Mean field games of energy storage devices: A finite difference analysis

Abstract

This paper considers a mean field game of energy storage devices (ESDs) in power systems, where electrovalency is affected by the storage population. The competition processes of ESDs are characterized by a pair of coupled partial differential equations (PDEs). The so‐called mean field equilibrium (MFE) is obtained by resolving the PDEs. The resulting MFE strategy is then broadcast to all local controllers in order to independently determine a control input for each device. Since PDEs are difficult to be explicitly calculated, a pair of difference schemes are designed for approximating the exact solutions of the PDEs. Then the sufficient condition of stability is analyzed. Based on the proposed difference schemes, a difference iterative scheme is designed for numerically calculating the MFE. Some simulation results show the effectiveness of the proposed iterative schemes.