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Balanced wye-wye system

  1. Jun 21, 2006 #1
    I would like to know what I'm doing wrong here. I am not getting what the book has.

    Q: In a balanced three-phase wye-wye system, the load impedance is [itex] 8+j4\Omega [/itex]. The source has phase sequence abc and [itex] \bar V_{an} = 120<0\,\,V_{rms} [/itex]. If the load voltage [itex] \bar V_{AN} = 116.62<-1.33\,\,V_{rms} [/itex] determine the line impedence.

    Please excuse me being lazy and not looking up how to properly represent polar numbers in LaTeX. Thus [itex] X < 90 [/itex] would mean a magnitude of [itex] X [/itex] with a phase angle of [itex] 90 [/itex] (in degrees).

    A:
    This is how I'm going about it:
    [tex] \bar Z_{load} = 8+j4 \Omega [/tex]
    [tex] \bar V_{an} = 120 < 0 \,\,V_{rms} [/tex]
    [tex] \bar V_{AN} = 111.62 < -1.33 \,\,V_{rms} [/tex]
    [tex] \bar Z_{line} = ? [/tex]

    So I simply setup a voltage divider:
    [tex] \bar V_{AN} = \bar V_{an}\left( \frac{\bar Z_{load}}{\bar Z_{line} + \bar Z_{load}}\right) [/tex]

    Solving for [itex] \bar Z_{line} [/itex] yields:

    [tex] \bar Z_{line} = \frac{\bar V_{an}\bar Z_{load}}{\bar V_{AN}}-\bar Z_{load} = \frac{(120<0)(8+j4)}{(116.62<-1.33)}-8+j4
    =0.134+0.306j \Omega[/tex]

    The book gets [itex] 0.5 + 0.5j \Omega [/itex]
     
    Last edited: Jun 21, 2006
  2. jcsd
  3. Jul 17, 2006 #2
    I am not a power expert, but it looks right to me. You math is right too. Tell me what your prof says.
     
  4. Jul 20, 2006 #3

    berkeman

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    Staff: Mentor

    I'm guessing the difference has to do with the Y shape of the load and line impedances. When they say that the load impedance is 8+j4, is that each of the three Y impedances, or the parallel combination of them, or some other variation? I haven't worked with Y-delta stuff much, so I don't know what the convention is. But maybe that's why the book has a different answer.


    EDIT -- Oops, I see now that this question was from last month. Sorry for the slow response, FrogPad. What turned out to be the error?
     
  5. Jul 28, 2006 #4
    Well I actually forgot about this post. This was for a summer class I was taking, so things were flying by. I'm actually back home right now (I go to school in a different state), so I don't have anything from that class with me.

    This post will either have to wait until I get back to school, or be lost forever.
     
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