TY - JOUR

T1 - Optimal Electricity Demand Response Contracting with Responsiveness Incentives

AU - Aïd, René

AU - Possamaï, Dylan

AU - Touzi, Nizar

N1 - Funding Information:
Funding: This work was supported by the Finance for Energy Markets Research Centre, the Isaac Newton Institute for Mathematical Sciences [Grant EP/R014604/1."], and Agence Nationale de la Recherche [Grants ANR-15-CE05-0024-02, ANR-16-CE05-0027].
Publisher Copyright:
Copyright: © 2022 INFORMS.

PY - 2022/8

Y1 - 2022/8

N2 - 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.

AB - 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.

KW - demand response

KW - moral hazard

KW - retail electricity markets

UR - http://www.scopus.com/inward/record.url?scp=85135541577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85135541577&partnerID=8YFLogxK

U2 - 10.1287/moor.2021.1201

DO - 10.1287/moor.2021.1201

M3 - Article

AN - SCOPUS:85135541577

SN - 0364-765X

VL - 47

SP - 2112

EP - 2137

JO - Mathematics of Operations Research

JF - Mathematics of Operations Research

IS - 3

ER -