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Synchronous Generator. Power engineering question.

  1. Oct 25, 2012 #1
    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

    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 + XdIa sin [itex]\phi[/itex])2 + (XdIacos[itex]\phi[/itex])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°

    ---

    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!
     
  2. jcsd
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