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Electrical Fundamentals & Circuit Analysis

Power Factor Calculator and Correction

Analyze active, reactive, and apparent power or calculate the capacitor-bank kvar needed to improve power factor.

Power factor and correction equations

Real power, reactive power, and apparent power form a right-angled power triangle. Power factor is the ratio of real power to apparent power. Correction supplies part of the reactive power locally to reduce source current.

Power triangle
S2=P2+Q2
Power factor
PF = P / S = cos φ
Required compensation
Qc=P[tanφ1−tanφ2]
Power-factor angles
φ1 = cos⁻¹(PF1), φ2 = cos⁻¹(PF2)
Three-phase line current
I = P / (√3 × V × PF)

where:

P
Active power of the load[kW]
Q
Reactive power of the load[kvar]
S
Apparent power supplied to the load[kVA]
PF
Power factor, equal to real power divided by apparent power
Qc
Capacitive reactive power required[kvar]
PF1
Existing power factor
PF2
Target power factor
φ
Phase angle corresponding to the power factor
I
AC line current[A]

The power-triangle result describes one operating point. A real correction bank needs practical steps, switching control, harmonic assessment, voltage margin, discharge, and thermal design.

How to calculate power factor

Choose the pair of values available from a meter, nameplate, or load study. The calculator completes the power triangle and reports power factor, phase angle, real power, reactive power, apparent power, and line current.

  1. Select single-phase or three-phase AC.
  2. Choose the known-value combination.
  3. Enter two power quantities or the meter readings.
  4. Review PF and phase angle.
  5. Use correction mode only when a capacitor-bank estimate is required.

Real, reactive, and apparent power

Real power P in kW performs useful work. Reactive power Q in kvar supports alternating electric and magnetic fields. Apparent power S in kVA is the RMS voltage-current loading seen by cables, transformers, and switchgear. These quantities satisfy S² = P² + Q² for the sinusoidal displacement-power model.

PF = P / S = cos φ

S² = P² + Q²

Power factor calculation example

A load using 100 kW at 125 kVA has a power factor of 0.80. The corresponding reactive power is 75 kvar and the phase angle is approximately 36.87°. On a balanced 400 V three-phase supply, 125 kVA corresponds to approximately 180 A of line current.

PF = 100 kW / 125 kVA = 0.80

Q = √(125² − 100²) = 75 kvar

I = 125,000 / (√3 × 400) ≈ 180 A

Single-phase and three-phase line current

For single-phase AC, apparent power is voltage multiplied by current. For balanced three-phase AC, use line-to-line voltage and the √3 factor. Power factor is required when calculating current from real power, but not when apparent power in kVA is already known.

Single-phase: I = P / (V × PF)

Three-phase: I = P / (√3 × VLL × PF)

Three-phase from kVA: I = S × 1000 / (√3 × VLL)

How to calculate capacitor kvar

Enter active power, existing power factor, target power factor, voltage, and phase. The calculator converts each power factor to its phase angle and subtracts the target reactive-power requirement from the existing requirement.

  1. Measure or obtain real kW and power factor.
  2. Choose a justified target.
  3. Calculate required kvar.
  4. Compare current before and after correction.
  5. Design practical switching steps and harmonic protection.

Power factor correction example

For a 100 kW load improving from 0.75 to 0.95 power factor, the mathematical compensation is approximately 55 kvar. The final bank may use several switched stages so correction follows the changing load.

Qc = 100 × [tan(cos⁻¹ 0.75) - tan(cos⁻¹ 0.95)]

Qc ≈ 55 kvar

Why line current decreases

With useful kW held constant, improved power factor lowers kVA. Lower apparent power reduces line current, conductor loss, voltage drop, and transformer loading, but it does not reduce the mechanical output power required by the load.

Displacement power factor and true power factor

The simple relation PF = cos φ applies directly to sinusoidal voltage and current and describes displacement power factor. Nonlinear loads introduce distortion, so a meter may report a lower true power factor even when displacement power factor is high. Use measured kW and true RMS kVA when harmonics are significant.

Harmonics and capacitor-bank design

VFDs, UPS systems, welders, rectifiers, and nonlinear loads can create harmonic resonance and excess capacitor current. Measure harmonic conditions and evaluate detuned reactors, filters, capacitor voltage margin, capacitor-duty contactors, discharge resistors, ventilation, and automatic controller settings.

Assumptions

  • Balanced steady-state AC load
  • Power-triangle analysis represents a sinusoidal displacement-power model
  • Active power remains constant after correction
  • Capacitor steps and harmonic resonance are not modeled

Important Warnings

  • Do not raise the target above the utility or project requirement; overcorrection can create leading power factor and overvoltage.
  • Sites with VFDs, UPS systems, rectifiers, or significant harmonics require harmonic measurement and detuned or filtered capacitor-bank review.

FAQ

How do I calculate power factor from kW and kVA?

Divide active power in kW by apparent power in kVA. For example, 100 kW divided by 125 kVA gives a power factor of 0.80.

How do I calculate reactive power in kvar?

When kW and kVA are known, use Q = √(S² − P²). A 100 kW, 125 kVA load has 75 kvar of reactive power in the sinusoidal power-triangle model.

What target power factor should I use?

A target around 0.95 is a common planning value, but the correct target depends on utility penalties, load variation, harmonics, and project requirements.

Why does correction reduce current?

For the same useful kW, improving power factor reduces apparent power and therefore reduces line current, cable loss, and transformer loading.

Does power factor correction reduce kWh consumption?

It normally does not reduce the useful energy required by the load. It can reduce upstream I²R losses and utility reactive-power charges, but the saving depends on the installation and tariff.

Why not correct power factor to exactly 1.00?

Load variation and capacitor tolerances can produce leading power factor or overvoltage when compensation is too high. Use the utility or project target and practical switched steps.

How do harmonics affect power factor correction?

Harmonics can lower true power factor and can overload or resonate with capacitor banks. Sites with VFDs, UPS systems, rectifiers, or other nonlinear loads need measurements and a detuned or filtered-bank review.

Is the calculated kvar a final capacitor-bank specification?

No. Round to a practical stepped bank only after checking load variation, switching frequency, harmonics, voltage, temperature, and capacitor tolerances.

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