Katsutoshi Kudo

Fractal analysis of electrical trees

Recently, fractal characteristics in pattern formation have been attracting much attention. A number of books and papers have been published on the fractal analysis of random patterns or structures occurring in nature. The geometrical patterns of dielectric breakdown, which include lightning, surface discharges and electrical trees, are known to be of a fractal nature. Their fractal patterns can be analyzed numerically using fractal dimensions. In this paper, a survey of the fractal analysis of electrical trees, both in experiment and in computer simulation, is given. Several methods for estimating the fractal dimension are summarized. The stochastic models for discharge patterns based on computer simulation are also summarized. Fractal analysis of real electrical trees in polymeric insulating materials is reviewed. For the experimental tree patterns, the fractal analysis of the projected 2-D and the reconstructed 3-D patterns is presented.

Estimation of 3D fractal dimension of real electrical tree patterns

In this study, we investigated methods of reconstructing higher-resolution three-dimensional (3D) patterns of real electrical tree patterns. We studied two kinds of reconstruction methods, and both methods were applied to the same specimen. One method is a mechanical preparation of serial cross sections and the other is a computerized tomography method using projections. Furthermore, to examine the fractal properties of reconstructed 3D tree patterns, the fractal dimension of their patterns was estimated by means of a box counting method. The results showed that both methods can reconstruct 3D electrical tree pattern accurately and the obtained patterns have fractal properties.<<ETX>>

Barrier effect of treeing in composite insulating materials with heat-adhesive interfaces of different polymers

A polymer/polymer composite system is widely used in high-voltage equipment and power cables. The interface of this composite system plays an important role in the electrical degradation, such as electrical treeing or partial discharge, of the composite system. Therefore, it is important to study the effect of an interface on the electrical treeing of polymer/polymer-composite insulating materials. In this paper, we describe the tree growth and complete breakdown characteristics of specimens with a polymer barrier film layer molded in ethylene vinyl acetate copolymer (EVA), in which the interface of EVA and the barrier film is perpendicular to the electric field under an AC voltage. It is found that with a barrier film, the tree growth is retarded on the barrier film, which then punctures the film, or develops along the edge of the film. It is also found that the pressure of decomposing gas in the tree channels plays an important role in tree propagation.

Fractal characteristics of real electrical trees

The fractal properties of 2-D projected electrical trees in PMMA (polymethyl methacrylate) and XLPE (cross-linked polyethylene) samples have been investigated. The results show that the tree structures are fractal objects although their tree patterns are obtained in a 2-D projection. The fractal dimension of the tree formed in PMMA is found to become constant as the applied voltage or the time duration is increased. Furthermore, the fractal dimension of the tree structures produced in XLPE is found to increase with increasing cross-linking of XLPE. It is concluded that there exists a relationship between the fractal dimension of the electrical trees and the physical properties of the polymers used.<<ETX>>

The 3-D fractal analysis of electrical trees using a serial sectioning method and a CT method

In order to reconstruct the 3D patterns of real electrical trees, we investigated the applicability of computerized tomography method (CTM) and the serial sectioning method (SSM). We also investigated the relationship between the fractal dimension of the reconstructed 3D patterns and that of projected 2D patterns of real electrical trees, from the point of view of fractal dimension. It was pointed out that it is important to estimate the fractal dimension of spatial patterns precisely and 3-dimensionally.

Directional properties of positive impulse tree propagation in oriented PET and PP barrier films molded in EVA

In this paper, we describe the directional properties of positive impulse tree propagation at an ethylene vinyl acetate copolymer (EVA) base polymer/oriented barrier film (polyethylene terephthalate (PET) and polypropylene (PP)) interface. It was found that, for biaxially oriented PET and PP barrier films, after a positive impulse tree enters a film, the tree develops preferentially in both directions of the machine direction (MD) and transverse direction (TD) drawings of the barrier film. It was also found that, for uniaxially oriented PP barrier films, after the tree enters a film, the tree develops preferentially in the direction of the MD drawing of the barrier film. These results indicate that the preferential direction of positive impulse tree propagation in oriented PET and PP films is closely related to the microstructures of oriented molecular chains in PET and PP barrier films.

Propagation characteristics of AC and impulse trees at the solid/solid interfaces of different polymers

In this paper, we investigate the tree propagation of the specimens having the polymer/polymer interfaces, which are perpendicular to the line of electric force. In addition, we describe the barrier effect on tree propagation under ac or impulse voltage application.

Fractal analysis of 3D simulated tree patterns considering critical field and potential drop

In this paper, we simulated 3D tree patterns with the field controlled random nature and used the parameters Vapp (applied voltage), Vd (potential drop in a tree channel), Ec (critical field for tree propagation) and /spl eta/ (the relation between local field and growing probability). As a result, the various shapes of tree patterns are obtained and the model holds more physical realizations.

Fractal analysis of 3D reconstructed patterns of real electrical tree

In this paper, we studied voltage-dependent characteristics of the tree shapes in cross-linked polyethylene (XLPE). We also studied the effect of voids on the tree shapes. In the case of the voidless samples, the tree length shows nonmonotonic behavior. In the case of samples with recessed voids, the tree length increases with increasing applied voltage. The tree shape is considered to consist of multiple groups of branches.

Effects of ions and waveforms on water tree initiation and propagation

In this paper, we describe an investigation of the effects of ions and waveforms on water tree initiation and propagation utilizing a new water electrode method. The results indicate that ferric ions contribute to water tree initiation and propagation. Moreover, a water tree was initiated when the waveform of a pulse simulating an inverter waveform was applied for 2 weeks even at room temperature, in spite of no ac voltage application.