1. DIGITAL DIFFERENTIAL RELAYS FOR TRANSFORMER PROTECTION USING WALSH SERIES AND LEAST SQUARES ESTIMATORS Ali Reza FEREIDUNIAN*, Ali Reza FEREIDUNIAN*, Mansooreh ZANGIABADI*, Mansooreh ZANGIABADI*, Majid SANAYE-PASAND*, Gholam POURNAGHI** * : ECE Dep., Faculty of Engg., University of Tehran,Tehran, IRAN *:* Kerman Regional Electric Company (KREC), Kerman, IRAN

2. Differential Protection  The fundamental principle of differential protection: sum of the currents entering a device through normal paths should be zero: Kirchhoff's Current Law (KCL).  If the currents enter (or leave) through abnormal paths, namely fault paths, then the sum of the currents through normal paths will not be zero.

3. Differential Protection Illustration

4. Problems in transformer differential protection:  inrush current,  CT inaccuracy,  CT saturation,  over-excitation. These problems produce fault trips (fault alarm when there isn’t any trip) or no alarm when there is a trip in transformer protection function

5. DIFFERENTIAL RELAY IMPLEMENTATION:  Current Sensor (CT): converts large amounts of current to small amounts  Data Acquisition System: gathering data  Filter: anti aliasing  Pre-processor: scaling and so on  Estimator: estimating peak & phase  Decision Maker (Classifier): fault/no fault

6. Effect of CT Saturation on a Sinusoidal Current:

7. WE HAVE USED TWO METHODS:  FOR ESTIMATING PEAK AND PHASE OF INPUT WAVE.

8. Walsh coefficients :

9. Walsh Series (Ctd):  W=A * F  F=A-1*W where  F=[ F0 F1 F2 F3 F4 F5 F6 F7 F8]  A-1=AT 

10. Least Squares :  A*X = B  E = A*X – B  = LPI(A) * B  LPI(A) =

11. Sampling:  12 point window (for half cycle estimation) or  24 points (for full cycle estimation) with with  24 sample/cycle sampling system

12. Least square frequncy response for fundamental frequency

13. The Decision Space

14. Inrush Pattern Recognition  A significant second harmonic: Inrush Current Pattern Recognition

15. A CASE STUDY  Real recorded data:  Transformer internal fault,  Transformer external fault,  Transformer inrush current

16. High and Low Voltage Side Currents for External Fault

17. High and Low Voltage Side Currents for Internal Fault

18. High and Low Voltage Side Currents for Inrush Current

19. Three Phases Differential Currents in External Fault

20. . Three Phases Differential Currents in Internal Fault

21. Three Phases Differential Currents in Inrush Current

22. Decision Space in External Fault for three Phases

23. Decision Space in Internal Fault for Three Phases

24. Decision Space in Inrush Current for Three Phases

25. Second/Fundamental Harmonic Ratio for External Fault

26. Second/Fundamental Harmonic Ratio for Internal Fault

27. Second/Fundamental Harmonic Ratio for Inrush Current

28. General Trip Alarm for External Fault

29. General Trip Alarm for Internal Fault

30. General Trip Alarm for Inrush Current

31. Summary  A digital differential relay for transformer protection was presented.  Two estimator systems: Walsh series and least squares algorithms were formulated and designed.  The differential protection decision maker subsystem was introduced.  Current signals harmonic components and second harmonic restraint concept were utilized in decision maker subsystem.

32. Conclusion  In a practical case study, the designed relay performance was tested under three real circumstances: external fault, internal fault and inrush current.  It was shown -using graphs and illustrations- that the presented relay issues trip alarm for transformer internal fault, and does not issue trip alarm for external fault and inrush current situations.

33. Conclusion (Ctd)  It were seen that both estimation algorithms perform their job correctly.  Walsh series acts better than least squares algorithm, especially on second harmonic estimation.  An anti alias filter (for example a Butterworth one) will improve response of the estimator.