Abstract
In recent years, single-phase frequency-locked loops (FLLs) are gaining more popularity as a signal processing and synchronization tool in a wide variety of engineering applications. In the power and energy area, a basic structure in designing the majority of available single-phase FLLs is the second-order generalized integrator-based FLL (SOGI-FLL), which is a nonlinear feedback control system. This nonlinearity makes the SOGI-FLL analysis complicated. To deal with this problem, some attempts to derive linear models for the SOGI-FLL have been made in very recent years. The available linear models, however, are not able to accurately predict the dynamic behavior, stability region, and robustness metrics of the SOGI-FLL. The situation is even worse for close variants of the SOGI-FLL because some of them have no linear model at all. Filling these gaps in research is the main goal of this article. To this end, the structural relationship among the SOGI-FLL and its variants is identified first. Based on this information and deriving the linear time-periodic (LTP) model of a recently proposed extended SOGI-FLL, the LTP models of the standard SOGI-FLL and its close variants are obtained. The accuracy assessment of these LTP models, discussion about their limitations, and performing the stability analysis using them are other contributions of this article.