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Reference Frame Theory

Reference Frame Theory. Background: Linear Transformation. We have seen that transformation can simplify the problem in power system. Choosing appropriate transformation can significantly reduce the problem. Can you mention the example of the transformation you have ever used?.

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Reference Frame Theory

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  1. Reference Frame Theory

  2. Background: Linear Transformation • We have seen that transformation can simplify the problem in power system. • Choosing appropriate transformation can significantly reduce the problem. • Can you mention the example of the transformation you have ever used?

  3. Transformation in Transformator • You can always express all variables & parameters in secondary of the transformator into corresponding primer or vice versa.

  4. Symmetrical Components • It was invented by Fortescue • It decomposes unbalance abc phase variables into three symmetrical component • Representative symmetrical components

  5. Symmetrical Components(2) • The transformation matrix is Where and the inverse

  6. Example Fault Va0 Va1 Va2 Vb0 Vb2 Vc1 Vb1 Vc2 Vc0

  7. We will begin other kind of transformations You will appreciate the benefit of using them later on

  8. Clarke’s Transformation • It transforms abc quantity into stationary and • coincides with phase a-axis and leads the by • The equation with The inverse

  9. Park’s Transformation • It was proposed by Robert H. Park from MIT • There are wide ranges of application from machine simulation, control, drives, etc. • This transform is one of the most important application for power engineers.

  10. Park’s Transformation (2)

  11. Park’s Transformation (3) • A vector in space can be seen from several coordinate • We can change from one coordinate to another coordinate

  12. Park’s Transformation (4)

  13. Park’s Transformation (5)

  14. The abc to dqo transformation

  15. The abc to dqo transformation (2)

  16. The abc to dqo transformation (3)

  17. The abc to dqo transformation (3)

  18. Commonly Used Reference Frame

  19. Transformation Between Reference Frame

  20. Application to Voltage Equation

  21. Application to Voltage Equation(2)

  22. Application to Flux Linkage

  23. Application to Flux Linkage (2)

  24. Application to Flux Linkage (3)

  25. Application to Flux Linkage (4)

  26. Application to Flux Linkage (5)

  27. Transformation of Balanced Set

  28. Transformation of Balanced Set (2)

  29. References • Power System Stability lecture notes by Dr. NaebboonHoochareon. • Dynamic Simulations of Electric Machinery: Using MATLAB/SIMULINK by Prof. Chee-MunOng • Analysis of Electric Machinery and Drive Systems by Prof. Paul C. Krause et.al.

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