  In this paper, we consider the problem of optimal demand response and 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, 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.
