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     

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     

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。     

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.     

Temperature rise of submarine cable on riser poles

Results of outdoor temperature-rise tests on submarine power cables installed under guards on riser pole are presented. Test data were used to determine ampacities for three steel-wire armored distribution class cables under specific solar radiation conditions. The measured data also compared well with results from an existing cable ampacity computer program. Some discrepancies, however, indicated that the program predictions could be improved if eddy-current and hysteresis losses were considered in the calculation method used for single-phase cables on riser poles. For a valid comparison between measurements and calculations, it was necessary to account for limitations in the existing computation method by conditioning some program inputs. Consequently, a technique was developed for deriving a single-valued program input that would represent the effect of time-varying solar radiation. A thermal circuit used to determine the transient response of the cable/guard system is presented, along with values for the thermal parameters of three submarine cables. A revised method used to calculate the external heat dissipation coefficient for vertical cable guards is also described     

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     

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     

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。     

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     

On the economic selection of medium voltage cable sizes innonsinusoidal conditions

Selection of cable size in the nonsinusoidal conditions is only based on ampacity considerations without any attention to the cost of the losses that will be suffered in the cable life. Since the cost of these losses (fundamental plus harmonics) can assume significant values, the selection of a cross section higher than required for ampacity considerations can result in a large reduction of cost. This paper proposes a method which allows the optimal economic selection of medium-voltage cables in nonsinusoidal operating conditions; it takes into account the initial investment costs and the Joule losses costs, including the additional costs due to current harmonics. It employs simplified expressions similar to those adopted by the IEC Standard in sinusoidal conditions, being the harmonic presence taken into account by a proper definition of a harmonic loss factor and by the introduction of harmonic coefficients to be predicted. Numerical applications to medium-voltage cables are developed and discussed in order to show the sensitivity of the cable optimum size to variations in the coefficients that characterize the harmonic presence     

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     

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     

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。     

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。     

管道内填充导热介质提高电缆载流量

电力电缆排管敷设时,因预埋管中空气热阻较大,使其载流量比直埋方式的载流量有显著下降。为提高预埋管敷设方式下电缆输送能力,可向管道内填充导热介质以改善管道的散热状况。采用基于坐标组合的有限差分法,编制了电缆排管敷设温度场和载流量通用计算程序。程序计算结果与模拟试验及现场试验结果相符。计算结果表明,单回路电缆填充导热介质可提高载流量约5.6%,降低缆芯温度约7°C。多回路电缆由于电缆间的互热效应,填充导热介质对提高载流量的作用显著减小。管道内填充导热介质,可降低电缆运行温度,提高电缆输送能力。     

Thermal modeling of portable power cables

The US Bureau of Mines investigated the performance of portable power cables under time-varying load conditions. This research had a twofold purpose: (1) to define the thermal characteristics of electrically overloaded trailing cables; and (2) to construct a thermal model for cables to predict cable temperature rises resulting from load currents. Several tasks were undertaken in support of these goals during the three-year research effort. Overload tests ranging from 2 to 12 times rated ampacity were conducted in the Pittsburgh Research Center's Mine Electrical Laboratory. A thermal model of energized type G-GC trailing cables was constructed based upon empirical data from the US Bureau of Mines load tests. This model was then incorporated into an interactive computer program that can assist designers and approvers of mining machines in selecting the appropriate size trailing cable. This program can be the basis for a cable protection system which ensures that cables are not the source of fires, ignitions, burns, or explosions underground     

直埋集群敷设配电缆的载流量多回路修正系数校核

配电网中电缆线路多、负荷重,集聚敷设十分常见。为了计算电缆集聚敷设载流量,开发了三芯电缆载流量计算软件。通过软件计算和现场试验,研究并校核了直埋敷设多回路修正系数。结果显示,单回路和四回路载流量试验结果与计算值吻合,验证了理论计算的正确性。多回路修正系数研究还表明,目前正在使用的直埋敷设多回路10 kV三芯电缆载流量修正系数偏大,不利于配电电缆线路的安全运行,建议采用所提出的直埋集聚敷设多回路修正系数推荐值对其进行修正。     

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