Wye-Delta 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.

A delta-wye transformer is a type of three-phase electric power transformer design that employs delta-connected windings on its primary and wye/star connected windings on its secondary. A neutral wire can be provided on wye output side. It can be a single three-phase transformer, or built from three independent single-phase units. An equivalent term is delta-star transformer. Delta-wye transformers are common in commercial, industrial, and high-density residential locations, to supply three-phase distribution systems.

 

Δ and Y circuits with the labels

Transformation Formulas

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Learnings and overview:

A bridge circuit can be simplified to a series/parallel circuit by converting half of it from a Δ to a Y network. After voltage drops between the original three connection points (A, B, and C) have been solved for, those voltages can be transferred back to the original bridge circuit, across those same equivalent points.

In solving the wye-delta and delta-wye transformation it is easier to determine the labels by creating a free body diagram of it with labels and transformed circuit. In this way you can easily solve for the total resistance of the circuit, and by the help of my past learnings in the series-parallel connections I can now understand how to solve the problems given. I have sometimes difficulties in determining the labels but I will try to research and study more about it :)