1. POWER CIRCUIT & ELECTROMAGNETICS EET 221 Transformer

2. A transformer is a device that changes ac electric energy at one voltage level to ac electric energy at another voltage level through the action of a magnetic field. Introduction

3. The most important tasks performed by transformers are: changing voltage and current levels in electric power systems. matching source and load impedances for maximum power transfer in electronic and control circuitry. electrical isolation (isolating one circuit from another or isolating dc while maintaining ac continuity between two circuits). It consists of two or more coils of wire wrapped around a common ferromagnetic core. One of the transformer windings is connected to a source of ac electric power – is called primary winding and the second transformer winding supplies electric power to loads – is called secondary winding.

5. An ideal transformer is a lossless device with an input winding and output winding. Ideal Transformer lossless a = turns ratio of the transformer

6. Power in ideal transformer Where  is the angle between voltage and current

7. Impedance transformation through the transformer The impedance of a device – the ratio of the phasor voltage across it in the phasor current flowing through it:

8. The equivalent circuit of a transformer Copper (I 2 R) losses: Copper losses are the resistive heating in the primary and secondary windings of the transformer. They are proportional to the square of the current in the windings. Eddy current losses: Eddy current losses are resistive heating losses in the core of the transformer. They are proportional to the square of the voltage applied to the transformer. Hysteresis losses: Hysteresis losses are associated with the arrangement of the magnetic domain in the core during each half cycle. They are complex, nonlinear function of the voltage applied to the transformer. Leakage flux: The fluxes Φ LP and Φ LS which escape the core and pass through only one of the transformer windings are leakage fluxes. These escaped fluxes produce a self inductance in the primary and secondary coils, and the effects of this inductance must be accounted for. The major items to be considered in the construction of such a model are:

9. Nonideal or actual transformer Mutual flux

10. Nonideal or actual transformer

11. E p = primary induced voltageE s = secondary induced voltage V p = primary terminal voltageV s = secondary terminal voltage I p = primary currentI s = secondary current I e = excitation currentI M = magnetizing current X M = magnetizing reactance I C = core current R C = core resistanceR p = resistance of primary winding R s = resistance of the secondary windingX p = primary leakage reactance X s = secondary leakage reactance Transformer equivalent circuit, with secondary impedances referred to the primary side

12. Nonideal or actual transformer Transformer equivalent circuit

13. Dot convention 1.If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the dots on each side of the core. 2.If the primary current of the transformer flows into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding.

14. Exact equivalent circuit the actual transformer a)The transformer model referred to primary side b)The transformer model referred to secondary side

15. Approximate equivalent circuit the actual transformer a)The transformer model referred to primary side b)The transformer model referred to secondary side

16. Exact equivalent circuit of a transformer E p = primary induced voltageE s = secondary induced voltage V p = primary terminal voltageV s = secondary terminal voltage I p = primary currentI s = secondary current I e = excitation currentI M = magnetizing current X M = magnetizing reactance I C = core current R C = core resistanceR p = resistance of primary winding R s = resistance of the secondary windingX p = primary leakage reactance X s = secondary leakage reactance

17. Primary sideSecondary side

18. Exact equivalent circuit of a transformer referred to primary side Exact equivalent circuit of a transformer referred to secondary side

19. Example A single phase power system consists of a 480V 60Hz generator supplying a load Z load =4+j3  through a transmission line Z Line =0.18+j0.24  Answer the following question about the system. a)If the power system is exactly as described above, what will be the voltage at the load be? What will the transmission line losses be? b)Suppose a 1:10 step-up transformer is placed at the generator end of the transmission line and a 10:1 step down transformer is placed at the load end of the line. What will the load voltage be now? What will the transmission line losses be now?

20. Example (a) (b) V=480  0 0 V IGIG + -V Load T1T1 T2T2 1:10 10:1 Z Line =0.18+j0.24  I Load I Line Z Load =4+j3  V=480  0 0 V IGIG + - V Load Z Load =0.18+j0.24  I Line I Load