Electric vehicles (EVs) have rapidly emerged as a cornerstone of sustainable transportation, lauded for their efficiency, cost-effectiveness, and environmental benefits. However, their widespread adoption brings significant challenges to power grid management, particularly in terms of charging efficiency and cost. Uncontrolled charging can strain power systems, increasing peak loads, reducing voltage quality, and shortening the lifespan of transformers. Addressing these issues, a team of researchers has developed a groundbreaking charging management strategy based on the Stackelberg game model, offering a dynamic solution that balances the needs of grids, retailers, and users.
The growing number of EVs on the road has made charging management a critical concern for utilities and policymakers worldwide. Traditional approaches to charging control often fall short: centralized strategies, which manage charging based on grid demands and user behavior, struggle to scale with the increasing number of EVs. Decentralized methods, such as static time-of-use pricing, can shift loads to off-peak hours but may inadvertently create new peaks during supposed low-demand periods, as users rush to take advantage of lower rates. These limitations highlight the need for a more adaptive and responsive approach.
Enter the Stackelberg game-based strategy, developed by Xu Hui, Chen Ping, Li Xianglong, Wang Peiyi, and Ma Longfei from the State Grid Beijing Electric Power Company. This model reimagines the charging process as a dynamic interaction between a leader (the electricity retailer) and multiple followers (EV users). The retailer, acting as the leader, sets prices to maximize its profits while considering grid performance, such as minimizing load variance. Users, as followers, adjust their charging power and timing based on these prices to meet their own needs—whether prioritizing speed (for urgent charging) or cost savings (when time is abundant).
What sets this model apart is its ability to account for the interdependencies between all stakeholders. Unlike previous game-theoretic approaches that focused solely on competition among users, this strategy positions the retailer as a mediator between the grid and users. The retailer’s pricing decisions directly influence user behavior, which in turn affects grid stability. By using backward induction to solve the game, the researchers ensure that both the retailer and users reach an equilibrium where neither can improve their outcome without harming the other—a state known as Stackelberg equilibrium.
To evaluate the effectiveness of their strategy, the team compared it against two common approaches: unordered charging and static time-of-use pricing. The results were striking. In simulations based on a residential community’s daily load patterns, unordered charging—where users charge arbitrarily—led to significant peak loads, with the grid’s peak-to-valley ratio reaching 2.09 MW and load variance at 0.35. These fluctuations risked overloading transformers and compromising voltage stability.
In contrast, the Stackelberg model reduced the peak-to-valley ratio to 1.36 MW and the load variance to 0.13. This smoothing of demand not only enhanced grid reliability but also lowered overall energy transmission losses. The improvement was even more notable when compared to static time-of-use pricing. While static pricing did reduce peak loads, it caused a secondary peak during off-peak hours as users clustered their charging, resulting in a load variance of 0.85—far higher than the 0.75 achieved by the game-based strategy.
Cost savings for users were another key advantage. The researchers found that the average charging cost per EV dropped from 44.48 yuan under static pricing to 33.09 yuan with the Stackelberg model. This reduction stems from the strategy’s ability to align prices with real-time grid conditions: higher prices during peak demand discourage unnecessary charging, while lower prices during lulls incentivize users to charge when the grid has excess capacity. Users with flexible schedules benefit most, as they can wait for optimal prices, while those with urgent needs (such as a near-empty battery) still have the option to charge at higher rates, ensuring their requirements are met.
The model’s adaptability is further enhanced by its adjustable parameters, which allow it to cater to different scenarios. For instance, the prediction horizon (k)—the number of hours the retailer uses to forecast demand—profoundly impacts performance. The team tested values of k from 2 to 10, finding that larger horizons improved grid stability (with load variance decreasing from 0.3 to 0.12) but increased computational complexity. A k value of 6 struck a balance, offering significant stability gains without excessive computational costs—a crucial consideration for real-world implementation.
Another critical parameter is the grid weight coefficient (α), which reflects the grid’s influence on the retailer’s profit function. When α is small, the retailer prioritizes its own profits, leading to higher user costs and greater grid instability. As α increases, the retailer focuses more on grid stability, reducing load variance but potentially lowering its own profits. The researchers determined that an α value of 1000 struck the right balance, minimizing variance to 0.18 while keeping retailer profits positive—ensuring both grid health and business viability.
The implications of this research extend beyond residential communities. As EV adoption accelerates, charging infrastructure will need to integrate seamlessly with smart grids to avoid bottlenecks. The Stackelberg model’s decentralized nature makes it scalable, as it does not require a central authority to micromanage each user’s charging. Instead, prices act as a signal, guiding user behavior toward optimal outcomes for the entire system.
Moreover, the model’s flexibility allows it to adapt to diverse environments, from urban centers with high EV density to rural areas with more sporadic demand. By adjusting parameters like the prediction horizon and grid weight coefficient, utilities can tailor the strategy to local conditions, ensuring efficiency without sacrificing user satisfaction.
Looking ahead, the researchers plan to explore how vehicle-to-grid (V2G) technology can enhance their model. V2G allows EVs to discharge energy back to the grid during peak demand, effectively turning them into distributed storage units. Integrating this capability into the Stackelberg framework could further stabilize the grid, reduce reliance on fossil fuels, and even generate additional income for EV owners—creating a true win-win for all stakeholders.
Critics might argue that dynamic pricing could disproportionately affect low-income users, who may not have the flexibility to charge during off-peak hours. However, the model’s design includes provisions for urgent charging, ensuring that users with time constraints can still access power when needed. Additionally, utilities could implement tiered pricing structures or subsidies to protect vulnerable users, making the transition to smart charging equitable.
In conclusion, the Stackelberg game-based charging strategy represents a significant leap forward in EV energy management. By harmonizing the interests of grids, retailers, and users, it addresses the dual challenges of grid stability and user affordability. As cities and countries strive to meet carbon neutrality goals, such innovative solutions will be essential to unlocking the full potential of electric mobility.
This research, published in the Computer Applications and Software (Vol. 41, No. 8, August 2024) with DOI: 10.3969/j.issn.1000-386x.2024.08.054, underscores the importance of interdisciplinary collaboration between power systems engineering and game theory. As Xu Hui and her colleagues demonstrate, the path to a sustainable transportation future lies not just in advancing EV technology, but in rethinking how we manage the energy ecosystem that powers it.
Authors: Xu Hui, Chen Ping, Li Xianglong, Wang Peiyi, Ma Longfei
Affiliation: State Grid Beijing Electric Power Company, Beijing 100031, China
Journal: Computer Applications and Software
DOI: 10.3969/j.issn.1000-386x.2024.08.054