New theory for phasor measurement

This paper provides an introduction to the principles and applications of a new theory for phasor measurement. Incorporating the former one as a particular case, the new theory is able not only to explain the "erratic" transient behavior of most of the phasor estimation algorithms used presently in digital relays, but also to provide filter design criteria to avoid their transient short-comings. From its new approach, based on signal space concepts and the quadrature modulated signal model, each instantaneous phasor estimate is regarded as the rotated projection of a signal segment onto the fundamental plane. Its capability to analyze transient phasors provoked by signals in transient state serves to assess the transient behavior of the filters, or predict the errors provoked by distorted fault signals. According to their projective properties, a distinction is made between circular and cycloid filters. By rejecting negative frequencies, circular filters produce circular paths, while negative frequency infiltration in cycloid filters generate cycloid curves at the output. Finally, phasor transitions of real signals using both types of filters are illustrated in order to confirm the theoretical results.