This paper presents a new frequency-adaptive synchronization method for grid-connected power converters which allows estimating not only the positive- and negativesequence components of the power signal at the fundamental frequency, but also other sequence components at multiple frequencies. The proposed system is called the MSOGI-FLL since it is based on a decoupled network consisting of multiple second order generalized integrators (MSOGI) which are frequency-adaptive by using a frequency-locked loop (FLL). In this paper, the MSOGI-FLL is analyzed and its performance is evaluated by both simulations and experiments.