With the rapid advancement of new energy technologies and increasing environmental requirements, electric vehicles have gradually replaced traditional fuel-powered vehicles, gaining a larger market share. However, the large-scale disordered charging of electric vehicles has led to significant peak-valley differences in the power grid and insufficient distribution transformer capacity. This necessitates effective management of the charge-discharge processes of large-scale electric vehicles to enhance the stability of distribution grid operation and better accommodate the integration of electric vehicles into the grid. In China, the electric vehicle market, often referred to as China EV, has experienced exponential growth, driven by government policies and technological innovations. The proliferation of electric vehicles in China presents both opportunities and challenges for the power system, particularly in terms of load management and grid stability. This study focuses on developing a coordinated control method for electric vehicle groups based on Logit protocol dynamic game theory to optimize charge-discharge scheduling and improve grid efficiency.
The无序 charging behavior of electric vehicles can exacerbate grid imbalances, especially during peak hours. To address this, demand response strategies have been explored to leverage electric vehicles as flexible resources. Previous research has employed various optimization models and algorithms, such as bi-level optimization and particle swarm optimization, to minimize charging costs and reduce load fluctuations. However, these approaches often overlook the dynamic interactions between electric vehicle aggregators and vehicle owners. In this context, game theory provides a robust framework for modeling such interactions, enabling the derivation of equilibrium solutions that balance the interests of all parties. Specifically, the Logit protocol, rooted in evolutionary game theory, allows for the modeling of bounded rationality and stochastic decision-making among electric vehicle users. This paper proposes a dynamic game-based approach using the Logit protocol to coordinate the charge-discharge behaviors of electric vehicle groups, with a focus on enhancing grid stability and economic benefits for China EV stakeholders.
The core of the method involves setting up an evolutionary game model where the electric vehicle population randomly selects strategies from a set of possible charge-discharge schedules. The strategy set φ includes all operational parameters for electric vehicles across different time periods, defined as follows:
$$ \phi = \{ s_1, s_2, \dots, s_m, \dots, s_M \} $$
where each strategy \( s_m \) is represented by a vector of charge-discharge powers over H time periods:
$$ s_m = \{ E_{m,1}, E_{m,2}, \dots, E_{m,H} \} $$
Here, \( E_{m,H} \) denotes the charge-discharge power for the m-th strategy during period H. The Logit protocol is used to define the conditional transition probability for strategy updates, incorporating a noise parameter θ to account for decision randomness:
$$ \rho_{i}^{m,k}[p_i(t)] = \frac{\exp\left( \frac{f_k^i(t)}{\theta} \right)}{\sum_{n=1}^{M} \exp\left( \frac{f_n^i(t)}{\theta} \right)} $$
In this equation, \( \rho_{i}^{m,k} \) represents the probability of electric vehicle i switching from strategy m to strategy k at time t, and \( f_k^i(t) \) is the fitness or cost function for strategy k. The noise level θ influences the exploration-exploitation trade-off; a higher θ encourages random strategy changes, while a lower θ favors strategies with higher fitness. This dynamic adjustment enables the electric vehicle population to evolve toward optimal charge-discharge patterns over time, considering real-time electricity prices and grid conditions.
Under this framework, the electric vehicle aggregator dynamically sets prices to minimize energy costs, forming a two-stage game model. The first stage involves the aggregator determining prices based on predicted demand, while the second stage involves electric vehicles adjusting their strategies in response. The overall process is illustrated in the flowchart below, which outlines the iterative solution approach for achieving Nash equilibrium in the game.
| Period Type | Time Interval | Price (CNY/kWh) |
|---|---|---|
| Peak | 08:00–11:00, 15:00–21:00 | 1.178 |
| Off-Peak | 12:00–13:00, 23:00–07:00 | 0.425 |
| Standard | 07:00–08:00, 11:00–12:00, 13:00–15:00, 21:00–23:00 | 0.775 |
The two-stage game model solution process begins with the electric vehicle population generating M initial strategies and their selection proportions. The cost and fitness functions are computed for each strategy, followed by the calculation of conditional transition probabilities using the Logit protocol. The discrete dynamic evolution equation updates the strategy selection proportions iteratively until equilibrium is reached. Subsequently, the electric vehicle aggregator integrates the total load from electric vehicles during demand response periods and updates the pricing offers. This cycle continues until convergence, outputting the optimal strategies for both electric vehicles and the aggregator. This method ensures that electric vehicles charge during off-peak hours when prices are lower, thereby reducing grid stress and optimizing energy usage for China EV applications.
To validate the proposed approach, a case study was conducted with a fleet of 2,000 electric vehicles, each with a battery capacity of 30 kWh. The electric vehicle aggregator had a maximum load capacity of 10 MW, and the charge-discharge efficiency of charging piles was set at 95%. Two pricing scenarios were considered: Scenario 1, where the aggregator leads by setting prices based on electric vehicle load predictions, and Scenario 2, where electric vehicles engage in real-time博弈 to influence pricing. The performance was evaluated using load peak-valley difference and load variance, with results compared against baseline methods like artificial neural networks (ANN) and particle swarm optimization (PSO).
| Scenario/Method | Load Peak-Valley Difference (MW) | Load Variance (MW²) |
|---|---|---|
| Base Load | 48.63 | 263.35 |
| Disordered Charging | 50.06 | 258.94 |
| Ordered Charging | 49.27 | 243.61 |
| Scenario 1 – ANN | 47.16 | 222.24 |
| Scenario 1 – PSO | 49.26 | 209.67 |
| Scenario 1 – Evolutionary Game | 41.22 | 182.45 |
| Scenario 2 – ANN | 53.24 | 211.58 |
| Scenario 2 – PSO | 49.15 | 202.64 |
| Scenario 2 – Evolutionary Game | 39.62 | 178.58 |
The results demonstrate that the evolutionary game approach significantly reduces load peak-valley differences and variances compared to other methods. In Scenario 1, the electric vehicle aggregator’s leadership in pricing ensures that electric vehicles charge below grid time-of-use prices, effectively regulating charge-discharge activities and minimizing grid impact. For Scenario 2, the real-time博弈 between electric vehicles leads to even lower costs and better load leveling, as electric vehicles optimize their schedules to maximize energy acquisition during low-price periods. This highlights the effectiveness of the Logit protocol in facilitating cooperative behavior among electric vehicle users, which is crucial for large-scale integration of China EV into the grid.
Economic analysis further underscores the benefits of the proposed method. The Nash equilibrium solution from the two-stage game model balances electric vehicle charging costs and aggregator energy costs, resulting in optimal charge-discharge schedules. The table below summarizes the economic outcomes for different scenarios and methods, including total costs for electric vehicles and net revenues for the aggregator.
| Scenario/Method | Total Electric Vehicle Cost (10,000 CNY) | Electric Vehicle Aggregator Net Revenue (10,000 CNY) |
|---|---|---|
| Disordered Charging | 2.25 | – |
| Ordered Charging | 1.78 | – |
| Scenario 1 – ANN | 1.41 | 0.33 |
| Scenario 1 – PSO | 1.26 | 0.31 |
| Scenario 1 – Evolutionary Game | 0.89 | 0.29 |
| Scenario 2 – ANN | 0.81 | 0.36 |
| Scenario 2 – PSO | 0.73 | 0.37 |
| Scenario 2 – Evolutionary Game | 0.52 | 0.33 |
In Scenario 2, the evolutionary game approach achieves the lowest total cost for electric vehicles and the highest net revenue for the aggregator. This is attributed to the ideal charge-discharge control schemes derived from the game, which reduce charging costs through discharge compensation during peak hours and enhance the aggregator’s profit margins. The dynamic pricing strategy encourages electric vehicles to participate in demand response, aligning their behavior with grid needs and promoting energy efficiency. For China EV ecosystems, this translates to significant economic savings and improved sustainability, supporting the broader goals of industrial energy conservation and emission reduction.
The mathematical formulation of the model involves optimizing the electric vehicle aggregator’s energy cost, denoted as \( C_{\text{agg}} \), which is a function of the total load \( L(t) \) and electricity price \( p(t) \) over time periods t=1 to T:
$$ C_{\text{agg}} = \sum_{t=1}^{T} p(t) \cdot L(t) $$
where \( L(t) \) is the aggregated load from all electric vehicles at time t, calculated as:
$$ L(t) = \sum_{i=1}^{N} \sum_{m=1}^{M} \rho_i^m(t) \cdot E_{m,t} $$
Here, N is the number of electric vehicles, and \( \rho_i^m(t) \) is the proportion of electric vehicle i selecting strategy m at time t. The fitness function \( f_m^i(t) \) for each strategy is defined based on the cost incurred by electric vehicle i under strategy m, incorporating charging costs and any incentives:
$$ f_m^i(t) = – \left( \sum_{t=1}^{T} p(t) \cdot E_{m,t} + \lambda \cdot (E_{m,t} – E_{\text{ref}})^2 \right) $$
The term \( \lambda \cdot (E_{m,t} – E_{\text{ref}})^2 \) represents a penalty for deviations from a reference energy level \( E_{\text{ref}} \), encouraging adherence to scheduled profiles. The evolutionary dynamics are governed by the discrete replication equation:
$$ \rho_i^m(t+1) = \rho_i^m(t) + \alpha \cdot \left( \rho_i^{m,k}[p_i(t)] – \rho_i^m(t) \right) $$
where α is the learning rate. This equation updates the strategy proportions based on the conditional transition probabilities, driving the system toward equilibrium. The iterative process continues until the change in proportions falls below a threshold, indicating convergence.
In practice, the implementation of this method requires robust communication infrastructure between electric vehicles and aggregators, which is increasingly feasible with smart grid technologies in China. The use of real-time data analytics and IoT devices can enhance the accuracy of load predictions and strategy adjustments. Moreover, the scalability of the approach makes it suitable for large-scale electric vehicle deployments in urban areas, where grid constraints are most pressing. By leveraging the Logit protocol, the model accommodates the inherent uncertainties in user behavior, providing a realistic and adaptive solution for charge-discharge coordination.
In conclusion, this study presents a novel framework for electric vehicle group charge-discharge coordination based on Logit protocol dynamic game theory. The key findings are: (1) The method ensures that electric vehicles charge during off-peak hours at lower prices, optimizing energy acquisition and reducing grid load fluctuations. (2) Through evolutionary game, electric vehicles achieve ideal charge-discharge schemes, lowering costs for aggregators and increasing their profits. These outcomes contribute to improved efficiency in electric vehicle群 operations, supporting the growth of China EV market and aligning with industrial energy-saving objectives. Future work could explore integration with renewable energy sources and multi-agent reinforcement learning for enhanced adaptability.