Polymer/polymer composite insulating systems have been widely used in high-voltage equipment and power cables. Such composite insulating systems always have an interface between two polymeric insulating materials. This interface may cause partial discharge and electrical treeing under high electric stresses. The electrical properties of this polymer/polymer interfacehave not yet been fully understood. It has been shown in previous studies that the propagation characteristics of electrical trees in polymer/polymer composite insulating materials considerably vary depending on the combination of polymers. It has also been suggested that the 3-dimensional tree simulation based on a DBM model considering growth probability is valid.In this study, we will investigate the 3-dimensional simulated tree considering a composite insulator interface based on a DBM model with growth probability. キーワード：高分子-高分子界面，バリア効果，トリー，シミュレーション，成長確率Keywords：polymer/polymer interface, barrier effect, electrical tree, simulation, growth probability

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Composite insulation systems consist of different insulators and their systems are widely used in high voltage equipment and in power cables. These interfaces are the weak part of the composite and play a decisive role in the electrical treeing and dielectric breakdown processes of the composite. Therefore, it is important to study the effects of their interfaces on the electrical treeing of polymer/polymer composite insulators.In this paper, we investigate the ac tree growth in the specimens having heat-adhesive interfaces between ethylene vinyl acetate copolymer (EVA) sheets and the other different polymer films. The polymer/polymer interfaces in our study are arranged as being parallel to the line of electric force. It is found that the characteristics of ac tree propagation in the vicinity of the polymer/polymer interfaces are considerably different at the combinations of different polymers.

Many complex patterns in nature such as discharge phenomena are known as fractal objects. With the development of computer system, their spatial structures of discharge patterns have been analyzed using a computer simulation.In this paper, we developed the 3-dimensional numerical simulation model of the electrical tree pattern considering growing probability and local electric field under a Laplace field. Using this numerical simulation model, we obtained the various shapes of electrical tree, such as tree-like, bush-like and densely bush-like (balllike) trees, and measured the fractal dimensions of these simulated patterns. Furthermore, we studied the relationship between fractal dimensions of 3-dimensional simulated patterns and those of 2-dimensionally projected patterns, and the results were compared with those of the real electrical trees.

Many complex patterns in nature such as surface discharge and lightning are known as fractal objects. It is well known that the electrical trees in polymeric insulating materials are also fractal objects. However, it is difficult to analyze the real electrical trees in a 3-dimensional space. With the development of a computer system, the stochastic models for electrical trees have been presented and the fractal analysis of their simulation trees has been performed.In this paper, we carried out the 3-dimensional simulation utilizing the stochastic model under a Laplace field, taking into account the growth probability, local field, critical threshold field and voltage drop along tree channelsUsing this numerical simulation model, we obtained the various shapes of simulation trees, such as branch-type, bush-type and densely bush-type trees, and estimated the fractal dimensions of their simulation trees.The results show that the obtained simulation tree patterns have a fractal character and the parameters in an adopted stochastic model influence the fractal character of simulation trees.

The three-dimensional reconstructed images of real electrical trees and their fractal characteristics are described. A method for three-dimensional reconstructed images of real electrical trees is based on serial sectioning of a specimen with a microtome, and stacking of the image-processed information from the sections using a personal computer. Specimens in this investigation were cross-linked polyethylene (XLPE) and the experiment for tree was carried out in a needle-plane electrode geometry under AC or impulse voltage application. The fractal dimensions for the three-dimensional reconstructed trees and their two-dimensional projected patterns were estimated mainly by means of a box counting method.The obtained results show that the three-dimensional reconstructed images of real electrical trees have fractal properties, and the fractal dimension for tree-like trees is less than 2 and the fractal dimension for balllike trees lies between 2 and 3. The results also indicate that there is a relationship between the fractal dimension of the three-dimensional reconstructed trees and that of the two-dimensional projected patterns.

In this paper, real electrical trees in polymeric insulating materials were discussed from the viewpoint of their fractal characteristics. Experiments on real electrical trees were carried out in the needle to plane electrode geometry under ac voltage application. Samples in this investigation were made of cross-linked polyethylene (XLPE). Two methods of reconstructing three-dimensional (3D) patterns of real electrical trees were developed. One is the computerized tomography method (CTM) and the other is the serial sectioning method (SSM). The relationship between tree characteristics and 3D fractal dimensions of tree patterns was studied. The experimental results showed that the spatial tree patterns have a fractal characteristics and that the tree characteristics can be characterized by fractal dimensions.

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