A Mathematical Modeling Approach to Characterize the Growth of the Electrical Tree in XLPE Insulation Under Lightning Impulse Overvoltage

Cross-linked polyethylene (XLPE), the most commonly used insulation system in underground cables, and gas-insulated substations are often subjected to high-voltage stresses of time-varying nature. Lightning overvoltages, fast transients, very fast transients, and AC voltages are the most common overvoltages striking the insulation. These stresses cause degradation of insulation, which is called treeing, and are considered as the major cause of the reduction in life of the insulation. The purpose of our work is the development of a stochastic model to inspect the spread of electrical trees under lightning impulse voltage. A numerical solution of Poisson's equation in the material is obtained first. The electric field distributions obtained on the surface of the material are used to compute the path of tree propagation by developing a program based on a probabilistic approach. The key parameters of the damage are evaluated by plotting histograms of the results obtained from many iterations. A statistical analysis of the obtained results has also been done, and the model has been found efficient.