Calculation
C = P·(tan φ₁−tan φ₂)/(2πf·U²)
The capacitor supplies the difference between original and target inductive reactive power.
Busch 2006, Abschnitt Blindleistungskompensation
Power-factor correction capacitor
The capacitor supplies the difference between original and target inductive reactive power.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Required shunt capacitance C — Total effective capacitance connected in parallel with the single-phase load at the calculated operating point.
- Real power P — Average real power of the load at the steady operating point to be corrected.
- Initial power factor cos φ₁ — Measured inductive displacement factor before the capacitor is connected.
- Target power factor cos φ₂ — Desired displacement factor after correction; must exceed cos φ₁ and not exceed 1.
- Capacitor RMS voltage U — Actual RMS voltage directly across the shunt capacitor.
- Supply frequency f — Frequency of the sinusoidal supply for which capacitance is sized.
Example
10 kW, cos φ₁=0.75, cos φ₂=0.95, 230 V and 50 Hz give Qc≈5.53 kvar and C≈333 µF.
Assumptions and limits
Single-phase sinusoidal inductive load at a constant operating point; three-phase connection, harmonics, resonance and switching stages are excluded.
Understand Power-factor correction capacitor
This calculator estimates shunt capacitance needed to move a single-phase inductive load from its existing to a target displacement factor at one fixed operating point.
What does this quantity describe?
Each cos φ is converted to tan φ. Required correction is Qc=P·(tanφ₁−tanφ₂), while a shunt capacitor supplies |Qc|=2πfCU² under sinusoidal voltage.
Formula and variables
C = P·(tan φ₁−tan φ₂)/(2πf·U²)
Qc = P · (tan φ₁ − tan φ₂)C = Qc/(2πfU²)
| Symbol / input | Meaning |
|---|---|
| Required shunt capacitance C | Total effective capacitance connected in parallel with the single-phase load at the calculated operating point. |
| Real power P | Average real power of the load at the steady operating point to be corrected. |
| Initial power factor cos φ₁ | Measured inductive displacement factor before the capacitor is connected. |
| Target power factor cos φ₂ | Desired displacement factor after correction; must exceed cos φ₁ and not exceed 1. |
| Capacitor RMS voltage U | Actual RMS voltage directly across the shunt capacitor. |
| Supply frequency f | Frequency of the sinusoidal supply for which capacitance is sized. |
Choose the inputs correctly
P is simultaneous real power, cos φ₁ the initial inductive displacement factor, cos φ₂ a realistic target, U voltage directly across the capacitor, and f supply frequency.
How to use the calculator
Measure P and cos φ₁ at the representative steady load, choose cos φ₂ above cos φ₁, and enter capacitor voltage and frequency. Check standard stages and overcorrection before rounding.
Worked example
Correcting 10 kW from 0.75 to 0.95 at 230 V and 50 Hz requires about 5.53 kvar capacitive or 333 µF.
Understand the result and units
C applies to this load point. At lower inductive load a fixed capacitor can overcorrect, so variable systems require staged or controlled banks.
P in W/kW, U in V, f in Hz and C with farad prefixes. Enter cos φ as a decimal, 0.95 rather than 95.
Typical applications
Preliminary sizing for single-phase motors and inductive lab loads, and learning the link between the power triangle and capacitor size.
Assumptions, limits and common mistakes
Not a three-phase capacitor-bank design. Star/delta connection, harmonic resonance, detuning, inrush, tolerance, ageing, fusing and discharge resistors are excluded.
Common mistake: Use voltage actually across the capacitor, not an unchecked line or phase voltage. Do not enter power factors as percentages or apply the model to an already capacitive load.
Frequently asked questions
What is “Power-factor correction capacitor” used for?
Preliminary sizing for single-phase motors and inductive lab loads, and learning the link between the power triangle and capacitor size.
Where do the input values come from?
P is simultaneous real power, cos φ₁ the initial inductive displacement factor, cos φ₂ a realistic target, U voltage directly across the capacitor, and f supply frequency.
What does the result not cover?
Not a three-phase capacitor-bank design. Star/delta connection, harmonic resonance, detuning, inrush, tolerance, ageing, fusing and discharge resistors are excluded.