 Power factor

The power factor is the ratio of active power to the product of RMS terminal electric potential difference and electric current:when the denominator is positive. It measures how effectively those terminal magnitudes support net average transfer. With signed absorbed power it can be negative for net generation; for an absorbing load the usual range is zero to one. The Cauchy-Schwarz inequality applied to the time average of $v(t)i(t)$ proves $|P|\le V_{\mathrm{rms}}{I}_{\mathrm{rms}}$.

For one-frequency sinusoids, $P=V_{\mathrm{rms}}{I}_{\mathrm{rms}}\cos \phi$, so the power factor is $\cos \phi$. The phase-only quantity for the fundamental is also called displacement power factor. The primary treatments make the RMS convention explicit.^[ref][ref]

A distorted current can give another result. For purely sinusoidal supply potential difference and a zero-mean current with fundamental RMS magnitude $I_1$,Only the in-phase fundamental contributes to the average product with that supply waveform. For an original example with fundamental3A in phase and third-harmonic RMS magnitude4A, total RMS current is5A. The displacement power factor is one but total power factor is0.6. Changing the fundamental phase alone would not remove this harmonic-current contribution.

At fixed absorbed active power and supply RMS potential difference, $I_{\mathrm{rms}}=P/(V_{\mathrm{rms}}\mathrm{pf})$. For an original900W,230V example, changing the factor from0.6 to0.9 changes source current from about6.52 to4.35A. In the same upstream resistance, the corresponding $I^{2}R$ loss becomes $(0.6/0.9{)}^2=4/9$ of its former value. This is a stipulated circuit calculation, not an assertion about a particular tariff or installation.

Power factor correction addresses the mechanism causing the low ratio. An ideal capacitive branch can offset inductive reactive power at one frequency; it does not automatically correct an arbitrary distorted current. State the waveform conditions and whether the reported number is total or displacement factor when comparing measurements.