Definition of harmonics

The term THD means Total Harmonic Distortion and is a widely used notion in defining the level of harmonic content in alternating signals.

Definition of THD
For a signal y, the THD is defined as:

[math]\displaystyle{ THD=\frac{\sqrt{\sum_{h=2}^{h=H} Y_h^2}}{Y_1} =\frac{\sqrt{Y_2^2+Y_3^2+...+Y_H^2}}{Y_1} }[/math]

This complies with the definition given in standard IEC 61000-2-2.Note that the value can exceed 1.
According to the standard, the variable H can be limited to 50. The THD is the means to express as a single number the distortion affecting a current or voltage flowing at a given point in the installation. The THD is generally expressed as a percentage.

Current or voltage THD
For current harmonics, the equation is:

 [math]\displaystyle{ THD_i=\frac{\sqrt{\sum_{h=2}^{h=H} I_h^2}}{I _1} }[/math]

The equation below is equivalent to the above, but easier and more direct when the total rms value is available:
[math]\displaystyle{ THD_i= \sqrt{\left (\frac{Irms}{I_1}\right)^2 - 1} }[/math] 

For voltage harmonics, the equation is:
[math]\displaystyle{ THD_u=\frac{\sqrt {\sum_{h=2}^{h=H} U_h^2}}{U_1} }[/math]

Relation between power factor and THD

(see Fig. M13)

When the voltage is sinusoidal or virtually sinusoidal, it may be said that:
P = P₁ = U₁.I₁.c'o'sφ₁
Consequently:

[math]\displaystyle{ PF=\frac{P}{S}=\frac{U_1.i_1.cos \phi_1}{U_1.I_{rms}} }[/math]
as:

[math]\displaystyle{ \frac{I_1}{I_{rms}}=\frac{1}{\sqrt {1 + THDi^2}} }[/math]

hence:
[math]\displaystyle{ PF=\frac{cos \phi_1}{\sqrt {1 + THDi^2}} }[/math]
Figure M13 shows a graph of [math]\displaystyle{ \frac{PF}{cos\phi} }[/math] as a function of THDi.

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Fig. M13: Variation in [math]\displaystyle{ \frac{PF}{cos\phi} }[/math] as a function of the THDi, where THDu = 0

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