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.     

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.     

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).     

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.     

Magnetic ac loss in multi-filamentary Bi-2223 / Ag tapes

The ac loss in high-T_c superconducting tapes with twisted and non-twisted filaments has been studied by a magnetic method. A brief overview of the theoretical background and the experimental set-up is presented. Measurements were made at 77 K in a magnetic field of 50 Hz frequency and 0.001–0.7 T amplitude. Application of dc transport current made it possible to distinguish between the loss components, arising from intra-grain and from filament currents. The magnitude of the filament loss component indicates that the filaments are fully coupled, which agrees with theory. In other measurements, the orientation of the external field with respect to the tape was varied. Knowledge of the ac loss in parallel and in perpendicular field is sufficient to predict the ac loss for any intermediate orientations of the 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.     

Electrical AC loss measurements of Bi-2223 tapes, performed under the Brite EuRam Research programme SACPA

A series of electrical AC loss measurements on Bi-2223 tapes have been performed under the Brite Euram project SACPA. This included, for the first time, a round-robin of independent self-field AC loss measurements between four laboratories. The very close agreement of data demonstrates the validity of the electrical technique and lays the basis for a measurement standard. Other preliminary measurements in SACPA showing the variation of losses with frequency, temperature and applied DC field are also reported.     

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.     

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。     

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.     

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.     

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.     

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 losses in multifilamentary Bi(2223) tapes with an interfilamentary resistive carbonate barrier

For the most common AC application frequencies, the main component of the AC losses in multifilamentary Bi(2223) tapes are caused by hysteresis- and coupling losses. These losses can be reduced enhancing the matrix resistivity and applying a twist to the filaments. We report on the AC loss properties of 37-filament tapes with AgAu (8 wt.%) matrix, and novel 19-filament tapes with SrCO₃ barriers between the filaments. We performed transport AC loss and magnetic AC loss measurements in parallel and perpendicular magnetic fields. Both kinds of tapes were also prepared with filament twists below a twist pitch of 20 mm. The influence of the different tape modifications on the AC loss behaviour is presented and compared with theoretical models to understand the effect of the resistive matrix. In the case of magnetic AC loss measurements, reduced AC losses due to decoupled filaments were observed for the twisted tapes with a resistive matrix in low parallel fields.     

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.     

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.     

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.     

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.     

High-Tc superconductors and AC loss in electrotechnical devices

To replace conventional normal conducting solutions in electrotechnical devices, high-T_c superconductors must offer distinct economical and technical benefits in terms of lower overall loss, volume and weight. Based on AC loss theory we design appropriate 50 Hz reference conductors for cables, transformers and other applications, calculate admissible limits for the conductor variables filament diameter, twist and matrix resistance and compare this to the present state of Bi-2223-tape conductors and AC loss measurements. Further the influence of perpendicular AC field components on losses is addressed. High current devices will require multistrand conductors, where nonuniform current distribution due to unbalanced magnetic coupling may result in partial saturation and enhanced losses. As an example we discuss the multilayer HTSC-cable and present a solution based on a ‘zero flux condition' for azimuthal and axial magnetic fields.     

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.