Abstract
In the frame of the thermal step method (TSM) used to characterize the space charge in dielectric materials, we present an original numerical technique for determining the electric field distribution in the bulk of a dielectric plate or cable. The first stage of our technique is the application of the finite element method (FEM) in order to find instantaneous distributions of temperature profiles. The calculation of the electric field distribution is based on these obtained profiles. During the stage of the determination, our mathematical treatment is based on the TSM charge q(t) in order to avoid numerical instabilities on the temperature derivatives. Therefore, we have transformed the integral equation for the TSM current I(t) used in previous works to an integral equation for the TSM charge q(t). The control of the instantaneous propagation of the thermal wave front, produced by submitting one face of the dielectric to a thermal step, and the application of Simpson's method to the integral equation of the TSM charge q(t), allow to determine the electric field distribution. The results of the electric field distribution are validated with those obtained in previous works. A good agreement and an improvement near the dielectric thickness boundaries are observed on these results. The numerical space charge density within the material is obtained by numerical derivation of the field according to Poisson's equation.