The fractal dimension estimate of water tree in XLPE dielectric

Water trees arise from the penetration of water into the XLPE dielectric of medium and HV power cables when operating in a humid or wet environment. The growth process and shape of water tree in XLPE dielectric under ac electric field is random and branched and cannot be described using Euclidean geometry. The fractal dimension and the branching tendency of water tree in XLPE dielectric are estimated based on partial electric breakdown and fractal theory in this paper. The shapes and structures of water trees observed by an optical microscope proved to have fractal characteristics, i.e., water trees are fractal objects.