Superconducting cables are described by current sheets using the continuum model of W. Carr Jr.  and assuming an anisotropic conductivity. Two different situations are considered: a) finite length of cable in spatially independent magnetic field; b) infinitely long cable in a periodical magnetic field.
Hartmann, R. A., Rem, P. C., & van de Klundert, L. J. M. (1987). Numerical solutions of the current distribution in superconducting cables. IEEE transactions on magnetics, 23(2), 1584-1587. https://doi.org/10.1109/TMAG.1987.1065018