Ampacity of cables in single covered trays

A mathematical thermal model is developed to predict the operating temperatures of cables in a single covered tray when there is load diversity in the power cable bundle. The model accommodates two different loading scenarios: one in which the heat is distributed evenly across the cable tray cross section; and one which concentrates the heavily loaded cables along the centerline, while surrounding them with more lightly loaded cables. The temperature predictions provided by the model are compared to data found in other IEEE papers, data collected in laboratory measurements, and new data from a four-year study of cable trays in an operating nuclear plant. Reasons for differences between the field data and the computer results are discussed. The model is used to evaluate the conservatism in the available Codes and Standards. A derating factor is introduced that is defined in terms of the ampacity of power cables in open-top trays. The derating factor accounts for the added thermal resistance present when a cover is placed over the cables, trapping a layer of stagnant air on top of the cable mass. The computer model is then used to predict values for the derating factor as a function of cable depth. The derating factor is shown to be independent of the composition of cables in the tray. The presence of a cover is shown to reduce the ampacity based on an uncovered tray by up to 25 percent depending on the depth of the cables in the tray     

Ampacity of diversely loaded cables in covered and uncovered trays

The existing code for ampacity of cables in a tray does not account for load diversity among the cables and it does not consider the presence of tray covers. This paper provides two factors that can be used to determine ampacity values for these two cases. These factors can be used in conjunction with existing code ampacity values so that cable ampacities can be calculated for diversely loaded, covered and uncovered trays. Also, the case of a few heavily loaded cables in an otherwise lightly loaded tray is addressed. This particular situation can produce nonconservative ampacity values if treated with a one-dimensional heat transfer model. The problem of both load diversity, and the presence of a cover are addressed with a computer code that has been described in previous papers. The computer model is designed to provide conservative ampacity values by assuming that the more highly-loaded cables are placed along the tray centerline and the lightly-loaded cables are positioned on the outer surfaces of the cable bundle. In this way the heavily-loaded cables are insulated from the environment and thus the program calculates a conservative cable temperature. The factors that account for load diversity show that a small percentage of cables in the tray can be loaded significantly beyond the code allowable ampacity value if the remainder of the cables are lightly loaded or unenergized. On the other hand, the code-allowable ampacity must be reduced by up to 25% when a solid cover is placed over the tray     

Rating power cables in wrapped cable trays

Conductor temperatures for a given ampacity loading is a function of ambient temperature inside the tray. In other words, the ampacity of cables included in these tray systems has to be rated at the ambient temperature inside the tray. Cable overheating and eventual failure can result if cables are overloaded or not derated for operation. IPCEA Pub. No. 54-440/WC lists cable ampacities in air ambient temperature of 40°C. Cables operating at temperatures above this have to be derated accordingly. An algorithm is presented for determining ambient temperatures in the cable tray for conditions of natural air convection with different cable loading. Hence, derated cable ampacities can be derived from those at 40°C. Although at present, there is no industry standard for wrapped cable trays, the method used here can be used to develop such a standard     

Influence of metallic trays on the ac resistance and ampacity of low-voltage cables under non-sinusoidal currents

This paper investigates the influence of metallic trays on the ac resistance of PVC insulated, low-voltage (0.6/1.0 kV) cables made according to CENELEC standard HD603. The investigation is made with a validated finite element model for the fundamental and higher harmonic frequencies. It is shown that the cable's effective resistance is affected significantly by the relative magnetic permeability and specific conductivity of the tray, while the tray's dimensions do not affect it. The orientation of the cable with respect to the tray also influences the ac resistance of the phase and neutral conductors. An ampacity derating factor is defined and calculated for various cable cross-sections and harmonic loads. The presence of a metallic tray is shown to cause an additional derating of cable's ampacity which is relatively significant at large cable cross-sections. Working examples demonstrate the application of the results in calculating the ampacity of low-voltage cables and in assessing the energy savings that will result from the use of active harmonic filters.     

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     

采用MATLAB仿真的变电站高压进线温度场和载流量数值计算

随着电力电缆在输配电线路中的广泛应用,准确确定电力电缆及其周围环境温度场的分布和电缆的载流量对于提高电力电缆的使用率、动态调整负荷具有重要的意义。为此,以地下排管敷设的交联聚乙烯电力电缆为研究对象,其实际模型为1个容量为250MVA、额定电压为230kV的变电站的高压进线。根据传热学和有限元法(finite element method,FEM)基本原理,建立了1种基于有限元法的水泥排管敷设电缆温度场计算模型,并对电缆及其周围环境的求解区域进行复合有限三角形单元剖分,即对电缆区域进行较密集的网格划分,而对电缆周围的土壤区域则进行较为稀疏的网格划分,以提高程序的运算精度和运行速度。结果表明:用MATLAB软件仿真,从而得到电缆及其周围环境的温度场分布,迭代计算了排管敷设交联聚乙烯电缆的载流量。证明使用有限元的方法分析地下电缆温度场,为电力工程中电缆载流量确定提供了一个比较可靠的计算方法。     

Ampacity of cables in single open-top cable trays

A mathematical thermal model that can predict the operating temperatures for cables when there is load diversity in single, horizontal, open-top cable trays is presented. The model accommodates two different loading scenarios-one in which the heat load is distributed evenly across the cable tray cross-section and a second one which concentrates the heavily loaded cables along the center-line and surrounds them with more lightly loaded cables. The second model is designed to yield a maximum cable temperature and to account for the load diversity that exists in a realistically operated tray. Temperature predictions provided by the model are compared with previous laboratory cable tray experiments and with data collected during a four year study in which cable temperatures were measured in an operating nuclear plant. Reasons for differences between the field data and the computer results are discussed. The model is used to evaluate the conservatism in the ICEA P54-440 as a result of load diversity     

Experimental validation of a thermal model for the ampacityderating of electric cables in wrapped trays

As a safety measure for certain applications in nuclear power stations, cable trays must be wrapped with a fireproof material. In this paper a new implementation of a thermal model is presented, suitable for the determination of the ampacity derating of electric cables in wrapped trays. Model simulation predictions have been compared with field tests to validate the model. Better agreement between simulations and experimental results is obtained when the standard procedure to determine the power loss in the cable mass is modified to account for the actual measured height of the cable mass in the tray     

交联电缆集群敷设载流量的数值计算

在人口稠密的大城市,电力通常通过直埋电力电缆集群来传输。电缆载流量是电缆设计和运行中的一个重要参数。IEC 60287标准给出了单一媒质即均匀土壤中电缆群稳态载流量的计算方法,并给出了有回填土的非单一媒质中电缆群的载流量修正计算方法。为给电缆工程的设计与运行提供科学依据,采用基于场路结合的有限差分法,提出了非单一媒质中电缆群的载流量数值计算方法,深入研究了不均匀土壤中的电缆载流量及其影响因素。计算结果表明,IEC外部热阻修正计算方法的计算精度与回填土热阻系数有关。回填土热阻系数较大时,IEC计算载流量显著偏低。     

复杂环境中海底电缆温度场及载流量模型研究

载流量是海底电缆运行调度的重要参数,受最高允许工作温度所制约,建立考虑复杂海洋环境中洋流影响的海底电缆温度场及载流量模型具有重要意义。针对传统解析法计算复杂、仅适用于特定敷设环境等问题,根据电 热 流多场耦合理论,基于有限元分析技术分别建立了埋设和铺设两种敷设方式下的高压三芯交联聚乙烯(XLPE)海底电缆温度场及载流量分析模型,并研究了洋流流速及温度对海缆载流量的影响。研究结果表明,所建模型与传统解析法相对误差在5%以内;相同环境因素下,铺设海缆稳态载流量比埋设高出200~330 A不等,且两者变化率在低流速时更灵敏,但不受洋流温度所影响;此外,短时应急载流量允许运行时间与其大小及初始缆芯温度成反比关系。     

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     

电力电缆载流量计算的研究与发展

电力电缆的载流量因受敷设方式、运行条件和周围环境等因素的影响而不易确定,准确计算各种复杂条件下电缆的载流量,对确保电缆的安全、经济运行具有重要的意义。文中介绍了电力电缆载流量计算的解析法和数值法的发展过程,分析了NM理论的不足和对它的改进,以及IEC60287载流量计算标准的基本内容和应用局限;介绍了三种主要的数值计算方法(有限差方法、边界元法和有限元法)在电缆载流量计算中的应用,并对这三种数值计算法的特点进行了论述。最后,建议在上述研究方法的基础上,针对具体的实际问题,提出后续研究的内容及方法。     

Rating of cables on riser poles, in trays, in tunnels and shafts-areview

This paper reviews rating of cables installed in air. The following cable installations are investigated: (1) cables on riser poles, (2) cables in open and closed trays, (3) cables wrapped in fire protection covers, (4) cables in horizontal tunnels, and (5) cables in vertical shafts. The rating of cables in these installations is computed by solving energy balance equations for the unknown surface temperature with a given conductor current. In ampacity computations the conductor current is adjusted iteratively until permissible cable conductor and surface temperatures are achieved. It is shown in the paper how the same energy balance equations can be used to compute the ratings of all the above cable installations     

Ampacity of wrapped cables

Analytical equations that permit quick computation of the ampacity of power cables wrapped with refractory silica are presented. Ampacity test results are given for several wrapping methods and cable configurations. These test results show that the analytical method is reasonably accurate in determining the ampacity of wrapped cable     

复杂运行条件下交联电缆载流量研究

载流量是决定电力电缆经济可靠性最重要的参数。针对城市地下电力电缆电网运行条件复杂化,电缆线路载流量因素难于确定的状况,首次在国内开展了110 kV交联电缆载流量的试验研究,模拟实际条件进行了110kV交联电缆在大埋深、多回路以及在各种负荷状态等条件下的电缆载流量试验。通过试验研究,给出了不同运行条件下电缆载流量,得到了不同敷设形式、负荷状况下电缆的负荷电流、导体温度、表面温度间的关系数据,并对电缆线路载流量的主要影响因素进行了分析。通过研究得到了几种特定敷设条件下电缆载流量试验的数据,给出了电缆线路典型的外部热环境参数参考值。研究结论能够直接用于城市电网的实际运行,并能作为电缆线路设计、优化以及运行时载流量控制的指导数据。     

Thermal analysis of power cable systems in a trench inmulti-layered soil

A system of three underground cables in a trench is modelled using the finite difference method. The model accommodates most of the geometrical parameters and the working conditions. The heat dissipation from each individual cable is calculated for various parameters including the cables' diameters, the trench width and the spacing between cables. Some of the geometrical dimensions have great influence on improving the total ampacity of the system     

土壤直埋电缆群额定载流量的计算

当多根电缆埋地敷设时,电缆之间热的相互影响使每根电缆的载流量不同程度的降低。每根电缆的载流量由IEC60287给定公式计算,其环境温度由土壤环境温度和其他电缆在该点的温升迭加所决定。其他电缆在该点的温升可以采用镜像法计算。这样,每一根电缆额定载流量将由其他电缆决定,用高斯-赛德尔迭代法对以额定载流量为变量的方程组进行求解,计算了电缆群等负荷、不等负荷以及环境因素对载流量的影响。试验结果表明,计算结果符合工程实际要求。     

窄通道下排管敷设电缆群负荷优化

电力管道施工过程中,有时不可避免地要经过道路狭窄或地下管网密集的区域,为了保证安全水平净距,通常将此段电缆群变更为通道较窄的布置方式,但这会导致电缆群载流能力减小。将传热学原理和矩阵论相结合,基于IEC 60287提出了一种窄通道下电缆群不等负荷的矩阵优化方案,针对几种典型排管敷设的窄线路建立了有限元模型并进行温度场仿真,验证了优化方案的准确性;最后通过对实际工程通道变窄前后的负荷进行对比设计了合适的窄线路,结果表明该通流方案可提高电缆的利用率,减小了通道变窄对载流能力的影响,窄线路采用不等负荷通流方案可提高电缆的输电能力,随着回路数的增加最大可提升6.53%。     

10kV三芯交联电缆载流量的试验研究

三芯电缆广泛应用于城市配电电网,其可靠运行与绝缘温度密切相关,因而电缆载流量的精确计算是电缆安全、可靠运行的保证。由于配电电缆的线路多、结构复杂、敷设方式多样,使得配电电缆线路的管理和载流量计算不像高压电缆那么规范。近几年一些非常规的敷设方式大量使用,使得配电电缆载流量的计算更加困难。为规范配电电缆载流量的计算,模拟了广州地区10kV三芯交联电缆典型敷设条件,在试验现场进行了单根空气、直埋、穿管敷设及2×3多回路密集敷设下的电缆载流量试验;编制了计算三芯电缆载流量的计算软件,将电缆本体各层温度降的试验值与软件计算值进行了对比,试验研究结果验证了理论计算的正确性。三芯电缆载流量的准确计算可为运行中负荷的控制提供参考,保证电缆的可靠性,并最大限度发挥电缆的输送能力。     

基于有限元法的地下电缆群温度场及载流量的仿真计算

结合传热学知识对地下直埋电缆温度场进行分析,构造出热传导方程和边界条件后,采用专业有限元软件建立了3根直埋单芯电缆的温度场模型,计算区域采用三角形单元剖分法。对电缆温度场分布及载流量的确定采用对分法进行迭代求解。通过仿真,分析了影响土壤直埋电缆载流量的各个因素以及各因素对载流量的影响规律,为工程实际提供了参考依据。