Thermal-electromagnetic modeling of superconductors

The numerical modeling is a very useful tool to design superconducting power devices. The current distribution across superconductors is important to calculate for example the AC losses, a key quantity. Several developments have been carried out and they give satisfying results. Nevertheless they assume in general a constant temperature operation. This hypothesis is often not valid: AC losses induce temperature increases. The operation of the SC fault current limiter itself implies temperature variations. We present a coupling between electromagnetic and thermal phenomena. For that, we chose a temperature-dependant power law model for the J(E) relation under the critical temperature. The problem is split into two with their physical models (electromagnetic and thermal) and their dedicated finite element solver. This structure makes possible different time steps, solvers, but also meshes. The coupling is performed by separately and successively solving the problems and by transferring data between the solvers. A special software, the supervisor, manages the total process. It pilots the solvers and the data exchanges. The solvers are based on the finite element code flux(c), developed by the CEDRAT company and the LEG. Validations have been carried out on a simple geometry: two infinite slabs supplied by a current. The results show that the temperature is an important factor for the current distribution across the superconductor, and thus for the AC losses. The cases of homogeneous and non-homogeneous temperature were studied by changing the thermal parameters. They also validate the interest of our coupling method and its feasibility.