Model Linearization Analysis for Three-Phase Unbalanced Phase-Locked Loop Techniques

This paper initiatively models the open-loop transfer functions of the phase-locked loop (PLL) methods such as DDSRF-PLL, DSOGI-PLL, and DCCF-PLL which are usually employed under three-phased unbalanced grid voltage conditions. First, DDSRF-PLL is divided into two structures, and DSOGI- PLL is divided into four structures through the adjustment of these PLL structures. Secondly, the open-loop transfer functions can be derived for the above seven PLL structures at the rated grid frequency through the model analysis and linearization of them, respectively. When the parameters of these PLL structures satisfy a certain relationship, we can come to a conclusion through comparison of the open-loop transfer functions of these PLL structures that some of the PLL structures are identical to each others. Finally, the PLL structure with the best overall performance index including stability and frequency response characteristics can be determined through the comparative analysis of the phase margins and crossover frequencies of the PLL structures with different open-loop transfer functions, which can be further validated through the simulation analysis.