Distributionally robust microgrid formation for service restoration in distribution systems against extended extreme events

Extended extreme events with long-lasting destructive effects may result in significant power outages and subsequent contingencies within the distribution system (DS). Microgrid formation (MF) has emerged as a crucial approach for service restoration (SR) under such circumstances since local resources can be utilized to provide temporary power supplies. This paper proposes a novel MF-based SR approach for the DS to maximize the expected weighted load served ratio (WLSR) by allocating mobile power sources and dynamic MF scheduling in the worst case against extended extreme events. Specially, a three-layer distributionally robust optimization SR model is developed in which the uncertainties resulting from subsequent contingencies and uncertain outputs from renewables can be effectively tackled using two different distribution ambiguity sets. Additionally, a two-step MF model allowing for de-energized nodes is incorporated into the SR model. Furthermore, to enhance the computational efficiency, a parallel solving strategy is developed, based on the column-and-constraint generation algorithm, the alternating optimization procedure, and the progressive hedging algorithm. Finally, the case studies are given to demonstrate that the proposed strategy has a good performance on enhancing system resilience by improving the WLSR index during extended extreme events with subsequent uncertainties and facilitating time-sensitive decision-making for SR. • Three-layer DRO model enhances restoration under extreme events with uncertainties. • Two-step microgrid formation framework addresses limitations of existing models. • Parallel solution strategy ensures scalable and efficient computational performance. • Offers improved robustness-optimality trade-off and better out-of-sample performance.