Power Factor Correction

Formulas

If an inductive load with an active power demand P has an uncorrected power factor of cosf₁ lagging, and is required to have a corrected power factor of cosf₂ lagging, the uncorrected and corrected reactive power demands, Q₁ and Q₂, are:

Q₁ = P tanf₁

Q₂ = P tanf₂

where tanf_n = (1 / cos²f_n – 1)^½

The leading (capacitive) reactive power demand Q_C which must be connected across the load is:

Q_C = Q₁ – Q₂ = P (tanf₁ – tanf₂)

The uncorrected and corrected apparent power demands, S₁ and S₂, are related by:

S₁cosf₁ = P = S₂cosf₂

Comparing corrected and uncorrected load currents and apparent power demands:

I₂ / I₁ = S₂ / S₁ = cosf₁ / cosf₂

If the load is required to have a corrected power factor of unity, Q₂ is zero and:

Q_C = Q₁ = P tanf₁

I₂ / I₁ = S₂ / S₁ = cosf₁ = P / S₁

Shunt Capacitors

For star-connected shunt capacitors each of capacitance C_star on a three phase system of line voltage V_line and frequency f, the leading reactive power demand Q_Cstar and the leading reactive line current I_line are:

Q_Cstar = V_line² / X_Cstar = 2pfC_starV_line²

I_line = Q_Cstar / Ö3V_line = V_line / Ö3X_Cstar

C_star = Q_Cstar / 2pfV_line²

For delta-connected shunt capacitors each of capacitance C_delta on a three phase system of line voltage V_line and frequency f, the leading reactive power demand Q_Cdelta and the leading reactive line current I_line are:

Q_Cdelta = 3V_line² / X_Cdelta = 6pfC_deltaV_line²

I_line = Q_Cdelta / Ö3V_line = Ö3V_line / X_Cdelta

C_delta = Q_Cdelta / 6pfV_line²

Note that for the same leading reactive power Q_C:

X_Cdelta = 3X_Cstar

C_delta = C_star / 3

Series Capacitors

For series line capacitors each of capacitance C_series carrying line current I_line on a three phase system of frequency f, the voltage drop V_drop across each line capacitor and the total leading reactive power demand Q_Cseries of the set of three line capacitors are:

V_drop = I_lineX_Cseries = I_line / 2pfC_series

Q_Cseries = 3V_drop² / X_Cseries = 3V_dropI_line = 3I_line²X_Cseries = 3I_line² / 2pfC_series

C_series = 3I_line² / 2pfQ_Cseries

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

S_rating = Ö3V_lineI_line