Real-Time Maximum Likelihood Frequency Estimation via Wirtinger Calculus for Low-Inertia Microgrids

Accurate frequency and ROCOF estimation is critical for coordinated primary control, distributed secondary regulation, and reliable ROCOF-based protection in low-inertia, converter-dominated power systems. Rapid frequency variations, harmonic distortion, and transient disturbances challenge conventional synchronization methods such as PLL-based approaches. This paper develops a real-time maximum-likelihood (ML) frequency estimator that reformulates the statistically optimal ML solution into a deterministic constant-time implementation suitable for embedded controllers. Operating in the complexα βdomain, closed-form gradient and Hessian expressions are derived using Wirtinger calculus to enable efficient scalar Newton updates. The key contribution lies in recasting the ML sufficient statistics as sliding demodulated sums updated through circular buffering and coherent rotator recursions, reducing computational complexity fromO(N)toO(1)per sample under uniform sampling. Simulation and experimental results demonstrate improved disturbance rejection, reduced peak ROCOF, and fast settling compared with SRF-PLL, DSOGI-PLL, and DFT-based estimators. DSP validation on a TI LaunchXL-F28379D confirms more than a sevenfold reduction in execution cost relative to the exact ML formulation, enabling statistically grounded frequency estimation with deterministic real-time performance.