Multi-Stage Robust Reactive Power Optimization in Active Distribution Networks With Discrete Intertemporal Constraints

Reactive power regulation is crucial for active distribution networks (ADNs). This paper studies the multi-stage reactive power optimization in ADNs with renewables considering intertemporal constraints imposed on total action times of discrete regulation facilities. First, we regard reactive power regulation as a sequential decision-making process and formulate it as a multi-stage robust optimization problem with hybrid continuous and discrete recourses. Then, we propose a customized implicit policy method to solve this problem, devising bounding variables and non-anticipative constraints of shunt capacitor bank (SCB) and on-load tap changer (OLTC). Next, the bounding variables are optimized prior to dispatch subject to non-anticipative constraints; with their help, intertemporal couplings are broken and the multi-stage robust optimization problem shrinks to a two-stage robust one, which can be solved by decomposition algorithms. Finally, we use the bounding variables to build a non-anticipative and robustly feasible policy based on time-decoupled optimal power flow (OPF) where intertemporal constraints are relaxed but satisfied at the optimums. Case studies on the modified IEEE 33-bus, 69-bus, and 123-bus systems verify the advantages of the proposed method.