3-D electrical network model of water tree

A 3-D computer model simulating electric properties of a water tree has been developed. The model is based on a regular, cubic lattice. Branched patterns of various sizes, grown from a needle electrode, were generated on the lattice by a random walk process to form the backbone structure of the water tree. Appropriate electric impedances were assigned to different regions, i.e. those occupied by the dielectric (polyethylene), water or empty cavities. The change of current in the ground electrode as a function water tree size was examined. Results were compared with the experimental results of J.D. Cross and J.Y. Koo (1984). Computer simulations show that if the water contained in water tree channels has conductivity higher then that of distilled water (10 ^-6 S/m), it can exist only in a dispersed form. If water tree channels were to be interconnected and completely filled with water, conductivity of the water should not be greater than that of distilled water. The latter case is not possible in the view of the presence of salts commonly found in water tree regions