A distorted 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 }. o The DC component I 0 is usually (but not always) equal to zero. o The fundamental component, I 1 is the only component that contributes to real power (and only the in-phase component). o All the other harmonic components contribute to the RMS harmonic distortion current, I d : Current Distortion

Undistorted cosine,  v = 0 Fundamental Harmonics “Quadrature” Current “In-Phase” Current

… For the fundamental frequency component (from previous slide): …which they are! As always, we have two ways of looking at this... RSRS Pure Reactance RPRP I1I1 I1I1 IPIP IQIQ G B Forehand Backhand

I1I1 IPIP IQIQ G B Non- Linearities I D (Harmonics) I Current Distortion +V-+V- P =P = Total RMS Current Fundamental Harmonics Apparent Power:

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: