Resilience Enhancement for Distribution System With Multiple Non-Anticipative Uncertainties Based on Multi-Stage Dynamic Programming

This paper proposes a day-ahead and intra-day co-optimized resilience enhancement strategy for distribution systems with outages under extreme events, namely, dynamic programming formulated multi-stage hybrid stochastic-robust optimization (DSRO). The DSRO model is a pioneering effort to simultaneously determine the day-ahead decision and the corresponding intra-day policies for microgrids formation, via coupling the two problem with value functions. It establishes a multi-stage framework to address the anticipative challenges inherent in the widely-used two-stage model. For coping with uncertainties, discrete Markov chains are incorporated to model subsequent contingencies, and an uncertainty set for wind generation is constructed to improve computational efficiency. To efficiently solve the DSRO model, a robust dual dynamic programming (RDDP) based solution method is presented, where the relaxed inner approximation method and Lagrangian hyperplanes are employed to handle the nonconvex challenges arising from discrete recourse variables. Case studies on the modified IEEE 14-Bus and 123-Bus distribution systems demonstrate the effectiveness of the proposed model and the solution methodology.