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.     

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.     

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.     

传输交流的Bi2223/Ag高温超导带在不同取向交流外场下的交流损耗

在高温超导的电力应用中，如超导电机、变压器等，多数情况下，高温超导带材在通以交流传输电流的同时还处于交变磁场中。此时，超导体的交流损耗不仅依赖于磁场的大小，还与磁场相对于超导带面的取向有关。本文在77K及工频50Hz情况下，实验研究了单根多芯Bi2223/Ag高温超导带及两带并联时的交流损耗随着外磁场与带面夹角的变化情况；以及交流磁场对临界电流的影响情况；并对单根带及两带并联的实验结果进行了比较与分析。     

Indirect measurement of AC current distributions in HTS tapes by a pickup coil method

It is necessary to develop HTS conductors with a large current capacity and low AC loss characteristics for practical use of HTS power devices. For large capacity power applications, HTS tapes such as Bi-2223 tapes and YBCO coated conductors are assembled. So, it is important to evaluate the characteristics of current distributions in such assembled HTS tapes. However, an adequate measurement method has not been established. In this study, we have tried the development of an indirect measurement method to evaluate the current distributions in stacked HTS tapes. In this method, the current distributions are indirectly found from the results of the field distributions measured by a pickup coil located around the surface of the sample tapes. To confirm the accuracy and the sensitivity of this method, current distributions in a test conductor made of copper tapes are measured. Numerical and measured current distributions are compared. Using this method, the current distributions in stacked Bi-2223 tapes are measured at room temperature and 77 K. On the basis of the obtained results, the characteristics of the AC current distributions in the HTS tapes are discussed.     

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.     

实用化超导材料研究进展与展望

超导技术是21世纪具有重大经济和战略意义的高新技术,在国民经济诸多领域具有广阔的应用前景,如在超导弱电应用中的超导量子干涉器、滤波器;在超导强电应用中的电缆、限流器、电机、储能系统、变压器、磁体技术、医疗核磁共振成像、高能物理实验和高速交通输运等。实用化超导材料是超导技术发展的基础。目前,国际上发现的实用化超导材料主要有低温超导线材、铋系高温超导带材、YBCO涂层导体、MgB₂线带材以及新型铁基超导线带材。文章在简要介绍超导材料发展历程的基础上,重点综述了上述实用化超导材料制备及加工、性能和应用方面的最新研究进展,并对相关领域存在的问题及今后的发展作出展望。     

Investigation of Bi-2223 high temperature superconducting tape as the material for gradient coil in MRI

The use of Bi-2223 high temperature superconducting (HTS) tape as a material for gradient coils in MRI is evaluated in this paper. Bi-2223 tapes have a very high critical current and a very low power loss. A HTS tape gradient coil is expected to provide much higher gradient strength and generate much lower heating than a copper coil. Measurements of the AC power loss of Bi-2223 tapes at typical operating frequencies for gradient coils are presented. The degradation of the critical current and its effect on the increase of AC power loss is analyzed. Practical technical issues such as resistance, gradient strength and mechanical performance are also discussed. A prototype Bi-2223 HTS tape gradient coil is evaluated to verify the concept.     

Evaluation of geometrical effect on magnetization loss in GdBCO coated conductor

The magnetization loss density in stacked GdBa₂Cu₃O_7−δ coated conductor was measured using a SQUID magnetometer in a magnetic field normal to the tape surface to investigate the effect of stack on the magnetization loss. The AC loss characteristics are successfully collapsed to a single curve by the normalization at all the measurement temperatures. The losses are similar at high magnetic fields regardless the number of tapes. In addition, the AC loss decreases with increasing the number of tapes in stack at low magnetic fields.     

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.     

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.     

Electro-mechanical behavior of single twisted high-temperature superconducting tape under transverse Lorentz force

In recent years, several cabling methods of high temperature superconducting (HTS) cable have been proposed; e.g., the conductor on a round core cable (CORC), the Roebel assembled coated conductor cable, the helical twisted stacking-tape cable (TSTC) and the twisted-stack slotted core HTS cable (TSSC). These cabling methods allow the high temperature superconducting tapes widely used in the high-field magnets. The single superconducting tape performance under applied loads directly relates to the transport performance of the cable and the choice of the cabling method. In this paper, we investigate the effect of twisting morphology on the electro-mechanical properties of HTS tapes. Particular attention is given to the transverse Lorentz force of a pre-twisted HTS tape. The analytical solution of the deflection of the HTS tape under transverse Lorentz force is derived. Then, the current distribution and AC loss of the tape are calculated by using H-formulation. The effects of twist angle and loading conditions are examined for different HTS tape lengths. The results show that the stiffness resistance ability to Lorentz force of the HTS tape can be increased in several ranges by increasing the twist angle. The twisting structure can also reduce current degradation and AC loss, and thus enhance the transport capacity of HTS tape. This study helps understand the electro-mechanical properties of pre-twisted HTS tapes and provides theoretical reference for the design of novel HTS cable structures.     

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.     

高温超导涂层导体——RE123双轴织构技术及其发展状态

本文对高温超导涂层导体及其双轴织构外延生长技术进行了全面的论述。内容分金属基体、缓冲层、超导层三个方面,根据金属基体的不同将缓冲层分成四个类型,即辊扎双轴织构金属基带(RABiTS)上外延缓冲层、自氧化外延(SOE)NiO缓冲层、离子束辅助沉积(IBAD)缓冲层和衬底倾斜沉积(ISD)缓冲层。总结了超导层沉积工艺和人工磁通钉扎中心的最新研究成果,评述和展望了高温超导涂层导体的当前国际状态和发展前景。     

Current distributions in multifilamentary conductors: the influence of intergrowths

The modelling of both critical and remanent states (i.e., the current density and field distributions) in periodic arrays of flat superconducting strips is important for calculating the AC losses in multifilamentary tapes made for power applications. We model the current and field profiles for such magnetically coupled conductors, and have measured these dependences for BSCCO-22223 tapes using a miniature scanning Hall probe technique. The results indicate that the filaments are also electrically connected to a significant extent, which must be caused by superconducting intergrowths between individual filaments.     

Discrete temperatures in high-temperature superconductors

The low-amplitude AC susceptibility on intact and deformed Bi2223/Ag tapes has been measured as a function of temperature, frequency, AC amplitude and DC magnetic field. The deformation resulted in the splitting of the χ″(T) peak into three peaks situated near 30, 58 and 90 K. In zero magnetic field, these temperatures were identified as the Kosterlitz–Thouless transition temperatures of low number stacks of superconducting layers. An external magnetic field redistributed the dissipation among the peaks, and moved them to lower temperatures (and suppressed the highest temperature peak). In a finite field, each peak corresponds to the stack melting temperature T_m. The melting temperature in each stack was found to be a field-dependent parameter, with a minimum value=T_KT of a stack of thickness that is less by one layer. The T_m decreases exponentially with the field, and the rate of decrease depends on the interstack Josephson and magnetic interactions. With a universal set of T_KT, the vortex melting line of a tape is a linear combination of the T_m(H) for the low-number stacks.     

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.     

Spatially-resolved measurement on time-dependent electromagnetic behavior in alternating current carrying coated conductor

Establishment of processing technology for multifilamentary coated conductors (CCs) is a key issue for superconducting electric power applications from the viewpoint of AC loss reduction. On the other hand, CCs sometimes have local inhomogeneity in the superconducting layers, and that will cause a current blocking in a filament or inhomogeneity of critical current among filaments in a multifilamentary CC. Therefore, we need an assessment method for local electromagnetic behavior on AC loss properties of CCs. In this study, we developed a method for visualizing time-dependent AC loss distribution in CCs by using scanning Hall probe microscopy. We succeeded in visualizing local current density, electric field and loss density simultaneously with a spatial resolution of a few hundred micrometers. The measurement system has possible scanning area of 150 × 50 mm² and current capacity of 500 A. This enables us to discuss the local electromagnetic behavior on a practical scale of CCs. We believe that this visualization method will be a very powerful tool to estimate the feasibility of processing technology for multifilamentary CCs.     

Measuring transport current loss of BSCCO/Ag tapes exposed to external AC magnetic field

BSCCO/Ag tape superconductors are developed for electrical power applications at liquid nitrogen temperatures. In these applications, e.g., superconducting transformers and power cables, an AC transport current and an AC magnetic field are present at the same time. A set-up to measure the influence of external AC magnetic field on the transport current loss, i.e., the voltage drop across a sample supplied with an AC transport current, has been developed. The magnetic field can be applied both parallel and perpendicular to the broad side of the tape conductor. An increase of the transport current loss due to the external AC magnetic field is observed. When a DC external magnetic field is applied the increase of the self-field loss can be described well by the decrease of the critical current due to the magnetic field. In the case of an AC external magnetic field this is only a minor effect. For magnetic field amplitudes higher than a certain threshold value the transport current loss is described reasonably well by the self-field loss and a dynamic resistance contribution calculated from the DC voltage–current relation in AC magnetic field.     

Development of YBCO power devices in Japan

A new Japanese national project, called M-PACC, to develop high temperature superconducting electric power devices started in June last year (FY2008–FY2012). This project aims to develop three different types of electric power devices that are expected to provide stable power supplies with large capacity and small size by using YBCO coated conductors. The first program is the development of a 2 GJ class superconducting magnetic energy storage system to control stable electric power systems. It is planned to develop several sets of element coils for a 20 MJ class system as a technological feasibility study for a 2 GJ class coil. The second program is the development of two different types of power cables with higher performance than existing power cables; one is a three-core 66 kV–5 kA class large current cable and the other is a single-phase 275 kV–3 kA class high voltage cable. These cable were required several technological developments, namely, large current and low AC loss, high voltage insulation and low dielectric loss, and power and heat balance for both cables. The third program is the development of a 20 MVA class power transformer with 66 kV/6.9 kV as a distribution transformer. In this project, power transformer systematization technology including 2 kA class large current coil technology, anti short-circuit wire winding technology, AC loss reduction technology, and winding technology will be developed.