An improved two-stage robust optimization approach with adaptive uncertainty set for power system economic dispatch

With the increasing penetration of wind power into the grid, maintaining power balance has become a significant challenge. To address the uncertainty, an improved two-stage robust optimization (RO) approach based on the adaptive uncertainty set is proposed for the day-ahead and real-time economic dispatch. The day-ahead economic dispatch solves the unit commitment (UC) problem in the first stage of RO, while the generation pre-schedule and reserve allocation under the worst-case scenario are determined in the second stage of RO. The traditional UC model is improved by considering of the start-up and shutdown processes. Besides, the consumption service reserve (CSR) is introduced to address the deviation of day-ahead forecast power. At the real-time dispatch stage, the two-stage RO is implemented again with the real-time uncertainty set to mitigate the power deviations through the flexible dispatching of CSR and energy storage systems. In the solution methodology, a nested decomposition algorithm based on column-and-constraint generation is developed for the two-stage RO. Case studies demonstrate that a better balance between solution robustness and operational economy is achieved compared to the deterministic dispatch and the traditional RO. Furthermore, the effectiveness and superiority of the coordinated operation between DAD and RTD are demonstrated by the fact that real-time average operating costs decrease by 43.36% with the proposed approach.