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From: Derek O'Connor on 5 Apr 2010 04:30
"Derek O'Connor" <derekroconnor(a)eircom.net> wrote in message <hpc5hj$es4$1(a)fred.mathworks.com>...
> "Darryl " <alfalfaNOT.THIS(a)value.net.nz> wrote in message <hp9026$cnj$1(a)fred.mathworks.com>...
> > Hi,
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> Your problem is called the Delta-Y or Y-Delta transformation for three-terminal networks (Y = star, in US terminology). I can't draw labelled diagrams here so I'll assume you will understand the following (using your labels):
>
> Ra, Rb, and Rc are the impedances of the Y-connected network, and Z1, Z2, and Z3, are the impedances of the equivalent Delta-connected network. The problem is to find Z1, Z2, Z3, in terms of Ra, Rb, Rc, or vice versa.
>
> I can't remember how to do this (simple algebraic manipulation), but I'm looking at one of the few remaining books I have on the subject, "Circuit Analysis of A-C Power Systems, Vol. 1", by Edith Clarke, Wiley, 1943. She gives the transformation formulas on pages 33 and 34. Here are the equations for (your) Y-Delta transformation:
>
> Let
>
> (i) S = RaRb + RaRc + RbRc. Then
>
> (ii) Z1 = S/Rc, Z2 = S/Rb, and Z3 = S/Rc
>
> So, your problem is solved by
>
> (1) Calculate Ra, Rb, Rc from your first set of of equations.
>
> (2) Calculate S, Z1, Z2, and Z3, using (i) and (ii).
>
> Note that if Ra=Rb=Rc=R (balanced circuit) then S = 3R^2 and Z1=Z2=Z3 = 3R, for the Y-Delta transformation, and if Z1=Z2=Z3 = Z, then Ra=Rb=Rc = Z/3, for Delta-Y transformation.
>
> Do check these formulas in a 'modern' book.
>
> Derek O'Connor.
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I just realised that without diagrams there is crucial information missing: I assume that you have three terminals labelled 'a','b','c', in your Y-connected circuit, and that Ra = impedance between terminal 'a' and neutral (middle of the Y), etc., and that Z1 = impedance between terminals 'a' and 'b' in the equivalent Delta-connected circuit, etc.

Again, check your textbook to make sure that I haven't permuted the a,b,c.

Derek O'Connor
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