With the rapid adoption of new energy vehicles, the demand for EV charging station infrastructure has surged, leading to significant challenges in urban areas where land resources are limited. Existing methods for EV charging station placement, such as those based on road networks or traffic flow, often fail to adequately meet charging demands, particularly when repurposing public parking facilities. Traditional approaches include discrete demand-based models like P-median and coverage models, as well as methods considering user behavior or multi-criteria deployment. Techniques like K-Means clustering and improved particle swarm optimization have also been applied. To address these gaps, we propose a novel optimization model that focuses on retrofitting public parking lots in urban built-up areas into EV charging station networks. Our approach integrates perspectives from operators, the power grid, and users, employing multi-objective optimization and the NSGA-III algorithm. By analyzing grid-based charging demand, we construct a cost-minimization model to determine the optimal layout for EV charging station deployment in public parking lots.
The core of our methodology involves a comprehensive model that minimizes social costs, including construction and maintenance expenses, power loss costs, travel time from demand points to EV charging station locations, user queuing time, and overall user expenditures. We apply this model through a case study, demonstrating its effectiveness in saving land resources and improving charging demand fulfillment rates. This research provides a new framework for developing EV charging station infrastructure in densely populated urban environments.
Model Formulation for EV Charging Station Retrofitting
We begin by defining the assumptions underlying our EV charging station layout model. First, we assume that existing parking spaces or lots are available and agreeable to retrofitting into EV charging station facilities. Second, the electrical requirements for these EV charging station installations are met. Third, all candidate parking spaces for retrofitting are considered homogeneous in conditions. Fourth, if no parking lot exists within a grid region, adjacent grids may be considered. Fifth, the number of electric vehicles in the study area remains relatively stable, with minimal influence from external regions. Sixth, vehicles generating charging demands have sufficient remaining battery capacity to reach an EV charging station.
The objective function aims to minimize the total social cost, encompassing five key components: construction and maintenance costs ($C_1$), power loss costs ($C_2$), travel time costs from demand points to EV charging station locations ($C_3$), user queuing time costs at EV charging station facilities ($C_4$), and user expense costs ($C_5$). The overall objective is expressed as:
$$ Z = \min(C_1 + C_2 + C_3 + C_4 + C_5) $$
The construction and maintenance cost for EV charging station retrofitting includes initial investment, equipment configuration, and ongoing maintenance. It is formulated as:
$$ C_1 = \sum_{k \in K} \left[ f(A_k) \cdot \frac{r_0 \cdot (1 + r_0)^{m_s}}{(1 + r_0)^{m_s} – T} + g(A_k) \right] $$
where:
$$ f(A_k) = C_q \cdot A_k + h \cdot A_k^2 $$
$$ g(A_k) = x \cdot f(A_k) $$
Here, $f(A_k)$ represents the fixed investment for retrofitting candidate EV charging station site $k$, $A_k$ is the number of charging piles at site $k$, $g(A_k)$ denotes the operation and maintenance costs, $K$ is the set of candidate parking lots for EV charging station retrofitting, $r_0$ is the discount rate, $m_s$ is the depreciation period, $C_q$ is the unit price of DC fast-charging facilities, $h$ is an investment coefficient, and $x$ is a proportionality coefficient.
Power loss costs account for energy dissipation during charging at EV charging station points, including line losses and battery utilization losses:
$$ C_2 = 365 \cdot q_1 \cdot A_m \cdot \omega_{CG} \cdot (C_l + C_w) $$
$$ C_w = q \cdot (1 – \eta) $$
where $q_1$ is the cost per kWh of power loss, $A_m$ is the number of charging piles in region $m$, $\omega_{CG}$ is the turnover rate of EV charging station piles, $C_l$ is the line loss per charging facility, $C_w$ is the battery utilization loss, $q$ is the electricity required per fast-charging session, and $\eta$ is the battery utilization rate of electric vehicles.
Travel time costs from demand points to EV charging station locations are calculated based on the distance from grid centroids to candidate sites:
$$ C_3 = 365 \cdot \sum_{k \in K} \left[ \frac{1}{v_{veh}} \cdot \gamma + Q_1 \cdot C_q \cdot A_k \cdot \lambda \cdot d_k \right] $$
where $v_{veh}$ is the average speed of electric vehicles in urban areas, $\gamma$ is the urban travel time cost coefficient, $Q_1$ is the electricity consumption per kilometer driven, $C_q$ is the electricity price for charging, $\lambda$ is the road non-linear coefficient, and $d_k$ is the straight-line distance from the demand point to candidate EV charging station site $k$.
User queuing time costs at EV charging station facilities arise when the number of charging vehicles exceeds available piles:
$$ C_4 = 365 \cdot \gamma \cdot \sum_{k \in K} (W_k \cdot A_k) $$
where $W_k$ is the expected waiting time for users at candidate EV charging station site $k$.
User expense costs include charging service fees and parking fees during charging sessions at EV charging station locations:
$$ C_5 = 365 \cdot \sum_{k \in K} \left[ A_k \cdot \omega_{CG} \cdot (C_{CG} + C_{PA,k}) \right] $$
where $C_{CG}$ is the charging price per vehicle per session, and $C_{PA,k}$ is the parking fee at site $k$ during charging time.
Constraints for EV Charging Station Deployment
We impose constraints to ensure practical and efficient EV charging station deployment. The number of charging facilities must at least meet the peak charging demand within a specified period, and the service level should exceed 0.8. The constraints are formulated as:
$$ Q_{m,\max}(\Delta t = 2) = \frac{2}{q} \leq A_m \leq P_A, \quad m \in M $$
$$ A_m \geq \frac{Q_m}{0.8 \cdot \omega_{CG} \cdot q} $$
where $Q_{m,\max}(\Delta t = 2)$ is the peak charging demand over two consecutive hours, $P_A$ is the number of existing parking spaces in region $m$, and $Q_m$ is the total charging demand in region $m$.
Additionally, the travel time from demand points to EV charging station sites must not exceed a maximum threshold:
$$ 0 \leq t \leq \frac{d_{\max}}{v_{veh}} $$
where $d_{\max}$ is the maximum distance from a demand point to the grid boundary.
Solution Using NSGA-III Algorithm
To solve the EV charging station layout model, we employ the NSGA-III algorithm, which is well-suited for multi-objective optimization. The algorithm begins by initializing parameters and generating a set of uniformly distributed reference points. The offspring population $Q_t$ is combined with the parent population $P_t$ to form $R_t = Q_t \cup P_t$, resulting in a population size of $2N$. Non-dominated sorting is applied to $R_t$, dividing it into layers $(F_1, F_2, \ldots, F_i)$. Selection starts from $F_1$ until the population size reaches $N$, with further screening based on reference points to include elite individuals in $P_{t+1}$. The process repeats until termination conditions are met, outputting the optimal solution set for EV charging station layout.
Key steps include linear crossover for genetic operations:
$$ X_{\text{new}} = \lambda \cdot X_1 + (1 – \lambda) \cdot X_2, \quad \forall \lambda \in [0,1] $$
and Gaussian mutation to maintain population diversity:
$$ X’_{id} \leftarrow G(X_{id}, 1/D) $$
where $X_{id}$ is the gene value before mutation, and $X’_{id}$ is the new gene value after mutation.
| Candidate Site | Parking Capacity (vehicles) | Turnover Rate | Average Parking Duration (h) | Parking Price (USD/h) | Distance to Demand Point (m) |
|---|---|---|---|---|---|
| Site 1 | 240 | 2.9 | 7.5 | 0 | 387 |
| Site 2 | 65 | 3.1 | 6.8 | 5 | 480 |
| Site 3 | 350 | 2.8 | 7.4 | 2 | 373 |
| Site 4 | 150 | 5.9 | 3.6 | 3 | 518 |
| Site 5 | 270 | 4.2 | 5.1 | 4 | 164 |
| Site 6 | 400 | 5.8 | 3.2 | 2 | 226 |
| Site 7 | 210 | 3.5 | 4.2 | 2 | 100 |
| Site 8 | 55 | 5.4 | 3.8 | 2 | 520 |
Case Study and Results
We conducted a case study in a built-up urban area, divided into 25 grid regions of 1000 m × 1000 m. Existing public EV charging station facilities were located in 11 grids, with significant unmet demand in others. Charging demand was predicted using a grid-based model, outputting 24-hour demand distributions for grids without EV charging station infrastructure. The total daily charging demand and peak demand were visualized through heat maps, identifying high-demand areas such as commercial centers and transportation hubs.
For instance, Grid 13 had a total daily charging demand of 4,350 kWh, with a peak demand of 620 kWh during hours 17 and 18. We evaluated 8 candidate public parking lots for EV charging station retrofitting in this grid, with a total of 1,740 parking spaces and an average utilization rate of 81.16%. The average parking fee was 2.5 USD/h. Distances from the grid centroid (demand point) to candidate EV charging station sites were calculated using geographical coordinates.
Using the NSGA-III algorithm, we set parameters as follows:
| Parameter | Description | Value |
|---|---|---|
| NIND | Initial population size | 200 |
| MAXGEN | Maximum generations | 800 |
| px | Crossover probability | 0.75 |
| pm | Mutation probability | 0.1 |
| GGAP | Generation gap | 0.95 |
Input data included a discount rate $r_0$ of 30%, depreciation period $m_s$ of 5 years, charging turnover rate $\omega_{CG}$ of 6, charging price $C_{CG}$ of 50 USD per session, electricity per charging session $q$ of 40 kWh, average vehicle speed $v_{veh}$ of 40 km/h, non-linear coefficient $\lambda$ of 1, time cost coefficient $\gamma$ of 1.79 USD/h, electricity consumption $Q_1$ of 0.17 kWh/km, electricity price $C_q$ of 1.8 USD/kWh, and expected waiting time $W_k$ of 0.1 h.
The optimization results indicated that the optimal EV charging station layout involved retrofitting 98 charging piles across four sites: Site 3 (8 piles), Site 4 (37 piles), Site 6 (31 piles), and Site 7 (22 piles). The total minimized cost was 5,864.32 thousand USD. This configuration met the total and peak charging demands while minimizing social costs. The iterative process converged after 800 generations, demonstrating the efficiency of the NSGA-III algorithm for EV charging station planning.
Conclusion
Our study presents a comprehensive model for optimizing EV charging station deployment in urban public parking lots, considering land resource constraints, grid-based charging demand, and multi-stakeholder costs. The model minimizes social costs, including construction, power loss, travel time, queuing time, and user expenses. Through a case study, we demonstrated that this approach can save approximately 384 m² of land per large-scale EV charging station and increase charging demand fulfillment by over 10%. This strategy supports sustainable urban development and the widespread adoption of electric vehicles. Future work could explore the optimal mix of fast and slow charging piles at EV charging station facilities to enhance economic and convenience factors.