Fairness of prosumers’ incentives in residential demand response: A practical decentralized optimization approach

This paper presents a new decentralized optimization-based approach for an aggregator involved in residential demand response programs. The proposed approach relies on an existing two-phase optimization framework, whereby prosumers optimize first their self-generation and household consumption, which are subsequently coordinated by the aggregator via incentives through the solution of a mixed-integer linear program. As a distinctive aspect, the notion of fairness in the distribution of incentives among prosumers is incorporated through new nonlinear constraints based on the Shapley Value while respecting standard demand response requirements. A mathematical approximation, which is proven to be exact under certain practical assumptions, is proposed to accommodate the new constraints into the linear model. Furthermore, a novel solution methodology, which combines the divide-and-conquer principle and Dantzig–Wolfe decomposition, is devised to tackle the resulting problem in a distributed fashion. For validation purposes, the behavior of the linear approximations is examined by comparing the results with those attained with their nonlinear counterparts. Moreover, scenarios for prosumers featuring different flexibility levels are generated to assess the practicality of the assumptions adopted. Simulations also show the scalability of the proposed tool by considering cases with up to 10,000 prosumers with computing times within an hour if distributed computing is implemented. Furthermore, as compared to classical Shapley Value approaches, a similar distribution of incentives is attained by the new solution methodology with relative less and acceptable computational effort. Finally, the impact of the new constraints on Peak-to-Average Ratio is quantified, obtaining an increment of up to 13.2% with respect to cases disregarding fairness.