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

Contingency Analysis of Power Networks : A System Theoretic Approach