How long is long enough? Finite-horizon approximation of energy storage scheduling problems
Energy storage scheduling problems, where a storage system is operated to maximize its profit in response to a price signal, are naturally formulated as infinite-horizon optimization problems, since storage systems operate continuously, without a foreseen end to their operation. Such problems can be solved to optimality with a rolling-horizon approach, provided that the planning horizon over which the problem is solved is long enough. Such a horizon is termed a forecast horizon. Despite its importance, the planning horizon is usually chosen arbitrarily for such applications. We introduce an easy-to-check condition that confirms whether a planning horizon is a forecast horizon, and which can be used to derive a bound on suboptimality when it is not the case. In practice, this condition enables practitioners to evaluate whether the planning horizon chosen is sufficient, thereby providing, for the first time, a practical means of evaluating and selecting planning horizons for energy storage scheduling problems. We also derive a lower bound on the minimum forecast horizon. Building on the theoretical results, we develop an algorithm to determine the minimum forecast horizon. It enables the identification, a posteriori, of the shortest planning horizon that guarantees optimal rolling-horizon decisions while avoiding unnecessary forecasting effort and computational cost. Numerical experiments illustrate the practical use of the proposed framework and investigate how storage system characteristics and electricity price patterns influence the minimum forecast horizon.