Physics-constrained reconstruction of missing power-system frequency data: An ADMM-based framework and diagnostic evaluation

Reliable high-rate frequency measurements are essential for power-system monitoring, protection, and control, yet telemetry pipelines often contain random losses, burst dropouts, and sensor-failure intervals. This study presents a diagnostic framework for evaluating physics-constrained reconstruction of missing system-frequency samples, rather than a claim of universal superiority over interpolation-based methods. The algorithmic component is an adaptive boundary-regularized ADMM formulation that combines observed-sample fidelity, total-variation regularization, an ODE-inspired dynamic-consistency penalty, and a local boundary-anchor term computed only from observed data. Experiments use public Great Britain 1 Hz system-frequency data and a reproducible HPC workflow. The evaluation compares linear interpolation, shape-preserving cubic interpolation, tuned Kalman smoothing, fixed physics-ADMM, and adaptive boundary-regularized ADMM under fixed block missingness, random independent losses, variable burst gaps, mixed missingness, long sensor-failure outages, and observed-sample noise. Results show that fixed physics-ADMM over-smooths short-to-medium gaps, increasing missing-only RMSE from 7.95 mHz for linear interpolation to 51.49 mHz. Adaptive boundary regularization reduces the fixed-model RMSE to 8.18 mHz, decreases normalized spectral error from 0.0437 to 0.00138, and lowers proxy-control error from 0.0539 to 0.00886. A synthetic graph-coupled multi-stream proof-of-concept reduces RMSE from 8.18 to 6.90 mHz, but this result is interpreted only as preliminary evidence of the potential value of spatial redundancy, not as real multi-bus PMU validation. The study concludes that physical constraints can help only when locally calibrated and, preferably, supported by multi-stream redundancy; otherwise, simple interpolation remains preferable for routine short gaps.