On the Equivalence of Battery Storage and Demand Response: Theoretical analysis and convex optimization

Abstract

Energy storage and demand response are two technologies that are both capable of smoothing over load fluctuations and variations in intermittent wind and solar generation in the electric grid. In this sense, demand response can be thought of as a type of energy storage; indeed, demand response technologies are often referred to as “virtual storage” devices. However, this implied equivalence between demand response and energy storage has never been subjected to a rigorous mathematical analysis. In this paper, we derive the amount of virtual storage capacity provided by a given amount of load flexibility for a idealized electric grid where the load and a portion of the generation are independent memoryless random processes. We find that the virtual storage capacity of demand response decreases with the amount of demand flexibility already existing on the grid. We formulate an optimization problem to find the best combination of storage and demand response that balances the intermittent generation with the load at minimum cost. We hypothesize that this optimization problem is convex and derive some properties of the optimal solution under this hypothesis.