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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 J c 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 J c 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 J c , which spurs the question whether the power-law is the most suitable description of the superconductor’s electrical behavior for this kind of analysis. [ABSTRACT FROM AUTHOR]

Abstract: Finite-element models are a powerful and widely used tool for evaluating the ac losses of HTS tapes and wires as well as of assemblies such as cables and coils. The H-formulation, which uses the magnetic field components as state variables, has proved to be an efficient implementation to solve 2-D problems, involving infinitely long or axially-symmetric geometries; an excellent agreement with experimental data has been found in many cases. However, the simulation of certain applications requires a full 3-D model. In this paper we report on the development of a 3-D model based on the H-formulation. We describe the implementation of Maxwell equations, the imposition of current constraints and we discuss the issues related to meshing 3-D volumes. The model is validated by comparing the results with those obtained with 2-D models in cases that can be investigated in 2-D; then, it is used to simulate cases that can be handled only in 3-D. [Copyright &y& Elsevier]

For describing the E–J relation of high-Tc superconductors (HTS) in power applications, where the applied current I is generally limited by Ic, the critical state model, a piecewise linear generalization, or a simple power-law of the type E=Ec(J/Jc)n are most often used. The power-law cannot be used for modelling the E–J relation with I≫Ic due to the unbound exponential increase of the electric field for currents above Ic, while in reality the non-linear HTS resistivity is limited by its normal state value. This paper presents a modified E–J model for describing the V–I characteristic of HTS tapes with applied currents largely exceeding Ic. This model is based on the power-law in combination with a parallel metallic branch and has a limited resistivity––the HTS one in the normal state. It can be used for black-box modelling of superconductors in a unlimited current range, as well as for numerical modelling of superconducting devices, which can be operated at currents far exceeding Ic; for example fault-current limiters or cables with over-critical current excursions. The model has been tested in a simple numerical implementation and the modified power-law has been implemented in finite element method simulations. It is shown that for bulk material with currents above 1.3–2Ic (depending on the n-value), the usual power-law results in excessive AC loss estimation. [Copyright &y& Elsevier]

Different measurement techniques have demonstrated that due to better alignment during the manufacturing process, the central filaments in multifilamentary Bi-2223 tapes have higher critical current density than the outer filaments. A numerical model of non-twisted tapes has been used in finite-element-method simulations. The model incorporates non-uniform lateral Jc distribution in accordance with direct Ic measurements, made along the width of a Bi-2223 tape. Two types of simulations are performed on 7 and 19-filamentary tapes with applied transport current––one with constant Jc in all filaments, and another with a Jc(x) dependence. The current distribution and AC loss in each filament are numerically calculated and compared. It is demonstrated that the current density distribution and power dissipation vary considerably in the different filaments, which is due to the position of the filament with respect to the edge of the tape and the different Jc values along the width. [Copyright &y& Elsevier]

• Many present HTS cable designs imitate twisted LTS cable designs. • AC losses calculated by analytical methods but supported by experimental results. • Main loss: hysteretic in twisted stacks, saturated coupling in non-twisted stacks. • All magnets built with twisted or non-twisted tapes have similar large losses. • Twisting a tape stack has modest effect on AC losses and inductance distribution. • HTS magnet design should be based on rigorous physical analysis, not on imitation. Almost all present High Temperature Superconducting (HTS) cable designs for magnets are based on twisted or transposed concepts that were developed for Low Temperature Superconducting (LTS) cables. However, requirements for LTS materials (like filament twisting) are in general not valid for HTS materials, which are extremely stable; for example, non-twisted multifilamentary Bi-2223 tapes have been successfully used in several magnets. Is twisting necessary for HTS cables? We investigated inductance mismatches and AC losses by numerical and analytical methods in twisted and non-twisted stacks of coated conductors; various experiments reported in the literature support the analysis. Large (hysteretic) losses are common in all magnets built with tapes and are far larger than in magnets built with LTS multifilamentary conductors, because of the aspect ratio and large width of the tape. In small magnets, losses and residual magnetisation could be reduced by replacing a wide tape with a non-twisted stack of narrow tapes. In large cables, we have found that twisting a stack of tapes reduces losses only marginally. Therefore, non-twisted stack cables could be designed to have losses comparable to those of twisted ones. Some examples of non-twisted large cables for fusion applications are discussed: non-twisted stack designs can be simpler, more robust and cost effective than twisted ones, but would require additional R&D. [ABSTRACT FROM AUTHOR]