Experimental evidence for an interaction effect in the coupling losses of cabled superconductors

It is experimentally demonstrated on a series of one-stage superconducting cables, composed from multifilamentary superconducting wires, that the coupling current losses being induced in the wire and in the cable matrix, contain interaction loss terms directly proportional to the wire twist pitch I_w. This proves partly their theoretically expected l_c.l_w-dependence. Different twisting directions in a one or multistage superconducting cable increase the ac losses and should be avoided. The magnitude of the effect can become important.     

A 3-D Numerical Model to Estimate the Critical Current in MgB<Subscript>2</Subscript> Wire and Cable with Twisted Structure

Due to the low material cost, high critical transition temperature and high-current-carrying capacity, MgB₂ round wire with twisted filaments has great potential for applications in engineering. Therefore, it is important to estimate their critical current for optimizing and realizing high-powered wire and cable. A 3-D model is presented to calculate the critical current of wire and cable with twisted filaments. The critical current is estimated based on the Biot-Savart law and self-consistent model. A comparison between 2-D and 3-D models is performed for the wire. We consider the effect of twist pitch on the critical current. Moreover, the critical current of 6-around-1 cable with different twist pitches is analyzed and discussed using the 3-D model. It can be found that twist pitch of filaments plays an important role on the critical current. The model and method may also be useful for other superconducting wires and cables.     

An additional loss source in cabled multifilamentary superconductors

It is shown that irregularities in the twist rate of a multifilamentary superconducting strand, which may occur in the cabling or braiding process of a high current conductor, give rise to additional matrix currents and enhanced ac losses. Electrodynamic equations for matrix and filament currents in a strand with a sudden change in twist rate are derived and damped wave solutions are given for an external harmonic field as well as for a ramp field. Inder unfavourable conditions the associated loss enhancement may become comparable to the regular matrix losses. This is also verified experimentally by magnetization measurements. Some recommendations for cable design are given.     

Investigation on AC loss of a high temperature superconducting tri-axial cable depending on twist pitches

High temperature superconductor (HTS) cables have been intensively studied because they are more compact compared with conventional copper cables. Since it is strongly expected that the HTS cables replace conventional power lines, some HTS cables are designed, manufactured, installed in power grids and tested to demonstrate full time operation. Recently, a tri-axial cable composed of three concentric phases has been developed, because of its reduced amount of HTS tapes, small leakage field and low heat loss when compared with single phase and co-axial HTS cables. The layers inside the tri-axial cable are subject to azimuthal fields applied from inner layers and axial fields applied from outer layers with different phase from their transport currents. These out-of-phase magnetic fields should be calculated under the condition of the three phase-balanced distribution of the tri-axial cable, and thereby AC losses should be evaluated. In this paper, the AC loss in the tri-axial HTS cable consisting of one layer per phase is theoretically treated for simplicity. The AC losses in the cable are calculated as functions of the twist pitches of HTS tapes. It is found that the AC losses rapidly decrease with increasing twist pitch.     

Losses in superconducting cables in pulsed magnetic fields

Measurements have been carried out of superconducting cables of different types in pulsed magnetic fields. Three types of samples have been made from multifilamentary Nb_0.5  Ti_0.5 superconductors: one, a cluster of isolated wires; two, a double-layer twisted flat cable; and three, one-layer twisted tube samples. Dependences have been studied of ac losses on the amplitude, direction and change velocity of the magnetic field as well as on the diameter of filaments and twist pitch. It is shown that the ac losses in unsoldered samples are close to those in the cluster of isolated wires.     

Circuit analysis model for AC losses of superconducting YBCO cable

Information about AC losses and electromagnetic behaviour is essential when designing superconducting cables. In this work, AC losses of coaxial YBCO cables are determined using circuit analysis based computational model tailored for the needs of the YBCO cable design work. In the equivalent circuit superconducting layers are connected in parallel, the layers have an inductive coupling between each other and AC loss within a layer generates an effective resistance. The layer currents can be solved from a set of circuit equations. The computational model takes into account that the current in the cable creates magnetic field, which generates magnetisation loss and affects strongly the critical current of the YBCO tapes. The model was applied on several coaxial superconducting YBCO cable designs, which had nominal currents of 1-10 kA (rms). Low AC loss values were predicted for these compact YBCO cable designs. For example, AC losses less than 4 W/m were predicted for 10 kA cables.     

Investigation of current distribution conditions in multiwire superconducting cables under the influence of self-magnetic field

The current distribution in a multi-wire round cable subjected to self-magnetic field is considered in this paper. A theoretical analysis of the current distribution process was made. The influence of layer parameters on the current distribution between the layers was determined. The theoretical analysis showed that it was necessary to twist two external layers into different directions with a minimum pitch to increase the current in the internal layers. It was shown that manufacturing round cable with more than two superconducting layers was unnecessary. Formulae are given allowing determination of the current in all layers. The theoretical conclusions were confirmed by the experimental results.     

Comparison study of cable geometries and superconducting tape layouts for high-temperature superconductor cables

High-temperature superconductor (HTS) rare-earth-barium-copper-oxide (REBCO) tapes are very promising for use in high-current cables. The cable geometry and the layout of the superconducting tapes are directly related to the performance of the HTS cable. In this paper, we use numerical methods to perform a comparison study of multiple-stage twisted stacked-tape cable (TSTC) conductors to find better cable structures that can both improve the critical current and minimize the alternating current (AC) losses of the cable. The sub-cable geometry is designed to have a stair-step shape. Three superconducting tape layouts are chosen and their transport performance and AC losses are evaluated. The magnetic field and current density profiles of the cables are obtained. The results show that arrangement of the superconducting tapes from the interior towards the exterior of the cable based on their critical current values in descending order can enhance the cable’s transport capacity while significantly reducing the AC losses. These results imply that cable transport capacity improvements can be achieved by arranging the superconducting tapes in a manner consistent with the electromagnetic field distribution. Through comparison of the critical currents and AC losses of four types of HTS cables, we determine the best structural choice among these cables.     

Coupling losses in superconducting,torus-shaped wires due to applied magnetic field changes

The stationary electric field, current pattern and coupling losses in a multfilamentary, superconducting, twisted, torus-shaped wire are calculated for a torus placed in a homogeneous magnetic field increasing in time at a constant rate and parallel to the torus plane. The radius of the wire is considered to be small compared to the mean radius of the torus. An important parameter for the problem is the ratio between the twist length of the superconducting filaments and the mean radius of the torus. In the configuration considered this parameter is small. The coupling losses are approximately inversely proportional to the square of this ratio. Furthermore, for the wire to have unsaturated parts, the analysis shows that the rate of change of the magnetic field must decrease when this ratio increases.Deceased.     

Experimental results of tri-axial HTS cable

Recently, a tri-axial cable composed of three concentric phases has been intensively developed, because it has advantages such as reduced high-temperature superconducting (HTS) tape, small leakage field and small heat loss as compared to three single-phase cables. However, there is an inherent imbalance in the three-phase currents in tri-axial cables due to the differences in the radii of the three-phase current layers. The imbalance of the currents causes additional loss and a large leakage field in the cable, and deteriorates the electric power quality. We have already proposed that it is possible to obtain a balanced three-phase distribution by adjusting all of the twist pitches. In order to verify the theory, we designed and fabricated a 1-m-long tri-axial HTS cable and carried out the cable test. The balanced three-phase voltages of the cable were measured by supplying an AC transport current with frequency from 50 to 500 Hz at 77 K. It is found from the test results that the balanced three-phase distributions can be realized by adjusting all of the twist pitches.     

AC Loss of a Multi-Layer per Phase Tri-Axial HTS Cable with?Balanced Current Distribution

Recently, high-temperature superconductor (HTS) cables have been widely studied because of their compactness and high power capacity compared to conventional copper cables. In HTS cables, AC loss is an important issue since large losses reduce the efficiency of the power line. Among HTS cables, tri-axial cable is under intensive investigation recently, since it has a smaller amount of HTS tapes, small leakage fields and small heat loss in leak when compared with the three single-phase cables. For realizing high current capacity, more than one layer is required for each phase; therefore AC loss of the multi-layer tri-axial HTS cable should be carefully examined. In the tri-axial cable, different phase currents produce the out-of-phase magnetic fields on the other phase layers. In case of multi-layer arrangement, net magnetic fields on layer surfaces may exceed the penetration field of the HTS tape. Therefore in this paper, we analyze the AC loss of a tri-axial HTS cable which is composed of two layers per phase. Here, we treat the tri-axial cable which consists of two different longitudinal segments and thus satisfies balanced phase and homogeneous current distribution condition by controlling twist pitch and length of separate segments.     

Numerical study on self-field losses of 30 m BSCCO HTS transmission cable

The self-field losses of the one phase of high-T_C superconducting (HTS) transmission cable are calculated by the electric circuit (EC) model. The one phase of HTS cable is constructed by the former of fine-strands copper rod, HTS conductor with four superconducting layers, the insulation made by polypropylene laminated paper, and HTS shielding with two superconducting layers, which was fabricated by Sumitomo Electric Industries (SEI). The length of the cable is 30 m. Each HTS layer comprises BSCCO tapes. The current-dependent resistance of HTS layers in EC model is estimated on the base of Norris expressions for ellipse. The calculated losses are compared with the experimental results measured by 4-terminal method by SEI. The calculation of alternating current (AC) losses, a summation of the self-field losses in HTS layers and the eddy-current losses in the former, is almost equal to the measurement at wide transport-current range below the lowest value of the layer critical current. This result indicates that the numerical calculation by EC model is quite reliable. The minimum AC loss is also calculated by obtaining the optimum helical-pitch lengths of HTS layers at transporting 1 kA_rms. The minimum loss is 36% lower than the loss of HTS cable designed by SEI at the transport current value. In HTS cable with the optimum helical-pitch lengths, the calculation of the layer currents are not uniform in HTS conductor but are almost uniform in HTS shielding, which is contradict to SEI’s one. It is considered that the numerical calculation by EC model is useful to obtain the optimum helical-pitch lengths in HTS cable with the minimum AC loss.     

Modelling the effect of twisting on electro-mechanical properties of Nb3Sn conductors

The influence of external loading on the superconducting filaments of Nb₃Sn wires depends on the wire structure, for example, on twisting. Electro-mechanical behaviour of wires can be studied with finite element models. Three-dimensional models, whose numerical solution is heavy, are generally needed for twisted wires. However, this paper presents a two-dimensional model for twisted conductors that can be used under certain loading situations. Computational tests showed that twisting influences the superconducting properties significantly and must be modelled only if the ratio of the twist pitch to the distance between the outermost filament and the wire axis is smaller than 25.     

Reduction of alternating current loss in a high-TC superconducting transmission cable by means of helical pitch adjustment

We have reported that the alternating current (ac) losses in a 66 kV_rms 3-core high-T_C superconducting (HTS) transmission cable fabricated by Tokyo Electric Power Company and Sumitomo Electric Industries Ltd. are calculated correctly by using an electric-circuit model. According to the calculated results, the circumferential field losses are dominant in the total ac losses in compared with the self-field losses and the axial-field losses. The helical pitches of each layer in the HTS cable are designed to obtain almost same layer currents, which gives the minimum self-field losses. We think that the optimum helical pitches giving the minimum total losses are different from the helical pitches designed by the companies and calculate the optimum values in the condition of the same helical direction of each layer in the cable. As a result, for example, it is found that the ac loss of 2.1 W m⁻¹ cc⁻¹ at transporting 1 kA_rms can be reduced to 1.8 W m⁻¹ cc⁻¹ (about 14% reductions) after redesigning the cable with the optimum helical pitches. The optimum helical pitches are obtained for each given transport current. After redesigning, the distribution of layer currents is not uniform and the circumferential fields are reduced.     

3D simulation of AC loss in a twisted multi-filamentary superconducting wire

In the AC loss simulation, it is a huge challenge to model the twisted wire at the filament level, due to the complex structure as well as long-time computation consumption. In this paper, we use 3D finite-element method based on H-formulation to study the AC loss in a twisted superconducting wire. The wire is treated as a homogenous material with the anisotropic conductivity in the filament region. We quantitatively simulate the AC loss induced by the AC transport current and magnetic field profile, and the effect of the twist pitch on the AC loss. In the case of AC transport current, larger pitch length leads to higher loss, and the pitch length effect is contrary to the case of applied magnetic field. The influences of the magnetic field direction and non-uniform current distribution subjected to the strand bending are also investigated. It is observed that, the transverse magnetic field has a more significant influence on the AC loss than the longitudinal magnetic field. The non-uniform current distribution can result in a higher AC loss, compared to a corresponding uniform current distribution.     

Development of an Impedance Matching Program for Balancing the Current Distribution in a Tri-axial HTS Power Cable

The tri-axial high temperature superconducting (HTS) power cable design has several advantages when compared with other HTS power cables. However, this design has an imbalance in the three phase currents, as the phase conductors of the tri-axial HTS power cable have different radii. The radii of the phase conductors impact the value of inductance and capacitance for the cable, and the values are determined by the winding pitch length and the winding direction. Thus, the current imbalance can be minimized through the adjustment of the winding pitch length, the radius of each layer, and the winding direction. It takes a lot of time to manually calculate an impedance and to find a matched impedance. So the impedance of the tri-axial HTS power cable, according to its shape, was analyzed and the impedance matching program (IMP) was developed using LabVIEW (Laboratory Virtual Instrument Engineering Workbench) to solve this problem. IMP finds the matching impedance automatically by calculating the impedance according to the tri-axial HTS cable dimension. Consequently, this could save a lot of time, and so this program will be applied to the design of the tri-axial HTS power cable effectively.     

Compact stranded superconducting conductors with both low ac loss and high stability. I. Proposal of a new design

A new method for designing compact stranded superconducting conductors is proposed as a solution to the dilemma that low loss and high stability cannot be simultaneously attained in the commonly used conductors. In our design, the twist directions of the conductor and those of the sub-cables in it are the same. In addition, the twist pitch of the sub-cables is relatively longer than that of the conductor. The sub-cables crossover each other in the conductor. Under the changing transverse magnetic fields oriented perpendicular to the broad face of the conductor, the induced voltages between the above-mentioned crossover sub-cables become small, so inter-sub-cable coupling losses are decreased. As a result, not only the total coupling loss in the conductor is decreased, but also high stability is maintained due to the low contact resistance between the sub-cables. Our method theoretically indicates such high performance as attaining both low ac loss and high stability. An example of our design is shown for a large-scale compact stranded superconducting conductor.     

A general treatment of losses in multifilamentary superconductors

Losses are calculated for a range of shapes of superconducting wire and cable. It is shown that the coupling losses can nearly always be expressed to a first approximation in terms of two parameters. One is the shape of the coil, the other (which contains most of the material parameters) is the time constant.The time constant is calculated for several cable types, including rectangular conductors, in which an exact solution for the field can be found at low frequencies. Maximum values for the loss are calculated and general conclusions for the design of cables are drawn.     

A low loss NbTi multifilamentary composite conductor for A.C. use

Investigations of a.c. losses and stability of a mixed-matrix NbTi multifilamentary conductor are presented. Fine filament size of 1.0 μm and a tight twist of 5.5 times the wire diameter 0.2 mm result in a time constant of the eddy current of 0.024 msec at 1.0 T. If this conductor is used in superconducting armature windings of rotating machines or in a.c. magnets, generating a maximum field of 1.0 T, economical benefits are expected at operation frequencies below 20 Hz.     

Could a cryoturbogenerator armature winding be superconducting?

A quantitative comparison of the total energy consumption of a superconducting cryoturbogenerator armature winding, including the refrigeration required by a classical winding, is presented. It takes into account the latest progress in multifilamentary superconductor technology as well as some important cryoturbogenerator parameters. Theoretical analysis, experimental and calculated results show that the main parameters are filament diameter, twist pitch length, transverse resistivity and mean critical current density. A suitable choice of these parameters, using modern composite technology, allows a 60–98% reduction of the classical armature winding losses.Further necessary development work is outlined.