= Leading power factor
A <leading power factor> describes an absorbing sinusoidal <electrical load> whose <electric current> leads its terminal <electric potential difference>. Under the <passive sign convention>, write
$$
v(t)=\sqrt2V\cos\omega t,\qquad i(t)=\sqrt2I\cos(\omega t+\theta),\qquad 0<\theta\le\pi/2.
$$
The current maximum occurs earlier by $\theta/\omega$. The <complex electrical power> is
$$
S=VI(\cos\theta-i\sin\theta),\qquad
P=VI\cos\theta,\quad Q=-VI\sin\theta<0.
$$
The negative <reactive power> is consistent with a capacitive terminal response. It does not imply negative mean absorbed <active power>.
For an original $100\,\mathrm V$, $2\,\mathrm A$ example with $\theta=\pi/3$, the <power factor> magnitude is $0.5$, <active power> is $100\,\mathrm W$, and <reactive power> is $-100\sqrt3\approx-173.21\,\mathrm{var}$. At $50\,\mathrm{Hz}$ the current leads by $1/(6f)\approx3.33\,\mathrm{ms}$. A load with the same RMS magnitudes and the opposite phase displacement has identical <active power> but a <lagging power factor> and opposite <reactive power>.
For an ideal <capacitor>, $i=C\,dv/dt$ gives a quarter-cycle current lead. Its mean <active power> is zero, although <instantaneous power> alternates as electrical <energy> enters and leaves the field. The primary one-frequency power derivation separates this quadrature exchange from net energy transfer.<AC Power Flow in Linear Networks by James L. Kirtley Jr.>[Energy and Power, equations 61–65 and 71]{ref}
An inductive load can acquire a <leading power factor> at the source when <power factor correction> supplies more capacitive <reactive power> than the load absorbs. The <current reduction interval for shunt reactive compensation> shows why mildly leading operation can still draw less source <electric current> than no correction, while excessive correction reverses that benefit.
Record phase direction or signed <reactive power> together with the numerical factor. The same positive cosine can describe leading and lagging loads, and a meter may assign a separate sign according to its display convention.<Power factor sign conventions in Schneider Electric FAQ FA212521>[Resolution and IEC/IEEE convention diagrams]{ref} For nonsinusoidal signals, state whether leading describes the fundamental <displacement power factor>; the complete <power factor> also depends on waveform distortion.
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