  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.
