Transformer Professor Mohamed A. El-Sharkawi

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 Basic Components Iron Core Insulated Copper Wire

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5

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

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

9 Basic Analysis: Reflected impedance

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

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

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

13 R1R1 X1X1 N1N1 N2N2 R2R2 X2X2 Ideal Transformer Windings Impedance

14 Core Hysteresis B H i N e + _

15 i

16 Core Model e i R Let i

17 Core Model Let i i e XlXl

18 e i RXlXl ii

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