(adsbygoogle = window.adsbygoogle || []).push({}); 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)

I_{a}= 75 A

X_{d}= 3 Ω / phase

Find the excited voltage E and the load angle δ.

2. Relevant equations

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

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

E^{2}= (U + X_{d}I_{a}sin [itex]\phi[/itex])^{2}+ (X_{d}I_{a}cos[itex]\phi[/itex])^{2}

Or this one:

3 E^{2}= (U + X_{d}Q/U)^{2}+ (X_{d}Q/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

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 Ealwayshave to be lower than per-phase voltage ofU?_{f}

Because in this case I get E > U_{f}( 236,1 > (380/√3) )

I appreciate any hints on this one!

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# Homework Help: Synchronous Generator. Power engineering question.

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