How long is long enough? Finite-horizon approximation of energy storage scheduling problems

TL;DR

This paper investigates how to determine the appropriate finite planning horizon for energy storage scheduling problems, providing conditions and algorithms to ensure near-optimal solutions with minimal computational effort.

Contribution

It introduces a practical condition to verify forecast horizons, derives bounds on their length, and offers an algorithm to identify the minimum forecast horizon for optimal storage scheduling.

Findings

Existence of forecast horizons is not guaranteed for all cases.

A lower bound on the minimum forecast horizon is derived.

The proposed method reduces computational and forecasting costs.

Abstract

Energy storage scheduling problems, where a storage is operated to maximize its profit in response to a price signal, are essentially infinite-horizon optimization problems as 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. However, the length of 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. By way of an example, we demonstrate that the existence of forecast horizons is not guaranteed for this problem. We also derive a lower bound on the length of the minimum forecast horizon. We show how the condition introduced can be used as part of an algorithm to determine the minimum forecast horizon of the problem, which ensures the determination of optimal solutions at the lowest computational and forecasting costs. Finally, we provide insights into the implications of different planning horizons for a range of storage system characteristics.