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Homework Help: 3 Phase Machine Line Current problem

  1. Aug 6, 2010 #1
    Hi guys,

    I would really appreciate some help with this problem(probably quite easy for anybody with Electrical Engineering experience).

    Thanks in advance

    1. The problem statement, all variables and given/known data

    A 415V, 50Hz, 3-phase supply is connected to a 3 phase load of 10kw with a power factor of 0.8 lagging. Find the magnitude of the line currents.


    2. Relevant equations

    P = VICos(power factor)

    Total Power = 3 V(p)I(p)cos(power factor)


    3. The attempt at a solution

    Attempted the question using the equations above, except I obtained the wrong answer.

    Correct answer = 17.39Amps
     
  2. jcsd
  3. Aug 6, 2010 #2
    Assuming the 415V is line to line rms and that the 10kW is the total wattage for all three phases:

    [tex]V_{\phi}=\frac{V_{LL}}{\sqrt{3}}[/tex]
    with [tex]V_{\phi}[/tex] being a per phase voltage and [tex]V_{LL}[/tex] being the line-to-line voltage.

    Next, we know that:
    [tex]P_{3\phi} = 3V_{\phi}I_{\phi}PF[/tex]
    with PF = powerfactor. And if this is star connected...
    [tex]I_{\phi}=I_{LL}[/tex]

    so
    [tex]P_{3\phi}=3\frac{V_{LL}}{\sqrt{3}}I_{LL}PF=\sqrt{3}V_{LL}I_{LL}PF[/tex]
    or
    [tex]I_{LL}=\frac{P_{3\phi}}{V_{LL}\sqrt{3}PF}[/tex]

    You seem to be confusing something. cos(angle) = PF. You don't say cos(PF). As far as I know, cos(PF) means nothing of importance.
     
  4. Aug 17, 2010 #3
    Thanks very much!
     
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