  Security-Constrained Optimal Power Flow (SCOPF) plays a crucial role in power
grid stability but becomes increasingly complex as systems grow. This paper
introduces PDL-SCOPF, a self-supervised end-to-end primal-dual learning
framework for producing near-optimal solutions to large-scale SCOPF problems in
milliseconds. Indeed, PDL-SCOPF remedies the limitations of supervised
counterparts that rely on training instances with their optimal solutions,
which becomes impractical for large-scale SCOPF problems. PDL-SCOPF mimics an
Augmented Lagrangian Method (ALM) for training primal and dual networks that
learn the primal solutions and the Lagrangian multipliers, respectively, to the
unconstrained optimizations. In addition, PDL-SCOPF incorporates a repair layer
to ensure the feasibility of the power balance in the nominal case, and a
binary search layer to compute, using the Automatic Primary Response (APR), the
generator dispatches in the contingencies. The resulting differentiable program
can then be trained end-to-end using the objective function of the SCOPF and
the power balance constraints of the contingencies. Experimental results
demonstrate that the PDL-SCOPF delivers accurate feasible solutions with
minimal optimality gaps. The framework underlying PDL-SCOPF aims at bridging
the gap between traditional optimization methods and machine learning,
highlighting the potential of self-supervised end-to-end primal-dual learning
for large-scale optimization tasks.
