Lagging power factor

A lagging power factor describes an absorbing sinusoidal electrical load whose electric current lags its terminal electric potential difference. With the passive sign convention, chooseThe current maximum occurs later by $\phi /\omega$. The RMS phasors give complex electrical powerIn this equation the supply phasor is the real number $V$, while $I^{\ast }$ denotes the conjugate of the current phasor. Positive $Q$ is inductive reactive power under this convention. The primary MIT notes derive the conjugation and the peak-versus-RMS factor.^[ref]

For an original $230\mathrm{V}$, $10\mathrm{A}$ example with $\cos \phi =0.8$, active power is $1840\mathrm{W}$ and reactive power is $1380\mathrm{var}$. At $50\mathrm{Hz}$, $\phi \approx 0.6435$ radians corresponds to a current delay of about $2.05\mathrm{ms}$. The factor $0.8$ gives the magnitude of the phase relationship, while the word lagging supplies the direction lost by the cosine.

An ideal inductor is the limiting case $\phi =\pi /2$: it alternately stores and returns magnetic energy, with zero mean active power. An absorbing resistive-inductive load usually has both positive active power and positive reactive power. An ideal parallel capacitor can reduce the source's quadrature electric current; sufficient extra capacitance eventually crosses into leading power factor rather than improving the factor indefinitely.

For distorted waveforms, specify whether lagging refers to the fundamental displacement power factor; one phase angle does not characterize arbitrary harmonic components. A signed meter display is also not a universal lead/lag label. The manufacturer's sign-convention explanation distinguishes phase direction from the convention used for displayed factor signs.^[ref]