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Y-Δ transform

In circuit design, 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…

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Simplification of networks

SimplifiedTorusPetersen family
3 related topics

Basic Y-Δ transformation

Complex impedanceOhmsPositive real numbersReactanceImaginary values
6 related topics

A proof of the existence and uniqueness of the transformation

Superposition theorem for electric circuitsKirchhoff's circuit lawsCurrent sourceSeries and parallel circuitsUniqueness theorem
5 related topics

Δ to Y transformation of a practical generator

Power systemsGeneratorsTransformersMotorsStator
5 related topics

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Overview

Basic Y-Δ transformation

A proof of the existence and uniqueness of the transformation

Simplification of networks

Graph theory

Demonstration

Δ to Y transformation of a practical generator

Bibliography

  • ISBN ISBN (identifier)

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Y-Δ transform

Nodes44
Edges43
Triples23
Avg. degree1.95
Density0.045455
Components1

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Y-Δ transform

Top relations

related to Graph theory · 6
Y-Δ transform → For, In, Petersen, The, Two, Y-Δ
related to Names · 4
Y-Δ transform → T-Π, The, The Y-Δ, Thus
related to Simplification of networks · 3
Y-Δ transform → Resistive, Series, The Y-Δ

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Important terminology

y-δ displaystyle circuit transform impedance text equivalent transformation three networks nodes network equations theory three-phase node voltages right used analysis

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
the bridge illustrated hereinstance ofbut for complex networks0.80text
they do not suffice.The Y-Δ transform can be used to eliminate one node at a timeinstance ofbut for complex networks0.80text
produce a network that can be further simplifiedinstance ofbut for complex networks0.80text
as shown.The reverse transformationinstance ofbut for complex networks0.80text
Δ-Yinstance ofbut for complex networks0.80text
which adds a nodeinstance ofbut for complex networks0.80text
is often handy to pave the way for further simplification as well.Every two-terminal network represented by a planar graph can be reduced to a single equivalent resistor by a sequence of seriesinstance ofbut for complex networks0.80text
parallelinstance ofbut for complex networks0.80text
Y-Δinstance ofbut for complex networks0.80text
and Δ-Y transformationsinstance ofbut for complex networks0.80text
Y-Δ transformrelated to Graph theoryIn0.60section
Y-Δ transformrelated to Graph theoryY-Δ0.60section

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