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Y-delta Transform




(A Δ-Y 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 Transformer s.)


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.


Delta-to-Wye transformation equations


:::General Idea: R_y = \over {\Sigma R_{\Delta}} }

: R_1 = \left( rac{R_aR_b}{R_a + R_b + R_c} ight)

: R_2 = \left( rac{R_bR_c}{R_a + R_b + R_c} ight)

: R_3 = \left( rac{R_aR_c}{R_a + R_b + R_c} ight)

Balanced System: R_{\Delta} = 3 imes R_y


Wye-to-Delta transformation equations


:::General Idea: R_{\Delta} = { \Sigma (R_{y i} R_{y j})_{all pairs} \over R_{y opposite} }

: R_a = \left( rac{R_1R_2 + R_2R_3 + R_3R_1}{R_2} ight)

: R_b = \left( rac{R_1R_2 + R_2R_3 + R_3R_1}{R_3} ight)

: R_c = \left( rac{R_1R_2 + R_2R_3 + R_3R_1}{R_1} ight)


IN GRAPH THEORY

In Graph Theory , the Y-Δ transform is used in contexts where there are no resistances labeling the edges, 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 Cycle s. 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