Find load angle and internal voltage of 3MVA generator

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Nominal power PN= 3MVA
Nominal Voltage UN= 3000v (Y)
Line frequency f=50 Hz
Number of ole pairs= 2
Synchronous Reactance X1= 2.5 ohms

There is no reactive power and the generator can be assumed as lossless.

Please calculate Load angel and pole wheel voltage Up

Formula and my solution,
I=PN/UN
I=3MVA/3000V
I=1000AUN=XI +Up
Up= 3000v-2.5*1000A
UP=500v which is wrong

Load angel ? I don't know
 

Discussion

In my opinion UN=V;UP=E. See the attached sketch.
 
Attachments
  • Phasor diagram of a synchronous generator with E, V, I, I.X1 and load angle δ between E and V, power angle φ between V and I, and equations listed below.
    Synchronous Generator Steady State.jpg
    36 KB · Views: 245
Sorry.Wrong sketch.
 
Attachments
  • Phasor diagram of a synchronous generator with E, V and I vectors from a common origin, labelled I.X1 across the E-V side, with angles delta between E and V and phi between V and I, and text giving the relations P = V.I.cos(phi) and P = E.I.sin(delta)/X1.
    Synchronous Generator Steady State.jpg
    37.7 KB · Views: 263
I am sorry. Two more parentheses are missing
 
Attachments
  • Phasor diagram with E, V and I vectors from a common origin, labelled I.X1 across E and V, with angles delta between E and V and phi between V and I, and equations listed below.
    Synchronous Generator Steady State.jpg
    39.7 KB · Views: 278
I am not sure what does represent UN=3000V[Y]. Since it is about 50 Hz IEC Standard IEC 60038 Table 3 Note 1:
These systems are generally three-wire systems unless otherwise indicated. The values indicated are voltages between phases.
So, the voltage is 3 kV between phases. The power has to be: √3.I.UN.cos(ϕ). The voltage per phase it is then 3000/√3=1732 V
 

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