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Optimal electricity demand response contracting with responsiveness incentives

Author

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  • Ren'e Aid
  • Dylan Possamai
  • Nizar Touzi

Abstract

Despite the success of demand response programs in retail electricity markets in reducing average consumption, the random responsiveness of consumers to price event makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. The variance of consumers' responses depreciates the value of these mechanisms and makes them weakly reliable. This paper aims at designing demand response contracts which 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 through a Principal--Agent problem, thus accounting for the moral hazard underlying demand response contracts. We provide closed--form solution for the optimal contract in the case of constant marginal costs of energy and volatility for the producer and constant marginal value of energy for the consumer. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline. Further, the consumer cannot manipulate the baseline at his own advantage. The second--best price for energy and volatility are non--constant and non--increasing in time. The price for energy is lower (resp. higher) than the marginal cost of energy during peak--load (resp. off--peak) periods. We illustrate the potential benefit issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data. We predict a significant increase of responsiveness under our optimal contract and a significant increase of the producer satisfaction.

Suggested Citation

  • Ren'e Aid & Dylan Possamai & Nizar Touzi, 2018. "Optimal electricity demand response contracting with responsiveness incentives," Papers 1810.09063, arXiv.org, revised May 2019.
  • Handle: RePEc:arx:papers:1810.09063
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    References listed on IDEAS

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    Cited by:

    1. Kaitong Hu & Zhenjie Ren & Junjian Yang, 2019. "Principal-agent problem with multiple principals," Working Papers hal-02088486, HAL.
    2. Romuald Elie & Emma Hubert & Thibaut Mastrolia & Dylan Possamai, 2019. "Mean-field moral hazard for optimal energy demand response management," Papers 1902.10405, arXiv.org, revised Mar 2020.
    3. Emma Hubert, 2020. "Continuous-time incentives in hierarchies," Papers 2007.10758, arXiv.org.

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