Initial reactive power Q₁
Reactive power before power factor correction.
Electricity · Industrial electricity
Power factor correction and reactive compensation
From active power P and the initial and target power factors, calculate Q before and after correction, required compensation Qc, and the reduction in apparent power.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Target reactive power Q₂
Reactive power corresponding to the target power factor.
Required compensation Qc
Capacitive reactive power to compensate to reach the target.
Initial apparent power S₁
Apparent power before correction.
Target apparent power S₂
Theoretical apparent power after correction.
Relation and numerical substitution
Qc = P · [tan(arccos(cosφ₁)) − tan(arccos(cosφ₂))]—
Sinusoidal steady state with active power P assumed unchanged by the correction. Power factors must satisfy 0 < cos φ ≤ 1 and the target must be greater than the initial value. The result sizes reactive power in kvar; it does not directly size capacitors in µF. Harmonics, resonance, capacitor tolerances and utility requirements are not included.
01Formulas and symbols
Formulas used
Q₁
P · tan(arccos(cosφ₁))Reactive power before correctionQ₂
P · tan(arccos(cosφ₂))Reactive power at the targetQc
Q₁ − Q₂Reactive power to compensateS₁
P / cosφ₁Apparent power before correctionS₂
P / cosφ₂Apparent power after correction02Assumptions and limits
Scope of validity
- Sinusoidal steady state with active power P assumed unchanged by the correction.
- Power factors must satisfy 0 < cos φ ≤ 1 and the target must be greater than the initial value.
- The result sizes reactive power in kvar; it does not directly size capacitors in µF.
- Harmonics, resonance, capacitor tolerances and utility requirements are not included.
03Validation example
Reference numerical case
- P = 10 kW, cos φ₁ = 0.80 and cos φ₂ = 0.95.
- Q₁ = 10 × tan(arccos 0.80) = 7.50 kvar.
- Q₂ = 10 × tan(arccos 0.95) ≈ 3.29 kvar.
- Qc = Q₁ − Q₂ ≈ 4.21 kvar; S falls from 12.50 to 10.53 kVA.
04References
Technical references
- IEC 60050-131 — International Electrotechnical Vocabulary: circuit theory.
- BIPM — The International System of Units (SI), 9th edition.