Service-Constrained Critical Energy-Headroom Boundaries for Current-Limited Grid-Forming Battery Converters

Grid-forming battery energy storage systems may remain synchronized yet fail to deliver active- and reactive-power service after severe disturbances. This paper develops a service-constrained critical energy-headroom framework for current-limited grid-forming converters. A 17-state averaged dq model separates converter-terminal, point-of-common-coupling, source, and battery-side power and retains current-control, modulation, DC-link, finite-source, thermal, state-of-charge, and reserve dynamics. A zero-inclusive global search refines feasibility-class transitions, retains disconnected feasible intervals, and reports the minimum reserve feasible for all larger tested reserves. For a 250 ms reference fault, finite conventional, adaptive active-power, and recovery-aware governor controls require 0.1498, 0, and 0.0029 pu-s, with scheduled-energy deficits of 0.165, 0.442, and 0.869 pu-s. The governor reduces headroom by 98.1% relative to finite control but requires nearly twice the adaptive deficit. In 500 paired uncertainty samples, feasibility is 95.8%, 100%, and 100%; all 21 discordant pairs favor each reference-reduction strategy (exact McNemar p=9.54×10−7). The independent Latin-hypercube construction, fixed random seeds, failure mechanisms, numerical resolution, and comparator-tuning boundary are reported explicitly. A stronger zero-headroom envelope resolves the adaptive controller’s failure domain, and all controls fail the repeated-fault test. The results support the boundary methodology, not superiority of the illustrative governor: reserve, delivered energy, current compliance, reactive support, limiter release, and recovery must be assessed jointly.