Allocating distributed generators for resilient distribution system under uncertain probability distribution of natural disasters

In this paper, a new distributionally robust defender-attacker-defender (DAD) model is proposed for the planning of line hardening and allocating distributed generators (DG), to hedge against the risk of disruptions brought by natural disasters or extreme weather conditions. In our approach, we consider the case that the true probability distribution of extreme weather is ambiguous, and minimize the load shedding with the worst-case scenario of weather distribution. Unlike conventional robust models, our approach takes advantage of moment information of the weather distribution that is learned from historical data. We reformulate the proposed model as a tractable two-stage robust optimization and employ a column-and-constraint generation algorithm to solve it. Case study on the IEEE 32-node distribution test system illustrates the effectiveness of the proposed method.