06 February, 2007

Y-Δ transformation

The Y-Δ transform, also written Y-delta, Wye-delta, kennelly's delta-star transformation, star-mesh transformation, T-Π or T-pi transform, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. In the United Kingdom, the wye diagram is known as a star.

The transformation is used to establish equivalence for networks with 3 terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for real as well as complex impedances.

Equations for the transformation from Δ-load to Y-load 3-phase circuit

The general idea is to compute the impedance Ry at a terminal node of the Y circuit with
impedances R', R'' to adjacent nodes in the Δ circuit by

where RΔ are all impedances in the Δ circuit. This yields the specific formulae

Equations for the transformation from Y-load to Δ-load 3-phase circuit

The general idea is to compute an impedance RΔ in the Δ circuit by

where Rp = R1R2 + R2R3 + R3R1 is the sum of the products of all pairs of impedances in the Y circuit and Ropposite is the impedance of the node in the Y circuit which is opposite the edge with RΔ. The formulae for the individual edges are thus

For more information on this topic visit the below links :
http://www.woodsbas.demon.co.uk/calcs/stod.htm ------ Online calculation
http://www.phptr.com/articles/article.asp?p=101617&seqNum=5&rl=1 ----- For AC

1 comment:

Anonymous said...

Thanks for the info. This help a lot