Layer-current waveform of coaxial multi-layer HTS cable considering the flux flow state

It is important to control the layer current distributions of coaxial multi-layer HTS cables because homogeneous layer current distribution decreases AC loss and increases the largest operational current. In a previous paper, we proposed a theory that can control current distribution based on the concept of flux conservation between two adjacent layers, and demonstrated the theory is in good agreement with experiment results. The theory was effective for an operational current less than the critical current of the cable. It is important to investigate current distribution under the condition of operational current more than the critical current of the cable because the cable experiences fault currents. We have extended the theory to treat the operational current more than the critical current by considering V-I nonlinear characteristics of HTS tapes including flux flow resistance and contact resistance between the cable and terminals. In order to verify the extended theory, we have fabricated a two-layer cable with the same twisting layer pitch, and hence caused inhomogeneous current distribution. It was observed that almost all of operational current less than the critical current flowed on the outer layer because of its lower inductance. When the operational current increased above the critical current of the second layer, the flux flow resistance appeared and distorted the current waveform with phase deviations. Finally, in the case of operational current more than the critical currents of both layers, flux flow resistance strongly affected current waveforms, and thereby the currents of both layers were determined by flux flow resistance. The extended theory simulated the layer current distribution waveforms and demonstrated good agreement with the experimental results under all operational current regions.     

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.     

火灾下平行钢丝束温度膨胀及高温蠕变试验研究

为研究开放空间拉索的火灾响应,该文考虑火源的空间辐射理论和拉索表面的环境换热边界,结合内部空腔辐射、接触传导、间隙导热三大基本传热理论,建立开放火灾下拉索腔体传热计算方法,并通过试验结果验证数值分析模型的准确性,分析预应力拉索在不同的内部传热方式、不同的包裹环境和不同的风环境下截面的温度场和应力场的时空分布特征,以及截面的轴力和弯矩的内力时变特征。结果表明：进行拉索的火灾响应分析时,考虑拉索的完整腔体传热模型可以比较准确地计算开放火灾下拉索截面的瞬态温度分布,随着曝火时间的增加,拉索截面的温度场和应力场分布呈现反对称状态且从二次分布特征向线性分布特征逼近,拉索截面会出现轴力损失和弯矩效应。相比于完整腔体传热模型,圆钢传热模型的截面应力分布均匀、轴力损失偏大且弯矩效应很小,空腔辐射模型的截面应力分布过于集中、弯矩效应偏大且轴力损失偏小。烟气包裹环境会加剧拉索截面的轴力损失和削弱拉索截面的弯矩效应。迎风环境会严重加剧拉索截面的轴力损失和弯矩效应。该文的研究成果可为索结构的抗火设计与防护提供理论依据。

     

Natural frequency spectrum of a flat superconducting cable

A matrix method is used to investigate the current damping process in a flat superconducting cable. A discrete spectrum of natural frequencies is obtained, each determining the rate of exponential damping of the corresponding induced current. Although the number of natural frequencies increases as the size of the cable increases, their spectrum remains finite because the maximum and minimum frequencies tend to finite limits. An analysis is made of the induced currents for the limiting frequencies. It is shown that in the range of minimum natural frequencies the induced currents are long-lived long current loops. At high frequencies the distribution of the induced currents in cable layers is sinusoidal. Pis’ma Zh. Tekh. Fiz. 25, 42–47 (July 12, 1999)     

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.     

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.     

Circuit analysis model for AC losses of superconducting YBCO cable

Information about AC losses and electromagnetic behaviour is essential when designing superconducting cables. In this work, AC losses of coaxial YBCO cables are determined using circuit analysis based computational model tailored for the needs of the YBCO cable design work. In the equivalent circuit superconducting layers are connected in parallel, the layers have an inductive coupling between each other and AC loss within a layer generates an effective resistance. The layer currents can be solved from a set of circuit equations. The computational model takes into account that the current in the cable creates magnetic field, which generates magnetisation loss and affects strongly the critical current of the YBCO tapes. The model was applied on several coaxial superconducting YBCO cable designs, which had nominal currents of 1-10 kA (rms). Low AC loss values were predicted for these compact YBCO cable designs. For example, AC losses less than 4 W/m were predicted for 10 kA cables.     

Experimental results of tri-axial HTS cable

Recently, a tri-axial cable composed of three concentric phases has been intensively developed, because it has advantages such as reduced high-temperature superconducting (HTS) tape, small leakage field and small heat loss as compared to three single-phase cables. However, there is an inherent imbalance in the three-phase currents in tri-axial cables due to the differences in the radii of the three-phase current layers. The imbalance of the currents causes additional loss and a large leakage field in the cable, and deteriorates the electric power quality. We have already proposed that it is possible to obtain a balanced three-phase distribution by adjusting all of the twist pitches. In order to verify the theory, we designed and fabricated a 1-m-long tri-axial HTS cable and carried out the cable test. The balanced three-phase voltages of the cable were measured by supplying an AC transport current with frequency from 50 to 500 Hz at 77 K. It is found from the test results that the balanced three-phase distributions can be realized by adjusting all of the twist pitches.     

Current redistribution and stability of superconducting triplex cable without electrical insulation carrying non-uniform current

When a small normal zone is produced in a strand in a superconducting cable by a local disturbance, current redistribution occurs and can help the recovery of its superconducting state. This effect of the current redistribution depends on the initial current distribution. In this paper, the initial current distribution in a triplex cable is controlled artificially to study its influence on the stability against local disturbances. A heat pulse is applied to a strand by a carbon paste heater to initiate the quench. Transient current distributions during quench or recovery process are measured by sets of Hall sensors placed at several locations along the cable axis. When the transport current is less than a threshold value, the stability is improved by the current redistribution from the heated strand to the others, even if the initial current distribution is not uniform. This threshold is related to the current margin of the heated strand, rather than to the current margin of the whole cable. Above this threshold current, the MQE against local disturbances is smaller in the cable with the non-uniform current distribution than in the cable with the uniform current distribution, when the total transport current is identical. If the current of the heated strand is identical and above the threshold, the MQE against local disturbances does not depend on the current distribution and agrees with the MQE of the single isolated strand. It means that the quench of one strand leads to the quench of the cable, and that the stability of one strand in the cable is not influenced by interaction with the others.     

An effective finite element approach for calculation of potential distribution in a multi-dielectric cable

The radial symmetry of the cable results in circular finite elements to evaluate the potential distribution in a multi-dielectric cable. Owing to this, a two dimensional analysis used in conjunction with triangular finite elements is reduced to one-dimensional analysis. This method therefore suggests an alternative proposal to calculate the potential distribution in a multi-dielectric cable with better accuracy.     

Investigation on AC loss of a high temperature superconducting tri-axial cable depending on twist pitches

High temperature superconductor (HTS) cables have been intensively studied because they are more compact compared with conventional copper cables. Since it is strongly expected that the HTS cables replace conventional power lines, some HTS cables are designed, manufactured, installed in power grids and tested to demonstrate full time operation. Recently, a tri-axial cable composed of three concentric phases has been developed, because of its reduced amount of HTS tapes, small leakage field and low heat loss when compared with single phase and co-axial HTS cables. The layers inside the tri-axial cable are subject to azimuthal fields applied from inner layers and axial fields applied from outer layers with different phase from their transport currents. These out-of-phase magnetic fields should be calculated under the condition of the three phase-balanced distribution of the tri-axial cable, and thereby AC losses should be evaluated. In this paper, the AC loss in the tri-axial HTS cable consisting of one layer per phase is theoretically treated for simplicity. The AC losses in the cable are calculated as functions of the twist pitches of HTS tapes. It is found that the AC losses rapidly decrease with increasing twist pitch.     

A 3-D Numerical Model to Estimate the Critical Current in MgB<Subscript>2</Subscript> Wire and Cable with Twisted Structure

Due to the low material cost, high critical transition temperature and high-current-carrying capacity, MgB₂ round wire with twisted filaments has great potential for applications in engineering. Therefore, it is important to estimate their critical current for optimizing and realizing high-powered wire and cable. A 3-D model is presented to calculate the critical current of wire and cable with twisted filaments. The critical current is estimated based on the Biot-Savart law and self-consistent model. A comparison between 2-D and 3-D models is performed for the wire. We consider the effect of twist pitch on the critical current. Moreover, the critical current of 6-around-1 cable with different twist pitches is analyzed and discussed using the 3-D model. It can be found that twist pitch of filaments plays an important role on the critical current. The model and method may also be useful for other superconducting wires and cables.     

Modal damping evaluation of hybrid FRP cable with smart dampers for long-span cable-stayed bridges

The paper presents a theoretical evaluation on modal damping of hybrid fiber reinforced polymer (FRP) cable with smart damper design in long-span cable-stayed bridge. The principles and design consideration of smart dampers were first clarified. Based on the energy principle, the theoretical equations of modal damping were derived for in-plane and out-of-plane vibrations, respectively. The parameters that influence the damping effect were further analyzed. Finally, an example of hybrid basalt and carbon FRP cable with smart dampers was selected to evaluate damping ratio in terms of the equations derived in the paper. The results show that (1) the smart dampers with discontinuous distribution benefit not only static and dynamic behavior of a cable but also optimization of damping; (2) the gap width, bonding, length and modulus of each smart damper can be optimized to obtain maximum of potential damping; (3) an example of smart damper designed hybrid FRP cable demonstrates its effectiveness for mitigating large magnitude of in-plane vibration, while more dominant damping effect is observed for suppressing out-of-plane vibration.     

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.     

Parametric estimation study of interstrand conductance in multi-strand superconducting cables

Interstrand conductance is a key parameter to understand the current distribution and stability events in multi-strand superconducting cables. In this paper, a new approach employing the parameter estimation method from system identification theory is applied to estimate the interstrand conductance from existing current distribution model based on experimental data of voltage differences at cable ends. Based on transient voltage measurements at cable ends this method estimates interstrand conductance conveniently and accurately under different conditions (temperature, cable length, cable compaction, etc.). The details of interstrand conductance between all combinations of sub-cables at different cabling stages were obtained. The influence of mechanical load on interstrand conductance was also studied. The experimental data sheds new light on how the mechanics of cable compaction and movement under simulated Lorentz load affects the electrical parameters, namely the interstrand conductance. The data are useful input for cable stability simulations and AC loss estimation, and the experimental method can be used to better characterize cables prior to magnet winding.     

Current test on a flexible superconducting core for a 2 GVA ac cable

A 5 m long prototype co-axial flexible superconducting cable core has been made and tested at currents up to 30kA. The inner and outer tubular conductors were both formed from helically-laid strips, and the dielectric between was lapped polyethylene tape. The dielectric was tested in separate experiments. The conductor strips contained layers of nobium, niobium-zirconium and high conductivity copper. The axial contraction of the cable core was restrained by titanium tie-rods and the lay angles of the conductor strips were chosen so that the core tightened radially on cooldown. Lead-filled termination cylinders between the ends of the cable and the current leads inhibited the formation and propagation of normal regions at high currents. Local and average ac loss measurements were made from 4.7 to 10.2 K and at current densities between 10 and 200 A mm^? with very satisfactory results.     

悬索桥缆索钢丝损伤超声导波检测数值模拟

为了实现对大跨悬索桥缆索钢丝损伤的有效检测,采用理论分析和数值模拟相结合的方法,对超声导波无损检测技术进行研究。通过理论求解钢丝中导波的频散曲线,分析频散特性和波结构,选取中心频率为200 kHz的L(0,1)模态进行钢丝断丝损伤检测;利用有限元软件,研究了钢丝中导波的频散特性和波结构,通过二维傅里叶变换技术对钢丝中的低阶导波模态进行识别,进一步分析了缺陷尺寸和角度对L(0,1)模态缺陷反射系数的影响;最后,对L(0,1)模态在两根钢丝和七根钢丝的断丝处的缺陷回波进行了数值模拟。数值模拟与理论分析结果相吻合,说明低频L(0,1)模态可以有效地对缆索钢丝断丝损伤进行远距离检测。     

香菇菌棒包装袋撑圆装置关键技术研究

目的 为了提高香菇包装机的包装效率,提升包装机的整体性能。方法 首先分析研究包装袋基本参数、拉伸特性、人工套袋方式,通过类比人工套袋得到撑圆装置设计方案。基于此方案,对撑圆装置的关键结构尺寸参数进行详细设计。结果 建立了三维模型并导入Ansys进行静力学分析,得到了撑圆装置的应力分布云图。撑圆机构动作过程中受到的最大压应力为2.48 MPa,远小于树脂材料弯曲强度67 MPa;最大变形量为0.175 mm,出现在撑圆机构最前端,不影响后序动作。结论 文中证明了撑圆装置结构设计的合理性和模型建立的准确性,为同类型结构的设计提供一定的理论参考。     

Nonlinear planar response of a cable under random excitation

In this study, the nonlinear planar response of a cable in its first symmetric mode of oscillation under two types of random forcing is investigated. The forcing could be either a narrowband excitation or a periodic function plus a white noise. A single mode approximation is used; wherein the cable is represented by an oscillator with both quadratic and cubic nonlinear stiffness terms. The equivalent linearization technique in conjunction with a stochastic sample stability analysis is employed in the response analysis. In particular, the effect of sag on the cable response is studied. The validity of the theoretical solutions is examined through limited digital simulation results.