  Cascading blackouts typically occur when nearly simultaneous outages occur in
k out of N 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 $k$ 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 N-3 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.
