Measurements of power and current components in unbalanced and distorted three-phase systems

The paper deals with the instantaneous power theory in three-phase circuits by using the instantaneous time phasors of voltage and current. Particularly it is shown that the instantaneous components of the current time-phasor in a rotating reference frame p-q, oriented in such a way that the instantaneous voltage time-phasor points to the p-axis direction, represent the active and reactive currents. These components give rise to instantaneous real and imaginary powers, respectively. The spectral analysis of the above-mentioned time-phasors gives the harmonic symmetrical components of positive and negative sequence of voltage and current three-phase systems. The line-by-line product of the voltage sequence spectrum by the complex conjugate of the current sequence spectrum gives the DC components of the instantaneous real and imaginary powers. The paper shows also that the instantaneous active and reactive currents are different from those defined on grounds of the Fryze's theory, which can be determined from the voltage and current sequence spectra.