An Extended Mean Field Game for Storage in Smart Grids We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as a network connection of a large number of nodes, where each node is characterized by a local electricity consumption, has a local electricity production (photovoltaic panels for example) and manages a local storage device. Depending on its instantaneous consumption and production rate 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 noncooperative game setting, we are led to the analysis of a nonzero 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. We are able to compare this solution to the optimal strategy of a central planner and in a linear quadratic setting, we obtain and explicit solution to the extended mean field game and we show that it provides an approximate Nash equilibrium for Nplayer game.

xcfxb5Nash meanfield games for general linearquadratic systems with applications Abstract   This paper is concerned with general meanfield (MF) linearquadratic (LQ) games of stochastic largepopulation system, where the individual diffusion coefficient can depend on both the state and the control of the agent. Moreover, the control weight in the cost functional could be indefinite. The asymptotic suboptimality property (namely,    xcfxb5   Nash equilibrium) of the decentralized strategies for the LQ games is derived through the consistency condition. The impact of the populationxe2x80x99s collective behaviors and the consistency of the mean field estimation are illustrated by the numerical results. A pricing problem is also studied, for which the decentralized suboptimal price is obtained.