Polymer materials are widely used in power electronics and power transmission and distribution systems because of their excellent dielectric properties. However, under the long-term coupling effect of mechanical stress, thermal effect, electrical stress and other factors inside the insulation material, it is easy to cause the growth of electrical trees, which will cause internal damage and deterioration of the material, and eventually lead to the harm caused by penetrating discharge. The numerical simulation method can provide reference for improving the insulation reliability of the system. However, some key parameters of the existing model are difficult to obtain directly from the experiment, and can only be realized through the model verification to achieve the microscopic electrical tree simulation of specific materials, and can not achieve the engineering tasks from material parameter testing to complex structure electrical tree prediction. Therefore, this paper aims to propose a method of electrical tree limb simulation with simple model and parameters that can be obtained by experiment, so as to improve the engineering applicability of electrical tree limb simulation.

The inverse power law is a phenomenological model directly based on the lifetime data of solid dielectric, which describes the physical process of the accumulation of electrical damage in solid dielectric to the generation of penetrating tree channels, and has the theoretical basis for describing the growth of electric treees. Therefore, this paper analyzes the physical relationship between the parameters of the inverse power model and the growth law of electrical trees, establishes the basic equation of local electrical damage based on the inverse power model, and establishes the electric tree simulation method based on the inverse power model combined with the electric field calculation and the material dispersion equation. Further, a sample of pin-plate electrode is used to demonstrate how to simulate the electrical tree by testing the basic parameters of the material. The experimental verification of the simulated results of electric treees is carried out, and the simulated growth law of electric treees is compared with the experimental growth law of electric treees. Finally, the difference between the proposed method and the phase-field simulation and WZ model is compared.

The final results show that the method proposed in this paper can effectively simulate the electrical trees by using the experimental material parameters. The simulated electrical trees in this paper agree with the experimental results in terms of morphology and growth law. In this method, the shape of electrical trees is correlated with voltage tolerance index and cumulative damage standard deviation, and the growth rate of electrical trees is correlated with voltage tolerance index and cumulative damage mean. Compared with the phase-field simulation and WZ model, the proposed method can simulate the gradual growth of electrical trees, and the model parameters can be obtained experimentally.