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Electrical Circuits - Three Phase Power - Y-Y transformer

  1. Sep 5, 2015 #1
    1. The problem statement, all variables and given/known data

    I took a few pictures of the circuit, it went across two pages so I took a few pictures, and closeups of certain parts to ensure that all the details can be seen

    For the circuit:

    http://s7.postimg.org/ywd4nrmsq/IMG_20150905_140403187_HDR.jpg
    Figure 1. Overview of Circuit Picture 1
    http://s13.postimg.org/p5i0bqwp2/IMG_20150905_140331854.jpg
    Figure 2. Overview of Circuit Picture 2
    http://s9.postimg.org/vv6dm2hlq/IMG_20150905_140357293.jpg
    Figure 3. Closeup of RHS of circuit
    http://s23.postimg.org/kvsc4okdm/IMG_20150905_140339083.jpg
    Figure 4. Closeup of LHS

    1)Find Load Current @ .85 p.f. lead and find load current @ full load
    2)Find real power
    3)Find Imaginary Power
    4)Apparent Power

    2. Relevant equations
    delta to wye conversion
    wye to delta conversion

    3. The attempt at a solution
    Alright. I'm pretty loss on how to analyze this circuit. In my undergraduate I touched upon three phase power, wye configurations, and delta configurations. This was a while back though.

    I know that you can convert a delta configuration to a wye configuration (and the other way around), however I don't know this is of any use in this case. I have never analyzed a circuit before were a wye configuration is in parallel with a delta configuration, as in this problem. So I'm a bit lost. I have searched the internet and cannot find any literature on analyzing the two configurations in parallel. Maybe I didn't look in the right places but I searched for some time. I have found plenty of documentation on solving such problems when it's a wye configuration or just a delta configuration, but nothing with both of them in parallel.

    I went through my book page by page and found a sort of similar problem with the two configurations in parallel. The book I'm using is "An Introduction to Electrical Machines and Transformers" second edition by George McPherson and Robert D. Laramore. I tried to find the solution online but was unable to do so. I also tried searching for the solutions manual. I was surprised I could find nothing, as the book is from 1990.

    http://s4.postimg.org/3t6pyu2yz/similar_problem.jpg
    Figure 5. A sort of similar problem in my book with the two configurations in parallel

    I also found in my book some documentation on analyzing a Y-Y transformer configuration with the load being in a Y configuration. Although this is helpful and a start, I can't apply this technique because the load in my circuit is a delta configuration in parallel with a Y configuration.

    http://s9.postimg.org/p6m0n1fcu/Y_Y_Y_load.jpg
    Figure 6. Documentation on analyzing a Y-Y transformer with a Y load
    http://s15.postimg.org/u5pikknwq/Y_Y_Y_load2.jpg
    Figure 7. Additional Information on analyzing a Y-Y transformer with a Y load

    Other than what I mentioned above, my book doesn't offer much help. As mentioned I have searched online for a few hours looking for documentation on analyzing and simplifying a delta configuration in parallel with a Y (wye) configuration but can't find any. I have found online though information that the Y-Y transformer isn't use that often because of issues with it being reliable.

    Any help would be greatly appreciated in analyzing this circuit. I don't know were to begin, and have searched literature for a few hours for aid in even beginning to analyze the circuit ,but can't find any. Even just some literature on analyzing a delta configuration in parallel with a Y configuration would be of help. Since my book is very old, and there is a similar problem in it, I know someone has had to solve a similar problem before, but I can't find any documentation on such a problem, other than what is mentioned.

    THANKS!
     
  2. jcsd
  3. Sep 6, 2015 #2
    What I'd do initially is convert any delta connections to wye connections and then create a one-line diagram of one singular phase of the circuit. From there you can simply analyze the circuit and apply to the other 2 phases by only adding their respective different phase angles. Search up one-line three phase circuit analysis. This will convert the difficult 3 phases into one simple to analysis phase and then you can use your existing single phase circuit theory knowledge to do the whole circuit.

    You'll need to know the differences between line and phase voltage and current to make sure you use the correct ones when working with delta and wye connections.

    Delta:
    Vline = Vphase and Iline = 3^(1/2)*Iphase

    Wye:
    Iline = Iphase and Vline = 3^(1/2)*Vphase

    For Power in these connections:

    Pd & Py = 3^(1/2)*Vline*Iline*Cos(theta) (Watts)
    |Sd| & |Sy| = Vline*Iline (VA)
    Qd & Qy = 3^(1/2)*Vline*Iline*Sin(theta) (VAr)
     
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