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Synchronous machine help asap- with solution attempt but wrong answer

  1. Jun 30, 2009 #1
    1. The problem statement, all variables and given/known data

    This was a lecture that wasnt taught to us but we were given sample problems with answer but no solutions and i tried to solve some but ends up with wrong answer.. so here's the given:

    a 3 phase 10kVA, 440V 60 Hz, y-connected alternator supplies the rated load at 0.8 power factor lagging. if the armature resistance is 0.5 and synchronous reactance is 10, find the voltage regulation at rated load. ANS: VR=48.0406%

    2. Relevant equations

    i think this are the equations to be used:


    %VR=[tex]\frac{V_{LCOMP}-V_{LRATED}}{V_{LRATED}}[/tex]*100
    V[tex]_{COMP\phi}[/tex]=V[tex]_{RATED\phi}+(I_{\phi}Z_{S\phi})[/tex]
    Z_{S\phi}=Re_{\phi}+JXe_{\phi}
    I_{\phi}=S/(V_{L}[tex]\sqrt{3}[/tex])

    3. The attempt at a solution

    THIS IS WHAT I'VE DONE:

    the given voltage is line and its a star connected :V_{L}=[tex]\sqrt{3}[/tex]V_{\phi}
    V_{\phi} is phase voltage

    so, i solved for the phase voltage:
    V_{\phi}=V_{L}/[tex]\sqrt{3}[/tex]=254.0341184V
    the phase current, I_{\phi}
    I_{\phi}=10kVA/(440[tex]\sqrt{3}[/tex])=13.12159703A
    and
    Z_{S\phi}=0.5+j10



    solution:

    V_{LCOMP}=[tex]\sqrt{((V_{LRATED}cos{\phi}+IR)^{2}+(V_{LRATED}sin{\phi}+IX)^{2}\[/tex]

    V_{LCOMP}=[tex]\sqrt{((254.0341*0.8+13.12159*0.5)^{2}+(254.0341*0.6+13.12159*10)^{2}}[/tex]
    V_{LCOMP}=352.78769V

    %VR=[tex]\frac{352.78769-254.0341}}{254.0341}[/tex]*100
    %VR=38.8749%

    please correct my solution.. i dont have any idea if i've done this right
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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