Energy peak shaving with local storage

We introduce a new problem inspired by energy pricing schemes in which a client is billed for peak usage. At each timeslot the system meets an energy demand through a combination of a new request, an unreliable amount of free source energy (e.g. solar or wind power), and previously received energy. The added piece of infrastructure is the battery, which can store surplus energy for future use, and is initially assumed to be perfectly efficient or lossless. In a feasible solution, each demand must be supplied on time, through a combination of newly requested energy, energy withdrawn from the battery, and free source. The goal is to minimize the maximum request. In the online version of this problem, the algorithm must determine each request without knowledge of future demands or free source availability, with the goal of maximizing the amount by which the peak is reduced. We give efficient optimal algorithms for the offline problem, with and without a bounded battery. We also show how to find the optimal offline battery size, given the requirement that the final battery level equals the initial battery level. Finally, we give efficient H-n-competitive algorithms assuming the peak effective demand is revealed in advance, and provide matching lower bounds. Later, we consider the setting of lossy batteries, which lose to conversion inefficiency a constant fraction of any amount charged (e.g. 33%). We efficiently adapt our algorithms to this setting, maintaining optimality for offline and (we conjecture) maintaining competitiveness for online. We give factor-revealing LPs, which provide some quasi-empirical evidence for competitiveness. Finally, we evaluate these and other, heuristic algorithms on real and synthetic data. (C) 2011 Elsevier Inc. All rights reserved.