3D characterization of electrical tree structures

Electrical trees are one of the main mechanisms of degradation in solid polymeric insulation leading to the failure of high voltage equipment. They are interconnected networks of hollow tubules typically characterized from two-dimensional (2D) projections of their physical manifestation. It is shown that complete characterization requires a three-dimensional (3D) imaging technique such as X-ray computed tomography (XCT). We present a comprehensive set of parameters, quantitatively characterizing two types of tree topology, conventionally known as bush- and branchtype. Fractal dimensions are determined from 3D models and from 2D projections, and a simple quantitative relationship is established between the two for all but dense bush trees. Parameters such as number of nodes, segment length, tortuosity and branch angle are determined from tree skeletons. The parameters most strongly indicative of the differences in the structure are the number of branches, individual channel size, channel tortuosity, nodes per unit length and fractal dimension. Studying two stages of a bush tree's development showed that channels grew in width, while macroscopic parameters such as the fractal dimension and tortuosity were unchanged. These parameters provide a basis for tree growth models, and can shed light on growth mechanisms.