Modeling AC ripple currents in HTS coated conductors by integral equations

In several HTS applications, the superconducting tapes experience the simultaneous presence of DC and AC excitations. For example in high-current DC cables, where the transport current is not perfectly constant, but it exhibits some ripples at different frequencies introduced by the rectification process (AC-DC conversion). These ripples give rise to dissipation, whose magnitude and possible influence on the device's cooling requirements need to be evaluated. Here we report a study of the AC losses in a HTS coated conductor subjected to DC currents and AC ripples simultaneously. The modeling approach is based on an integral equation method for thin superconductors: the superconducting tape is modeled as a 1-D object with a non-linear resistivity, which includes the dependence of the critical current density Jc on the magnetic field. The model, implemented in a commercial finite-element program, runs very fast (the simulation of one AC cycle typically takes a few seconds on standard desktop workstation): this allows simulating a large number of cycles and estimating when the AC ripple losses stabilize to a constant value. The model is used to study the influence of the flux creep power index n on the stabilization speed and on the AC loss values, as well as the effect of using a field-dependent Jc instead of a constant one. The simulations confirm that the dissipation level should not be a practical concern in HTS DC cables. At the same time, however, they reveal a strong dependence of the results upon the power index n and the form of Jc, which spurs the question whether the power-law is the most suitable description of the superconductor's electrical behavior for this kind of analysis.