Numerical modelling of dynamic resistance in high-temperature superconducting coated-conductor wires

The use of superconducting wire within AC power systems is complicated by the dissipative interactions that occur when a superconductor is exposed to an alternating current and/or magnetic field, giving rise to a superconducting AC loss caused by the motion of vortices within the superconducting material. When a superconductor is exposed to an alternating field whilst carrying a constant DC transport current, a DC electrical resistance can be observed, commonly referred to as 'dynamic resistance.' Dynamic resistance is relevant to many potential high-temperature superconducting (HTS) applications and has been identified as critical to understanding the operating mechanism of HTS flux pump devices. In this paper, a 2D numerical model based on the finite-element method and implementing the H-formulation is used to calculate the dynamic resistance and total AC loss in a coated-conductor HTS wire carrying an arbitrary DC transport current and exposed to background AC magnetic fields up to 100 mT. The measured angular dependence of the superconducting properties of the wire are used as input data, and the model is validated using experimental data for magnetic fields perpendicular to the plane of the wire, as well as at angles of 30 degrees and 60 degrees to this axis. The model is used to obtain insights into the characteristics of such dynamic resistance, including its relationship with the applied current and field, the wire's superconducting properties, the threshold field above which dynamic resistance is generated and the flux-flow resistance that arises when the total driven transport current exceeds the field-dependent critical current, I-c(B), of the wire. It is shown that the dynamic resistance can be mostly determined by the perpendicular field component with subtle differences determined by the angular dependence of the superconducting properties of the wire. The dynamic resistance in parallel fields is essentially negligible until J(c) is exceeded and flux-flow resistance occurs.