With the rapid proliferation of battery electric vehicles globally, the planning and deployment of charging and swapping infrastructure have emerged as critical bottlenecks impacting the sustainable development of the electric transportation sector. The inherent autonomy and diversity in user charging and swapping demands present significant challenges for grid integration and resource optimization. Traditional planning approaches often rely on probabilistic forecasts of battery electric vehicle load, which can lead to substantial prediction errors and suboptimal infrastructure allocation, resulting in issues such as uneven station distribution, inefficient resource utilization, and prolonged user waiting times. To address these challenges, this work proposes a novel framework that integrates a reservation-based network access mode for battery electric vehicles with an optimization model for configuring multiple types of charging and swapping equipment. This approach aims to accurately capture user demand, reduce forecasting uncertainty, and meet the diverse needs of battery electric vehicle users through an optimal mix of equipment with different power ratings.
The core innovation lies in the reservation mechanism, which allows battery electric vehicle users to schedule their charging or battery swapping sessions in advance via a mobile application. This system leverages real-time and historical data, including traffic conditions from GPS navigation layers, to recommend the most cost-effective and time-efficient station and service type. By adopting this mode, operators can gain precise insights into the spatio-temporal distribution of demand, enabling more informed planning decisions. Furthermore, to cater to the variety of user preferences—such as desired dwell time, initial state of charge (SOC), and cost sensitivity—the model incorporates four primary types of charging and swapping equipment: slow charging piles, fast charging piles, super-fast charging piles, and battery swapping stations. The optimization problem is formulated to minimize the annualized total social cost, encompassing investment, operation, maintenance, and grid loss costs, while satisfying technical constraints of the distribution network and user accessibility limits.
The proposed mathematical model is a mixed-integer nonlinear programming (MINLP) problem, which is transformed into a mixed-integer second-order cone programming (MISOCP) model via second-order cone relaxation (SOCR) techniques for computational tractability. A case study based on realistic geographic and traffic data from an urban district, coupled with a standard IEEE 33-node distribution system and distributed photovoltaic generation, validates the model’s effectiveness. Multiple configuration scenarios are analyzed to compare the trade-offs between cost, equipment mix, and service quality. The results demonstrate that the reservation-based mode significantly enhances planning accuracy and that a diversified portfolio of charging and swapping equipment can better serve the heterogeneous needs of battery electric vehicle users, though optimal configurations depend on balancing economic objectives with user experience.
Reservation-Based Charging and Swapping Mode for Battery Electric Vehicles
The reservation-based mode establishes a tri-layer system framework integrating the power network layer, the GPS navigation and traffic information layer, and the charging/swapping equipment operation layer. Communication via 5G or WiFi networks enables data exchange, and cloud computing provides optimized station selection for battery electric vehicle users. The operational workflow is as follows:
- User Request Initiation: When the battery state of charge (SOC) of a battery electric vehicle falls below a user-defined threshold, the user submits a reservation request through a mobile application, specifying the desired service time and any preferences.
- Data Transmission: The application transmits key parameters—including the current vehicle SOC, real-time location, and requested service time window—to a cloud-based management platform.
- Station Options Generation: The cloud platform identifies all feasible charging and swapping stations within a user-defined maximum travel time based on the vehicle’s location and service type compatibility.
- Traffic-Aware Routing: The GPS navigation layer provides historical and real-time traffic speed data for relevant road segments. The average traffic speed $$ \tilde{v}_{mn,k} $$ for a road segment $$ L_{mn} $$ at time interval $$ k $$ is estimated from historical data of multiple battery electric vehicles:
$$ \tilde{v}_{mn,k} = \frac{1}{N_{\text{res},k}} \sum_{w=1}^{N_{\text{res},k}} v_{w,mn,k} $$
where $$ v_{w,mn,k} $$ is the historical speed of battery electric vehicle $$ w $$ on segment $$ L_{mn} $$ at time $$ k $$, and $$ N_{\text{res},k} $$ is the number of battery electric vehicles recorded on that segment during that period. - Optimal Station and Service Selection: The cloud platform solves a cost-minimization problem to recommend the specific station and the most suitable type of charging or swapping service. The total cost considered includes the electricity cost, the travel time cost (which depends on distance and traffic speed), and any potential waiting costs.
- Service Execution: The user proceeds to the recommended station at the appointed time for the reserved service, minimizing queuing and ensuring service availability.
This mode transforms uncertain, stochastic demand into scheduled, manageable loads. By analyzing historical reservation data, operators can forecast future demand patterns for battery electric vehicles with greater accuracy, forming a reliable basis for infrastructure planning.
Modeling Multi-Type Charging and Swapping Equipment
To address diverse user needs, four distinct types of charging and swapping equipment are considered, each with different power ratings, service times, and cost structures. The characteristics are summarized in the table below.
| Equipment Type | Representative Model / Standard | Rated Power (kW) | Typical Service Time | Annualized Investment Cost per Unit ($) | Annualized O&M Cost per Unit ($/year) | Economic Lifetime (years) |
|---|---|---|---|---|---|---|
| Slow Charging Pile (AC) | Smart AC Charger (e.g., Xcharge-C1 type) | $$ P_{\text{EVCP}}^{\text{slow}} = 7 $$ | 5–10 hours | 380 | 80 | 15 |
| Fast Charging Pile (DC) | Smart DC Charger (e.g., Xcharge-C6 type) | $$ P_{\text{EVCP}}^{\text{fast}} = 60 $$ | 1–2 hours | 1500 | 120 | 15 |
| Super-Fast Charging Pile (DC) | Ultra-Fast DC Charger (e.g., Xcharge-C9 Mini type) | $$ P_{\text{EVCP}}^{\text{super}} = 120 $$ | 15–30 minutes | 3600 | 280 | 15 |
| Battery Swapping Station | Standard Battery Pack (e.g., for Nio ET5, 100 kWh) | — (Instant Swap) | 5–10 minutes | 1200 (per battery pack) | 180 (per pack per year) | 10 |
The choice of service type for a given battery electric vehicle is determined by the user’s intended dwell time $$ T_{\text{Stay,EV},n} $$ and the initial battery SOC $$ \text{SOC}_n $$, with the goal of maximizing energy replenishment within the available time. The selection logic is formalized as follows:
For a battery electric vehicle $$ n $$ with battery capacity $$ \text{Cap}_n $$, the required energy is $$ \text{Cap}_n (1 – \text{SOC}_n) $$. The vehicle selects the service type $$ P_{\text{EV},n} $$ according to:
$$
P_{\text{EV},n} =
\begin{cases}
P_{\text{EVCP}}^{\text{slow}}, & \text{if } \text{Cap}_n (1 – \text{SOC}_n) \leq P_{\text{EVCP}}^{\text{slow}} T_{\text{Stay,EV},n} \\
P_{\text{EVCP}}^{\text{fast}}, & \text{if } P_{\text{EVCP}}^{\text{slow}} T_{\text{Stay,EV},n} < \text{Cap}_n (1 – \text{SOC}_n) \leq P_{\text{EVCP}}^{\text{fast}} T_{\text{Stay,EV},n} \\
P_{\text{EVCP}}^{\text{super}}, & \text{if } P_{\text{EVCP}}^{\text{fast}} T_{\text{Stay,EV},n} < \text{Cap}_n (1 – \text{SOC}_n) \leq P_{\text{EVCP}}^{\text{super}} T_{\text{Stay,EV},n} \\
\text{Battery Swapping}, & \text{if } \text{Cap}_n (1 – \text{SOC}_n) > P_{\text{EVCP}}^{\text{super}} T_{\text{Stay,EV},n}
\end{cases}
$$
This rule ensures that users with short dwell times opt for higher-power charging or swapping to achieve sufficient recharge, while those with longer dwell times may choose slower, often cheaper, options. The SOC is assumed to be uniformly distributed between 0 and 1 for the fleet of battery electric vehicles, and a vehicle is considered sufficiently charged if $$ \text{SOC}_n \geq 0.9 $$.
Mathematical Formulation for Optimal Configuration
The optimization model aims to determine the optimal locations and quantities of each type of charging and swapping equipment within a distribution network, considering the reservation-based demand from battery electric vehicles. The objective is to minimize the annualized total social cost, subject to power flow constraints, equipment constraints, and user access constraints.
Objective Function
The total annualized cost $$ C_O $$ comprises investment cost $$ C_{\text{Inv}} $$, operation and maintenance (O&M) cost $$ C_{\text{Ope}} $$, and the cost of energy losses in the distribution network $$ C_{\text{Loss}} $$:
$$
\min C_O = C_{\text{Inv}} + C_{\text{Ope}} + 91.25 \sum_{s=1}^{4} \sum_{k=1}^{24} C_{\text{Loss}}^{s,k}
$$
The factor 91.25 represents the approximate number of days per season (365/4), used to scale the daily loss cost to an annual basis per season. Each season $$ s $$ and time interval $$ k $$ models a representative snapshot.
Investment Cost: This includes the annualized cost of charging piles and spare batteries for swapping stations. Using capital recovery factors, the investment cost for equipment at candidate nodes $$ i \in \Omega_{\text{bus}} $$ is:
$$
C_{\text{Inv}} = r_{\text{EVCP}} \sum_{i \in \Omega_{\text{bus}}} \left( c_{\text{EVCP}}^{\text{slow}} N_{\text{EVCP},i}^{\text{slow}} + c_{\text{EVCP}}^{\text{fast}} N_{\text{EVCP},i}^{\text{fast}} + c_{\text{EVCP}}^{\text{super}} N_{\text{EVCP},i}^{\text{super}} \right) + r_{\text{ESS}} \sum_{k=1}^{24} \sum_{i \in \Omega_{\text{bus}}} \left( \theta_{\text{ESS}} N_{\text{ESS},i}^{k} \right)
$$
where $$ N_{\text{EVCP},i}^{\text{slow}}, N_{\text{EVCP},i}^{\text{fast}}, N_{\text{EVCP},i}^{\text{super}} $$ are integer variables for the number of each charger type at node $$ i $$; $$ N_{\text{ESS},i}^{k} $$ is the number of battery packs needed at swapping station $$ i $$ at time $$ k $$ (to ensure a 24-hour cycle); $$ c $$ and $$ \theta $$ are unit costs; and $$ r_{\text{EVCP}} $$ and $$ r_{\text{ESS}} $$ are annualization factors calculated as $$ r = \frac{\alpha (1+\alpha)^y}{(1+\alpha)^y – 1} $$, with discount rate $$ \alpha = 0.03 $$ and equipment lifetimes $$ y_{\text{EVCP}} = 15 $$ years, $$ y_{\text{ESS}} = 10 $$ years.
Operation and Maintenance Cost: Proportional to the installed capacity or usage:
$$
C_{\text{Ope}} = \sum_{i \in \Omega_{\text{bus}}} \left( \varepsilon_{\text{EVCP}}^{\text{slow}} P_{\text{EVCP},i}^{\text{slow}} + \varepsilon_{\text{EVCP}}^{\text{fast}} P_{\text{EVCP},i}^{\text{fast}} + \varepsilon_{\text{EVCP}}^{\text{super}} P_{\text{EVCP},i}^{\text{super}} \right) + \sum_{k=1}^{24} \sum_{i \in \Omega_{\text{bus}}} \left( \varepsilon_{\text{ESS}} P_{\text{ESS},i}^{k,\text{rated}} \right)
$$
Here, $$ \varepsilon $$ are unit O&M costs, $$ P_{\text{EVCP},i} $$ are the aggregated power ratings of installed chargers (e.g., $$ P_{\text{EVCP},i}^{\text{slow}} = P_{\text{EVCP}}^{\text{slow}} \times N_{\text{EVCP},i}^{\text{slow}} $$), and $$ P_{\text{ESS},i}^{k,\text{rated}} $$ is the total capacity of battery packs at the swapping station.
Network Loss Cost: Based on the resistive losses in distribution lines:
$$
C_{\text{Loss}}^{s,k} = c_{\text{Loss}} \sum_{i \in \Omega_{\text{bus}}} \sum_{j \in \Omega_i} \left( I_{i,j}^{s,k} \right)^2 R_{i,j} \Delta t
$$
where $$ c_{\text{Loss}} = 80 \$/\text{MWh} $$, $$ I_{i,j}^{s,k} $$ is the current magnitude on branch $$ ij $$ at season $$ s $$ and time $$ k $$, $$ R_{i,j} $$ is the branch resistance, and $$ \Delta t $$ is the time interval duration (e.g., 1 hour).
Constraints
1. Distribution Network Power Flow Constraints: The DistFlow branch equations are used to model radial distribution networks. For each branch $$ (i,j) $$ and time snapshot:
$$
\begin{align}
\sum_{i \in \Pi_j} \left[ P_{i,j} – (I_{i,j})^2 R_{i,j} \right] &= \sum_{k \in \Omega_j} P_{j,k} + P_j \\
\sum_{i \in \Pi_j} \left[ Q_{i,j} – (I_{i,j})^2 X_{i,j} \right] &= \sum_{k \in \Omega_j} Q_{j,k} + Q_j \\
U_j^2 &= U_i^2 – 2(R_{i,j} P_{i,j} + X_{i,j} Q_{i,j}) + (I_{i,j})^2 (R_{i,j}^2 + X_{i,j}^2)
\end{align}
$$
where $$ P_{i,j}, Q_{i,j} $$ are active and reactive power flows; $$ U_i $$ is the voltage magnitude at node $$ i $$; $$ \Pi_j $$ and $$ \Omega_j $$ are sets of parent and child nodes, respectively. The net load $$ P_j $$ includes conventional load, photovoltaic generation (if present), and the demand from battery electric vehicle charging/swapping at node $$ j $$.
2. Voltage and Current Limits:
$$
\begin{align}
U_{i,\min} &\leq U_i \leq U_{i,\max} \\
I_{i,j} &\leq I_{i,j,\max} \\
(I_{i,j})^2 &= \frac{P_{i,j}^2 + Q_{i,j}^2}{U_i^2}
\end{align}
$$
3. Charging and Swapping Demand Modeling from Battery Electric Vehicles: For each season $$ s $$, time $$ k $$, and candidate station node $$ c $$, the aggregated charging power for each type is:
$$
P_{\text{EVCP},c,s,k}^{\text{type}} = P_{\text{EVCP}}^{\text{type}} \sum_{w \in \Omega_{\text{EV},c,s,k}^{\text{type}}} B_{\text{EV},c,s,k,w}^{\text{type}}, \quad \forall \text{type} \in \{\text{slow, fast, super}\}
$$
where $$ \Omega_{\text{EV},c,s,k}^{\text{type}} $$ is the set of battery electric vehicles that have reserved type “type” at node $$ c $$, and $$ B_{\text{EV},c,s,k,w}^{\text{type}} $$ is a binary variable indicating whether vehicle $$ w $$ chooses that service. Similarly, for battery swapping, the number of swaps demanded at node $$ c $$ is $$ \sum_{w} B_{\text{EV},c,s,k,w}^{\text{swap}} $$.
4. Equipment Quantity Constraints: The number of installed chargers must meet the maximum concurrent demand at each location:
$$
N_{\text{EVCP},c}^{\text{type}} \geq \max_{s,k} \left( \sum_{w \in \Omega_{\text{EV},c,s,k}^{\text{type}}} B_{\text{EV},c,s,k,w}^{\text{type}} \right), \quad \forall c, \forall \text{type}
$$
For battery swapping stations, the total number of battery packs must suffice for the daily cumulative demand due to the 24-hour cycle:
$$
N_{\text{ESS},c} \geq \sum_{k=1}^{24} \sum_{w \in \Omega_{\text{EV},c,s,k}^{\text{swap}}} B_{\text{EV},c,s,k,w}^{\text{swap}}, \quad \forall c, \forall s
$$
5. User Access and Station Selection Constraints: A battery electric vehicle $$ w $$ can only select a station $$ c $$ if the travel time from its origin, based on historical traffic speeds, does not exceed a maximum acceptable time $$ T_w^{\max} $$ (e.g., 15 minutes). The travel time to station $$ c $$ is $$ \frac{\text{dis}(\text{pos}_{\text{EV},w}, \text{pos}_c)}{\tilde{v}_{\text{EV}-c,k}} $$, where $$ \tilde{v}_{\text{EV}-c,k} $$ is the average traffic speed on the route at time $$ k $$. This is enforced by:
$$
B_{\text{EV},c,s,k,w}^{\text{type}} = 1 \Rightarrow \frac{\text{dis}(\text{pos}_{\text{EV},w}, \text{pos}_c)}{\tilde{v}_{\text{EV}-c,k}} \leq T_w^{\max}, \quad \forall c, w, s, k, \text{type}
$$
Each vehicle must choose exactly one station and one service type per reservation:
$$
\sum_{c \in \Omega_c^{\text{feas}}(w)} \sum_{\text{type}} B_{\text{EV},c,s,k,w}^{\text{type}} = 1, \quad \forall w, s, k
$$
where $$ \Omega_c^{\text{feas}}(w) $$ is the set of stations within the maximum travel time for vehicle $$ w $$.
Model Transformation and Solution via Second-Order Cone Relaxation
The original model contains non-convex constraints due to the quadratic terms in the power flow equations (e.g., $$ (I_{i,j})^2 $$ and $$ U_i^2 $$). To obtain a computationally tractable formulation, a second-order cone relaxation (SOCR) is applied. Define new variables:
$$
\hat{U}_i = U_i^2, \quad \hat{I}_{i,j} = I_{i,j}^2
$$
The power flow equations become linear in these new variables. The key non-convex constraint $$ (I_{i,j})^2 = (P_{i,j}^2 + Q_{i,j}^2) / U_i^2 $$ is relaxed to a second-order cone constraint:
$$
\left\| \begin{bmatrix} 2 P_{i,j} \\ 2 Q_{i,j} \\ \hat{I}_{i,j} – \hat{U}_i \end{bmatrix} \right\|_2 \leq \hat{I}_{i,j} + \hat{U}_i
$$
This relaxation is exact for radial distribution networks under typical operating conditions. The resulting model is a Mixed-Integer Second-Order Cone Programming (MISOCP) problem, which can be solved efficiently using commercial solvers like Gurobi or CPLEX. The overall transformed optimization problem is:
$$
\begin{aligned}
& \min \; C_O = C_{\text{Inv}} + C_{\text{Ope}} + 91.25 \sum_{s,k} C_{\text{Loss}}^{s,k} \\
& \text{subject to:} \\
& \quad \text{Linearized DistFlow constraints with } \hat{U}_i, \hat{I}_{i,j} \\
& \quad \text{Second-order cone constraints for current-power relations} \\
& \quad \text{Voltage limits: } U_{i,\min}^2 \leq \hat{U}_i \leq U_{i,\max}^2 \\
& \quad \text{Current limits: } \hat{I}_{i,j} \leq (I_{i,j,\max})^2 \\
& \quad \text{Equipment quantity and demand constraints} \\
& \quad \text{User access constraints with binary variables } B_{\text{EV},c,s,k,w}^{\text{type}} \\
& \quad \text{Integer constraints for charger counts } N_{\text{EVCP},i}^{\text{type}}
\end{aligned}
$$
Case Study and Numerical Analysis
A comprehensive case study is conducted to validate the proposed model, using realistic data from an urban district. The distribution network is the standard IEEE 33-bus system, with a base voltage of 12.66 kV and apparent power base of 100 MVA. Voltage limits are set at 0.95–1.05 p.u., and branch current limits are 400 A. Candidate nodes for installing charging and swapping equipment are {5, 8, 14, 17, 20, 22, 26, 30}. Distributed photovoltaic (PV) units are assumed at nodes 7 and 24. The conventional load profiles for residential, commercial, and office areas are derived from historical data, with seasonal variations as shown in previous figures.
The fleet consists of 500 battery electric vehicles, each with a battery capacity of 100 kWh (modeled similar to a Nio ET5). Their reservation requests are generated based on realistic travel patterns, with SOC uniformly distributed between 0.2 and 0.9. The maximum acceptable travel time $$ T_w^{\max} $$ is 15 minutes for all users. Traffic speeds are categorized into three levels (low congestion: 35 km/h, medium: 25 km/h, high: 15 km/h) depending on time of day and area type (residential, commercial, office), as summarized in the following table.
| Area Type | High Congestion (15 km/h) | Medium Congestion (25 km/h) | Low Congestion (35 km/h) |
|---|---|---|---|
| Residential | 07:00–09:00, 18:00–21:00 | 09:00–18:00 | 00:00–07:00, 21:00–24:00 |
| Commercial | 17:00–21:00 | 10:00–17:00, 21:00–24:00 | 00:00–10:00 |
| Office | 08:00–10:00, 17:00–20:00 | 10:00–17:00 | 00:00–08:00, 20:00–24:00 |
To analyze the impact of equipment diversity, seven configuration scenarios are defined, each allowing a different subset of the four equipment types. The scenarios are labeled as follows:
| Scenario | Slow Charging Piles | Fast Charging Piles | Super-Fast Charging Piles | Battery Swapping | Description |
|---|---|---|---|---|---|
| Scenario 1 | ✓ | ✓ | ✓ | ✓ | All four types available |
| Scenario 2 | ✓ | ✓ | ✓ | ✗ | No battery swapping |
| Scenario 3 | ✓ | ✓ | ✗ | ✓ | No super-fast chargers |
| Scenario 4 | ✗ | ✓ | ✓ | ✗ | Only fast and super-fast chargers |
| Scenario 5 | ✓ | ✓ | ✗ | ✗ | Only slow and fast chargers |
| Scenario 6 | ✓ | ✗ | ✗ | ✗ | Only slow chargers |
| Scenario 7 | ✗ | ✓ | ✗ | ✗ | Only fast chargers |
The model is implemented in MATLAB using the YALMIP toolbox and solved with the Gurobi solver. The optimization determines the optimal number of each equipment type at each candidate node, the scheduling of battery electric vehicles to stations, and the resulting network operation.
Results and Discussion
The optimal equipment configurations for each scenario are summarized in the table below, showing the total number of each type deployed across all nodes.
| Scenario | Slow Chargers | Fast Chargers | Super-Fast Chargers | Battery Packs | Total Equipment Count | Investment Cost ($) | O&M Cost ($) | Loss Cost ($) | Total Annual Cost ($) |
|---|---|---|---|---|---|---|---|---|---|
| Scenario 1 | 11 | 27 | 3 | 3 | 44 | 5,069.40 | 6,390 | 68.42 | 11,527.82 |
| Scenario 2 | 11 | 27 | 5 | 0 | 43 | 5,250.49 | 5,430 | 71.63 | 10,752.12 |
| Scenario 3 | 11 | 27 | 0 | 5 | 43 | 4,446.07 | 6,630 | 63.86 | 11,139.93 |
| Scenario 4 | 0 | 32 | 5 | 0 | 37 | 5,528.59 | 5,040 | 78.97 | 10,647.56 |
| Scenario 5 | 11 | 27 | 0 | 0 | 38 | 3,868.34 | 4,350 | 66.64 | 8,284.98 |
| Scenario 6 | 31 | 0 | 0 | 0 | 31 | 986.77 | 2,790 | 51.09 | 3,827.86 |
| Scenario 7 | 0 | 30 | 0 | 0 | 30 | 3,895.15 | 3,720 | 71.55 | 7,686.69 |
Several key observations emerge from the results. First, the total annual cost is lowest in Scenario 6 (only slow chargers) at $3,827.86, and highest in Scenario 1 (all four types) at $11,527.82. This highlights the significant cost premium associated with deploying high-power and battery swapping infrastructure. However, cost alone does not capture service quality. Scenarios with limited equipment types may force battery electric vehicle users to accept longer charging times or travel farther, reducing convenience.
Second, comparing Scenarios 2 and 3 to Scenario 1 shows that removing one high-cost option (battery swapping or super-fast chargers) reduces total cost by approximately 6–7%, while the total equipment count remains similar. This indicates that the demand from battery electric vehicles is flexible and can be shifted to other available types without drastically increasing the number of units, thanks to the reservation system’s ability to optimize station assignment.
Third, Scenarios 4 and 5, which offer only two types, show further cost reductions (up to 28% lower than Scenario 1). In Scenario 5 (slow and fast chargers), the fast chargers bear the majority of demand, as they provide a balance between speed and cost. The absence of super-fast chargers and swapping stations means that users with very short dwell times may experience inconvenience, but the model compensates by assigning them to fast chargers and potentially adjusting travel choices.
Fourth, the network loss cost is relatively small compared to investment and O&M costs, but it varies across scenarios due to differences in load distribution. Scenarios with more high-power chargers (e.g., Scenario 4) tend to have slightly higher losses because of concentrated high loads at certain nodes.
To further illustrate the trade-offs, consider the user perspective. The reservation system ensures that each battery electric vehicle is assigned to a feasible station within the travel time limit. The average travel time and waiting time are minimized by the optimization. In scenarios with more equipment types, users have a higher likelihood of finding a suitable service matching their time constraints, thus improving the overall charging experience for battery electric vehicle owners.
The spatial distribution of equipment also varies. For instance, in Scenario 1, nodes with high conventional load (e.g., commercial areas) tend to receive more fast and super-fast chargers to serve users with short dwell times, while residential nodes get more slow chargers. This aligns with the typical patterns of battery electric vehicle usage.
Sensitivity and Robustness Considerations
While the base case assumes perfect knowledge of reservation requests, in practice, uncertainties exist in battery electric vehicle arrival times, SOC levels, and traffic conditions. The model can be extended to a two-stage stochastic or robust optimization framework to handle such uncertainties. For example, the demand from battery electric vehicles could be modeled as a set of scenarios with probabilities, and the equipment configuration decisions could be made in the first stage, while operation and scheduling decisions adapt in the second stage. The core SOCR structure remains applicable, but the problem size increases.
Another sensitivity aspect is the impact of distributed PV generation. The presence of PV reduces the net load during sunny periods, potentially allowing more charging of battery electric vehicles without overloading the grid. In our case, the PV generation at nodes 7 and 24 helps shave peak loads, indirectly influencing the optimal placement of chargers by reducing congestion on certain branches.
The discount rate $$ \alpha $$ and equipment lifetimes also affect the annualized costs. A sensitivity analysis on these parameters would show how the optimal mix shifts with economic conditions. Generally, a higher discount rate favors cheaper, shorter-lived equipment, while a lower rate makes high-investment options more attractive over the long term.
Conclusion
This work presents a comprehensive optimization framework for configuring multi-type charging and swapping equipment for battery electric vehicles under a reservation-based access mode. The integration of reservation systems allows for precise demand capture and reduced forecasting errors, while the inclusion of multiple equipment types—slow, fast, super-fast chargers, and battery swapping stations—caters to the diverse needs of battery electric vehicle users. The mathematical model, formulated as a mixed-integer second-order cone program, efficiently balances investment, operation, maintenance, and grid loss costs against user accessibility constraints.
The case study demonstrates that while offering a full suite of charging and swapping options maximizes user convenience, it comes at a significant economic cost. Conversely, configurations with only one or two equipment types can drastically reduce costs but may compromise service quality for some battery electric vehicle users. The optimal strategy likely lies in a balanced mix that aligns with the specific demographics, travel patterns, and grid conditions of the service area. The reservation mechanism proves invaluable in optimizing resource utilization and minimizing user wait times, making it a promising approach for future infrastructure planning.
Future research could incorporate uncertainty in battery electric vehicle demand and renewable generation, consider dynamic pricing mechanisms, and explore the integration of vehicle-to-grid (V2G) capabilities. Additionally, the model could be extended to multi-objective optimization, explicitly trading off cost, user satisfaction, and environmental impacts. As the adoption of battery electric vehicles accelerates globally, such advanced planning tools will be essential for building efficient, resilient, and user-friendly charging and swapping networks.