An Efficient Numerical Technique for the Simulation of Charge Transport in Polymeric Dielectrics

In recent years, the use of HVDC cables has grown exponentially. One of the main challenges that remains concerns the space charge accumulation inside the insulating materials. A better understanding of the mechanisms governing this phenomenon is essential to improve the performance of HVDC systems. Numerical simulations are often employed to achieve this goal. For this reason, it is important to perform them in an efficient way. In this work, we test several numerical techniques, aiming to assess which one is the best to use for fast and reliable simulations. We consider a well-known bipolar dynamic model from the literature for our simulations. The model considers a single level of deep traps and is implemented in a one-dimensional Cartesian coordinate system, considering a thin specimen of polymeric material. We compare three different time discretization methods: a fully explicit, a semi-implicit, and a fully implicit approaches. For the advective flux discretization, we compare the first-order upwind scheme (FOU) with a second-order upwind scheme coupled with the Koren flux limiter (SOU/KL). Regarding the computation of the polarization current, we introduce a simple approach using Sato's equation and compare it with the well-established approach based on the total current density.