Analysis of development of electrical trees in insulators using local fractal dimension

Patterns of electrical trees in insulators are estimated numerically by fractal dimension. However they are not simple fractal but multifractal. They can be estimated by global spectrum and singularity, which do not have clear local information. A local fractal dimension and its spectrum are introduced. Local fractal dimension maps of impulse trees were calculated and the development considered by it and its spectrum. The change of the pattern of the impulse trees in applying the next impulse voltage can be predicted by considering the difference in the local fractal dimension spectrum in each stage.