WYE-DELTA / DELTA-WYE conversions involving reciprocals

[BlackJackJacques]

Wading through old, archived EE treatises involving the MVA method of performing short-circuit analyses and I came across a Delta to Wye conversion for two sources connected to a common bustie feeder (one source on each end of the bus-tie feeder) where the author computed "S/Y, where S is the sum of products (Y1*Y3) + (Y1*Y2 + (Y2*Y3) - OR - the computation one would use to determine Delta from a Y configuration. Similarly, if you took the inverse for each element in the standard Delta to Y formula, it equals the Y to Delta conversion and that proves out fine. I understand treating two series elements as one would treat two parallel resistors, etc., and what the author did was sound and makes sense. However, I can not find in any modern book or pub, or web reference describing this clever application. Does anyone know of published guidance in this regard, and/or is this something lost to antiquity? Thanks in advance.

Jim

 

[argotier]

The cross symmetry between the Y-D / D-Y formulas for impedances and admittances is well known, I thought I could easily find a book excerpt to show you but you are right, is not that easy.

But you don't need a documented source to validate it, you can derive one from the other by hand with a little work.

Here is well explained.

And for the curious, here is the original paper by Kennelly showing the Y-D and D-Y transformations for the first time (Page 413 - Electrical World, Volume 34. 1899).

 

[BlackJackJacques]

Thank you argotier. Yes, I concur, deriving is straight forward and thank you for your references - I will tag and archive. The Kennelly paper is priceless!
Thanks again

Jim

 

[cuky2000]

Here is another source that I found helpful using the SC MVA method.

 

[BlackJackJacques]

Yes Cukey2000, thank you. That is the very document that caused my question.