Demand-side energy management under time-varying prices

Under time-varying electricity prices, an end-user may be stimulated to delay flexible demands that can be shifted over time. In this article, we study the problem where each end-user adopts an energy management system that helps time flexible demands fulfillments. Discomfort costs are incurred if demand is not satisfied immediately upon arrival. Energy storage and trading decisions are also considered. We model the problem as a finite horizon undiscounted Markov Decision Process, and outline a tractable approximate dynamic programming approach to overcome the curse of dimensionality. Specifically, we construct an approximation for the value-to-go function such that Bellman equations are converted into mixed-integer problems with structural properties. Finally, we numerically demonstrate that our approach achieves close performance to the exact approach, while dominating the myopic policy and no-control policy. Most importantly, the proposed approach can take advantage of the price differences and efficiently shift demands.