The fractal analysis of water trees: an estimate of the fractal dimension

Water trees result from ac electrical aging of the polymeric insulation of medium and HV power cables in a humid or wet environment. As suggested by their name, they arise from penetration of water in the polymer. Visual observation with the help of an optical microscope shows tree (bush) type structures. This suggests that water trees might be fractal objects. Calculation of the fractal dimension from experimental samples may confirm the fractal characteristics and also give information on the damage caused to the polymer. In this work images of water trees taken under the optical microscope, dyed by methylene blue and etched for scanning electron microscopy (SEM), were studied in order to estimate the fractal dimension using a box-counting algorithm. The photographs, made using an optical microscope (scale of 100 μm), of the dyed samples were obtained from laboratory-aged low-density polyethylene (LDPE) specimens using accelerated techniques. Different field amplitude and frequency and also time of aging were used and the dimension values were compared. SEM images resulting from aged cross-linked polyethylene (XLPE) cables revealed a structure at a different scale (~3 μm). Each photograph was analyzed to compare regions with and without water trees