A park-vector approach to displacement and distortion in three-phase systems: The role of the power factor and the imaginary power

The classic phasorial formalism employed to represent the single-phase systems in the time domain can be extended to the three-phase systems by means of the Park approach. It analytically extends the phasorial approach to the Gauss plane in terms of three-phase vectors, so that the power phenomena, which in the single-phase systems are represented by real quantities, are expressed, in the three-phase systems, by complex quantities. The power factor concept is extended as well, and the imaginary power can be introduced as an extension to the three-phase systems, of the reactive power concept. By analyzing the Park three-phase vectors in the frequency domain, a decomposition of the power factor into two terms can be attained: the first term takes into account the displacement effects, while the second term takes into account the distortion effects. Examples are given to show the meaning of the proposed decomposition in practical situations.