Week 6: Wye-Delta Transformations

Wye-Delta Transformations

What is  Y-Δ transformation? 

- 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. It is widely used in analysis of three-phase electric power circuits.

- 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.

Illustration of the transformation in its T-Π representation

Formulas:

Equations for the transformation from Δ-load to Y-load:

Equations for the transformation from Y-load to Δ-load:

Δ and Y circuits with the labels which are used in this article.

Reflection:

This week, I learned that 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 impedances. 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 impedances. I also learned that this topic is one of the easiest topic we have ever tackled in our Circuit Class because it only uses a specific formula unlike other topics.

Video:

Wye-Delta Transformation:

Delta-Wye Transformation:

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