Phase Field Modeling on By-Product Migration in Crosslinking Polymers for HVDC Cable Insulation Applications

Cross-linking by-products has been considered as one of the crucial factors for dielectric properties of cross-linked polyethylene, which plays an important role in the insulation performance of high voltage direct current (HVDC) cables. It migrates across cable insulation incorporating space charge effect, temperature variation of conductivity, etc., which makes it a long-standing puzzle of manipulating the electric field distribution for HVDC cable insulation, especially with the increasing voltage level. Nevertheless, there still lacks a theoretical model describing the migration of the by-products, especially for cable insulation with sizeable dimensions. In this article, a phase field model is established to simulate the migration of acetophenone (i.e., one of the by-products) through calculating the free energy landscape considering the competition between the diffusion driven by concentration gradient and the uphill diffusion caused by by-product aggregation. The results show that the time-dependence migration during degassing leads to an uneven distribution of acetophenone across the cable insulation, which is in good coincidence with the measured results for a full-size cable. Accordingly, the distortion of the electric field in HVDC cable insulation due to the radial distribution variation of acetophenone has been estimated regarding the relationship between by-product content and conductivity, and a method of manipulating the distribution of acetophenone is proposed to optimize the distribution of the electric field in cable insulation. Our work provides a numerical approach for the simulation of by-product migration in crosslinked polymers for insulation applications.