An Extended Mean Field Game for Storage in Smart Grids

• Published in: Journal of optimization theory and applications Vol. 184; no. 2; pp. 644 - 670
• Main Authors: Alasseur, Clémence, Ben Taher, Imen, Matoussi, Anis
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2020; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Economic models; Electric power distribution; Electricity; Electricity consumption; Electricity pricing; Energy conservation; Energy costs; Energy storage; Engineering; Game theory; Mathematics; Mathematics and Statistics; Nodes; Operations Research/Decision Theory; Optimization; Smart grid; Theory of Computation; 49K99; 49J53; Stochastic renewable generation; Extended mean field game; Stochastic control; Nash equilibrium; Distributed generation; Mean field games; Smart grid; Optimal storage
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-019-01619-3

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 N -player game.