Grid converters synchronized by phase-locked loops (PLLs) could suffer from stability problems, especially being connected to a weak grid or high penetration of converters. The existing literature assesses the stability of the paralleled PLL-synchronized converters at the same point of common coupling (PCC) using identical control and system parameters. However, in an actual grid, the parameters of grid converters are normally different due to different manufacturers. In this regard, this article aims to study the stability indices and margins of two PLL-synchronized converters with different parameters, particularly with different PLL bandwidths and power injections. The main purpose of this article is to provide a general design guidelines of PLL bandwidths of two converters (can be extended to two wind/solar farms) for stable operation in practical grids. The state-space model of the PLL-synchronized converter based on the component connection method is developed and eigenvalue-based analysis is used to investigate the interactions between the two converters. Moreover, the stability borders of two PLL-synchronized converters using different PLL bandwidths and power setpoints are studies. Monte Carlo simulations and experimental results are provided to validate the effectiveness of the developed model and theoretical analysis.
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