An Improved Analytical Thermal Rating Method for Cable Joints

1. Comments 1: The proposed modeling approach, as shown in Figs. 6 and 7, has already been published in several publications in different applications. The reviewer acknowledges that this is a different application. Nevertheless, the authors should mentioned this fact.  For list of references on the application of this model the authors could, for example, look at the book “Rating of electric power cables in unfavorable thermal environment” by G.J. Anders, published by John Wiley in 2005.

Response 1: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

As stated by the reviewer, there is a similarity between the model we used and that used by the literature he mentioned and indeed should supplement the references. However, our model has been further changed, the established model is the cable connector rather than the cable, and the calculation method of some parameters has also been changed. Based on the reviewers’ comments, the authors have supplemented abbreviations mentioned by the reviewer. The specific modifications are as follow:

The thermal model in the radial direction was established in reference to literature [26], and the model in the axial direction was established based on the same method. (On page8, paragraph4)

26. Anders G J, Institute of Electrical and Electronics Engineers. Rating of electric power cables in unfavorable thermal environment[M]. Hoboken, NJ, USA: Wiley, 2005.

Comments 2: I would be careful in dismissing the models presented in references [18] and [8] as the results obtained by those models were supported by the measurements.

Response 2: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

The reason for choosing these two references is that they have relatively more citations and better recognition. So it can be contrasted with the newly established model of the authors and reflect its innovation.

Comments 3: Laying depth of <= 1.2 m is by far not sufficient, since high voltage and EHV cables are deeper.

Response 3: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

However, in this manuscript, buried cables are not analyzed, but the situation of cable joints in the air is analyzed.

Comments 4: Moisture of soil information is interesting, but mostly the distance of the groundwater table will be decisive. And this may strongly change in the future. Drying-out is not discussed by authors’ in "dynamic calculations".

Response 4: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

However, in this manuscript, buried cables are not analyzed, but the situation of cable joint in the air is analyzed. In addition, the study in this manuscript is focused on the steady state of the cable joint, not the dynamic state. The authors will consider these questions in subsequent studies.

Co Comments 5: There is some discrepancy in the wording in Section 2. Just after equation (6) the authors state: “In the TEA method, it is assumed that there is no axial heat flux existing between the central element and the adjacent elements of cable joint…” and then after equation (11), they state: “The TEA method takes full account of the axial heat flux in conductor between the cable joint and adjacent cable.”  This should be addressed.

Response 5: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

As mentioned by the reviewer, the assumption and subsequent descriptions of the TEA method are contradictory in the manuscript, which makes readers confused. What the authors were trying to express in assumption was it is assumed that there is no axial heat flux existing between the central element and the adjacent elements of cable joint except for the conductor and copper shell, because the heat flux along the axial direction mainly exists in the materials with high thermal conductivity [25]. Based on the reviewers’ comments, the authors have supplemented corresponding statements. The specific modifications are as follow:

In TEA method, because the heat flux along the axial direction mainly exists in the materials with high thermal conductivity [21] and the copper shell has a smaller temperature gradient as it is too far away from the heat source, it is assumed that there is no axial heat flux existing between the central element and the adjacent elements of cable joint except for the conductor, neither between the cable terminal element and its adjacent elements. (On page4, paragraph3)

21. Nakamura S, Morooka S, Kawasaki K. Conductor temperature monitoring system in   underground power transmission XLPE cable joints. IEEE Transactions on Power Delivery, 1992, 7: 1688-1697.

Comments 6: Please look at frequent repetition of the same word or structure in one sentence. There are also some minor spelling mistakes.

Response 6: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

Based on the reviewers’ comments, the authors have gone through the manuscript carefully and corrected all grammatical and lexical errors. In addition, the authors have invited an English-speaking expert to polish the manuscript.

Comments 1: TEA, FEA (the finite element analysis) - These abbreviations are not explained.

Response 1: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

Based on the reviewers’ comments, the authors have supplemented abbreviations mentioned by the reviewer. The specific modifications are as follow:

1. traditional electrothermal analysis (i.e. TEA) (On page3, paragraph 2).

2. finite element analysis (i.e. FEA) (On page2 paragraph 5).

Comments 2: Table 1. Detailed information of the cable joint

Component Conductor tube - Thickness [mm]. The diameter should be at this point. I suggest using a formula Thickness/Diameter [mm]

Response 2: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

It can be seen that the main insulation of the cable joint changes with the axial direction, so it cannot be described by fixed parameters.

Figure 2. Cable joint 2D simulation model: 1-Block, 2-Copper shell, 3-Filling glue, 4-PVC belt, 5-Joint main insulation, 6-Copper screen tube, 7-Connection tube, 8-Air gap, 9-Shielding tube, 10-Conductor, 11-XLPE insulation, 12-Buffer layer, 13-Air gap, 14-Aluminum sheath, 15 -Outer sheath.

Comments 3: Fig. 4b The surface temperature distribution curves.

I don't understand the breakdown of the characteristic curve around point 0. What surface does this graph cover?  Please explain.

Response 3: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

As mentioned by the reviewer, the authors lacked an explanation of how the curve shown in figure 4b changes around point 0, which makes readers confused. This is because the authors assumed that the temperature and convection coefficient of air is constant. When the calculation object is changed from a cable to a cable joint, the surface area of the cable joint is greatly increased relative to the cable, and the radial thermal power mainly comes from the conductor Joule heat, which does not change. Therefore, the temperature of the joint surface is reduced relative to the cable surface, reducing the temperature difference with the air and maintaining the radial heat dissipation power. Based on the reviewers’ comments, the authors have supplemented corresponding statements. The specific modifications are as follow:

Thus, the third type of boundary condition was adopted for the surface of cable joint and cable [13] and the natural heat transfer coefficient is set at 7.5W/m·K^-1, and the air temperature is set at 19.5℃. (On page6, paragraph2)

This is because the surface area of the cable joint is larger than the cable, resulting in an increase in radial heat dissipation power, and the radial heat dissipation power is unchanged, so the surface temperature of the cable joint is reduced to maintain the same heat dissipation power. (On page7, paragraph3)

Comments 4: Fig. 8 Comparison of theoretical and simulation results.

What instrument was used to the temperature measure? How was this measurement performed?  Please provide technical details.

Response 4: The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

The authors can directly obtain the temperature distribution of the whole cable joint and cable through finite element analysis method, and only need to set the sampling path to get the temperature on the path.

Comments 5: Other

As a user of thermal imaging techniques, I have one more comment.

Thermography enables quick diagnosis of power lines.  In this way, you can check whether parts of power installations heat up evenly.  This technique (NDT) detects potential threats.  The Authors do not notice this solution.  It would be an excellent validation of the proposed method.

Response 5：The authors are highly grateful to the editor and reviewers for making valuable suggestions for improving the quality of manuscript.

As mentioned by the reviewer, the method proposed in this paper can be combined with thermography to obtain the surface temperature, and then as the input of our thermal model, so as to realize the rapid calculation of the joint hot spot temperature. Based on the reviewers’ comments, the authors have supplemented corresponding statements. The specific modifications are as follow:

In practical application, the surface temperature of cable joint can be obtained by thermal imaging technology as input quantity, and the conductor temperature can be solved quickly.(On page2, paragraph4)