A robust optimization method for power systems with decision‐dependent uncertainty

Abstract

Abstract Robust optimization is an essential tool for addressing the uncertainties in power systems. Most existing algorithms, such as Benders decomposition and column‐and‐constraint generation (C&CG), focus on robust optimization with decision‐independent uncertainty (DIU). However, increasingly common decision‐dependent uncertainties (DDUs) in power systems are frequently overlooked. When DDUs are considered, traditional algorithms for robust optimization with DIUs become inapplicable. This is because the previously selected worst‐case scenarios may fall outside the uncertainty set when the first‐stage decision changes, causing traditional algorithms to fail to converge. This study provides a general solution algorithm for robust optimization with DDU, which is called dual C&CG. Its convergence and optimality are proven theoretically. To demonstrate the effectiveness of the dual C&CG algorithm, we used the do‐not‐exceed limit (DNEL) problem as an example. The results show that the proposed algorithm can not only solve the simple DNEL model studied in the literature but also provide a more practical DNEL model considering the correlations among renewable generators.

Keywords

• correlations
• decision‐dependent uncertainty
• do‐not‐exceed limit
• renewable energy
• robust optimization