1. EE 1205 Lecture 04 - Wye/Delta & Delta/Wye Conversions

2. Resistive Wye Circuit Eqn 1

3. Resistive Wye Circuit Eqn 2

4. Resistive Delta Circuit Eqn 3

5. Resistive Delta Circuit Eqn 4

6. Delta-Wye Derivation Use Eqn 4 to solve for delta voltages: Eqn 5 Simplifying: Eqn 6

7. Delta-Wye Derivation Equating the row 1, column 2 term of eqn 2 to the row 1, column 2 term of eqn 6:

8. Delta-Wye Derivation Equating the row 1, column 1 term of eqn 2 to the row 1, column 1 term of eqn 6: Removing R3:

9. Delta-Wye Derivation Similarly, it can be shown that:

10. Wye-Delta Derivation Use Eqn 2 to solve for wye currents: Eqn 15 Simplifying: Eqn 16

11. Wye-Delta Derivation Equating the row 1, column 2 term of eqn 4 to the row 1, column 2 term of eqn 16: Then Equating the row 1, column 1 term of eqn 4 to the row 1, column 1 term of eqn 16:

12. Wye-Delta Derivation Removing R3: Similarly, it can be shown that:

13. Wye/Delta Conversion (1/2) Wye Delta

14. Wye/Delta Conversion (2/2)

15. Delta/Wye Conversion

16. Effects of D-Y & Y-D Conversions • D-Y Conversion eliminates a loop but adds a node. • Y-D Conversion eliminates a node but adds a loop.

17. Y-D Conversion Example Find Rab Several Methods: We choose to eliminate node c, then simplify.

18. Y-D Conversion Calculations

19. New Circuit

20. Further Simplifications