Transformer K-Factor From the Harmonic Spectrum (UL 1561)
Computes the transformer K-factor from a measured harmonic current spectrum.
Example
You enter
- Fundamental current (per unit) 1
- 3rd harmonic (per unit) 0.33
- 5th harmonic (per unit) 0.2
- 7th harmonic (per unit) 0.14
- 9th harmonic (per unit) 0.09
- 11th harmonic (per unit) 0.06
- 13th harmonic (per unit) 0.05
You get
- K-factor 4.61
- Recommended K-rating 9
Checked against published worked examples from: UL 1561 / IEEE C57.110.
Details, formula, and sources
ScopeK = sum(Ih^2 x h^2) / sum(Ih^2) with the harmonics entered as per-unit of the fundamental (UL 1561 / IEEE C57.110), then rounds up to the next standard K-rating (K-1 standard, then K-4 / K-9 / K-13 / K-20 / K-30 / K-40). The measured spectrum and the manufacturer govern.
Formula or tableK = sum(Ih^2 x h^2) / sum(Ih^2) over h = 1,3,5,7,9,11,13 with harmonics in per-unit of the fundamental; round up to the next standard K-rating (K-1, K-4, K-9, K-13, K-20, K-30, K-40).
Source and editionTransformer K-factor for nonlinear loads, UL 1561 and IEEE C57.110, by name.
Free accessThe K-factor weights each harmonic by the square of its order; a near-linear load (K close to 1) needs only the lowest K rating, K-4; only a pure sine (K exactly 1) stays at K-1. The measured spectrum and the manufacturer govern the final selection.
What governsEstimate. AHJ and licensed electrician govern. Verify against the NEC edition adopted in your jurisdiction.
API field namesi1, i3, i5, i7, i9, i11, i13, k_factor, recommended_k_rating
- K-factor definition sum of (per-unit harmonic current squared times harmonic order squared) divided by the sum of (per-unit harmonic current squared)UL 1561 / IEEE C57.110
- Standard K-ratings the tabulated ladder K-1 (standard) / K-4 / K-9 / K-13 / K-20 / K-30 / K-40UL 1561