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Given a power grid modeled by a network together with equations describingthe power flows, power generation and consumption, and the laws of physics, theso-called N-k problem asks whether there exists a set of k or fewer arcs whoseremoval will cause the system to fail. The case where k is small is ofpractical interest. We present theoretical and computational results involvinga mixed-integer model and a continuous nonlinear model related to thisquestion.

The N-K Problem in Power Grids: New Models, Formulations and Numerical Experiments (extended version)