Formula
Qc = P · (tan φ₁ − tan φ₂) φ = arccos(power factor) S = P / cos φ Three-phase current I = S / (√3 · V), single-phase I = S / V Single-phase C = Qc / (2πf · V²) Three-phase delta, per phase C = Qc / (3 · 2πf · V²) Three-phase star, per phase C = Qc / (2πf · V²) (V = line-to-line voltage)
Active power P stays the same while reactive power falls from P·tan φ₁ to P·tan φ₂; the difference is the capacitor rating Qc. A capacitor supplies Q = V²·2πf·C, so the capacitance follows from the voltage across each capacitor (line-to-line in delta, line-to-line/√3 in star) and the number of phases.
The factor tan φ₁ − tan φ₂ is the same number as in kvar-per-kW tables. Automated tests compare it with the table in the Schneider Electric Electrical Installation Guide (0.80→0.95: 0.421; 0.70→0.90: 0.536; 0.75→1.00: 0.882; 0.85→0.95: 0.291).
Choosing inputs
- Load power and present power factor: use readings from a power analyser or meter, or the average power factor on your electricity bill. A motor nameplate power factor applies at rated load; at part load it is lower.
- Target power factor: 0.9 to 0.95 is common. Pushing closer to 1.0 needs rapidly more capacitance and risks a leading power factor when the load drops.
- Voltage: the voltage where the capacitors connect. Use line-to-line voltage for three-phase.
Worked example
A 100 kW three-phase load at 400 V, 50 Hz, raised from 0.80 to 0.95:
- tan φ₁ = tan(arccos 0.80) = 0.75; tan φ₂ = tan(arccos 0.95) ≈ 0.3287
- Qc = 100 × (0.75 − 0.3287) ≈ 42.1 kvar
- Apparent power 125 → 105.3 kVA; line current 180.4 → 151.9 A (about 16 % less)
- Capacitance: about 279 µF per phase in delta, about 838 µF per phase in star
The calculator opens with these values. In practice, choose a standard rating at or above the result, or split it into several steps.
Limitations
- Reference values; review by a qualified electrician or engineer is required. Capacitor installation, protection and discharge devices must follow local electrical regulations (for example IEC 60364) and be designed and installed by qualified people.
- With harmonic-rich loads such as drives and rectifiers, capacitors can cause resonance; consider detuning reactors. Harmonics are not covered here.
- If the capacitor's rated voltage differs from the system voltage, its actual output scales by (system voltage / rated voltage)². Series reactors also raise the capacitor terminal voltage.
- For capacitors connected directly at motor terminals, too much capacitance can cause self-excitation after switch-off; follow the motor maker's recommended rating.
References
- Schneider Electric, Electrical Installation Guide, Chapter L "Power factor correction", How to determine the optimum level of compensation (kvar/kW table, 500 kW 0.75→0.93 example)
- Eskom, Power Factor Sizing Guide (correction multiplier table and worked examples)