Hi guys
I was doing the question in the attachment but I am unsure if I had done it correctly. I am required to find the power factor of an unbalanced system.
The way I found the powerfactor is to find the complex power for each phase, add them together and work out the angle from there. Is this the right way to go about it?
Can someone please let me know or if I am incorrect point me in the right direction.

 

Unless you show your intermediate working it's impossible to check your results.

The question itself is rather curious. One tends to think of power factor in 3-phase systems in the context of a balanced loading on each phase. In this case the loads are anything but balanced. In such circumstances the individual phase power factors are usually more relevant. However in your case there is no neutral connection between the source and unbalanced load so the concept of power factor becomes even more "fuzzy".

The individual phase loads are inductive in two cases and capacitive in the third - how does one lump them together as an effective inductive or capacitive load? I'm not convinced simply summing the individual terms has any real meaning.

Anyway, show us some of your working at the important steps.

BTW: If your result is the summation of the individual load apparent power values, then I obtain a different answer [577.286+j104.58 VA]. Perhaps another member can confirm the discrepancy or otherwise.

Regarding power factor in unbalanced systems: The Standard Handbook for Electrical Engineers [Tenth Edition] by Fink & Carroll states in Section 3-76 "The power factor of a polyphase circuit which is balanced is the same as that of the individual phases. When the phases are not balanced, the true power factor is indeterminate."