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Simulation of electrical tree growth in solid insulating materials

Simulation des Wachstums elektrischer Bäume in Festisolierstoffen

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In this paper the electrical tree growth in solid insulating materials is modeled using von Neumann's Cellular Automata (CA). The model is based upon the assumption that the electric stress at the end of a conducting tip quite often approaches the dielectric strength of the material and that progressive breakdown can occur by electrical tree formation. Because of tree advancement, the potential distribution into the insulating material changes with time and is calculated at each time step. An algorithm for the simulation of electrical tree growth in solid dielectrics based on this model has been developed. The algorithm is also used to simulate breakdown in solid dielectrics containing square or spherical voids.

Übersicht

In diesem Artikel wird das Wachstum der elektrischen Bäume in Festisolierstoffen mittels von Neumannscher zellularer Automaten modelliert. Dieses Modell geht davon aus, daß das elektrische Feld an der Spitze der Elektrode oft in der Nähe der dielektrischen Festigkeit vom Material liegt und das ein fortschreitender Durch-schlag durch elektrische Bäume möglich ist. Durch das Wachsen der elektrischen Bäume ändert sich die Spannungsverteilung innerhalb des Festisolierstoffes mit der Zeit und wird in jedem Zeitschritt berechnet. Ein Algorithmus für die Simulation des Wachstums eines elektrischen Baums in Festisolierstoffen ist entwickelt worden. Der Algorithmus kann auch den Durchschlag in Festisolierstoffen mit zylindrischen oder kugelförmigen Hohlräumen simulieren.

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References

  1. Budenstein P (1980) On the Mechanism of Dielectric Breakdown of Solids. IEEE Trans. Elec. Insul., vol. 15: 225–240

    Google Scholar 

  2. von Hippel A (1937) Electric Breakdown of Solid and Liquid Insulators. J. Appl. Phys., vol. 8: 815–832

    Google Scholar 

  3. Froehlich H (1937) Theory of Electrical Breakdown in Ionic Crystals. Proc. Roy. Soc. A., vol. 160: 230–241

    Google Scholar 

  4. Froehlich H (1941) On the Dielectirc Strength of Mixed Crystals. Proc. Roy. Soc. A, vol. 178: 493–498

    Google Scholar 

  5. Froehlich H (1947) On the Theory of Dielectric Breakdown in Solids. Proc. Roy. Soc. A, vol. 188: 521–532

    Google Scholar 

  6. Seitz F (1949) On the Theory of Electron Multiplication in Crystals. Phys. Rev., vol. 76: 1376–1393

    Google Scholar 

  7. Klein N (1978) Electrical Breakdown Mechanisms in Thin Insulators. Thin Sol. Fil., vol. 50: 223–232

    Google Scholar 

  8. Klein N (1982) Electrical Breakdown of Insulators by One-Carrier Impact Ionization. J. Appl. Phys., vol. 53, no. 8: 5828–5839

    Google Scholar 

  9. Stark KH, Garton CG (1995) Electric Strength of Irradiated Polythyne. Nature, vol. 176: 1225–1226

    Google Scholar 

  10. Croitoru Z (1959) Space Charges in Dielectrics. Progr. in Diel., vol. 6: 105–146

    Google Scholar 

  11. Niemeyer L, Pietronero L, Wiesmann HJ (1984) Fractal Dimension of Dielectric Breakdown. Phys. Rev. Lett., vol. 52, no. 12: 1033–1036

    Google Scholar 

  12. Dissado LA, Williams PI (1994) Physical origin for differences in electrical tree structure. Proc. of IEEE Conference on Electrical Insulation and Dielectric Phenomena-(CEIDP'94), Arlington, TX, USA, 418–423

  13. Dissado LA, Dodd SJ, Champion JV, Williams PI (1995) Electrical tree propagation: from stochastic models to a quantative physical description. Proc. of the 1995 IEEE 5th International Conference on Conduction and Breakdown in Solid Dielectrics, Leicester, UK, 16–22

  14. Peitgen H, Jurgens H, Saupe D (1992) Chaos and Fractals, Springer-Verlag

  15. von Neumann J (1966) Theory of Self-Reproducing Automata, University of Illinois, Urbana

    Google Scholar 

  16. Kitchin DW, Pratt OS (1958) Treeing on Polyethylene as a Prelude to Breakdown. AIEE Trans. Power App. Sys., vol. PAS-77, Pt. III: pp. 180–186

    Google Scholar 

  17. McMahon EJ, Perkins JR (1964) Evaluation of Polyolefin High Voltage Insulating Compounds; Dendrite (tree) Formation under Highly Divergent Fields. IEEE Trans. Power App. Sys., vol. PAS-83: 1253–1260

    Google Scholar 

  18. Laurent C, Mayoux C, Sergent A (1981) Electrical Breakdown due to Discharges in Different Types of Insulation. IEEE Trans. Elec. Insul., vol. 16: 52–58

    Google Scholar 

  19. Arima I, Watanabe T (1981) Current Pulses Caused by Electrical Tree Development. IEEE Trans. Elec. Insul., vol. 16: 543–551

    Google Scholar 

  20. Shibuya Y (1977) Void Formation and Electrical Breakdown in Epoxy Resin. IEEE Trans. Power. App. Sys., vol. 96: 198–206

    Google Scholar 

  21. Mitsui H (1981) Electrical Failure Properties of Cast Epoxy Resins. IEEE Trans. Elec. Insul., vol. 16: 533–542

    Google Scholar 

  22. Ieda M (1980) Dielectric Breakdown Process of Polymers. IEEE Trans. Elec. Insul., vol. 15: 206–224

    Google Scholar 

  23. Dorlane O (1982) Thermally Stimulated Discharge of Polyethylene Following A.C. Stressing. IEEE Trans. Elec. Insul., vol. 17: 199–202

    Google Scholar 

  24. Patsch R (1992) Electrical and Water Treeing. A Chairman's View. IEEE Trans. Elec. Insul., vol. 27: 532–542

    Google Scholar 

  25. Wolfram S (1994) Cellular Automata and Complexity, Addison Wesley, Reading, Massachusetts

    Google Scholar 

  26. Gerhard M, Schuster H (1989) A Cellular Automaton Describing the Formation of Spatially Ordered Structures in Chemical Systems. Physica D, vol. 36: 209–221

    Google Scholar 

  27. Gerhard M, Schuster H, Tyson JJ (1990) A Cellular Automaton Model of Excitable Media. Physica D, vol. 46: 392–415

    Google Scholar 

  28. Weimer JR, Tyson JJ, Watson LT (1992) Diffusion and Wave Propagation in Cellular Automaton Models of Excitable Media. Physica D, vol. 55: 309–327

    Google Scholar 

  29. Karafyllidis I, Thanailakis A (1995) Simulation of Two-Dimensional Photoresist Etching Process in Integrated Circuit Fabrication Using Cellular Automata. Modelling and Simulation in Materials Science and Engineering, vol. 3: 629–642

    Google Scholar 

  30. Karafyllidis I, Thanailakis A (1996) Simulation of the Image Reversal Submicron Process in Integrated Circuit Fabrication. Semiconductor Science and Technology, vol. 11: 214–220

    Google Scholar 

  31. Vichniac GY (1984) Simulating Physics with Cellular Automata. Physica D, vol. 10: 96–116

    Google Scholar 

  32. Wilding NB, Trew AS, Hawick KA, Pawley GS (1991) Scientific Modeling with Massively Parallel SIMD Computers. Proceedings of the IEEE, vol. 79: 574–585

    Google Scholar 

  33. Toffoli T (1984) Cellular Automata as an Alternative to (rather than an Approximation of) Differential Equations in Modeling Physics. Physica D, vol. 10: 117–127

    Google Scholar 

  34. Matzke DJ (1994) Impact of Locality and Dimensionality Limits on Architectural Trends, Proceedings of the Workshop on Physics and Computation, PhysComp'94, IEEE Computer Society Press, Los Alamitos, California, 30–35

    Google Scholar 

  35. Omtzigt ETL (1994) Computational Spacetimes, Proceedings of the Workshop on Physics and Computation, PhysComp'94, IEEE Computer Society Press, Los Alamitos, California, 239–245

    Google Scholar 

  36. Minsky M (1982) Cellular Vacuum. International Journal of Theoretical Physics, vol. 21: 537–551

    Google Scholar 

  37. Feynman RP (1982) Simulating Physics with Computers. International Journal of Theoretical Physics, vol. 21: 467–488

    Google Scholar 

  38. Zeigler BP (1982) Discrete Event Models for Cell Space Simulation. International Journal of Theoretical Physics, vol. 21: 573–588

    Google Scholar 

  39. Toffoli T (1984) CAM: A High-Performance Cellular Automaton Machine. Physica D, vol. 10: 195–204

    Google Scholar 

  40. Karafyllidis I, Andreadis I, Tzxionas P, Tsalides Ph, Thanailakis A (1996) A Cellular Automaton for the Determination of the Mean Velocity of Moving Objects and its VLSI Implementation. Pattern Recognition, vol. 29: 689–699

    Google Scholar 

  41. Anndreadis I, Karafyllidis I, Tzionas P, Thanailakis A, Tsalides Ph (1996) A new Hardware Module for Automated Visual Inspection Based on a Cellular Automaton Architecture. Journal of Intelligent and Robotic Systems vol. 16: 89–102

    Google Scholar 

  42. O'Dwyer JJ (1982) Breakdown in Solid Dielectrics. IEEE Trans. Elec. Insul. vol., 17: 484–487

    Google Scholar 

  43. Cooper R (1983) Breakdown in Solids. Electrical Insulation, Book, Eds. Peter Peregrinus, London, England

    Google Scholar 

  44. Bruning AM (1984) Design of Electrical Insulation Equipment. Ph.D. Diss., Univ. of Missouri, Columbia

    Google Scholar 

  45. Ames WF (1992) Numerical methods for Partial Differential Equations. Academic Press, Boston

    Google Scholar 

  46. Bartnikas R, Novak JP (1993) On the Character of Different Forms of Partial Discharge and their Related Terminologies. IEEE Trans. Elec. Insul., vol. 28: 956–968

    Google Scholar 

  47. Mason JH (1951) The Deterioration and Breakdown of Dielectrics Resulting from Internal Discharges. Proc. IEE, vol. 98: pp. 44–59

    Google Scholar 

  48. Mason JH (1953) Breakdown of Insulation by Discharges. Proc. IEE, vol. 100 (II A): 149–158

    Google Scholar 

  49. Danikas MG, Atten P, Saker A (1994) Streamer Propagation over a Liquid/Solid interface. IEEE Trans. Diel. Insul., vol. 1: 348–350

    Google Scholar 

  50. Kreuger FH (1991) Industrial High Voltage, Eds. Delft University Press, Delft, 12–13

  51. Crichton GC, Karlsson PW, Pedersen A (1989) Partial Discharges in Ellipsoidal and Spherical voids. IEEE Trans. Elec. Insul., vol. 24: 335–342

    Google Scholar 

  52. Billing JW, Groves DJ (1974) Treeing in Mechanically Strained HV Cable Polymers Using Conducting Polymer Electrodes. Proc. IEE, vol. 121: 1451–1456

    Google Scholar 

  53. Danikas MG, Tanaka T (1994) Aging and Related Phenomena in Modern Electric Power Systems. IEEE Trans. Diel. Elec. Insul., vol. 1: 548–549

    Google Scholar 

  54. Holboll JT, Braun JM, Fujimoto N, Stone GC (1991) Temporal and Spatial Development of Partial Discharges in Epoxy Related to the Detected Electrical Signal. Ann. Rep. CEIDP, Knoxville, USA, 581–588

  55. Danikas MG, Gazzana Priaroggia P, Metra P, Miramonti G (1995) Research on the Breakdown Under Type Test on Non-Pressurized Paper-Insulated HVDC Cables. Eur. Trans. Elec. Power Eng. (ETEP), vol. 5, no. 1: 63–65

    Google Scholar 

  56. Tanaka T, Ikeda Y (1971) Internal Discharges in Polyethylene with an Artificial Void. IEEE Trans. Power App. Sys., vol. PAS-90: 2692–2702

    Google Scholar 

  57. Morshuis PHF (1995) Assessment of Dielectric Degradation by Ultrawide-Band PD Detection. IEEE Trans. Diel. Elec. Insul., vol. 2: 744–760

    Google Scholar 

  58. Wolter KD, Tanaka J, Johnson JF (1982) A study of the Gaseous Degradation Products of Corona-Exposed Polyethylene. IEEE Trans. Elec. Insul., vol. 17: 248–252

    Google Scholar 

  59. Turner NH, Bruning AM (1995) Analysis of electrical insulator surfaces by X-ray photoelectron spectroscopy. IEEE Trans. Diel. Elec. Insul., vol. 2: 1140–1146

    Google Scholar 

  60. Knuth D (1981) Seminumerical Algorithms. Addison Wesley, Reading Massachusetts.

    Google Scholar 

  61. Jocteur R, Favrier E, Auclair H (1977) Influence of Surface and Internal Defects on Polyethylene Electrical Routine Test on VHV Cables. IEEE Trans. Power App. Sys., vol. PAS-96: 513–523

    Google Scholar 

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Karafyllidis, I., Danikas, M.G., Thanailakis, A. et al. Simulation of electrical tree growth in solid insulating materials. Electrical Engineering 81, 183–192 (1998). https://doi.org/10.1007/BF01236238

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