Is Using A Complex Control Gain in Three-Phase FLLs Reasonable?

A frequency-locked loop (FLL) is a stationary reference frame adaptive recursive filter with a high popularity in different engineering applications, particularly for extracting the grid voltage parameters and synchronization of power converters. In three-phase applications, the reduced-order generalized integrator-based FLL (ROGI-FLL) is a standard structure and a basic unit for designing more advanced FLLs. Very recently, to supposedly enhance the ROGI-FLL performance, using a complex control gain (instead of the traditional real one) in its structure has been proposed in the literature. Applying such a control gain, however, has some drawbacks that have not been discussed before. Explaining these shortcomings is the main objective of this letter. To facilitate this task, a small-signal model for a basic complex-coefficient ROGI-FLL (CC-ROGI-FLL) is obtained and analyzed. A numerical performance comparison between the CC-ROGI-FLL and ROGI-FLL is also conducted.