An Exact and Scalable Problem Decomposition for Security-Constrained Optimal Power Flow

In this paper, we present decomposition techniques for solving large-scale instances of the security-constrained optimal power flow (SCOPF) problem with primary response. Specifically, under each contingency state, we require that the nodal demands are met and that the synchronized units generating below their limits follow a linear model for primary response. The resulting formulation is a mixed-integer linear program since the primary response model introduces disjunctions to the SCOPF problem. Unfortunately, exact methods relying on traditional Benders' decomposition do not scale well. As an alternative, we propose a decomposition scheme based on the column-and-constraint-generation algorithm where we iteratively add disjunctions and cuts. We provide procedures for preprocessing dedicated cuts and for numerically determining the post-contingency responses based on the master problem solutions. We also discuss heuristics to generate high-quality primal solutions and upper bounds for the method. Finally, we demonstrate the efficiency of the proposed method on large-scale systems.