Physics-Regularized Graph Temporal Frequency Prediction with Conformal Auditing and Bounded Storage Support in Low-Inertia Transmission Systems

Early assessment of frequency security in low-inertia transmission systems requires nodal forecasts that account for post-contingency topology, electromechanical consistency, and predictive uncertainty. This study develops a dynamic-topology graph recurrent predictor with swing-equation regularization, two-level conformal calibration, and a bounded grid-forming battery energy storage system (GFM-BESS) support interface. Early measurements and the post-contingency network are used to forecast 3s nodal frequency and phase-angle trajectories. Node-pooled residuals calibrate marginal uncertainty, event-maximum residuals assess simultaneous event coverage, and state-of-charge and power headroom constrain gain allocation. On the IEEE 39-bus system, physics regularization reduces the swing-equation residual from 4.18pu to 1.16pu, a 72% reduction in equation residual. Under extreme parameters on the IEEE 39-bus system, nadir and RoCoF errors are 2.44% and 7.93% lower than those of GCN-GRU. On the IEEE 118-bus system, the nadir MAE is 0.00958Hz and the swing-equation residual is 0.8994pu. Event-maximum calibration attains in-distribution event coverages of 0.934 and 0.935 on the IEEE 39- and 118-bus systems, respectively; the corresponding widths of 0.317Hz and 1.119Hz exceed the 0.20Hz decision margin, so the audit withholds an automated event-level safety verdict while bounded support remains active. On the IEEE 39-bus system, forecast-driven support improves the mean nadir by 0.00844Hz and lowers the violation rate from 46.14% to 43.43% relative to no storage. At the main setting β=1, gain saturation limits the incremental nadir change from the interval radii to 1.46×10−5 Hz. Joint reporting of point error, physics residual, interval calibration, and closed-loop response provides an auditable basis for model and controller design.