General math question for 3 phase circuit

DYLH

Joined Aug 13, 2013
29
This is not related to a course or homework.. more just general understanding.

In a 3ph wye distribution system, let's say I have the following connected loads
100VA @ 0.9 PF connected A to neutral
125VA @ 0.85 PF connected B to neutral
300VA @ 0.95 PF connected A to B
(nothing on C)

Is there a proper mathematical way to compute the apparent power on lines A and B?

I know how to compute the currents of each load, and compute the resulting current on each line, considering the phase angle of A, B, and AB, and the phase angle shift due to power factor. However, if I wanted to stay in apparent power units, and not first convert to current, is a procedure possible? Alternatively, (or additionally) Is it legitimate to compute the current, then compute the power from the resulting current, using the phase angle as an input to compute the resulting power factor on each line? It would seem not, as the resulting angle no longer solely represents a power factor, but rather, a combination of power factor and phase angle due to the different voltages (e.g., 30deg between An and AB).

Thx