Adjustable robust optimization with decision-dependent uncertainty for power system problems: A review

The increasing uncertainty caused by volatile renewable generation and random electricity demand has always been a critical challenge in power system operations. Robust optimization (RO) is a powerful tool for effectively addressing this uncertainty. As the interplay between uncertain factors and decision-making becomes more prevalent, RO with decision-dependent uncertainty (DDU) has attracted increasing attention. DDU significantly changes how the uncertainty set in RO is modelled and how the problems are solved. This study provides a comprehensive overview of the recent developments in RO with DDU for power system problems. We begin by introducing various models of DDU, classified according to their underlying causes. Next, we summarize the state-of-the-art solution algorithms for RO with DDU, such as variants of the column-and-constraint generation (C&CG) algorithm, variants of Benders decomposition, and multiparametric programming. Furthermore, we explore the application of RO with DDU in power systems. Based on our findings, we propose several research directions that may be valuable for future studies.