Traditional simulation-based method for resilience assessment of distribution systems is very time consuming since the network topology is characterized with a large number of scenario-specific optimization models. In this paper, we propose a methodology for fast resilience assessment of distribution systems with a non-simulation-based method, which can significantly improve the assessment accuracy and computational efficiency. First, a probabilistic metric is proposed to assess the system resilience against extreme events, which quantifies the system performance starting from the pre-event stage to the post-event stage. Then, a mixed-integer linear programming (MILP) is proposed to model the energization paths (EPs) with binary decision variables. Subsequently, the resilience metric-related probability events are built using the EPs. Last, the probabilistic resilience metric is explicitly expressed based on the total probability formula, conditional probability formula and EP-topology simplification methods. In the proposed method, the topology evolution along with the system degradation, restoration (part healed) and recovery (all healed) is characterized with a non-simulation-based method, rather than the multiple scenarios in traditional methods. The numerical tests validate the effectiveness of the proposed method and superiority over the simulation-based approach.
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