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Extension of Delta-Wye and Wye-Delta Conversions Applicable to Electric Circuits with Voltage Sources


  • Department of Smart IT, U1 University, Eumbong, Asan – 31415, Korea


Objectives: To generalize the conventional delta–wye and wye–delta conversions. Methods/Statistical Analysis: The delta–wye and wye–delta conversions have been used to simplify complex electric circuits (networks) consisting of resistors. Three terminal networks consisting of resistors and voltage sources in a wye configuration and in a delta configuration are compared. Findings: In this paper we obtained the conversion relations for emfs from the delta configuation to the wye configuration and vice versa. As an example of the generalization, the conversions are applied to a Wheatstone-bridge type circuit of five batteries and five resistors to obtain its Thévenin’s equivalent. The conversions are applicable to ac as well as dc circuits. As an example of ac circuits the currents through unbalanced loads in a wye configuration connected to a three-phase generator in a delta configuration are calculated. Application/Improvements: The generalized conversions allow to simplify dc and ac circuits.


Delta-Wye Conversion, Electric Circuit, Voltage Source, Wye-Delta Conversion

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