M. S. Naderi et al.: A Hybrid Transformer Model for Determination of Partial Discharge Location in Transformer Winding 1070-9878/07/$25.00 © 2007 IEEE 436 A Hybrid Transformer Model for Determination of Partial Discharge Location in Transformer Winding Mohammad S. Naderi , M. Vakilian School of Electrical Engineering, Sharif University of Technology, Tehran 11365-9363, Iran T.R. Blackburn, B.T. Phung, Mehdi S. Naderi School of Electrical Engineering, University of New South Wales, Sydney, NSW 2052, Australia and A. Nasiri Electrical Engineering Department, University of Wisconsin-Milwaukee, Milwaukee, WI 53202, USA ABSTRACT Partial discharges are well known as a source for insulation degradation in power transformers. A hybrid transformer model is introduced to simulate the transformer winding transient response. Transformer structural data is used to determine the hybrid model parameters. Calculations of the hybrid transient model parameters are based on the parameters of the lumped parameter equivalent transformer model and electromagnetic rules. Modern computation techniques and optimizations are employed beside this model for PD location using the multi conductor transmission line model and also to analyze its propagation aimed at achieving (i) more reliable simulation results (ii) less computational time (iii) accurate results for a wide range of frequency. The simulation results on a 66 kV, 25 MVA fully interleaved winding are presented. The measurement results on this winding are employed to validate this model. Index Terms — Hybrid transformer model, partial discharge, PD location, PD propagation, power transformer, structural data 1 LIST OF SYMBOLS i 1 Current in the first filament µ 0 Permeability of the vacuum A 1 Vector potential related to current i 1 dl 1 Differential element of first filament dl 2 Differential element of second filament ds Differential element of surface spaning path s Surface a Radius of first filament b Radius of second filament c Distance between first and second filaments d Distance of the differential element to the first filament r Distance between the differential element of the first filament and the second one r' Wire radius Ө Angle of the differential element of the second filament γ An angle equal to θ divided by 2 Ф 2 Magnetic flux linking the second filament B Magnetic field on the surface M Mutual inductance V Voltage of first coil V' Voltage of second coil μ c Permeability of the conductor ε Permittivity of the insulation I n Unit matrix R s Resistance per unit length of conductor d 1 and d 2 Cross-sectional dimensions of rectangular conductor α Initial voltage distribution coefficient σ Conductivity f Frequency n Number of conductors in the model [L] Inductance matrix [C] Capacitance matrix [R S ] Diagonal resistance matrix [G] Conductance matrix [Z] Impedance matrix Manuscript received on 26 April 2006, in final form 12 September 2006.