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Synchronization with the grid voltage is critical in the control of grid-connected power converters. Under unbalanced grid condition, the conventional synchronous reference frame phase-locked loop (SRF-PLL) does not work well due to the effect of the fundamental negative sequence component. This paper proposes a new synchronization method, the sinusoidal amplitude integrator based phase locked loop (SAI-based PLL), to efficiently eradicate the effect of the fundamental negative sequence component. As a result, it can accurately and quickly estimate the amplitude and phase angle of the fundamental components of grid voltages in unbalanced grid conditions. In addition, when dc offset and harmonics are contained in the grid voltage, a multi-SAI-based PLL method is developed to extract the synchronization signal. The proposed SAI-based PLL incorporates the sinusoidal amplitude integrator into the conventional SRF-PLL. Its operation is analyzed using the complex-vector notation. Simulation and experimental results on the performance of the proposed SAI-based PLL and comparison with other synchronization methods are presented. [ABSTRACT FROM AUTHOR]