Distortion Factor as a function of total harmonic distortion
Coming to grips with the semantics and vocabulary that apply to “distortion” takes a little discipline, but it isn’t all that intimidating. All you need is a little patience to go over the relevant algebra and not scribble.
Two phrases are commonly encountered in discussions of harmonic distortion. One is total harmonic distortion (THD), and the other is distortion factor (DF). The definition of the first phrase is universally accepted, but the second phrase is often used rather loosely defined and there is no universally accepted definition for it. We now look at distortion and its relationship to power factor (Figure 1).
Some authors have used DF and THD as if they were synonyms, but they are not. The two terms are taken as what was once shown at the following URL:
https://www.p3-inc.com/blog/entry/understanding-total-harmonic-distortion-thd-in-power-systems
(Sadly, this URL was no longer functioning when I last looked for it.)
Figure 1 Power factor, displacement factor and DF equations.
In examining power factor, if we have zero distortion so that voltage and current are both pure sinusoids, the cosine of the angular difference between the voltage and current waveforms becomes the power factor all by itself. However, we do have waveform distortion and harmonics are involved, so we must take DF into account as well.
We will now look at how the above equation changes as DF arises.
First, we reiterate the definition of THD and then we do one more step as shown in Figure 2.
Figure 2 Defining THD as per IEC 61000-2-2 and its square to easily define DF in Figure 3.
That step of showing THD² will be important in just another moment as we address DF (Figure 3).
Figure 3 Deriving DF by dividing the fundamental by the all-inclusive power and taking the square root of it, leading to the definition of THD.
Power delivered to a load is that of the fundamental frequency signal as I1² plus that of the second harmonic signal as I2² plus that of the third harmonic signal as I3² and so on and so on to as many harmonics as there are in the driving waveform.
As seen in the first line of Figure 3, we look at the ratio of the power delivered by the fundamental divided by the all-inclusive power and take the square root of that ratio, that leads to the DF. A little algebraic manipulation then takes us to the equation for DF as a function of THD.
Easy, wasn’t it, but that’s okay. This makes my head spin too.
John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).
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