Accurate Modeling of PLL With Frequency-Adaptive Prefilter: On the Positive Feedback Effect

Phase locked loops (PLLs) with frequency-adaptive prefilters could suppress input disturbances and thus are widely studied. However, their accurate models are absent in the literature. In particular, the impact of frequency adaption (FA) is underestimated. This letter proposes the accurate and analytical modeling method with focus on the impact of frequency adaption, by taking the PLL based on dual second-order generalized integrator (DSOGI) as an example. The proposed model can precisely describe the transient behaviors of DSOGI-PLL, especially the couplings among amplitude, phase angle, and frequency. Moreover, it reveals that the FA creates a positive feedback path, which is the essential reason for the instability phenomenon and the key factor limiting the PLL performance. Experimental results have verified the accuracy of the proposed model.

I. Introduction

Phase locked loop (PLL) is a widely used technique for grid synchronization [1]. Since the standard PLL is vulnerable to input unbalance and distortions [2], additional filters are commonly incorporated, such as the moving average filter [3], [4], notch filter [5], delayed signal cancellation operator [6]–[7], dual complex-coefficient filter [8], dual second-order generalized integrator (DSOGI) [9], and others [2]. It is preferable to place the filters before PLL as it does not generate phase delay for the control loop [2]. Besides, parameters of the additional filters are usually frequency adaptive, so as to handle the grid frequency variation in practice. Beneficially, these advanced PLLs could effectively suppress input disturbances at the steady state, even the grid frequency deviates greatly from the nominal value.