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Optimal Electricity Demand Response Contracting

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MESW01 - Flexible operation and advanced control for energy systems

Co-authors: Dylan Possamaï (Columbia University), Nizar Touzi (Ecole Polytechnique)We address the moral hazard underlying demand response contracts in electricity markets, we formulate the interaction problem between producer and the consumer by means of a Principal-Agent problem. The producer, acting as the Principal, is subject to the generation costs related to the level and the volatility of generation, thus accounting for the limited flexibility of production. Based on the continuous-time consumption of the Agent, representing a single consumer, she sends an incentive compensation in order to encourage him to reduce his average consumption and to improve his responsiveness defined as the volatility of his consumption. We provide closed-form expression for the optimal contract that maximizes the utility of the principal in the case of linear energy valuation. We provide rationality for the form of the observed demand-response contracts, that is a fixed premium for enrolment and a proportional price for the energy consumed. However, we show that the pre mium should be an increasing function of the duration of the demand response event. Further, we show that optimal contracting allows the system to bear more risk as the resulting consumption volatility may increase, but the corresponding risk is now optimally shared between the two actors. We calibrate of our model to publicly available data of the London demand-response trial, and we infer that a significant increase of responsiveness can be expected by the implementation of the control of the consumption volatility. We find that the responsiveness control would lead a significant increase of the value of the producer. We examine the stability of our explicit optimal contract by performing appropriate sensitivity analysis, and show that the linear approximation of the energy value function of the consumer provides a robust approximation of the optimal contract.

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