Abstract
Second-order generalized integrator (SOGI) combined with frequency-locked loop (FLL) is widely used in grid synchronization. Recently, continuous linear time-periodic (LTP) models have been proposed to analyze the stability of SOGI-FLL and its variants. However, they are not accurate enough for discrete methods and not convenient to include harmonics in the input voltage signal. Besides, when the FLL is present, the transfer functions of the closed-loop SOGI are no more accurate. This paper firstly introduced a universal SOGI-FLL in both continuous and discrete forms, which contains two observer gains and a proportional-integral (PI) controller in the FLL to improve the dynamics. Secondly, its discrete LTP models are derived in both dq frame and in αβ frame. The dq-frame model uses amplitude and phase angle as input and output variables, while the up-frame model uses in-phase and quadrature components as input and output variables. Finally, harmonic analysis is carried by harmonic transfer function (HTF) based on the up-frame model. Simulations and experimental results verified the correctness of the models and the harmonic analysis.
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