Learning Adaptive Topology-Aware Line Margins for AC Optimal Power Flow under Forecast Uncertainty and Distribution Shift

Power-system operation is increasingly exposed to weather-driven uncertainty as variable renewable generation expands. Fixed transmission margins can be either unnecessarily conservative or insufficiently secure. We propose a learning-augmented strategy that adapts line margins before each AC optimal power flow (AC-OPF), using offline AC supervision and selectively invoking online scenario sampling for uncertain decisions. On a synthetic GB-inspired seven-bus network exposed to solar forecast uncertainty, the hybrid achieves 94.7\% realised AC feasibility while reducing objective by 7.5\% and increasing feasibility by 1.9 percentage points relative to a fixed conservative margin. Under extreme solar uncertainty it remains 12.3\% cheaper and 1.7 points more feasible. The results show that adaptive state-dependent transmission margins can improve the economic and security trade-off while retaining conventional AC-OPF for dispatch.