With the rapid growth of electric vehicle adoption in China, the integration of large-scale electric vehicle charging and discharging demands into the power grid has become a critical challenge. The disordered connection of electric vehicles during peak periods can lead to significant load pressure on the power system, exacerbating peak-valley differences and increasing operational costs. To address these issues, I propose a novel scheduling strategy based on an improved crisscross optimization algorithm under the vehicle-to-grid (V2G) mode. This approach focuses on balancing grid load while minimizing charging costs for electric vehicle users, leveraging the bidirectional energy flow capabilities of V2G technology. By establishing a dual-layer scheduling model and enhancing the optimization process, the method aims to achieve efficient and stable grid operation. In this article, I will detail the methodology, experimental validation, and key findings, supported by mathematical formulations and comparative analyses.
The V2G mode enables electric vehicles to act as distributed energy storage units, allowing them to charge from the grid during off-peak hours and discharge back to the grid during peak demand. This bidirectional interaction helps in flattening the load curve and reducing the reliance on conventional power sources. However, the stochastic nature of electric vehicle charging behaviors, influenced by user travel patterns and battery characteristics, complicates the scheduling process. In China, the expansion of EV infrastructure has highlighted the need for intelligent scheduling solutions that can adapt to dynamic grid conditions. The proposed method addresses this by integrating a dual-layer optimization framework, where the upper layer minimizes the peak-valley difference in grid load, and the lower layer focuses on reducing the charging costs for electric vehicle users. The improved crisscross optimization algorithm, incorporating a roulette wheel selection mechanism, is employed to solve this complex model efficiently.
To model the electric vehicle charging and discharging behavior, I first analyze the statistical distributions of arrival and departure times for electric vehicles. Let \( t_x \) and \( t_y \) represent the arrival and departure times, respectively, which follow normal distributions as given by:
$$ h_s(x) = \begin{cases}
\frac{1}{a_s \sqrt{2\pi}} \exp\left[ -\frac{(x – b_s)^2}{2a_s^2} \right], & \text{if } b_s – 12 < x \leq 24 \\
\frac{1}{a_s \sqrt{2\pi}} \exp\left[ -\frac{(x + 24 – b_s)^2}{2a_s^2} \right], & \text{if } 0 < x \leq b_s – 12
\end{cases} $$
and
$$ h_s(y) = \begin{cases}
\frac{1}{a_e \sqrt{2\pi}} \exp\left[ -\frac{(y – b_e)^2}{2a_e^2} \right], & \text{if } 0 < y \leq b_e + 12 \\
\frac{1}{a_e \sqrt{2\pi}} \exp\left[ -\frac{(y – 24 – b_e)^2}{2a_e^2} \right], & \text{if } b_e + 12 < y \leq 24
\end{cases} $$
where \( a_s \), \( b_s \), \( a_e \), and \( b_e \) are constants derived from empirical data on electric vehicle usage patterns. The charging time \( t_{ij} \) for an electric vehicle is calculated based on the state of charge (SOC) and battery capacity:
$$ t_{ij} = \begin{cases}
\frac{(u_n – u_s) F_s}{P_{\text{charge}} z_p}, & \text{if } u_s > u_n \\
\frac{(u_n – u_s) F_s}{P_{\text{discharge}} z_d}, & \text{if } u_s \leq u_n
\end{cases} $$
Here, \( u_s \) and \( u_n \) denote the initial and desired SOC levels, \( F_s \) is the battery capacity, \( P_{\text{charge}} \) and \( P_{\text{discharge}} \) are the charging and discharging powers, and \( z_p \) and \( z_d \) represent the charging and discharging efficiencies, respectively. These parameters are essential for characterizing the flexibility of electric vehicle clusters in the scheduling model.
The dual-layer scheduling model is formulated to address both grid and user perspectives. The upper-layer objective function aims to minimize the peak-valley difference \( G \) in grid load, expressed as:
$$ \min G = \frac{1}{t – t_{ij}} \left( Z_{d,t} + \sum_{n=1}^{L_0} Z_{n,t} – Z_{d,e} – Z_{a,b} \right) + \Upsilon $$
where \( Z_{d,t} \) is the load from non-EV devices at time \( t \), \( Z_{n,t} \) is the load from EV charging/discharging in region \( n \), \( Z_{d,e} \) and \( Z_{a,b} \) represent the energy output from distributed sources in different regions, and \( \Upsilon \) is a deviation function defined as:
$$ \Upsilon = t_{ij} \sum_{n=1}^{L_0} (Z_{n,t} – Z_{d,e})^2 $$
Constraints for the upper layer include charging capacity limits and peak load constraints:
$$ \sum_{n=1}^{L_0} E_{n,t} = \sum_{n=1}^{L_0} Z_{n,t} G $$
and
$$ \sum_{n=1}^{L_0} p_n S K \leq E_{n,t} \leq \sum_{t=1}^{L_0} p_t S K $$
where \( E_{n,t} \) is the scheduled load, \( p_n \) and \( p_t \) are average charging/discharging powers, \( S \) is the charging loss rate, and \( K \) is the EV response rate. Additionally, the peak load must satisfy:
$$ Z_{n,\max} \leq Z_{0,\max} $$
The lower-layer objective function minimizes the charging cost \( s \) for electric vehicle users:
$$ \min s = \left( \sum_{t_0=1}^{t} d_{t_0} Z_{c,i} – \sum_{t_0=1}^{t} f_{t_0} H_{c,i} \right) (a + b – t_0) K $$
where \( Z_{c,i} \) and \( H_{c,i} \) are the charging and discharging powers for EV \( i \), \( d_{t_0} \) and \( f_{t_0} \) are charging/discharging parameters at time \( t_0 \), and \( a \) and \( b \) are charging and discharging times. Constraints for the lower layer include battery capacity limits:
$$ 0 \leq r_{s,i} N_2 + N_3 \leq r_{c,i} N_1 $$
and grid load limits:
$$ b Z_{n,t} + a Z_{d,e} < Z_{\max} $$
To solve this dual-layer model, I employ an improved crisscross optimization (CSO) algorithm that integrates a roulette wheel selection mechanism. The CSO algorithm involves horizontal and vertical crossover operations to explore the solution space. For horizontal crossover, two parent particles \( X(i) \) and \( X(j) \) generate offspring as follows:
$$ M_{hc}(i,d) = r_1 X(i,d) + (1 – r_1) X(j,d) + c_1 [X(i,d) – X(j,d)] $$
$$ M_{hc}(j,d) = r_2 X(i,d) + (1 – r_2) X(j,d) + c_2 [X(i,d) – X(j,d)] $$
where \( r_1 \), \( r_2 \), \( c_1 \), and \( c_2 \) are random numbers in specified ranges. The improved algorithm avoids local optima by dynamically adjusting the crossover parameters and using roulette wheel selection to prioritize fitter solutions. The optimization process is summarized in the following steps:
- Initialize the population of charging demand features based on historical data.
- Set iteration count and evaluate fitness functions for both layers.
- Perform horizontal and vertical crossovers to generate new solutions.
- Apply constraints and update the population using roulette wheel selection.
- Check convergence criteria; if met, output the optimal scheduling scheme.
For experimental validation, I consider a case study in an urban area of China with 2,000 electric vehicles and 11 charging points. The parameters for the upper and lower layers are set as shown in Table 1.
| Parameter | Value |
|---|---|
| Electric Vehicle Battery Capacity (kWh) | 22 |
| Total Dispatchable Electric Vehicles | 1,800 |
| Daily Travel Distance (km) | 20 |
| Charging/Discharging Power (kW) | 5.6 |
| Average Energy Consumption (kWh/km) | 0.15 |
| Number of Iterations | 200 |
| Charging Efficiency (%) | 95 |
| Discharging Efficiency (%) | 95 |
| Full Charging Time (hours) | 4.0 |
The convergence performance of the improved CSO algorithm is compared with existing methods, such as the “vehicle-road-network” scheduling strategy and long-term scheduling approaches. The results, illustrated in Figure 4, show that the proposed method achieves near-zero optimization error and converges within 50 iterations, outperforming the alternatives which get stuck in local optima. This demonstrates the efficacy of the improved CSO in handling the complexity of electric vehicle scheduling.
To evaluate the impact on grid load, I analyze the peak-valley difference before and after scheduling. As shown in Figure 5, the proposed method reduces the peak-valley difference to below 20 kW and maintains stability, whereas other methods exhibit higher and fluctuating values. This highlights the ability of the dual-layer model to balance load effectively. Furthermore, the scheduling time is tested under varying numbers of electric vehicles. Figure 6 indicates that the proposed method completes scheduling in less than 2.5 hours, even with 1,800 vehicles, showcasing its computational efficiency.
Table 2 provides a comparative analysis of charging costs, where the proposed method achieves the lowest total and average costs, along with reduced peak charging power. This underscores the economic benefits for both users and grid operators.
| Metric / Method | Reference Method 1 | Reference Method 2 | Proposed Method |
|---|---|---|---|
| Total Charging Cost (CNY) | 14,000 | 13,500 | 12,000 |
| Average Charging Cost (CNY/vehicle) | 90 | 95 | 80 |
| Peak Charging Power (MW) | 7.2 | 5.5 | 5.2 |
In conclusion, the proposed scheduling strategy based on the improved CSO algorithm effectively addresses the challenges of electric vehicle integration in China’s power grid. By leveraging V2G technology and a dual-layer optimization model, it minimizes peak-valley differences and charging costs while ensuring grid stability. The algorithm’s robustness and efficiency are validated through extensive experiments, demonstrating its superiority over existing methods. Future work will focus on enhancing load stability control and extending the approach to larger-scale networks. The growth of China’s EV market necessitates such innovative solutions to achieve sustainable energy management.