Distributionally robust CVaR optimization for resilient distribution system planning with consideration for long-term and short-term uncertainties

Climate change is exerting excessive strain on the environment, leading to an ever-increasing frequency of extreme weather events that negatively impact distribution systems. To mitigate these impacts, this paper presents a distributionally robust conditional value-at-risk (DR-CVaR) optimization approach for resilience-oriented distribution system planning. Firstly, a resilience-oriented distribution system planning model is developed, which incorporates flexible operational resources, such as mobile energy storage prepositioning and demand response program, in the emergency response phase. Then, the uncertainties associated with extreme weather events are addressed using a DR-CVaR optimization approach, where the short-term uncertainty in the occurrence of outages caused by specific extreme weather events is addressed through a distributionally robust optimization approach, while the long-term uncertainty regarding the risk of potential extreme weather events is addressed by a conditional value-at-risk optimization approach. The DR-CVaR model is eventually transformed into an equivalent three-level model and solved using a customized nested column-and-constraint generation algorithm. Finally, case studies are conducted based on the IEEE 33-bus distribution system under several extreme weather events. The numerical results show that the proposed model can reduce the load shedding cost as well as investment cost, which confirms the effectiveness and superiority of the proposed model.