Modeling Phase-Locked Loop-Based Synchronization in Grid-Interfaced Converters

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Grid converters need a synchronization which is often a phase-locked loop (PLL) to get connected to the grid. In the literature, impedance-based models using small-signal technique have been widely utilized to describe the behaviors of PLL-synchronized grid converter. However, most of them target at specific problems and are able to represent the phenomenon under certain scenarios. For the analysis during phase transient, like phase jump due to grid fault, an accurate model is still missing. To address this issue, a general impedance-based model using Maclaurin expansions for its trigonometric function approximation has been proposed in this paper, so that it can well represent the system behavior during phase transient. Moreover, different deepness of the general model can be scaled, leading to different models including phasorial model, current source model, impedance-based model with/without PLL effects. A guideline on how to choose a proper model based on the problems to be studied and grid conditions has been provided in this paper. Simulation and experimental results are given to validate the effectiveness of the model and the theoretical analysis.