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Mean-Field Games and Dynamic Demand Management in Power Grids

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Abstract

This paper applies mean-field game theory to dynamic demand management. For a large population of electrical heating or cooling appliances (called agents), we provide a mean-field game that guarantees desynchronization of the agents thus improving the power network resilience. Second, for the game at hand, we exhibit a mean-field equilibrium, where each agent adopts a bang-bang switching control with threshold placed at a nominal temperature. At equilibrium, through an opportune design of the terminal penalty, the switching control regulates the mean temperature (computed over the population) and the mains frequency around the nominal value. To overcome Zeno phenomena we also adjust the bang-bang control by introducing a thermostat. Third, we show that the equilibrium is stable in the sense that all agents’ states, initially at different values, converge to the equilibrium value or remain confined within a given interval for an opportune initial distribution.

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Acknowledgements

This research was supported by the 2012 “Research Fellow” Program of the Dipartimento di Matematica, Università di Trento and by the PRIN 20103S5RN3 “Robust decision making in markets and organization”.

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Author notes

  1. Dario Bauso

    Present address: Department of Engineering Science, University of Oxford, Oxford, UK

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050, Povo-Trento, Italy

    Fabio Bagagiolo & Dario Bauso

  2. DICGIM, Università di Palermo, Viale delle Scienze, 90128, Palermo, Italy

    Dario Bauso

Authors
  1. Fabio Bagagiolo
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  2. Dario Bauso
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Correspondence to Dario Bauso.

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Bagagiolo, F., Bauso, D. Mean-Field Games and Dynamic Demand Management in Power Grids. Dyn Games Appl 4, 155–176 (2014). https://doi.org/10.1007/s13235-013-0097-4

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