The $N-k$ Problem in Power Grids: New Models, Formulations, and Numerical Experiments

Given a power grid modeled by a network together with equations describing power flows, power generation and consumption, the so-called $N-k$ problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. The case where k is small is of practical interest. We present theoretical and numerical results involving a mixed-integer linear model and a continuous nonlinear model related to this problem.