# Synchronous Generator. Power engineering question.

1. Oct 25, 2012

### Pavoo

1. The problem statement, all variables and given/known data
Consider following: a three-phase synchronous generator which is under excited and drives a load with the power factor of 0.9 .

U = 380 V (Main supply voltage)
Ia = 75 A
Xd = 3 Ω / phase

Find the excited voltage E and the load angle δ.

2. Relevant equations

E can be calculated using various equations and methods, here's an example:

E2 = (U + XdIa sin $\phi$)2 + (XdIacos$\phi$)2

Or this one:

3 E2 = (U + XdQ/U)2 + (XdQ/U)2

P = active effects
Q = reactive effects

For δ an equation like this can be used:

P = (3*E*Uf)/Xd * sin δ

3. The attempt at a solution

The correct solution should be (my book says so):
E = 203 V and δ = 83,3°

I get, using all the above equations:
P = 44,4 kW , Q = -21,5 kVAr

E = 236,1 V and δ = 59°

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Questions:
1. Am I just counting wrong here?

2. In the case of under-excited generator, does the E always have to be lower than per-phase voltage of Uf ?

Because in this case I get E > Uf ( 236,1 > (380/√3) )

I appreciate any hints on this one!