Three dimensional characterisation of electrical trees

Most of the geometric analysis of the structure of electrical trees has been performed using a two-dimensional (2-D) approach. However, electrical trees grow three-dimensionally (3D). The authors have recently shown that electrical trees can be 3-D imaged. A 3-D virtual replica can be created and through it, the tree characteristics analysed. Laboratory created electrical trees in polymeric insulation were scanned using X-ray computed tomography (XCT) for 3-D model reconstructions. Here global parameters such as diameter of tree channels, tree surface and volume are determined. The fractal dimension from 2-D projected patterns are shown to be lower than the fractal dimension from the entire 3-D model for both bush and branchtype trees. Local parameters such as numbers of channels, area covered by them and proportion of area degraded at a given cross-section are also calculated. Using the skeleton for analysing the tree structure, indices such as number of vertices, segment length, vertex density, tortuosity and branch angle are presented. Among them, vertex density provides a marked difference in value between a bush and a branch-type electrical tree. Using this 3-D approach for analysis achieves a more complete insight into treeing phenomena.