Modelling Magnetisation and Transport AC Loss of HTS Tapes near Ferromagnetic Materials Using an Integral Equation Method

The integral equation formulation of Maxwell’s equations proposed by Brandt provides an alternative to the H and T-A formulations for modelling high-temperature superconducting (HTS) tapes. A modified version of Brandt’s method in the literature models ferromagnetic domains near the tapes by considering the ferromagnetic domains as equivalent surface current. This paper extends this method by including the effect of external magnetic field acting on the ferromagnetic and HTS domains. The proposed method is used on a benchmark problem, which considers an HTS tape with a ferromagnetic substrate under an external time-varying magnetic field. The results agree closely (error in average ac loss less than 3%) with the widely-used T-A formulation implemented in COMSOL down to 2 mT. In addition, the proposed method is also applied to HTS tapes carrying transport ac current in a slot of a machine’s stator iron core, and HTS tapes in a stator iron slot in a machine under working conditions. It is found that ac loss calculated by the proposed method increases as the discretization size of the ferromagnetic material’s boundary decreases, and overshoots the value calculated by the T-A formulation in COMSOL when using very fine discretization.