How to determine phase angle of a three-phase circuit

Question

I am experiencing difficulties with a question:

A balanced three-phase load shown in the diagram is connected across a 380V, 50 Hz three-phase supply, ABC phase sequence. The voltage V_AB is taken as reference.

Part of the question I am trying to answer includes converting the WYE circuit to a Delta circuit as I have done:

Now, my main question is how do I work out the phase angle of each component?
My textbook does not have notes on how to determine the phase angle. All they say is V_BC is generally used as the reference phasor. But in this case, V_AB is used as the reference phasor and I don't know how to determine the angles for the phasor diagram. I thought of rotating the reference diagram of V_BC so that V_AB = 0, V_AC = 120 and V_BC = 240. Would I be correct on this approach? Please advise

Answer 1

Now, my main question is how do I work out the phase angle of each component?

Draw a phasor diagram: -

In delta, the loads are connected across three line voltage namely Vab, Vbc and Vca. These are shown above on the diagram - they are 120 degrees apart. It's simpler because the three delta loads are all equal and mainly reactive (hence the angle close to 90 degrees). So, for each of the individual line voltages, the current will lag by 76 degrees.

Here's another diagram that is for a delta load that might be easier to visualize: -

Important to note is that Ia = Iab - Ica and this tells you how the individual load currents sum to give you the phase current.