Fractal analysis of the treeing process from luminous discharge image and measurement of discharge magnitude

Abstract

The purpose of this study is to analyze the growth of trees generated in PMMA from the apex of a void created by a needle tip. The analysis was based on fractal theory. In the measurement system, PMMA blocks were used with electrodes consisting of a needle and a plate. One cycle of an applied ac voltage was divided into twenty successive phase angle sections, labeled 41, $2, . . . , 4 2 0 , from one negative peak to the next negative peak of the applied voltage. The quantitative evaluation of the fractal dimension D of the luminous discharge pattern was performed for each section, particularly, for the sections q57, 8,9,17,18 and 19 where the discharge luminescence reached around the tip of the tree. It was noted that some samples revealed substantially different tree patterns even under the same measurement conditions. The reasons for the different trees have been investigated by determining D and attempting to correlate tree growth and the change of tree length with aging. When D of the discharge luminescence at 47/ 8,9,17,18 and 19 were large, luminescence with complex branches were generated. The present results indicate that tree growth and branching depend on the discharge at 47,8,9,17, 18 and 19.

Measurement and simulation of electrical tree growth and partial discharge activity in epoxy resin

“…The results obtained qualitatively agree with experimental data of other investigations of electrical treeing in epoxy resin and other polymers under similar conditions. The calculated fractal dimensions are close to the values obtained for branch-type trees, for example in [6,13,35,36]. The decelerating growth at the first stage of tree propagation (figure 4) has also been observed in many other investigations, for example [5,6,37,38].…”

“…The calculated fractal dimensions are close to the values obtained for branch-type trees, for example in [6,13,35,36]. The decelerating growth at the first stage of tree propagation (figure 4) has also been observed in many other investigations, for example [5,6,37,38]. This growth mode can be related to the non-uniformity of the electric field distribution.…”

“…The extension of a PD determines only the maximum magnitude of a PD, since for the same L the number of channels and the total length S may be different. The relation between the magnitudes of various PDs and the luminous discharge patterns was studied by Ehara et al [6]. They found that the area of the luminous part of a tree structure increases with the magnitude of the corresponding PD event.…”

“…In order to understand the electrical treeing behaviour it is necessary to consider the tree growth and the PD activity simultaneously. The recent development of electronic-optical and electronic measurement systems has made it possible to study the correlation between the PD behaviour, spatial distribution of light emission of PDs, and the spatial-temporal development of the tree structure [2][3][4][5][6][7]. Despite the continued investigation and the new experimental data, the electrical treeing has not yet been quantitatively described.…”

Sub-fractal structure of single partial discharge in an electrical tree

“…Here, we should point out that the sub-fractal dimension of one PD pulse is different from the fractal dimension of the accumulated light emission of PDs [17]. As the accumulated light emission of PDs tends to cover the whole structure of the tree in the early stage of tree growth, the fractal dimension of the accumulated-light-emission image should not differ much from the base-fractal dimension of the tree (as reported in [17]).…”