Robust Unit Commitment With Multi-State Uncertainty: A Novel Formulation and Scalable Solution Method

To mitigate the conservatism of scheduling schemes derived from the two-stage robust unit commitment model (TS-RUCM), this paper proposes a novel multi-state uncertainty set (MSUS) considering the uncertain wind power output (WPO). The MSUS formulates WPO uncertainties with higher resolution by introducing multiple discrete state values within the uncertain interval. Additionally, the MSUS limits extreme fluctuations of WPO uncertainties among state values through transition indicators embedded in multiple transition constraints. The state values and transition indicators are calculated using the conditional quantile regression technique and Markov chain analysis. This systematic and scientific approach allows the MSUS to effectively exclude low-probability WPO scenarios, thereby significantly mitigating the conservatism of the scheduling schemes. Moreover, to accelerate the computation of the TS-RUCM based on the MSUS, this paper proposes an improved inexact column and constraint generation (II-C&CG) method. The II-C&CG method employs an adaptive tolerance strategy and refined backtracking to solve master and subproblems inexactly while ensuring finite convergence, significantly reducing computational time. Case studies demonstrate the effectiveness and advantages of both the MSUS and the II-C&CG method.