The k factor is the sum of(individual current harmonics squared times harmonic number squared). Harmonics in p.u. (1 = 100 percent).
It takes the effect of higher frequency components on copper losses as well as iron losses into account. It is used for power transformers of all kinds - dry or oil filled.
Fluke has some papers on this. There is also a discussion on
The k factor can be used to derate transformers - k-factor = 10 means that you shall derate a transformer around 20 percent. It can also be used to specify transformers. If you have a k factor = 15 and buy a transformer for 1000 kW at k factor 15, you will get a transformer that doesn't need to be derated.
Buying a couple of US-spec tfmrs for an offshore platform and the tfmr vendor's asking me what's the k-factor I want to use for the tfmrs. I reckon I can do away with k-1 or k-4 because 80% of loads are motors, but I reckon I should forward a copy of the load list to the vendor for him to judge himself what the best k rating would be.