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This paper presents a new multiresonant frequency-adaptive synchronization method for grid-connected power converters that allows estimating not only the positive- and negative-sequence components of the power signal at the fundamental frequency but also other sequence components at other harmonic frequencies. The proposed system is called MSOGI-FLL since it is based on both a harmonic decoupling network consisting of multiple second-order generalized integrators (MSOGIs) and a frequency-locked loop (FLL), which makes the system frequency adaptive. In this paper, the MSOGI-FLL is analyzed for single- and three-phase applications, deducing some key expressions regarding its stability and tuning. Moreover, the performance of the MSOGI-FLL is evaluated by both simulations and experiments to show its capability for detecting different harmonic components in a highly polluted grid scenario.