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Identifying the multiple critical components in power systems whose absence together has severe impact on system performance is a crucial problem for power systems known as <inline-formula><tex-math notation="LaTeX">$(N-x)$</tex-math></inline-formula> contingency analysis. However, the inherent combinatorial feature of the <inline-formula><tex-math notation="LaTeX">$N-x$</tex-math></inline-formula> contingency analysis problem incurs by the increase of <inline-formula><tex-math notation="LaTeX">$x$</tex-math></inline-formula> in the <inline-formula><tex-math notation="LaTeX">$(N-x)$</tex-math></inline-formula> term, making the problem intractable for even relatively small test systems. We present a new framework for identifying the <inline-formula><tex-math notation="LaTeX">$N-x$</tex-math></inline-formula> contingencies that captures both topology and physics of the network. Graph theory provides many ways to measure power grid graphs, i.e., buses as nodes and lines as edges, allowing researchers to characterize system structure and optimize algorithms. This article proposes a scalable approach based on the group betweenness centrality concept that measures the impact of multiple components in the electric power grid as well as line outage distribution factors that find the lines whose loss has the highest impact on the power flow in the network. The proposed approach is a quick and efficient solution for identifying the most critical lines in power networks. The proposed approach is validated using various test cases, and results show that the proposed approach is able to quickly identify multiple contingencies that result in violations.

Generalized Contingency Analysis Based on Graph Theory and Line Outage Distribution Factor