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An Extended Mean Field Game for Storage in Smart Grids

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Abstract

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.

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Acknowledgements

The authors wish to thank the anonymous referees for all the pertinent remarks she/he made. The author’s research is part of the ANR Project CAESARS (ANR-15-CE05-0024) and PACMAN (ANR-16-CE05-0027) and of PANORISK project. The third author was partially supported by chaire Risques Financiers de la fondation du risque, CMAP-Ecole Polytechniques and Chair Risques Emergents ou Atypiques en Assurance supported by Mutuelle du Mans Assurance, Le Mans University, Risk Foundation and Ecole Polytechnique.

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Authors and Affiliations

  1. EDF R&D Paris-Saclay and Finance for energy Market Research Centre (FIME), Paris, France

    Clémence Alasseur

  2. CEREMADE, Université Paris Dauphine and Finance for Energy Market Research Centre (FIME), Paris, France

    Imen Ben Taher

  3. Laboratoire Manceau de Mathématiques & FR CNRS No. 2962, Institut du Risque et de l’Assurance, Le Mans Université, Le Mans, France

    Anis Matoussi

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  1. Clémence Alasseur
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  2. Imen Ben Taher
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  3. Anis Matoussi
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Correspondence to Anis Matoussi.

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Communicated by Nizar Touzi.

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Alasseur, C., Ben Taher, I. & Matoussi, A. An Extended Mean Field Game for Storage in Smart Grids. J Optim Theory Appl 184, 644–670 (2020). https://doi.org/10.1007/s10957-019-01619-3

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  • DOI: https://doi.org/10.1007/s10957-019-01619-3

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