A high-dimensional steady-state structural framework for regional transmission interface capacity planning using...

The increasing deployment of heterogeneous flexibility resources, including energy storage, pumped-hydro units, and demand response, has substantially reshaped steady-state power-flow patterns in multi-area transmission networks. Conventional transmission planning approaches based on fixed dispatch assumptions or a limited set of representative snapshots are often insufficient to capture the structural effects induced by coordinated flexibility across regions. This paper proposes a physics-informed learning framework for planning-level analysis of steady-state transmission interfaces, with the objective of characterizing the structural behavior of power flows over a broad ensemble of plausible future operating conditions. A large set of representative steady-state scenarios is constructed to reflect long-horizon variations in renewable generation, load profiles, and flexibility activation. These scenarios are embedded into a graph-based representation learning architecture that integrates nodal injections, PTDF-guided propagation, and nonlinear structural correction mechanisms. The learned representation enables the extraction of planning-oriented metrics, including interface flow envelopes, structural sensitivity gradients, stress persistence indicators, and weak-corridor identification scores. Case studies on a realistic multi-area test system show that several critical transmission interfaces exhibit persistent proximity to their structural limits, with sensitivity levels exceeding 90 MW per 100 MW of regional injection shift and stress persistence ratios above 80% across the scenario ensemble. The results further indicate that flexibility deployment does not uniformly alleviate congestion: while some corridors experience a reduction in structural stress, others exhibit amplified interface loading under coordinated storage and demand-response actions. By explicitly capturing these interaction-driven structural behaviors and their associated percentages, the proposed framework provides a complementary analytical tool for transmission planning, enabling interface screening and reinforcement prioritization beyond snapshot-based or purely linear analyses.