管内电缆导体传输交流损耗的理论计算和实验

交流损耗是大型超导核聚变实验装置如国际热核聚变实验堆和中国聚变工程实验堆稳定性的重要指标。然而应用于核聚变装置的管内电缆导体(CICC)在无外场下传输损耗数值计算很少。首先分析基于分布参数等效电路方法对CICC的N根股线的电流进行描述和分析;之后算出整个导体的电流分布,从而求出导体的传输电流损耗;同时,将数值计算结果与临界态模型结果作对比,以验证该计算模型的可行性;提出改进的CICC交流损耗测量方法,为国内下一步测试CICC及其线圈奠定了实验基础;最后,提出适用于单根圆股线的定标法则,为计算CICC的传输电流损耗奠定理论基础。     

Theoretical investigation on skin effect factor of conductor in power cables

This paper describes a newly derived theoretical equation on the skin effect factor of power cables, and its application to large‐size OF and XLPE cables with segmental conductors, including insulated wires. The skin effect factors calculated with the new equation were fit very well to measurements in a wide range of conductor sizes. In the new equation, the important factor which characterizes the skin effect of segmental conductors is the “equivalent conductivity ratio” v defined by the ratio of longitudinal conductivity in axial direction of conductor to conductivity of conductor wires. Since the obtained ratio v in XLPE cable was three times greater than that in OF cable, the larger longitudinal eddy current passing from a wire to another increased the eddy current loss in conductor, which increased the conductor loss of XLPE cable. The new equation enables us to investigate quantitatively the dominant loss component affecting the skin effect factor. Then, the skin effect factors and coefficients for OF and XLPE cables were investigated with the new equation. It was revealed that the best number of separation, in which the skin effect reached a minimum, existed in OF and XLPE cables with segmental conductors. In addition, it was confirmed that the skin effect coefficients ks1 calculated with the new equation were very consistent with those used in JCS. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 165(1): 18–34, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20576     

Boundary element estimation of current density distribution and eddy current loss in bundled multi-wire cables

A numerical approach to the estimation of the current density distribution and the eddy current loss in bundled multi-wire cables using the boundary element method is proposed. Under the assumption of the gradual twist of the bundled wires, the cables are modelled to be two-dimensional with respect to their cross-sections. Three-phase transmission lines of cyclic symmetrical configuration are considered for which a reduction method is utilized to provide efficient computation. Some numerical demonstrations are made for three types of three-phase transmission-line models, consisting of a single wire and three and seven bundled wires. Two cases are considered: one in which the bundled wires are electrically contacted one to another on their surfaces and one in which they are independently insulated. The equivalent resistance is also calculated to examine the skin effect. The skin effect and the effectiveness of the multi-wire configuration to reduce the skin effect are well demonstrated.     

Sizing of cables in randomly-filled trays with consideration forload diversity

A method for demonstrating increased ampacity of cables in trays with loading diversity is given. Ampacity tables for sizing cables in randomly-filled cable trays are provided in NEMA WC 51-1986 based on a model developed by J. Stolpe which ensures that the maximum cable temperature does not exceed the insulation rating (typically 90°C) under worst-case conditions. The Stolpe model intentionally disregards the reduced heating effect of deenergized or lightly-loaded cables to ensure that all possible hot spot conditions are enveloped. Other methods have been proposed to credit loading diversity in order to justify increased ampacity. However, since they involve certain assumptions about the heat distribution within the cable mass, these methods may fail to identify individual overloaded conductors. This paper describes a simple method which considers the performance of individual conductors while providing a means of increasing ampacity as a result of loading diversity     

Magnetic instability of ac multifilamentary superconductors in spatially distributed magnetic field

Alternating current (ac) superconducting machines such as superconducting generators, transformers, or resistive current limiters need large‐current‐capacity conductors. These conductors are generally fabricated as multistrand cables stacked with multifilamentary NbTi superconductors whose current capacity is a few tens of amperes. ac quench current degradation has often been observed in ac use of such multistrand cables. Several reasons for this degradation have been pointed out: nonuniformity of each strand current, mechanical disturbances, thermomagnetic instability, and ac losses. However, it has not as yet been overcome. Since the angle between the strand axis and the cable axis changes along the cable axis in multistrand cables, the strands are exposed to a spatially (axially) distributed magnetic field, which has longitudinal and transverse components changing periodically due to multiple cabling. This paper mainly discusses the thermomagnetic instability due to the distributed transverse magnetic field, which was compared with the self‐field instability and the longitudinal field instability experimentally and theoretically. It was confirmed that the ac quench current degradation due to the distributed transverse field could be induced by the following: nonlinear E–j characteristic, strong dependence of E–j characteristic on magnetic field in low field region, uniformity of the axial current profile inside the superconductor with the high resistive matrix, and the poor thermal diffusion of CuNi/NbTi composites. © 2000 Scripta Technica, Electr Eng Jpn, 131(1): 45–55, 2000     

应用第2代高温超导体的冷绝缘超导电缆输电导体层间均流技术

冷绝缘高温超导电缆的导电层一般设计为多层结构以满足大电流载流特性,但伴随层数的增加,超导体上的集肤效应会引起电缆输电导体各层电流分布不均匀的问题,从而造成电缆损耗增加和传输性能下降。采用基于动态惯性权重因子的粒子群优化算法,提出了电缆导体层电流层间均流优化的设计方法。应用第2代高温超导材料钇钡铜氧涂层导体,通过建立超导电缆的等效电路模型,考虑电场、磁场等约束因素,对一根1km长,110kV/3kA等级的冷绝缘高温超导电缆进行优化设计,获得了电缆本体结构参数及输电导体层和屏蔽层的电流分布。比较优化前后层电流的结果可知,优化后超导电缆各导体层电流与平均电流相比最大不平衡率小于3.5%,各屏蔽层电流达到均布,较好地实现了电缆各导体层电流均匀分布的优化目标。最后,超导模型样缆载流特性实验也验证了优化设计方法的有效性。     

Ampacities of power cables wound on reels

This paper presents a mathematical model that is capable of calculating the ampacity of a wide variety of power cable designs consisting of an arbitrary number of layers on a cable reel. The model considers round cables with copper conductors. The validity and accuracy of the ampacity model were verified by comparing the predicted temperature distribution within the reel with measured temperatures collected during an extensive testing program conducted at the US Bureau of Mines (USBM). The mathematical model predicted a temperature distribution within the cable layers that was very close to the measured variation in temperature. The value of the program is illustrated by calculating ampacities for several copper conductor sizes     

Proximity effect and eddy current losses in insulated cables

Insulated cables are generally designed according to thermal criteria: the current rating depends on the permissible temperature inside the insulation. As the heating of a cable mainly results from Joule losses, it is worthy to determine the current distribution in its metallic components (the core and the metallic screen for single core cables). The current distribution in tables is affected by the skin effect and the proximity effect due to neighbouring cables of the circuit itself or from parallel links. A general method is developed to calculate the current distribution in the core and the screen of a single-core cable, starting from Maxwell equations. The stress is set upon skin and proximity effects, taking into account the influence of the frequency. Joule losses are calculated in some practical cases of three-phase links     

Current distribution in superconducting multistrands for ac use before and after quenching

A superconducting multistranded cable is used to realize high current capacity for ac use. The critical current value of the cable is reported to be less than the simple summation of the individual critical current value of each strand. The causes for such a degradation of the critical current value have not been revealed. This paper investigates the current distribution in multistrands before and after their quenching by using seven-strand superconducting cable and 7x7 cable. The following experimental results are derived: (1) the quenching is initiated at one strand in the cable; (2) the current in the quenched strand is transferred into the other strands; (3) an avalanche of quenching is induced among the strands; and (4) the central strand is quenched finally among the strands. The critical current values of the 7- and 7 × 7-stranded cables also are measured. These values are in good agreement with the predicted values based on the mutual inductance among the strands. It is concluded that the unbalance of the current distribution in the superconducting multistrands can be one of the promising causes for the degradation of the critical current value.     

XLPE三芯电缆稳态并联热路模型及实验验证

交联聚乙烯材料的三芯电缆广泛应用于低压配电网中,但长期以来,关于电缆载流量计算的研究多集中于单芯电缆。考虑到三芯电缆与单芯电缆的结构差异,在IEC 60287标准计算的基础上,利用传热学知识,理论推导了三芯电缆并联结构的6层4节点稳态热路模型。采用形状因子法计算热阻参数,利用外表皮温度反推计算得到电缆各层温度。为了验证计算的准确性,设计了空气敷设和土壤敷设两种敷设方式下的升流实验,测量得到稳态时导体线芯、绝缘层、铠装层和外表皮温度,并与理论温度计算值进行了比较分析。分析结果表明,利用提出的热路模型进行三芯电缆载流量计算的误差在允许范围内,可应用于工程实际。     

500 kV充油海底电缆导体温度分布式光纤传感监测及应用

依据海南联网系统500 kV海底电缆捆绑特殊海底光缆的实际情况,通过分布式光纤传感技术结合经有限元仿真模型优化的IEC60287热路模型的方法可以监测海底电缆内部的温度分布。在实验室中搭建岸上模拟实验平台,利用中压电缆捆绑光纤的结构进行捆绑电缆岸上模拟实验。同时,将经验证的温度监测方法应用于海南联网系统500 kV海底电缆,以C相空气段为例监测捆绑电缆光单元的温度。采用有限元仿真计算电缆表面的温度,根据电缆表面的温度基于热路模型推导出对应的导体温度,得到电缆导体在实际运行过程中的温度变化。岸上模拟实验测量的导体温度与数值计算得到导体温度的误差低于1.77%, 验证了海底电缆导体温度监测方法的准确性。     

Calculation of current division in parallel single-conductor powercables for generating station applications

A matrix solution method is presented that enables the engineer to determine the phase current distribution among the individual conductors in parallel single-conductor power cables. Use of a commercial mathematics software package on a desktop MS-DOS personal computer to solve the resulting matrices is illustrated. Results of field measurements on a six-conductor-per-phase cable installation are compared with calculation results. Application of the results to cable assessment activities is discussed, including ampacity verification for increased loads, cable insulation life assessment studies, and cable impedance input into station service system analysis     

等传输容量铜、铝导体海缆技术经济性比较

针对铜资源日益紧张造成电线电缆行业原材料成本压力的问题,分析铜、铝材料性能差异,完成等传输容量下铜、铝导体截面换算,依据现有生产工艺,采用解析法,完成铜、铝导体海缆参数计算,对比分析铜、铝导体海缆的技术经济性,进一步研究铝导体连接性能。结果表明：等传输容量条件下,铜、铝导体海缆单位质量近似相等,两者损耗及短路电流特性相近,铜导体海缆材料成本为铝导体海缆的110%~180%,采用交流氩弧焊可使铝导体接头具备良好电气与机械性能,铝导体海缆经济性更优。     

Cooling characteristics of a large-current capacity AC superconducting cable

Diameter of the superconducting ac composite strand is small, typically 0.1 mm, because the strand must be twisted in a very short pitch to reduce coupling losses. Therefore, current capacity of the single strand is small and in the range of ～10 A. In large-scale electric power apparatus, the conductors must be able to carry large currents and hundreds of these composite strands should be bundled. The composite strand is highly unstable and susceptible to a very small disturbance due to a frictional wire motion because the main matrix of the wire is highly resistive CuNi. For stable operation of an ac superconducting winding, every strand in the bundle cable should be fixed firmly. An effective technique to fix strands is to impregnate the winding by epoxy. In this case, the ac losses in the winding are to be cooled by heat conduction through the epoxy. Therefore, it is important to estimate the temperature rise of the winding to discuss the fact that the epoxy impregnation technique is applicable to the ac superconducting electric power apparatus. In this paper, the mechanism of thermal conduction of the epoxy-impregnated winding at the 4.2 K region is discussed based on experimental data and the temperature rise of a large-scale cable bundles by 7 × 7 × 7 strands calculated considering thermal resistivity at the interface between the epoxy and the strand. The calculated value agrees well with the measured value.     

Evaluation of indoor cable capacitances taking into account conductor proximity and dielectric heterogeneity effects

This paper is the second part of a two-paper set dealing with capacitances computations for indoor cable systems currently being employed for high-frequency signaling. In the first part, a harmonic expansion technique was used to accurately determine the capacitances of a three-conductor cable with an unbounded insulating medium. A generalization of the technique for n-conductor cable configurations is presented here, taking into account not only the proximity phenomena among conductors but also the dielectric medium heterogeneity effects arising from the finiteness of the cable insulating medium. Particular applications regarding typical triplex cables are presented. Numerical results concerning cable capacitances and cable wave-propagation parameters for odd-mode operation are analyzed and discussed.     

Algorithm to predict dry-band arcing in fiber-optic cables

Utilities frequently use ADSS (all dielectric self-supporting) fiber-optic cables installed on transmission lines 3-6 m below the high voltage conductors. Dry-band arcing occurs on the fiber-optic cables when the cables are polluted and wet. This has been assumed to cause cable failures. An equivalent circuit has been developed to represent the polluted fiber-optic cable in the high voltage environment. The objective of this paper is to present a novel numerical method that can be used to predict dry-band arcing in fiber-optic cables. KCL (Kirchoff's current law) is used to derive node point equations for the equivalent circuit. Forward elimination and backward substitution of node voltage is used to solve the equations. The effect of pollution, tower arrangement, and conductor sag is analyzed. The numerical method has speed advantages over circuit simulation methods. This method includes conductor sag, nonuniform pollution, and variable capacitance. This algorithm can be used to predict dry band arcing in fiber-optic cables     

电动汽车共模电流传导特性的研究

在电动汽车中,沿车辆底盘和电缆传导的共摸电流是产生电磁传导干扰和共模辐射的重要原因。本文针对电动汽车中主要电磁干扰源的BOOST电源变换器,建立了电磁干扰源和共模电流传导路径的等效电路模型,指出在电缆中传导的共模电流决定于电缆一底盘的阻抗特性。电缆-底盘阻抗的传输线模型分析表明,该阻抗呈容抗、串联谐振、感抗和并联谐振交替出现的特征,使共模电流的各频率分量具有不同的沿电缆分布特性。共模电流的解析结果和试验测量结果基本吻合。为了抑制共摸电流,提出了共模电感的合理布置和取值范围。     

Practice and Accepted Rules of Shielding Power Cables

The Insulated Power Cable Engineers Association voltage limits differ from those permitted by the 1975 National Electrical Code for nonshielded extruded insulated conductors rated 2001 to 8000 V. These differences have created among cable users a renewed interest in the subject of power cable shielding. A brief history of shields has been employed as an introduction to a review of shielding. Electric field patterns in nonshielded versus shielded cable are described along with reasons for shielding and the several functions performed by shields. It is shown how electric stresses can create tracking or surface discharge in typical nonshielded cable installations Also reviewed are methods of minimizing shield losses in single-conductor shielded cables     

Estimation of the temperature rise in cylindrical conductors subjected to heavy 10/350 μs lightning current impulses

Lightning is a very high-energy phenomenon, which can pose serious dangers for human beings and the environment. Although much progress has been made in the area of lightning protection, there are still many cases of fires caused by lightning and power and telecommunication system outages. We have carried out an experimental and mathematical investigation into the temperature rise in cylindrical conductors subjected to heavy 10/350 μs lightning current impulses. The temperature rise measurements took place in one of the most reliable laboratories in Europe (BET, Menden, in Germany). The proposed mathematical models used to estimate the temperature rise in cylindrical conductors assumed both a uniform and non-uniform current density distribution by taking into account the transient skin effect. In addition, verification of the mathematical results were studied. Suggestions for further investigations are also provided. The experimental results are consistent with the results from the mathematical models. It is convincingly shown that copper conductors can be influenced by the transient skin effect. The additional temperature rise however, caused by the transient skin effect, is minimal, and can be neglected.