A Generalized Design Framework of Notch Filter Based Frequency-Locked Loop for Three-Phase Grid Voltage

Despite many intensive researches regarding frequency-locked loops (FLLs) in recent years, the basic problems of principles, models, and structures of FLL algorithms remained open. Conventional FLL comprises a notch filter and a frequency adaptive loop. The notch filter can be categorized into two types: real coefficient filter (RCF) and complex coefficient filter (CCF). However, the principles, models, and structures of RCF and CCF are generally explained by various theories, and thus, a unified understanding and further developments of FLLs are restricted. This paper proposes a generalized design framework of FLLs based on the Popov adaptive theory. Grounded on the proposed framework, three main contributions can be achieved: 1) the mathematical equivalence of RCF-based FLLs and CCF-based FLLs are revealed; 2) not only the wellknown FLLs (e.g., the DSOGI-FLL and the AVF-FLL) can be derived, but also the other FLLs with novel features can be generated, and thus, the existing case designs of FLLs are developed into a family of designs; 3) the performance differences in terms of stability and convergence speed of the FLLs are quantitatively analyzed, and thereby an enhanced FLL (referred to as EFLL) is recommended. The designs and analyzes have been verified by both simulations and experiments.