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

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.