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Energy inconsistency among Li-ion battery cells widely exists in energy storage systems, which contributes to the continuous deterioration of the system durability and overall performance. Researchers have proposed various kinds of battery energy equalizers to reduce such inconsistency. Among them, the inductor equalizer is a predominant type in fast equalization applications. However, it requires relatively more complex control than other types of equalizers. In order to reduce the control complexity of inductor equalizers, a bidirectional multi-input and multi-output energy equalization circuit based on the game theory is proposed in the present work. The proposed equalizer has the modularized circuit topology and the mutually independent working principle. A static game model is developed and exploited for the mathematical description and control analysis of an energy equalization circuit comprised of these equalizers. The feasible control of each equalizer was obtained by solving a series of linear equations for the Nash Equilibrium of the model among the states of charge of the battery cells. The complexity of equations grows linearly with the cell number. The equivalent simulation model for the four-cell equalization is established in the PISM software, where the operational data and simulation results justify the static game model and verify the control validation, respectively. It is concluded that the proposed inductor equalizer is suitable for large-scale battery strings in energy storage systems, electrical vehicles, and new energy power generation applications.

Bidirectional Multi-Input and Multi-Output Energy Equalization Circuit for the Li-Ion Battery String Based on the Game Theory