Please, lets not get caught up too much in this calculation; remember that all these calculations are _always_ approximations. We assume sinusoidal loads. We assume nominal voltage. We have been assuming unity power factor. We assume lots of things.
Lets try things by 'ignoring' phase angles. First we calculate the current for the three phase load, using VA/ V / root(3)
A 'pure' 240kVa 240V three phase load is 577A/phase (approximately!) Of course, this calculation automatically includes the phase angle differences between the various three phase legs.
Then we calculate the single phase loads using VA/V
A 34 KVA 120V single phase load is 283A
A 41 KVA 120V single phase load is 342A
Then we just add the numbers up on the various legs. This, of course, neglects the phase angle difference between the single and three phase load, giving.
A: 860A B 577A C 919A
This as compared to the calculation which includes the phase angle differences:
A:835A B577A C 890A
(Bob and I appear to be getting exactly the same numbers using different calculation methods, which IMHO is a rather good check)
In other words, by ignoring the phase difference one gets about 3% difference in the calculated currents versus including the phase angles but assuming that the three phase load has a unity power factor.
Now, let us change our assumptions, and use a 0.8 lagging power factor for the 3 phase load. This is a lagging phase angle of about 37 degrees. If I put the new phase angles into the calculation, I get:
A:919A B 577A C 771A
That is to say that our initial assumption of unity power factor for the three phase load leads to a much larger potential error than just adding currents up and ignoring the phase difference between the single and the three phase loads.
-Jon
