Influence of DC external magnetic field on AC transport current loss of HTS tape

We measured the AC transport current loss of Bi 2223 multifilament Ag-sheathed tape under DC external magnetic field of 0–0.2 T. There were discrepancies between the measured data and Norris' formula for elliptical model in the range of low value of I_p/I_c (I_p and I_c are peak of the AC transport current and critical current of the tape respectively), while without DC background field, the loss of the tape was close to Norris' formula. Theoretically speaking, even with the DC background field and decreased critical current the AC transport current loss of the tape follows Norris' formula which is derived from the Bean model. When DC background field is applied to the HTS tape, n value of the power law E–J characteristics decreases together with the decrease of J_c. Dependence of the AC transport current loss on the n value was analyzed by numerical calculation. The results show that the loss depends on the n value and that decrease of the n value is one of the causes of the discrepancies between the measured data and Norris' formula.     

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.     

高温超导YBCO带材的交流损耗的FEM仿真分析

对高温超导带材YBCO的交流损耗进行了仿真分析。运用有限元FEM方法,基于Maxwell方程组的数值建模,引入了基于实验数据的power-law对交流损耗进行计算。首先对自场下的交流损耗值进行了仿真计算并分析了带材的电流密度与磁场分布情况,并通过与实验测量数据做比较验证仿真方法的有效性。其次分别对不同幅值下的平行场与垂直场下的交流损耗进行了计算,将自场、平行场以及垂直场下的电流密度与磁场强度的分布以及交流损耗值进行了对比分析。     

Decrease of magnetic AC loss in twisted-filament Bi-2223 tapes

In AC power-engineering applications, a large part of the AC loss in the superconductor is due to magnetization by the external field. This magnetic AC loss has been well described for the low-T_c conductors. In Bi-2223 tapes the picture is different due to strong anisotropy, granularity and flux creep. Magnetic AC loss in various twisted and non-twisted Bi-2223 tapes has been measured at power frequencies by a pickup method. The results are compared to theoretical models of magnetization loss. When the field is parallel to the tape plane, the filaments in twisted tapes can be decoupled and the AC loss is decreased even when the matrix is pure silver. The extra effect of higher-resistance matrix materials is studied. In perpendicular field it is more difficult to decouple the filaments, due to the particular tape geometry. Contrary to a wire, there are essential differences between the AC loss mechanisms in a long twisted tape and those in a short piece of non-twisted tape. Finally, the dynamic resistance caused by the AC magnetic field is examined.     

Numerical modelings of superconducting wires for AC loss calculations

Superconducting properties of superconducting wires as well as the influence of their composite structure and twisting should be taken into account for their numerical modeling for AC loss calculations. Furthermore, complicated electromagnetic conditions in electrical apparatuses under which superconducting wires are used influence their AC loss properties; superconducting wires carry their transport current and are exposed to the external magnetic field whose direction and magnitude vary spatially. A series of numerical models of superconducting tapes based on the finite element method has been developed. In each model, some of the above-mentioned factors that could influence the AC loss properties are taken into account. The models are formulated with the current vector potential and the scalar magnetic potential (T–Ω method). Superconducting property is given by the E–J characteristic represented by a power law. The current distributions in non-twisted and twisted superconducting tapes carrying their transport current and/or exposed to the external magnetic field are calculated with these models to estimate their AC loss. The current distribution in a short piece of superconducting tape exposed to AC magnetic field is also calculated.     

Self-field AC losses of textured Bi2Sr2CaCu2O8+δ thin rods

Self-field AC losses of polycrystalline Bi-2212 thin rods textured by a Laser Floating Zone (LFZ) melting technique have been measured at 77 K. With the optimal processing parameters, these rods, of 1.6–2 mm diameter and 10 cm length, have a transport critical current density of 3 kA/cm² in the self-field which decreases to about 1.5 kA/cm² in fields of 0.02 T applied perpendicular to the rod axis. The self-field AC losses have been measured in DC magnetic fields up to 0.03 T. The measurements in zero field show that for a large current range the losses are dominated by hysteresis losses as described by the Critical State Model for a cylinder. For the measurements in DC fields the losses show an increasingly resistive-like dependence with current, while the hysteretic component expected from the CSM becomes less important. Measurements at different frequencies also indicated that the loss per cycle in fields is strongly frequency dependent.     

Magnetic coupling and self-field AC losses of two neighbouring Ag sheathed PbBi2223 tapes

The magnetic interaction between two neighbouring superconducting tapes has significant influences on their self-field AC losses. While the two tapes are independent of each other when separated far apart, they are expected to be fully coupled and behave as a single tape when placed very near. One of the consequences of such coupling is the increase in the self-field loss per tape, which is double of that for an uncoupled tape carrying the same current. In order to assess the interactions among tapes in systems such as a power cable, a better understanding is necessary on the critical distance where the coupling becomes important. Experimental measurements on the self-field losses in two neighbouring Ag sheathed PbBi2223 tapes were carried out with the two tapes separated by various distances, while placed either side by side (side-configuration) or one on top of the other (top-configuration). The results indicates that the critical coupling distance for the top-configuration is about 5 mm, where the increase in loss per tape is about 10%. The critical length for the side-configuration is found to be of the same order of magnitude.     

外场下机械振动对高温超导带材交流损耗的影响

高温超导带材在磁场中传输交变电流时,将受到电磁力的作用而产生机械振动,振动对带材的交流损耗将产生影响.本文讨论了振动情况下交流损耗的测量方法,在平行于带面的直流磁场下,测量了Bi-2223/Ag高温超导带材在不同振动情况下的交流损耗.结果显示:当传输电流频率偏离样品的共振频率时,振动对带材的交流损耗影响不大;只有当电流频率在共振频率附近时,样品产生剧烈振动,交流损耗才有明显的增加;另外,带材振动时的交流损耗随频率变化曲线的斜率比不振动时略有增加.     

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 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.     

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.     

Experimental study on AC losses in Ag sheathed PbBi2223 tapes with twist filaments

Experimental measurements of AC losses were carried out on Ag sheathed PbBi2223 tapes with twisted and untwisted filaments. Losses were measured at 77 K as function of frequency and magnetic field parallel and perpendicular to the tape surface, using appropriate pick-up loops. Both the first and third harmonics of the signal were measured, in order to distinguish between the hysteresis loss and other types of loss. The effect of filaments uncoupling by twisting was clearly identified. For a tape with a twist pitch of 10 mm and I_c=40 A (20 kA cm⁻²) operating at 43 Hz, the filaments are uncoupled in fields less than 40 mT, which is greater than the full penetration field for both the filaments and the tape. Hence, a reduction in the hysteretic loss of the superconducting core is realised at power frequency between 10 and 40 mT. Results form the self-field loss measurement implies the uncoupling of twisted filaments at relative low transport current (I<0.5I_c)     

AC loss in a high-temperature superconducting coil

In a typical superconducting coil made of BSCCO/Ag tape, both amplitude and direction of the magnetic field determine the critical current, resistive voltage and AC loss. The distribution of the magnetic field along and across the superconducting tape in a coil is rather complex. This gives rise to the question: how accurate can one predict the critical current, V–I characteristic and AC loss of the AC coil from results of short sample measurements? To answer this question, we have measured and compared the characteristics of a short sample and a small coil employing 14 m of the same tape at 77 K. The comparison is performed as follows. First, a short sample is characterised with regard to the field dependence of the critical current, V–I characteristic and the AC loss. Second, the distribution of the magnetic field along the tape in a coil is accurately calculated. From the data, the voltage along the tape and the loss of the tape in the coil are found. Finally, the resistive voltage and the AC loss of the complete coil are calculated and compared to measured AC losses in the frequency range of 0 to 160 Hz, typical for power applications.     

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.     

A simple electromagnetic method of cyclic loss measurement for superconducting wires in a combined alternating transverse magnetic field and transport current

We measured cyclic losses in a superconducting wire, carrying alternating transport current, simultaneously exposed to an alternating transverse magnetic field. Samples of Bi-2223 Ag-sheathed tapes have configuration of a double-layer non-inductive coil, which itself is a pickup coil to measure the AC losses. Potential taps were attached to both terminals of the sample coil. The external field was applied along the axis of the sample coil. In this procedure, we can estimate an averaged Poynting's vector on a cylindrical surface between the two layers by means of signals from a pair of the potential taps and from pickup coils for the external magnetic field and the transport current. We can also measure a magnetization and an extended transport-current components of AC losses in addition to a total cyclic loss for a combined alternating external field and transport current. Obtained results are compared with numerical predictions of the critical state model taking into account the magnetic field dependence of critical current density.     

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.     

一种铁基超导带材交流损耗的测量

近年来铁基超导材料的发现掀起了又一轮新型超导材料研究的热潮,各种配方的铁基超导材料不断被制备出来,转变温度也不断提高,中国科学家在该领域取得了十分突出的成果,制备出了多种铁基超导材料,但对其交流损耗特性研究鲜有报道,而实际应用中交流损耗的特性又十分重要,因此搭建了一套采用探测线圈法的交流损耗测量平台,测试了一种中国科学院电工研究所采用PIT工艺制作的单芯铁基超导带材的交流损耗。该文介绍了采用探测线圈法测量超导材料交流损耗的一种测量平台的搭建与标定,以及采用标定过的测量平台在液氦温度下测量的一种采用PIT工艺制作的单芯铁基超导带材的交流损耗;并与计算得到的铁基带材超导芯的磁滞损耗和包套的涡流损耗进行了比较分析,得出了其交流损耗与背景磁场频率成正比,其涡流损耗可以忽略的结论。     

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.     

Bi-2223复合导体直流磁场下自场损耗热稳定性分析

对于一种Bi-2223的复合导体,利用ANSYS软件,我们分析了在直流磁场下励磁过程中,自场损耗对复合导体热稳定性的影响;然后假定Bi-2223超导带内不同的损耗值,通过计算,确定了达到超导带分流温度的最小损耗值。     

Numerical calculation of current density distributions in high temperature superconducting tapes with finite thickness in self field and external field

The current density distribution of high temperature superconducting (HTS) tapes is modeled for the combined case of an alternating self and applied magnetic field. This numerical analysis is based on the two-dimensional Poisson equation for the vector potential. A one-dimensional current (z-direction) and a one-dimensional applied field (y-direction) are assumed. The vector potential is rewritten into an equation of motion for the current density J(x,y,t). The model covers the finite thickness of the conductor and an n-power E–J relation. The magnetic field dependence of J_c is also included in this E–J relation. A time-dependent two-dimensional current distribution that is influenced by the aspect ratio of the conductor and the material properties in E=f(J,B) is calculated numerically. The numerical results are compared with the experimental results for the AC loss of a tape driven by a transport current. Finally, a total AC loss factor is given for two cases in magnetic field direction, perpendicular and parallel to the conductor broad side.