An Extended Mean Field Game for Storage in Smart Grids

TL;DR

This paper models a large-scale power network with distributed generation and storage as an extended mean field game, providing explicit solutions and analyzing the approximate Nash equilibrium in a stochastic setting.

Contribution

It introduces an extended mean field game model for power networks with storage, offering explicit solutions and comparing decentralized strategies to a central planner.

Findings

Explicit solution for the extended mean field game in a linear quadratic setting

Approximate Nash equilibrium for large N-player game

Comparison between decentralized strategies and central planning

Abstract

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as network connection a large number of nodes, where each node is characterized by a local electricity consumption, has a local electricity production (e.g. photovoltaic panels), and manages a local storage device. Depending on its instantaneous consumption and production rates as well as its storage management decision, each node may either buy or sell electricity, impacting the electricity spot price. The objective at each node is to minimize energy and storage costs by optimally controlling the storage device. In a non-cooperative game setting, we are led to the analysis of a non-zero sum stochastic game with $N$ players where the interaction takes place through the spot price mechanism. For an infinite number of agents, our model corresponds to an Extended Mean-Field Game (EMFG). In a linear quadratic setting, we obtain and explicit solution to the EMFG, we show that it provides an approximate Nash-equilibrium for $N$-player game, and we compare this solution to the optimal strategy of a central planner.