With the rapid development of the battery electric vehicle market, the optimal allocation of charging infrastructure has become a critical factor constraining the industry’s sustainable growth. The number of charging facilities is experiencing explosive growth, yet their layout, configuration, and utilization efficiency face numerous challenges. Issues such as uneven distribution, irrational configuration, and low utilization rates are prominent. Therefore, it is particularly important to proactively address these problems to ensure the healthy development of battery electric vehicle adoption. Current research on charging station siting and capacity determination primarily focuses on construction costs, station coverage, and traffic flow, often overlooking user charging convenience and demand diversity. This study proposes an optimized siting and equipment configuration scheme by integrating vehicle trajectory data and user charging behavior, aiming to balance economic efficiency with service quality.
Existing literature on battery electric vehicle charging station planning often employs methods like genetic algorithms, ArcGIS-based spatial analysis, and demand point models to minimize social costs or maximize coverage. However, these approaches frequently neglect the actual charging behavior and satisfaction of battery electric vehicle users. As battery electric vehicles and charging stations become more widespread, user experience increasingly impacts station utilization and profitability. Ignoring factors like charging wait times and travel distance to stations can lead to underutilized equipment and user attrition. Moreover, most studies consider only single-power charging modes (e.g., slow or fast charging), failing to account for the diverse needs of battery electric vehicle users who may require different charging speeds based on their schedules and battery status. This study addresses these gaps by incorporating real-world GPS trajectory data, geographic information, and multi-type charging equipment into a comprehensive optimization framework.
The core of this research lies in analyzing actual vehicle trajectory data to understand travel patterns and charging demands. We process GPS data from battery electric vehicles (or conventional vehicles as proxies) to identify frequent stop points and high-demand areas. Using clustering algorithms like K-means and spatial analysis tools like ArcGIS, we map these points to real road networks and determine potential charging hotspots. This geographic foundation supports the subsequent optimization of charging station locations. Furthermore, we model user charging behavior by considering multiple charging equipment types: slow charging piles (SCP), fast charging piles (FCP), and super-fast charging piles (SFCP). Battery electric vehicle users select charging power based on their remaining battery charge and available parking time, which influences the station’s equipment mix. A mathematical optimization model is then constructed to minimize total socio-economic costs—including construction, operation, and maintenance—while maximizing coverage and meeting load constraints. The model also incorporates real-time navigation factors, such as travel time based on traffic conditions, to enhance user satisfaction. Finally, a case study using taxi GPS data from Chaoyang District, Beijing, validates the proposed method, demonstrating its effectiveness in achieving cost-efficient and service-oriented charging infrastructure planning.
Data Processing and Analysis of User Charging Behavior for Battery Electric Vehicles
The foundation of our optimization approach is the analysis of real-world vehicle trajectory data. In this study, we utilize GPS records from taxis in Chaoyang District, Beijing, to simulate the travel patterns of battery electric vehicles. The data includes timestamps, geographic coordinates (longitude and latitude), passenger count, and speed. However, raw GPS data often contains inaccuracies due to signal interference or device errors. Therefore, we first preprocess the data by cleaning and removing invalid points, such as those outside the study area or with implausible speeds. After preprocessing, we obtain approximately 9,928 valid data points representing potential daily charging demands for battery electric vehicles in the region.
To identify spatial patterns, we apply the K-means clustering algorithm to the cleaned trajectory data. This algorithm groups geographically proximate points into clusters, each representing a frequent stop or high-demand area. The optimal number of clusters (k) is determined using the elbow method and silhouette coefficient analysis. For instance, in our case study, we find that k values between 17 and 22 yield stable clusters with high silhouette scores. These clusters correspond to candidate locations for charging stations. We then use ArcGIS to perform spatial analysis, matching the clustered points to the road network and creating buffer zones with a service radius (e.g., 2.5 km) around each candidate site. This helps assess the coverage capability of potential charging stations and ensures that they are accessible within a reasonable distance for battery electric vehicle users.
User charging behavior is modeled by considering three types of charging equipment: slow charging piles (SCP) with power ratings of 5–10 kW, fast charging piles (FCP) at 50 kW, and super-fast charging piles (SFCP) at 250 kW. Battery electric vehicle users choose among these based on their remaining charging demand and available parking time. Let \( \Delta Q_n \) denote the remaining charging demand for vehicle \( n \), calculated as \( \Delta Q_n = Cap_n \times (1 – SOC_n) \), where \( Cap_n \) is the battery capacity and \( SOC_n \) is the state of charge. The available parking time is \( T_{stay} \). The charging power selection rule is as follows:
$$ P_n = \begin{cases}
P_{slow} & \text{if } \Delta Q_n \leq P_{slow} \cdot T_{stay} \\
P_{fast} & \text{if } P_{slow} \cdot T_{stay} < \Delta Q_n \leq P_{fast} \cdot T_{stay} \\
P_{super} & \text{if } \Delta Q_n > P_{fast} \cdot T_{stay}
\end{cases} $$
This rule ensures that users select the appropriate charging mode to efficiently meet their needs without overloading the battery or wasting time. For example, a battery electric vehicle with a large remaining charge and short parking time might opt for a super-fast charger, whereas one parked overnight could use a slow charger. This behavioral model is crucial for determining the mix of charging equipment at each station.
To forecast charging load demand, we employ the Monte Carlo simulation method. This involves modeling the arrival of battery electric vehicles at charging stations as a stochastic process, typically following a Poisson distribution based on historical traffic data. The simulation iteratively generates vehicle arrivals, charging demands, and power consumption across different times of the day. The convergence criterion ensures stable load predictions:
$$ \max \left( \frac{| \mathbf{A}^{(k)} – \mathbf{A}^{(k-1)} |}{|\mathbf{A}^{(k-1)}| + \epsilon} \right) < \delta $$
where \( \mathbf{A}^{(k)} \) is the average load matrix from the \( k \)-th simulation, \( \epsilon \) is a small positive constant to prevent division by zero, and \( \delta \) is a convergence threshold (e.g., 0.01). This process yields temporal and spatial load distributions, which inform the capacity planning of charging stations. By simulating various scenarios, we can account for peak demand periods—such as evening hours when many battery electric vehicles return home—and ensure that stations are adequately equipped to handle fluctuations.
Mathematical Model for Charging Station Siting and Capacity Determination
The optimization model aims to determine the optimal locations and capacities of charging stations for battery electric vehicles, considering multiple objectives and constraints. The primary goal is to minimize total socio-economic costs while maximizing service coverage and satisfying technical limitations. We formulate this as a mixed-integer linear programming (MILP) problem, which can be solved using solvers like CPLEX.
The objective function combines cost minimization and coverage maximization. First, the annualized socio-economic cost \( CO \) includes construction costs \( C_{Inv} \), equipment costs \( C_{Dev} \), operation and maintenance costs \( C_{Ope} \), and electricity consumption costs \( E_j \) for each candidate station \( j \). Weighting factors \( \gamma \), \( \delta \), and \( \epsilon \) adjust the influence of each cost component:
$$ \min CO = \sum_{j=1}^{n} \left( C_{Inv} + \gamma C_{Dev} + \delta C_{Ope} + \epsilon E_j \right) x_j $$
where \( x_j \) is a binary decision variable equal to 1 if station \( j \) is selected, and 0 otherwise. Second, coverage is measured as the proportion of demand points within the service radius \( R \) of any selected station. Let \( T_n \) be the coverage rate when \( n \) stations are built, calculated as:
$$ T_n = \frac{\sum_{j=1}^{n} \sum_{i \in \{ x’_j : \text{dist}(x_i, C_j) \leq R \}} 1}{C_{\text{total}}} $$
where \( C_{\text{total}} \) is the total number of demand points. To integrate coverage into the cost objective, we convert it into a coverage loss cost by introducing a penalty coefficient \( p \). The combined objective function becomes:
$$ \min F = CO + p \cdot (1 – T_n) $$
By tuning \( p \), we can balance the trade-off between cost and coverage. For instance, a higher \( p \) places greater emphasis on coverage, potentially leading to more stations.
The model includes several constraints to ensure feasibility and efficiency. Load constraints prevent overloading of individual stations and the grid. For each station \( i \) at time \( t \), the load \( P_{i,t} \) must not exceed its maximum capacity \( P_{i}^{\max} \):
$$ P_{i,t} \leq P_{i}^{\max} $$
Additionally, the total load across all stations must be within the grid’s supply capacity \( P_{g,t} \):
$$ \sum_{i=1}^{n} P_{i,t} \leq P_{g,t} $$
Real-time navigation constraints account for travel time based on traffic conditions. The average travel speed \( v_t \) on a road segment at time \( t \) is computed from GPS data of battery electric vehicles:
$$ v_t = \frac{1}{N_t^{\text{EV}}} \sum_{w=1}^{N_t^{\text{EV}}} v_w(t) $$
where \( v_w(t) \) is the instantaneous speed of vehicle \( w \). The travel time from a battery electric vehicle’s current location to a charging station \( c \) is:
$$ T_{w,c}(t) = \frac{\text{dist}(S_w, S_c)}{v_t} + \mu(t) $$
where \( \mu(t) \) is a congestion factor. This time must not exceed a maximum allowable time \( T_{\max} \) (e.g., corresponding to the service radius). Furthermore, each battery electric vehicle user is assigned to only one charging station per charging event:
$$ \sum_{c \in \Omega} B_{c,t,w} = 1 $$
where \( B_{c,t,w} \) is a binary variable indicating whether vehicle \( w \) charges at station \( c \) at time \( t \), and \( \Omega \) is the set of stations within \( T_{\max} \).
Finally, constraints on the number of multi-type charging equipment ensure that each station has sufficient chargers to meet demand. Let \( N_{slow} \), \( N_{fast} \), and \( N_{super} \) denote the maximum numbers of SCP, FCP, and SFCP at a station, respectively. The actual usage must not exceed these limits:
$$ \begin{aligned}
\sum_{c=1}^{n} B_{c,t}^{slow} &\leq N_{slow} \quad \forall c \in \Omega \\
\sum_{c=1}^{n} B_{c,t}^{fast} &\leq N_{fast} \quad \forall c \in \Omega \\
\sum_{c=1}^{n} B_{c,t}^{super} &\leq N_{super} \quad \forall c \in \Omega
\end{aligned} $$
These constraints ensure that the charging infrastructure can accommodate the projected demand from battery electric vehicles without causing shortages or excessive wait times.
Case Study: Application in Chaoyang District, Beijing
To validate the proposed method, we conduct a case study using taxi GPS data from Chaoyang District, Beijing. The data, collected on August 6, 2020, includes 9,928 valid trajectory points after preprocessing. We assume these points represent the daily charging demands of battery electric vehicles in the region. The geographic scope is bounded by longitude 116.38°E to 116.65°E and latitude 39.85°N to 40.05°N. Using ArcGIS, we map the trajectory points to the road network and perform spatial clustering.
Based on the elbow method and silhouette coefficient analysis, we determine that the optimal number of clusters ranges from 17 to 22. We evaluate each candidate set of stations by calculating coverage rates and annual comprehensive costs. The service radius is set to 2.5 km, aligning with urban planning standards for charging infrastructure. The coverage rate is determined by counting demand points within the buffer zones of selected stations. Costs are estimated based on typical expenses for large, medium, and small charging stations, as shown in Table 1.
| Station Scale | Construction Cost (104 CNY) | Land Cost (104 CNY) | Annual O&M Cost (104 CNY) | Grid Loss Cost (104 CNY) | Total Annual Cost (104 CNY) |
|---|---|---|---|---|---|
| Large | 31.34 | 36.30 | 27.82 | 0.76 | 96.22 |
| Medium | 18.33 | 20.22 | 13.22 | 0.38 | 52.15 |
| Small | 9.56 | 10.09 | 6.51 | 0.17 | 26.33 |
Table 1: Cost data for different types of charging stations (in 10,000 Chinese Yuan).
We compute the coverage and cost for different numbers of stations, as summarized in Table 2. The penalty coefficient \( p \) is set to 150 (in 104 CNY) to balance coverage loss and construction cost. The combined objective function \( F \) is minimized for each scenario.
| Number of Stations | Large | Medium | Small | Coverage Rate | Annual Comprehensive Cost (104 CNY) | Combined Cost \( F \) (104 CNY) |
|---|---|---|---|---|---|---|
| 17 | 4 | 6 | 7 | 92.56% | 882.09 | 894.37 |
| 18 | 3 | 7 | 8 | 93.32% | 864.35 | 874.37 |
| 19 | 3 | 7 | 9 | 94.33% | 890.68 | 899.68 |
| 20 | 3 | 7 | 10 | 95.23% | 917.01 | 924.01 |
| 21 | 1 | 10 | 10 | 95.30% | 881.02 | 887.02 |
| 22 | 0 | 12 | 10 | 95.58% | 889.10 | 894.10 |
Table 2: Comparison of different station configurations.
The results indicate that 18 stations yield the lowest combined cost of 874.37 (104 CNY) with a coverage rate of 93.32%. This configuration balances economic efficiency and service availability. Further increasing the number of stations improves coverage but raises costs, making 18 stations the optimal choice. The detailed locations and capacities of these 18 stations are listed in Table 3.
| Station ID | Daily Charging Vehicles | Station Type | Longitude (°) | Latitude (°) |
|---|---|---|---|---|
| 1 | 572 | Medium | 116.5029 | 39.9232 |
| 2 | 837 | Large | 116.4068 | 39.9731 |
| 3 | 513 | Medium | 116.5846 | 39.9174 |
| 4 | 136 | Small | 116.5695 | 40.0078 |
| 5 | 331 | Small | 116.4502 | 39.8327 |
| 6 | 447 | Small | 116.4991 | 39.8660 |
| 7 | 545 | Medium | 116.4920 | 39.9639 |
| 8 | 753 | Medium | 116.4636 | 39.9905 |
| 9 | 276 | Small | 116.3739 | 39.9931 |
| 10 | 921 | Large | 116.4472 | 39.9188 |
| 11 | 187 | Small | 116.5860 | 39.8560 |
| 12 | 355 | Small | 116.5479 | 39.9630 |
| 13 | 744 | Medium | 116.4469 | 39.9541 |
| 14 | 780 | Medium | 116.4742 | 39.9182 |
| 15 | 355 | Small | 116.5383 | 39.9190 |
| 16 | 640 | Medium | 116.5044 | 40.0172 |
| 17 | 434 | Small | 116.4115 | 40.0070 |
| 18 | 1102 | Large | 116.4571 | 39.8808 |
Table 3: Details of the 18 optimal charging stations.
Next, we analyze the charging load distribution using Monte Carlo simulation. The battery electric vehicle model assumes a capacity of 80 kWh (e.g., similar to a Nio ET5). The charging equipment includes slow chargers (7 kW), fast chargers (60 kW), and super-fast chargers (120 kW). The simulation reveals that approximately 50% of charging demand occurs during peak hours (16:00 to 22:00). The average load profile across the 18 stations shows significant variation throughout the day, with peaks in the evening. This load information is used to determine the optimal mix of charging equipment at each station.
We compare three scenarios to illustrate the importance of multi-type charging equipment for battery electric vehicles:
- Scenario 1: Only slow charging piles (SCP).
- Scenario 2: Slow and fast charging piles (SCP and FCP).
- Scenario 3: Slow, fast, and super-fast charging piles (SCP, FCP, and SFCP).
Using the optimization model, we solve for the number of each charger type at each station while minimizing socio-economic costs. The results for Scenario 3 are shown in Figure 1 (represented descriptively due to HTML constraints). The total number of chargers across all stations is 374, comprising 54 SCP, 264 FCP, and 56 SFCP. This mix caters to diverse user needs: slow chargers for long-duration parking, fast chargers for moderate charging speeds, and super-fast chargers for quick top-ups. The socio-economic costs for each scenario are compared in Table 4.
| Scenario | Investment Cost (104 CNY) | O&M Cost (104 CNY) | Total Cost (104 CNY) |
|---|---|---|---|
| 1 (SCP only) | 54.817 | 130.88 | 185.697 |
| 2 (SCP + FCP) | 63.897 | 69.84 | 133.737 |
| 3 (SCP + FCP + SFCP) | 66.243 | 67.60 | 133.843 |
Table 4: Socio-economic costs for different charging equipment scenarios.
Scenario 1 is impractical due to the high number of slow chargers required (over 300 at some stations), leading to excessive space and maintenance costs. Scenario 2 reduces costs significantly but may not meet the needs of battery electric vehicle users requiring ultra-fast charging. Scenario 3 offers the best balance, with a minimal cost increase compared to Scenario 2 while providing faster charging options. This enhances user satisfaction, especially for those with time-sensitive demands, such as taxi or ride-hailing drivers. The dominance of fast chargers (about 70% of the total) underscores their role as the backbone of charging infrastructure for battery electric vehicles, supplemented by super-fast chargers for peak demand.
Discussion and Implications
The proposed method demonstrates the value of integrating real-world GPS data, user behavior modeling, and multi-objective optimization in planning charging infrastructure for battery electric vehicles. By considering actual travel patterns, we can identify high-demand areas that might be missed by traditional methods based solely on population density or traffic flow. The use of ArcGIS for spatial analysis ensures that charging stations are geographically feasible and accessible. Moreover, incorporating multi-type charging equipment addresses the diverse needs of battery electric vehicle users, which is crucial for promoting widespread adoption.
The case study results highlight several practical insights. First, the optimal number of stations is sensitive to the trade-off between cost and coverage. The penalty coefficient \( p \) allows planners to adjust this trade-off based on policy goals—for example, a higher \( p \) might be used in urban centers to ensure dense coverage for battery electric vehicles. Second, the equipment mix is critical for economic efficiency. While fast chargers are cost-effective for most situations, including some super-fast chargers can significantly improve service quality without drastically increasing costs. This is particularly important as battery technology advances and battery electric vehicles with larger capacities become more common, requiring faster charging to reduce downtime.
Furthermore, the real-time navigation constraints incorporated in the model reflect the dynamic nature of urban traffic. By accounting for travel time variability, the planning process can better estimate the effective service radius of charging stations. This is especially relevant for battery electric vehicle users who may be deterred by long detours to charging points. Future work could integrate real-time data streams from intelligent transportation systems to further refine these constraints.
The socio-economic cost analysis reveals that investing in a diversified charging infrastructure can be financially viable. The total cost of Scenario 3 is only marginally higher than Scenario 2, yet it offers superior flexibility and user experience. This suggests that policymakers and investors should consider multi-type configurations when deploying charging networks for battery electric vehicles. Additionally, the model can be extended to include renewable energy integration, vehicle-to-grid (V2G) capabilities, or battery swapping stations, providing a more comprehensive framework for sustainable mobility.
Conclusion
In this study, we developed an optimization method for configuring multi-type charging equipment for battery electric vehicles based on GPS data. The approach combines vehicle trajectory analysis, user charging behavior modeling, and mathematical optimization to determine the optimal locations and capacities of charging stations. Key contributions include the use of real-world data to inform planning, the consideration of multiple charging equipment types to meet diverse user needs, and the integration of coverage and cost objectives in a unified model.
The case study in Chaoyang District, Beijing, validated the method, showing that 18 charging stations achieve the best balance between cost and coverage. The optimal equipment mix comprises slow, fast, and super-fast chargers, with fast chargers constituting the majority. This configuration minimizes socio-economic costs while ensuring that battery electric vehicle users have access to suitable charging options. The results underscore the importance of data-driven planning and user-centric design in the rollout of charging infrastructure for battery electric vehicles.
Future research could explore several directions. First, incorporating dynamic electricity pricing and grid constraints could enhance the economic and operational efficiency of charging stations. Second, expanding the model to include long-term forecasts of battery electric vehicle penetration and technological changes would improve its robustness. Third, applying the method to other cities or regions could provide comparative insights and generalize the findings. Ultimately, as the adoption of battery electric vehicles accelerates, such optimized planning methods will be essential for building resilient, efficient, and user-friendly charging networks that support the transition to sustainable transportation.