On The Detection of Minimum Forecast Horizon For Real-Time Scheduling of Energy Storage Systems in Smart Grid

TL;DR

This paper tackles the problem of identifying the minimum forecast horizon $T^*$ required for rolling-horizon ESS scheduling to replicate the globally optimal control under price uncertainty. It introduces a trajectory-alignment criterion, rather than end-state matching, and proposes an algorithm to determine the smallest $T$ for which first-stage actions $\\hat{p}_t^{(T)}$ align with the global optimal sequence $p_t^*$ within a tolerance $\\varepsilon$. Using a realistic DK1 price series and a detailed ESS model, the study finds $T^* = 60$ hours in the exemplar case, with shorter horizons causing substantial suboptimality, while certain ESS parameter settings can eliminate the existence of a finite horizon that guarantees convergence. The work provides a practical, action-level horizon framework for ESS scheduling and suggests avenues for analytical bounds and stochastic extensions to improve real-time decision-making under price volatility. Overall, the results offer operational guidance on horizon selection and establish a foundation for theory-driven guarantees in storage scheduling under uncertainty.

Abstract

The increasing integration of energy storage systems (ESSs) into power grids has necessitated effective real-time control strategies under uncertain and volatile electricity prices. An important problem of model predictive control of ESSs is identifying the minimum forecast horizon needed to exactly simulate the globally optimal control trajectory. Existing methods in the literature provide only sufficient conditions and might ignore real-world inconsistencies in control actions. In this paper, we introduce a trajectory-alignment-based definition of the minimum forecast horizon and propose an algorithm that identifies the minimum planning horizon for which all rolling-horizon control decisions match those of the full-horizon global optimization. Using real price data from the bidding zone DK1 in Denmark of the Nord Pool day-ahead market and a realistic ESS model, we illustrate that $60$ hours of forecast horizon allows us to exactly simulate the global control sequence and economic outcomes. In addition, we illustrate that under other parameter configurations, no forecast horizon ensures full convergence, demonstrating the sensitivity of the existence of a forecast horizon to various parameters. Our findings provide an operationally significant framework for minimum forecast horizon detection in storage scheduling and pave the way for the analytical description of this important planning measure.

Figures (11)

• Figure 1: Day-ahead hourly electricity prices of DK1 between January and March 2024.
• Figure 2: Cumulative profit from the global optimization over 2,184 hours.
• Figure 3: Global optimal charging and discharging schedule.
• Figure 4: State of energy (SoE) trajectory under the global solution.
• Figure 5: Forecast horizon match matrix.

Theorems & Definitions (1)

• Definition 1: Minimum Forecast Horizon