Distributed Control of Micro-Storage Devices with Mean Field Games

This paper proposes a fully distributed control strategy for the management of micro-storage devices that perform energy arbitrage. For large storage populations, the problem can be approximated as a differential game with infinite players (mean field game). Through the resolution of coupled partial differential equations (PDEs), it is possible to determine, as a fixed point, the optimal feedback strategy for each player and the resulting price of energy if that strategy is applied. Once this price is calculated, it can be communicated to the devices, which are able to independently determine their optimal charge profile. Simulation results are provided, calculating the fixed point through numerical integration of the PDEs. The original model is then extended in order to consider additional elements, such as multiple population of devices and demand uncertainty.