Frequency Estimators for SOGI FLL: Modeling, Design, and Equivalence for FLL Advancements

Different frequency estimators have been reported for frequency-locked loop (FLL) implementations. One example is the widely employed gradient descent (GD) estimator in second-order generalized integrator (SOGI) FLL. Whether this estimator differs from those in some existing FLLs is unknown. Therefore, in this article, GD and two other estimators with amplitude normalization in the stationary and synchronous reference frames are developed for SOGI FLL implementation. By obtaining a linear model of SOGI FLL with the three estimators, the equivalence of their FLL is established. Thus, it is shown that when the estimator parameters are designed based on the established equivalence, the FLL dynamics is dictated by the SOGI stage. Thus, research involving orthogonal signal generation is crucial to FLL's rapid advancements. Furthermore, harmonic rejection in SOGI FLL with the estimators is considered where it is shown that SOGI FLL with amplitude normalization in the synchronous reference frame is ideal for applications involving harmonics.