Simulation on Surface Tracking Pattern using the Dielectric Breakdown Model

  • Kim, Jun-Won (Dept. of Electrical and Electronic Engineering, Soongsil University) ;
  • Roh, Young-Su (Dept. of Electrical and Electronic Engineering, Soongsil University)
  • Received : 2010.07.05
  • Accepted : 2011.01.13
  • Published : 2011.05.02


The tracking pattern formed on the dielectric surface due to a surface electrical discharge exhibits fractal structure. In order to quantitatively investigate the fractal characteristics of the surface tracking pattern, the dielectric breakdown model has been employed to numerically generate the surface tracking pattern. In dielectric breakdown model, the pattern growth is determined stochastically by a probability function depending on the local electric potential difference. For the computation of the electric potential for all points of the lattice, a two-dimensional discrete Laplace equation is solved by mean of the successive over-relaxation method combined to the Gauss-Seidel method. The box counting method has been used to calculate the fractal dimensions of the simulated patterns with various exponent $\eta$ and breakdown voltage $\phi_b$. As a result of the simulation, it is found that the fractal nature of the surface tracking pattern depends strongly on $\eta$ and $\phi_b$.


  1. N. Yoshimura, M. Nishida and F. Noto, "Influence of electrolyte on tracking breakdown of organic insulation materials", Trans. IEEE. EI, vol. 16. pp. 510-519, 1981.
  2. K. M. Song, Y. Roh, and H. R. Kwak, “Surface Discharge Characteristics of Phenolic Resin Treated by Heat and Its Structure Analysis”, J. KIIEE vol.20, no.8, pp. 71-79 Sep. 2006.
  3. S. T. Park and Y. Roh, “A Study on the Characteristics of Organic Insulating Materials Carbonized by a Leakage Current”, J. KIIEE vol. 23, no.2, pp. 161-167 Feb. 2009.
  4. Kebbabi and Beroual, “Fractal analysis of creeping discharge patterns propagating at solid/liquid interfaces: influence of the nature and geometry of solid insulators”, J. Phys. D: Appl. Phys. 39 (2006) 177-183
  5. V Rajini and K Udaya Kumar, “Surface tracking in polymers: a pattern discrimination technique using fractals”, J. Phys. D: Appl. Phys. 39 (2006) 3695-3701
  6. Candela R, Mirolli G and Schifani R, “PD recognition by means of statistical and fractal parameters and a neural network” IEEE Trans. Electr. Insul. 7 (2000) 87-94K.
  7. Kudo, “Fractal Analysis of Electrical Trees”, IEEE Transactions on Dielectrics and Electrical Insulation 5, (1998) 713-727
  8. T. A. Witten, Jr. and L. M. Sander, “Diffusion-Limited Aggregation, a Kinetic Critical Phenomenon”, Physical Review Letters, vol.47, no.10, pp. 1400-1403, Nov. 1981.
  9. L. Niemeyer, L. Pietronero, and H. J. Wiesmann, "Fractal Dimension of Dielectric Breakdown", Physical Review Letters, vol.52, no.12, pp.1033-1036, March 1984
  10. N. Femia, L. Niemeyer and V. Tucci, “Fractal characteristics of electrical discharges: experiments and simulation”, J. Phys. D: Appl. Phys., vol. 26, pp.619-627, 1993.
  11. J. H. Mathews and K. D. Fink, “Numerical Methods using Matlab”, Pearson Prentice Hall, 2004

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