Resilience of power distribution is pertinent to the energy grid under severe weather. This work develops an analytical formulation for large-scale failure and recovery of power distribution induced by severe weather. A focus is on incorporating pertinent characteristics of topological network structures into spatial temporal modeling. Such characteristics are new notations as dynamic failure- and recovery-neighborhoods. The neighborhoods quantify correlated failures and recoveries due to topology and types of components in power distribution. The resulting model is a multi-scale non-stationary spatial temporal random process. Dynamic resilience is then defined based on the model. Using the model and large-scale real data from Hurricane Ike, unique characteristics are identified: The failures follow the 80/20 rule where 74.3% of the total failures result from 20.7% of failure neighborhoods with up to 72 components “failed” together. Thus the hurricane caused a large number of correlated failures. Unlike the failures, the recoveries follow 60/90 rule: 59.3% of recoveries resulted from 92.7% of all neighborhoods where either one component alone or two together recovered. Thus about 60% recoveries were uncorrelated and required individual restorations. The failure and recovery processes are further studied through the resilience metric to identify the least resilient regions and time durations.
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