[Paper Review] Estimation of Self-Field Critical Current and Transport-Magnetization AC Losses of Roebel Cables

Francesco Grilli, M. Vojenčiak+2 more|arXiv (Cornell University)|Oct 21, 2015

Magnetic Properties and Applications20 references3 citations

TL;DR

This study presents finite-element numerical models to estimate the self-field critical current and transport-magnetization AC losses in 31-strand Roebel cables made from HTS coated conductors from SuperOx and SuperPower. The models incorporate the angular dependence of critical current density $J_c(B,\theta)$ at 77 K and successfully predict both $I_c$ within 9% of experimental values and AC losses within 40% of calorimetric measurements under simultaneous AC transport current and field, confirming the method's accuracy for real-world superconducting winding applications.

ABSTRACT

Roebel cables made of HTS coated conductors are regarded as promising cables for winding applications in virtue of their large engineering current density and low losses. The composing meander-shaped strands are assembled very tightly into the cable, which results in a strong electromagnetic interaction between them. This interaction profoundly influences the effective self-field critical current ($I_c$) of the cable, which is much lower than the sum of the $I_c$s of the composing strands. Also the AC losses are influenced by the material's properties and by the geometrical configuration of the cable. Being able to predict the effective critical current and AC losses of such cables is very important for a proper design of applications: due to the complexity of the cable's geometry and of the material's properties, this prediction can only be performed with advanced numerical tools. In this contribution we use finite-element-based models to compute the effective $I_c$ and the AC losses of Roebel cables composed of 31 strands using tapes from two manufacturers. The AC losses are analyzed in the simultaneous presence of transport current and background perpendicular field proportional to the current, which mirrors the situation occurring in a winding. Our models include the angular dependence of $J_c(B,θ)$ at~77 K, which is very different for the two materials. By means of a successful comparison of the simulation results to experimental data obtained with a calorimetric method measuring the evaporation of liquid nitrogen, this work confirms the applicability and efficiency of our numerical techniques for simulating the electromagnetic behavior of Roebel cables and devices thereof.

Motivation & Objective

• To estimate the effective self-field critical current ($I_c$) of 31-strand Roebel cables made from HTS tapes from different manufacturers.
• To model and predict AC losses in Roebel cables under simultaneous AC transport current and perpendicular background magnetic field, mimicking real winding conditions.
• To validate numerical simulations against experimental calorimetric measurements of nitrogen evaporation due to AC losses.
• To investigate the influence of $J_c(B,\theta)$ angular dependence on cable performance, particularly for materials with distinct pinning characteristics.
• To assess the accuracy of finite-element modeling in capturing complex electromagnetic interactions in tightly packed Roebel cables.

Proposed method

• Finite-element magnetostatic modeling was used to extract $J_c(B,\theta)$ from measured angular $I_c$ dependencies of SuperOx and SuperPower tapes.
• The $J_c(B,\theta)$ model was implemented in time-dependent finite-element simulations to compute current density and magnetic field distributions across the cable cross-section during AC cycles.
• Simulations included the self-field effect and the interaction between transport current and applied perpendicular field, with field amplitude proportional to current (as in windings).
• The critical current of the cable was estimated using both global (MAX) and local (average) criteria, with comparison to experimental $I_c$ measurements.
• AC losses were calculated by integrating power dissipation over one AC cycle and compared to calorimetric measurements via nitrogen evaporation rate.
• The models accounted for material-specific $J_c$ anisotropy, including peak positions and angular broadening due to artificial pinning centers in SuperPower tapes.

Experimental results

Research questions

• RQ1 How accurately can finite-element models predict the self-field critical current of Roebel cables when accounting for inter-strand electromagnetic coupling and $J_c(B,\theta)$ anisotropy?
• RQ2 What is the impact of simultaneous AC transport current and perpendicular magnetic field on the current and magnetic field distribution in Roebel cables?
• RQ3 How do the AC losses in Roebel cables change under combined current and field excitation compared to single-excitation cases?
• RQ4 To what extent do numerical simulations of AC losses agree with calorimetric measurements in real cables?
• RQ5 How do differences in $J_c(B,\theta)$ between SuperOx and SuperPower tapes affect cable performance in terms of $I_c$ and losses?

Key findings

• The numerical model predicted the self-field critical current of the Roebel cable within 9% of the experimental value, demonstrating high accuracy despite complex inter-strand coupling.
• The model successfully reproduced the asymmetric current and magnetic field distributions caused by the simultaneous action of transport current and perpendicular field, with peak flux densities reaching 120 mT on one side and 70 mT on the other.
• AC losses increased by more than one order of magnitude when a background field was applied in proportion to the transport current, compared to losses under transport current alone.
• Calorimetric measurements confirmed that the simulated AC losses agreed with experimental data within 40%, validating the numerical approach for engineering design.
• The angular dependence of $J_c(B,\theta)$—particularly the presence of two distinct peaks in SuperOx and a flatter profile in SuperPower—significantly influenced both $I_c$ and loss behavior.
• The discrepancy between simulated and measured loss slopes, though not fully explained, was attributed to experimental uncertainties in the calorimetric technique and material variations.