Spectral analysis of instantaneous powers in single-phase and three-phase systems with use of p-q-r theory

Three linearly independent instantaneous powers have been defined in the time domain in three-phase four-wire systems with the use of p-q-r theory. Any three-phase circuit can be transformed into three single-phase circuits by the p-q-r transformation. Thus the instantaneous powers in any three-phase systems can be analyzed as the same way of instantaneous power in single-phase systems. This paper analyzes the instantaneous powers spectrally in the frequency domain for single-phase systems and three-phase systems. Each instantaneous power in three-phase systems has its own spectral pattern that is characterized by the spectral distribution of the system voltages and currents. The instantaneous power in single-phase systems has its own spectral pattern different from that of three-phase systems. From the spectral analysis of the instantaneous powers, powers are newly defined in the frequency domain. The definition of the powers is consistent through single-phase systems and three-phase systems and agrees well with the traditional definition of powers in sinusoidal single-phase systems. Based on the defined powers, some useful power quality factors are defined to evaluate power qualities for various circuit conditions.