AC losses in multifilamentary HTS-composite tapes based on BiPbSrCaCuO

Some results of AC loss measurements are presented for 19, 61, 127-filamentary Bi-2223/Ag tapes prepared by the ‘powder-in-tube' method. All measurements have been made at T=77 K under sinusoidal transport current with frequency in the range of 30–600 Hz and the current amplitude up to 30 A. The measurements have been carried out both in self field conditions and at the external magnetic field applied to the tape at the different angles. The dependencies of the AC losses on current amplitude and frequency have been obtained. It is found that for all tapes the current amplitude dependencies of the AC losses show good agreement with the Norris prediction for an elliptical or strip geometry. The AC loss dependencies on frequency were linear. The measurements of AC losses in external magnetic field show that the change of AC losses is only through the change of the critical current. So the transport AC losses in the tapes are the ‘saturation losses' that is they are different from classic hysteresis losses.     

Finite element analysis of AC loss in non-twisted Bi-2223 tape carrying AC transport current and/or exposed to DC or AC external magnetic field

AC losses in Bi-2223 superconducting tapes carrying AC transport current and/or exposed to DC or AC magnetic field are calculated with a numerical model based on the finite element method. Superconducting property is given by the E–J characteristic represented by a power law using equivalent conductivity. First, transport loss and magnetization loss are calculated numerically and compared with measured values. The calculated losses almost agree with the measured losses. Frequency dependencies of calculated and measured transport losses are compared with each other. Next, the influence of DC external magnetic field on the transport loss is studied. DC external magnetic field reduces n that is an exponent in the power law connecting resistivity and current density. The numerically calculated transport loss increases with increasing DC magnetic field. Finally, the total loss of superconducting tape carrying AC transport current in AC magnetic field is calculated. In the perpendicular magnetic field, the calculated total loss is lager than the sum of the transport loss and the magnetization loss, while they almost agree with each other in the parallel magnetic field.     

AC loss of low temperature superconducting AC wire caused by longitudinal and azimuthal AC magnetic field components

We investigated the AC loss characteristics of a low temperature NbTi AC wire by measuring the AC transport current losses in the external AC magnetic field whose components are the longitudinal and transverse ones. The measurement results showed that the AC losses were significantly dependent on the directions and magnitudes of the external longitudinal field component. The AC losses caused by the longitudinal and azimuthal field components were estimated by our previously derived model. The theoretical results well explained the dependence of the AC losses on the longitudinal field components. It was also shown that the AC losses can be substantially reduced by the proper choice of the twisting way.     

The frequency dependence of AC transport losses in stacked Bi—2223／Ag superconducting tapes

AC transport losses in a single superconducting tape, double-and triple-stacked Bi-2223/Ag superconducting tapes were measured by use of electrical method. The measurements were carried out at 77K with the frequency of AC transport currents ranging from 50 to 100Hz. The dependence of AC losses on frequency and the number of tapes in the stack were presented and analysed.     

高温超导YBCO带材的交流传输电流损耗测量

文中对不同频率不同幅值的交变电流下高温超导体YBCO带材的交流传输损耗进行了实验研究。实验在77K下,对Superpower公司生产的SCS4050型号带材采用电测法通过锁相放大器进行了交流损耗值的测量,并将其工作电流为50Hz时的测量结果与Norris矩形模型估算值进行了对比,同时也给出了15Hz到300Hz不同频率下交流损耗测量结果的比较分析。     

AC transport current loss of assembled conductor of HTS tapes

We study experimentally and theoretically the AC transport current loss characteristics of a tape in multiple tapes assembled in single layer and subject to external field produced by transport currents of adjacent tapes. We measured the AC transport current losses of a Bi2223 silver-sheathed tape in a single layer arrangement of three tapes using our newly developed potential leads arrangement to avoid spurious loss components caused by the magnetization in the adjacent tapes. In the paper, the influence of the external AC field produced by adjacent tapes on the loss characteristics is studied based on the experimental results and theoretical analysis.     

Calculation of AC losses in HTSC wires with arbitrary current voltage characteristics

A method for the calculation of magnetic field dynamics and AC losses in superconductors with smooth current–voltage characteristics is described. It is based on an integral equation for the current density, recently used by Brandt for magnetic relaxation. Brandt's equation is generalized to include arbitrary external magnetic fields and transport currents. One of the benefits of the integral equation formulation is that no boundary conditions ‘at infinity' are required, thus restricting the calculation region to the conductor cross section. The method is applied to superconducting tapes in oblique external fields. A further extension of the theory is shown to be applicable to the calculation of coupling losses in twisted multifilamentary superconductors.     

Comparison of transport and magnetic AC losses in Bi-2223/Ag tapes — the role of superconducting core geometry

AC losses were measured by 4-probe transport method and by external magnetization method in three samples of Bi-2223/Ag tape: a multifilamentary tape with separated filaments, another multifilamentary tape with ‘bridges' between filaments, and a two-shell tape. The transport losses agreed with those calculated using I_c from DC experiment. Magnetization experiments gave indications about the various paths of induced currents. For the tape with well separated filaments the main part of screening current closes inside individual filaments. Additional screening of the whole filamentary zone involves the normal metal matrix, leading to frequency dependent losses. In the case of tape with ‘bridged' filaments, supercurrents interconnect the filaments into bundles whose screening (and loss) is frequency-independent. Matching the experimental data indicates that a typical bundle was composed of 8 filaments. Magnetic losses of the two-shell tape were explained by a model for magnetization of superconducting wire with elliptical cross-section.     

Twist effect on hysteresis loss in Bi2223 multifilamentary wires exposed to an AC magnetic field

We fabricated Bi2223 multifilamentary sample wires with various twist pitches and investigated the electromagnetic properties experimentally. They showed monofilamentlike electromagnetic properties regardless of twisting due to the contacts among filaments and/or proximity effect. The observed AC losses in the non-twisted sample wire agreed roughly with the theoretical prediction for a homogeneous superconducting slab with the same thickness of the filamentary region on the basis of Irie–Yamafuji model. However the AC losses in the twisted wires deviated from the theoretical ones, especially for the amplitude around the theoretically predicted penetration field of the slab. We showed that the observed AC loss properties can be explained by both the twist effect for the macroscopic shielding current and the contribution of the local shielding current.     

Calculating transport AC losses in stacks of high temperature superconductor coated conductors with magnetic substrates using FEM

In this paper, the authors investigate the electromagnetic properties of stacks of high temperature superconductor (HTS) coated conductors with a particular focus on calculating the total transport AC loss. The cross-section of superconducting cables and coils is often modeled as a two-dimensional stack of coated conductors, and these stacks can be used to estimate the AC loss of a practical device. This paper uses a symmetric two dimensional (2D) finite element model based on the H formulation, and a detailed investigation into the effects of a magnetic substrate on the transport AC loss of a stack is presented. The number of coated conductors in each stack is varied from 1 to 150, and three types of substrate are compared: non-magnetic weakly magnetic and strongly magnetic. The non-magnetic substrate model is comparable with results from existing models for the limiting cases of a single tape (Norris) and an infinite stack (Clem). The presence of a magnetic substrate increases the total AC loss of the stack, due to an increased localized magnetic flux density, and the stronger the magnetic material, the further the flux penetrates into the stack overall. The AC loss is calculated for certain tapes within the stack, and the differences and similarities between the losses throughout the stack are explained using the magnetic flux penetration and current density distributions in those tapes. The ferromagnetic loss of the substrate itself is found to be negligible in most cases, except for small magnitudes of current. Applying these findings to practical applications, where AC transport current is involved, superconducting coils should be wound where possible using coated conductors with a non-magnetic substrate to reduce the total AC loss in the coil.     

AC losses dependence on a CuNi layer location in NbTi CICC

In the frame of the ITER fusion program, large Cable In Conduit Cables (CICC) made with NbTi superconductors are foreseen for the poloidal field system. These coils are pulsed and so subjected to fast variations in magnetic field. Superconductors have then to be designed in order to reduce AC losses to an acceptable level. A solution could be to insert a copper nickel resistive barrier in the copper stabilizer surrounding the filamentary area of the composite. The purpose of this barrier is to reduce interstrand coupling currents. In order to predict the effect of this barrier on AC losses, a modeling of a 36 strands CICC has been realized. According to this code, the ability of the resistive barrier to reduce coupling currents is dependent on its location. For this study, three CICC with three barrier locations, from the inner to the outer diameter of the copper crown stabilizer, have been produced. AC losses have been measured and compared to our numerical model.     

AC losses in circular arrangements of parallel superconducting tapes

The DC and AC properties of superconducting tapes connected in parallel and arranged in a single closed layer on two tubes (corresponding to power cable conductor models with infinite pitch) with different diameters are compared. We find that the DC properties, i.e., the critical currents of the two arrangements, scale with the number of tapes and hence appear to be independent of the diameter. However, the AC loss per tape (for a given current per tape) appears to decrease with increasing diameter of the circular arrangement. Compared to a model for the AC loss in a continuous superconducting layer (Monoblock model) the measured values are about half an order of magnitude higher than expected for the small diameter arrangement. When compared to the AC loss calculated for N individual superconducting tapes using a well known model (Norris elliptical) the difference is slightly smaller.     

高温超导YBCO线圈交流损耗的频率特性

YBCO线圈的交流损耗直接关系到YBCO设备的运行成本及稳定性。实现对YBCO线圈交流损耗的快速、准确测量,对于开展YBCO涂层导体的应用研究具有重要的意义。文中采用电测量法,在77K、零场和不同频率条件下,对YBCO线圈通以不同运行电流时产生的交流传输损耗进行测量。构建了YBCO线圈交流损耗的数值计算模型,对YBCO线圈交流损耗进行理论研究,最后将实验数据与理论计算结果进行比较,两者结果基本一致。可以发现,YBCO线圈在频率低于75Hz时,交流传输损耗随频率的增大而减小,当频率从75Hz增加到195Hz时,交流传输损耗随频率的增大而增加。     

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.     

Frequency dependence of AC loss in Bi(2223)Ag-sheathed tapes

The AC self-field loss in Bi(2223)Ag-sheathed tapes with different number of filaments has been measured between 59 and 2500 Hz by means of a dual lock-in amplifier. Due to the wide frequency range of the measurements, we have been able to dissociate quantitatively the different self-field loss contributions: hysteretic, eddy current and resistive loss (near I_c). This is an important advantage compared to single frequency measurements where such loss dissociation is only qualitative. The hysteresis losses of the different tapes fall between Norris' predictions for elliptical and strip cross-section. The relative weight of eddy current loss is found to be inversely proportional to the current ratio—the higher the i, the less is their contribution. Frequency-independent resistive loss due to flux-creep is observed for high currents at low frequencies; this loss becomes quickly negligible with the increasing frequency.     

Measurements of AC losses in different former materials

A high temperature superconducting cable may be based on a centrally located cylindrical support, a so-called former. If electrically conductive, the former can contribute to the AC losses through eddy current losses caused by unbalanced axial and tangential magnetic fields. With these measurements we aim at investigating the eddy current losses of commonly used former materials. A one layer cable conductor was wound on a glass fibre reinforced polymer (GFRP) former. By inserting a variety of materials into this, it was possible to measure the eddy current losses of each of the former candidates separately; for example copper tubes, stainless steel braid, copper braid, corrugated stainless steel tubes, etc. The measured data are compared with the predictions of a theoretical model. Our results show that in most cases, the losses induced by eddy currents in the former are negligible. However, for materials with a low resistivity the eddy current losses may become significant, e.g., for high purity Cu or Al.     

Estimation of Jc(B) dependence from self-field alternating current (AC) losses measured on Bi-2223/Ag tapes

Transport AC losses measured in self-field conditions on multifilamentary Bi-2223 tapes are often found to be lower than those calculated within the framework of the critical state model for a bulk wire with elliptical cross section, though generally higher than predicted for a strip. This effect is sometimes ascribed to the non-ideal geometry of the tapes, which does not exactly reproduce either shape. Here we propose an alternative explanation assuming that the critical current density of superconducting material depends on magnetic field. In practice, we analyzed the AC loss curve and deduced different I_c values for the individual data points, using the standard Norris equation for elliptical conductor. This gives the relation between ‘calculated' I_c and the self-field associated to AC transport current, which can be regarded as an alternative way to qualify the dependence of J_c on magnetic field. Important is that this procedure covers the range of fields below the self-field at I_c where the measurement in background DC field can not be used to determine J_c(B).     

AC transport and magnetic characterisation of multifilamentary Ag-BSCCO(2223) tapes with different filament arrangements

AC losses in multifilamentary tapes depend on various parameters. Among them, geometrical factors such as overall tape width and thickness as well as the precise arrangement of the filaments are expected to have an important influence. Several theoretical models describe this dependency. In order to study these geometrical effects experimentally, we prepared a series of Bi(2223)/Ag tapes with gradually changing filament arrangements and tape aspect ratio, and characterised them by AC transport and magnetic measurements. The results are compared to model predictions.     

Magnetic measurement of transport AC losses in Bi-2223/Ag tapes

Magnetic nature of the losses in superconducting wire carrying AC current implies that it should be possible to determine these losses in a contactless way. Ribbon-like samples are quite favorable for such an experiment, because a notable portion of magnetic flux related to losses ‘escapes' the sample volume and can be detected by an appropriate pick-up coil. In this case, a model describing the AC current penetration into the tape, based, e.g., on the critical state model, allows one to derive the losses from the pick-up coil signal. Because this signal is proportional to the number of coil turns, extension of the accessible range of measured voltages (and losses) can be achieved. We demonstrate the data obtained on a 1 cm long portion of a low-loss multifilamentary tape carrying AC current with frequency 35 Hz. The pick-up coil technique allowed us to reach loss level more than one order below the experimental limit for direct measurements.     

具有不同临界电流的Bi2223/Ag多芯超导带材的自场损耗和交流电流电压特性

对具有不同临界电流的Ｂｉ２２２３／Ａｇ多芯超导材的交流电流电压特性进行了测量和评价,当传输电流的有效值Ｉｎｎｓ小于临界电流Ｉｃ时,交流电压的大小与传输电流的频率成正比;但Ｉｎｎｓ接近临界电流时,不同频率所对应的交流电压的大小之间的差别减小了,所有的曲线都汇聚成一条曲线,传输电流的频率分别为４０Ｈｚ,６０Ｈｚ,８０Ｈｚ,２００Ｈｚ及３００Ｈｚ时,我们测量了交变传输电流在Ｂｉ２２２３／Ａｇ带材中产生的自场损耗。结果表明当传输电流的频率较低时,实验结果与基于Ｂｅａｎ模型的Ｎｏｒｒｉｓ方程预期的结果一致;另外,实验结果表明存在一个电流Ｉ′,它的值小于任何一个样品的临界电流,本实验中Ｉ′的值是１０安培,在传输相同大小的电流Ｉｎｎ且Ｉｎｎｓ〈Ｉ′时,Ｂｏｉ２２２３／Ａｇ带材的交流损耗与它的临界电流成正比;但当Ｉｎｎｓ〉Ｉ′