Power factor correction: capacitor bank rating
Reactive power of a capacitor bank that raises the power factor from cos φ_1 to cos φ_2, and the resulting reduction of the supply current and line losses.
Q_c = P · (tg φ_1 − tg φ_2)I_2 / I_1 = cos φ_1 / cos φ_2ΔP_2 / ΔP_1 = (cos φ_1 / cos φ_2)²Capacitor output is proportional to the voltage squared: a 400 V bank at 380 V gives about 90 % of its rating. For individual motor correction, keep the capacitor rating below about 90 % of the motor's no-load reactive power, or the motor may self-excite after switching off. With variable frequency drives and other non-linear loads, use detuned banks with anti-resonance reactors.
Source: Power triangle: Q = P · tan φ
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
Plants with induction motors: usually 0.7–0.85.
Usually 0.92–0.97; correcting to 1 does not pay off and risks overcompensation at light load.
Unit converter for this formulaPower · Reactive power · Apparent power · Fraction and percent
- kW1
- W1,000
- MW0.001
- PS (metric hp)1.35962
- kcal/h859.845
- hp1.34102
- BTU/h3,412.14
PS is the metric horsepower (735.5 W), hp the mechanical horsepower (745.7 W).
- tg φ_1 — tan φ before correction–
- S_2 — Apparent power after correction–
- ΔI — Reduction of the supply current–
- ΔP_loss — Reduction of load losses in the line and transformer–
More in Motors and transformers
Design apparent power from the installed load, the demand factor and cos φ, and the transformer rating from the standard series for the allowed loading and the number of transformers in the substation.
Synchronous speed from the supply frequency and the number of poles, slip from the rated speed, and the speed on a variable frequency drive — for example, of an ESP motor or a pumping unit drive.
Estimate of the voltage dip on the substation busbars during direct-on-line starting of an induction motor, and of its reduced starting torque — to check whether a large pump or compressor can be started from a given transformer.
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.