Y-delta transform

induction motors and drives. It is related to three phase theory (or polyphase systems). The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ.

Basic Y-Delta transformation

The transformation is used to establish equivalence for networks with 3 terminals.

For equivalence, the resistance between any pair of terminals must be the same for both networks.

Transformation equations

<math>R_1 = \left( \frac{R_aR_b}{R_a + R_b + R_c} \right)<math>

<math>R_2 = \left( \frac{R_bR_c}{R_a + R_b + R_c} \right)<math>

<math>R_3 = \left( \frac{R_cR_a}{R_a + R_b + R_c} \right)<math>

Wye-to-Delta transformation equations

<math>R_a = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_2} \right)<math>

<math>R_b = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_3} \right)<math>

<math>R_c = \left( \frac{R_1R_2 + R_2R_3 + R_3R_1}{R_1} \right)<math>

Configurations

Two different configurations:

Y windings - low speed, high-voltage [standard]

Delta winding - high speed, low-voltage

Y/Delta selection can be used like a gear for the motor speed. Switching ?on-the-fly" starts in the Y winding and changes to Delta winding where performance can be improved.

Y connection

To minimise the number of electrical connections to a generator, one end of each winding is connected to a common point called the 'neutral' or 'star' point. The other end of each winding has its own connection. This results in four connections to the generator: one neutral and three phases. This has the advantage that the neutral wire can be made thinner than the phase wires, therefore saving weight and cost. In some systems the neutral wire is omitted and the return currents are allowed to flow through the ground.

Delta connection

When the generator is connected with three wires, with each wire attached to opposite ends of two adjacent windings, a delta connection is formed.

Delta connections can be ungrounded, which was once common. Today, there are some corner-grounded delta systems, where point A is grounded, and some midpoint-grounded delta systems, where a point on the winding midway between A and C is grounded, and a few zigzag-grounded systems that derive a neutral for grounding purposes using a zigzag transformer.

Terminology

United States&nbsp&nbsp&nbsp	United Kingdom
Grounded	Earthed
Wye or Y	Star

See also

• Analysis of resistive circuits
• Electrical network: single phase electric power, alternating-current electric power, Three-phase power, polyphase systems
• Lists: List of transforms, List of mathematical topics