Robust and Optimal Consumption Policies for Deadline-Constrained Deferrable Loads

The paper analyzes the optimal response of an individual smart load with deferrable demand for electricity, to exogenous and stochastic price processes. It is assumed that a smart load can delay a time-flexible energy demand up to a fixed deadline. Under mild assumptions on the regularity of the stochastic price process, it is shown that the optimal strategy is to consume only when the price is less than or equal to a certain threshold that depends only on the time left to the deadline and the price statistics. This analysis is performed under both perfect and partial information about the statistics of the price process. Robust policies with performance guarantees are derived for the partial information case. Such performance bounds are also used for deriving upper and lower bounds on the economic value of load-shifting. Numerical simulation results based on price data from wholesale electricity markets suggest that when information must be empirically extracted from data, the robust policies provide various theoretical and practical advantages over the full information policies.