Unbalanced three-phase three wire system

Discussion in 'Homework Help' started by progrocklover, Jan 31, 2011.

  1. progrocklover

    Thread Starter New Member

    Jan 31, 2011
    3
    0
    I am stuck on a example on my notes. Below is the Example.

    Supply: 400V, 50Hz, 3-phase, 3-wire
    Load: non-reactive, star connected
    phase A - 10kW
    phase B - 6kW
    phase C - 4kW
    Find: current in all 4 conductors

    Here is a part of the solution:
    Va = 231 /_ 0 degree, Vb=231 /_120 degree, Vc=231 /_120 degree
    Ra=(Va)^2/Wa = 231^2/10x1000 = 5.336Ω
    Rb=(Vb)^2/Wb = 231^2/6x1000 = 8.893Ω
    Rc=(Vc)^2/Wc = 231^2/4x1000 = 13.340Ω

    However, In the alternative solution, it gives another way to find out the answer. It first calculates the voltage at the star point(Vn) which is equal to 22.91 /_19.06 degree.

    I am confused. Take Ra as an example, if the voltage at star point is not equal to zero, then the voltage across Ra = Va-Vn, which means
    Ra=(Va - Vn)^2/Wa.

    Can anyone explain this to me?

    Any help would be appreciated:)
     
  2. progrocklover

    Thread Starter New Member

    Jan 31, 2011
    3
    0
    Sorry, I made a mistake, it should be Find: current in all 3 conductors
     
  3. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    Your point is valid.

    The method of calculating the resistance values is incorrect. Is that your method or something given in class or in a textbook. With an unbalanced load the line to floating star point voltage obviously can't be assumed to be the line to neutral voltage.

    I suspect the only way to solve the problem is to indeed find the offset star point voltage and go from there.
     
    Last edited: Feb 1, 2011
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