Calculation of AC Magnetizing Loss of ReBCO Superconducting Tapes Subjected to Applied Distorted Magnetic Fields

In recent years, there are fast-increasing concerns on the utilizations of superconducting rotating electrical machines in different application areas, such as ship propulsion systems, aircraft drivers, and wind turbine generators, since these machines exhibit the merits of high current density, compact design, high power density, light weight, high torque density as well as high efficiency. One of the main limitations in front of the vast use of superconducting tapes in the fabrication of electrical machineries is AC magnetizing loss when tapes are exposed to an external magnetic field, which can decrease the critical current density of wires, as well. In the literature, most of the research works have been done on calculation of the AC magnetizing loss under a pure external magnetic field, while in reality, magnetic flux lines in AC electrical machines are usually distorted with harmonics because of different reasons such as distorted leakage flux, distributed coils of a winding in several slots, cogging fields, mechanical faults, etc. Since these distorted fields contain harmonics, then in this paper, the AC magnetizing loss of superconducting tapes has been electromagnetically modeled and calculated when they are subjected to nonsinusoidally distorted external magnetic fields. The magnetic field dependency of critical current density has been considered in a proposed finite element model. The results have shown that the AC magnetizing loss increases significantly under a distorted applied field compared with a sinusoidal one. In addition, the loss increase depends on the harmonic content which would increases drastically with total harmonic distortion of the applied magnetic field.     

Influence of Critical Current Density on Guidance Force Decay of HTS Bulk Exposed to AC Magnetic Field Perturbation in a Maglev Vehicle System

Superconducting maglev vehicle is one of the most promising applications of HTS bulks. In such a system, the HTS bulks are always exposed to AC external magnetic field, which is generated by the inhomogeneous surface magnetic field of the NdFeB guideway. In our previous work, we studied the guidance force decay of the YBCO bulk over the NdFdB guideway used in the High-temperature superconducting maglev vehicle system with the application of the AC external magnetic field, and calculated the guidance force decay as a function of time based on an analytic model. In this paper, we investigated the influence of the critical current density on the guidance force decay of HTS bulk exposed to AC field perturbation in the maglev vehicle system and try to adopt a method to suppress the decay. From the results, it was found that the guidance force decay rate was higher for the bulk with lower critical current density. Therefore, we could suppress the guidance force decay of HTS bulk exposed to AC external magnetic field perturbation in the maglev vehicle system by improving critical current density of the bulk.     

Magnetic Field Angular Dependence of Magnetization Loss in ReBCO Superconducting Tapes

In the applications of high-temperature superconductors (HTS), the HTS tapes are usually exposed to the external magnetic field with different orientations. The critical current and AC loss are affected by both the field amplitude and field angles due to the anisotropy of HTS tapes. In this work, we first introduce the experimental system to measure the magnetization loss in HTS tapes based on the calibration-free method. Then, we present the magnetization loss results in 4.8-mm-wide AMSC wire, 4-mm-wide SuperPower wire, 4-mm-wide SuNam wire, and 10-mm-wide Fujikura wire in a perpendicular applied field at 77 K. The field amplitude is up to 100 mT, and the frequency varies from 44.2 to 87.1 Hz. We also present the magnetization loss in AMSC wire, SuperPower wire, SuNam wire, and Fujikura wire at different field angles. The field angle varies from 10 to 90 ^° in 10 ^° steps. The loss reduction with the decreasing of the field angle shows the anisotropic property of HTS tapes. We finally plot the measured magnetization loss of the samples as a function of the magnetic field amplitude normalized by the field angle to verify an empirical formula.     

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.     

Influence of High Temperature Superconducting Transformer Geometry on Leakage Magnetic Field

Leakage magnetic fields in high temperature superconducting (HTS) transformer windings reduce the critical current and increase the ac losses in HTS tapes. Moreover, because of the anisotropic properties of the HTS tapes, the influence of the radial component of the leakage field on critical current and ac losses is much stronger than that of the axial one. For these reasons, leakage magnetic fields must be carefully considered in HTS transformer design. In this paper, we report a study of the influence of the core structure and the winding configuration on the leakage field by the finite-element method (FEM), and offer some suggestions for reducing the maximal radial component of leakage field to make the HTS transformer more efficient.     

Study on cross section of high temperature superconducting coil

It is in particular of importance for HTS coils to secure a larger central magnetic field and/or a large stored energy with shorter length of HTS tapes. The critical current of an HTS tape depends on both the flux density and the flux angle against tapes. From this point, the performance improvement of HTS coils is taken into account with an analytical model. The minimum volume coil derived from the Fabry Factor constant curve is taken concerning the original coil shape, which is often employed in low temperature superconducting coils. The coil critical current was analyzed in consideration of the anisotropic properties of the tape.The electric field of HTS tapes in the coil was calculated at the coil critical current and the high electric field portion were cut out. The optimal coil cross section is obtained by iterating this calculation process. As a result, the critical current and the stored energy density of the coil were improved. The stored energy density increased about 17% and the central magnetic field was almost kept constant regardless of 19% reduction of HTS tapes, as compared with the original coil with the rectangular cross section.     

AC loss measurements of twisted and untwisted BSCCO multifilamentary tapes

AC losses in twisted and untwisted BSCCO multifilamentary superconducting tapes with Ag matrix developed in DAPAS program were measured by an electrical method. Magnetization and transport losses were measured by a pick-up coil and by a voltage taps. Total AC loss during simultaneous application of AC transport current and an AC transverse magnetic field was given by the sum of the magnetization and transport losses measured during this simultaneous application. The magnetization loss without transport current of untwisted and twisted tapes was measured first to evaluate the effect of twisting to decouple filaments. Then, the total AC loss of the twisted tape was measured in transverse magnetic fields with various amplitudes and orientations, while the amplitude of the transport current was fixed. The measured total AC loss in a parallel transverse magnetic field was compared with some theoretical models to study the detailed characteristics of the measured total AC loss of the sample.     

Numerical Evaluation of Levitation Force Oscillation of HTS Bulk Exposed to AC Magnetic Field over NdFeB Guideway

The levitation force of the YBCO bulk over an NdFeB guideway used in the high-temperature superconducting (HTS) maglev vehicle system is oscillated by the application of the AC external magnetic field. In our previous work, we interpreted that the oscillation is due to the shielding current fluctuation caused by fluctuant external magnetic field. In this paper, based on the Bean model, an analytical model is adopted to evaluate the levitation force. Comparing with the experimental results, the calculated results show good matching. The model can reveal the oscillation characteristics of the levitation force of HTS bulk which is being exposed to AC external magnetic field. Therefore, the levitation force oscillation of the HTS bulk in the maglev vehicle system can be evaluated by this numerical method.     

Influence of Work Height on Guidance Force Decay of HTS Bulk Exposed to AC Magnetic Field Perturbation in a Maglev Vehicle System

Bulk superconductors have great potential for various engineering applications, especially in superconducting maglev vehicle systems using high-temperature superconducting bulks. In such a system, the HTS bulks were always exposed to AC external magnetic field, which was generated by the inhomogeneous surface magnetic field of the NdFeB guideway. In our previous work, it was observed that the guidance force of the YBCO bulk over the NdFdB guideway used in the high-temperature superconducting maglev vehicle system was decayed by the application of the AC external magnetic field. In this paper, we investigate the influence of the work height on the guidance force decay of HTS bulk exposed to an AC field perturbation in the maglev vehicle system and try to adopt a method to suppress the decay. From the experimental results, it was found that the decay rate of the guidance force was smaller at higher work height in the case of the same field-cooled height. So we could suppress the guidance force decay of HTS bulk exposed to AC external magnetic field perturbation in the maglev vehicle system by increasing the work height of the bulk.     

Conceptual Design of a Field Coil for 5 MW HTS Synchronous Machine

Compared with a conventional rotating machine, a superconducting rotating machine fabricated by High Temperature Superconducting (HTS) tape has superior performance and efficiency due to the HTS field coil for the rotor which can generate high magnetic flux intensity. The two primary factors for the design of the HTS rotational machine are how to construct the optimal magnetic field path through the air gap located between the rotor and the stator and how to enhance the linkage magnetic flux density between the armature coil in the stator and the field coil in the rotor. A 5 MW HTS motor for ship propulsion is planned for development in early 2011 by a Korean collaboration group of KERI and DOOSAN Heavy Industry. As a part of this R&D efforts, we designed and analyzed the field coil for a 5 MW HTS synchronous motor. In this paper, the computational results of the magnetic field distribution on the whole winding regions of the HTS field coil of the superconducting rotating machine will be also presented and discussed.     

A Numerical Study on AC Losses of a Double Layer Polygonal BSCCO Conductor by Finite Element Method

High-temperature superconductor (HTS) cables are candidates for power transmission cables in the near future. A cylindrical arrangement of HTS tapes for the cable has proved able to reduce the AC loss. Many studies on AC loss characteristics of HTS cables have been done, but few numerical models of the cable were verified by experiments. In this paper, a numerical model of the double-layer polygonal bismuth strontium calcium copper oxide (BSCCO) conductor is developed. Current density and magnetic field intensity distribution in the inner and outer layers are also investigated. The numerical results of the AC loss for different layer current distributions are identical with the experimental ones. Accordingly, the reliability of the numerical model is verified. By using this model, the influence of distance between the inner and outer layers, gap between two neighboring wires, and layer current distribution on AC losses of different layers is evaluated. The results show that increasing distance between layers and narrowing gap between wires are effective to reduce AC loss, while the unbalance of layer current distribution increases the AC loss of the double-layer conductor.     

Influence of Thermal Conductivity on Guidance Force Decay of HTS Bulk Exposed to AC Magnetic Field Perturbation in a Maglev Vehicle System

Bulk superconductors have great potential for various engineering applications, especially in a high-temperature superconducting (HTS) maglev vehicle system. In the vehicle system, the stable levitation can be achieved without any complex control system owed to the pinning effect of the bulks. However, the HTS bulks in the vehicle system were always exposed to the time-varying external magnetic field, which was generated by the inhomogeneous surface magnetic field of the NdFeB guideway. In our previous work, we studied the guidance force decay characteristics of the YBCO bulk over the NdFdB guideway used in the HTS maglev vehicle system by an experiment in which the AC external magnetic field generated by an electromagnet was used to simulate the time-varying external magnetic field caused by the inhomogeneity of the guideway, and calculated the guidance force decay as a function of time based on an analytic model. In this paper, we investigated the influence of thermal conductivity on the guidance force decay of HTS bulk exposed to AC field perturbation in the maglev vehicle system and tried to adopt a method to suppress the decay. From the results, it was found that the guidance force decay rate was higher for the bulk with the lower thermal conductivity. So, we could reduce the guidance force decay of the HTS bulk exposed to the AC external magnetic field perturbation in the maglev vehicle system by improving the thermal conductance of the bulks.     

The Effect of the External Magnetic Field on the Current-Voltage Characteristic of HTS Josephson Junction Arrays

No Heading The role of the external magnetic field in performance specialty of the high-temperature superconducting (HTS) Josephson junction array (JJA): HTS Y Ba₂Cu₃O_7–0.05 bicrystal JJA with 180 junctions, is considered. The junctions are created on the yttrium-stabilized zirconium (fianite) substrate with the bicrystal grain boundary. The experimental confirmation of the current density changes under the influence of the external DC magnetic field is obtained. The dependence of current density on the penetrated magnetic field is investigated. The optimal shielding factor needed to obtain high supercurrents in considered system is determined.PACS numbers: 73.21.Ac, 73.30.+y, 74.72.Bk, 74.76.Bz, 74.80.Dm     

Oscillation Characteristics of Levitation Force of YBCO Bulk Exposed to AC Magnetic Field above NdFeB Guideway

In the present High Temperature Superconducting (HTS) maglev vehicle system, the nonuniformity of the magnetic field along the movement direction above the NdFeB guideway is inevitable due to the assembly error and inhomogeneity of the material property of the NdFeB magnet. In order to investigate the influence of the nonuniformity on the levitation performance of the HTS bulk, the experiment involved an electromagnet, which is supplying AC current to simulate the nonuniformity of the external magnetic field. The levitation force of the HTS bulk is measured when applying AC current on the electromagnet coils. The results indicate that the levitation force abruptly changes and oscillates after applying AC external magnetic field. The effect of the amplitude of the AC magnetic field on the levitation force is studied; the result shows that the oscillation amplitude of the levitation force increases with the amplitude of the AC external magnetic field and is independent of the Field Cooling Height (FCH) of the bulk.     

Detecting and describing the inhomogeneity of critical current in practical long HTS tapes using contact-free method

The nondestructive and contact-free apparatus for measuring local critical current of long high temperature superconducting (HTS) tapes is presented. The local critical current of tape is acquired by using Hall probe array sensor to measure the remanent field after exposed to dc external magnetic field since the critical current is proportional to remanent field based on Bean critical state model. A detailed experiment on multifilamentary Bi2223/Ag tape is made to validate reproducibility, reliability, resolution, nondestructiveness and usefulness for manufacturer and user of tapes. The parameter COV (coefficient of critical current variation) is suggested for quantitatively describing the inhomogeneity and quality of practical long HTS tape based on Gaussian statistical analysis. The developed apparatus can detect HTS tape at velocity of 100 m/h with resolution smaller than 3 mm in liquid nitrogen.     

Decay Characteristics of Levitation Force of YBCO Bulk Exposed to AC Magnetic Field above NdFeB Guideway

The superconducting maglev vehicle is one of the most promising applications of HTS bulks. In such a system, the nonuniformity of the magnetic field along the movement direction above the NdFeB guideway is inevitable due to the assembly error and inhomogeneity of the material property of the NdFeB magnet. So it is required to study the characteristics of levitation force of the bulks affected by the non-uniform applied magnetic fields along the moving direction. In this paper, we will study the characteristics of the levitation force relaxation between the HTS bulk and the NdFeB guideway by an experiment in which AC external magnetic field generated by an electromagnet is used to simulate the time-varying external magnetic field caused by the inhomogeneity of the guideway. From the experimental results, it has found that the levitation force is decreasing with the application of the AC external magnetic field, and the decay increasing with the amplitude of the applied magnetic field and is almost independent of the frequency.     

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.     

The effect of the external magnetic field on the current-voltage characteristic of HTS Josephson junction arrays

The role of the external magnetic field in performance specialty of the high-temperature superconducting (HTS) Josephson junction array (JJA): HTS YBa₂Cu₃O_7−0.05 bicrystal JJA with 180 junctions, is considered. The junctions are created on the yttrium-stabilized zirconium (fianite) substrate with the bicrystal grain boundary. The experimental confirmation of the current density changes under the influence of the external DC magnetic field is obtained. The dependence of current density on the penetrated magnetic field is investigated. The optimal shielding factor needed to obtain high supercurrents in considered system is determined.     

Angular Dependence of Transport AC Losses in Superconducting Wire with Position-Dependent Critical Current Density in a DC Magnetic Field

Transport AC losses play a very important role in high temperature superconductors (HTSs), which usually carry AC transport current under applied magnetic field in typical application-like conditions. In this paper, we propose the analytical formula for transport AC losses in HTS wire by considering critical current density of both inhomogeneous and anisotropic field dependent. The angular dependence of critical current density is described by effective mass theory, and the HTS wire has inhomogeneous distribution cross-section of critical current density. We calculate the angular dependence of normalized AC losses under different DC applied magnetic fields. The numerical results of this formula agree well with the experiment data and are better than the results of Norris formula. This analytical formula can explain the deviation of experimental transport current losses from the Norris formula and apply to calculate transport AC losses in realistic practical condition.     

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.