Optimal Energy Management of a Residential Prosumer: A Robust Data-Driven Dynamic Programming Approach

Prosumers are agents that both consume and produce energy. This article studies the optimal energy management of a residential prosumer which consists of a renewable power plant and an energy storage unit. Energy could stream among power grid, renewable plant, storage unit, and demand, providing a highly flexible energy supply and the opportunity of arbitrage. To capture the uncertainty of renewable generation and electricity price, as well as the rolling horizon feature of the multiperiod energy management, the problem is formulated as a robust data-driven dynamic programming (RDDP). Kernel regression is utilized to build the empirical conditional distribution in a data-driven manner, and all candidates that reside in a Wasserstein metric-based ambiguity set are taken into account to tackle the inexactness of the empirical distribution. The RDDP can be transformed into a series of convex optimization problems with cost-to-go functions in their constraints. The piecewise linear expression of the cost-to-go function is retrieved from dual linear programs. Through such an analytical expression of cost-to-go functions, the RDDP can be solved via backward induction, unlike the popular stochastic dual dynamic programming technique that incorporates forward and backward passes. Case studies validate the performance and advantage of the proposed RDDP approach.