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On Distributed Scheduling of Flexible Demand and Nash Equilibria in the Electricity Market

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  • Antonio Paola

    (Imperial College London)

  • David Angeli

    (Imperial College London)

  • Goran Strbac

    (Imperial College London)

Abstract

This paper presents a novel game theory approach for large-scale deployment of price-responsive electrical appliances. In the proposed distributed control scheme, each appliance independently schedules its power consumption on the basis of a broadcast demand/price signal, aiming to complete its task at minimum cost. The conflicting interactions of the appliances, competing for power consumption at the cheapest hours of the day, are modelled through a differential game with a continuum of players, and efficient deployment of flexible demand is characterized as a Nash equilibrium. A novel approach is adopted to derive necessary and sufficient equilibrium conditions: intrinsic properties of the problem (price monotonicity, unidirectionality of power transfers) are exploited to perform an equilibrium study based on sublevel sets of the considered demand profiles. As a result, it is possible to determine for which penetration levels of flexible demand, types of appliances and inflexible demand profiles it is possible to achieve an equilibrium. Such stable configuration is achieved through the broadcast of a single demand/price signal and does not require iterated exchange of information between devices and coordinator. In addition, the global optimality of the equilibrium is proved, necessary conditions for Pareto optimality are derived, and a preliminary analysis of devices with partial time availability is carried out. The performance of the proposed control strategy is evaluated in simulation, considering realistic future scenarios of the UK power system with large penetration of flexible demand.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:4:d:10.1007_s13235-017-0237-3
    DOI: 10.1007/s13235-017-0237-3
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    References listed on IDEAS

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    1. 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.
    2. Strbac, Goran, 2008. "Demand side management: Benefits and challenges," Energy Policy, Elsevier, vol. 36(12), pages 4419-4426, December.
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    Cited by:

    1. Dong, Zihang & Zhang, Xi & Strbac, Goran, 2021. "Evaluation of benefits through coordinated control of numerous thermal energy storage in highly electrified heat systems," Energy, Elsevier, vol. 237(C).

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