Analysis of development of electrical tree in silicon rubber using local fractal dimension

Patterns of electrical trees in insulators have been investigated numerically using fractal dimension. The complexity of the pattern of the tree increases with applied voltage. The degree of the complexity depends on the polarity of the applied voltage. The change of the pattern of the tree can be indicated by the fractal dimension. However, in high voltages the fractal dimensions of the trees are almost same one in both polarities. This means that the pattern of the tree consist of some fractal patterns. Thus we must focus on the local pattern of the tree which is estimated by local fractal dimension. In this paper, the pattern is analyzed by the local fractal dimension method, i.e. local fractal dimension map and local fractal dimension spectrum. The needle electrode in a silicon rubber has been applied three or four times with impulse voltage. The local fractal dimension maps and its spectra have been compared and then the next growth of the tree or branches has been predicted using the local fractal dimension map. In addition, the change of the local fractal dimension of the tree along the branch has been investigated.