A method for nonlinear electric-thermal coupling calculations of bushings based on unbiased gradient-free smooth domains.

High-voltage dry-type bushings, serving as the crucial junctions in DC power transmission, represent equipment with the highest failure rate on the DC primary side, underscoring the critical importance of monitoring their condition. Presently, numerical simulation methods are commonly employed to assess the internal state of bushings. However, due to limitations in the efficiency of multi-physics field computations, the guidance provided by numerical simulation results in the field of power equipment condition assessment is relatively weak. This paper focuses on solving the electrical-thermal coupling in high-voltage dry-type bushings. Addressing the most widely used tetrahedral mesh in numerical computations, we propose an efficient solution method based on the concept of "smooth domains." This method involves partitioning the volume centroids of the elements into multiple smooth domains within the computational domain. Electric and thermal conduction matrix calculations occur within these smooth domains, rather than within the grid or element interiors. This approach eliminates the need for traditional element mapping and complex volume integration. To demonstrate the effectiveness of this method, we use high-voltage dry-type bushings as a case study, comparing the performance of our approach with traditional finite element algorithms. We verify the algorithm's computational efficiency and apply it to the analysis of typical temperature anomalies in bushings, further illustrating its suitability for electrical equipment condition assessment.