  The security-constrained optimal power flow (SCOPF) is fundamental in power
systems and connects the automatic primary response (APR) of synchronized
generators with the short-term schedule. Every day, the SCOPF problem is
repeatedly solved for various inputs to determine robust schedules given a set
of contingencies. Unfortunately, the modeling of APR within the SCOPF problem
results in complex large-scale mixed-integer programs, which are hard to solve.
To address this challenge, leveraging the wealth of available historical data,
this paper proposes a novel approach that combines deep learning and robust
optimization techniques. Unlike recent machine-learning applications where the
aim is to mitigate the computational burden of exact solvers, the proposed
method predicts directly the SCOPF implementable solution. Feasibility is
enforced in two steps. First, during training, a Lagrangian dual method
penalizes violations of physical and operations constraints, which are
iteratively added as necessary to the machine-learning model by a
Column-and-Constraint-Generation Algorithm (CCGA). Second, another different
CCGA restores feasibility by finding the closest feasible solution to the
prediction. Experiments on large test cases show that the method results in
significant time reduction for obtaining feasible solutions with an optimality
gap below 0.1%.
