Prediction of resistive and hysteretic losses in a multi-layer high-Tc superconducting cable

In this work, a model of a multi-layer high-Tc superconducting (HTS) cable that computes the current distribution across layers as well as the AC loss is presented. Analyzed is the case of a four-layer cable, but the developed method can be applied to a cable with an arbitrary number of layers. The cable is modelled by an equivalent circuit consisting of the following elements: nonlinear resitances, linear self and mutual inductances, as well as nonlinear, hysteretic inductances. The first take into account the typical current-voltage relation for superconductors, the second introduce coupling among the layers and depend on the geometrical parameters of the cable, the third describe the hysteretic behaviour of superconductors. In the presented analysis, the geometrical dimensions of the cable are fixed, except for the pitch length and the winding orientation of the layers. These free parameters are varied in order to partition the current across the layers such that the AC loss in the superconductor is minimized. The presented model allows to evaluate rapidly the current distribution across the different layers and to compute the corresponding AC loss. The rapidity of the computation allows calculating the losses for many different configurations within a reasonable time. The model has so firstly been used for finding the pitch lengths giving an optimal current distribution across the layers and for computing the corresponding AC loss. Secondly, the model has been refined taking into account the effects of the magnetic self-field, which, especially at high currents, can sensibly reduce the transport capacity of the cable, in particular in the outer layers.