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Optimal Electricity Demand Response Contracting with Responsiveness Incentives

Author

Listed:
  • René Aïd

    (FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF, LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Dylan Possamaï

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Nizar Touzi

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

Abstract

Demand response programs in retail electricity markets are very popular. However, despite their success in reducing average consumption, the random responsiveness of consumers to price events makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. This paper aims at designing demand response contracts that allow to act on both the average consumption and its variance. The interaction between a risk-averse producer and a risk-averse consumer is modelled as a principal–agent problem, thus accounting for the moral hazard underlying demand response contracts. The producer, facing the limited flexibility of production, pays an appropriate incentive compensation to encourage the consumer to reduce his average consumption and to enhance his responsiveness. We provide a closed-form solution for the optimal contract in the linear case. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline and where the consumer is charged a price for energy and a price for volatility. The first-best price for energy is a convex combination of the marginal cost and the marginal value of energy, where the weights are given by the risk-aversion ratios, and the first-best price for volatility is the risk-aversion ratio times the marginal cost of volatility. The second-best price, for energy and volatility, is a decreasing nonlinear function of time inducing decreasing effort. The price for energy is lower (respectively, higher) than the marginal cost of energy during peak-load (respectively, off-peak) periods. We illustrate the potential benefits issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data.

Suggested Citation

  • René Aïd & Dylan Possamaï & Nizar Touzi, 2022. "Optimal Electricity Demand Response Contracting with Responsiveness Incentives," Post-Print hal-03670395, HAL.
  • Handle: RePEc:hal:journl:hal-03670395
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    Cited by:

    1. Ren'e Aid & Annika Kemper & Nizar Touzi, 2023. "A Principal-Agent Framework for Optimal Incentives in Renewable Investments," Papers 2302.12167, arXiv.org.
    2. Rene Aid & Anupama Kowli & Ankur A. Kulkarni, 2023. "Signalling for Electricity Demand Response: When is Truth Telling Optimal?," Papers 2302.12770, arXiv.org, revised Jul 2023.
    3. Camilo Hern'andez & Dylan Possamai, 2023. "Time-inconsistent contract theory," Papers 2303.01601, arXiv.org.
    4. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.
    5. Aïd, René & Kemper, Annika & Touzi, Nizar, 2023. "A Principal-Agent Framework for Optimal Incentives in Renewable Investments," Center for Mathematical Economics Working Papers 675, Center for Mathematical Economics, Bielefeld University.

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