Delta Star and Star Delta Transformation

Standard 3-phase circuits or networks take on two major forms with names that represent the way in which the resistances are connected; a Star connected network which has the symbol of the letter, Υ (wye) and a Delta connected network which has the symbol of a triangle, Δ (delta). If a 3-phase, 3-wire supply or even a 3-phase load is connected in one type of configuration, it can be easily transformed or changed it into an equivalent configuration of the other type by using either the Star Delta Transformation or Delta Star Transformation process. Having now defined what is a Star and Delta connected network, it is possible to transform the Υ into an equivalent Δ circuit and also to convert a Δ into an equivalent Υ circuit using the transformation process. This process allows us to produce a mathematical relationship between the various resistors giving us a Star Delta Transformation as well as a Delta Star Transformation.

Delta Star Transformation

To convert a delta network to an equivalent star network we need to derive a transformation formula for equating the various resistors to each other between the various terminals.

Star Delta Transformation

The transformation from a Star network to a Delta network is simply the reverse of above.
By rewriting the previous formulas a little we can also find the transformation formulas for converting a resistive star connected network to an equivalent delta network giving us a way of producing the required transformation.

Both Star Delta Transformation and Delta Star Transformation allows us to convert one type of circuit connection into another type in order for us to easily analyze the circuit. These transformation techniques can be used to good effect for either star or delta circuits containing resistances or impedances.