Research Paper3-D thermal analysis and contact resistance evaluation of power cable joint
Introduction
Along with the wide application of power cables in the urban power grid, cable accidents are increasing day by day. The statistics has shown that more than 70% of the failures occurred at cable joints. Due to the imperfect installation process of cable joints, the great contact resistance usually results in inner overheating. Therefore, to prevent accidents of power cable joint, it is important to propose a method to evaluate the contact resistance and detect the unqualified cable joints [1].
Over the past few decades, many attentions have been concentrated on the thermal analysis of power cable due to its overheating, and the methods can be categorized into two different kinds, one is analytical method based on IEC-60287 [2], and the other is numerical method [3], [4] including boundary element method (BEM), finite element method (FEM), finite volume method (FVM), finite difference method (FDM), etc. Olsen et al. used a new algorithm in the calculation of the dynamic temperatures of power cables, and both the thermal resistivity and the specific heat of the cable surroundings varying with time were taken into consideration [5]. Sedaghat and de Leon investigated the steady-state temperature of power cables in free air for the most common configurations, and presented improvements to the IEC standards to rate cables under general operating conditions [6]. Canova et al. investigated the thermal behavior of the cable directly buried in the ground, both in transient and steady-state conditions [7]. Pilgrim et al. used computational fluid dynamics analysis to calculate the cable ratings in air-filled troughs [8]. Anders et al. developed a theoretical model for determining the current rating of cables installed in a side-walk trough [9]. de Lieto Vollaro et al. investigated the thermal analysis of the power cables buried in non-homogeneous soils [10] and homogeneous soil [11], and an experimental study conducted on a scale model was presented [12]. Degefa et al. studied the effects of natural convection on longitudinal heat transfer and on the air-gap thermal resistance of cables inside conduit installation [13]. Lin and Hu used software ANSYS for temperature field calculation and analysis of power cable joint [14]. Wu et al. established a 2-D axial model of 110 kV cable joint in ANSYS software for thermal analysis [15]. Liang et al. used 3-D FEM method to calculate the temperature field and ampacity of cable buried in local conduit [16]. Kovac et al. developed an assessment of the generated heat per unit time and volume within the solid sheaths of a cable line [17].
The above works are mainly focused on the rating calculation of power cable, in which the heat transfer in cable joint is not considered, because the conductor temperature of cable joint is lower than that of cable body for the qualified cable joint. Different from the power cable body, power cable joints are man-made, and the unqualified installation can lead to great contact resistance and the overheating problem of cable joint. When the overheating of the cable joint occurs, the thermal effect of cable joint on the cable rating calculation should be taken into consideration. However, for the temperature property analysis of cable joint, heat transfer in radial and axial directions should be taken into consideration. At the same time, how to check the quality of the cable joint is a big problem that needs to be solved. But so far, there are no effective methods to evaluate the installation quality of the power cable joint. As one of the installation quality problems, large contact resistance can cause the overheating problem of the cable joint.
On this background, based on the previous current simulation model and thermal circuit model, a 3-D electromagnetic-thermal coupling analysis model of cable joint was established. With the given boundary conditions, the electromagnetic field and temperature field distributions were calculated. A method was presented to deal with the influence on the thermal distribution of power cable joint caused by the contact resistance RJ, in which RJ was considered in the resistance of a united element. Example calculation for a XPLE power cable joint was described in details, and the accuracy of the method was verified. The influences of contact coefficient k, ambient temperature Tamb and load current I on cable joint thermal distribution were investigated. Finally,a process to evaluate the contact resistance RJ was presented accoring to the numerical relationship between the cable temperature difference ΔT, contact coefficient k, and load current I, and this process can be used to detect the unqualified cable joint. Results indicate that to ensure the safe operation with lower conductor temperature, the k should be less than 2.7.
Section snippets
Methodology
The temperature field distribution of cable joint is determined by the electromagnetic losses and the external environment, and in this section, an electromagnetic-thermal coupling model [18], [19] for cable joint is described.
Calculation parameters of cable joint
The commonly used 8.7/15 kV YJV 1 × 400 XLPE cable was taken for an example, and its parameters are shown in Table 1.
The lengths of different parts of the cable joint (as shown in Fig. 1) are listed in Table 2.
For a single cable joint laid in the air, the laying parameters are given in Table 3.
Mesh generation
In this paper, COMSOL Multiphysics software package is used to investigate the electromagnetic losses distribution and temperature distribution of the cable joint. The tetrahedral meshes were used to
Method and model verification
For the 8.7/15 kV cable described in the above section, the electromagnetic-thermal field distributions on a cable body cross section 2.5 m away from the center of cable joint were calculated, and the results were compared with the analytical results, as shown in Table 4. The heat source of cable body conductor Qv for analytical method is calculated based on the IEC-60287 standard [25], [26]. Results in Table 4 indicate that the relative errors are within 5%, and the calculation accuracy is
Analysis of influence factors
The influences of k, Tamb and I on the temperature distribution of the power cable were studied in this section.
Evaluation of contact resistance
According to the influence rules of k, Tamb and I on Tj, Tb and ΔT in section 5, it can be known that Tj and Tb are influenced by k, Tamb and I, but ΔT is little affected by Tamb. To reduce the number of variables, k, I and ΔT were chosen to form the evaluation model. More calculations were carried out to obtain large amounts of data (I, k, ΔT), and these data are shown in the form of 2-D coloring contour, as shown in Fig. 17. The range of k is from 1 to 10 and the range of I is from 300 A to
Conclusions
For the overheating problem of the unqualified cable joint, the electromagnetic-thermal coupling analysis model was established, and the contact resistance was taken into consideration. The modeling results were verified by analytical results, measured results and reference results. Based on this model, the influences rules of contact resistance, ambient temperature and load current on the cable temperature were investigated. Finally, a mathematical method by using temperature difference and
Acknowledgement
This work was supported by the Fundamental Research Funds for Central Universities (No. CDJZR14155501).
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