A distorted periodic current waveform can be decomposed into a set of orthogonal waveforms, (e.g. by Fourier analysis). The RMS value of the composite waveform (I) may be computed as the root-sum-squared of the RMS values of all of the orthogonal components {I h }. 1.The DC component, I 0, is usually (but not always) equal to zero. 2.The fundamental component, I 1, is the only component that contributes to real power. 3.All the other components contribute to the RMS harmonic distortion current, I d : Current Distortion

Undistorted cosine,  v = 0 Fundamental Harmonics

Current Distortion

Total Harmonic Distortion (THD) is defined as the ratio of the RMS harmonic distortion current I D to the RMS value of the fundamental component I 1 : thus… (assuming zero DC) Total Harmonic Distortion THD can be measured using a distortion analyser.

If the form of the current waveform i(t) is known... Determine I D by Fourier Analysis: Given i(t) having period T,  = 2  /T: Compute I DC and I RMS The first Fourier coefficient is: DPF = cos(  1 ) Note:

Apparent power, S, is defined as the product of RMS voltage V, and RMS current I : Apparent Power We now can express Real Power in terms of apparent power S, DPF and THD :

Power Factor Power Factor is defined as the ratio of real power to apparent power: