derivation square root of 3 for for delta and wye transformers

Discussion in 'Math' started by EL7819, Oct 13, 2011.

  1. EL7819

    Thread Starter New Member

    Apr 15, 2011
    20
    0
    Hello,

    I hope I have this in the right forum. I was wondering how mathematicians and or engineers derived the square root of 3 as a constant for delta and wye balanced 3 phase transformers mostly? If not an answer articles to read is fine, anything to point me in the right direction.
    My guess would be that there are three
    branches and it has something to do with the pythagoreom thereom. I am not sure? If my spelling and or grammer is in some way wrong, I apologize for my insolence.
    Thank you, any help is greatly appreciated.
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    You are close. It is a generalization of that theorem called the cosine law. The three branches imply that the angles between the vectors is 120 degrees, and the cosine law allows the vector length to be calculated for angles other than 90 degrees (which Pythagorus' theorem is limited to).

    http://mathworld.wolfram.com/LawofCosines.html

    so  c^2=a^2+b^2-2ab \cos(\theta)

    becomes

     c^2=V^2+V^2-2V^2 \cos(120)

    or

     c^2=2V^2(1-\cos(120))=3V^2

    then take the square root of each side to get the following.

     c=\sqrt{3}V

    So c represents the line to line voltage Vab or Vbc or Vca, and V represents the phase voltage Va, or Vb or Vc, and the calculation is basically a vector addition (or more accurately vector subtraction) problem.
     
    Last edited: Oct 14, 2011
    Skadi likes this.
  3. MrChips

    Moderator

    Oct 2, 2009
    12,449
    3,365
    Just a minor typo. I know you meant

     c=\sqrt{3}V
     
  4. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469

    Thank you! :) I corrected it. That damn cut and paste operation gets me every time. :eek:
     
  5. EL7819

    Thread Starter New Member

    Apr 15, 2011
    20
    0
    Thank you for your help.
     
  6. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    @EL7819

    You can use the "Thanks" button to show your gratitude towards another member. This way the forum can stay clutter-free.
     
  7. Denny Singleton

    New Member

    May 11, 2016
    1
    2
    3 Phase.JPG
     
    GopherT and BR-549 like this.
Loading...