# How to show that voltages on diagram are 120° apart?

So i'm doing a matlab simulation of delta wye transformer and would need to show the phase shift between voltages. Here is a picture of input voltages so how would I show on this graph mathematically or graphically that these voltages are 120 degrees apart?

I tought of doing it like on this picture, to find degrees or radians and compare them, but on the graph from simulink above numbers are small so I don't know how.

• Compute the phase angle when blue equals yellow. Jan 22 '20 at 18:01
• You could do a simple fundamental frequency DFT to calculate the voltage phasors. Then plot all of them on a phasor diagram. Jan 23 '20 at 1:15

A slightly off-beat approach:

Figure 1. Intersection of the curves.

Because they're sinewaves we can use some trig functions.

• At (1) the blue phase is at 0. Let's call this 0°.
• At (2) the blue phase is at 2400. That will be 90°.
• At (3) and (4), the intersection point with the other phases, the voltage is 1200 which is half the peak. We know that $$\ sin\ a = 0.5 \$$ has two solutions: 30° and 150° and that these are 120° apart.
• And how would it be then for this one imgur.com/a/Cckv1p9 ?
– user226621
Jan 22 '20 at 23:04
• That's a different question. Jan 22 '20 at 23:10

The easy way would be to put your vertical grid lines at 60 or 120 degree spacing. Then you'll see that the rising-edge zero-crossings of phase 2 are 120 degrees after phase 1, and the zero-crossing of phase 3 is 120 degrees after that.