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 | ||||||
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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] |
There is a mistake in one formula of the series reactor: QLseries = Vdrop^2 / XLseries. Remove the factor “3”.
IS TOLERENCE OF VOLTAGE DROP IN THREE PHASE SERIES REACTOR ?