Understanding Power Factor Correction: A Tutorial with Worked Calculations

In 2014 at Batu Hijau, we had a 2.5 MVA transformer feeding a process building that was consistently running at 92% loading. The loads were mostly motor-driven — crushers, conveyors, pumps — and the aggregate power factor was 0.71. After installing a 400 kVAR automatic capacitor bank, the transformer loading dropped to 73%. We did not remove a single load. We did not change a single cable. We simply stopped forcing the transformer and cables to carry reactive current that does no useful work.

This tutorial explains the physics behind power factor correction and walks through the calculation from start to finish.

The Power Triangle

Every AC load draws two types of current. Real current does useful work — turning shafts, generating heat, producing light. Reactive current sustains the magnetic fields in motors, transformers, and inductors. It flows back and forth between the source and the load, doing no work but occupying cable capacity and generating losses.

These two components form the power triangle:

• P (kW) — Real power. The horizontal leg. This does work.
• Q (kVAR) — Reactive power. The vertical leg. This sustains magnetic fields.
• S (kVA) — Apparent power. The hypotenuse. This is what the transformer and cables must carry.

A power factor of 0.72 means only 72% of the apparent power is doing useful work. The remaining reactive component forces the entire upstream system — cables, switchgear, transformers — to be oversized.

Why Low Power Factor Is a Problem

The practical consequences of low power factor are measurable at every point in the electrical system:

Higher Current for the Same Real Power

For a 500 kW three-phase load at 415 V:

At PF 0.72, the current is 39% higher than at unity. That means larger cables, larger switchgear, higher I2R losses, and higher voltage drop — all to deliver the same useful power.

Utility Penalties

Most industrial tariffs penalise power factors below 0.90 or 0.85. The penalty mechanisms vary by jurisdiction — reactive energy charges (kVARh), demand charges based on kVA instead of kW, or direct PF surcharges. In Australia, many network service providers apply penalties below 0.90.

Reduced System Capacity

A 1000 kVA transformer at PF 0.72 can only deliver 720 kW of useful power. Correct the power factor to 0.95 and the same transformer delivers 950 kW. That is 230 kW of additional capacity without touching the hardware.

Worked Calculation: Sizing a Capacitor Bank

Let us size a capacitor bank for the following installation:

• Total real power: 500 kW
• Current power factor: 0.72 (lagging)
• Target power factor: 0.95 (lagging)
• System voltage: 415 V, three-phase, 50 Hz

Step 1: Calculate Current Reactive Power

Step 2: Calculate Target Reactive Power

Step 3: Calculate Required Capacitor kVAR

We need a 318 kVAR capacitor bank to improve the power factor from 0.72 to 0.95.

Step 4: Verify the Before-and-After Impact

Let us quantify what this correction achieves:

A 24% reduction in current means cables that were running hot now have headroom. Voltage drop improves proportionally. The transformer has 168 kVA of freed capacity.

Capacitor Bank Selection

Fixed vs Automatic Stepped Banks

For installations with relatively constant loading (a continuously running process plant), a fixed capacitor bank can work. But most installations have variable loads, and a fixed bank risks over-correction — pushing the power factor leading, which causes voltage rise and potential resonance.

Automatic stepped banks use a power factor controller that monitors the system PF in real time and switches capacitor steps in and out as loads change. For our 318 kVAR requirement, a typical configuration might be:

• Bank rating: 350 kVAR (next standard size above 318)
• Steps: 7 x 50 kVAR, controlled by a 7-step PF controller
• Switching: Contactors with pre-insertion resistors (to limit inrush) or thyristor switching for fast response

IEC 60831-1, Clause 4 — Ratings and dimensions — self-healing capacitors for AC power systems

Harmonic Considerations: When Standard Capacitors Fail

This is where many power factor correction installations go wrong. Standard capacitors present a decreasing impedance with increasing frequency. If the system has significant harmonic currents — common in installations with variable frequency drives (VFDs), UPS systems, LED lighting, or arc furnaces — the capacitors can amplify harmonics through resonance.

The resonant frequency of the system with the capacitor bank is:

Where f1 is the fundamental frequency (50 Hz), Ssc is the system short-circuit power in kVA, and Qcap is the capacitor bank rating in kVAR.

If this resonant frequency coincides with a harmonic frequency present in the system (typically the 5th harmonic at 250 Hz or the 7th at 350 Hz), the result is harmonic amplification — high circulating currents that overheat capacitors, blow fuses, and distort voltage waveforms across the facility.

Detuned Reactors: The Standard Solution

A detuned reactor is a series inductor added to each capacitor step. The reactor is sized so that the LC combination has a resonant frequency below the lowest significant harmonic. The standard detuning percentage is 7% for 5th harmonic filtering (resonant at 189 Hz, safely below the 5th harmonic at 250 Hz) or 14% for 3rd harmonic environments.

Since 189 Hz is below 250 Hz (5th harmonic), the capacitor-reactor combination presents an inductive impedance at all harmonic frequencies above 189 Hz. This prevents harmonic amplification and makes the bank safe for harmonic-rich environments.

When NOT to Apply Power Factor Correction

There are situations where connecting capacitors causes more harm than good:

1. Directly at VFD output terminals. The capacitors interact with the drive's output stage and can damage the power semiconductors. Always connect PFC on the supply side of the drive, never the motor side.

2. On circuits with high harmonic distortion and no detuning. As described above, resonance will amplify harmonics and destroy the capacitors.

3. When the power factor is already above 0.95. The incremental benefit is minimal and the risk of over-correction increases.

4. On generator-fed systems without careful analysis. Capacitive loading on synchronous generators can cause voltage regulation instability, particularly under light load conditions. Generator AVR tuning must account for the capacitor bank.

Practical Installation Notes

A properly installed capacitor bank requires more than just the capacitors themselves:

• Fuses or MCCBs rated for 1.5 times the capacitor rated current (capacitors draw inrush current and may carry harmonic overcurrent)
• Contactors rated for capacitor switching duty (standard AC3 contactors will weld their contacts from the inrush transient)
• Discharge resistors to bring the voltage to below 50 V within 60 seconds of disconnection, per IEC 60831-1 Clause 15
• Ventilation — capacitors and reactors generate heat, particularly detuned banks where the reactor losses are significant

IEC 60831-1, Clause 15 — Discharge device requirements

Power factor correction is one of the highest-return investments in electrical infrastructure. The calculation is straightforward. The engineering challenge is in the harmonic analysis and proper bank specification. Get those right, and a capacitor bank will run for 15-20 years with minimal maintenance, paying for itself within the first year through reduced losses and avoided utility penalties.