Cable Backfill Research Articles

Experimental Study on the Effect of Soil Moisture Content on Critical Temperature Rise for Typical Cable Backfill Materials

The increased utilization of power grid requires operating power cables close to their thermal limit. Buried power cables in such condition experience thermal instability where thermal resistance increases as the moisture migrates away from the proximity of the cable forming a dry-out zone. While it is common to use a two-zone model to account for the dry-out zone in ampacity calculations, there is a limited number of studies on characterizing backfill materials for their critical temperature rise ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> ), especially for crushed rock sands. In addition, dependency of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> on moisture content is sometimes not acknowledged. This study measures the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> for three typical backfill materials and investigates the relationship between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> and moisture content. The results show that crushed rock sand has higher <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> compared to natural sand. Overall, large range of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> was measured depending on moisture content and type of soil. Ampacity calculations with the established <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> show that at low moisture content, the thermal resistivity of the soil has a higher influence on ampacity than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> . At relatively high moisture content, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta \theta_{x}$</tex-math></inline-formula> becomes the predominant factor governing the overall ampacity.

Drying of cable backfill by vapour diffusion balanced by capillary water suction: a laboratory experiment with altered groundwater levels

The performance of underground infrastructures, such as an electrical transmission cable, is strongly affected by transmission-induced high temperatures, which have an impact on the properties of the cable and the electric load. Therefore, it is essential to determine if a high load will cause a dry out of a sandy thermal backfill close to the cable. This paper aims at describing processes and establishing criteria for when a dry out can occur. Processes that are addressed are e.g., vapour diffusion and capillary water transport. Criteria of interest are e.g., groundwater levels and capillarity of soil. A new pilot laboratory experiment, with varying groundwater levels, was developed to investigate the dry out of the cable sand in close proximity to an operating cable. The experimental results show that a thermal backfill can withstand a dry out, at a high current load in a cable, if there is a capillary contact to a groundwater level 2 m below the backfill material.

The effect of soil thermal conductivity and cable ampacity on the thermal performance and material costs of underground transmission line

This paper presents an optimisation of material costs of a 400 kV cable line arranged in a flat formation for different values of soil thermal conductivity and cable ampacity. The Finite Element Method is adopted to calculate the temperature field within the cable system. The Particle Swarm Optimisation method is used to minimise the material costs of the cable system. To ensure safe and reliable operation of the cable line, the temperature of the cable core should be lower than 90 °C. Under this assumption, the design optimisation is performed to calculate the optimum size of cable bedding cross-sectional area and select the nominal cable conductor area correctly. An application of two commonly used cable backfill materials is studied: Fluidized Thermal Backfill and Sand-Cement Mix. The calculations are performed for current rating varied from 1,000 A to 1,400 A, and thermal conductivity of soil varied from 0.6 W/(m × K) to 1 W/(m × K). The results showed that for a low soil thermal conductivity, i.e. 0.7 W/(m K), it is possible to reduce the overall material cost of the system (cables cost and thermal backfill material cost) when applying Fluidized Thermal Backfill (FTB) instead of commonly used Sand-Cement Mix. The reason is that FTB application allows reducing the cross-sectional area of power cables, which cost has a major effect on the overall material cost of the underground transmission line.

Multiobjective optimization of underground power cable systems

This paper presents a modified Jaya algorithm (MJaya) for optimizing the material costs and electric-thermal performance of an Underground Power Cable System (UPCS). Three power cables arranged in flat formation are considered. Three XLPE high voltage cables are situated in the thermal backfill layer for ensuring the optimal thermal performance of the cable system. The cable backfill dimensions, cable backfill material, and cable conductor area are selected as design variables in the optimization problem. In the study, the Finite Element Method model is validated experimentally.The Particle Swarm Optimization (PSO), Jaya, and MJaya algorithms are used for multiobjective optimization in order to design a cable system in such a way to minimize the cable backfill costs and maximize the allowable electric current flowing through the cables. For the case study, calculations performed using the Jaya algorithm indicated 1.7 mln Euro cable system costs while cable ampacity is equal to I = 1460 A. The calculations are performed for the objective function values equal to w1 = 0.5 and w2 = 0.5. Such an optimization parameters set allow obtaining low costs of UPCS alongside with reasonable cable line ampacity.What is more, the results of the optimization obtained by Jaya, MJaya, and PSO algorithms are compared. Therefore, Coverage and Hypervolume metrics are incorporated. It is concluded that both the Jaya and MJaya algorithms performed better when compared to the PSO algorithm.

Analysis of an application possibility of geopolymer materials as thermal backfill for underground power cable system

The circular economy is a closed cycle that allows one to reuse the industrial waste, as well as minimize the energy and resources losses during the production process. This paper presents an innovative idea of the application of a geopolymer cable backfill for underground power cable system installation. The closed cycle, in this case, is formulated as follows: the primary resource is the waste from the combustion of fossil fuels, i.e., fly ash that is utilized to form the geopolymer matrix. The geopolymer then is used as thermal backfill in underground power cable systems. Utilization of combustion by-products in the form of a geopolymer is a highly profitable solution since landfill waste disposal, in this case, generates considerable costs for the electrical energy producers. In typical applications, geopolymers are used as insulators. By adding individual components, the thermal conductivity of 2.0 W/(m K), higher than of typical thermal backfills (Fluidized Thermal Backfill), which value is close to 1.5 W/(m K), is reached. What is very important, geopolymers can absorb water better than typical sand–cement mixtures. As a result, a high thermal conductivity with the temperature increase is maintained. The application of geopolymers as thermal backfills has the potential to improve the flexibility of underground power cable systems, as well as to minimize the material costs of installation. The case study is presented to show the economic benefits of using the combustion by-products as a geopolymer thermal backfill. The finite element method model of an underground power cable system is developed, and optimization of backfill dimensions is provided to minimize the material costs using the geopolymer thermal backfill and to maximize the underground power cable system performance. The main result of this paper is that the application of geopolymers leads to a decrease in underground power cable system costs, compared to traditional backfill (sand–cement mixture). The reason is the higher value of thermal conductivity, which allows selecting a cable with a smaller cross-sectional area. Also, the environmental benefits of geopolymer application for cable bedding are discussed.Graphic abstract

The Effect of Drying around Power Cables on the Vadose Zone Temperature

Core Ideas We show the impact of soil hydraulic properties on its critical temperature. Ambient conditions have a larger impact in some fields than local soil parameters. We introduce a parameter for optimizing cable backfill based on hydraulic properties. The effects of moisture migration away from power cables depend strongly in most soils on whether the soil has reached the so‐called critical conditions (e.g., critical temperature) for a dry‐out. However, research on how to estimate this critical temperature has been limited. We solved numerically a differential equation for the planar case of steady‐state coupled heat and mass transfer in porous media, using the van Genuchten–Mualem model for the hydraulic properties of the medium. The critical isotherm is assessed by the temperature at which the steepest change occurs in the moisture content with temperature. We considered the impact of the properties of the surrounding medium and of the ambient temperature and moisture content on the dry‐out temperature. We found that seasonal variations in ambient conditions in a field in Italy have a greater impact on the critical temperature than the variations in soil properties in that field (under the assumption of a nearly uniform moisture content with depth). However, our analysis shows that, under certain conditions, a change in the van Genuchten parameter n and in a specific combination of parameters that we call a dynamic parameter can have as large an effect on the critical temperature. This suggests a direction in the optimization of backfill materials.

Thermal performance optimization of the underground power cable system by using a modified Jaya algorithm

This paper presents a modified Jaya algorithm for optimizing the material costs and electric-thermal performance of an Underground Power Cable System (UPCS). A High Voltage (HV) underground cable line with three 400 kV AC cables arranged in flat formation in an exemplary case study is considered. When buried underground, three XLPE high voltage cables are situated in thermal backfill layer for ensuring the optimal thermal performance of the cable system. The study discusses the effect of thermal conductivities of soil and cable backfill material on the UPCS total investment costs. The soil thermal conductivity is assumed constant and equal to 0.8 W/(m K). The cable backfills considered in the study are as follows: sand and cement mix, Fluidized Thermal Backfill™ (FTB) and Powercrete™ a product of Heidelberg Cement Group. Constant thermal conductivities of the backfills in the dry state are assumed, respectively, 1.0 W/(m K), 1.54 W/(m K) and 3.0 W/(m K). The cable backfill dimensions and cable conductor area are selected as design variables in the optimization problem. The modified JAYA algorithm is applied to minimize material costs of UPCS under the constraint that the cable conductor temperature shall not exceed its optimum value of 65 °C. The cable temperature is determined from the two-dimensional steady state heat conduction equation discretized using the Finite Element Method (FEM). The performance of the modified Jaya algorithm was compared with classical Jaya and PSO algorithms. The modified Jaya algorithm, for the presented case study, allows one to obtain lower values of the cost function.

Thermal analysis of underground power cable system

The paper presents the application of Finite Element Method in thermal analysis of underground power cable system. The computations were performed for power cables buried in-line in the ground at a depth of 2 meters. The developed mathematical model allows determining the two-dimensional temperature distribution in the soil, thermal backfill and power cables. The simulations studied the effect of soil and cable backfill thermal conductivity on the maximum temperature of the cable conductor. Also, the effect of cable diameter on the temperature of cable core was studied. Numerical analyses were performed based on a program written in MATLAB.

The effect of soil and cable backfill thermal conductivity on the temperature distribution in underground cable system

The paper presents a mathematical model of heat transfer in the underground cable system. The computations were performed for flat formation of power cables buried in the ground at a depth of 2 meters. The model allows determining the two-dimensional temperature distribution in the soil, thermal backfill and power cables. The simulations studied the effect of soil thermal conductivity on the maximum temperature of the cable conductor. Furthermore, the effect of thermal backfill soil conductivity on the cable conductor temperature was studied. Numerical analyses were performed based on a program written in MATLAB.

The performance analysis of a new thermal backfill material for underground power cable system

Lafarge Gruntar™ material is proposed in this paper as a new thermal backfill component, and different mass fractions such as 5%, 10%, and 15% are examined. The thermal properties of the developed backfill are determined by experiments with respect to water content and time. Based on the experimental data it is found that the 15% mass fraction Lafarge Gruntar™ material provides the most favorable thermal conductivity i.e. over 1.00W/(mK) in the dry state. This paper also presents a thermal performance optimization procedure for the high voltage underground power cable system. The new thermal backfill material is considered to be installed within the cable system to improve its thermal performance. The analyzed system consists of three underground power cables situated in a flat formation (in−line arrangement) in thermal backfill, buried in the native soil. To avoid extensive mechanical loads caused by vibrations, when locating beneath a paved ground (e.g. under road crossings), the cables are situated in High Density Polyethylene (HDPE) casing pipes filled with sand−bentonite mixture. The pipes are then placed into a thermal backfill and buried in the native soil. The Installation of thermal backfill material is relatively expensive since in many cases the buried line is installed over many kilometers. Therefore, it is important to determine the optimal dimensions of the cable bedding layer to minimize the material and installation costs while keeping efficient heat dissipation from the cables. The momentum-type Particle Swarm Optimization (PSO) solver, with a dynamic penalty function, is used to minimize the cable backfill cross-sectional area while not exceeding the allowable temperature of the cable operation. The performed optimization procedure obtains the converged solution. The temperature distribution in soil, cables, and the cable backfill layer is determined using the Finite Element Method. The Campbell − de Vries thermal conductivity model is employed for the soil surrounding the underground power cable system. An MATLAB code is written for solving the heat conduction equation and to determine the temperature distribution within the underground power cable system. By using the momentum-type Particle Swarm Optimization algorithm, it is possible to design the best-found dimensions of the cable bedding layer (width and height). Moreover, the dynamic penalty function employed in the optimization procedure has assured the determination of the maximum temperature of cable conductor close to its best-found value.

지중송전관로 되메움재의 종류에 따른 열 소산 효과의 비교에 관한 연구

지중송전관로를 통한 송전용량 증대를 위해서는 송전 시 발생하는 열을 빠르게 소산시킬 수 있도록 습윤 시 <TEX>$50^{\circ}C$</TEX>-cm/Watt, 건조 시 <TEX>$100^{\circ}C$</TEX>-cm/Watt 이하의 열 저항률을 갖는 재료를 되메움재로 사용하는 것이 요구되며, 이를 위해 선행연구에서는 요구되는 조건을 만족시키는 열 소산 되메움재를 개발하였다. 이 연구에서는 개발된 열 소산 되메움재의 열 소산효과를 알아보기 위하여 1회선의 단면을 현장에 설치하고 개발된 열 소산 되메움재와 강모래, 현장토에 대하여 열을 직접 가하고 일정한 지점에서 온도를 측정함으로서 현장시험을 수행하였고, 시험결과와 유한요소해석과의 비교를 통해 열 소산효과를 비교하였다. 비교결과, 열원과 가까운 지점에서는 개발된 열 소산 되메움재가 강모래와 현장토에 비해 열평형상태에 빨리 도달하는 것으로 나타났으며, 열평형에 도달하는 온도도 높은 것으로 나타나 열 소산효과가 우수한 것으로 나타났다. 또한 다른 지점에서도 개발된 되메움재가 다른 재료보다 온도가 높아 열 소산효과가 우수한 것으로 나타났다. 또한 함수비의 변화에도 열 소산효과가 크게 변화하지 않는 것으로 나타났다. Backfill material with thermal resistivity which has <TEX>$50^{\circ}C$</TEX>-cm/Watt in wet and <TEX>$100^{\circ}C$</TEX>-cm/Watt in dry is requested to improve the power transfer capability for dissipation of heat production in underground power cables. In the field test performed by buried cable backfills, the backfill material developed from this study is compared with river sand and weathered soil (native soil) to investigate the effect of heat transfer in various seasons and locations of thermal sensors. As a result, the developed backfill material is faster approaching yielding temperature (critical heat) than that of river sand and weathered soil, and it has good dissipation capacity rather than other materials by keeping moisture content at dry season.

Thermal instability in buried cable backfills : Brandon, T L; Mitchell, J K; Cameron, J T J Geotech Engng Div ASCEV115, N1, Jan 1989, P38–55

Thermal instability in buried cable backfills : Brandon, T L; Mitchell, J K; Cameron, J T J Geotech Engng Div ASCEV115, N1, Jan 1989, P38–55

Thermal Instability in Buried Cable Backfills

Buried high voltage power cables generate heat when a current is passed through the conductor, and failure of the cable may occur if the conductor or insulation temperature exceeds the design limit. Thermal instability, a moisture migration phenomenon causing a decrease in soil thermal conductivity, has caused thermally induced failure of cables and may be a problem in the case of other buried heat sources as well. Thus accurate methods for predicting thermal instability are needed. Until recently, such problems have been mainly in the domain of electrical and mechanical engineers; however, geotechnical engineers are now frequently involved in the study of this problem. The Hartley and Black method, based on the assumption that the ratio of the time to instability to the diameter squared of the heat source is a constant for a given heat input rate, is investigated. Laboratory tests, scaled model tests, and field tests were used to provide a wide range in the diameter of the tubular heaters employed (1.6 t...

Calculation of Temperature Distributions within Cable Trench Backfill and the Surrounding Soil

A computer program was developed to study the steady-state temperature distribution within the cable trench backfill and the surrounding soil. The calculations within the bounded region were carried out using the finite element procedure with the integral equation (Green's identity) as a constraint.

Optimization of Power Cable and Thermal Backfill Configurations

The design problem of selecting the optimal parameter values associated with cable trench and thermal backfill is formulated as a nonlinear programming problem and solved using a multi-dimensional gradient optimization method. The technique considers all design parameters simultaneously and provides the optimal solution which either minimizes the cost of backfill and trench production subject to an ampacity constraint or maximizes the cable ampacity subject to a cost constraint. In either formulation, upper and lower bounds on design parameters as well as other thermal and physical constraints are included. The important role of backfill parameters in reducing the effects of environmental fluctuations on cable ampacity is exploited in the optimization analysis via defining functional sensitivity profiles which may be used to ensure secure and reliable designs. The paper includes a description of the computer program which was developed for the optimization of general cable configurations in thermal backfill.

Optimization of Power Cable and Thermal Backfill Configurations

Optimization of Power Cable and Thermal Backfill Configurations

Thermal Stability and its Prediction in Cable Backfill Soils

Thermal instability, in the context of heat dissipation from buried cables, refers to the condition tion in which the thermal resistivity of the soil continuously increases with time to a value close to that of its dry state. This "thermal runaway" condition leads to a large increase in cable temperature. The thermal instability in cable backfills is a direct result of net moisture migration away from the heat source below a critical moisture level. Moisture migration in cable backfills can be caused by either a natural drying process resulting from evapotranspiration or by the thermal gradient from the heat source. This paper deals with the latter case, for which a theoretical prediction and experimental verification are provided. A transient heat probe method of predicting thermal instability in cable backfills is discussed.

Moisture control of cable environment with particular reference to surface troughs

The rate of dissipation of heat from buried cables is dependent on the thermal resistivity of the surrounding backfill. It is well known that, for granular materials, e.g. sands, the thermal resistivities vary markedly with the moisture contents, and high resistivities can be reached because of drying. The paper discusses the factors that lead to moisture migration, and gives practical information on methods of controlling the moisture content in cable backfills. Information on mean wind speeds, hours of daylight and average rainfall are collated to support the theory of establishing a `moisture-control season? that is suitable for UK installations. Results of field trials are analysed, and indicate the major effect of rainfall and the smaller effect of solar radiation on the performances of cables laid at different depths. Difficulties associated with calculating water losses are outlined, and the results of experiments to establish a rate of loss from surface troughs are recorded. Recent cable circuits with automatic-moisture-control facilities are described. These have been confined to surface-trough in stallations employing cement-bound-sand backfills, but the possibility of extending the technique to cable reserves and other types of installation is suggested. The economic advantages of moisture control and future trends resulting from savings in cost and space are also discussed.

The Thermal Behavior of Cable Backfill Materials

The thermal behavior of a number of soils including those frequently used for high-voltage cable backfill has been studied in the laboratory and in the field. Initially, thermal resistivity tests using a probe and thermal moisture migration tests were carried out in the laboratory. From these tests it was found that well-graded granular materials behaved the best. In particular "limestone screenings," a by-product from rock quarries, was found to have highly desirable thermal properties. A full-scale field test was made by means of a simulated cable installation. The materials tested included a uniform sand, a manufactured sand and "limestone screenings." The placement moisture and density of the materials was varied as well as the heat input. Observations of moisture and temperature gradient were made over a two and one- half year period. The results of this study confirmed the results of the earlier laboratory tests. The screenings and the manufactured sand, both of which were well graded, exhibited a low resistivity which remained stable during both dry and wet periods. The uniform sand had a higher initial thermal resistivity and became unstable due to moisture migration during dry periods of the year. Subsequently, a few simple tests have been made to investigate the flow of vapor and liquid in soil under a thermal gradient. A tentative explanation of the varying behavior of the materials, based on their respective porosity characteristics, is given.