Reactors

Formulas

Shunt Reactors

For star-connected shunt reactors each of inductance L_star on a three phase system of line voltage V_line and frequency f, the lagging reactive power demand Q_Lstar and the lagging reactive line current I_line are:

Q_Lstar = V_line² / X_Lstar = V_line² / 2pfL_star

I_line = Q_Lstar / Ö3V_line = V_line / Ö3X_Lstar

L_star = V_line² / 2pfQ_Lstar

For delta-connected shunt reactors each of inductance L_delta on a three phase system of line voltage V_line and frequency f, the lagging reactive power demand Q_Ldelta and the lagging reactive line current I_line are:

Q_Ldelta = 3V_line² / X_Ldelta = 3V_line² / 2pfL_delta

I_line = Q_Ldelta / Ö3V_line = Ö3V_line / X_Ldelta

L_delta = 3V_line² / 2pfQ_Ldelta

Note that for the same lagging reactive power Q_L:

X_Ldelta = 3X_Lstar

L_delta = 3L_star

Series Reactors

For series line reactors each of inductance L_series carrying line current I_line on a three phase system of frequency f, the voltage drop V_drop across each line reactor and the total lagging reactive power demand Q_Lseries of the set of three line reactors are:

V_drop = I_lineX_Lseries = 2pfL_seriesI_line

Q_Lseries = 3V_drop² / X_Lseries = 3V_dropI_line = 3I_line²X_Lseries = 6pfL_seriesI_line²

L_series = Q_Lseries / 6pfI_line²

Note that the apparent power rating S_rating of the set of three series line reactors is based on the line voltage V_line and not the voltage drop V_drop:

S_rating = Ö3V_lineI_line

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]

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