Multi-layer Cables Research Articles

Synergistic ductility deformation and helical design of carbon nanotube fiber composites

Twisting attracts more attention in adjusting the mechanical behavior and failure mechanism of materials, which could be implemented to understand and design the deformation behavior of helical structures. Herein, we developed a general helical model to theoretically investigate the mechanical response and geometric evolution of twisted carbon nanotube (CNT) fiber. The in-situ experimental results of CNT fibers in scanning electron microscopy were used to verify the correctness of the theory. For the structure with a large helical angle, the interfacial force and uncoordinated interlayer deformation during elongation are the key factors determining its unique tensile-torsional coupled motion. By helical design, the elongation and deformation of brittle fiber in composite structure can be delayed to achieve synergistic fracture with ductile fiber. The breaking order of these two fibers under stretching can be further regulated by changing the degree of twisting. Based on these theoretical results, the outer brittle fibers could also be used to predict the tensile necking and fracture locations of inner ductile materials. This approach can be achieved by changing the helical geometry and failure strain, and this work would throw light on the mechanical design of multi-layer cables and fiber composites.

Study on the response of the winding direction of multi-layer CORC cable to its electromagnetic characteristics

A Conductor on Round Core (CORC) cable wound with a high-temperature superconductor is an important cable concept for high-current density applications. It is widely used in large power systems because of its advantages of good flexibility and high engineering current density. However, the complex design structure of CORC cable makes it very difficult to understand its electromagnetic properties (such as AC loss). In particular, the different winding directions of each layer in multi-layer cable have a great influence on its electromagnetic characteristics. In this paper, the H-method is used to solve the electromagnetism and mechanics equations. The influence of the winding direction of CORC cable on its electromagnetic field distribution characteristics, AC loss, and mechanical variation under the action of external magnetic field is investigated. The AC loss study of single-layer cable reveals that when the applied magnetic field is increased from 0.01 to 0.02 and 0.03 T, the AC loss peak of the cable increases by 107 and 103 orders of magnitude, respectively, indicating that the effect of low applied magnetic field on the AC loss of the cable is more significant. For multi-layer cables, cables with opposite winding directions have a greater depth of current density penetration than cables with the same winding direction. In addition, the mechanical variations of multi-layer cables with different winding orientations are explored. The results show that the Mises stress in the cable with the same winding direction is about 32% higher than that of the cable with the opposite winding direction, which indicates that the method of winding the cable in the opposite direction between adjacent layers of tape can avoid excessive mechanical stress.

Efficient finite element modelling of helical strand cables utilising periodicity

This paper proposes a repeated unit cell (RUC) FE modelling strategy for multilayered helical strand cables subject to tensile loading and bending with an initial tensile load. The approach utilises the axial periodicity in helical structures to reduce computational domain to two cable periods. A novel mesh creation method allowing the exact geometry of helical strands to be discretised into solid elements while maintaining flat end surfaces is proposed. Periodic boundary conditions (PBC) allowing for geometric and material nonlinearity are used to implement cyclic loads to study hysteresis in single and multilayered cables. Comparisons made to existing experimental and analytical results validate the models ability to capture hysteresis due to plasticity and geometric effects such as the stick–slip transition in bending. Examination of the cross-sectional stress distribution shows plasticity initiates at contact points at loads which are 25% of the load at which the cable tensile response deviates from linearity.

Understanding ac losses in CORC cables of YBCO superconducting tapes by numerical simulations

Alternating current (ac) losses in conductor-on-rounded-core (CORC) cables of YBCO high-temperature superconducting (HTS) tapes are a significant challenge in HTS power applications. This study employs two finite element analysis (FEA) models to investigate the contributions from different ac loss components and provide approaches for reducing ac losses in cables. An FEA model based on the T-A formulation treats the cross section of thin superconducting layers as 1D lines and, therefore, only can predict the ac loss generated by the perpendicular magnetic field. In contrast, the model based on H-formulation can be performed on the actual 2D rectangular cross section HTS tapes to provide the total ac losses generated by magnetic fluxes penetrating from both the edges and surfaces of HTS tapes, although this model requires more computing time and memory. The 1D and 2D simulation models were validated by cross comparing the results from both models and by comparing sub-section and full cross section models. Subsequently, two models relate cable design and operational parameters to the surface and edge losses of a two-layer CORC cable by considering the (1) relative contributions of edge and surface losses to the overall ac losses; (2) effect of the current distribution between inner and outer HTS layers on ac losses; (3) impact of the tape alignment on ac losses in each HTS layer; (4) influence of the thickness of HTS layers on ac losses; (5) effect of size and number of inter-tape gaps on ac losses; and (6) contribution frequency on the ac losses. The research results given in this paper are therefore not only valuable to suggest strategies for reducing ac loss in multi-layer cables but also for developing more accurate and effective methods to calculate ac loss in CORC HTS cables.

Study of the Fire Behavior of Multilayer Cables in a Mine Tunnel

Fires caused by cables occur frequently in mines, which endanger the safety of workers. To explore the characteristics of a multilayer cable fire in a mine tunnel, multilayer cable fire simulations were carried out using the Fire Dynamics Simulator (FDS). The influence of cable tray spacing, ignition position, and tunnel ventilation speed on the characteristics of the fire were studied. The results showed that these factors change the amount of contact between the cable and air, the heat accumulation, and the heat transfer by the flame interaction between the cables. It was also noted that increasing the spacing or wind speed both made the peak of heat release rate (PHRR) initially increase and then decrease. The influence of wind speed on the cable burnout rate in the upstream and downstream sides of the fire source was not consistent, and the wind speed had a sensitive effect on the cable burn out rate in the upstream side of the fire source. The higher the ignition position was, the longer the arrival time of PHRR was and the slower the fire developed. There was a higher burn velocity close to the ceiling. The cable hooks obstructed the cable fire. This study provides a theoretical basis for cable fire prevention and control in mine tunnels.

Experimental Study On the Critical Current of CORC Cable Under Cyclic Bending-straightening

To develop the application potential of conductor on round core (CORC) cables in the next generation of fusion magnets and accelerator magnets, fully automatic mechanized winding technology is required for the long CORC cables manufacturing. Meanwhile, the manufacturing and usage of the CORC cable are both limited by the strain sensitivity of the wound ReBCO tape on the CORC cable, because the processes may cause the superconducting layer of the ReBCO tape damaged when the strain limit is exceeded. The strains can arise from the manufacturing, bending, cooling, and operation of the cable and magnet, especially for the needed cyclic bending-straightening procedure for a long and multilayer cable winding layer by layer. Thus in this manuscript, a 1-m-long 12-layer CORC cable was manufactured to study the influence of cyclic bending on the critical current carrying performance of the CORC cable. It is consisted of 28 ReBCO tapes from Fujikura with 4 mm width and 0.05mm substrate thickness. The central core has an outer diameter of 3.85 mm. The cyclic bending-straightening experiment was conducted with a bending diameter of 900 mm and 700 mm, the Ic was tested at 77 K and self-field. After the cyclic bending test, the sample was bended to a diameter of 95 mm, which is planned to be used for the following insert solenoid coil, and has been verified no influence on the critical current carrying performance if bended without cyclic bending-straightening treatment. The results show that the required diameter for the reel experiencing cyclic bending-straightening procedure for ReBCO cable winding is suggested to be larger than 700 mm, especially for the equipment used for multilayer cables winding.

Failure prediction method of the anchor cables in the metro stations under unilateral deep excavation

To ascertain the anchor cable failure caused by the overturning and slipping of the station structure under unilateral excavation with zero distance from the station, this study takes the balance of the station-cable system under zero-distance unilateral excavation as the research object, and derives the total anti-slip force and anti-overturning moment of the cables based on the Rankine’s earth pressure theory and the force balance of the metro station. In addition, a novel failure prediction method is proposed to judge the failure of the station-cable system under various design conditions by taking the supporting capacity of the multi-layer cables as the evaluation index and multiple main influencing factors as the control indexes, so as to predict the structural risk. This method comprehensively considers multiple independent variables such as excavation depth, groundwater level, interval spacing and anchor cable design angle. Furthermore, based on Pearson correlation analysis, the sensitivity of the cable supporting force to various factors decreases in the following order: excavation depth > groundwater level > interval spacing > station width > cable design angle. Therefore, reducing the excavation depth is the most effective way to reduce the risk of the station-cable system caused by unilateral excavation. If it is necessary to increase the excavation depth, the cover-excavation reverse method can be used to indirectly reduce the effective excavation depth, thereby ensuring the safety of the structural system. This method can predict the risks of similar projects and reduce the occurrence of accidents.

A 3-D FDTD Thin-Wire Model of Single-Core Coaxial Cables With Multiple Conductive Layers

In this article, a thin-wire model of single-core coaxial cables with three or more conductive layers is proposed for transient analysis using the finite-difference time-domain (FDTD) method. The multilayer cable is regarded as a series of 2-conductor coaxial transmission lines. The currents in these lines can be, however, unbalanced, and may not return via earth, such as in the case of a direct lightning strike. The FDTD method is employed to evaluate electromagnetic coupling outside the cable. Frequency-dependent surface impedances of conductors are fully considered using the Bessel functions. They are integrated into the time-domain analysis with a vector fitting technique. Updating equations for both lossless and lossy cables are derived. The proposed model is validated transmission line theory analytically and with the traditional FDTD method numerically. Good agreements are observed. Finally, the proposed model is applied to analyze the transients in a cable connection station under a direct lightning strike.

Effects of interlayer distance and cable spacing on flame characteristics and fire hazard of multilayer cables in utility tunnel

Fire safety of utility tunnel, which is significantly affected with cables, has arouse public concern. This work experimentally investigated influences of interlayer distance (d) and cable spacing (s) on flame characteristics and fire hazard of multilayer cables in utility tunnel. Larger interlayer distance leads to higher flame height but lower flame width. The flame width decreases with an increase in cable spacing, while the flame height increases first and then reduces. The flame height reaches the highest value when s = 1.0 cm. Flame spread rate (vf) progressively increases from bottom layer to the top when d = 4.5–7.0 cm, while the trend is inverse for d = 9.5–10 cm vf over the middle layer presents the lowest value when s = 1.0–2.5 cm, while vf gradually reduces from the bottom layer to the top for s = 3–4 cm. The maximum temperature of the pyrolysis zone of top cable layer gradually decreases as d rises, but rises in the bottom layer. When s = 1.0–2.5 cm, the highest temperature is observed in the middle cable layer, while in the top layer when s = 3–4 cm.

Dependence of AC Loss on Structural Compactness of Superconducting Power Cables With Narrow Coated Conductors

Superconducting power cables with high capacity and high efficiency are regarded as a key technology to realize the next-generation power networks. Coated conductors (CCs) have been extensively used to develop such cables, particularly more than 4+ mm-wide CCs. Recent research shows that narrow CCs (e.g., 2 mm) prove to have a pronounced advantage on cable ac loss reduction. Besides, thanks to laser cutting technique, it becomes possible to cut wide CCs into narrow strips without considerable damage. Hence, narrow CCs are attracting more and more attention and have turned into a practical option for developing more efficient superconducting cables. However, studies on cables with narrow CCs are far from sufficient. This paper is to clarify the dependence of ac loss characteristics on structural compactness in superconducting cables consisting of narrow CCs. A set of numerical models have been developed on the 2D FEM method to simulate both monolayer and multilayer cables including 1-, 2-, 4-, and 6-layer cables. The former three types are practical cables currently under development and the last one is a future option for ultrahigh power transmission. Narrow CCs with the same critical current were selected for all the cables that are designed with various structures from compact to loose configurations. Within these cables, numerical electromagnetic analysis has been carried out to study and clarify how their loss characteristics are affected by structural compactness.

Vibration Control on Multilayer Cable Moving through the Crossover Zones on Mine Hoist

Mine hoist is an important piece of equipment in mine hoist systems, and we achieve deep mine hoist through the multilayer winding, but the cable always undergoes severe shock and vibration during the winding process, and the dynamic load and wear would greatly reduce the lifetime of the cable and cause potential safety hazard. In this paper, we start from the course of crossing over of winding cable, use the methods of differential geometry, mechanics, and mathematical analysis, study the movements of the crossover, and derive the important formula that can reduce the vibration of cable during the course of crossover: the formula about central angle of the crossover arc. The results display that four factors contribute to central angle of the crossover arc, that is, the gap of the rope grooves, friction coefficient of the cable, and diameter of the drum and the cable. The result can provide valuable information for designing multilayer winding mine hoist.

Dispersion Modeling and Analysis for Multilayered Open Coaxial Waveguides

This paper presents a detailed modeling and analysis regarding the dispersion characteristics of multilayered open coaxial waveguides or cables. The electromagnetic model is based on a layer recursive computation of axial-symmetric fields in connection with a magnetic frill generator excitation that can be calibrated to the current measured at the input of the cable. The layer recursive formulation enables a stable and efficient numerical computation of the related dispersion functions, as well as a detailed analysis regarding the analytic and asymptotic properties of the associated determinants. Modal contributions as well as the contribution from the associated branch-cut (nondiscrete radiating modes) are defined and analyzed. Measurements and modeling of pulse propagation on an 82-km-long HVDC power cable are presented as a concrete example. In this example, it is concluded that the contribution from the dominating axial-symmetric transverse magnetic mode is sufficient, and that the contribution from the branch-cut is negligible for all practical purposes, and in particular if the exterior domain is lossy. The main contribution of this paper is to provide the necessary modeling and analysis tools for a quantitative study of these phenomena.

AC loss reduction of outer-diameter-fixed superconducting power transmission cables using narrow coated conductors

AC loss reduction of superconducting power transmission cables is of great importance to promote their application in power grids. To meet certain installation conditions, cables are required to be designed with fixed outer diameters. This paper focuses on outer-diameter-fixed monolayer and multilayer (2-layer and 4-layer) superconducting power transmission cables constructed with coated conductors. Detailed numerical analysis of their AC loss reduction by replacing generally used 4-mm wide coated conductors with 2-mm wide narrow ones are presented. A 2-D FEM numerical model was developed to calculate AC losses of the cables. For detailed and comprehensive analysis, a series of variable parameters, such as number of layers, critical current density (Jc) distributions of coated conductors and load rate, are varied at well selected values to study their influences on the AC loss reduction. It is obtained and testified that 2-mm wide narrow coated conductors can effectively reduce AC losses in both monolayer and multilayer cables, even though more gaps are introduced. The knowledge presented is helpful for designing and fabricating practical cables.

Lateral critical current density distributions degraded near edges of coated conductors through cutting processes and their influence on ac loss characteristics of power transmission cables

The critical current density (Jc) near the edges of coated conductor could impact the ac loss characteristics of the cables comprising coated conductors. A wide coated conductor is often cut into narrower coated conductors in fabrication processes, and the Jc might degrade near the edges of coated conductors through the cutting process. This possible degradation of Jc could depend on cutting technology. Lateral Jc distributions of coated conductors cut by using a mechanical slitter as well as a laser were measured by the magnetic knife method. The measured coated conductors are fabricated by PLD process on clad type textured-metal substrates with reduced magnetism. Based on the degradation of Jc near the edges of coated conductors which was determined experimentally, ac losses of multi-layer cables as well as mono-layer cables were calculated numerically to evaluate the impact of the Jc degradation near the edges of coated conductors on the their ac loss characteristics.

Ac loss reduction of multilayer superconducting power transmission cables by using narrowcoated conductors

The ac loss characteristics of coated conductors are dominated by the magnetic fieldcomponent normal to their superconductor layer. Multilayer cables as well asmonolayer cables consisting of 4 mm-wide coated conductors (named 4 mm cables)and those consisting of 2 mm-wide coated conductors (named 2 mm cables) weredesigned, and numerical electromagnetic field analyses were performed in their crosssections to calculate their ac losses. Trapezoidal lateral critical current densityJc distributions with shoulders as well as uniform ones were assumed incoated conductors for the analyses. The former models the degradedJc near the edges of coated conductors. In the case of the monolayer, thecalculated ac losses of the 2 mm cables were comparable to those of the 4 mmcables. In the cases of the multilayers, the calculated ac losses of the 2 mmcables were obviously less than those of the 4 mm cables. The degradedJc near the edges of coated conductors more seriously affects the ac loss characteristics of the 2 mmcables than those of the 4 mm cables. However, even if we consider the influence of the degradedJc near the edges of coated conductors, 2 mm-wide coated conductors are more profitable than4 mm-wide coated conductors in multilayer cables from the viewpoint of ac loss reduction.

AC loss characteristics of superconducting power transmission cables: gap effect andJc distribution effect

Four groups of superconducting power transmission cables composed of coated conductors with 4.0 mm widthand 2 µm superconductor thickness have been designed, including mono-layer, two-layer, four-layerand six-layer cables. In each group, three types of cables have been constructed with gapsof different size between adjacent coated conductors, which are classified into small gap,medium gap and large gap. Moreover, different lateral critical current density(Jc) distributions, specifically a uniform distribution and a trapezoidal distribution with a slopingshoulder, have been assumed while calculating the AC losses of these cables numerically byusing a one-dimensional FEM model. Numerical results show that AC losses in mono-layercables are significantly influenced by gaps between coated conductors as well as lateralJc distribution, while cables with many layers are hardly affected by them. Thisproves that small gaps between coated conductors are not absolutely essentialto reduce AC losses in multi-layer cables, and a sloping shoulder of theJc distribution is more allowable in multi-layer cables than in mono-layer cables.The AC loss distributions among layers in six-layer cables are presentedand the reasons for different influences of the gap as well as the lateralJc distribution in mono-layer and multi-layer cables are discussed.

Numerical minimization of AC losses in coaxial coated conductor cables

Power cables are one of the most promising applications for the superconducting coated conductors. In the AC use, only small resistive loss is generated, but the removal of the dissipated heat from the cryostat is inefficient due to the large temperature difference. The aim of this work is to minimize the AC losses in a multilayer coaxial cable, in which the tapes form current carrying cylinders. The optimized parameters are the tape numbers and lay angles in these cylinders. This work shows how to cope with the mechanical constraints for the lay angles and discrete tape number in optimization. Three common types of coaxial cables are studied here to demonstrate the feasibility of optimization, in which the AC losses were computed with a circuit analysis model formulated here for arbitrary phase currents, number of phases, and layers. Because the current sharing is practically determined by the inductances of the layers, the optima were obtained much faster by neglecting the nonlinear resistances caused by the AC losses. In addition, the example calculations show that the optimal cable structure do not usually depend on the AC loss model for the individual tapes. On the other hand, depending on the cable type, the losses of the optimized cables may be sensitive to the lay angles, and therefore, we recommend to study the sensitivity for the new cable designs individually.

Numerical Analysis of AC Loss Characteristics of Multi-Layer HTS Cable Assembled by Coated Conductors

In this paper, effects of geometrical configuration on AC loss characteristics of cable conductors assembled by multiple YBCO tape in polygonal arrangement were numerically studied. The previously developed numerical model was modified to analyze the AC loss in the HTS tape in the polygonally assembled multi-layer cable. By using the numerical model, the influences of the cable geometrical parameters, especially the effects of the tape width and the tape-to-tape gap, on AC loss properties were evaluated.

Numerical calculation of AC losses in multi-layer superconducting cables composed ofcoated conductors

Two types of four-layer cables composed of coated conductors, with practicalcross-sectional geometries and various critical currents, were designed. The AC lossesin the cables were numerically calculated using a numerical model employing aone-dimensional FEM (1D model). The AC loss of each layer in the four-layer cable withw = 4.0 mm was compared with Norris’s analytical values,QNS, for a widerange of It/Ic. The AC loss in the first (innermost) layer was smaller than itsQNS, whereas the losses in the outer layers were close to, or much larger than, theirQNS. These results indicate that, in multi-layer cables, the AC loss in an outerlayer increases because of the magnetic field generated by the current inthe inner layers, and the entire AC loss of the cable is dominated by theAC losses in the outer layers. The AC losses in the four-layer cables withw = 3.3 mm, which had smaller gaps between the conductors, were smaller than those for the cable wherew = 4.0 mm. These results showed the effectiveness of using narrower conductorsand decreasing the gaps to reduce AC loss in multi-layer cables composedof coated conductors. The AC losses of the four-layer cable withw = 3.3 mmand Icc/w = 500 A cm−1 at 1 and 3 kArms were much smaller than the measured AC losses in cables fabricated withYBCO-coated conductors or BSCCO tapes. The AC loss in a four-layer cable with practicalcross-sectional geometries should approximately be within an order of magnitude of theirQNS.

AC Loss Reduction of Coaxial Multi-Layer HTS Cable

Reducing AC losses, cable size and cost of HTS tapes are required for the practical application of HTS power transmission line. We have theoretically investigated the relationship between AC losses and cable parameters such as layer radius and twisting pitch and direction in coaxial multi-layer HTS cable using our developed simulation method and revealed that the larger number of HTS tapes and twisting pitch are desirable for reduction of AC losses. In this paper we investigated influence of twisting pitch and direction on cable size and total amount of HTS tapes under a condition of constant AC losses. The diameter of each layer and total amount of HTS tapes in the cable with the same twisting direction are much smaller than those of alternate twisting direction. The cable with the same tape current would be better than that of the same layer current because of the smaller difference of the number of tapes per layer. In the cable with the same tape current, cable size decreases with the number of layers in spite of almost the same amount of total HTS tapes in the whole cable. In cable design, we cannot handle the restrictions of AC loss and load factor individually; it would be difficult to satisfy both the conditions of low AC loss and high load factor. AC losses could be reduced by increasing critical current of HTS tape without the restriction of load factor, while AC losses increases with the critical current with the restriction of load factor.