Dynamic resistance, which occurs when a HTS coated conductor carries a DC current under an AC magnetic field, can have critical implications for the design of HTS machines. Here, we report measurements of dynamic resistance in a commercially available SuperPower 4 mm-wide YBCO coated conductor, carrying a DC current under an applied AC magnetic field of arbitrary orientation. The reduced DC current, It/Ic0, ranged from 0.01 to 0.9, where It is the DC current level and Ic0 is the self-field critical current of the conductor. The field angle (the angle between the magnetic field and the normal vector of the conductor wide-face) was varied between 0° and 90° at intervals of 10. We show that the effective width of the conductor under study is ~12% less than the physical wire width, and we attribute this difference to edge damage of the wire during or after manufacture. We then examine the measured dynamic resistance of this wire under perpendicular applied fields at very low DC current levels. In this regime we find that the threshold field, Bth, of the conductor is well described by the non-linear equation of Mikitik and Brandt. However, this model consistently underestimates the threshold field at higher current levels. As such, the dynamic resistance in a coated conductor under perpendicular magnetic fields is best described using two different equations for each of the low and high DC current regimes. At low DC currents where It/Ic0  0.1, the non-linear relationship of Mikitik and Brandt provides the closest agreement with experimental data. However, in the higher current regime where It/Ic0 ≥ 0.2, closer agreement is obtained using a simple linear expression which assumes a current-independent penetration field. We further show that for the conductor studied here, the measured dynamic resistance at different field angles is dominated by the perpendicular magnetic field component, with negligible contribution from the parallel component. Our findings now enable the dynamic resistance of a single conductor to be analytically determined for a very wide range of DC currents and at all applied field angles.

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Dynamic resistance plays an important role in certain high-Tc superconducting (HTS) applications where an HTS coated conductor carries a DC current exposed to an AC magnetic field. Here, we report measurements of the dynamic resistance in a 4 mm-wide YBCO coated conductor under a perpendicular AC magnetic field at 77 K, 70 K, and 65 K. Dynamic resistance was measured at three different frequencies for the reduced current, i (It/Ic0), ranging from 0.04 to 0.9, where It is the DC current level and Ic0 is the self-field critical current of the conductor at each temperature. At all three temperatures, the threshold magnetic field (Bth) values increase with reducing DC current. These results show that, for a given set of applied conditions, dynamic resistance decreases with decreasing operating temperature, which we attribute to the temperature dependent increase in the critical current of the wire. We show that measured Bth values at all three temperatures agree well with the analytical values from nonlinear Mikitik and Brandt equation for i ≤ 0.2 and with a simple linear expression that assumes a current-independent penetration field for i > 0.2. We further show the measured Bth curves at different temperatures normalized by critical current density collapse into one common curve. The above result implies that dynamic resistance in coated conductors at different temperatures under perpendicular AC magnetic fields can be scaled simply using measured Ic0 values at those temperatures and analytical equations.

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In many high-temperature superconducting (HTS) applications, HTS coated conductors carry a DC current under an external AC magnetic field. In such operating conditions, dynamic resistance will occur when the traversing magnetic flux across the HTS conductors. Consequently, AC loss within the superconductors is composed of the dynamic loss component arising from dynamic resistance and the magnetization loss component due to the AC external magnetic field. In this work, the dynamic resistance and the total loss in a three-tape HTS coated conductor stack were measured at 77 K under perpendicular AC magnetic fields up to 80 mT and DC currents (Idc) up to the critical current (Ic). The stack was assembled from three serial-connected 4 mm wide Superpower wires. The measured dynamic resistance results for the stack were well supported by the results from 2D H-formulation finite element modelling (FEM) and broadly agree with the analytical values for stacks. The FEM analysis shows asymmetric transport DC current profiles in the central region of the superconductor. We attribute the result to the superposition of DC currents and the induced subcritical currents which explains why the measured magnetization loss values increase with DC current levels at low magnetic field. The onset of dynamic loss for the stack for low i (Idc/ Ic) values is much slower when compared to that of the single tape and hence the contribution of the dynamic loss component to the total loss in the stack is much smaller than that of the single tape. Dynamic loss in the stack becomes comparable to the magnetization loss at i = 0.5 and becomes greater than the magnetization loss at i = 0.7. Both magnetization loss and dynamic loss in the stack are smaller than those of the single tape due to shielding effects.

One of critical issues for HTS transformers is achieving sufficiently low AC loss in the windings. Therefore, accurate prediction of AC loss is critical for the HTS transformer applications. In this work, we present AC loss simulation results employing the H-formulation for a 1 MVA 3-Phase HTS transformer. The high voltage (HV) windings are composed of 24 double pancakes per phase wound with 4 mmwide YBCO wire. Each double pancake coil has 38 ¼ turns. The low voltage (LV) windings are 20 turn single-layer solenoid windings wound with 15/5 (15 strands of 5 mm width) Roebel cable per phase. The numerical method was first verified by comparing the numerical and experimental AC loss results for two coil assemblies composed of two and six double pancake coils (DPCs). The numerical AC loss calculated for the transformer was compared with the measured AC loss as well as the numerical result obtained using the minimum magnetic energy variation (MMEV) method. The numerical AC loss result in this work and experimental result as well as the numerical result using MMEV at the rated current agree to within 20%. Further simulations were carried out to explore the dependence of the AC loss on the gap between the turns of the LV winding. The minimum AC loss at rated current in the 1 MVA HTS transformer appears when the gap between turns is approximately 2.1 mm turn gap in the LV winding. This is due to the change of relative heights between the HV and LV windings which results in optimal radial magnetic field cancellation. The same numerical method can be applied to calculate AC loss in larger rating HTS transformers.

The dynamic resistance which occurs when a superconductor carrying DC current is exposed to alternating magnetic field plays an important role in HTS applications such as flux pumps and rotating machines. We report experimental results on dynamic resistance in a four-tape coated conductor stack when exposed to AC magnetic fields with different magnetic field angles (the angles between the magnetic field and normal vector component of the tape surface, ) at 77 K. The conductors for the stack are 4 mm-wide SuperPower SC4050 wires. The field angle was varied from 0 ˚ to 120 ˚ at a resolution of 15 ˚ to study the field angle dependence of dynamic resistance on field angle as well as wire Ic (B, ). We also varied the field frequency, the magnetic field amplitude, and the DC current level to study the dependence of dynamic resistance on these parameters. Finally, we compared the measured dynamic resistance results at perpendicular magnetic field with the analytical models for single wires. Our results show that the dynamic resistance of the stack was mainly, but not solely, determined by the perpendicular magnetic component. Ic (B,) influences dynamic resistance in the stack due to tilting of the crystal lattice of the superconductor layer with regard to buffer layers.  Index Terms-Dynamic resistance, HTS stack, Angle dependence.