Relationship between the Fractal Dimension of Creeping Discharges Propagating at Solid/Gas Interfaces and the Characteristics Parameters of Interfaces

A. Beroual(1*), M-L. Coulibaly(2), A. Girodet(3), O. Aitken(4)

(1) Ecole Centrale de Lyon, University of Lyon, Ampere CNRS UMR 5005, 36 avenue Guy de Collongue, 69134 Ecully, France
(2) ALSTOM Grid Power Transformers, TICC – 129, Avenue de Paris, 91300 Massy, France
(3) ALSTOM Grid – 130, Rue Léon Blum, BP 1321, 69611 Villeurbanne Cedex, France
(4) ALSTOM Grid – 130, Rue Léon Blum, BP 1321, 69611 Villeurbanne Cedex, France
(*) Corresponding author

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


This paper is aimed at the fractal analysis of surfaces discharges propagating over insulators immersed in gas and the relationship between the physical parameters influencing these discharges and the fractal dimension of these latter. It is shown that: (1) the observed experimentally discharges propagating at the surface of high voltage insulators made of different materials in presence of gas submitted to standard lightning impulse voltage in divergent electric field have a fractal dimension; and (2) there is a relationship between the fractal dimension of these discharges and the physical and geometrical characteristic parameters of solid/gas insulating system that are the thickness (e) and the dielectric constant of insulator (εr) as well as the gas and its pressure
Copyright © 2014 Praise Worthy Prize - All rights reserved.


Surface Discharges; Solid/Gas Insulating System; Gas Pressure; Fractal Dimension

Full Text:



T. S. Sudarsham and R. Dougal, "Mechanisms of surface flashover along solid dielectrics in compressed gases", Review, IEEE Trans. of Electr. Insul., No. 21, 1986, pp. 727-746.

C. X. Wang, A. Wilson and M. W. Watte, "Surface charge flashover sustained by electrostatic surface charge on epoxy resin insulator in SF6", IEE Proc., A Sci. meas. techno. Vol. 140, No. 5, 1993, pp. 346-350.

I. Al Bawy and O. Farish, "Insulator flashover in SF6 under impulse voltage conditions", IEE Proc. A, Vol. 138, 1991, pp. 89-97.

D. Shibutani H. Naoki and H. Okubo, “Impulse Creepage Discharge Propagation Mechanisms in N2/SF6 Gas Mixtures” Trans. of the Institute of Elect. Eng. of Japan, Vol.121-B, N° 4, 2001, pp. 455 - 460.

N. L. Allen and B. H. Tan, "Initiation of positive corona on insulator surface". Proc. of the 12th Int. Symp. on High Voltage Engineering, Vol. 3, pp. 5-8, 2001, Bangalore, India.

N. L. Allen and P. N. Mikropoulos, "Streamer propagation along insulating surfaces in air", IEEE Trans. Electr. Insul., Vol. 6, No. 3, 1999, pp. 357-362.

M. Akyuz, L. Gao, V. Cooray, T. G. Gustavsson, S. M. Gubanski and A. Larsson, "Positive streamer discharge along insulating surface", IEEE Trans. Electr. Insul., Vol. 8, No. 6, 2001, pp. 902-910.

N. L. Allen and D. C. Faircloth, "Corona propagation and charge deposition on a PTFE surface", IEEE Trans. Electr. Insul., Vol. 10, No. 2, 2003, pp. 295-304.

T. Jing, "Surface charge accumulation: an inevitable phenomenon in DC GIS", IEEE Trans. Electr. Insul., Vol. 2, No. 5, 1995, pp. 771-778.

K. D. Srivastava and J. Zhou, "Surface charging and flashover of spacers in SF6 under impulse voltages", IEEE Trans. Electr. InsuL, Vol. 26, No. 3, 1991, pp. 428- 442.

K. Nakanishi, A. Yoshioka, Y. Shibuya and T. Nitta, "Charge accumulation on spacer surface at DC stress in compressed SF6 gas", Gaseous Dielectrics III, Edition Pergamon, New York, USA, 1982, pp. 365-373.

H. Fujinami, T. Takuma, M. Yashima, T. Kawamoto, "Mechanism and effect of DC charge accumulation on SF6 gas insulated spacers", IEEE Trans. Electr. InsuL, Vol. 22, 1987, pp. 333-340.

A. Knecht, "Development of surface charge accumulation on epoxy resin spacers stressed with direct applied voltage", Gaseous Dielectrics III, Edition Pergamon, New York, USA, 1982, pp. 356-364.

R. A. Fouracre, F. A. Twema, S. J. MacGregor and M. J. Given, "The influence of charge on surface flashover", 11th Int. Symp. on High Voltage Engineering., No. 467, Vol. 3, 1999, pp. 329-332.

I. Gallimbertti, I. Marchesi and L. Niemeyer, "Streamer corona at an insulating surface", Proc. of 7th Int. Symp. on High Voltage Engineering, pp. 1-4, 1991, Dresden, German.

N. L. Allen and A. A. R. Hashem, "The role of negative ions in the propagation of discharges across insulating surfaces", J. Phys. D. Appl. Phys., Vol. 35, 2002, pp. 2551-2557.

S. Sato, W. S. Zaengl and A. Knecht, "A numerical analysis of accumulated surface charge on DC epoxy resin spacer", IEEE Trans. Electr. Insul., Vol. 22, 1987, pp. 333- 340.

T. Jing and P. H. F. Morshuis, "Evaluation of Field-steering Techniques in GIS with Respect to Surface Charge Accumulation", Proc. of 4th Int. Conf. on Conduction and Breakdown in Solid Dielectrics, pp. 102-106, 1992, Sestri Levante, Italy.

A. Beroual, M. L. Coulibaly, O. Aitken and A. Girodet, Effect of Micro-fillers in PTFE Insulators on the Characteristics of Surface Discharges in Presence of SF6, CO2 and SF6-CO2 Mixture, IET Generation, Transmission and Distribution, October 2012, Vol. 6, Issue 10, 2012, pp. 951- 957.

A. Beroual, M. L. Coulibaly, O. Aitken and A. Girodet, Investigation on Creeping Discharges Propagating over Epoxy Resin and Glass Insulators in Presence of Different Gases and Mixtures, The European Physical Journal – Applied Physics, Volume 56, Issue 03, December 2011, pp. 30802-30809.

G. C. Lichtenberg, Novi Comm. Soc. Reg. Sci. Gott 8, 168, 1777.

B. B. Mandelbrot, “Fractals, Form, Chance and Dimension”, San Francisco, Freeman, 1977

Y. Sawada, S. Ohta, M. Yamazaki and H. Honjo, ‘‘Self-similarity and a phase transition-like behaviour of a random growing structure governed by a non-equilibrium parameter”, Phys. Rev. A, Vol. 26, no. 6, 1982, pp. 3557-3563.

L. Niemeyer, L. Pietronero and H. J. Wiesmann, ‘‘Fractal dimension of dielectric breakdown”, Phys. Rev. Letter, Vol. 33, 1984, pp. 1033–1036.

H. J. Wiesmann and H. R. A. Zeller, ‘‘fractal model of dielectric breakdown and prebreakdown in solid dielectrics”, J. Appl. Phys., Vol. 60, 1986, pp. 1770–1773.

L. Kebbabi and A. Beroual, Fractal analysis of creeping discharges propagating at solid/liquid interfaces: influence of the nature and geometry of solid insulators, J. of Physics D: Applied Physics 39 (2006), pp. 177-183.

K. Kudo, "Fractal analysis of electrical trees", IEEE Trans. Dielect. and Elect. In., Vol. 5, Issue 5, 1998, p. 713-727.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2022 Praise Worthy Prize