Editing Power factor (section)

=== Distortion power factor ===
The '''distortion power factor''' is the distortion component associated with the harmonic voltages and currents present in the system.
:<math>
\begin{align}
\mbox{distortion power factor}
& = \frac{ I_1}{I_{rms}} \\
& = \frac{I_1} {\sqrt{I_1^2+I_2^2+I_3^2+I_4^2+\cdots}} \\
& = \frac{1} { \sqrt{1+ \frac{I_2^2+I_3^2+I_4^2+\cdots}{I_1^2}}} \\
& = \frac{1} {\sqrt{ 1+THD_i^2}} \\
\end{align}
</math>

<math>\mbox{THD}_i</math> is the [[total harmonic distortion]] of the load current. 
:<math>THD_i = \frac{\sqrt{\displaystyle\sum_{h=2}^\infty I_h^2}} {I_1}= \frac{\sqrt{I_2^2+I_3^2+I_4^2+\cdots}} {I_1}</math>

<math>I_1</math> is the fundamental component of the current, <math>I_{rms}</math> is the total current, and <math>I_h</math> is the current on the h<sup>th</sup> harmonic; all are [[root mean square]] values (distortion power factor can also be used to describe individual order harmonics, using the corresponding current in place of total current). This definition with respect to total harmonic distortion assumes that the voltage stays undistorted (sinusoidal, without harmonics). This simplification is often a good approximation for stiff voltage sources (not being affected by changes in load downstream in the distribution network). Total harmonic distortion of typical generators from current distortion in the network is on the order of 1–2%, which can have larger scale implications but can be ignored in common practice.<ref>{{Citation |url=http://ecmweb.com/power-quality/effects-harmonics-power-systems |title=Effects of Harmonics on Power Systems |first=C. |last=Sankaran |year=1999 |publisher=Electro-Test |quote=...and voltage-time relationship deviates from the pure sine function. The distortion at the point of generation is very small (about 1% to 2%), but nonetheless it exists.}}</ref>

The result when multiplied with the displacement power factor is the overall, true power factor or just power factor (PF):
:<math>\mbox{PF} = \frac{\cos{\varphi}} {\sqrt{ 1+THD_i^2}}</math>