambda }_j=\left\{\begin{array}{l}{\displaystyle \frac{d_1\cdot \mathrm{H}}{C_0}}\cdot x_1,g=1\\ \left[{\displaystyle \sum _{i=1}^y\begin{array}{l}{\displaystyle \prod _{j=1}^g\frac{d_g\cdot \mathrm{H}}{C_0}}+\left(1-\frac{d_1\cdot \mathrm{H}}{C_0}\right)\cdot \left(\frac{d_1\cdot \mathrm{H}}{C_0}+\frac{d_2\cdot \mathrm{H}}{C_0}\right)+\dots \\ +\left(1-\frac{d_1\cdot \mathrm{H}}{C_0}\right)\cdot \left(\frac{d_1\cdot \mathrm{H}}{C_0}+\frac{d_2\cdot \mathrm{H}}{C_0}+\dots +\frac{d_g}{C_0}\right)\cdot x_g\end{array}}\right],g\ge 2\end{array}\right.$$

(5)

In the queuing system formed by electric vehicles arriving at charging stations for charging, the pattern of electric vehicles arriving at charging stations can be represented by the Poisson distribution, generally following the principle of first come, first served. The queuing rule is a multi-service desk waiting system; service providers generally provide serial services. In summary, the electric vehicle charging queue system can be seen as a limited service desk queue system, namely, system $M/M/b/K$. Among them, $b$ is the number of charging stations within the charging station (due to the constraint of charging station definition, each station requires at least three charging devices). $K$ indicates the maximum car capacity that the charging station space can accept. When the number of cars reaches $K$, the system will shut down and vehicles that need to be charged will directly move to the next charging station. Therefore, if there is a true customer arrival rate ${\lambda }_{ej}$ that is less than ${\lambda }_j$, the effective arrival rate is

$${\lambda }_{ej}={\lambda }_j\left(1-P_K\right)$$

(6)

② The average service capacity of charging stations per unit time

$${\mu }_j=\left\{\begin{array}{l}{\displaystyle \frac{n}{t_f}},0\le n<b_j\\ {\displaystyle \frac{b_j}{t_f}},b_j\le n<K\end{array}\right.$$

(7)

③ Service intensity of charging station queuing system

$$\begin{array}{l}{\rho }_j={\displaystyle \frac{{\lambda }_j}{{\mu }_j}}\\ {\rho }_{b_j}={\displaystyle \frac{{\lambda }_j}{b{\mu }_j}}\end{array}$$

(8)

④ The probability of all charging stations in the charging station being idle

$$p_{j0}=\left\{\begin{array}{l}{\left[{\displaystyle \sum _{n=0}^{b_j-1}\frac{{\rho }_j^n}{n!}+\frac{{\rho }^{b_j}\left(1-{\rho }_{b_j}^{N-b_j+1}\right)}{b_j!\left(1-{\rho }_{b_j}\right)}}\right]}^{-1},{\rho }_{b_j}\ne 1\\ {\left[{\displaystyle \sum _{n=0}^{b_j-1}\frac{{\rho }_j^n}{n!}+\frac{{\rho }^{b_j}\left(K-b_j+1\right)}{b_j!}}\right]}^{-1},{\rho }_{b_j}=1\end{array}\right.$$

(9)

In the formula, ${\rho }_{j0}$ represents the probability that the charging station at point $j$ is idle.

⑤ Probability distribution of $n$ customers in the system

$$p_n=\left\{\begin{array}{l}{\displaystyle \frac{{\rho }^n}{n!}}{p}_0,0\le n<b_j\\ {\displaystyle \frac{{\rho }^n}{b_j!b^{n-b_j}}}{p}_0,b_j\le n\le K\end{array}\right.$$

(10)

⑥ Average platoon leader

$p_n$ is the probability distribution of the system after reaching a steady state. From a stationary distribution $p_n$, $n=0,1,2,....,K$, the average queue length of cars waiting at the gas station is

$$l_q={\displaystyle \sum _{n=b_j}^K\left(n-b_j\right)}{p}_n=\left\{\begin{array}{l}{\displaystyle \frac{p_0{\rho }^{b_j}{\rho }_{b_j}}{b_j!{\left(1-{\rho }_{b_j}\right)}^2}}\left[1-{\rho }_{b_j}^{K-b_j+1}-\left(1-{\rho }_{b_j}\right)\left(K-b_j+1\right){\rho }_{b_j}^{K-b_j}\right],{\rho }_{b_j}\ne 1\\ {\displaystyle \frac{p_0{\rho }^{b_j}\left(K-b_j\right)\left(K-b_j+1\right)}{2b!}},{\rho }_{b_j}=1\end{array}\right.$$

(11)

⑦ Queue waiting time

$$W_{qj}={\displaystyle \frac{l_q}{{\lambda }_{ej}}}$$

(12)

To avoid long queues, assuming $W_{q\max }$ is the maximum acceptable waiting time for travelers while charging at the charging station, the system queue time constraint ${\phi }_j{W}_{qj}\le W_{q\max }$ is obtained.

⑧ Charging waiting time

$$T_c={\displaystyle \frac{C_0-C_j}{P}}$$

(13)

⑨ Number of charging stations

The sum of the number of charging stations at each point should not exceed the number of charging stations provided by the government or enterprises.

$${\displaystyle \sum _{r\in R}{\displaystyle \sum _{s\in S}{b}_j}}\le B$$

(14)

⑩ The speed of electric vehicles

The speed of electric vehicles on the road cannot exceed the maximum speed limit, and the formula is

$$v_a\le v_{\max }$$

(15)

3. Algorithm Introduction

This study constructs a bi-level planning model, with the upper-level planning model being the classic user-balanced traffic model. Following Wardrop’s first principle [20], which states that in a state of user equilibrium, all paths used have equal and minimum travel time, the travel time for unused routes is greater than or equal to the minimum travel time. The upper-level planning of this article is solved using the built-in solver of MATLAB R2021asoftware. The lower-level planning model is a generalized minimum cost model, whose objective function and constraints constitute a mixed integer nonlinear programming problem. Due to the high complexity of the problem, this article focuses on using the Grey Wolf Optimizer (GWO) algorithm for solving, and compares its optimization performance with GA and PSO. The GWO algorithm simulates the social hierarchy and hunting behavior of grey wolf populations, and has the characteristics of fast convergence speed and strong global search ability. The optimization process of the GWO is shown in Figure 3.

4. Case Study

4.1. Example Road Network

This article takes the city of Hefei in Anhui Province as an example, with a jurisdiction area of 1339 square kilometers. As of the end of June 2024, the number of electric vehicles has reached 295,600, and it is expected that the number of electric vehicles will exceed 500,000 by the end of 2025. According to statistics from June 2024, a total of 210,000 charging infrastructure facilities have been built in the city, of which only 23,000 are public charging facilities. By categorizing and calculating the requirements for charging infrastructure in electric vehicles, it is expected that a total of 22,000 new charging facilities will be added by the end of 2025.

The government department plans to develop a resort here, so new charging facilities need to be added. As shown in Figure 4, by analyzing the main road network structure of the selected area, it can be seen that the road intersections mainly form a quadrilateral grid. Therefore, the field grid can serve as the basic unit of road network composition, and the entire road network can be abstracted as a combination of multiple field grids. Given the high complexity of the actual road network and the complexity of data acquisition, this paper describes the study and design of a simplified road network model based on the grid structure for simulation.

To study the layout scheme of urban charging stations and traveler behavior, simulation experiments were conducted using a nine-node simplified road network, as shown in Figure 5. The road network includes a pair of starting points (O, D). Charging stations are located at nodes A, B, C, D, E, F, and G, with a site selection status of 0–1 decision variables. The number of charging stations at each station must meet the capacity constraints of [3,10].

There are six paths in this road network:

Path 1: L1—L2—L9—L12	Path 2: L1—L8—L4—L12
Path 3: L1—L8—L11—L6	Path 4: L7—L3—L4—L12
Path 5: L7—L3—L11—L6	Path 6: L7—L10—L5—L6

4.2. Parameter Settings

This article investigates the selected time periods for parameter survey, which are Friday evening from 5:00 pm to 6:00 pm, Saturday morning from 10:00 am to 11:00 am, and Monday morning from 07:30 am to 8:30 am. The traffic volume of the road network during peak and off peak periods is surveyed and studied simultaneously, with 30 min groups. The original traffic volume survey data are calculated using equivalent conversion to determine peak hours, and the 30 min equivalent traffic volume conversion result of the highest peak hour is used as the peak hour traffic volume of the road section to be evaluated. Combined with the traffic equivalent conversion calculation, the daily traffic flow of this road network is relatively constant, and the overall traffic volume fluctuates slightly. The EV-equivalent traffic conversion table is shown in

Table 1. EV-equivalent traffic conversion.

Vehicle Classification	Urban Roads
Electric Vehicles	1.0
Passenger Cars	1.0
Medium/Large Buses	2.0
Light Trucks	1.0
Heavy/Medium Trucks	2.0
Tricycles	0.6
Motorcycles	0.4
Bicycles	0.2
E-bikes	0.3
Other Motor Vehicles	1.0
Other Non-motorized Vehicles	2.0

. The specific parameters are shown in

Table 2. Road network-related parameters.

Road	${\mathit{L}}_{\mathit{a}}$	${\mathit{T}}_{\mathit{a}}^0$	${\mathit{d}}_{\mathit{a}}$	Road	${\mathit{L}}_{\mathit{a}}$	${\mathit{T}}_{\mathit{a}}^0$	${\mathit{d}}_{\mathit{a}}$
1	380	9	1.9	7	200	7	1
2	480	12	2.4	8	140	7	1
3	510	9	1.9	9	120	6	0.9
4	640	12	2.4	10	280	10	1.4
5	380	10	1.9	11	190	10	1.4
6	440	12	2.2	12	190	10	1.4

and

Table 3. Model parameters.

Parameter	Meaning	Value	Parameter	Significance	Value
$c_0$	The amount of electricity when fully charged	50	$X$	Total traffic of vehicles on the road network	2358
$p$	Charging efficiency of charging stations	60	$\eta$	Price per kilowatt hour per unit of electricity	1
$B$	Total number of charging stations	20	$U$	Per capita hourly wage	13.7
$m$	Quality of electric vehicles	1700	$w_{q\max }$	The maximum acceptable waiting time for customers	10
$v_{\max }$	Maximum speed limit on the road	60	$\mu$	Road rolling friction force	0.016
$H$	Average power consumption per kilometer	0.2

Residential: The reference for the parameters of electric vehicles is the commonly seen BYD Qin in the current market.

.

4.3. Result Analysis

This study constructs an example based on actual road network data and systematically compares the solving performance of the genetic algorithm (GA), Grey Wolf Optimization algorithm (GWO), and particle swarm optimization algorithm (PSO). Through multiple independent experimental observations, it was found that the GWO algorithm exhibits significant advantages in the convergence speed dimension, with the lowest average iteration times, indicating its efficient spatial search capability. The PSO algorithm performs the best in terms of solution quality stability. Overall, the fast convergence of the GWO is suitable for time-sensitive road networks, while the strong robustness of PSO is more suitable for road networks with higher stability requirements. The comparative analysis results of generalized minimum cost iteration for different algorithms are shown in Figure 6 and Figure 7. The comparison between the generalized minimum cost solved by three algorithms and the generalized minimum cost of user travel under actual road network conditions is shown in

Table 4. Comparison between actual and algorithmic results.

Comparison Between Actual and Algorithm	GWO	GA	PSO	Actual User Travel Situation
Generalized minimum cost	155,711,793.43	156,266,892.20	156,011,872.56	1,896,387,349.53

.

This study systematically quantified the performance differences of three algorithms in generalized system cost control. More importantly, through spatial distribution modeling and capacity configuration analysis, the key impact of algorithm selection on the layout of charging facilities has been revealed. The main conclusions include three points. Firstly, the distribution of charging stations shows significant spatial heterogeneity. Secondly, there is a fluctuation range of 10–20% in the rated capacity configuration scheme of charging piles at key nodes. Finally, the GWO algorithm achieved a Pareto front solution for charging demand coverage and device utilization under cost constraints. The location selection of charging stations and the fixed capacity of charging piles for the three algorithms are shown in Figure 8. The optimal layout of charging stations and charging piles with fixed capacity based on the actual road network and algorithm is shown in Figure 9.

4.4. Sensitivity Analysis

To evaluate the structural robustness of the generalized minimum cost model and identify key sensitivity parameters, this study designs a univariate perturbation test. The proportion of electric vehicle traffic in the total traffic flow is taken as the core control variable, and the remaining parameters are fixed. Systematic deviations are applied in the range of [−60%,+60%] with a step size of ±20%. The model is run after each disturbance and the second-order response output is recorded. One is the generalized minimum cost dynamics, and the other is the spatial distribution variation in the charging station location decisions. By observing the fluctuation pattern of the output value with the disturbance of the proportion of electric vehicles in the total traffic flow, accurately analyzing the impact strength and critical failure threshold of the input parameter on the planning scheme, and providing uncertainty resistance basis for core decision-making, the final result is the floating situation shown in Figure 10 and Figure 11.

By conducting a sensitivity analysis on the proportion of electric vehicle traffic flow in the total traffic flow using the generalized minimum total cost model, the dual impact of traffic volume changes on algorithm performance and charging network planning decisions was revealed. Firstly, in terms of computational efficiency, as the proportion of electric vehicle traffic in the total traffic gradually decreases, the decrease in traffic significantly improves the convergence speed of the three algorithms, manifested as a systematic reduction in the number of iterations required to reach the termination condition. Secondly, when the proportion of traffic flow decreases to about 60%, the objective function values obtained by the GA and PSO tend to be consistent. This indicates that in low traffic load scenarios, the model structure may be simplified, significantly improving the accuracy and stability of these two types of algorithms, enabling them to approach the global optimal solution more reliably.

On the other hand, at the level of charging infrastructure planning, analysis has found that its strategy exhibits significant traffic dependence and key node stability. Under the condition that the proportion of electric vehicle traffic in the total traffic flow reaches 80%, the optimal location of charging stations and the configuration of charging pile capacity show robustness and are not affected by traffic volume fluctuations. When the proportion of electric vehicle traffic in the total traffic flow reaches 60%, the economic efficiency is weakened due to the level of traffic flow and the characteristics of driving distance, which triggers spatial decision restructuring. Location B has been excluded from the site construction plan and replaced by location E, which has higher demand potential, reflecting the sensitivity of planning to the spatial distribution of demand. When the proportion of electric vehicle traffic in the total traffic reaches 40%, the probability of user charging behavior significantly decreases in some areas, resulting in a concentration of network planning towards a few core nodes exhibiting network shrinkage characteristics.

It is particularly crucial that, regardless of how the traffic flow on the road network changes within the range of 20%–100%, location D is always identified as an indispensable core hub for the entire charging network. Not only is the site selection decision constant, but the number of charging stations configured is always significantly higher than all other sites. This highlights its key anchor role in network topology and meeting user needs, providing a crucial basis for planning high-resilience charging networks.

5. Conclusions

This paper systematically addresses the problem of coordinated optimization for electric vehicle charging station siting and capacity determination using a bi-level programming model. At the theoretical level, we innovatively construct an upper-level user equilibrium traffic flow distribution model and a lower-level generalized minimum cost model. The upper-level model aims to minimize total road network travel time. The traffic flow allocation of the electric vehicle is solved as an input to the underlying model. The lower-level model minimizes the generalized cost—integrating driving time, charging waiting time, charging duration, and electricity expenses. The location and capacity of the electric vehicle charging station are obtained by solving. Global optimization is achieved through bidirectional iteration between traffic flow distribution and user cost optimization.

In the empirical application phase, using the road network of a holiday resort in Hefei as a case study and employing GA, GWO, and PSO algorithms, the optimized solution demonstrates a 91.8% reduction in generalized travel cost, a 37% decrease in charging pile idle rate, and a reduction in average user waiting time to 7.2 min, significantly outperforming the current layout.

During sensitivity testing, we changed traffic flow by ±60%. When traffic flow stayed above 80%, all charging stations remained the same. When traffic flow was near 60%, station B replaced station E to save money. When traffic flow dropped to 40%, station G replaced station F, making the network smaller. But central station D always kept 7 to 10 charging piles in every situation.

The study demonstrates that this model provides urban EV charging infrastructure planning with an efficient and robust decision-making tool. In the future, the conditions of power grid load will be fully considered, the power grid load balancing model and user behavior preference model will be integrated, and interdisciplinary research on the synergy of “transportation–energy–behavior” will be deepened so as to promote the evolution of charging networks from single-point optimization to systemic resilience.