With the rapid advancement of new energy technologies and increasing environmental requirements, electric vehicles are gradually replacing 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 charging and discharging processes of large-scale electric vehicles to enhance the stability of the distribution grid and better support the integration of massive numbers of electric vehicles into the power system. In China, the proliferation of electric vehicles, often referred to as China EV, has posed unique challenges to grid management due to the concentrated demand patterns. Therefore, exploring cooperative control methods for electric vehicle groups is crucial for optimizing grid performance and promoting industrial energy savings and emission reduction.
To deeply analyze the demand response capabilities on the load side, numerous scholars have investigated the role of electric vehicles in grid demand response. For instance, some researchers proposed a two-layer optimization model-based scheduling strategy with the objective of minimizing the charging cost for vehicle owners. They employed improved particle swarm optimization-simulated annealing algorithms to solve the model, effectively reducing new load peaks and peak-valley differences while lowering costs for participating users. Others developed feedforward decoupling double-closed-loop and constant current charging-discharging control strategies to achieve bidirectional power flow between electric vehicles and the grid. Additionally, studies on time-of-use electricity prices guided daily load conditions, constructing optimal charging-discharging models for electric vehicles and using multi-objective genetic algorithms like NSGA-II based on Pareto optimality for solutions. These approaches demonstrated that ordered charging-discharging algorithms could compensate for charging costs through discharging. Building on these foundations, this paper designs a cooperative control method for electric vehicle groups based on Logit protocol dynamic game theory and conducts performance analysis.
In the initial stage of evolutionary game theory, the electric vehicle population randomly selects M strategies. The strategy set φ encompasses all operational parameters of electric vehicles across different time periods, expressed as follows:
$$ \phi = \{s_1, s_2, \dots, s_m, \dots, s_M\} $$
where each strategy \( s_m \) is defined as:
$$ s_m = \{E_{m,1}, E_{m,2}, \dots, E_{m,H}\} $$
Here, \( s_m \) represents the m-th randomly generated strategy, and \( E_{m,H} \) denotes the charging-discharging power during time period H for the m-th strategy. This formulation allows for a comprehensive representation of the electric vehicle behavior under varying conditions, which is essential for modeling the dynamics of China EV fleets.
Using the Logit protocol, we set up an evolutionary game model modification protocol, establishing the following conditional transition probability:
$$ \rho_{i}^{m,k}[p_i(t)] = \frac{\exp\left(\frac{f_k^i(t)}{\theta}\right)}{\sum_{n=1}^{M} \exp\left(\frac{f_m^i(t)}{\theta}\right)} $$
In this equation, \( \theta \) represents the noise level, which influences the decision-making process of electric vehicles. This probability mechanism helps in modeling the bounded rationality of electric vehicle users, a critical aspect in real-world scenarios involving China EV adoption. Under the dynamic pricing of electric vehicle aggregators, we establish a simulation model with the optimization goal of minimizing the energy cost for electric vehicle aggregators. The entire process is illustrated in the two-stage game model for power demand response scheduling, as shown in the flowchart below. This model effectively captures the interactions between electric vehicle aggregators and the electric vehicle population, ensuring optimal scheduling decisions.
The two-stage game model solution process involves several steps. Initially, under constraints, the electric vehicle population generates M initial population strategies and their respective selection ratios. The scheduling layer then computes the cost function and fitness function for the electric vehicle population. Based on the conditional transition probabilities, the selection ratios of each strategy are updated according to discrete dynamic evolution equations. This iterative process continues until an evolutionary equilibrium is reached. Subsequently, the electric vehicle aggregator integrates the total electric vehicle load during demand response periods and updates the quoted prices for these periods. If the conditions are satisfied, the strategies for both electric vehicles and the aggregator are output; otherwise, the process repeats. This approach ensures a balanced and efficient scheduling mechanism for electric vehicle groups.
To validate the proposed method, we conduct a case study with specific parameter settings. The jurisdiction includes 2,000 electric vehicles, each with a battery capacity of 30 kWh. The electric vehicle aggregator can handle a maximum load of 10 MW. The charging and discharging efficiency of the charging piles is set at 95%. The time-of-use electricity prices are detailed in the following table:
| Item | Time Period | Price (yuan/kWh) |
|---|---|---|
| Peak | 08:00–11:00, 15:00–21:00 | 1.178 |
| Off-Peak | 12:00–13:00, 23:00–07:00 | 0.425 |
| Normal | 07:00–08:00, 11:00–12:00, 13:00–15:00, 21:00–23:00 | 0.775 |
We create two pricing scenarios to analyze the effectiveness of the proposed model. In Scenario 1, the electric vehicle aggregator acts as the leader, setting charging and discharging prices based on the electric vehicle population’s following behavior. In Scenario 2, the electric vehicle aggregator dynamically sets prices through real-time game interactions with the electric vehicle population. The degree of peak shaving and valley filling is evaluated using load peak-valley difference and load variance. The calculation results are presented in the table below:
| Parameter | 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 |
By comparing the test results in the table, we assess the peak shaving and valley filling performance of electric vehicles. In Scenario 1, the electric vehicle aggregator and electric vehicles collaboratively regulate the charging and discharging control process, ensuring that electric vehicles charge under conditions lower than the grid’s time-of-use electricity prices. This achieves the effect of regulating electric vehicle charging and discharging, enabling more electric vehicles to perform control functions and effectively reducing the grid’s load peak-valley difference and variance. For Scenario 2, electric vehicles establish lower-cost charging and discharging strategies through evolutionary game theory, further reducing the charging and discharging electricity prices set by the electric vehicle aggregator. This ensures that the electric vehicle optimization scheduling process obtains higher electricity quantities, allowing Scenario 2 to further reduce the load peak-valley difference and load variance compared to Scenario 1. This demonstrates the efficacy of the Logit protocol in managing China EV fleets for grid stability.
Economic analysis is conducted based on the Nash equilibrium solution determined by the two-stage game model, which balances electric vehicle charging and the electric vehicle aggregator’s electricity costs, thereby identifying the optimal electric vehicle charging and discharging scheme. The economic results under various scenarios and scheduling methods are shown in the table below:
| Parameter | Total Cost of Electric Vehicles (10,000 yuan) | Net Income of Electric Vehicle Aggregator (10,000 yuan) |
|---|---|---|
| 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 – PSO | 0.81 | 0.36 |
| Scenario 2 – PSO | 0.73 | 0.37 |
| Scenario 2 – Evolutionary Game | 0.52 | 0.33 |
From the table, it is evident that in Scenario 2, electric vehicles achieve the lowest total cost, while the electric vehicle aggregator attains the highest net income. This indicates that through evolutionary game theory, electric vehicles obtain an ideal charging and discharging control scheme, further reducing the charging costs for the electric vehicle aggregator. When peak shaving scheduling is involved, subsidies can be provided through discharging, effectively reducing charging costs. Moreover, the optimized charging and discharging scheduling scheme for electric vehicles also decreases the energy costs for the electric vehicle aggregator, significantly enhancing the conversion profit of the electric vehicle aggregator. These findings highlight the economic benefits of integrating China EV into smart grid systems using advanced game-theoretic approaches.
The conditional transition probability in the Logit protocol model is derived from the principles of bounded rationality in evolutionary game theory. It can be expressed in a more generalized form as:
$$ \rho_{i}^{m,k}[p_i(t)] = \frac{\exp\left(\beta \cdot U_{m,k}(t)\right)}{\sum_{n=1}^{M} \exp\left(\beta \cdot U_{m,n}(t)\right)} $$
where \( U_{m,k}(t) \) represents the utility of strategy k for electric vehicle i at time t, and \( \beta \) is a parameter controlling the level of rationality. In our context, \( \beta = \theta^{-1} \), which aligns with the noise level in the original formulation. This probability mechanism ensures that strategies with higher utilities are more likely to be adopted, promoting efficient decision-making among electric vehicle users.
Furthermore, the optimization objective for the electric vehicle aggregator can be formulated as minimizing the total energy cost, subject to constraints such as power balance and capacity limits. The cost function is defined as:
$$ C_{\text{total}} = \sum_{t=1}^{T} \left[ p_{\text{grid}}(t) \cdot c_{\text{grid}}(t) + \sum_{i=1}^{N} \left( p_{\text{ch},i}(t) \cdot c_{\text{ch}} – p_{\text{dis},i}(t) \cdot c_{\text{dis}} \right) \right] $$
where \( p_{\text{grid}}(t) \) is the power purchased from the grid at time t, \( c_{\text{grid}}(t) \) is the grid electricity price at time t, \( p_{\text{ch},i}(t) \) and \( p_{\text{dis},i}(t) \) are the charging and discharging powers of electric vehicle i at time t, respectively, and \( c_{\text{ch}} \) and \( c_{\text{dis}} \) are the associated costs. The constraints include:
$$ \sum_{i=1}^{N} p_{\text{ch},i}(t) \leq P_{\text{max,ch}} $$
$$ \sum_{i=1}^{N} p_{\text{dis},i}(t) \leq P_{\text{max,dis}} $$
$$ SOC_{i,\text{min}} \leq SOC_i(t) \leq SOC_{i,\text{max}} $$
These constraints ensure that the charging and discharging activities do not exceed the system limits and that the state of charge (SOC) of each electric vehicle remains within safe bounds. By incorporating these into the game-theoretic framework, we achieve a robust and scalable solution for managing electric vehicle groups.
In the context of China EV, the proposed method addresses the specific challenges of high-density urban areas where electric vehicle adoption is rapidly increasing. The Logit protocol dynamic game model provides a flexible and adaptive approach to coordinate the charging and discharging behaviors of numerous electric vehicles, reducing the strain on the grid and enhancing overall efficiency. The use of evolutionary game theory allows for the emergence of stable strategies that benefit both the electric vehicle users and the aggregators, fostering a sustainable ecosystem for electric vehicle integration.
In conclusion, this study on cooperative control of electric vehicle groups based on Logit protocol dynamic game theory yields the following beneficial results: First, it ensures that electric vehicles charge under conditions lower than the grid’s time-of-use electricity prices, guaranteeing that the electric vehicle optimization scheduling process obtains higher electricity quantities, thereby achieving the effect of regulating electric vehicle charging and discharging and effectively reducing the grid’s load peak-valley difference and variance. Second, the electric vehicle aggregator achieves the highest net income, as electric vehicles, through evolutionary game theory, obtain an ideal charging and discharging control scheme, reducing the charging cost for the electric vehicle aggregator and significantly enhancing the conversion profit of the electric vehicle aggregator. This research contributes to improving the charging and discharging efficiency of electric vehicle groups and holds high value for industrial energy saving and emission reduction, particularly in the context of China EV development.
The future work will focus on extending the model to incorporate real-time data and machine learning techniques for better prediction and decision-making. Additionally, we plan to explore the integration of renewable energy sources with electric vehicle charging stations to further enhance the sustainability of the power system. The scalability of the proposed method will be tested in larger and more diverse electric vehicle populations, ensuring its applicability in various scenarios, including those specific to China EV markets.