Calculation of AC Losses of CICC for Superconducting Outsert Coils in a Hybrid Magnet

This paper is devoted to predict AC loss of cable in conduit conductor （CICC） which is of importance in the design of conductors. The consideration for the conductor＇s design and main parameters for the magnets are introduced. In order to attain a good accuracy in the calculation of AC losses, the field distribution within superconducting outsert should be considered. Calculation of the AC losses, including hysteresis losses and coupling losses, is conducted. An emphasis is put on the hysteresis loss during the ramp up of the current to the operational current （15.3 kA） and the coupling loss of the conductor in a power-down condition for insert. The results are obtained to be 74.9 kJ and 950 J for 40 T hybrid magnets, respectively. Based on the calculation, a brief analysis of losses effect on the conductor design and the operation of magnet is given for the purpose that the capacity of the cryogenertor can be evaluated and the stability regime can be improved in our future work on the hybrid magnets.

Analysis and Calculation of AC Losses Test of EAST PF Model Coil

The poloidal field model coil （PFMC） of EAST was a large NbTi superconducting coil. The PFMC was designed and constructed by Institute of Plasma Physics, CAS, and it was tested during 2003 at our institute. One of the most important performance testing items was the AC （Alternating Current） loss. It was able to measure the AC losses by the calorimetric method. The results will be useful for the evaluation of the AC losses of the poloidal coil and provide meaningful data for future operation of the EAST device.

DC performance and AC loss of cable-in-conduit conductors for International Thermonuclear Experimental Reactor

A reliable prediction of AC loss is essential for the application of International Thermonuclear Experimental Reactor(ITER) cable-in-conduit conductors(CICCs);however,the calculation of AC loss of ITER CICCs is a cumbersome task due to the complicated geometry of the multistage cables and the extreme operating conditions in ITER.In this paper,we described the models developed for hysteresis and coupling loss calculation,which can be suitable for the construction of ITER magnetic system.Meanwhile,we compared the results of theoretical analysis with the SULTAN test result to evaluate the numerical model we used.In addition,we introduced the n-value and AC loss with transport current for CICCs based on the DC measurement results at SULTAN,which lays the foundation for the further study.

Numerical and experimental analysis of AC loss for CFETR CS model coil

The central solenoid(CS) is an important component of China Fusion Engineering Test Reactor, for producing, forming and stabilizing plasma in the superconducting tokamak. It is a complicated work to design and manufacture the large superconducting CS magnet, so it is meaningful to design a central solenoid model coil(CSMC) and analyze its electromagnetic properties in advance. In this paper, the structure, design parameters and magnetic field distribution of the CS model coil are discussed. The peak power of radial and axial turn conductors and time bucket loss are analyzed by using piecewise-linear method. The CSMC AC loss with different Nb3 Sn CICCs and AC loss of ITER CS coil are compared. The special electrometric method to measure AC loss of the CS model coil for future reference is presented.

Field and current driven versions of Brandt method for calculating transport ac loss of superconducting cylinder and strip

As an elegant and fast numerical tool for solving time‐dependent electromagnetic field problems in hard superconductors,Brandt’s method has played an important role in understading the magnetic behavior of superconducting strips,discs,bars and cylinders in various aspect ratios.However,the application of this convenient method was mainly in magnetization processes.Traditionally,the solution of current transport problem needs to introduce a driving electric field E_(a),which requires a low efficiency iterative process and E_(a) itself was not clearly explained.In this work,three integral algorithms based on the Brandt’s method are developed to deal with current transport problems,which directly adopt the applied current as a boundary condition.Namely the current(I)‐driven version and two current‐field‐driven versions A and B.Moreover,the arbitrary applied magnetic field can also be included in the I‐driven version.The derivation with all necessary formulas for the methods are given in this work.As an example,the new methods,as well as the traditional method are used for calculating transport ac loss Q of a superconducting cylinder or strip obeying a power‐law relation of E∝J^(n)as a function of a given I(t).Derived from the Ampère law and the differential rather than the integral expression of the Faraday law,the current‐driven version can be used for more accurate and much quicker computation.Being an intermediate quantity,E_(a)(t) in the two current‐field‐driven versions is accurately calculated under the given I(t),but version B is much quicker than A.Problems relating to E_(a)(t) and Q stabilization process are discussed.

Numerical simulation on AC loss in REBCO tapes carrying non-sinusoidal currents

AC loss is one of the greatest obstacles for high‐temperature superconducting(HTS)applications.In some HTS applications,coated conductors carry non‐sinusoidal currents.Thus,it is important to investigate the effect of various waveforms on AC loss in coated conductors.In this work,transport AC loss in a 4 mm‐wide REBCO coated conductor carrying sinusoidal and non‐sinusoidal currents,is numerically investigated.The current amplitudes,the frequency of the transport current,and n‐value are varied.Non‐sinusoidal transport current waveforms studied include square,five types of trapezoidal,and triangular waveforms.Simulated results show that,for a given current amplitude,AC loss for the square current waveform is the greatest,that for the triangular waveform is the smallest.The sequence of AC loss in the conductor for different current waveforms coincides with the penetration depth,which implies the penetration depth determines the AC loss of the coated conductor.Furthermore,the transport AC loss in the conductor was found to decrease with frequency as f2=n for non‐sinusoidal transport current.

Electromagnetic analysis and AC losses of triaxial cables with multiple 2G-HTS layers per phase

For an accurate estimation of the AC losses of superconducting triaxial cables,in this paper we present a two‐dimensional model capable to provide a global assessment of multi‐layer triaxial cables,validated against the reported AC‐losses measurements on single‐phase cables provided by the Russian Scientific and Research Institute of the Cable Industry(VNIIKP).Four models are presented,the first being a single‐phase cable of 50 tapes and the others being three triaxial cables made of up to 135 coated conductors distributed in up to 9 layers.A systematic study is devised,where the number of layers per phase increases from 1 to 3,with at least 14 tapes distributed across each layer of the first(innermost)phase,15 in the secondary(middle)phase,and 16 in the third(outermost)phase,respectively.Remarkably,our results reveal that the simple strategy of considering an unbalanced distribution for the amplitudes of the applied current,can generally balance the magnetic field between the three phases even for the bilayer and trilayer cables,resulting in negligible magnetic leaks in all situations.Besides,our high‐resolution simulations allow to see for the first time how the transport and magnetization currents distribute across the thickness of all the superconducting tapes,from which we have found that the AC‐losses of the 2nd phase is generally higher than at the other phases at low to moderate transport currents,I_(tr)<0:8I c,being I_(c) the critical current of the corresponding tapes.Nevertheless,depending on whether the I_(c) of the SC tapes at the 3rd phase layers is lower than the one at the 2nd phase,the layers at the third phase can exhibit a considerable increment on the AC losses.This is result of the considered magneto angular anisotropy of the superconducting tapes,which lead to intriguing electromagnetic features that suggest a practical threshold for the applied transport current,being it 0:8I_(c).Likewise,the relative change in the AC‐losses per adding layers,per phase,and as a function of the entire range of applied transport current is disclosed.

AC loss and contact resistance in highly flexible rebco cable for fusion applications

High Temperature Superconductor(HTS)materials can operate at higher magnetic fields up to 20 T with high critical current and higher operating temperature,compared to low temperature superconductors(LTS).A Highly Flexible REBCO Cable(HFRC)is introduced at the Institute of Plasma Physics,Chinese Academy of Sciences(ASIPP);a cabling method that is suitable for REBCO HTS tape having anisotropic material properties in its thin REBCO layer.This type of HTS superconducting cable shows high potential for applications in nuclear fusion.The alternating currents and magnetic fields in tokamak type of fusion magnets,cause AC power losses in such cables,which can provoke instability of the conductor by induced currents and increase the temperature.As a first step in characterizing the electromagnetic(EM)performance of an HFRC cable,the AC loss and contact resistance of the HFRC prototype cable were measured at the University of Twente.The measurements were done in liquid helium(4.2 K)with AC magnetic fields,applied perpendicular to the cable's long axis.The AC loss was measured simultaneously by a calibrated gas flow calorimeter utilizing the helium boil-off method,and by the magnetization method using pick-up coils.For the applied test conditions,no coupling loss could be distinguished as a part of the overall AC loss.It is suggested that this might be explained by the shielding of the conductor interior from the applied magnetic field by the outer tape layer due to the high critical current density of the REBCO tape,leading to a high penetration field.

Optimizing coil configurations for AC loss reduction in REBCO HTS fast-ramping magnets at cryogenic temperatures

AC loss is one of the critical issues for designing REBCO fast‐ramping magnets operating at cryogenic temperatures.There are many ways to reduce AC loss for coil windings.However,it is not clear which method is the most effective way to minimize AC loss in the coil windings for a given Ampere‐turns.In this work,we numerically studied coil configurations of several small superconducting magnets constructed from 12 mm SuperPower REBCO coated conductors,for fast‐ramping application with the same Ampere‐turns to identify the lowest AC loss among them.The HTS magnets have a total turn number of 50 and inner diameter of 30 cm,carrying AC current operating in the temperature range of 20–40 K at 25 Hz.We incorporated several existing loss reduction strategies including spacing between the turns for single pancake coils,grading Ic values for the solenoid configuration,and applying flux diverters to shape the magnetic field around the coil windings.The simulation was implemented using a homogenized H‐formulation.Across all studied loss reduction methods,the use of flux diverters has the largest impact in AC loss reduction.The AC loss values in the solenoid winding comprising a stack of five single pancake coils with 0.1 mm turn‐to‐turn gap with the flux diverters agree well with those in the single pancake coil for 2 mm turn‐to‐turn gap with the flux diverters.Solenoid type coil configurations with flux diverters generate much smaller AC loss than the single pancake type with flux diverters when they generate the same center magnetic field.

Numerical analysis of magnetization AC losses in high-temperature superconducting slabs subjected to uniform strains

High-temperature superconductors in superconductor apparatuses are subjected to mechanical strains under operating conditions.These strains cause the degradation of the critical current densities and influence AC losses in the superconductors.Based on the dynamic process of thermomagnetic interaction,we report the results of numerical analysis of AC losses in an infinite high-temperature superconducting slab subjected to a uniform in-plane strain in an alternating external magnetic field parallel to the sample surface.The numerical analysis shows the details of electromagnetic phenomena in the slab and the dependences of AC loss on various external parameters including the uniform strain in the slab and the amplitude and frequency of the external magnetic field.In this paper,we find that whether the magnetic field fully penetrates the superconductor is the key factor that influences the features of AC loss.When the magnetic field cannot fully penetrate the superconductor,the loss rises with increasing strain or decreasing frequency.When the magnetic field can fully penetrate the superconductor,the feature is just opposite.We also analyze the effects of periodic strain on AC loss.It is interesting to find that when the periodic strain frequency equals the external magnetic field frequency,the AC loss reaches the maximum,regardless if the magnetic field fully penetrates the superconductor or not.

Calculation model of AC loss for CICC(cable-in-conduit conductor) based on strain

The CICC (cable-in-conduit conductor) in ITER (International Thermal-nuclear Experimental Reactor) will run in high-current, fast transient magnet field and complex environment. In response to the impact of magnet fields above 10 T, the Nb3Sn conductor has been introduced. However, the AC (alternating current) loss mechanism of Nb3Sn conductor on strain has not been explored. So, it is necessary to study the AC loss calculation method with transient electromagnetic field and wide range of strain, the coupling current in complex field and current signal of field is simplified to the spectrum effects of coil excitation, and calculation technology of AC loss, which contains the frequency, magnet field, coil characteristics and other parameters, is constructed to meet the discrete Fourier transform (DFT). By comparative analysis of simulation, it is found that the AC loss calculation of the conductor with spectrum algorithm is closer to the actual project value than the traditional algorithm. For the rapid excitation, in particular plasma discharge and burst, spectrum algorithm and the traditional algorithm are consistent. For the relative error calculation of hysteresis loss and coupling loss, it is found that the coupling loss is cumulative linearly, where the hysteresis loss is not so. As a function of the amplitude, frequency and phase angle, the relative error is less than 40%. The results showed that the method of Fourier restructuring is satisfactory.

一种面向高频链AC-DC矩阵变换器的高频变压器绕组优化设计方法

针对高频链AC-DC矩阵变换器中高频变压器绕组损耗大的问题,提出了一种高频变压器绕组优化设计方法,该方法首先建立了漏感模型和绕组损耗模型,并基于模型合理选择关键参数作为优化参数,应用有约束的多目标遗传优化算法对关键参数进行寻优,最后得到一套高频变压器绕组的优化设计方案。仿真和实验结果表明,该方法与传统面积乘积法(AP)法相比,绕组损耗可降低10%以上,变换器整机效率最高提升了1.07%,由此证明,该变压器绕组优化设计方法可以通过降低高频变压器的绕组损耗,达到降低高频链AC-DC矩阵变换器损耗、提升变换器整体效率的目的。

An applicable calorimetric method for measuring AC losses of 2G HTS wire using optical FBG

We present a new calorimetric method for measuring alternative current(AC)losses of high-temperature superconducting(HTS)tapes by optical fiber Bragg grating(FBG),which is particularly well suited for the AC loss measurement of Re BCO wires,so-called the second generation(2G)HTS wires.Compared with conventional calorimetric methods,the suggested method is both free of electromagnetic disturbance,magnetic field,and fast as well as simple.Self-field AC losses are measured by the optical FBG method and the conventional lock-in-amplifier(LIA)technique,respectively.The results show that the measured AC loss is in good agreement with those measured by the electric method,thus the presented calorimetric method would be available for measuring the AC loss of 2G wire and is expected to be generalized for the measurement of AC loss or thermal performances of HTS bulk.

地铁车站低压配电系统电动机设备采用AC 660V配电的研究

通过分析电动机定子绕组接线形式,输入电压与电磁功率、转矩关系,以及电动机负荷配电系统元件、电缆,从而得出地铁电动机设备均可采用AC 660V供电的结论。通过对比分析说明地铁电动机设备采用AC 660V供电时,具有大幅节约有色金属,降低初期投资及减小线缆损耗的优势。

交流双边供电系统供电能力分析

牵引供电系统采用双边供电方式可以取消相邻牵引变电所供电臂电分相,我国轨道交通直流供电系统基本采用双边供电方式,交流供电系统尚未应用该方式。本文针对交流双边供电系统,从电压损失、电流需求、牵引网能耗等方面进行分析,并给出研究结论。

六通道高温超导导体载流性能和交流损耗特性的仿真研究

为了满足未来聚变装置磁体系统大电流、强磁场以及优良机械特性的要求,提出一种六通道TSTC-CICC高温超导导体,并采用自洽模型和T-A法,对三种结构的六通道高温超导导体的载流性能和交流损耗特性进行了二维有限元仿真研究,其中结构1中带材堆叠方向垂直于径向方向,结构2中带材堆叠方向平行于径向方向,结构3中带材堆叠方式既有垂直于径向又有平行于径向两种方式。由研究结果可知,结构1导体的临界电流最大,结构2导体的最小,结构3导体的介于两者之间。结构1和结构3导体在低磁场下具有较好的临界电流各向同性特性。三种结构导体的临界电流随外磁场角度及磁场强度的变化各不相同。结构1导体的传输交流(AC)损耗最小,结构2导体的传输AC损耗最大,结构3导体的AC传输损耗介于两者之间。在不同角度的外磁场中,三种结构的导体表现出的AC损耗各不相同。

变速抽蓄机组失磁故障分析及保护研究

变速抽蓄机组(VSPSU)的励磁及控制方式复杂且易发生失磁故障,配置针对性的失磁保护对保障其安全运行至关重要。该文基于直流励磁系统和交流励磁系统的差异分析,将VSPSU的失磁故障划分为对称失磁和不对称失磁两种故障形式,并主要针对对称失磁故障开展研究。首先,分别从故障位于机侧和网侧角度出发分析VSPSU发生对称失磁故障后的电气量变化特性及其故障危害;然后,推导证明了传统失磁阻抗圆保护判据在VSPSU中应用时不具有可靠性,VSPSU缺乏具有针对性的保护方案;最后,基于VSPSU的失磁故障特性,提出了针对机侧对称失磁故障的下抛阻抗圆判据和针对网侧对称失磁故障的直流电压判据,两者结合形成了对VSPSU对称失磁故障的保护方案。仿真结果表明,该文所提方案可有效地检测VSPSU在各种运行工况下的对称失磁故障,以满足VSPSU对失磁保护可靠性的要求。

高转速下车用扁线电机交流损耗分析与优化

为降低高转速下扁线电机的交流损耗,提高电机的运行效率,以一台8极48槽扁线永磁同步电机为研究对象,建立扁线电机模型,分析交流损耗的影响规律,并以关键结构参数为变量,提出一种基于响应面设计的遗传算法优化方案,仿真结果表明,高速工况下,电机交流损耗降低约6.8%,各转速下电机效率均有所提升,且高效区间的平均占比提高约7.8%。

电动汽车用扁线异步电机性能分析与计算

随着电动汽车行业的高端化发展,异步电机以其优越的性能特点及成熟的制造工艺,成为电动汽车辅驱电机的首选。为满足高效率、高功率密度、良好的NVH等性能需求,扁线绕组被逐渐应用于电动汽车驱动电机中。为深入研究交流损耗对扁线电机定子铜耗及效率的影响,揭示扁线电机性能较传统圆线电机的优势所在,本文以一台自主设计的峰值功率为140kW的扁线绕组异步电机为研究对象,首先,从数学模型与仿真计算两方面出发,分析了交流损耗的变化规律,并基于考虑交流损耗前、后电机性能的变化情况,说明了扁线绕组的交流损耗是影响电机效率的关键因素之一。在仿真过程中,为缩短仿真耗时,介绍了一种并行瞬态求解算法在异步电机中的应用原理。最后,对具有相同定子槽面积及转子结构的扁线电机与圆线电机的性能进行仿真计算与对比分析,结果表明,与圆线电机相比,扁线电机具有更高的效率、功率密度及更好的热性能等运行特点。

预处理Jacobian-free Newton-Krylov法在求解超导电磁场问题中的应用

该文阐述了Jacobian-free Newton-Krylov(JFNK)法的基本原理及其双端预处理形式的迭代格式,选择处于时变(非均匀)外磁场中的二维超导体为研究对象,建立了基于矢量磁位法的控制超导体电磁特性的偏微分方程及相关的非线性有限元矩阵方程和数值迭代策略。以时变外磁场中具有高尺寸比的超导薄带的交流损耗问题和永磁外场中块状高温超导体的磁悬浮问题为计算实例,在肯定计算程序有效性的基础上,检验了预处理JFNK法求解这2类典型问题时的计算性能,证实了预处理JFNK法能较为快速地求解大型超导非线性电磁场问题,可作为开发超导电磁场数值计算程序的优选方法。