Mathematical modeling of nonstationary processes of heat and mass transfer in a rectangular cable channel

This work is devoted to solving the problem of heat and mass transfer in a rectangular cable channel laid in the earth mass, taking into account the electric and magnetic dynamics processes in the metal elements of the power cable. The current load of power cables depends on the temperature field in the cable construction, which in turn the following factors influence: the conditions of heat transfer, thermal characteristics of the materials used, the induced currents in a metal screen of power cables, etc. The proposed mathematical model of the processes of complex heat and mass transfer is based on the laws of conservation of mass, momentum, and energy. For the electrodynamics problem, equations of current density and a magnetic potential vector based on Maxwell equations are used. The problem was solved numerically under conditions of natural convection with taking into account the radiant energy by the finite element method in the Ansys Fluent software package. As a result, the power of heat losses in the metal structural elements of the power cable and the velocity and temperature fields in the cable channel were calculated. The temperature fields in the cable channel are presented and analyzed depending on the location of power cables. The different operating modes of the cable line are discussed. To analyze the heat processes in the cable channel, the nonstationary problem defining the heating time of cable lines to the limit values is solved. The heating curves of the cable lines operating in unsteady mode are obtained. The maximum operating time of the cable line in an overload and short circuit is determined.     

Control of Electrical Energy Distribution in a Cable Channel

The load distribution between 18 cable lines located in an underground cable channel is considered. It is found that a current distribution control system in the cable channel needs to be developed to optimize the load conditions, as well as prevent possible overheating. The possibility of using a mathematical model of heat and mass transfer processes in the channel to determining the optimal current loads of cable lines is considered. A mathematical model of heat and mass transfer processes in the cable channel is constructed that makes it possible to study the temperature conditions of the channel under different configurations and line loads. Search algorithms of optimal operating currents under varying loads are developed that take into account the requirements for permissible temperatures and categories of consumers. The unsteady condition of overload of one of the lines due to an emergency is investigated. The heating curves of current-carrying conductors of the emergency cable line and those adjacent to it are plotted. The value of the current is determined to which it is necessary to reduce the load in one of the lines to maintain the system operability.     

Mathematical simulation and control of the capacity of cable lines in an underground channel

A mathematical model of complex heat transfer in a cable channel under the conditions of natural convection is developed. The model is implemented in the ANSYS software package using the finite element method. Convective heat transfer and the effect of climatic conditions on the temperature field in the cable channel and a land tract are studied. The optimal transmitted power is estimated, and possible ways to control the capacity of cables are demonstrated.     

Thermal performance of underground power cables with constant andcyclic currents in presence of moisture migration in the surroundingsoil

A numerical methodology for thermal analysis of buried power cables in presence of heat and moisture migration in the surrounding soil is presented. The governing equations are solved via a finite volume methodology and both cable and soil are incorporated in the problem formulation. The developed program is versatile and user-friendly, and was implemented in a personal computer. Results are presented for constant and cyclic loads, stressing the importance of moisture migration in power cable design     

Determination of the optimal working conditions of cable lines in an underground cable channel

Mathematical modeling of heat transfer processes inside a cable channel taking into account natural convection and radiation between the cable surface and tube and the loss in shields was carried out. An underground cable channel consisting of eight lines with a voltage of 6 kV and six lines with a voltage of 35 kV was investigated. The conductor section is 150 mm². Cables of APvVng-LS brand were placed in a triangle inside polyethylene tubes. The patterns of temperature fields obtained under variance of different various factors were determined, the permissible currents were calculated, and the optimal circuits of connection of cable lines depending on the selected criterion were proposed. The two-dimensional nonstationary problem of complicated heat and mass transfer and heat conductivity inside the underground cable channel was solved by the finite elements method using the ANSYS software package. The range of permissible operating currents depending on the location of cable lines and priority of their connection was determined. The effect of the temperature of the environment on the permissible current was considered. The optimal ranges of thermal permissible currents taking into account the shield loss were calculated. The optimal connection circuits of the cable lines depending on the problem being solved were obtained. An estimation of transferred power for every considered connection method is presented. Conclusions for practical application of the method of connection of the cable line were drawn. The fields of application of this mathematical model were proposed.     

双回路电缆护套环流计算及影响因素分析

为分析电缆线路中的环流,推导了双回路敷设电缆护套环流的计算方程,并自行编制运算程序实现了计算机求解。结合某电力设计院两回路电缆的实际敷设及运行参数,计算了直线排列交叉互联情况下电缆护套中的环流,并对影响金属护套中环流值大小的相关因素作了简单分析,减小环流值的方法有增大接地电阻、使电缆紧密排列、保证电缆交叉互联段长度相等等。同时,提供了对应单回路敷设情况下的计算结果进行比较,结果表明计算护套环流时双回路不能以单回路情况简化。相关推导过程及程序设计思想可推广应用于双回路电缆的其它敷设形式或更高回路数的电缆线路。     

地下电力电缆隧道通风系统的模拟计算

应用CFD软件对地下电力电缆隧道的通风散热系统进行模拟计算,分析其不同换气次数工况下的散热效果以及温度、速度分布。结果表明,电力电缆隧道的通风系统能有效带走电缆产生的热量。随着风量的增加,散热量得到了小幅提升,大量空气未经完全换热就从中间低阻通道流走。建议优化电缆布置,避免电缆紧贴舱室壁面。     

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     

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     

空气敷设下10kV三芯电缆应急时间计算

当10 kV三芯电缆因故障或检修而需要加载较大的应急负荷时,在电缆导体温度达到最高温限值之前,电缆允许过载的应急时间为多长,是电力部门极其关注和亟待解决的问题。为此以空气敷设的10 kV三芯电缆为研究对象,建立了电缆本体及空气介质的暂态热路模型,并将其等效简化为一阶RC暂态热路模型,计算了10 kV三芯电缆热时间常数,推导出空气敷设三芯电缆在应急负荷下应急时间的计算公式,并设计了空气敷设电缆在不同初始负荷下的应急温升实验,通过对比实测和理论计算数据,验证了该模型和应急时间计算公式的可靠性,可为应急状况下指导电力负荷调度和控制电缆检修工作的时间提供重要参考。     

直埋电力电缆温度场计算模型

研究了埋设于复杂土壤中的电力电缆在暂态和稳态情况下的温度场和载流量,用有限差分法离散传热方程,对电缆和土壤区域分别采用极坐标和直角坐标;为了加快计算速度,采用了不均匀网络。本模型适用于电力电缆稳态和短路或过载等暂态的温度场和载流量的计算。     

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     

单芯高压电力电缆金属护套感应电流的研究之二——计算程序的编制和应用

对单芯电缆交叉互联金属护套感应电流进行了研究。为了控制实际电缆线路工程中单芯电缆的护套感应电流,建立了复杂通道条件下,单芯电缆护套感应电流计算的数学模型,提出了通过调整电缆排列来预控感应电流的方法,并编制了相应程序,以实现护套感应电流的计算和预控。全文共分两大部分:第一部分为感应电流的计算和预控;第二部分为计算程序编制和应用。     

单芯高压电力电缆金属护套感应电流的研究之一——感应电流的计算和预控

对单芯电缆交叉互联金属护套感应电流进行了研究。为了控制实际电缆线路工程中单芯电缆的护套感应电流,建立了复杂通道条件下,计算单芯电缆护套感应电流的数学模型,提出了通过调整电缆排列来预控感应电流的方法,并编制了相应程序,以实现护套感应电流的计算和预控。全文共分两大部分:第一部分为感应电流的计算和预控;第二部分为计算程序编制和应用。     

Compensation of cable voltage drops and automatic identification of cable parameters in 400 Hz ground power units

In this paper a new cable voltage drop compensation scheme for ground power units (GPU) is presented. The scheme is able to predict and compensate the voltage drop in an output cable by measuring the current quantities at the source. The prediction is based on an advanced cable model that includes self and mutual impedance parameters. The model predicts the voltage drop at both symmetrical and unbalanced loads. In order to determine the cable model parameters an automatic identification concept is derived. The concept is tested in full scale on a 90-kVA 400-Hz GPU with two different cables. It is concluded that the performance is significantly improved both with symmetrical and unsymmetrical cables and with balanced and unbalanced loads.     

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。     

基于电热加速老化试验的XLPE电缆绝缘性能研究

为了掌握电缆绝缘性能与温度之间的关系,在实验室对运行年限不同的10 kV高压XLPE电缆进行电热加速老化试验,测量不同的载流量下电缆分别在空气和沙土中的温度变化数据。试验测量数据和温升曲线表明,运行中电缆的温度变化与所加载的流量和周围环境介质均有关系,运行年限相同的电缆在空气中的温度变化较在沙土中的要大,运行年限越久的电缆不论在空气中还是在沙土中温升都较快。基于电热加速老化试验方法研究运行年限不同的电缆的温度变化情况,为电缆绝缘性能的判断提供参考依据。     

PLC在公路隧道监控系统中的应用

盐田坳隧道计算机控制系统成功应用，完全改变了隧道监控系统继电器——接触器传统控制模式．中长隧道因控制电缆过长，电缆芯数多，控制电缆又多，感应电压引起泄漏电流过大，隧道内各种干扰源多的特点，对监控系统的干扰问题得到彻底解决．     

电缆群排管敷设形式下的分流运行优化方法

夏季地下排管电缆聚集运行温度异常,电缆温度过高会加速电缆绝缘材料的老化,热量累积到一定程度,还可能引起起火事故。为降低地下排管中电缆运行温度,提出了电缆群排管敷设形式的优化方法。基于有限元法计算地下排管中电缆群运行温度场,建立了电缆群敷设形式优化计算模型。以电缆群中最高温电缆的温度降到最低为目标函数,电缆群中总载流量不变为约束条件,对电缆群中温度较高的电缆进行分流优化计算。通过Comsol Multiphysics软件仿真计算的结果可见,与未优化之前相比,采用优化方法后排管中最高温电缆的导体芯温度降低了约11%,电缆群最大温差降低了3.6℃,增加了电缆群温度场分布的均匀度,优化效果显著。     

东海大桥高压电缆工程设计

洋山深水港110 kV变电站的电源线路是敷设于东海大桥的箱梁内的两回110 kV 630 mm2交联电缆,是目前世界上最长的敷设于桥梁的高压电缆,详尽介绍了在东海大桥电缆工程设计时,应对桥梁伸缩、振动,以及如何处理电缆金属护套的接地等技术难题所采取的措施.