<i>J</i>-<i>Φ</i> coupled model based on integral methods and magnetic networks for superconductor

Abstract Current numerical simulations of superconducting tapes in electrical applications predominantly utilize the H and T-A formulations within the COMSOL platform. In comparison, the integral method (also known as the J model) can enhance computational speed by one to two orders of magnitude. However, the integral method only focuses on the numerical modelling of the superconducting region, leading to two main drawbacks: it cannot model ferromagnetic materials in space, nor the distribution of external magnetic fields outside the superconducting tape. These limitations hinder the application of the integral method as a fast computation model. This paper innovatively couples the magnetic network model ( Φ ) with the integral method model ( J ) which is named J-Φ by using MATLAB. Three critical challenges and their solutions are addressed, including the transmission of external magnetic fields, the calculation of the K matrix, and the selection of the coupling time step. The J-Φ coupled numerical model not only resolves the two mentioned limitations but also maintains a very high computation speed—computation time is only 1% of that of the T-A model. The J-Φ formulation’s calculations for magnetic field distribution, current distribution, dynamic loss and AC loss are consistent with those of the T-A and H formulation. The J-Φ model developed here will accelerate the application of the J model in electrical equipment.