Fractal Characteristics of AC Electrical Trees in Polymeric Insulating Materials
Satoru Maruyama, Shozo Kobayashi, Katsutoshi Kudo · IEEJ Transactions on Fundamentals and Materials · 1993
Branching structure of two-dimensional projected electrical trees in polymeric insulating materials is discussed from the viewpoint of fractal analysis. Samples in this investigation were polymethyl-methacrylate resin (PMMA) and cross-linked polyethylene (XLPE). The physical properties of XLPE samples were varied by the degree of cross-linking. The experiment was carried out under AC voltage application. The generated tree was photographed with a camera through a microscope. The obtained photograph was digitized by using a scanner and imageprocessed with a personal computer. After that, the tree length was measured and then the fractal dimension of tree was estimated using a scale covering method.The results show that the electrical tree shape patterns, which were obtained from PMMA and XLPE specimens, are fractal objects and they can be quantified by means of fractal dimensions. Furthermore, the results show that there is a relationship between the degree of crosslinking of XLPE used and the fractal dimension of electrical tree patterns in XLPE.