Beyond Binary Controllability: Reachability Margins for Power Systems via Scalable Screening

This paper studies unreachability screening for power systems, focusing on the inadequate control authority that arises under stressed grid conditions. Its main result is an infeasibility \textit{margin} for linearized differential algebraic equation models that quantifies how far a prescribed terminal target lies from the reachable set in finite time. The paper specifically develops a conic benchmark method together with two first order methods based on projected subgradients and bundle updates for scalably repeated screening. Studies on IEEE benchmark networks show reduced terminal reachability under stressed conditions and tighter actuation limits, while first order methods remain accurate and substantially faster on large systems. Comparisons with standard reachability methods such as CORA further demonstrate the usefulness and scalability of the proposed infeasibility margins. All results and codes are included in a Github repository.