What is Star-Delta Transformation?

In electrical engineering, three-phase loads (like industrial motors, heater banks, or transformers) can be connected in two primary configurations: Star (Y) or Delta (Δ).

The Star-Delta Transformation (also known as Kennelly's Theorem) is a mathematical technique used to simplify complex electrical networks. It allows engineers to calculate the equivalent resistance or impedance of a circuit if it were rewired from one configuration to the other, without changing the voltage or current drawn from the external supply.

1. Balanced Loads (The Quick Rule)

If all three phases of the load are identical (e.g., three identical motor coils), the system is considered Balanced. The conversion is incredibly simple:

• Star to Delta: Multiply the resistance by 3. (R_Δ = 3 × R_Y)
• Delta to Star: Divide the resistance by 3. (R_Y = R_Δ / 3)

This explains why an industrial motor wired in Delta draws significantly more current and produces more torque than when wired in Star—the effective phase resistance is lower, and the phase voltage is higher.

2. Unbalanced Loads (Kennelly's Theorem)

If the loads are unequal (e.g., a fault in one heating element), you must use the full transformation formulas. Our engine automates these calculations:

Star to Delta Formulas:

Tip to remember: The equivalent Delta resistance between two nodes is the sum of all Star cross-products, divided by the Star resistance of the opposite node.

Delta to Star Formulas:

Tip to remember: The equivalent Star resistance at a node is the product of the two adjacent Delta resistances, divided by the sum of all three Delta resistances.