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     

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     

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     

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.     

Ampacity of cables in trays surrounded with fire barrier material

A computer program that is capable of calculating the ampacity of power cables in a single tray that is surrounded by a fire barrier system is described. The program is used to determine the effect of the fire barrier design on the ampacity of the cables for a wide variety of cable, tray and fire barrier conditions. The calculated ampacity values are compared to values published in the ICEA/NEMA P54-440 resulting in a fire barrier ampacity correction factor. This factor convenient and simple to use, because quantitatively shows how much the conductor current must be reduced when the tray is surrounded by fire barrier material. Ampacity correction factors are provided for different fire barrier thicknesses with differing thermal resistivities. The program is also used to perform a sensitivity study so that those conditions which most greatly affect the cable ampacity can be identified. Results predicted by the program are compared to data measured during an extensive experimental test program carried out by TVA. The computer-predicted ampacity values and tray temperatures are shown to compare well with values measured during the test program     

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     

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     

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     

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。     

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     

地下电缆载流量评估影响因素数值分析

利用有限元法对影响地下电缆温度场分布的地表空气温度、电缆埋地深度、土壤热阻系数、有无回填土、电缆排列方式、电缆接地方式等因素进行了分析,利用弦截法计算地下电缆群载流量,给出电缆载流量随各项参数变化的关系,为根据实际环境和敷设条件选择合适的电缆载流量提供依据。     

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。     

Steady-state operating conditions of very long EHVAC cable lines

In the present paper the authors investigate steady-state capabilities of very long EHVAC underground cable lines, without intermediate compensating stations, installed in meshed networks. Analytical formulas of cable length-loading relationship are presented to this purpose. The study shows that, in optimal operating conditions, most of the ampacity of such long underground cable lines can be exploited for active power transmission. Non-optimal operating envelopes are studied, showing the effect of terminal voltages and line losses on cable utilization and evidencing limited derating under realistic hypotheses. A parametric analysis of loading limits and possible voltage violations along the cable is shown; a simple criterion for optimal utilization of lossy cable lines is also proposed. Line-end shunt compensation requirements for integration of long EHVAC cable lines in transmission networks are then specified. Studies performed for both ideal and real cables and shunt reactors show that active power transmission of 100 km long, 400 kV-50 Hz underground cable lines can attain 90% of their thermal limit, without intermediate compensating stations. Excess reactive power and temporary overvoltages are effectively controlled by line-end compensation around 90%.     

Cable crossings-derating considerations. I. Derivation of deratingequations

Dangerously high interference temperatures can occur at points where cables cross external heat sources even when the crossing occurs at 90°. For perpendicular and oblique crossings, these interference temperatures are usually ignored for distribution circuits, whereas for transmission cables, corrective actions in physical installation condition are sometimes taken. Analytical solutions are almost never used to determine the effect of external heat source 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 the intersection of a pipe-type cable by a distribution circuit is presented to show the effect of perpendicular and oblique crossings on the ampacity of both circuits. In this practical example, the ampacity of the pipe-type cable is significantly affected for a range of crossing angles. A conservative practice, used by many utilities in cases like this, would be to assume that the cables are parallel. However, in our example for a 90° crossing, such an approach would unnecessarily decreases the ampacity of the pipe-type cable by almost 20%     

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.     

Pipe-type cable ampacities in the presence of harmonics

This paper explores the effect of harmonics on high-pressure fluid filled pipe-type transmission cable ampacity. Industry currently calculates the current carrying capacity of underground power cable based on the assumption of a purely sinusoidal 60 Hz current. However, increasing levels of harmonics on power systems have raised concern about their effect on cable ampacities. The issue has already been addressed for distribution cables. This paper begins with a discussion of Neher and McGrath's classic equations and some recent revisions, and develops a closed form composite equation accurately reflecting the effect of harmonics. The effect of frequency on the loss ratio is shown and supported by comparison with measured data at 60 Hz and a finite element analysis at a number of harmonic frequencies. The effect of specific harmonic scenarios is shown in light of the IEEE standard on harmonics. The results are used to develop a derating factor to compensate for current harmonics on transmission systems     

Calculation of cable ampacities including the effects of harmonics

The objective of this article is to develop a method of calculation of cable ampacity in the presence of harmonics for a cable system. A simple general equation has been developed that can be used to calculate the harmonic derating factor (HDF), and neutral harmonic derating factor (NHDF), of a cable system. A review of a generalized method of calculating ampacity of a cable system is presented in the Appendix using matrix techniques     

断续负载条件下中低压电力电缆载流特性研究

在某些断续负载、大传输容量的应用中,为确保供给电能的中低压电力电缆安全可靠地工作,需要预测其载流特性。本文主要针对断续负载条件下中低压电缆的非稳态发热过程及相关问题,一方面从理论角度,解决电缆在特定负载条件下的发热特性问题;另一方面,结合具体载流试验,分析电缆的发热过程及规律。     

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。     

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