  We consider joint energy storage management and load scheduling at a
residential site with integrated renewable generation. Assuming unknown
arbitrary dynamics of renewable source, loads, and electricity price, we aim at
optimizing the load scheduling and energy storage control simultaneously in
order to minimize the overall system cost within a finite time period. Besides
incorporating battery operational constraints and costs, we model each
individual load task by its requested power intensity and service durations, as
well as the maximum and average delay requirements. To tackle this finite time
horizon stochastic problem, we propose a real-time scheduling and storage
control solution by applying a sequence of modification and transformation to
employ Lyapunov optimization that otherwise is not directly applicable. With
our proposed algorithm, we show that the joint load scheduling and energy
storage control can in fact be separated and sequentially determined.
Furthermore, both scheduling and energy control decisions have closed-form
solutions for simple implementation. Through analysis, we show that our
proposed real-time algorithm has a bounded performance guarantee from the
optimal T-slot look-ahead solution and is asymptotically equivalent to it as
the battery capacity and time period goes to infinity. The effectiveness of
joint load scheduling and energy storage control by our proposed algorithm is
demonstrated through simulation as compared with alternative algorithms.
