Synchronous Generator. Power engineering question.

[Pavoo]

Homework Statement

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)
I_a = 75 A
X_d = 3 Ω / phase

Find the excited voltage E and the load angle δ.

Homework Equations

Under excited generator -> generator consumes VAr (the load is leading).

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

E² = (U + X_dI_a sin $\phi$)² + (X_dI_acos$\phi$)²

Or this one:

3 E² = (U + X_dQ/U)² + (X_dQ/U)²

P = active effects
Q = reactive effects

For δ an equation like this can be used:

P = (3*E*U_f)/X_d * sin δ

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 U_f ?

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

I appreciate any hints on this one!

 

[KataKoniK]

1. It seems like you may have made a mistake in your calculations or used the wrong equations. I suggest double checking your work and making sure you are using the correct equations for the given scenario.

2. In the case of an under-excited generator, the E value can vary and does not necessarily have to be lower than the per-phase voltage of Uf. It depends on the specific conditions and parameters of the generator.