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Mean-Field Games and Dynamic Demand Management in Power Grids

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  • Fabio Bagagiolo
  • Dario Bauso

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Fabio Bagagiolo & Dario Bauso, 2014. "Mean-Field Games and Dynamic Demand Management in Power Grids," Dynamic Games and Applications, Springer, vol. 4(2), pages 155-176, June.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:2:p:155-176
    DOI: 10.1007/s13235-013-0097-4
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    References listed on IDEAS

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    1. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    2. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    3. repec:dau:papers:123456789/3001 is not listed on IDEAS
    4. Oecd, 2011. "Country notes," OECD Journal on Budgeting, OECD Publishing, vol. 11(2), pages 69-213.
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    Cited by:

    1. Roxana Dumitrescu & Marcos Leutscher & Peter Tankov, 2024. "Energy transition under scenario uncertainty: a mean-field game of stopping with common noise," Mathematics and Financial Economics, Springer, volume 18, number 4, December.
    2. Fabio Bagagiolo & Dario Bauso & Raffaele Pesenti, 2016. "Mean-Field Game Modeling the Bandwagon Effect with Activation Costs," Dynamic Games and Applications, Springer, vol. 6(4), pages 456-476, December.
    3. Ellen Webborn & Robert S. MacKay, 2017. "A Stability Analysis of Thermostatically Controlled Loads for Power System Frequency Control," Complexity, Hindawi, vol. 2017, pages 1-26, December.
    4. Yunhan Huang & Quanyan Zhu, 2022. "Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review," Dynamic Games and Applications, Springer, vol. 12(1), pages 7-48, March.
    5. Antonio Paola & David Angeli & Goran Strbac, 2018. "On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market," Dynamic Games and Applications, Springer, vol. 8(4), pages 761-798, December.
    6. Wouter Baar & Dario Bauso, 2022. "Mean Field Games on Prosumers," SN Operations Research Forum, Springer, vol. 3(4), pages 1-27, December.
    7. Joseph Andria & Rosario Maggistro & Raffaele Pesenti, 2023. "Sustainable Management of Tourist Flow Networks: A Mean Field Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 730-761, February.
    8. Fabio Bagagiolo & Dario Bauso & Rosario Maggistro & Marta Zoppello, 2017. "Game Theoretic Decentralized Feedback Controls in Markov Jump Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 704-726, May.

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