Power factor

In power analysis, the power factor (pf) is like a compensating factor due to the load. To deliver the same power, we need to compensate by an amount given by the pf. it’s given by:

$$\text{pf}=\frac{P}{|S|}=\frac{V_{RMS}{I}_{RMS}\cos \theta }{V_{RMS}{I}_{RMS}}=\cos \theta$$

Since power is given by:

$$P=V_{RMS}{I}_{RMS}\cos \theta$$

For a purely resistive load, the phase shift is 0. But for a capacitive or inductive load, the phase shift $\theta \ne 0$. To see the same power as the resistive load, we need to have a larger amplitude in voltage and current.

If the power factor is lagging, then this means on the power triangle ${\phi }_V>{\phi }_I$ and $\theta >0$.

Utilities providers usually apply special charges if customers have loads with low power factors.