3/Phase AC theory help required

Discussion in 'Homework Help' started by blizzard, Jan 14, 2009.

  1. blizzard

    Thread Starter New Member

    Jan 14, 2009
    Can anyone tell me when calculating phase voltage in a balanced three phase system, why is it line voltage divided by root three. Why root three ? Why not line voltage divided by three ? Thanks for the help my electrical theory is a bit rusty lol.
  2. MareBear


    Oct 29, 2008
    its the formula for the wye configuration. |Vline| = sqrt(3)|Vphase| i dont know the proof to it, i just know its a given formula
  3. blizzard

    Thread Starter New Member

    Jan 14, 2009
    Thx for the reply, but I really needed to know why root 3 and not divided by three. It looks like this one is proving a toughy but thanks to all who have a go.
  4. Wendy


    Mar 24, 2008
    I'm not sure of the exact answer myself, but I believe it has to do with the 120° phase shift between them. Probably a trig function.
  5. vvkannan

    Active Member

    Aug 9, 2008
    hello blizzard,
    let Vr =V/_0,
    Vy = V/_-120deg

    and Vz = V/_-240deg phase voltages of a balanced three phase system

    now the line voltage Vry = Vr - Vy
    = V/_0 - V /_-120
    = V(1 - (cos120 - j sin120)
    =V(3/2 +j0.866)
    taking the magnitude we get Vry = V(sqrt 3)
  6. blizzard

    Thread Starter New Member

    Jan 14, 2009
    Thx all for having ago not to sure about the last reply man wtf is that LOL. Bills reply put me on the right tracks with the trig. I found this explanation and really just sums it up nicely.

    Three phase voltages are 120 degs apart. If you draw a vector sum diagram as in a three-phase wye connection, join the ends of the three lines together. Those lines using trig will be 1.732 (root 3) times longer than the phase lines. If you draw to scale it shows no probs.

    Cheers D
    Last edited: Jan 15, 2009