  In this work, we have proposed a system theoretic method to compute
sensitivities of different lines for $N-k$ contingency analysis in power
network. We have formulated the $N-k$ contingency analysis as the stability
problem of power network with uncertain links. We have derived a necessary
condition for stochastic stability of the power network with the link
uncertainty. The necessary condition is then used to rank order the
contingencies. We have shown due to interaction between different uncertainties
the ranking can substantially change. The state of the art $N-k$ contingency
analysis does not consider the possibility of interference between link
uncertainties and rank the links according to the severity of $N-1$
contingencies. We have presented simulation results for New England $39$ bus
system as a support of our claim.
