Power Factor Correction

Sizing shunt capacitors for a target power factor, and the cautions that come with them.

1. What this check does

Computes the reactive power a shunt capacitor bank must supply to raise a load from its present power factor to a target, and the resulting apparent power and line current.

2. Inputs used

Real power (kW), present and target power factor.
Optional: system voltage and phases, for currents.

3. Formulas and assumptions

Capacitor kVAR

Q_c = P\,\bigl(\tan\varphi_1 - \tan\varphi_2\bigr), \qquad \varphi = \arccos(\mathrm{PF})

Apparent power

S = \dfrac{P}{\mathrm{PF}}

Current

I = \dfrac{S \times 1000}{\sqrt{3}\,V}

Three-phase, kVA and V line-to-line.

Symbols

$P$	Real power, unchanged by correction	kW
$\varphi_1,\ \varphi_2$	Power factor angle before and after correction	°
$Q_c$	Capacitor rating	kVAR
$S$	Apparent power	kVA
$V$	Line-to-line voltage	V
$I$	Line current	A

Two overlapping power triangles sharing the kW side; the capacitor kVAR reduces kVAR from Q1 to Q2 and the angle from phi1 to phi2. — **Figure 1.** Capacitor kVAR shortens the reactive side of the triangle.

One-line with transformer, bus, capacitor bank and a VFD load, with a note on parallel resonance. — **Figure 2.** Where the capacitor sits, and why harmonics matter.

Real power is unchanged by the correction.
Capacitor kVAR is at rated voltage; actual output varies with the square of the applied voltage.
A warning is raised when a fixed bank sized for full load would leave little margin before the power factor turns leading.

4. What is NOT checked

Harmonic resonance and detuning.
Switching transients and capacitor inrush.
Utility tariff rules for power factor.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

IEEE Std 18 — shunt power capacitors
IEEE Std 1036 — application of shunt capacitors
IEEE Std 519 — harmonic control

6. Validation cases

No worked example with a published answer is registered for this page yet. Have one we should add? Use the Feedback link. All cases: Validation.

7. Known issues and changes

See the Engineering Notes. Try the tool: PF Correction.