# Harmonic distortion indicators - Power factor

The power factor λ is the ratio of the active power P (kW) to the apparent power S (kVA). See Chapter Power Factor Correction.

${\displaystyle \lambda ={\frac {P(kW)}{S(kVA)}}}$

The Power Factor must not be mixed-up with the Displacement Power Factor (cos φ), relative to fundamental signals only.

As the apparent power is calculated from the r.m.s. values, the Power Factor integrates voltage and current distortion.

When the voltage is sinusoidal or virtually sinusoidal (THDu ~ 0), it may be said that the active power is only a function of the fundamental current. Then:

${\displaystyle P\approx P_{1}=U_{1}\ I_{1}\ \cos \varphi }$

Consequently:

${\displaystyle \lambda ={\frac {P}{S}}={\frac {U_{1}\ I_{1}\ \cos \varphi }{U_{1}\ I_{rms}}}}$

As: ${\displaystyle {\frac {I_{1}}{I_{rms}}}={\frac {1}{\sqrt {1+THD_{i}^{2}}}}}$ (see Definition of harmonics),

hence: ${\displaystyle \lambda \approx {\frac {cos\varphi }{\sqrt {1+THD_{i}^{2}}}}}$

Figure M6 shows a graph of λ/cosφ as a function of THDi, for THDu ~ 0.

Fig. M6 – Variation of λ/cosφ as a function of THDi, for THDu ~ 0