Create a Phasor Diagram Easily: Step-by-Step Guide & Helpful Tips

[Cassy85]

Hi, I'm struggling to find out how to create a phasor diagram. I have attached a photo of the question any help would be greatly appreciated.

This is what I have attempted so far.
It's question 2b I am really struggling with.
I'm not looking for the answers just looking for some direction.

1. Calculate phase current

Phase current = 250003 x 415 x 0.8
Phase current = 25.1 Amps
cos-10.8=36.87
I = 25.1 ∠36.87° Amps

1. Calculate the stator reactive voltage drop IXs

Voltage drop = IaXs
25.1 x 4 ∠36.87° + 90°
Voltage drop (IXs) = 100.4 ∠126.87° volts

 

[Babadag]

First no such motor "synchronous induction motor" does exist .Since the power factor is leading it is about synchronous motor when the excitation current is more than rated.
The motor has an a.c. winding in stator part and a d.c. winding [poles] on the rotor. Since it is a separately E noted, the generated voltage is equal to supply voltage.
The generated voltage has to be in the load case.
If the power mentioned is "input power" the apparent power it is the ratio 25/0.8.

The loaded current it is 25000/0.8/√3/415=43.475 A

 

[Babadag]

Actually this is the current from the network. The current in the motor winding in triangle it is only 25.1A, indeed.

 

[Babadag]

In my opinion, the power factor and Xs are calculated from the network point of view so for an equivalent star motor. In this case the current IA= 43.475 A and is leading the phase-to-neutral voltage VAN with φ= 36.87 degrees. Then the voltage drop [total] is IA*[cosφ+jsinφ]*jXs and the reactive part is jIA*cosφ*Xs.

 

[Babadag]

The vectorial diagram it could be like this one:

 

[Babadag]

My mistake. The voltage considered for equivalent motor is not
“the leading the phase-to-neutral voltage” as I said but the phase-to-phase voltage. So, the vectorial diagram on the trigonometric circle it has to be like this: