Capacity Expansion Strategy for EV Charging Stations Considering Cellular Traffic Simulation and User Satisfaction

Abstract

The spatial layout of urban electric vehicle (EV) charging stations affects both user charging experience and regional traffic flow. To meet the demand for shorter charging waiting time amid the rapid growth of EV ownership, this paper proposes a charging station expansion strategy integrating cellular traffic simulation and user satisfaction. First, the Cell Transmission Model (CTM) is used to simulate real-time traffic flow based on regional road network data, and an energy consumption model is combined to predict the spatiotemporal distribution of charging loads. Second, a bi-level optimization model is developed for station expansion: the upper layer minimizes comprehensive post-expansion cost, while the lower layer maximizes user satisfaction by optimizing vehicle admission strategies. The bi-level problem is solved iteratively by combining a heuristic algorithm with mixed-integer linear programming. A case study in an urban area of Hunan Province shows that the proposed strategy improves regional charging capacity and user satisfaction, with the average road operating speed increasing by 4.21 km/h after expansion.

1. Introduction

Developing new energy vehicles has become a strategic measure for China to address climate change and promote green development. However, the rapid adoption of electric vehicles (EVs) has introduced large-scale stochastic electricity demand, posing significant challenges to the safe and stable operation of power grids [1,2]. Simultaneously, EVs also participate in the dynamic evolution of transportation networks as mobile traffic entities. This dual role makes rational charging station expansion critical for improving users’ charging accessibility and alleviating traffic congestion. Formulating such expansion schemes requires accurate characterization of the spatiotemporal distribution of EV charging loads and a comprehensive optimization model that considers distribution network capacity and operational cost [3].

Traditionally, short-term charging load forecasting has relied on combining travel chain principles with Monte Carlo simulations [4]. To overcome the limitations of these early probability-based methods, recent studies have integrated external environmental and traffic factors to improve accuracy. For instance, variables such as time, weather, and traffic delay factors have been coupled with machine learning and spatiotemporal graph convolutional networks to enhance nodal load predictions [5,6,7]. To better capture the spatial distribution of EV charging demand and traffic-related factors, recent studies have incorporated GIS-based traffic information, semi-dynamic traffic network models, and real-time speed-flow interactions into charging demand forecasting [8,9,10]. In addition, dynamic traffic assignment, mesoscopic traffic simulation, agent-based models, and SUMO-based microscopic traffic simulation have been applied to charging infrastructure planning and traffic impact analysis [11,12,13]. Although these studies have advanced the modelling of charging demand and traffic-network interactions, they mainly focus on new station siting, charging demand estimation, traffic disturbance assessment, or joint electricity-transportation network planning. Few studies have addressed the capacity expansion of existing charging stations while integrating real-time traffic flow evolution, charging load forecasting, user satisfaction, and vehicle admission strategies into a unified optimization framework.

Regarding charging station configuration, research has evolved from single-objective cost minimization to comprehensive planning that considers both economic viability and user behavior. Bi-level optimization models and multi-objective frameworks have been widely adopted to balance charging station operating costs with user economic losses, travel distance, and urgency of demand [14,15,16,17,18]. Nevertheless, these models often oversimplify the impact of regional traffic flow. Even when speed-flow relationships or Yen’s algorithm are introduced to calculate travel time [19,20], they still ignore the microscopic behaviors of vehicles (e.g., lane-changing, acceleration) within the traffic stream. Furthermore, while extensive research focuses on the initial sizing and siting of charging stations, there is a notable scarcity of studies addressing the secondary capacity expansion planning for existing, overloaded facilities. Table A1 of Appendix A compares existing traffic-aware EV charging station planning studies with the proposed method.

This paper focuses on the capacity expansion problem of existing EV charging stations under the coupled operation of urban traffic networks and charging service systems. Starting from the dynamic evolution of regional traffic flow and users’ charging accessibility, an EV charging station expansion planning strategy integrating cellular traffic simulation and user satisfaction is proposed. First, a spatiotemporal charging load forecasting model is established by combining the CTM with travel chain theory. By representing traffic flow evolution at the cell level, the CTM provides a physical basis for linking road traffic conditions with EV energy consumption, thereby improving the characterization of regional charging demand. Second, a bi-level optimization model for charging station expansion is formulated. The upper-level model minimizes charging station operating cost to determine the number of charging piles, while the lower-level model maximizes user satisfaction by optimizing the vehicle admission strategy. The bi-level problem is solved using a nested approach that combines a genetic algorithm (GA) with mixed-integer linear programming (MILP). Finally, a case study of charging station expansion in an urban area of Hunan Province is conducted to verify the feasibility and effectiveness of the proposed strategy.

2. Spatiotemporal Forecasting of Charging Load Considering Road Network Traffic Flow

The spatiotemporal distribution of EV charging loads is highly influenced by the uncertainties of road network traffic conditions. Since this distribution serves as the demand foundation for capacity expansion planning, improving the accuracy of spatiotemporal charging load forecasting by incorporating road network traffic status is a prerequisite for formulating a reasonable expansion plan. To this end, real-time simulation of traffic flow in the road network is conducted based on travel chain principles and the CTM to enhance prediction accuracy.

2.1. Road Network Traffic Flow Simulation

2.1.1. Road Topology Modeling

Based on graph theory and the principles of macroscopic transportation planning, this paper introduces the Traffic Analysis Zone (TAZ) partitioning method to perform dimensionality reduction modeling of complex urban traffic networks [21]. First, the regional map is partitioned according to land-use attributes to extract typical urban functional zones, including residential, office, commercial, industrial, and leisure areas. Second, the aggregation points of traffic flow and electrical load within each functional zone are extracted as virtual centroids (nodes) of the road network. Urban arterial roads carrying cross-district traffic are mapped as connecting corridors (edges), which are subsequently converted into a backbone road network topology consisting of nodes and edges. Meanwhile, traffic flow parameters for each road, such as equivalent length, number of lanes, and signal timings, are statistically recorded. Finally, the power distribution network is mapped onto the road network topology based on geographic information relationships, with charging stations marked as the intersection points between the transportation and distribution networks. This process results in a coupled road-power distribution network topology map, as shown in Figure 1.

Figure 1. Joint topology diagram of road network and distribution network.

2.1.2. Travel Chain Theory

The nodes traversed by a vehicle during a complete trip are categorized according to their respective functional zones. The resulting sequence, termed the functional zone chain, is defined as the vehicle’s travel chain, which characterizes its spatiotemporal travel features. A complete complex travel chain comprises more than two destination functional zones, as illustrated in Figure 2. This travel chain indicates that the vehicle stays in a residential area during the t₀-t₁ interval, moves from the residential area to an office area during t₁-t₂, remains in the office area during t₂-t₃, travels from the office area to a commercial area during t₃-t₄, stays in the commercial area during t₄-t₅, and returns from the commercial area to the residential area during t₅-t₆. The travel chain represents the origin and destination (OD) of the vehicle during its journey. By utilizing the Floyd algorithm for path decision-making, the specific travel routes of vehicles within the road network can be obtained [22].

Figure 2. Spatiotemporal characteristics of complex travel chains.

2.1.3. Cell Transmission Model

Considering the large variability, uncertainty, and nonlinearity of traffic flow in urban road networks, the CTM is adopted to simulate short-term traffic evolution in the charging demand forecasting model, thereby improving its adaptability and prediction accuracy. CTM is generally regarded as a macroscopic traffic flow model. It discretizes roads into consecutive cells and describes flow propagation between adjacent cells based on traffic flow conservation. In this paper, CTM is used to characterize aggregate traffic states, including road-segment speed, density, and flow. The advancing and lane-changing rules are only used to update cell occupancy states and calculate traffic flow indicators, and do not change the macroscopic nature of CTM. The complete urban road network traffic simulation model consists of interconnected CTMs corresponding to individual roads [23]. The parameters of each CTM are determined by actual road network parameters, while the number of vehicles generated at the origin of each CTM is determined by vehicle travel paths.

For a single road segment, the cell transmission system is shown in Figure 3. Each unit cell has the same length, and its value is either 0 or 1, indicating whether it is occupied by a vehicle at the current time step. Traffic flow conservation is satisfied between adjacent cells, and inter-cell flow is determined by adjacent cell occupancy, road capacity, and cell state update rules. To describe congestion propagation and changes in road operating conditions, the update rules are divided into advancing transfer and lane-changing transfer. The number of vehicles in each cell satisfies Equation (1)

$$\left\{\begin{array}{l}{n}_{i,j}(t)=n_{i,j}(t-1)+y_{i,j}(t)-y_{i,j+1}(t)\\ y_{i,j}(t)=y_{i,j}^{\prime }(t)+y_{i,j}^{″}(t)\end{array}\right.$$

(1)

where n_i,j(t) is the number of vehicles in the cell at row i and column j at time t; y_i,j(t) is the cell traffic flow at row i and column j at time t; y′_i,j(t) and y″_i,j(t) are the cell traffic flows resulting from advancing and lane-changing behaviors, respectively. The specific descriptions of vehicle behaviors are as follows:

Figure 3. Cell transmission model single road diagram.

• Advancing Behavior

Advancing transfer is used to describe the update of vehicle occupancy states between adjacent cells. Whether a vehicle can move forward is determined by the available space in the downstream adjacent cell, thereby forming traffic flow between adjacent cells. The cell traffic flow corresponding to advancing transfer is calculated using Equation (2).

$${y^{\prime }}_{i,j}(t)=\left\{\begin{array}{l}\hspace{1em}{n}_{i,j}(t-1)=n_{i,j-1}(t-1)=0, \\ \hspace{1em}{n}_{i,j-2}(t-1)=1\\ 1,\mathrm{if}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{or}\\ \hspace{1em}{n}_{i,j+1}(t-1)=n_{i,j-1}(t-1)=1, \\ \hspace{1em}{n}_{i,j}(t-1)=0\\ 0, \mathrm{else}\end{array}\right.$$

(2)

The equivalent travel speed of vehicles in a cell is defined by Equation (3).

$$v_{i,j}(t)=\left\{\begin{array}{l}{\displaystyle \frac{2\cdot L_n}{1000\cdot dt}}, \mathrm{if} n_{i,j+1}(t)=n_{i,j+2}(t)=0\\ {\displaystyle \frac{L_n}{1000\cdot dt}}, \mathrm{if} n_{i,j+1}(t)=0,n_{i,j+2}(t)=1\\ 0,\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{else}\end{array}\right.$$

(3)

where v_i,j(t) is the equivalent travel speed of vehicles in the cell at row i and column j, L_n is the length of the vehicle in the cell, and dt is the simulation step of the CTM.

• Lane-changing Behavior

When congestion occurs on a single road, vehicles within the cells will determine whether there is space in adjacent lanes and execute lane-changing behavior, as shown in Figure 4. The calculation model for traffic flow during lane-changing behavior is given by Equation (4).

$${y^{″}}_{i,j}(t)=\left\{\begin{array}{l}\hspace{1em}{n}_{i,j-1}(t-1)=n_{i,j}(t-1)=n_{i,j+1}(t-1)=0, \\ \hspace{1em}{n}_{i+1,j}(t-1)=n_{i+1,j-2}(t-1)=1\\ 1,\mathrm{if}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} \mathrm{or}\\ \hspace{1em}{n}_{i,j-1}(t-1)=n_{i,j}(t-1)=n_{i,j+1}(t-1)=1, \\ \hspace{1em}{n}_{i-1,j}(t-1)=n_{i-1,j-2}(t-1)=0\\ 0, \mathrm{else}\end{array}\right.$$

(4)

Figure 4. Channel change behavior diagram of cell transmission model.

In summary, after establishing the CTMs for all roads, setting the simulation duration to dT yields the simulated traffic flow conditions for each individual road in the road network over a dT duration. Traffic flow conditions are described using the number of lane changes, travel speed, and traffic density, with the calculation methods shown in Equations (5)–(7).

$$v={\displaystyle \frac{{\displaystyle \sum _{t=1}^{dT}\frac{{\displaystyle \sum _{i,j\in N}{v}_{i,j}(t)}}{N_t}}}{dT}}$$

(5)

$$\rho ={\displaystyle \frac{{\displaystyle \sum _{t=1}^{dT}\frac{N_t}{N}}}{dT}}$$

(6)

$$p={\displaystyle \sum _{t=1}^{dT}{\displaystyle \sum _{i=1}^n{y^{\prime }}_{i,j}(t)}}$$

(7)

where v, ρ, p are the travel speed, traffic density, and lane-change frequency of the road segment within the duration dT, respectively; v_i,j(t) is the travel speed of each vehicle at time t; N_t is the number of cells with a status of 1 at time t; and N is the total number of cells in the model.

2.2. Model for Predicting the Spatio-Temporal Distribution of Charging Load

The State of Charge (SOC) of an electric vehicle significantly influences the charging and travel decisions of EV users. When the electrical energy consumed during travel causes the SOC to drop to the user’s minimum expected SOC, a charging demand is generated. Consequently, the spatiotemporal forecasting of charging load requires calculating the energy consumption of each EV during its trip to determine real-time SOC levels. By integrating this information with the vehicle’s spatiotemporal position, the spatiotemporal distribution of the charging load can be derived.

2.2.1. EV Energy Consumption Model

EV energy consumption is influenced by factors such as the actual travel mileage, road conditions, and user driving habits [24,25]. To address this, an EV energy consumption model considering environmental factors is constructed, as specifically shown in Equation (8).

$$\Delta E={\displaystyle \sum _{i=1}^m({\lambda }_l{l}_i+{\lambda }_v{v}_i+{\lambda }_{\rho }{\rho }_i+{\lambda }_p{p}_i)}$$

(8)

where l_i, v_i, ρ_i, and p_i are the length, travel speed, traffic density, and lane-change frequency of the ith road segment in the EV’s trip; λ_i is the energy consumption coefficient per kilometer; λ_v is the energy consumption coefficient converted from travel speed; λ_ρ is the energy loss coefficient caused by frequent motor start-stops and speed changes due to traffic congestion; and λ_p is the energy loss coefficient caused by motor speed variations during lane-changing and merging behaviors of the EV.

2.2.2. Charging Demand Forecasting Model

By combining the aforementioned models and algorithms, a spatiotemporal distribution forecasting model for the charging load is constructed. By inputting parameters such as target road network data, simulation step, simulation duration, number of vehicles, and EV penetration rate, the spatiotemporal distribution data of the charging load can be obtained. The specific steps are as follows:

• Road network topology construction

Create road attributes including length, number of lanes, and signal timings, and create node attributes including whether it is a charging node and its corresponding functional zone.

• Initialization

Set the number of simulated vehicles i, simulation step dT, simulation duration T, EV penetration rate k, and the user’s minimum expected SOC; simulate the initial SOC of EVs using a normal distribution.

• Vehicle travel route generation

Generate the vehicle origin-destination matrix based on travel chain theory considering travel scenarios such as commuting, business, leisure, and socializing; utilize the Floyd algorithm to determine the shortest path as the vehicle’s travel route.

• CTM traffic simulation

Track vehicle travel routes and use them as traffic demand inputs for the CTM to simulate the macro-level traffic flow state of the road network, thereby obtaining the travel speed v, traffic density ρ, and lane-change frequency p for each road.

• EV energy consumption calculation

Calculate EV energy consumption ΔE based on road condition data and record the SOC of the EV at the end of each simulation step.

• EV charging assessment

In actual road networks, the perception of remaining power by EV users exhibits bounded rationality characteristics (i.e., range anxiety). This paper introduces a Logit discrete choice model to transform the absolute power threshold judgment into a probability-based triggering mechanism [26]. The probability of a user generating a charging intention at time t is defined as shown in Equation (9):

$$P_{charge}(t)={\displaystyle \frac{1}{1+e^{\beta (SOC(t)-SO{C}_{min})}}}$$

(9)

where β is the sensitivity coefficient representing the user’s sensitivity to the power level; SOC(t) is the current state of charge of the vehicle; and SOC_min is the minimum power threshold expected by the user.

The specific model prediction flowchart is illustrated in Figure 5.

Figure 5. Overall flow chart.

3. Optimal Configuration Model of Charging Stations Considering User Satisfaction

Current charging station configuration studies mainly aim to minimize the operating cost or maximize the revenue of joint charging station operators. However, with the increasing number of EV users, reduced user satisfaction caused by unreasonable charging station configuration directly affects users’ charging experience and travel choices, which is unfavorable for the development of the EV industry [27]. To address this issue, this paper establishes an optimal charging station configuration model considering user satisfaction. The model accounts for charging station revenue while maximizing users’ charging satisfaction.

In the context of charging station expansion planning, user charging satisfaction reflects the convenience with which users can obtain charging services, namely charging accessibility. Charging accessibility is used to characterize how easily users can reach a charging station and obtain charging services under the interaction between supply-demand relationships and mobility [28]. In this paper, charging distance and charging waiting time are selected to quantify user satisfaction [29]. Specifically, they refer to the distance traveled by EV users after generating charging demand and the waiting time from arrival at a charging station to the start of charging. To emphasize the importance of user satisfaction, a bi-level optimization model is used to solve this problem. The decision-making processes of the two levels are independent, which provides the lower-level optimization with greater flexibility.

3.1. Upper-Level Model

The upper-level model determines the specific expansion plan for the area, including the locations of charging stations and the number of charging points at each station.

3.1.1. Objective Function

The upper-layer optimization model aims to minimize the daily operating cost of the charging station operator after expansion. The specific components of the operating cost are as follows:

$$\min F_{\mathrm{up}}=C_{oper}+{\displaystyle \frac{C_{pos}+C_{equ}}{365T_{use}}}$$

(10)

where F_up is the objective of the upper-layer model; C_oper is the daily operation and maintenance cost of the charging station, including electricity purchase cost, line loss cost, and charging service outage maintenance cost; C_pos is the expansion construction cost of the charging station, including land-related cost, expansion installation cost, and grid-connection cost; C_equ is the equipment configuration cost of newly added charging station.

• Construction Costs

$$C_{pos}={\displaystyle \sum _{i=1}^m(P_i+P_{con})}\times S_i$$

(11)

where P_i is the land price cost at the location of node i; P_con is the comprehensive installation cost for the expansion of a single charging pile, including the purchase and installation costs of materials such as cables, wires, towers, and power distribution equipment during expansion; S_i is the number of EV charging piles added at node i; and m is the number of nodes with expansion plans.

• Operating Cost

$$\left\{\begin{array}{l}{C}_{\mathrm{oper}}=C_{\mathrm{ener}}+C_{\mathrm{loss}}+C_{\mathrm{ser}}\\ C_{\mathrm{ener}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^m{p}_{\mathrm{eb},t}\cdot P_{i,t}}}\\ C_{\mathrm{loss}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^m\eta \cdot P_{i,t}}}\\ C_{\mathrm{ser}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^m{p}_{\mathrm{s},t}\cdot P_{i,t}}}\end{array}\right.$$

(12)

where C_ener is the energy purchase cost; C_loss is the line loss cost; C_ser is the service cost; p_eb,t is the unit electricity buy price at time t; P_i,t is the charging power at node i at time t; η is the line loss rate during charging of the charging pile; and p_s,t is the charging service and maintenance cost at time t.

• Equipment Cost

$$C_{\mathrm{equ}}={\displaystyle \sum _{i=1}^m{p}_{\mathrm{eq}}\cdot N_i}$$

(13)

where p_eq is the unit configuration price of a charging pile, and N_i is the number of charging piles planned for expansion in the ith charging station.

3.1.2. Constraints

• Expansion cost Constraint

In the expansion scheme, the total cost required for expansion must be lower than the revenue obtained from providing charging services during the operating life after the expansion.

$$C_{\mathrm{total}}=365C_{\mathrm{oper}}\cdot T_{\mathrm{use}}+C_{\mathrm{pos}}+C_{\mathrm{equ}}$$

(14)

$$M_{\mathrm{charge}}=365T_{use}{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^m{p}_{es,t}\cdot P_{i,t}}}$$

(15)

$$C_{\mathrm{total}}\le M_{\mathrm{charge}}$$

(16)

where C_total is the total cost of expansion and O&M during the operating life; M_charge is the revenue generated by providing charging services; and p_es,t is the charging electricity price at time t (including the charging service fee).

• Charging Pile Expansion Quantity Constraint

In the expansion plan, the number of charging piles added at each node must comply with the reasonable expansion quantity for that node. The total number of charging piles in the charging station after expansion must not cause the maximum charging load to exceed the capacity upper limit of the distribution network node to which the station belongs. In this study, the expansion scheme is constrained by the available capacity of the existing distribution network nodes. This setting ensures that the planned charging piles can be connected without violating the current grid capacity limits. For planning scenarios that allow grid-side reinforcement, the model can be extended by adding an upgrade capacity variable at each distribution node and incorporating the corresponding reinforcement cost into the upper-level cost function. When building a new charging station, the number of piles must be greater than the minimum number of piles required for station construction.

$$(1-a_i)\cdot N_{\min }\le N_i+N_{\mathrm{orgin},i}\le (1-a_i)\cdot N_{\max }$$

(17)

where N_min, N_origin,i, and N_max are the minimum number of piles required to establish a charging station at a node, the original number of charging piles at the node, and the maximum number of charging piles the node can accommodate, respectively; a_i is a decision parameter, which takes the value of 1 when node i does not need additional charging piles and 0 when it does.

• Charging Station Expansion Location Constraint

In the expansion plan, ensuring a reasonable distance between charging stations can reduce the idle rate of charging piles. Furthermore, an excessively small distance between charging stations will lead to the deterioration of traffic conditions near the stations due to centralized charging.

$$D_{\mathrm{N}2\mathrm{N}}\ge d_{\min }$$

(18)

where D_N2N is the distance between any two nodes with expansion plans, and d_min is the minimum distance between charging stations.

3.2. Lower-Level Model

The lower-layer model guides users’ charging decisions through charging distance and the number of charging piles, thereby determining the acceptance of EVs by each charging station in each time period within the area after the expansion.

3.2.1. Objective Function

The lower-layer model aims to improve user charging satisfaction by minimizing the charging distance and charging wait time that affect charging accessibility, specifically expressed as:

$$\min F_{\mathrm{down}}=f(D_{\mathrm{c}},T_{\mathrm{w}})$$

(19)

where D_c is the charging distance of the user, and T_w is the charging wait time of the user.

To eliminate the influence of different magnitudes and dimensions between variables on the optimization, dynamic normalization is used to update the maximum and minimum values of the variables during optimization iterations and perform normalization based on the current iteration values, as follows:

$$\min F_{\mathrm{down}}={\displaystyle \frac{D_{\mathrm{c}}-D_{\mathrm{iter},\min }}{D_{\mathrm{iter},\max }-D_{\mathrm{iter},\min }}}+{\displaystyle \frac{T_{\mathrm{w}}-T_{\mathrm{iter},\min }}{T_{\mathrm{iter},\max }-T_{\mathrm{iter},\min }}}$$

(20)

where iter is the iteration generation; D_iter,max and D_iter,min are the maximum and minimum values of the user charging distance in the iter^th iteration; T_iter,max and T_iter,min are the maximum and minimum values of the user charging wait time in the iter^th iteration.

• Charging Distance

$$D_{\mathrm{c}}={\displaystyle \sum _{t=1}^T{\displaystyle \sum _{i=1}^n{d}_i\cdot {N^{\prime }}_{i,t}}}$$

(21)

where d_i is the distance from the charging load at node i to the nearest charging station; N′_i,t is the number of EVs with charging demand at node i during time period t; and n is the number of nodes in the area.

• Charging Wait Time

$$T_{\mathrm{w}}={\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^{{N^{″}}_i}{t}_{i,j}}}$$

(22)

where N″_i is the number of EVs received by charging station i for charging services; t_i,j is the cumulative wait time of the jth EV in charging station i during the charging process, from arrival at the station until the commencement of charging.

3.2.2. Constraints

• Charging vehicle quantity constraint

In each time period, the number of EVs currently charging at each charging station should not exceed the number of charging piles configured at that station, and the total number of EVs received by all charging stations should not exceed the number of EVs with charging demand in that period.

$${\displaystyle \sum _t^{T_{fc}}{N^{‴}}_{i,t}}\le N_i$$

(23)

$${\displaystyle {\displaystyle \sum _{i=1}^m}{N^{″}}_{i,t}}\le {\displaystyle {\displaystyle \sum _{i=1}^n}{N^{\prime }}_{i,t}}$$

(24)

where T_fc is the average duration of a single EV charging session; N‴_i,t is the number of EVs currently charging at charging station i during time period t; and N″_i,t is the number of EVs received by charging station i for charging services during time period t.

• User wait time constraint

Based on the principle of bounded rationality, users will make secondary charging decisions while waiting for charging, comprehensively considering the current estimated wait time and the time spent traveling to a nearby idle station

$$t_{i,j}\le T_{i,j}+{T^{\prime }}_{i,j},i\in m,j\in {N^{″}}_i$$

(25)

where T_i,j is the time taken for the jth vehicle at charging station i to travel to the nearest idle charging station, and T′_i,j is the time margin of bounded rationality for the user’s charging strategy.

• User charging distance constraint

When a user generates a charging demand, the target charging station selected by the user must satisfy the current SOC status of the EV.

$$d_i\le {\displaystyle \frac{SO{C}_{i,j,t}\cdot X_j}{{\epsilon }_j}},i\in n,j\in {N^{\prime }}_{i,t},t\in T$$

(26)

where SOC_i,j,t is the state of charge of the jth EV with charging demand at node i during time period t; X_j is the battery capacity of the jth EV; and ε_j is the energy consumption per unit distance of the jth EV.

3.3. Model Solving

The optimal configuration model of charging stations considering user satisfaction is a bi-level optimization model, which is solved through iterative optimization of the upper and lower layers. The upper-layer model first makes decisions to determine the configuration of charging piles, which serves as a constraint for the lower-layer charging acceptance strategy. Based on the decisions from the upper layer and considering user satisfaction, the lower-layer model formulates charging acceptance decisions to guide user charging, thereby increasing the operational revenue of the charging station by reducing operating costs and enhancing operating income. Due to the non-convex nature of the lower-layer constraints, the common method of treating the lower layer as KKT conditions equivalent to the upper-layer constraints is not applicable [30]. Specifically, the non-convexity mainly arises from the discrete charging-station assignment decisions and their coupling with time-varying capacity constraints. The charging distance depends on the selected station for each demand node, while the waiting time is affected by EV arrivals, charging pile availability, and queue accumulation across different time periods. These assignment-capacity and queueing relationships introduce integer decision variables and piecewise logical constraints. Therefore, the model is solved using a nested approach combining a heuristic algorithm and a solver. Specifically, the upper-layer model is solved using Genetic Algorithm, while the lower-layer model, due to its large number of decision variables, is solved using the Cplex solver via the Yalmip toolbox. The detailed solution process is illustrated in Figure 6.

Figure 6. Flowchart for solving the two-layer model.

4. Case Studies

4.1. Basic Information

Taking the regional road network of a city in Hunan Province as an example, the selected road network is 25 km long in the east–west direction and 15 km wide in the north–south direction, with a total coverage area of approximately 400 km². Detailed information of the regional road network was collected based on GIS system data, and topological modeling was performed on the network; specific road network information is shown in Table A2 and Table A3 of Appendix A. In addition, functional zones were divided based on the node functions within the region, resulting in 9 residential area nodes, 6 office area nodes, 6 leisure area nodes, 5 commercial area nodes, and 4 industrial area nodes. Specific functional zone data are provided in Table A4 of Appendix A.

The topological structure and charging station distribution of the area are shown in Figure 7, where red nodes represent nodes containing charging stations, and each charging station initially has 20 charging piles. The unit land prices for each functional zone are listed in Table A5 of Appendix A.

Figure 7. Topology of regional road network and distribution.

4.2. Charging Load Forecast

From the full-period traffic flow parameters of each road in Figure 8, it can be observed that the travel speeds on roads 2–9, 3–10, 5–14, 6–15, 9–18, 11–20, 13–22, and 15–23 are relatively slow. Most of these are feeder roads of urban main roads, which generally have fewer lanes and serve as critical connections between major functional zones. Moreover, charging stations are more concentrated along these roads, resulting in relatively higher road densities. Regarding lane-change frequency, road 10–11 exhibits a higher frequency compared to other segments. This is mainly because the road is relatively short and serves as an expressway within the network; the control effect of traffic signals at both ends on vehicle density is significant, thereby increasing the opportunities for vehicles to change lanes. The parameter settings for the charging load forecasting model are listed in Table 1.

Figure 8. Spatio-temporal traffic flow parameters before road expansion: (a) Road speed; (b) Road density; (c) Number of lane changes.

Table 1. Related parameters of charging load forecasting model.

Parameters	Value
Simulated vehicle i	5000 vehicles
EV penetration rate k	0.4
Simulation step size dT	15 min
EV Capacity	85 kWh
Mean Initial SOC of EVs	0.7
Minimum SOC expectation for users	0.25
Average SOC upon completion of charging	0.85
Charging power of charging stations	7 kW
Range energy consumption coefficient λl	0.02
Travel speed energy consumption coefficient λv	0.0125
Traffic density energy consumption coefficient λρ	1.5
Lane-changing frequency energy consumption coefficient λp	9.3 × 10−4
Charging power of charging stations	7 kW

According to the prediction results in Figure 9, 19:00–24:00 is the peak period for daily charging load, while 0:00–5:00 is the off-peak period, which aligns with the charging patterns of urban EV users.

Figure 9. Spatiotemporal distribution of charging load.

4.3. Expansion of Charging Stations

To verify the effectiveness and superiority of the proposed optimal expansion strategy, a comparison is conducted between the optimal strategy and an average allocation strategy. Relevant parameters for the optimal strategy are provided in Table A6 of Appendix A, and information regarding local electricity purchase prices and charging prices is shown in Table A7 of Appendix A. The specific strategies are as follows:

Strategy 1: Based on the prediction results of the spatiotemporal distribution of the charging load, the expansion scheme for charging stations is obtained using the bi-level optimal configuration model that considers user satisfaction.

Strategy 2: Under the condition of deploying the same total number of charging piles as in Strategy 1, the expansion scheme is obtained by equally distributing the number of added charging piles among all nodes.

Two sets of expansion schemes are obtained by combining the above two strategies (as shown in Table 2). Strategy 1 adds a total of 200 charging piles across different nodes. Strategy 2 distributes these 200 charging piles equally among all nodes; due to rounding issues for the number of units, the surplus charging piles are deployed at nodes near the regional center. Data regarding the actual expansion costs, operating expenses, and revenues for the two strategies are presented in Table A8 of Appendix A.

Table 2. Expansion results for each strategy.

Node Number	Number of Charging Stations		Node Number	Number of Charging Stations		Node Number	Number of Charging Stations
	Strategy 1	Strategy 2		Strategy 1	Strategy 2		Strategy 1	Strategy 2
1	0	8	11	21	9	21	6
2	20	20	12	6	9	22	7
3	25	8	13	6	9	23	6
4	24	20	14	6	9	24	20
5	6	8	15	6	9	25	20
6	6	8	16	20	9	26	6
7	6	8	17	6	8	27	6
8	24	20	18	6	8	28	20
9	6	9	19	11	8	29	6
10	6	9	20	6	8	30	6

4.4. Analysis of the Effects of Capacity Expansion

4.4.1. Charging Station Capacity

The expansion schemes obtained from the two aforementioned strategies are incorporated into the spatiotemporal charging load forecasting model considering road network traffic flow. The vehicle acceptance status, EV charging wait times, and EV charging distances for each charging station are then statistically analyzed. The vehicle acceptance status of charging stations before expansion is shown in Figure 10a; the expansion status under the average strategy is shown in Figure 10b; and the expansion status under the optimal strategy is shown in Figure 10c.

Figure 10. Spatio-temporal Vehicle Reception at Each Charging Station: (a) reception status prior to expansion; (b) reception under the average strategy expansion; (c) reception under the capacity expansion optimization strategy.

As observed in Figure 10a, some charging stations reached full capacity at 10:00 before expansion, indicating that the current number of charging piles in the area is insufficient to meet existing charging demand. From Figure 10b,c, it can be seen that after the expansion of the charging stations, the full-load condition of charging piles at each station is delayed until 16:30, demonstrating that the expansion schemes effectively enhance the carrying capacity of the charging stations. Furthermore, the Gini coefficient is utilized as a quantitative index for the balance of charging station acceptance, with the specific calculation methods shown as follows:

$$k_{gini}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{N_{total}}{\displaystyle \sum _{j=1}^{N_{total}}\left|{\tau }_i-{\tau }_j\right|}}}{2N_{total}^2{\mu }_{\tau }}}$$

(27)

$${\tau }_i={\displaystyle \frac{N_i^{″}}{N_i}}$$

(28)

where k_gini is the Gini coefficient of the charging stations, describing the balance of vehicle acceptance among charging stations—a value closer to 0 indicates a more uniform distribution of acceptance among the stations; N_total is the total number of charging stations in the area; τ_i is the utilization rate of charging piles at charging station i; and μ_τ is the average utilization rate of charging piles across all stations. The Gini coefficients of the charging stations under different strategies are shown in Figure 11.

Figure 11. Gini coefficient of vehicle reception at charging stations under different strategies.

As shown in Figure 11, during the idle period (0:00–6:30) and the period with sufficient pile availability (6:30–15:00), the Gini coefficient inevitably becomes excessively large under both strategies because the number of vehicles seeking charging is far lower than the number of available charging piles. However, during the optimal guidance period (15:00–24:00), the rational configuration of charging pile quantities using the optimization strategy improves the imbalance in charging station acceptance to a certain extent. This improvement is even more significant as charging demand gradually increases (15:00–20:00), indicating that the vehicle guidance within the proposed strategy effectively mitigates the imbalance in acceptance among charging stations.

4.4.2. User Satisfaction Optimization

As illustrated in Figure 12, the proposed optimization strategy, Strategy 1, significantly improves charging accessibility compared to the traditional average strategy, Strategy 2. Regarding the wait times shown in Figure 12a, Strategy 2 ultimately exacerbates queuing due to imbalanced station acceptance. In contrast, Strategy 1 effectively mitigates this congestion, reducing the cumulative number of queuing vehicles by 216 compared to Strategy 2. Furthermore, in terms of spatial efficiency in Figure 12b, Strategy 1 substantially shortens the pre-expansion average charging distance from 8.56 km to 1.71 km and increases the daily served EVs from 348 to 736. Compared to the 2.89 km average distance and 591 EVs served under Strategy 2, Strategy 1 accommodates 145 more users while further reducing the travel distance by 1.18 km. Overall, by allocating new charging piles to stations with persistent demand gaps and guiding EVs to stations with better accessibility, the proposed expansion scheme reduces local queuing and charging detours, thereby improving charging service efficiency.

Figure 12. Comparison before and after capacity expansion: (a) User charging wait times; (b) User charging distances.

To further validate the proposed framework, comparative experiments were conducted with conventional expansion strategies and representative optimization algorithms, including PSO and NSGA-II. The detailed results are listed in Table A9 of Appendix A. Under the same charging demand, the proposed method achieves a lower average charging distance and a smaller upper-level objective value than most comparison methods, while maintaining a competitive number of served and waiting vehicles. This indicates that the proposed framework provides a more balanced expansion scheme in terms of operating cost, charging accessibility, and service efficiency.

4.4.3. Traffic Flow Optimization

The traffic flow indicators for each road in the network during each time period after expansion under different strategies—including travel speed, road density, and lane-change frequency—were statistically analyzed; specific data are provided in Figure 13. The sum of the changes in indicators for all roads within each time period was calculated, along with the cumulative daily change. The optimization effects of the two expansion strategies are compared in Figure 14, Figure 15 and Figure 16. In addition, the coupling relationship among traffic state, SOC evolution, charging demand, and station expansion decisions was further analyzed. The detailed results are provided in Appendix B, Figure A1. The analysis shows that congestion increases cumulative energy consumption and accelerates SOC decline, thereby advancing the charging demand trigger point. The generated charging demand is then aggregated at charging stations, and stations with larger capacity gaps require larger expansion scales.

Figure 13. Traffic flow indicators for each road following capacity expansion: (a) travel speeds under Strategy 1; (b) travel speeds under Strategy 2; (c) vehicle density under Strategy 1; (d) vehicle density under Strategy 2; (e) number of lane changes under Strategy 1; (f) number of lane changes under Strategy 2.

Figure 14. The cumulative speed variations in each road under different expansion strategies.

Figure 15. The cumulative traffic density variations in each road under different expansion strategies.

Figure 16. The cumulative lane change times of each road under different expansion strategies.

As shown in Figure 14, after expansion, road operating speeds in the network increase significantly. The proposed strategy increases the daily cumulative operating speed by 197.83 km/h and the average road speed by 4.21 km/h compared with before expansion. By contrast, the conventional average strategy increases these values by only 98 km/h and 2.09 km/h, respectively. Compared with the average strategy, Strategy 1 further improves the cumulative speed by 99.83 km/h and the average road speed by 2.12 km/h.

As seen in Figure 15, road density decreases significantly after expansion under both strategies. Under the proposed optimization strategy, the cumulative traffic density of roads in the network decreases by 0.453; under Strategy 2 (average expansion), it decreases by 0.519. Comparing the strategies, Strategy 1 shows an average decrease of 0.0096 per road, while Strategy 2 shows an average decrease of 0.011 per road, indicating similar optimization effects.

As shown in Figure 16, the difference in the optimization effect of different expansion strategies on the lane-change frequency of traffic flow is more pronounced. Using the proposed optimization strategy, the total daily lane-change frequency for all vehicles on all roads in the area increases cumulatively by 886 times, whereas the average strategy results in an increase of 181 times (average increases of 19 times and 4 times per road, respectively). It can be seen that the proposed optimization strategy has a certain increasing effect on the lane-change frequency, thereby enhancing road capacity to some extent.

In conclusion, the proposed optimization strategy improves charging service efficiency while also mitigating traffic disturbances caused by charging detours and station congestion, particularly in terms of increasing road operating speed and reducing road density. This further verifies the practical value of coordinated traffic-charging expansion planning.

4.4.4. Sensitivity Analysis

To evaluate the robustness of the proposed framework, sensitivity analyses were conducted for three key parameters: EV penetration rate, charging threshold SOC, and user behavior coefficient. The detailed results are shown in Figure A2, Figure A3 and Figure A4.

For the EV penetration rate, the results show that system performance remains stable when the penetration rate increases from 0.2 to 0.4. The service rate remains close to 1, and the number of waiting vehicles stays nearly zero. When the penetration rate further increases to 0.5 and 0.6, the number of waiting vehicles, average charging distance, and comprehensive performance index increase significantly. This indicates that the system gradually approaches its capacity bottleneck under high-load conditions.

For the charging threshold SOC, its impact on the results is relatively limited within the range of 0.15–0.35. The number of waiting vehicles remains zero, the service rate remains 1, and the average charging distance and comprehensive performance index show only slight fluctuations. This suggests that the proposed framework is robust to changes in the charging threshold within a reasonable range.

For the user behavior coefficient, the system remains relatively stable when the coefficient ranges from 0.6 to 1.0. When the coefficient increases to 1.2 or above, the number of waiting vehicles and average charging distance increase, while the service rate slightly decreases. This indicates that intensified user behavior increases pressure on local charging stations, and the proposed framework can capture the corresponding performance degradation. Additional analyses were conducted to examine the robustness of the proposed model under different operating scenarios and the effects of service-related factors on user satisfaction. The detailed results are provided in the Supplementary Materials, Figures S1 and S2.

5. Conclusions

As the number of electric vehicle (EV) ownership increases year by year, to solve the problem of current charging facilities lagging behind and being unable to meet charging demand, an EV charging station expansion strategy is proposed that comprehensively considers cellular traffic simulation and user satisfaction. A case study was conducted based on the expansion needs of charging stations in a certain urban area of Hunan Province, and the main conclusions are as follows:

(1)

The spatiotemporal distribution forecasting method for charging load considering road network traffic flow can effectively support the real-time prediction of regional charging load demand and obtain regional road network traffic information in real time, providing key data support of charging demand for the expansion scheme.

(2)

The optimal configuration method for charging stations considering user satisfaction helps to significantly improve user charging satisfaction while enhancing the carrying capacity of charging stations. Comparing before and after expansion, the average charging distance of users was cumulatively reduced by 6.85 km, and the daily number of users waiting for charging was cumulatively reduced by 326.

(3)

The proposed strategy guides EV charging decisions by optimizing the allocation of the number of charging piles, thereby improving the traffic conditions of the road network in the area where the charging stations are located. Compared with the average allocation strategy, the proposed strategy shows significant effects in improving travel speed, reducing road density, and decreasing lane-change frequency.

With the rapid development of EVs, diversified energy replenishment methods will be more widely applied. Future research will further incorporate grid-side reinforcement options and their investment costs into the expansion planning framework, and examine the impact of ultra-fast charging, battery swapping, and other specialized replenishment methods on charging facility expansion strategies. In addition, microscopic traffic simulation platforms such as SUMO or VISSIM, together with real vehicle trajectory data, will be introduced to further calibrate and validate the traffic simulation and optimization framework under more diverse urban traffic scenarios.