A Scalable Formulation for Look-Ahead Security-Constrained Optimal Power Flow

We consider the look-ahead security-const- rained optimal power flow (LASCOPF) problem under transmission line and generator contingencies. We first formulate LASCOPF under the
$N-1$
contingency criterion (
$\text{LASCOPF}_1$
) using the dc power flow model. We observe that the number of decision variables in the comprehensive formulation increases quadratically with the number of look-ahead intervals,
$T$
, making the problem infeasible to solve for large
$T$
. To overcome this, we propose the reduced LASCOPF problem (
$\text{LASCOPF-r}_1$
) in which the number of decision variables increases only linearly with
$T$
. Thereafter, we prove that, barring borderline cases, if
$\text{LASCOPF}_1$
is feasible then the optimal solutions of
$\text{LASCOPF}_1$
and
$\text{LASCOPF-r}_1$
are equivalent. We then extend our results to the
$N-k$
contingency criterion (
$\text{LASCOPF-ru}_k$
) for any collection of
$k$
contingencies, and we prove that the ordering of the contingencies does not affect the optimal solution. We then illustrate
$\text{LASCOPF}_1$
on a simple 2-bus 2-generator system. We show the numerical benefits of the proposed
$\text{LASCOPF-r}_1$
formulation on the IEEE 118-bus, the IEEE 300-bus, and the 2383-bus Polish systems.