# Y-delta transform

The Y-delta transform (also written Wye-delta transform or Kennelly's Delta-Star transformation) or star-mesh transformation is a mathematical technique to simplify 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.

(A Y-delta transformer, on the other hand, is an electrical device that converts Three-phase electric power without a neutral wire into 3-phase power with a neutral wire. It is generally built from 3 independent transformers.)

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## Basic Y-Delta transformation

The transformation is used to establish equivalence for networks with 3 terminals. Where three elements terminate at one point (node) and none is a source, the node is eliminated by transforming the impedances.

For equivalence, the impedance between any pair of terminals must be the same for both networks.

### Transformation equations

[itex]R_1 = \left( \frac{R_aR_b}{R_a + R_b + R_c} \right)[itex]
[itex]R_2 = \left( \frac{R_bR_c}{R_a + R_b + R_c} \right)[itex]
[itex]R_3 = \left( \frac{R_cR_a}{R_a + R_b + R_c} \right)[itex]

### Wye-to-Delta transformation equations

[itex]R_a = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_2} \right)[itex]
[itex]R_b = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_3} \right)[itex]
[itex]R_c = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1} \right)[itex]

## Terminology

United States United Kingdom
Grounded Earthed
Wye or Y Star

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