New Background Field Estimation Methods for Improving Numerical Multiscale Model in AC Loss Calculation

A numerical multiscale model is used to resolve the high computation complexity in the ac loss calculation of large-scale superconducting devices and proves advantageous with regard to time and memory requirements. In the multiscale model, the background field estimation method is of crucial importance to the calculation accuracy. In this paper, we propose four new background field estimation methods, including the Jacobi Gauss- Seidel hybrid and iteration methods, to improve the accuracy and expand the application scope of the multiscale model. A high temperature superconducting solenoid magnet is used to test the performance of these four methods and the results are compared with those of the H-formulation reference model and the multiscale model with a Jo uniform background field estimation method. Results show that in the 19 A/50 Hz ac transport current test case: the Jacobi Gauss- hybrid and iteration methods reduce the error of the ac loss mean value/peak value to 7.88%/5.89%, 5.71%/2.4%, 3.22%/1.22%, and 1.83%/0.69% with the total time cost reduced by 15.7, 8.9, 13.5, and 7.8 times. The multiscale model is expected to achieve even higher accuracy in applications where the ac loss is relatively small due to its coincidence property. The greatly improved accuracy makes the multiscale model a reliable substitute for the H-formulation model. In addition, the idea of iteration and back substitution in background field correction widely expands the application scope of the multiscale model. Alternative background field estimation methods allow the multiscale model to be applied flexibly according to the requirement of the calculation speed and accuracy. The feature of small degrees of freedom resolves the high computation complexity of the ac loss calculation model and reduces the memory requirement. All these merits make the multiscale model competitive in the calculation of ac loss.