Wye-Delta Transformations

One of the more confusing elements of three-phase power is the winding connection schemes for inductive devices such as transformers and motors. Although most of us with a basic knowledge of AC power understand how motors and transformers operate, we seldom delve into those mysterious winding connections and their impact on performance.

This simple, three-part series will not make you an expert, but I hope it will make these connections a little more understandable.

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.

Basic Y-Δ transformation

The transformation is used to establish equivalence for networks with three terminals. Where three elements terminate at a common node and none are sources, the node is eliminated by transforming the impedances. For equivalence, the impedance between any pair of terminals must be the same for both networks. The equations given here are valid for complex as well as real impedances.

Equations for the transformation from Δ-load to Y-load 3-phase circuit

The general idea is to compute the impedance at a terminal node of the Y circuit with impedances , to adjacent node in the Δ circuit by

where are all impedances in the Δ circuit. This yields the specific formulae
 

 

Equations for the transformation from Y-load to Δ-load 3-phase circuit

The general idea is to compute an impedance in the Δ circuit by

where is the sum of the products of all pairs of impedances in the Y circuit and is the impedance of the node in the Y circuit which is opposite the edge with . The formula for the individual edges are thus

Try this video to learn more...