Online Modified Greedy Algorithm for Storage Control under Uncertainty

TL;DR

This paper introduces the Online Modified Greedy (OMG) algorithm for energy storage control under demand and price uncertainties, providing theoretical performance bounds and demonstrating its effectiveness through numerical experiments.

Contribution

The paper proposes a simple, effective online algorithm with proven sub-optimality bounds for energy storage management under uncertainty, and offers a method to evaluate heuristic algorithms.

Findings

OMG's sub-optimality approaches zero in certain scenarios

The algorithm provides a reliable lower bound for optimal cost

Numerical results confirm theoretical performance bounds

Abstract

This paper studies the general problem of operating energy storage under uncertainty. Two fundamental sources of uncertainty are considered, namely the uncertainty in the unexpected fluctuation of the net demand process and the uncertainty in the locational marginal prices. We propose a very simple algorithm termed Online Modified Greedy (OMG) algorithm for this problem. A stylized analysis for the algorithm is performed, which shows that comparing to the optimal cost of the corresponding stochastic control problem, the sub-optimality of OMG is bounded and approaches zero in various scenarios. This suggests that, albeit simple, OMG is guaranteed to have good performance in some cases; and in other cases, OMG together with the sub-optimality bound can be used to provide a lower bound for the optimal cost. Such a lower bound can be valuable in evaluating other heuristic algorithms. For the latter cases, a semidefinite program is derived to minimize the sub-optimality bound of OMG. Numerical experiments are conducted to verify our theoretical analysis and to demonstrate the use of the algorithm.