Source-linked AI summary
Roebel cables from REBCO coated conductors: a one-century-old concept for the superconductivity of the future
Wilfried Goldacker, Francesco Grilli, Enric Pardo, Anna Kario, Sonja I. Schlachter, Michal Vojenciak
TL;DR
HTS applications need conductors that provide both high current-carrying capacity and sufficiently low AC losses. This review surveys HTS Roebel cables, their design and characterization, and reports that the concept combines full transposition with compact, high-current cable structures. A practical boundary is that Roebel strands face critical issues around the edge, while the design’s flexibility is also identified as a disadvantage.
Problem
HTS applications require high-current conductors with sufficiently low AC losses, because many devices exceed the capacity of a single coated-conductor tape.
Method
The paper reviews HTS Roebel cable concepts, design and production methods, modelling, characterization, and alternative high-current cable designs.
Results
HTS Roebel cables provide full strand transposition with compact construction, and further development may scale their current capacity beyond 20 kA at fields.
Takeaways & Limitations
Further development of Roebel cables may support manufacturers in pursuing increased current-carrying capability and reduced AC losses.
Takeaways & Limitations
The Roebel strand around the edge is a critical issue, while the design’s flexibility is identified as a disadvantage.
Abstract
from arXiv · showhide
Energy applications employing high-temperature superconductors (HTS), such as motors/generators, transformers, transmission lines and fault current limiters, are usually operated in the alternate current (AC) regime. In order to be efficient, the HTS devices need to have a sufficiently low value of AC loss, in addition to the necessary current-carrying capacity. Most applications are operated with currents beyond the current capacity of single conductors and consequently require cabled conductor solutions with much higher current carrying capacity, from a few kA to up to 20-30 kA for large hydro-generators. A century ago, in 1914, Ludwig Roebel invented a low-loss cable design for copper cables, which was successively named after him. The main idea behind Roebel cables is to separate the current in different strands and to provide a full transposition of the strands along the cable direction. Nowadays, these cables are commonly used in the stator of large generators. Based on the same design concept of their conventional material counterparts, HTS Roebel cables from REBCO coated conductors were first manufactured at the Karlsruhe Institute of Technology (KIT) and have been successively developed in a number of varieties that provide all the required technical features such as fully transposed strands, high transport currents and low AC losses, yet retaining enough flexibility for a specific cable design. In the past few years a large number of scientific papers have been published on the concept, manufacturing and characterization of such cables. Times are therefore mature for a review of those results. The goal is to provide an overview and a succinct and easy-to-consult guide for users, developers, and manufacturers of this kind of HTS cables.
1. Introduction
HTS applications require conductors that combine high current capacity with sufficiently low AC losses. The introduction traces these requirements from Roebel’s 1914 copper cable to HTS Roebel cables and their geometric constraints.
- Many applications exceed the current capacity of a single coated-conductor tape and therefore require assembled high-current cables.
- HTS devices commonly operate in AC regimes, where keeping AC losses below an acceptable threshold is essential for superconducting solutions.
- Roebel’s 1914 copper cable reduced AC losses by segmenting conductors into insulated strands and fully transposing them along the cable direction.
- Roebel cables became standard high-current, low-loss conductors in large conventional generator stator windings.
- Applied superconductivity adopted the same strand-structure and transposition principles to reduce AC losses under AC currents or ramped fields.
- The EURATOM magnet in the Large Coil Task used an early superconducting Roebel cable made from transposed NbTi strands.
- HTS coated conductors cannot tolerate the tight in-plane bends of traditional Roebel geometries, requiring new cable solutions.
2. Cable design and preparation
The paper examines modifications to the basic Roebel cable design and alternative concepts for high-current cables. It also discusses cable design and production methods.
- The section discusses cable design and production methods for HTS Roebel cables.
- It examines possible modifications of the basic Roebel cable design and alternative concepts for high-current cables.
- The first HTS Roebel cable was demonstrated by Siemens Corporate Technology.
2.1. The evolution of HTS Roebel cables
HTS Roebel cables evolved from early coated-conductor demonstrations toward higher-current, more reliable and scalable designs, while retaining the Roebel concept of meander-shaped, transposed strands. Progress included improved punching, stabilization, strand homogeneity, current capacity and reduced AC losses.
- Manufacturing development: Precision punching at KIT enabled the first REBCO coated-conductor Roebel cable, while IRL pursued automated fabrication of long cable lengths.Subsequent designs modified strand structure to increase current and improve thermal and mechanical stability.
- Early demonstrations: The first coated-conductor Roebel cable used 16 punched DyBCO strands and carried 500 A at 77 K, about half the sum of individual-tape critical currents.The unstabilized cable later burned through because it lacked quench protection.
- Current performance: Self-field reduced transport current by 60% relative to the sum of individual-strand critical currents because of the generated self-field.The self-field pattern was calculated numerically using a Biot-Savart-based method.
- Scaling current capacity: A 45-strand cable made from 3-fold stacks carried 2.6 kA at 77 K in self-field over 1.1 m, with an 18.8 cm transposition length.Increasing transposition length to add more strands is constrained by the material’s limited in-plane bending ability.
- Applications and development: Roebel cables’ reduced AC losses compared with stacked tapes motivated their application in HTS transformers.The REBCO Roebel structure was proposed in 1997, but bending, strand shaping and assembly solutions were developed later.
2.2. Design parameters
Roebel cable design is specified through geometric parameters governing transposition, spacing, crossover shape and mechanical stress. Numerical calculations and manufacturing constraints guide parameter choices for current capacity, mechanical performance and assembly.
- Geometric parameters: The cable geometry is described by tape width, transposition length, clearance, crossover width, inter-strand gap, crossover angle, fillet radius and inner radius.These parameters are shown in the Roebel-cable nomenclature schematic.
- Geometric parameters: The transposition length helps determine the number of applicable strands for a specific application.Current values are 115.7 mm for 4 mm-wide tape and 126 mm for 12 mm-wide tape.
- Manufacturing constraints: IRL selected a larger cable-centre clearance and fewer strands per unit cable length to better match automated assembly machinery.Hand-made KIT cables have narrower inter-strand gaps than fully automatic IRL cables.
- Mechanical performance: Increasing the inner radius and using a sharp outer crossover edge reduces von Mises stress under tensile loading.These trends were obtained from calculations targeting mechanical performance and current capacity.
- KIT parameter choices: KIT commonly uses an inner radius Ri = 2 mm, 1-2 mm strand-edge clearance for wider tapes, and a 30° crossover angle.For WT = 4 mm, no strand-edge clearance is used, provided there is sufficient inter-strand gap.
- Manufacturing constraints: When several strands are cut in parallel from wider coated-conductor material, crossover width WX is predetermined by the meander period, strand width and edge-clearance geometry.For a single strand, crossover width and angle can be adjusted for current performance.
- Mechanical performance: Geometrical constraints can make the crossover section the current-limiting part of the strand.The inner radius opposite the outer fillet is important for managing stresses at this point.
2.3. Production methods
Roebel-cable production combines strand formation with challenging assembly, using mechanical punching and specialized machinery to balance precision, speed, flexibility, and cable density.
- Laser cutting is flexible and avoids defects, but its production speed is not economically attractive.
- Mechanical punching was identified as the best strand-forming method, achieving <50 micron precision for strand width.
- Punching offers adjustable transposition lengths and typically processes 50 meters of tape per hour.
- Cable assembly requires complex bending around strands while avoiding over-bending or plastic deformation.
- Innovative machinery enables long-length production, while KIT still makes samples up to 5 m by hand.
- Multi-stacking enables dense packing, reduced central gaps, and adaptable cable designs, but automatic stacking remains difficult.
2.4. Design options and modifications
Roebel-cable performance can be modified through strand count, transposition, stacking, coupling, stabilization, insulation, and filamentation, with application-specific trade-offs.
- Design parameters: Increasing strand number enhances critical current, while transposition length must satisfy application requirements such as coil size and loss reduction.
- Multi-stacking: Multi-stacking increases current capability, but stacked tapes are not fully transposed and are generally unsuitable for windings.
- Multi-stacking: For bus bars or straight high-current lines with limited bending, multi-stacking can enhance cable current carrying capability.
- Strand coupling: Ag/resin paste provides moderate coupling with tolerable coupling AC losses, but impregnation makes the cable stiff and unsuitable for strong bending.
- Strand coupling: An inter-strand resistance of 0.1 mΩ caused no significant coupling-loss increase up to 200 Hz while allowing current sharing.
- Stabilization and insulation: A typically 20 μm epoxy-acrylate coating was applied without affecting current capacity, although coverage at sharp conductor edges is imperfect.
- Characterization: Representative transport-current measurements are complicated because connecting all strands redistributes current at the contacts.
2.5. Alternative Concepts
Alternative HTS cable concepts include CORC and TSTC designs, offering different combinations of twisting, fabrication simplicity, current scalability, flexibility, and engineering current density.
- CORC: CORC cables helically arrange coated conductors around a cylindrical former in one or several layers.
- CORC: CORC provides strand twisting, easy fabrication, and flexible current capacity through the number of tapes used.
- CORC: CORC assembly has been performed by hand, and its engineering current density is significantly lower than that of Roebel cables.
- CORC: CORC cables demonstrated self-field critical currents of 2800 A and 7561 A at 77 K.
- TSTC: TSTC solders three coated-conductor stacks into grooved copper rods and twists them, but thermal strains remain a problem.
- TSTC: Long-length assembly of thick TSTC stacks had not yet been performed.
- CORC: The CORC concept was developed for LHC-upgrade activities alongside other MgB2 and HTS coated-conductor cable concepts.
- Comparison: Figure 10 presents CORC and TSTC as cable designs alternative to the Roebel concept.
3. Physical properties of Roebel cables
Roebel cables carry high currents, but their transport performance depends strongly on self-field, temperature, cable geometry, and mechanical loading. Measurements demonstrate substantial capacity at both 77 K and lower temperatures, while transverse stress and strand-edge damage remain important constraints.
- Current distributions and self-field pattern: Self-field reaches several hundred mT near cable edges and can substantially reduce critical current.Biot–Savart and FEM analyses account for the complex field distribution, field orientation, and coated-conductor anisotropy.
- DC transport currents at 77 K: 2.6 kA at 77 K was the highest reported self-field transport current, measured in a 15 × 3-fold stacked-strand cable.The cable used 12 mm-wide SuperPower coated conductor and had a 188 mm transposition length.
- DC transport currents at 77 K: At 77 K, wide high-current cables provide 1–2 kA, while smaller cables provide 0.3–0.8 kA without strand stacking.Multi-stacking can increase current capacity by a factor of 2–3, subject to fabrication and application restrictions.
- DC transport currents below 77 K: 14 kA was reached at 4.2 K in a 12 mm-wide KIT cable at approximately 0.5 T parallel background field.The cable contained ten 5.5 mm-wide strands, and transport current increased by more than a factor of 10 from 77 K to 4.2 K.
- Mechanical properties of Roebel cables: Transverse loading can be highly nonuniform: some strands degraded by more than 30% at only 10 MPa, despite other tests showing less than 2% degradation above 100 MPa.Extracted strands showed local surface damage associated with the meander structure.
4.1. Experimental techniques for measuring AC losses
AC-loss measurements use voltage loops or taps for transport loss and pickup-coil or calibration-free methods for magnetization loss. The complex transposed geometry makes tap placement, lead subtraction, finite-sample effects, and modeling assumptions important to interpretation.
- Transport-loss measurements: Transport AC loss is commonly measured from in-phase voltages using taps soldered to a strand over an integer multiple of the transposition length.This averages the loss signal over the strand’s different cable positions.
- Transport-loss measurements: For N strands, transport loss can be estimated from the mean in-phase voltage of strand loops, using Icable, loop length d, and frequency f.The method follows single-tape transport-loss principles while accounting for multiple strand voltage measurements.
- Transport-loss measurements: Current-lead taps simplify placement but include a usually large resistive signal that must be subtracted from the cable voltage.The lead signal can exceed the cable signal, making this approach particularly sensitive to subtraction accuracy.
- Magnetization-loss measurements: Magnetization loss is measured on a sample at least one transposition length long in a uniform applied field, using pickup coils or calibration-free methods.Short samples can admit magnetic flux through their ends, complicating estimates of strand or filament uncoupling.
- Analytical modeling: Bean’s slab model provides an approximate loss estimate when applied field greatly exceeds self-field, using strand or cable width for uncoupled or coupled cases.The model assumes constant critical current density and a sharp critical-state E(J) relation.
- Numerical modeling: Numerical models represent cable layers and current sharing between strands more realistically than analytical models, but results depend on the assumed current distribution.Models may allow currents to distribute freely between electrically parallel strands or impose equal sharing; equal distribution gives lower losses.
4.3.1. Transport loss
Transport loss depends on current, field orientation, strand coupling, spacing, and conductor architecture. Transposition can reduce loss, but comparisons show that spacing and self-field geometry also contribute substantially, while striation and substrate effects alter the loss mechanisms.
- Geometry and spacing: Larger strand spacing increases critical current and decreases transport loss, but reduces engineering current density.Spacing is therefore useful when transport loss dominates, with a direct density trade-off.
- Transport-loss comparisons: At It=0.99Ic, an eight-strand Roebel cable had about 30% lower transport loss than a four-tape series-connected stack.At low currents the losses were similar, whereas the Roebel cable was lower at medium-high currents.
- Transport-loss comparisons: The 30% lower loss versus a stack was attributed mainly to the Roebel cable’s central gap, which lowers self-field through looser strand spacing.This comparison therefore does not isolate transposition as the sole source of loss reduction.
- Effect of transposition: Transposition reduced transport loss by about 20% relative to untransposed strands.Because current was already approximately balanced in the thin cables without transposition, the reduction was moderate.
- Frequency dependence: Uncoupled-cable magnetization loss changes by roughly 10% over one frequency decade, with coupling important at low fields or frequencies and curves converging at higher fields.At high fields, the coupling contribution becomes less important.
- Coupling and striation: Striated strands further reduce loss, while coupled cables can show higher loss than uncoupled cables because they behave as monolithic conductors at high field.Coupling currents dominate at low frequencies in the coupled case.
- Field orientation: For perpendicular fields, transport loss scales with the perpendicular field component and increases with transport current; more parallel fields reduce the relative magnetization contribution.The balance between transport and magnetization losses changes with field orientation.
5. Summary and outlook
HTS Roebel cables combine fully transposed strands, compact designs, high current capacity, reduced AC losses, and useful bending flexibility. Their commercial availability and continued development support applications from rotating machinery and transformers to high-field and fusion magnets, although mechanical-stress tolerance remains to be conclusively proved.
- Technical features: Full strand transposition in a compact cable design leads to high engineering current densities for AC applications.The review identifies this as a distinctive Roebel-cable feature.
- Technical features: Design options can increase transport current, stabilization, and geometry while retaining good bending capability for coil applications.Applications include stator and rotor windings, transformers, and magnets.
- Outlook: Roebel cables are commercially available, while higher production speed, lower coated-conductor material use, and greater design flexibility may expand market penetration.An advanced route would begin REBCO coating on an already meander-shaped Roebel substrate to reduce production costs.
- Applications: REBCO coated conductors can increase current-carrying capability by exceeding one order of magnitude when operating below 77 K.The review highlights particular interest in operation at 4.2 K and above for magnets.
- Limitations: For accelerator and high-field magnets exceeding 40 T, tolerance to mechanical stresses still requires conclusive proof.This remains a stated boundary for the proposed applications.
- Applications: More than 20 kA appears scalable at around 13 T and 4.2–50 K, matching requirements identified for next-generation DEMO fusion magnets.The passage describes this as potential rather than a conclusively demonstrated operating limit.