Reactive power ($Q$)

Reactive power is the imaginary part of complex electrical power in sinusoidal steady operation. With RMS phasors, the passive sign convention and $e^{j\omega t}$ time convention,where $\phi$ is potential-difference phase minus current phase. Inductive current lag gives positive $Q$, while capacitive current lead gives negative $Q$. Its conventional unit is the reactive volt-ampere, written var. These definitions retain the specified phasor and sign conventions.^[ref]

The physical role is periodic energy exchange rather than an additional dissipated-energy average. For an ideal inductor, $v=Ldi/dt$ and stored energy is $w=L{i}^2/2$, so $p=dw/dt$. Its energy returns to its initial value after a steady cycle and mean absorbed power is zero. Nevertheless,For an ideal capacitor, $Q_C=-\omega C{V}_{\mathrm{rms}}^2$, with the negative sign representing the opposite exchange phase. Primary circuit derivations explicitly separate these exchanges from resistor dissipation.^[ref]

For an original example, $L=20\mathrm{mH}$, $I_{\mathrm{rms}}=5\mathrm{A}$ and $f=50\mathrm{Hz}$ give $Q_L\approx 157.08\mathrm{var}$. Peak stored energy is0.50J and mean stored energy0.25J, consistent with $2\omega ⟨w⟩$. Zero ideal average dissipation therefore does not mean zero current or zero energy storage.

For a separate ideal single-frequency compensation example, a100V load with $S=400+j300\mathrm{VA}$ can have its source reactive component canceled by a parallel capacitor satisfyingThe capacitor contributes $-j300\mathrm{VA}$, leaving400W of source active power and4A RMS source current. This illustrates power factor correction under the stated ideal assumptions, rather than selecting a real component or proving its ratings.

Reactive exchange can increase the current carried through resistive wiring and thereby affect real losses. For distorted waveforms, definitions of non-active power need additional care; the one-frequency imaginary-part definition should not silently be extended to every waveform.

The reactive volt-ampere, conventionally called the var and written with symbolvar, expresses reactive power. The official SI text notes the IEC's special name and states that its coherent unit is identical to the volt ampere. The name identifies the reactive quantity; it is not a different base-unit dimension.^[ref]

In sinusoidal steady operation with RMS magnitudes $V,I$ and relative phase $\phi$,Thus100V RMS,2A RMS and a lagging phase with $\sin \phi =0.6$ give120var. Under the same passive and phasor conventions, a leading phase of equal magnitude gives−120var. The signed value describes exchange phase rather than negative dissipated heating. The prefix relation is $1\mathrm{kvar}=1000\mathrm{var}$.

A reactive-power value is also not an amount of stored energy in joules. For an ideal inductor in sinusoidal steady operation,For an original200var example at50Hz, mean stored energy is $200/[2(2\pi 50)]\approx 0.3183\mathrm{J}$ and peak stored energy is twice that. The average absorbed active power is nevertheless zero in the ideal inductor. The primary circuit treatment derives this separation between energy storage and mean dissipation.^[ref]

In a sinusoidal100V example with $S=400+j300\mathrm{VA}$, the reactive component is300var, the active component400W and apparent power500VA. Adding400 and300 as ordinary scalar powers would not give the500VA magnitude. Complex electrical power retains the phase relation needed for this combination.