Fractal-based electric field enhancement modeling of vacuum gap electrodes

Abstract

The objective of this paper is to study the characteristics of the microscopic electric field enhancement at the micro-projections on the contact surface based on the fractal modeling of the micro-projections in vacuum interrupters. In this paper, the distortions of the microscopic electric field caused by the micro-projections were studied in the case of the applied voltage 60 kV and the contact gap 2 mm. Moreover, the microscopic enhancement factor β m for the various micro-projections with the height-radius ratio being less than or equal to 50 were investigated. First, the basic Weirstrass-Mandelbrot (W-M) fractal function was introduced and simplified into the modeling of the various micro-projections with the height-radius ratio 0.2, 0.4, 1, 2, 10 and 50 respectively. Then, the electric field distributions were analyzed based on these micro-projection fractal models. The simulation results showed that the micro-projections would cause a distortion of the microscopic electric field at the micro-projections on the contact surface, especially in the case of the higher height-radius ratio. In this paper, with the height-radius ratio of the micro-projections increasing from 0.2 to 50, the microscopic enhancement factor β m based on the fractal models would increase from 16 to 3667. In comparison with the idealized ellipsoid model, to the same height-radius ratio of the micro-projection, the microscopic enhancement factor β m based on the fractal models was about four times higher than that based on the ellipsoid models. Furthermore, the microscopic electric field at the micro-projections would have a significant influence on the micro-particles impact phenomena and other microscopic physical phenomena which could give rise to the vacuum breakdown. The results could provide some useful information to understand the physical mechanism to trigger the vacuum breakdown.