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