Introduction As global climate issues grow increasingly severe and the environmental pollution caused by traditional fuel vehicles becomes more evident, electric vehicles (EVs) have gained widespread favor worldwide as clean and efficient transportation. However, when a large number of EVs are connected to the power grid as random loads, their inherent volatility and disorder pose significant challenges to grid stability. Existing scheduling schemes often lack comprehensive analysis of both user and grid demands, failing to achieve efficient and orderly EV charging. To address this, I propose an orderly scheduling optimization method for EVs that integrates a road-electricity coupling model, aiming to provide theoretical and practical guidance for EV charging management while promoting sustainable development.
1. EV Charging Path Modeling
1.1 Shortest Charging Path Prediction Model Most lead-acid batteries perform optimally with a discharge depth of approximately 80%, meaning charging is ideal when the battery state of charge (SOC) drops to 20%. When an EV’s battery level is ≤20%, it must travel to a charging station. The optimal path analysis focuses on the distance between the EV and charging stations, using battery power as the decision criterion.
Consider a transportation network where an EV at point E on road BC must choose the nearest charging station. Let \(l_{ba}\) be the distance from B to A (charging station), \(l_{cd}\) the distance from C to D (charging station), and x the distance from E to B (\(0 ≤ x ≤ l_{bc}\)). The total travel distance \(M(x)\) is the minimum of two paths:\(M(x) = \min \left\{ x + l_{ba}, \, l_{bc} – x + l_{cd} \right\}, \quad 0 \leq x \leq l_{bc} \quad \text{(1)}\) This model integrates traffic network topology, charging station distribution, and EV location to predict the shortest charging path.
1.2 Road Section Weighting Model Combining Traffic and Power Grid Information To real-time optimize paths, I introduce the average real-time speed of each road section for weighting:\(w_2 = \frac{w_1}{v_{(ab, t)}} \quad \text{(2)}\) Here, \(w_1\) is the actual speed, \(w_2\) is the weighted speed, and \(v_{(ab, t)}\) is the average speed of road section ab at time t. Using the Floyd algorithm, insert an intermediate node into the path. If the total distance via the intermediate node (\(l_1\)) is shorter than the direct path (l), the former is chosen, optimizing route efficiency.
2. Optimization of EV Charging Path Model
2.1 Objective Function The goal is to minimize charging-related time and cost. Let \(T_0\) be the time when an EV sends a charging request, and \(t_1\) the travel time to the optimal charging station. The arrival time \(T_{\text{reach}}\) is:\(T_{\text{reach}} = T_0 + t_1 \quad \text{(3)}\) Using the FCFS queuing model, the expected number of vehicles \(a_n(T, T+t)\) arriving at charging station n in interval \((T, T+t)\) is:\(a_n(T, T+t) = \sum_{p \in R} 6 \sum_{i=1}^{t-t} \prod_{j=0}^{j=i-1} \left[ 1 – \psi_{p, t}^{(p)} \right] \cdot \eta_{1, p, i, t}\)\(\eta_{p, p(1), i} = \frac{1}{1, \pi=p(1) \Lambda t_{0, p}(i)} + (i-1) \cdot \sigma \in (T, T+1)\) (Additional queuing model equations follow similarly, adapted from the original.)
2.2 Constraints 2.2.1 User Time Cost The time cost \(C_{\text{time}}\) is calculated as:\(C_{\text{time}} = \varepsilon \sum_{i=1}^{N} \sum_{j=1}^{T} W_{i, j}^{u} q(X_i, t_j) \tau \quad \text{(5)}\) where \(W_{i, j}^{u}\) is the average waiting time at station i during slot j, \(q(X_i, t_j)\) is the traffic flow, \(\tau\) is the simulation duration per slot, and \(\varepsilon = 1.8\) converts time to cost. This must satisfy:\(C_{\text{time}} \leq C_{\text{limit}} \quad \text{(6)}\) where \(C_{\text{limit}}\) is the maximum acceptable time cost.
2.2.2 Power Grid Load The grid’s maximum load \(Q_{\text{stor}}^i\) must exceed 1.2 times the EV load demand \(Q_{\text{sta}}^i\) to allow 20% scheduling reserve:\(Q_{\text{stor}}^i > 1.2 Q_{\text{sta}}^i \quad \text{(7)}\)
2.3 Solution Method: Adaptive Particle Swarm Optimization (APSO) Using APSO, define particles as potential solutions in matrix \(N = (n_1, n_2, \dots, n_N)^T\), where \(n_i = (n_{i1}, n_{i2})\) represents position. Iteratively update particle velocity \(V_a^{b+1}\) and position \(N_a^{b+1}\):\(V_a^{b+1} = \omega V_a^{b} + c_1 r_1 \left( N_a^{b+1} – N_a^{b} \right) + c_2 r_2 \left( N_a^{\text{gbest}} – N_a^{b} \right) \quad \text{(8)}\)\(N_a^{b+1} = N_a^{b} + V_a^{b+1}\) The inertia weight \(\omega\) decreases with iterations:\(\omega(j) = \omega_1 – (\omega_1 – \omega_2) \left( \frac{j}{T_{\text{max}}} \right)^2 \quad \text{(9)}\) Parameters \(s_1(j)\) and \(s_2(j)\) are adjusted using hyperbolic tangent functions to balance local and global search:\(s_1(j) = \tanh \left( -c + 2c \frac{T_{\text{max}} – j}{T_{\text{max}}} \right) \frac{s_{\text{max}} – s_{\text{min}}}{2} + \frac{s_{\text{max}} + s_{\text{min}}}{2} \quad \text{(10)}\)
3. Simulation Results and Analysis 3.1 Simulation Setup Using XA City’s road and grid structure, I built a simulation network with 16 charging stations, each having 80–120 charging spots. The time-of-use electricity price is shown in Table 1.
| Time Period | Price (USD/kWh) |
|---|---|
| Peak (9:00–12:00, 18:00–21:00) | 0.35 |
| Off-peak (23:00–7:00) | 0.15 |
| Normal (others) | 0.25 |
| Table 1. Time-of-Use Electricity Prices |
3.2 Comparison of Scheduling Strategies Three schemes were tested:
- Scheme A: Shortest-distance charging station selection.
- Scheme B: Lowest-price charging station selection.
- Scheme C: Proposed road-electricity coupling model.
At 10:00, Scheme A caused severe congestion at Station 9 (≈300 EVs), while Schemes B and C reduced this to 53.21% and 53.58% of Scheme A’s load, respectively, demonstrating more even distribution. Table 2 shows the variance of charging loads at 12:00:
| Evaluation Index | Scheme A | Scheme B | Scheme C |
|---|---|---|---|
| Variance (MW²) | 1.771 | 1.042 | 0.781 |
| Table 2. Charging Load Variance at 12:00 |
Scheme C’s significantly lower variance confirms its effectiveness in balancing grid load and improving charging efficiency.
4. Conclusion This study presents an EV scheduling optimization method integrating road-electricity coupling, using Floyd algorithm for path planning and APSO for model solution. Simulation results show that the proposed method reduces charging waiting time, balances grid load, and decreases costs compared to traditional strategies. By addressing both user needs and grid stability, this approach supports EV proliferation and sustainable energy management, offering valuable insights for charging infrastructure planning and grid operation.