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Mean-field moral hazard for optimal energy demand response management

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Document pages: 54 pages

Abstract: We study the problem of demand response contracts in electricity markets byquantifying the impact of considering a mean-field of consumers, whoseconsumption is impacted by a common noise. We formulate the problem as aPrincipal-Agent problem with moral hazard in which the Principal - she - is anelectricity producer who observes continuously the consumption of a continuumof risk-averse consumers, and designs contracts in order to reduce herproduction costs. More precisely, the producer incentivises the consumers toreduce the average and the volatility of their consumption in different usages,without observing the efforts they make. We prove that the producer can benefitfrom considering the mean-field of consumers by indexing contracts on theconsumption of one Agent and aggregate consumption statistics from thedistribution of the entire population of consumers. In the case of linearenergy valuation, we provide closed-form expression for this new type ofoptimal contracts that maximises the utility of the producer. In most cases, weshow that this new type of contracts allows the Principal to choose the risksshe wants to bear, and to reduce the problem at hand to an uncorrelated one.

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