A finite-element method solution of the zero-sequence impedance ofunderground pipe-type cable

In order to provide adequate circuit protection for underground pipe-type cable systems from ground fault currents, it is important to be able to determine the zero-sequence impedance of pipe-type cables. For better knowledge of the impedance, a more accurate method needs to be developed. In this paper, we present a numerical method for computing the zero-sequence impedance of a pipe-type cable. This method is developed based on a finite-element analysis. Special attention is paid to the nonlinear B-H characteristic of the steel pipe, and an iterative procedure is employed for determining the permeability varying in the steel pipe. To validate the numerical method presented, measurements are made for the zero-sequence impedance at different current levels. A good agreement is observed between the numerical results and the measurement data     

Ampacity reduction factors for cables crossing thermallyunfavorable regions

When power cables cross regions with unfavorable thermal conditions, temperatures higher than the design value can occur. If the region is wide enough, the rating of the cable will usually be based on the assumption that the entire route is characterized by the same conditions. In a majority of cases, the unfavorable thermal environment will be very short, usually a few meters (e.g., street crossing). In these cases, the effect of the crossing is usually ignored. However, the conductor temperature in such cases may be much higher than in the remainder of the route and cable derating is required. Only rarely are analytical solutions used to determine the effect of unfavorable short sections of the route on the ampacity of the rated cable. The main reason no computations are performed is an absence of either derating formulas or derating tables (curves) and not the lack of a need. To fill this gap, an analytical solution for the computation of the derating factors has been developed and is presented in this paper. The solution is simple and accurate enough to be suitable for standardization purposes. A numerical example involving a pipe-type cable crossing a street is presented to show the effect of street crossings on the ampacity of the cable circuit. In this practical example, the ampacity of the pipe-type cable has to be derated considerably     

Cable crossings-derating considerations. II. Example of derivationof derating curves

For pt.I see ibid., vol.14, no.3, p.705-14 (1999). Cables crossing other heat sources either perpendicularly or at oblique angles will experience a rise in conductor temperature which should result in ampacity derating. In the first part of the paper a mathematical model for calculation of derating factors was presented. In this paper, a practical numerical example is considered with a 138 kV pipe-type cable crossing a 10 kV distribution circuit. The numerical analysis presented confirms experimental findings reported in the literature that the cable crossing may elevate conductor temperature by as much as 20°C     

利用模拟热荷法计算地下电缆稳态温度场

根据电场和温度场的相似性,提出了用于计算地下电缆群稳态温度场的模拟热荷法。利用热路的方法将电缆金属套损耗和铠装层损耗归算到电缆导体。利用调和平均法对电缆导体外的多层介质进行处理,最终将电缆等效为导体和外护层的2层结构。根据换热量相等的原则,将地表空气对流换热系数等效为一定厚度的土壤。在电缆线芯和空气中用模拟热荷代替原来的线芯损耗和空气对土壤温度场的影响。然后根据镜像法,按照地表空气等温、导体等温以及外护层和土壤边界温度梯度相同列出约束方程组。利用高斯法求解方程组,求得地下电缆群稳态温度场的分布。试验和有限元仿真验证了模拟热荷法在地下电缆群稳态温度场计算中的有效性。     

Thermal Performance of Direct Buried Pipe-Type Cable Splices

With actual test data collected from the 230kV pipe-type cable described in reference (1), computer models were developed which allow the determination of the thermal characteristics and the ampacity of direct buried pipe-type cable splices. Computer techniques developed in (1), the accuracy of which were verified by field data collected from operating pipe cables, were again used in developing the computer models for this project.     

Short-Term Transient Temperature Calculations and Measurements for Underground Power Cables

A time-dependent heat transfer model based on the complete Fourier integral was developed for calculating cable temperatures during short-term transient conditions. A cyclic heat transfer calculation is used to obtain the initial temperature-time profile of the cable before the transient loading begins. The short-term transient model uses a lumped parameter formulation for the different cable regions and the Fourier integral to approximate the transient heat loss profile. Calculated conductor, jacket, and conduit temperatures show reasonable agreement with experimental results for a number of short-term transient tests with cables in a typical duct bank arrangement.     

Update on the Development of Reduced Wall 138kV HPOF Cables and Joints for Re-Conductoring of Existing 69kV Lines on the Florida Power & Light Company System

A reduced wall 138kV HPOF pipe-type cable having a 700 kcmil (355 mm2) compact round copper conductor and 348 mils (8.8 mm) of insulation and two types of joints have been developed for re-conductoring existing 69kV HPOF feeders utilizing 5 inch (127 mm) outside diameter pipes on the Florida Power & Light Company (FP& L) system. Laboratory test results on the cable and two joints, one employing hard paper and the other high density crepe paper tapes, are reported. The commercial cable installation is described. Test results are also given on an improved design reduced wall 138kV HPOF pipe-type cable having a 2000 kcmil (1015 mm2) compact segmental copper conductor and 379 mils (9.6 mm) of insulation and a high density crepe paper joint intended for re-conductoring a 69kV HPOF pipe-type feeder using the existing 6-5/8 inch (168 mm) outside diameter pipes. The cable and joint satisfactorily passed all requirements of AEIC CS2-82 (4th Edition) [4].     

Factors influencing ampacity and temperature of underground power cables

This paper presents the factors that influence ampacity and temperature rise of three-phase, single-core 33- and 500-kV XLPE underground cables (UGC) using CYMCAP software. These factors are conductor cross-sectional area, soil thermal resistivity, cable burial depth, cable separation, sheath bonding, bedding and backfill heights and thermal conductivities, nearby parallel heat source, formation of dry zone, loss tangent and segmented conductors. Results reveal that increasing the separation distance between phases gives higher ampacity, contrary to the burial depth. The rate of conductor temperature reduction due to the increase in the bedding thermal conductivity is more pronounced than that achieved by increasing backfill thermal conductivity. Furthermore, increasing the native thermal conductivity and/or the maximum conductor temperature increases the UGC ampacity and consequently increases the induced sheath voltage. Sheath losses are significant in transmission UGC where the load currents are always high. High conductor temperature and hence degradation rate is expected for UGC carrying currents of highly fluctuating loads. UGC must be derated as they age (increasing loss tangent), or when dry zones are formed around them, or when a nearby parallel heat source. Finally, it is found that the increase in the number of conductor segments nonlinearly increases the UGC ampacity.     

基于分布式光纤测温系统的单芯电缆瞬态温度场数值计算

为了保证地下电缆的可靠运行,电力部门的常规做法是在电缆表面安装分布式光纤温度传感器（DTS）,对电缆的热状态进行直接监测。由于电缆的载流量取决于导体的持续运行最高温度,因此基于传热学原理,利用通用有限元软件对计算场域进行自动划分,通过提取得到的单元与节点信息自主编制有限元计算程序,结合实时变化的负荷数据及DTs测量的电缆表面温度,分析计算了单芯电缆的瞬态温度场。通过110kV1×630mm^2交联聚乙烯电缆的试验研究,对比电缆导体温度的测量值和计算值,结果表明,自主编制的有限元计算程序能够准确地计算电缆的瞬态温度场,为电缆安全高效的运行提供了有效的理论依据。     

计及轴向传热的中低压单芯电缆导体温升状态空间模型

电力电缆导体温度可为线路载流量及运行状态的评估提供依据。然而,在当前电缆温度计算中,导体的轴向温度分布通常被忽略,无法准确描述电缆运行的热动态过程。为此,基于热平衡原理,在状态空间内提出了计及轴向传热的中低压单芯电缆导体的温升模型。为克服模型参数难以确定的问题,提出了基于粒子群优化算法的电缆热路参数辨识方法。为验证模型精度,建立了电缆温升实验平台,在不同电流下对空气中敷设电缆进行了轴向温升实验。计算结果与实验结果的对比表明,当电缆存在轴向温度梯度时,所提状态空间模型结果精度高于IEC60287标准模型,能够满足中低压单芯电缆导体在不同电流条件下的轴向温升计算要求。     

地下电缆群稳态温度场和载流量计算新方法

根据地表对流和深层土壤温度不变的原则,将地下电缆群开域温度场等效为闭域温度场,应用有限元分析了给定电缆负荷电流的地下电缆群闭域温度场分布.采用热路法将电缆金属套损耗归算到电缆导体,应用调和平均法对电缆导体外的薄层进行处理,最终将电缆等效为导体和外护两层结构,减少了剖分节点数,提高了计算精度和收敛速度.采用弦截法计算了地下电缆群载流量.试验和计算结果表明,利用有限元计算地下电缆群温度场和载流量满足工程实际需求.     

基于暂态热路模型及反演算法的电缆接头导体温度监测

对电缆接头温度进行实时监测对于预防电缆接头的热致事故是十分重要的,但传统的基于精确热网络模型的温度反演算法实现难度非常大。建立了计入电缆接头分布式热容的暂态热路模型,并据此推导出电缆接头导体温度反演算法。同时,利用仿真软件模拟各种负荷状态下电缆接头温度的变化,为电缆接头温度反演算法的研究提供技术手段。通过实验室模拟,证实了所提出的监测方法的有效性。     

基于表面温度场的电缆线芯温度在线诊断研究

线芯温度是电缆的一个重要参数,当电缆过负荷时,其线芯温度高于允许温度,使电缆绝缘加速老化,甚至造成绝缘介质热击穿。文中提出了一种基于电缆表面温度场的对电缆线芯温度进行在线诊断的方法。该方法采用红外热象仪拍摄电缆的表面热图象,可根据电缆的表面温度、结构参数,物性参数和环境温度,通过建立传热数学模型,对电缆的线芯温度进行反演计算,并与其允许温度进行比较,实现了电习温度的非接触,在线诊断。     

基于材料导热系数的单芯高压电缆导体温度动态分析

电缆导体温度是电缆安全运行的重要参数,基于110 kV交联聚乙烯单芯电缆的稳态等效热路,运用节点法从理论上推导了稳态下电缆导体温度与各层结构材料的导热系数的关系式,利用归一化灵敏度原理分析了导体温度对电缆各层结构材料的导热系数改变的灵敏程度,并设计了阶跃电流温升试验。理论推导和分析试验数据得到:稳态时,电缆导体温度对各层结构材料导热系数的灵敏度与材料的导热系数成反比;稳态时电缆导体温度计算值对气隙层、绝缘层导热系数灵敏,而对垫层、外护套导热系数不灵敏。由此可为实现电缆导体温度和载流量的准确计算,如何准确选取电缆的物性参数提供参考。     

Investigation of the magnetic field produced by unbalanced phase current in an underground three-phase pipe-type cable

This paper presents a numerical technique for investigating the magnetic field produced by an underground three-phase pipe-type cable, which may carry unbalanced phase current. The numerical technique is based on finite element method and the equivalence principle. To validate the numerical technique, numerical results of the magnetic field generated by a pipe-type cable carrying balanced phase current are compared with the existing measurement data first. Then, the numerical results of the magnetic field generated by unbalanced phase current in a pipe-type cable are presented and analyzed. Through the analysis of the data, we observe that the zero-sequence current returning in the pipe, resulting from the unbalanced phase current, may significantly alter the magnetic field above the pipe.     

单芯电缆线芯温度的非线性有限元法实时计算

考虑电缆材料热性参数是温度的函数及忽略热量沿着线芯轴向传输所造成的线芯温度计算误差,为提高电缆线芯温度计算的精度,提出基于非线性有限单元法计算电缆导体的温度。研究电缆导体径向、轴向温度梯度以及热量扩散规律,分析运行电流、外界环境温度等因素对电缆线芯轴向、径向温度分布的影响。根据传热学原理,研究电缆热性参数随温度变化对电缆导体温度的影响,建立电缆导体温度计算三维非线性有限元模型,并通过实验数据对非线性有限元模型进行验证和修正。实验和有限元仿真的对比表明：忽略电缆热量沿着轴向传输以及热性参数的改变会造成线芯温度计算误差;所提出的电缆导体温度实时计算非线性有限元模型的有效性,为高温下运行电缆导体温度监测与负荷预测奠定了基础。     

柔性直流输电系统用直流交联聚乙烯绝缘电缆导体最高温度提高到90℃的可行性

以实际直流交联聚乙烯(DC XLPE)电缆工程设计示例,表明将柔性直流输电(VSC)系统用DC XLPE电缆的导体的最高运行温度提高到90℃,其技术经济效果显著。按DC XLPE电缆抑制空间电荷要求,阐明DC XLPE电缆绝缘的直流恒定电流电场中空间电荷密度与绝缘温度梯度和XLPE绝缘的体积电阻率的温度系数成正比而与导体最高温度不直接相关。通过合理的DC XLPE电缆工程设计和正确选用DC XLPE电缆,可以在提高DC XLPE电缆传输功率和减小绝缘温差抑制空间电荷方面取得优化结果。320 kV及以下XLPE电缆在导体最高温度90℃下运行,绝缘损耗远低于导体损耗,DC XLPE电缆发生热不稳定的可能性很低。对VSC系统用DC XLPE电缆导体运行温度提高到90℃的可行性表示肯定的意见,对实现目标提出具体的措施建议。     

考虑轴向传热的单芯电缆线芯温度实时计算模型研究

为了研究轴向传热对电缆线芯温度的影响,首先以单芯电缆的三维微元热路模型为基础,建立了考虑单芯电缆轴向与径向传热的三维热路模型,且根据该三维热路模型实现了单芯电缆线芯温度实时计算的理论推导。其次,通过不同敷设环境下分别加载恒定与阶跃电流的实验,讨论了电流、电缆敷设环境与外界环境温度等因素对轴向、径向温度分布的影响。实验结果表明,电流是决定轴向温度梯度变化趋势的主要因素,空气中电缆的线芯温度上升速度最快,土壤中电缆次之,水中电缆最慢。最后通过有限元仿真工具,对比了空气中电缆中间接头三维有限元模型与二维有限元模型计算的线芯温度。研究结果表明,只考虑电缆径向传热的二维热路模型会造成线芯温度计算的误差,而考虑电缆轴向与径向传热的三维热路模型能够提高计算的精度。     

基于FEM的直埋电缆载流量与外部环境关系的计算

利用有限元法对有外部热源的直埋电缆区域进行剖分,计算了给定电缆负荷的温度场.利用对分法计算了导体温度等于绝缘长期耐受温度时的电缆负荷,确定了有外部热源和地表空气温度变化时的直埋电缆的载流量.计算结果给出了电缆载流量随电缆与外部热源间距的变化规律,以及电缆载流量随地表空气温度的变化规律,为工程实际提供了参考依据.     

Cyclic Temperature Calculations and Measurements for Underground Power Cables

Two time-dependent heat transfer models were developed for calculating cyclic temperature-time profiles for underground power cables with any cyclic load. A fully distributed model allows for temperature variation with radial distance and time in each cable region. A lumped parameter model sets up a thermal circuit and solves for the temperature of each cable region as a function of time. Results from both models are compared with experimental temperature profiles for five cyclic tests for cables in a typical duct bank arrangement. The comparison shows good agreement for cable conductor and jacket temperatures and some error for conduit profiles.