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# Reactors

### Formulas

#### Shunt Reactors

For star-connected shunt reactors each of inductance Lstar on a three phase system of line voltage Vline and frequency f, the lagging reactive power demand QLstar and the lagging reactive line current Iline are:

QLstar = Vline2 / XLstar = Vline2 / 2pfLstar

Iline = QLstar / Ö3Vline = Vline / Ö3XLstar

Lstar = Vline2 / 2pfQLstar

For delta-connected shunt reactors each of inductance Ldelta on a three phase system of line voltage Vline and frequency f, the lagging reactive power demand QLdelta and the lagging reactive line current Iline are:

QLdelta = 3Vline2 / XLdelta = 3Vline2 / 2pfLdelta

Iline = QLdelta / Ö3Vline = Ö3Vline / XLdelta

Ldelta = 3Vline2 / 2pfQLdelta

Note that for the same lagging reactive power QL:

XLdelta = 3XLstar

Ldelta = 3Lstar

#### Series Reactors

For series line reactors each of inductance Lseries carrying line current Iline on a three phase system of frequency f, the voltage drop Vdrop across each line reactor and the total lagging reactive power demand QLseries of the set of three line reactors are:

Vdrop = IlineXLseries = 2pfLseriesIline

QLseries = 3Vdrop2 / XLseries = 3VdropIline = 3Iline2XLseries = 6pfLseriesIline2

Lseries = QLseries / 6pfIline2

Note that the apparent power rating Srating of the set of three series line reactors is based on the line voltage Vline and not the voltage drop Vdrop:

Srating = Ö3VlineIline

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]