1. Processing of multiple frequency test data of Traction Auto Transformer Helen Di Yu Power Systems Research Group University of Strathclyde

2. PSRG University of Strathclyde 20042 Outline of Presentation  Introduction  Experimental data of Traction AT  Method of converting time domain experimental data into frequency domain form  Calculation of frequency domain form  Mathematical modelling the AT transform  Results & Conclusions

3. PSRG University of Strathclyde 20043 1. Introduction  Equipment features in multiple frequencies and especially at high frequencies play important role in Railway Power supply systems  Practical experiments using a wide range of frequencies for key equipments  Numerical data processing over the experiment data

4. PSRG University of Strathclyde 20044 2. Experimental data of Traction AT  Capacity:15MVA  Rated voltages: 55kV and 27.5kV  Experimental test: experiment conditions: open and short circuit situations frequency range: 100Hz to over 12kHz sampling recording frequency: 4.8*10 4 samples/sec.

5. PSRG University of Strathclyde 20045 3. Converting time domain experimental data into frequency domain form Method: Discrete Fourier Transform(DFT) & Fast Fourier Transform(FFT)  DFT  FFT When N s is big, using FFT to increase the computational speed on considering the similarity of many of the elements in the matrix produce the same frequency components

6. PSRG University of Strathclyde 20046 4. Frequency domain results*  (1) Voltages and currents at Short Circuit  (2) Main frequency increment at Short Circuit  (3) Voltages and currents at Open Circuit  (4) Main frequency increment at Open Circuit  (5) Impedances at short circuits**  (6) Impedances at open circuits** * Least Square method is adopted to decrease the effect of experiment errors ** determined with Ohm theory:

7. PSRG University of Strathclyde 20047 5. Numerical Model of Traction Auto Transformer Impedances in multiple frequencies

8. PSRG University of Strathclyde 20048 5.1 General T-type equivalent circuit of AT

9. PSRG University of Strathclyde 20049 5.2 Equivalent circuit components Components:  Primary side Leakage Impedances  Secondary side Leakage Impedances  Magnetizing impedances  Capacitance Involving:  Resistance  Reactance  Capacitance

10. PSRG University of Strathclyde 200410 5.3 Constructing Impedance Function  Functions of frequency dependent in a multiple frequency condition:

11. PSRG University of Strathclyde 200411 5.4 Difficulties in the fitting process  To fit large frequency spectrum: from 50Hz to 12000Hz  To fit all impedance components: leakage resistance leakage reactance magnetizing resistance magnetizing reactance capacitance  To fit both open and short circuit conditions

12. PSRG University of Strathclyde 200412 5.5 Practical Curve fitting method  Comprising: Local optimization Wide optimization Synthetic optimization

13. PSRG University of Strathclyde 200413 5.5.1 Local optimization  (1) Initial process  (2) Small offset modification  (3) Linear (Tangent) modification  (4) Parabola modification  (5) Least approaching for synthetic error of element  (6) Creation of the coefficient set

14. PSRG University of Strathclyde 200414 5.5.2 Wide optimization  Purpose: to speed up the optimization process  Method: Genetic Algorithm  Procedures: (1) choose seed (2) establish Seeds Pool (3) randomly choose parent seeds (4) mate parent seeds (5) generate offspring (6) grow up offspring to get new seed

15. PSRG University of Strathclyde 200415 5.5.3 Synthetic optimization  Procedures: Use Wide optimization to generate new offspring Use Local Optimization to grow up the offspring  Effects: Generation after generation, the grown-up offspring, the new Seed, possesses better genes  Results: The chromosomes of the Seed that represent the impedance coefficients leads to a satisfying level of synthetic error index to approach the Target Function

16. PSRG University of Strathclyde 200416 5.6 Fitting Results (one example)  Fitting comparison of the impedance model with the ‘Target Function’ (Open Circuit)

17. PSRG University of Strathclyde 200417 6. Conclusions(1)  Experiment test samples of Traction Auto Transformer in time domain forms are transformed into frequency domain forms by using Discrete Fourier Transform  Frequency domain forms of the AT are obtained including current, voltage and impedance parameters  T-type model of the AT is applied to represent the transformer

18. PSRG University of Strathclyde 200418 6. Conclusions (2)  Mathematical expressions are proposed to represent the parameters of the model  Curve fitting process to minimize the synthetic errors between the Target function and the mathematical expression have been applied by using local and wide optimization process  The final results for the AT transformer model and its numerical expression are accomplished to represent the Traction Auto Transformer model in mathematical forms and is ready to use in the electrified traction power supply system calculation **** By the courtesy of Network Rail

19. PSRG University of Strathclyde 200419 THANK YOU