1. Transformer Professor Mohamed A. El-Sharkawi

2. 2 Why do we need transformers? Increase voltage of generator output –Transmit power and low current –Reduce cost of transmission system Adjust voltage to a usable level Create electrical isolation Match load impedance Filters

3. 3 Basic Components Iron Core Insulated Copper Wire

4. 4

5. 5

6. 6 i1i1 i2i2 N1N1 e1e1 + _ N2N2 e2e2 + _ Primary Secondary

7. 7 Basic Analysis:Voltage i1i1 i2i2 N1N1 e1e1 + _ N2N2 e2e2 + _ Volts/turn is constant Voltages are in phase (no phase shift) Magnitudes vary with turns ratio.

8. 8 Basic Analysis: Power and current i1i1 i2i2 N1N1 e1e1 + _ N2N2 e2e2 + _ Currents are in phase. Current ratio is opposite to the voltage ratio

9. 9 Basic Analysis: Reflected impedance

10. 10 Ideal Transformer: Ratings 100 MVA, 13.8/138 KV Apparent Power Primary Voltage Secondary Voltage N2N2 N1N1 + - V 1 I 1 I 2 + - V 2

11. 11 Ideal Transformer: Ratings 100 MVA, 138/13.8 KV N2N2 N1N1 + - V 1 I 1 I 2 + - V 2

12. 12 Actual Transformer Windings: –Resistance –Inductance Core: –Eddy Current –Hysteresis i1i1 i2i2 N1N1 e1e1 + _ N2N2 e2e2 + _

13. 13 R1R1 X1X1 N1N1 N2N2 R2R2 X2X2 Ideal Transformer Windings Impedance

14. 14 Core Hysteresis B H i N e + _

15. 15 i

16. 16 Core Model e i R Let i

17. 17 Core Model Let i i e XlXl

18. 18 e i RXlXl ii

19. 19 RoRo XoXo R1R1 X1X1 R2R2 X2X2 V1V1 I1I1 IoIo I2I2 V2V2 E1E1 E2E2 N1N1 N2N2 Equivalent Circuit