Optimal demand response with energy storage management

We consider the problem of optimal demand response with energy storage management for a power consuming entity. The entity's objective is to find an optimal control policy for deciding how much load to consume, how much power to purchase from/sell to the power grid, and how to use the finite capacity energy storage device and renewable energy, so as to minimize his average cost, being the disutility due to load-shedding and cost for purchasing power. Due to the coupling effect of the finite size energy storage, such problems are challenging and are typically tackled using dynamic programming, which is often complex in computation and requires substantial statistical information of the system dynamics. We instead develop a low-complexity algorithm called Demand Response with Energy Storage Management (DR-ESM). DR-ESM does not require any statistical knowledge of the system dynamics, including the renewable energy and the power prices. It only requires the entity to solve a small convex optimization program with 6 variables and 6 linear constraints every time for decision making. We prove that DR-ESM is able to achieve near-optimal performance and explicitly compute the required energy storage size.