In a three-phase system, impedance is connected across each phase to exert a balanced load across the phases. The configuration of impedance can be of two types: Star configuration or delta configuration. These two configurations can be interchanged without affecting the equivalent resistances obtained between any two points of the network. A star-delta transformation means that a star network can be converted to its equivalent delta network. We will study star-delta transformation in this article.
Star Configuration
A star network configuration is made by joining all the starting and ending points of three wires in a three-phase system. A wire is taken out from the common joining point, which is known as a neutral wire.
For a star network, the following expressions of current, voltage, and power are applicable:
Total power is given by:
Delta Configuration
In delta configurations, opposite ends of wires are connected to form a delta-shaped network. The Delta network does not include a neutral wire connection:
The following expressions for calculating line current, line voltage, and power shall be used:
Total power is calculated as:
Star-Delta Transformation
A star network can be converted into its equivalent delta network, and a delta network can be converted into its equivalent star network. This helps a lot in simplifying the mathematical calculations. The equivalent resistance between any two points of a star network will be the same at those points in the delta network:
Delta connections are used at the receiving ends of power systems, like the configurations at the power generation sides where the power is being transmitted to further distribution networks. However, star connection is used where the supply is to be provided to consumers. This is the reason that star networks have additional neutral wire to facilitate the neutral wire requirements at the consumer end.
Star-Delta Transformation
A star connection of impedance can be converted into a delta connection, if we can derive the equations for A, B & C resistances of the delta network from the star resistances.
By equating and simplifying the resistances between points 1 & 2, 2 & 3, and 3 & 1, we get the following equations:
Example
If resistances in the star network are X=50, Y=100 and Z=150, calculate the delta network resistances.
Using the above equations, finding resistance A:
Finding resistance, B as from the above equations:
Finding resistance, C as from above equations:
Conclusion
A three-phase system can be converted from star to delta and delta to star without affecting the equivalent resistances between any two points of the network. These transformations can help in finding the network parameters like current, voltage, and impedance at any point without performing complex mathematical nodal & mesh calculations.
