Power Transformer Models

1. Power Transformer Models by Kinlay Dorjee & James Wang

2. Presentation Outline • Introduction • Ideal transformer • Practical transformer • Conclusion • Questions/Discussion

3. Introduction Typical power system scheme Generator Step up Transformer Transmission Line Step down Transformer Load

4. Introduction Importance of Power Transformers: • Generation voltage restriction of about 25 kV. • Isolates the Generator from the over voltage transients in the Overhead lines.

5. Ideal Transformer • Assumption • 1. Zero Winding Resistance • 2. Permeability of the core is infinite -- Zero Magnetic Reluctance • The transformer flux is totally confined to the magnetic core – No Flux Leakages • 4. Zero hysteresis and eddy-current losses in the core

7. Ideal Transformer Ampere’s Law Faraday’s Law

8. Practical transformer and its model Mutual flux due to currents i1 and i2 Leakage flux and mutual flux due to i1 alone Leakage flux and mutual flux due to i2 alone

10. Instantaneous form

11. Phasor form

12. Define Rearrange the V1 equation, we get

13. Rearrange the V2 equation, we get

15. Practical Power Transformer Model with secondary current and voltage redefined

16. Defining: Leakage inductances Leakage reactances Shunt magnetizing susceptance

17. Defining: Transformer equivalent circuit with magnetizing current neglected

18. Practical Power Transformer Model

19. Conclusion • Depending on the requirements, the Power Transformer can be modeled in many different ways: • In the practical model, Bm is neglected because magnetizing current is very small compared with the load current. But for some other studies, the branch may be necessary to account for the exciting current in the transformers. • Similarly, the resistance is neglected in most models because the reactance is much larger. • When dealing with the power system stability studies, resistance component should be included in the transformer model to provide necessary damping.

20. References • Power System Analysis by John J. Grainger and William • D. Stevenson, Jr. Published by McGraw Hill, Inc. • Electric Energy Systems Theory by Olle l. Elgerd. • Published by TATA McGraw Hil. • Power System Engineering by I J Nagrath & D P • Kothari. Published by TATA McGraw Hill.