Rapid calculation methods for critical current of high-temperature superconducting excitation winding based on J-model

Abstract In high-temperature superconducting (HTS) excitation motors, the excitation current of the HTS winding is limited by its critical current. The rated excitation current must remain below this limit, with an adequate safety margin to minimize the risk of quenches. Rapid determination of this critical current is essential for improving motor design efficiency. Conventional finite element methods (FEMs) obtain the critical current by calculating the E – I curve, but the computation becomes time-consuming when numerous HTS tapes are involved. To overcome this limitation, this paper combines the J-model with multiple current control strategies to quickly determine the critical current. Considering the nonlinear variation of superconducting current density, control methods with strong robustness and strong convergence are adopted, such as hysteresis control, bisection method and PI control. The FEM based on the H formulation is employed to identify key control parameter and verify accuracy of the method. The proposed method is further used to analyze how key electromagnetic parameters of HTS excitation motors affect the critical current of the HTS winding. Results demonstrate that the method achieves high accuracy and computational efficiency. Finally, a ring-shaped coil and a racetrack-shaped HTS coil are used to verify the universality and accuracy of the method in other superconducting devices. In summary, the proposed critical current calculation method significantly improves the efficiency of performance evaluation and optimization for superconducting coils across diverse applications.