### Formulas

#### Shunt Reactors

For star-connected shunt reactors each of inductance **L _{star}** on a three phase system of line voltage

**V**and frequency

_{line}**f**, the lagging reactive power demand

**Q**and the lagging reactive line current

_{Lstar}**I**are:

_{line}**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**and frequency

_{line}**f**, the lagging reactive power demand

**Q**and the lagging reactive line current

_{Ldelta}**I**are:

_{line}**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**on a three phase system of frequency

_{line}**f**, the voltage drop

**V**across each line reactor and the total lagging reactive power demand

_{drop}**Q**of the set of three line reactors are:

_{Lseries}**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**and not the voltage drop

_{line}**V**:

_{drop}**S _{rating} = Ö3V_{line}I_{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. | ||||||

BCEfGhIjLPQ | 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] | QRStVWXYZfw | 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] |