Self-Consistent Modeling of the <formula formulatype="inline"><tex Notation="TeX">$I_{c}$</tex></formula> of HTS Devices: How Accurate do Models Really Need to Be?

Abstract

Numerical models for computing the effective critical current of devices made of high-temperature superconducting tapes require the knowledge of the J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (B,θ) dependence, i.e., of the way the critical current density J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> depends on the magnetic flux density B and its orientation θ with respect to the tape. In this paper, we present a numerical model based on the critical state with angular field dependence of J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> to extract the J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (B,θ) relation from experimental data. The model takes into account the self-field created by the tape, which gives an important contribution when the field applied in the experiments is low. The same model can be also used to compute the effective critical current of devices composed of electromagnetically interacting tapes. In this paper, we consider three examples: two differently current-rated Roebel cables composed of ten strands from REBCO coated conductors and a power cable prototype composed of 22 Bi-2223 tapes. The critical currents computed with the numerical model show good agreement with the measured ones. The simulations reveal also that several parameter sets in J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (B,θ) give an equally good representation of the experimental characterization of the tapes and that the measured I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> values of cables are subjected to the influence of experimental conditions, such as I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> degradation due to the manufacturing and assembling process and nonuniformity of the tape properties. These two aspects make the determination of a very precise J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (B,θ) expression probably unnecessary, as long as that expression is able to reproduce the main features of the observed angular dependence. The easiness of use of this model, which can be straightforwardly implemented in finite-element programs able to solve static electromagnetic problems, is very attractive both for researchers and device manufactures who want to characterize superconducting tapes and calculate the effective critical current of superconducting devices.