Power factor correction calculator

Motors, transformers and ballasts need reactive power to build their magnetic field. That energy flows back and forth through the installation without doing work, but it raises the current, heats the cables and, on many supplies, it is charged for. A capacitor bank supplies it next to the load and raises the power factor (cos φ). This calculator gives the kVAR of the bank and the µF of each capacitor.

How it is calculated

Q = P × (tan φ₁ − tan φ₂)

P is the active power, φ₁ the angle for the current power factor and φ₂ the one for the target. From the kVAR you get the capacitance of each capacitor (V is the line-to-line voltage and f the frequency):

• Three-phase, capacitors in delta: C = Q / (3 × 2π × f × V²)
• Three-phase, capacitors in star (wye): C = Q / (2π × f × V²)
• Single-phase: C = Q / (2π × f × V²)

Example

A plant drawing 50 kW at a power factor of 0.75 that wants to reach 0.95: tan φ₁ = 0.882 and tan φ₂ = 0.329, so Q = 50 × (0.882 − 0.329) ≈ 27.7 kVAR. With delta-connected capacitors at 400 V and 50 Hz, each one about 183 µF. The current drops from 96 A to 76 A, 21 % less. At 480 V and 60 Hz the same bank would need about 106 µF per capacitor.

Why correct the power factor

• The bill: many utilities charge commercial and industrial customers for reactive energy or low power factor, typically below about 0.9 to 0.95.
• The installation: with less current, cables and transformers have more headroom, and losses and voltage drop go down. Sometimes correcting the power factor avoids having to upgrade a feeder.

How it is done in practice

• Automatic bank at the main switchboard: a controller measures the power factor and switches in the capacitor steps needed. It is the usual choice when the load changes during the day.
• Individual correction of large motors that run many hours: the capacitor is connected after the motor contactor, so it is switched off with the motor.
• With VFDs or a lot of electronics there are harmonics, and detuned banks (with reactors) are used so the capacitors do not resonate.

To understand the topic in depth: Practical electrical theory, with theory and a practice test.

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