When Does Learned Constraint Selection Pay in Security-Constrained Optimisation? A Boundary Map from SCOPF to Unit Commitment

arXiv:2611.15142v1 Announce Type: cross Abstract: Learning-to-optimise methods for security-constrained optimal power flow (SCOPF) predict the security constraints that bind on each instance and solve only the reduced problem, with reported speed-ups of two to four orders of magnitude over the full problem. We ask whether learned selection beats the strongest learning-free alternative: a fixed umbrella set enforcing every constraint observed to bind in training. Our criterion, the price of a spare, answers this in advance: an enforced but inactive constraint is free, so the umbrella is exactly optimal wherever feasible, and learning can pay only where a spare decision carries a price. We test it systematically, including every PGLib-OPF network up to 10,000 buses. For SCOPF on a fixed network the umbrella is never beaten: its median size is five constraints across 43 networks, with no size trend, and our selector, while reproducing speed-ups of published magnitude (about x80,000 at case500), gains at most 0.25 ms over the umbrella and violates constraints on 4-5% of instances. Configuration diversity can break the umbrella's coverage on a small, densely meshed network but not at 2,000 buses, and we certify coverage with conformal risk control. In unit commitment, where a spare has a price, a static commitment loses 4-12% out of sample, and a predict-repair-reduce pipeline recovers it (cost gap 0.2-2.9%, fully feasible, 16-161x faster than the MILP). In our experiments, whether learning pays depends not on problem size but on whether a spare carries a price.