Harmonics, K-factor and transformers: when non-linear loads call for derating

A transformer rated 1 000 kVA is rated for 1 000 kVA of sinusoidal 50 Hz current. Feed it with the same RMS current at 50 Hz plus 5th, 7th and 11th harmonics and the winding losses rise noticeably, because eddy-current losses grow with the square of the frequency. This is the reason behind the K-factor and the "harmonic derating" you find in data-centre and industrial specifications.

Where harmonics come from

• Six-pulse rectifiers and variable-speed drives: 5th and 7th harmonics, THDi 30–80 % without filters.
• UPS systems and server power supplies: 3rd (in the neutral!), 5th, 7th.
• LED and fluorescent lighting drivers.
• PV and battery inverters: modern units are well below 5 % THDi and are usually not a concern.

The K-factor

The K-factor (UL 1562 / IEEE C57.110) weights each harmonic current by the square of its order:

K = Σ (Ih / I1)² · h² for h = 1, 2, 3, …

A pure sine wave has K = 1. A load with 20 % 5th and 14 % 7th harmonic has K ≈ 1 + 0.04·25 + 0.02·49 ≈ 3. The European equivalent is the "factor K" in EN 50464-3 / IEC 61378, which leads to a derating factor rather than a transformer class.

K-factor	Typical load	Standard transformer capacity
1	Motors, heating, incandescent lighting	100 %
4	Offices with IT equipment, mixed drives	≈ 85–90 %
13	Data centre, UPS-dominated load, welding	≈ 70–75 %
20	Rectifier plants, large drive systems	≈ 60 %

Three ways to deal with it

1. Derate a standard unit. For a 700 kVA K-13 load, choose a 1 000 kVA transformer. Simple, and the larger unit also has a lower uk-related voltage distortion. Often the cheapest route for PNACHO ratings, since the next size up costs less than a special design.
2. Specify a K-rated design. Transposed or foil LV windings, larger neutral conductor (for 3rd-harmonic loads up to 173 % of phase current), reinforced cooling. Longer lead time; justified for large data centres.
3. Filter at the source. Active harmonic filters or 12-pulse drives reduce THDi to below 5 %, and the transformer sees an almost sinusoidal current. Usually the most economical solution above 1 MVA.

For PNACHO transformers

Both series handle the harmonic content of ordinary commercial and industrial loads (K ≤ 4) at their nameplate rating. For UPS-dominated or rectifier loads, send us the harmonic spectrum or the K-factor from the load study; we select the rating with the appropriate margin – for example a PNACHO-D one size larger with the AF fan kit, which adds a cooling reserve exactly where harmonic losses appear.