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Coupling a Power Dispatch Model with a Wardrop or Mean-Field-Game Equilibrium Model

Author

Listed:
  • F. Babonneau

    (ORDECSYS
    Universidad Adolfo Ibañez)

  • R. T. Foguen

    (GERAD, Polytechnique Montréal)

  • A. Haurie

    (ORDECSYS
    University of Geneva
    GERAD, HEC Montréal)

  • R. Malhamé

    (GERAD, Polytechnique Montréal)

Abstract

In this paper, we propose an approach for coupling a power network dispatch model, which is part of a long-term multi-energy model, with Wardrop or Mean-Field-Game (MFG) equilibrium models that represent the demand response of a large population of small “prosumers” connected at the various nodes of the electricity network. In a deterministic setting, the problem is akin to an optimization problem with equilibrium constraints taking the form of variational inequalities or nonlinear complementarity conditions. In a stochastic setting, the problem is formulated as a robust optimization with uncertainty sets informed by the probability distributions resulting from an MFG equilibrium solution. Preliminary numerical experimentations, using heuristics mimicking standard price adjustment techniques, are presented for both the deterministic and stochastic cases.

Suggested Citation

  • F. Babonneau & R. T. Foguen & A. Haurie & R. Malhamé, 2021. "Coupling a Power Dispatch Model with a Wardrop or Mean-Field-Game Equilibrium Model," Dynamic Games and Applications, Springer, vol. 11(2), pages 217-241, June.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:2:d:10.1007_s13235-020-00357-w
    DOI: 10.1007/s13235-020-00357-w
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    References listed on IDEAS

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    1. Antonio Frangioni & Claudio Gentile, 2006. "Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints," Operations Research, INFORMS, vol. 54(4), pages 767-775, August.
    2. Frédéric Babonneau & Alain Haurie, 2019. "Energy technology environment model with smart grid and robust nodal electricity prices," Annals of Operations Research, Springer, vol. 274(1), pages 101-117, March.
    3. Li, Pei-Hao & Pye, Steve, 2018. "Assessing the benefits of demand-side flexibility in residential and transport sectors from an integrated energy systems perspective," Applied Energy, Elsevier, vol. 228(C), pages 965-979.
    4. Babonneau, Frédéric & Caramanis, Michael & Haurie, Alain, 2016. "A linear programming model for power distribution with demand response and variable renewable energy," Applied Energy, Elsevier, vol. 181(C), pages 83-95.
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