signal although not explicitly considered in the design the proposed frf pll scheme must reduce also the effects of harmonic distortion existent in the three phase signal the model the idea behind the proposed approach is to propose a model that can reproduce the three phase signal in the most accurately way then based on this model a state estimator plus an adaptation law for the angular frequency are designed in what follows it is considered that the three phase signal is composed only by a fundamental component with the fundamental frequency given by u03c9 2 u03c0f moreover it is considered that the signal originally in three phase coordinates has been transformed to fixed frame u03b1 u03b2 coordinates using the following clarke transformation this non normalized clarke 39 s transformation could be preferred since u03bd u03b1 u03bd 1 thus preserving the amplitude and phase angle of u03bd u03b1 equal to those of u03bd 1 however the algorithm is not restricted to this transformation and thus the following normalized transformation could be used as well without further changes in the scheme all along the document bold typeface characters represent either vectors or matrices while normal typeface characters represent scalars as the unbalanced operation case is considered then.