Wye-Delta Transformation

What is Wye-Delta Transformation?
The Y-Δ transform is known by a variety of other names, mostly based upon the two shapes involved, listed in either order. The Y, spelled out as wye, can also be called T or star; the Δ, spelled out as delta, can also be called triangle, Π (spelled out as pi), or mesh. Thus, common names for the transformation include wye-delta or delta-wye, star-delta, star-mesh, or T-Π. 


Wye to Delta Conversion:

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

Equations for Wye-Delta:

Delta to Wye Conversion:

Equation for Delta to Wye Conversion:

The equations can be presented in an alternate form based on the total resistance (Rd) of R₁, R₂, and R₃ (as though they were placed in series):

Rd = R₁+R₂+R₃ 

and:

R_A = (R₁*R₃) / Rd

R_B = (R₂*R₃) / Rd

R_C = (R₁*R₂) / Rd

The Y-Δ transform, also written Wye-Delta and also known by many other names, 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. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899.

Arthur Edwin Kenelly