## Shunt Reactors

**
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_{line}^{2} / X_{Lstar} = V_{line}^{2}
/ 2pfL_{star}
I_{line} = Q_{Lstar} / Ö3V_{line}
= V_{line} / Ö3X_{Lstar}
L_{star} = V_{line}^{2} / 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_{line}^{2} / X_{Ldelta} = 3V_{line}^{2} / 2pfL_{delta}

I_{line} = Q_{Ldelta} / Ö3V_{line} = Ö3V_{line} / X_{Ldelta}

L_{delta} = 3V_{line}^{2} / 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_{line}X_{Lseries} = 2pfL_{series}I_{line}
Q_{Lseries} = 3V_{drop}^{2} / X_{Lseries} =
3V_{drop}I_{line} = 3I_{line}^{2}X_{Lseries}
= 6pfL_{series}I_{line}^{2}
L_{series} = Q_{Lseries} / 6pfI_{line}^{2}
**

**
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_{line}I_{line}