Risk of Cascading Blackouts Given Correlated Component Outages
Cascading blackouts typically occur when nearly simultaneous outages occur in <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> out of <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> components in a power system, triggering subsequent failures that propagate through the network and cause significant load shedding. While large cascades are rare, their impact can be catastrophic, so quantifying their risk is important for grid planning and operation. A common assumption in previous approaches to quantifying such risk is that the <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> initiating component outages are statistically independent events. However, when triggered by a common exogenous cause, initiating outages may actually be correlated. Here, copula analysis is used to quantify the impact of correlation of initiating outages on the risk of cascading failure. The method is demonstrated on two test cases; a 2383-bus model of the Polish grid under varying load conditions and a synthetic 10 000-bus model based on the geography of the Western US. The large size of the Western US test case required development of new approaches for bounding an estimate of the total number of <inline-formula><tex-math notation="LaTeX">$N-3$</tex-math></inline-formula> blackout-causing contingencies. The results suggest that both risk of cascading failure, and the relative contribution of higher order contingencies, increase as a function of spatial correlation in component failures.