Abstract
As the market share of electric vehicles (EVs) continues to rise, their uncoordinated charging has caused significant grid peak-valley differences and transformer capacity issues. This study presents a dynamic game-based cooperative control method for EV charge-discharge scheduling using the Logit protocol. By establishing an evolutionary game model and conditional transition probability, the method guides EVs to charge during off-peak hours, minimizing grid load fluctuations and enhancing operational efficiency. Simulation results demonstrate that the proposed approach reduces charging costs for EV aggregators and improves profit margins, highlighting its value for industrial energy conservation.
1. Introduction
The rapid proliferation of electric vehicles has brought about both environmental benefits and challenges for power grids. As EVs replace traditional fuel vehicles, their unorganized charging patterns exacerbate grid peak-valley differences and strain distribution transformer capacities . This issue necessitates effective management of large-scale EV charge-discharge processes to stabilize grid operations and enhance power matching capabilities.
Previous research has explored demand response strategies for EVs. For example, scholars have proposed double-layer optimization models and control strategies to minimize charging costs and regulate power flow . However, existing methods often lack adaptability to dynamic market interactions. This study aims to address this gap by introducing a Logit protocol-based dynamic game framework, enabling real-time coordination between EV aggregators (EVAs) and EV users.
2. Methodology: Logit Protocol-Based Dynamic Game Model
2.1 Evolutionary Game Strategy Set
In the initial evolutionary game phase, the EV population randomly acquires M strategies. The strategy set \(\varphi\) encompasses all operational parameters for EVs across different time periods, expressed as:\(\left\{ \begin{array}{l} \varphi = \{s_1, s_2, \cdots, s_m, \cdots, s_M\} \\ s_m = \{E_{m,1}, E_{m,2}, \cdots, E_{m,H}\} \end{array} \right.\) where \(s_m\) denotes the m-th strategy, and \(E_{m,H}\) represents the charge-discharge power during the H-th time period for strategy m -.
2.2 Logit Protocol for Conditional Transition Probability
The Logit protocol modifies the evolutionary game model by defining the conditional transition probability:\(\rho_{s,k}^{i}\left[p^{i}(t)\right] = \frac{\exp\left[f_{k}^{i}(t)\theta^{-1}\right]}{\sum_{n=1}^{M} \exp\left[f_{s i}^{i}(t)\theta^{-1}\right]}\) Here, \(\theta\) denotes the noise level, which influences the rationality of strategy selection among EV users . This probability framework allows EVs to adaptively switch strategies based on real-time price signals and grid conditions.
2.3 Two-Stage Game Model for Demand Response
The proposed model operates in two stages:
- Scheduling Layer: EVAs integrate total load demands across demand response periods and update price bids.
- Evolutionary Layer: EVs adjust strategies based on cost functions and fitness values, iterating until evolutionary equilibrium is reached.
The solution process involves:
- Generating initial strategies and selection ratios for the EV population.
- Calculating cost functions and fitness values.
- Updating strategy selection ratios using discrete dynamic evolutionary equations.
- Outputting optimal strategies for EVs and EVAs -.
3. Case Study and Simulation Setup
3.1 System Parameters
The case study considers a jurisdiction with 2,000 EVs, each equipped with a 30 kW·h battery. The EVA can handle a maximum load of 10 MW, and charging/discharging efficiency is set to 95%. The time-of-use (TOU) electricity prices are detailed in Table 1 -.
| Project | Time Period | Price [CNY/(kW·h)] |
|---|---|---|
| Peak | 08:00–11:00, 15:00–21:00 | 1.178 |
| Valley | 12:00–13:00, 23:00–07:00 | 0.425 |
| Flat | 07:00–08:00, 11:00–12:00, 13:00–15:00, 21:00–23:00 | 0.775 |
| Table 1. Time-of-Use Electricity Prices for EVs |
3.2 Scenarios for Peak-Valley Load Regulation
Two scenarios are designed:
- Scenario 1: EVA leads, with EVs following to calculate charge-discharge prices.
- Scenario 2: EVA sets prices based on real-time load 博弈 (game) results from the EV population.
4. Results and Analysis
4.1 Peak-Valley Load Reduction Performance
Table 2 compares load indicators across different scenarios and methods:
| Parameter | Load Peak-Valley Difference (MW) | Load Variance (MW²) |
|---|---|---|
| Basic Load | 48.63 | 263.35 |
| Uncoordinated Charging | 50.06 | 258.94 |
| Coordinated 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 |
| Table 2. Load Indicators Under Different Scheduling Scenarios |
In Scenario 1, the EVA and EVs coordinate to regulate charging during off-peak TOU periods, reducing the peak-valley difference to 41.22 MW and variance to 182.45 MW². Scenario 2 further optimizes strategies through evolutionary game, achieving a peak-valley difference of 39.62 MW and variance of 178.58 MW² -. These results confirm that dynamic game-based scheduling effectively mitigates grid load fluctuations.
4.2 Economic Analysis
Table 3 presents the economic outcomes for different scenarios:
| Parameter | Total EV Cost (10,000 CNY) | EVA Net Profit (10,000 CNY) |
|---|---|---|
| Uncoordinated Charging | 2.25 | – |
| Coordinated 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 (Evolutionary Game) | 0.52 | 0.33 |
| Table 3. Economic Results Under Different Scenarios |
Scenario 2 achieves the lowest total EV cost (0.52×10⁴ CNY) and highest EVA net profit (0.33×10⁴ CNY). The evolutionary game enables EVs to derive optimal charge-discharge strategies, reducing EVA charging costs and increasing profits through peak shaving via discharging -.
5. Discussion
The Logit protocol dynamic game framework enhances EV charge-discharge coordination by:
- Incorporating real-time price signals into strategy selection, guiding EVs to charge during valley periods .
- Enabling EVAs to balance power costs and profits through Nash equilibrium solutions .
- Reducing peak-valley differences by up to 19.5% compared to uncoordinated charging, demonstrating its effectiveness in grid stabilization.
The model’s adaptability to dynamic market interactions surpasses traditional methods like ANN and PSO, as shown by lower load variances and costs -. This approach also aligns with industrial energy-saving goals, as optimized scheduling minimizes energy waste during charging/discharging cycles.
6. Conclusions
This study introduces a Logit protocol-based dynamic game method for EV group charge-discharge coordination, yielding key findings:
- The method successfully regulates EV charging during off-peak TOU periods, reducing grid peak-valley differences and load variances .
- Evolutionary game theory enables EVAs to achieve optimal profit margins while minimizing EV charging costs, enhancing overall system efficiency .
- The proposed framework offers significant potential for industrial energy conservation and emission reduction, supporting the sustainable integration of EVs into smart grids.
Future work will focus on integrating renewable energy sources and refining real-time pricing mechanisms to further optimize EV-grid interactions.