Methods and systems for synchronizing an electric grid having unbalanced voltages are provided. A voltage vector may be filtered in a quadrature tracking filter (QTF) to generate a quadrature signal. The inputs to the QTF may be either single input, multiple outputs, or alternatively, multiple inputs, multiple outputs. Furthermore, the second state of either of the two QTF transformations may be either positive or negative. A phase-locked-loop (PLL) operation may be performed on the quadrature signal to monitor a voltage vector between the grid and a connected power converter. The QTF and PLL methods are suitable for either single-phase applications or n-phase (any number of phases) applications.