Non-Cooperative Game Algorithm for Capacity Allocation in Hybrid Energy Storage Systems with Batteries and Supercapacitors

In hybrid energy storage systems, the collaborative operation of batteries and supercapacitors (SCs) can integrate their respective advantages to overcome the limitations of single energy storage devices. Batteries exhibit high energy density, making them suitable for long-term energy storage and release, while supercapacitors offer high power density and rapid charge/discharge capabilities, ideal for compensating instantaneous power fluctuations. Determining the optimal capacity allocation for these two storage components to achieve peak system performance represents a critical research challenge.

Non-cooperative game theory provides an effective framework for addressing hybrid energy storage capacity configuration. In this model, batteries and supercapacitors are treated as independent decision-makers, each optimizing their individual benefits (such as cost, efficiency, or lifespan), while the overall system performance depends on their interactions. The key to this game-theoretic approach lies in finding the Nash equilibrium solution - a state where neither participant can unilaterally change their strategy to gain additional benefits given the other's fixed strategy.

To implement this methodology, an iterative optimization algorithm can be employed. First, establish utility functions for both batteries and supercapacitors, typically incorporating factors like cost, efficiency, and cycle life. The algorithm then alternately optimizes the capacity strategies of both components through successive iterations, ensuring each step drives individual utilities toward their optima. The system eventually converges to a Nash equilibrium point where both strategies stabilize, and neither party can independently improve their benefits. Implementation typically involves defining objective functions using mathematical programming and solving through alternating optimization loops with convergence checks.

This approach is not only applicable to energy storage optimization in power systems but can also be extended to other scenarios requiring multi-device coordination, such as electric vehicle power distribution and renewable energy grid integration. Through game-theoretic analysis, capacity configuration solutions that balance economic efficiency and reliability can be systematically identified. The algorithm structure allows for modular expansion to include additional storage devices or optimization criteria as needed.