A new calculation approach for dielectric space charge characterization from nano to macro-scales by the thermal step method

In this paper, a new calculation approach is developed and applied, for the first time, to different dielectric scales using the thermal step method (TSM). The thermal aspect of the approach concerns insulating materials from nano to macro-scales. The theoretical approach is based on the ballistic-diffuse transport taking into account the relaxation time of heat phonons and their effects on the trapped space charges. These effects are revealed on the temporal evolution of the induced image charges that constitute the electrical signal of the thermal step method. The temperature distributions and the TSM induced image charges are obtained by applying the numerical finite element method, the Newmark direct integration, the mean value theorem and the composite Simpson approximation. In a first step, the results of the temperature distributions are validated with those obtained by Boltzmann and Chen models for nano-polyethylene sample. In a second step, our approach is validated with TSM previous works using the Fourier's model for space charge characterizations in the micro and macro-dielectrics. The validated results of the TSM induced image charges for micro and macro-scales show good agreements, and prove that our approach is a consistent tool to be applied in space charge characterizations for different dielectric scales.