Application of FEA to Image-based Models of Electrical Trees with Uniform Conductivity

X-ray computed tomography and serial block-face SEM have provided detailed three-dimensional reconstructions of electrical trees for the first time. The application of finite element analysis (FEA) to the analysis of electrical fields in an epoxy block containing a tree is considered. Illustrations are provided by way of a number of case studies. It is shown that the limitations of FEA do not arise from the discrete nature of the meshing: rather uncertainties are more concerned with material properties in high fields on the micrometer scale, the limitations imposed by the pixel size of the imaging technique, and the discrete nature of the image reconstruction technique. For a dynamic model of tree growth space charge dynamics on the same physical scale need also to be modelled. A meshing strategy is used, calibrated against the charge simulation method, to ensure accurate but manageable computations in critical parts of a tree such as branch tips. Examples of field values are given using geometric constructs and low-field material characteristics as illustrative values. The field variation around a conducting tree structure, including the maximum field direction as a branch starts to bifurcate, is determined as an example. These yield values in excess of those expected if space charge movement was considered, but consistent with analytical calculations.