Hysteresis loss calculations of 2D and 3D large-scale HTS coil models: from multi-scale method to multi-dimension method

Abstract Here we propose a new approach capable of calculating the hysteresis loss of 3D HTS coil models based on the modeling framework of the multi-scale method. The study enhances the multi-scale method for 2D simulations by introducing the homogenization technique to simplify the topological features of coils’ cross sections. With the simplification, a 3D A -formulation magnetostatic model is built for magnetic field estimation, while a 2D H -formulation superconducting model is solved for the tape’s current density and hysteresis loss. Since different spatial dimensions are employed in the submodels, we refer to it as the multi-dimension method. We demonstrate the data transferring between the 2D or 3D homogenized coil submodel and the 2D single-tape submodel. The benchmark results show that hysteresis losses from the developed models and reference models are in good agreement, with errors of less than 1% and 6% in simulating the target 2D solenoid coil and 3D racetrack coil, respectively. The distributions of current density and magnetic field in both models are highly consistent. Meanwhile, the developed models speed up the calculations by one to five times compared with the reference models. Due to the easy calculation of 3D magnetostatic models and 2D superconducting models, the multi-dimension method may pave a new way to 3D electromagnetic simulations for larger-scale and more complex high temperature superconducting conductors and coils.