I don't do a lot of single phase work, so I'm rusty on the calculations. If I want to power three, 100 A, 208 V, single-phase loads, all supplied from one, three-phase, 480-120/208V transformer. What is the loading on that transformer? I keep working myself in circles on whether the 1.732 applies or not.
There is a square root formula for translating phase-to-phase current into the corresponding phase-to-neutral current. If all three phase-to-phase loads are equal you will see that the three terms under the square root are add up to 3*current^2, which shows you how sqrt(3) gets involved.
Ia = sqrt(Iab^2 + Ica^2 + Iab*Ica) + Ia0
Ib = sqrt(Iab^2 + Ibc^2 + Iab*Ibc) + Ib0
Ic = sqrt(Ibc^2 + Ica^2 + Ibc*Ica) + Ic0
Iab, means current of loads connected across phases a and b.
Ia0, means the sum of phase A-to-neutral loads and the impact of balanced three phase loads on phase A, before you consider the phase-to-phase loads on 2-pole breakers.
Ia is the total current on the phase A conductor.
Apply the same concept to the other subscripts.
Notice that it is the two phase-to-phase possibilities that contain an "a" in the subscript, that apply to phase A. Similarly, with phases B and C. You square each of them, and you multiply a mixed product of both of them. Add all three terms, and take the square root o the sum. Then add on the current not associated with phase-to-phase loads.
