Reactive power · capacitor sizing

Power Factor Correction Worked Example: kVAr, kVA and Current

Power-quality guide · Reviewed 22 Sep 2026 · ElectroDesigner

Power-factor correction reduces reactive power and apparent power for the same active kW. For a sinusoidal load model, the required capacitor-bank rating follows directly from the change in phase angle between the existing and target power factors.

In this article1. Equations 2. Worked example 3. Current reduction 4. Practical selection 5. Assumptions and limits

1. Core equations

φ = arccos(PF)

Q = P × tanφ

Qc = P × (tanφ₁ − tanφ₂)

Apparent power before and after correction is:

S = P / PF

For a balanced three-phase system:

I = P × 1000 / (√3 × U_LL × PF)

2. Worked example: 100 kW from PF 0.78 to 0.95

Assume a 100 kW, 400 V three-phase load operating at power factor 0.78. The target is 0.95.

Q₁ = 100 × tan(arccos 0.78) = 80.23 kVAr

Q₂ = 100 × tan(arccos 0.95) = 32.87 kVAr

Qc = 80.23 − 32.87 = 47.36 kVAr

The theoretical requirement is therefore about 47.36 kVAr. A real installation normally uses practical capacitor-bank steps rather than treating 47.36 kVAr as an equipment catalogue rating.

3. What happens to kVA and current?

S₁ = 100 / 0.78 = 128.21 kVA

S₂ = 100 / 0.95 = 105.26 kVA

I₁ = 185.05 A at 400 V, 3φ

I₂ = 151.93 A at 400 V, 3φ

The active load remains 100 kW; the upstream apparent-power requirement and line current fall because less reactive current is supplied from the source.

Run the Power Factor Correction Calculator

4. Practical capacitor-bank selection

Calculate the theoretical kVAr requirement at the governing operating point.
Check the load profile so a fixed bank does not over-compensate at light load.
Use automatic stepped compensation where the reactive demand varies materially.
Check utility or project limits for the target power factor rather than automatically aiming at unity.
Assess harmonic distortion and resonance before selecting a plain capacitor bank on networks with drives, UPS systems or other nonlinear loads.
Verify voltage, frequency, switching duty, capacitor tolerance, detuning reactor and manufacturer thermal limits.

5. Assumptions and limits

The equations above use the displacement power factor model for a sinusoidal fundamental-frequency calculation.
Distortion power factor in harmonic-rich systems needs separate consideration.
Capacitor banks can interact with network inductance and create or amplify resonance.
Correction does not reduce the active kW consumed by the load.
Final step sizes, detuning and switching arrangement must be selected for the actual network and load profile.

Adjacent checks

Use the Harmonic Filter Sizing Calculator before adding capacitors to a harmonic-rich network, and read Active vs Passive Harmonic Filters when mitigation strategy is part of the same power-quality study.

Engineering references

Method reference: Schneider Electric Electrical Installation Guide — theoretical principles to improve power factor and the wider Power Factor Correction chapter. The guide gives the same Qc = P(tanφ − tanφ′) relationship and emphasizes installation-specific compensation selection.