Y-Δ transform
The Y-Δ transform (also written Y-delta transform or 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. In the UK the wye diagram is known as a star.
(A Y-Δ 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.)
Basic Y-Δ 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
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Wye-to-Delta transformation equations
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In graph theory
In graph theory, the Y-Δ transform is used in contexts where there are no resistances labelling the edges to worry about, so it simply means replacing a wye subgraph of a graph with the delta subgraph. A Y-Δ transform preserves the number of edges in a graph, but not the number of vertices or the number of cycles. Two graphs are said to be Y-Δ equivalent if one can be obtained from the other by a series of Y-Δ transforms and their inverses, Δ-Y transforms.
The Petersen graph family is an example of a Y-Δ equivalence class.
See also
References
- William Stevenson, "Elements of Power System Analysis 3rd ed.", McGraw Hill, New York, 1975, ISBN 0070612854
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