Trees growth-current and losses modelling in solid electrical insulations

This paper presents an attempt of modelling the treeing structures expanding in an insulating polymer. By assuming the treeing shapes to simple geometries and by considering the polymer /tree interface with or without charge, we establish a mathematical expression describing the dynamics of the propagation.This shows the relationship between the treeing length, the current and the loss factor and their dependency on many parameters such as the amplitude, the duration and the shape of the applied voltage, the frequency, the electrode geometry thickness of the polymer sample, the electrode gap and radius, the density of the polymer, the permittivities and conductivities of both polymer and tree.We also discuss the time- lag to breakdown. We have also led an experimental investigations which results allows us to validate those obtained by the mathematical model, and to show the correlation between the electrical tree propagation (length and time to breakdown) in the case of the different parameters considered.