= Reactive power overcompensation
\b[<Reactive power overcompensation>] occurs when capacitive correction exceeds the inductive <reactive power> that it is intended to cancel. Under the <passive sign convention> and a positive-frequency sinusoidal supply, the source then sees negative net <reactive power>, producing a <leading power factor>. This can happen when a fixed <capacitor bank> remains connected as the inductive load falls. Eaton's application paper discusses excessive leading operation and the use of switched correction stages.<Capacitor Application Issues by Thomas M. Blooming and Daniel J. Carnovale>[SectionV, printed p6, switched-bank control and overcompensation]{ref}
Consider an ideal fixed RMS <electric potential difference> $V$ at <angular frequency> $\omega$, supplying a load that absorbs constant $P>0$ and $Q_L>0$. Let $Q_{\mathrm{cap}}=\omega CV^2\ge0$ be the magnitude of the correction's <reactive power>; its signed contribution is $-Q_{\mathrm{cap}}$. Adding ideal shunt <capacitance> gives
$$
Q_{\mathrm{net}}=Q_L-\omega CV^2,
\qquad
I_{\mathrm{source}}=\frac{\sqrt{P^2+Q_{\mathrm{net}}^2}}V.
$$
The model holds the load and supply fixed while changing $C$. It omits losses and additional network dynamics. <Optimal shunt capacitance for sinusoidal power factor correction> follows by minimizing the squared <root mean square> <electric current>:
$$
\boxed{C_*=\frac{Q_L}{\omega V^2},\qquad I_{\min}=\frac PV.}
$$
For $C<C_*$ the remaining <reactive power> is positive and the <power factor> is lagging. For $C>C_*$ it is negative and the <power factor> is leading. The overcompensation threshold is $C_*$, but the <current reduction interval for shunt reactive compensation> is wider. Comparing the square of the corrected and uncorrected <electric current> gives
$$
I(C)^2-I(0)^2
=\frac{(Q_L-Q_{\mathrm{cap}})^2-Q_L^2}{V^2}
=\frac{Q_{\mathrm{cap}}(Q_{\mathrm{cap}}-2Q_L)}{V^2}.
$$
Thus \b[source RMS current is reduced for $0<C<2C_*$], equals the uncorrected value at $C=2C_*$, and is larger for $C>2C_*$. An overcompensated operating point between $C_*$ and $2C_*$ still draws less source <electric current> than the uncorrected load.
For an original example, keep the parent article's chosen $P=1000\,\mathrm W$, $Q_L=750\,\mathrm{var}$, $V=200\,\mathrm V$ and 50 hertz. The uncorrected source draws 6.25 amperes at <power factor>0.8. Full cancellation needs $C_*\approx59.68\,\mathrm{\mu F}$ and reduces source <electric current> to 5 amperes. A 100 microfarad correction gives $Q_{\mathrm{net}}\approx-506.64\,\mathrm{var}$ and 5.605 amperes, with a leading factor about0.8920. A 150 microfarad correction instead gives about $-1134.96\,\mathrm{var}$ and7.563 amperes, worse than no correction. The crossing is $2C_*\approx119.37\,\mathrm{\mu F}$.
\Image[/reactive-power-overcompensation.png]
{title=Leading operation begins before correction increases current above the uncorrected value}
{description=Original constant-load model at 200 volts RMS and 50 hertz with 1000 watts active power and 750 vars inductive reactive power. Optimal correction is about 59.68 microfarads. Between 59.68 and 119.37 microfarads the source is leading but still draws less current than the uncorrected load; above 119.37 microfarads it draws more.}
The optimum changes with the load. If the example load's $P$ and $Q_L$ both halve while its original optimal correction remains connected, then $P=500\,\mathrm W$ and $Q_{\mathrm{net}}=-375\,\mathrm{var}$. Source <electric current> is 3.125 amperes and the factor is 0.8 leading. This dependence motivates <automatic power factor correction>. The cited controller description measures system <electric potential difference> and <electric current>, using external <current transformers>, and switches discrete <capacitor bank> stages to follow a target.<Capacitor Application Issues by Thomas M. Blooming and Daniel J. Carnovale>[Section V.D, printed p.6, staged control; Section VI.C, printed p.8, CT Location for Automatic Banks]{ref}
Retain the phase or sign of $Q_{\mathrm{net}}$ when reporting the result. A bare <power factor> magnitude does not distinguish leading from lagging; the manufacturer FAQ also illustrates how a meter's signed display depends on its convention.<Power factor sign conventions in Schneider Electric FAQ FA212521>[Resolution and displayed IEC/IEEE convention diagrams]{ref} The calculation assumes <sinusoidal steady state>; <current distortion factor> is a separate consideration for nonsinusoidal current.
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