Probabilistic N‐k failure‐identification for power systems

This article considers a probabilistic generalization of the N‐k failure‐identification problem in power transmission networks, where the probability of failure of each component in the network is known a priori and the goal of the problem is to find a set of k components that maximizes disruption to the system loads weighted by the probability of simultaneous failure of the k components. The resulting problem is formulated as a bilevel mixed‐integer nonlinear program. Convex relaxations, linear approximations, and heuristics are developed to obtain feasible solutions that are close to the optimum. A general cutting‐plane algorithm is proposed to solve the convex relaxation and linear approximations of the N‐k problem. Extensive numerical results corroborate the effectiveness of the proposed algorithms on small‐, medium‐, and large‐scale test instances; the test instances include the IEEE 14‐bus system, the IEEE single‐area and three‐area RTS96 systems, the IEEE 118‐bus system, the WECC 240‐bus test system, the 1354‐bus PEGASE system, and the 2383‐bus Polish winter‐peak test system.