Numerical simulation of electric currents through insulating materials

Abstract

A numerical simulation of electric currents is carried out through solid dielectrics from a model based on the local polarization. A degradation of material was considered to be produced from one of the electrodes and we simulated it by admitting modifications in the chemical structure of the material, which implies an alteration in the value of the corresponding dipole moments that characterize the material, as well as the concentration of the latest. Different simulations are achieved according to the ratio of the degraded thickness and the temperature.

Dielectric characterization and conduction modelling of a water tree degraded LDPE

“…A Debye-type conduction model based on the dielectric relaxation of independent dipoles for polyethylene was presented in [22]. A more realistic new approach to the modelling of these processes is proposed in this work [32].…”

“…The application of the "Many Body Universal Model of Dielectric Relaxation" implies that for a long enough measuring time, a "slow down" process in polarization is activated: it is due to the mechanism of local redistribution of energy (flip-flop transitions) which results in a power dependence for polarization current, with a negative exponent whose absolute value is m∈(0,2). Because of the mathematical complexity of this theory, we propose in this paper a modification of the model of non-interacting dipoles presented in [22], in order to take into account interactions. With the aid of the new model we have tried to explain the variations of parameters in the power current law (best-fitted dependence for the polarization current measurements) as a function of (a) the degree of degradation by water trees and (b) the polarization voltage.…”

“…Due to the difficulty for the interpretation of the physical meaning in the coefficients of the power current response supplied by the "Many Body" theory −especially from an experimental/applied point of view−, we propose a simplified alternative approach: departing from the non-interacting dipoles model (mathematical equations, numerical calculations and simulations developed in [22]), we introduce a simple mathematical algorithm that accounts for dipole interactions. This new model also predicts a power current law for the response of the dielectric material (similar dependence of the experimental Curie-von Schweidler law, I(t)=I 0 t -m ) but this time, coefficients {I 0 ,m} can be readily determined as easy functions of the microscopic/macroscopic parameters of the material.…”

“…Nevertheless, in order to have a deeper look into material, we were interested in developing a "microscopic" modelling of conduction in PE. Hence, on the basis of a previously published Debye-like model [22] and taking into account the idea of dipole interaction from the 'Many Body Universal Model of Dielectric Relaxation' [23,24,25], we propose a new conduction model for water tree degraded LDPE that reproduces the Curie-von Schweidler potential dependence of real current measurements and permits an easy physical interpretation of their fitting parameters. Consequently, in this article, we characterize the conduction processes in new and aged polyethylene by using experimental results and we present a new theoretical model for the conduction processes.…”

A new approach to the modelling of the conduction processes in a water tree degraded LDPE

“…Experimental results are interpreted from the proposed model of interacting dipoles by using equation (11). Nevertheless, for small water-tree degraded layers, an interpretation of the exponent parameter m of experimental polarization curves is not possible as m<l. According to equation (12i), this model can only explain the current curves corresponding to a higher level of degradation which gives experimental exponents m greater than unity ( m l ) : i.e.…”