Having a bit of a night of it tonight, I do apologise. Quite a simple observation has left me wondering.
If we consider a 45A single-phase load and a balanced 45A three-phase load, star, assuming both with a purely resistive load, does the maths resolve as follows?
45A SP -
kVA
= (UI x PF) / 1000
= (230 x 45 x cos 1) / 1000
= 10.35kVA
45A TP -
kVA
= (√3 x Ul x Il x PF) / 1000
= (√3 x 400 x 45 x cos 1) / 1000
= 31.17kVA
So via the TP load Il for each phase is 45A? So rearranging for Il and solving for a TP load with the same VA rating as the SP load, 10.35kVA we get -
Il
= kVA / (√3 x Vl x PF)
= (10.35 / (√3 x 400 x cos)) x 1000
= 14.9A
So the TP load here is 14.9A for each phase?