Vulnerability Analysis of Power Grids With Line Switching

Vulnerability analysis of a power grid, especially in its static status, is often performed through solving a bi-level optimization problem, which, if solved to optimality, yields the most destructive interdiction plan with the worst loss. As one of the most effective operations to mitigate deliberate outages or attacks, transmission line switching recently has been included and modeled by a binary variable in the lower level decision model. Because this bi-level (or an equivalent min-max) problem is a challenging non-convex discrete optimization problem, no exact algorithm has been developed, and only a few recent heuristic procedures are available. In this paper, we present an equivalent single-level reformulation of this problem, and describe a column-and-constraint generation algorithm to derive the global optimal solution. Numerical study confirms the quality of solutions and the computational efficiency of the proposed algorithm. Discussion and analysis of the mitigation effect of line switching are presented.