From: dhky@shaw.ca   
      
   On 28/10/2013 2:04 PM, Salmon Egg wrote:   
   > In article <526DC75B.2080803@shaw.ca>, Don Kelly  wrote:   
   >   
   >>> For example, use upper case letters to label the delta resistors (or   
   >>> impedances). Use lower case letters for the Y such that A and a do not   
   >>> touch, etc. Then A, B, C, a, b, c form three balanced bridges.   
   >>>   
   >>> A*a = B*b = C*c = A*B*C/(A+B+C) = a*b + b*c + c*a.   
   >>>   
   >>> Thus, once you do one of the two calculations on the right, you have the   
   >>> cross multiplication product that balances the bridges.   
   >>>   
   >> This is interesting -you have hit a core of the problem. Going from A   
   >> (Z12) B (Z23c) C (Z31) to a b c or z1n z2bn z3n works nicely -i.e going   
   >> delta to wye. However there may be a problem going the other way- to   
   >> deal with this one must say Z12 =A =(z1n*z2n +z1n*z3n+z2n*z3n)/ z3n or   
   >> (ab+ac+bc)/c   
   >> The problem is that the numbers are right but as you have indicated A   
   >> and a do not touch. There is a rotation which is a problem of   
   >> nomenclature - what is fixed is the terminals 1, 2,3  and we are dealing   
   >> with Z12 etc or z1n etc (n being a 4th or neutral terminal not present   
   >> in the delta).   
   >   
   > I have seen transformations, in Wikipedia for example, where the   
   > nomenclature is not symmetrical. That is why I would have used A=Z23.   
   > B=Z31 and C=Z12. Because each resistor in the delta will have one and   
   > only one resistor in the wye which is not touching it, the pairs of such   
   > resistors are Aa, Bb, and Cc. If you know one of these products you know   
   > them all. Knowing either the delta or the wye values give a nice   
   > symmetrical equation for this product.   
   >   
   > To my mind, the transformation was used to break a network down to   
   > series and parallel connections that are easy to calculate. I almost   
   > never did that. I used mesh currents to get a set of simultaneous   
   > equations. Before that, the Kirchhoff laws were the way to go. With   
   > modern computers, there is hardly any reason to use the transformation.   
   > The only benefit I can think of is that comparison of the delta and wye   
   > equivalents gives some insight into a particular combination.   
   >   
   > It could be that I am missing the entire point.   
   >   
   You are right-  One does need double subscripts to deal with this   
   properly. You know what is going on and the format and have put the clue   
   in considering the "one and only resistor in the wye that is not   
   touching" You use, properly a double subscript notation. Dealing with an   
   idiot box, inputis of the  form  a b c where awhat is referred to may be   
   Zab,Zbc, Zca or in the reverse case Zan,Zbn, Zcn. Check it out regarding   
   the preservation of the terminals A B C.   
      
   As to the need for the transformation- I agree- use Kirchoff.   
    From my viewpoint as it appears is yours,  use of I =YV (mesh) is   
   better than V-ZI (loop) simply because in  most cases it results in   
   fewer simultaneous equations and is generally better for computer   
   modelling because once a choice of reference bus is made (in power   
   systems it is easy), the rest can be automated. It is messier with loop   
   methods as there are so many choices.   
   --   
   Don Kelly   
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