Transformer K-Factor
Enter harmonic currents, load and transformer data to get K, the K-rating and the derated capacity.
Step-by-step
- Enter valid values to begin.
The fundamental is fixed at 100%. K = Σ(Ih²h²) / ΣIh²; with currents normalised to the RMS value this is the same number as the harmonic loss factor FHL. Derating uses the simplified IEEE C57.110 expression with a single eddy-current fraction PEC-R at rated load; 0.08 is only a typical value for conventional dry-type units, so use the figure from the transformer test report. The model ignores other stray losses, ambient and altitude, and assumes the entire load is the same spectrum. Even harmonics and interharmonics are not entered.
Transformer K-Factor: Sizing for Drives and Rectifier Loads
Core Engineering Principles
A transformer is rated for sine-wave current, which a drive or rectifier does not draw. Winding losses come in two parts: I²R loss, which follows RMS current, and eddy-current loss in the conductors, which follows the square of frequency. As far as the eddy term goes, 1 A at the 11th harmonic heats like 121 A of fundamental. So we weight every harmonic by h², and K is that weighted average. A standard unit only has eddy loss budgeted for K = 1.
We have two ways out: derate a standard unit by the IEEE C57.110 expression, or buy a K-rated dry-type (UL 1561) with finer, transposed conductors and a double-sized neutral. Delta primaries trap triplen currents (3rd, 9th, 15th) in the winding, while a wye secondary neutral carries their arithmetic sum. A 12-pulse rectifier, line reactors or an active filter cut K far more cheaply than any nameplate, because the harmonics are still there otherwise.
Imax (pu) = √[(1 + PEC-R) / (1 + FHL × PEC-R)] • kVAusable = kVArated × Imax
FHL = K when the currents are normalised to the RMS value
NEC & Standard References
IEEE C57.110 is the recommended practice for establishing transformer capability when supplying nonsinusoidal load currents, and it is the source of the derating method used here. UL 1561 covers dry-type general-purpose and power transformers, including the K-factor ratings of 4, 9, 13, 20, 30, 40 and 50 marked on the nameplate. IEC 61378-1 covers convertor transformers for industrial applications. Take PEC-R from the manufacturer’s test report; 0.08 is only a typical dry-type figure. Check the edition adopted on your project.1. ΣI² = 100² + 30² + 14² + 7² + 5² + 3² + 2.5² = 11,185.25.
2. Σ(I²h²) = 10,000 + 22,500 + 9,604 + 5,929 + 4,225 + 2,601 + 2,256.25 = 57,115.25.
3. K = 57,115.25 / 11,185.25 = 5.11, so a K-9 unit is the next rating up.
4. THDi = √1,185.25 / 100 = 34.4%, and the RMS current is 1.058 × the fundamental.
5. Imax = √(1.08 / (1 + 5.106 × 0.08)) = 0.876 pu, so the standard unit is good for 150 × 0.876 = 131.3 kVA.
The load is 150 kVA, so the standard unit is overloaded. Use a K-9 unit, or a standard unit of at least 150 / 0.876 = 171 kVA.
- K-rating does not reduce harmonics. The generator, upstream feeder and capacitors still see the distorted current, and voltage distortion stays the same.
- Nameplate K means capability. A K-13 unit is not a K-13 load; calculate K from measurements.
- Overloaded neutral. Triplens add in the neutral instead of cancelling; size the downstream neutral to match.
- Use a true-RMS analyzer. Average-responding meters under-read distorted current badly.
- Measure at full load. Spectra shift with load, so light-load readings often understate K.