Power quality calculator: THD, K-factor, unbalance and reactive power

What this calculator does

Three calculations that come out of any power-quality survey, and that are almost always done by hand in a spreadsheet back at the office.

Harmonics: THD and K-factor

From the fundamental and the odd harmonics up to the 13th:

THD = √(Σ I_h²) / I₁

referred to the fundamental, the form used by EN 50160 and IEC 61000-4-30, and the K-factor:

K = Σ (I_h² · h²) / Σ I_h²

The K-factor is what decides the transformer. Additional eddy-current losses grow with the square of the harmonic order, so 30% of third harmonic does not heat 30% more: it heats as if the RMS current were considerably higher. A pure sine wave gives K = 1; power-electronic loads reach 4, 13 or more, and that is exactly the figure a transformer for non-linear loads is specified with.

The calculator also gives the total RMS value, which is what protections actually measure and what the cabling has to carry: a neutral sized on the fundamental falls short when third harmonic is present, because triplen harmonics add in the neutral instead of cancelling.

Voltage unbalance

From the three line voltages, the calculator applies the exact method — the ratio of the negative-sequence component to the positive one:

β = (U₁₂⁴ + U₂₃⁴ + U₃₁⁴) / (U₁₂² + U₂₃² + U₃₁²)²

VUF = √((1 − √(3 − 6β)) / (1 + √(3 − 6β)))

and also the simple method (largest deviation from the mean), because many manufacturer guides use it and it helps to be able to compare. EN 50160 limits unbalance to 2%.

Power-factor correction

Q = P × (tan φ₁ − tan φ₂)

Besides the kvar, the calculator shows the capacity released: the kVA the transformer and the cabling get back as the current falls. That is usually the economic argument missing from the report, because well-executed correction sometimes avoids replacing a transformer.

One warning: where harmonics are present, the bank cannot be a bare capacitor. The capacitor-transformer combination forms a resonant circuit and, if its resonant frequency lands near a harmonic that is present, the current is amplified and the bank destroys itself. With appreciable THD you need detuned equipment.

Worked example

A board with 100 A of fundamental and 30 A of third harmonic, voltages of 400, 398 and 403 V, and 100 kW at 0.80 power factor.

• THD = 30% and K-factor = 1.66 → the transformer feeding this board needs margin
• Total RMS: 104.4 A against the 100 A of the fundamental
• Unbalance: 0.4% by the exact method → within EN 50160
• To reach 0.95: 42.1 kvar, releasing 19.7 kVA of capacity

What this calculator does not do

It works from a spectrum you type in, not from the full recording: it computes no weekly percentiles, which is how EN 50160 compliance is assessed, and it does not distinguish dips, interruptions and transients. It does not size filters or check bank resonance, which requires the short-circuit power. And the K-factor it returns is that of the spectrum entered: the design figure must come from a recording of the real load.

What measures it

The spectrum, the unbalance and the power factor are recorded by a power quality analyser compliant with IEC 61000-4-30, which is what makes the measurements defensible in front of the utility. For low-voltage installations, multifunction testers include harmonic measurement.