Research on a Universal Analytical Thermal Circuit Model for Civil Electric Cables

Comments 1: [The research results are interesting and appropriate, and the general presentation is adequate and well aligned with the current societal challenges and their solutions. The study appears to be original and scientifically sound and is likely to be of great interest to readers. However, given the assumption of highly precise determination of the temperature of the tested cables, several important aspects are not considered in the current calculations. In particular, the effects of actual contact thermal resistance at the boundary between the conductor and the insulator, as well as radiative heat transfer, are neglected, although they may significantly affect the accuracy of the calculation. Furthermore, the manuscript provides insufficient information regarding the quality of the interface between the insulator and the conductor within the cable.]

Response 1: Thank you for this insightful comment. We acknowledge that contact resistance and radiation exist physically. However, for civil electric cables which are typically manufactured with tight extrusion, the contact between layers is very close, making contact resistance minimal compared to the insulation's bulk resistance.  Similarly, internal heat transfer is dominated by conduction.

We have added a clear statement in Section 2.1 to clarify these assumptions:

"To simplify the analytical model while maintaining engineering accuracy, given the tight extrusion manufacturing process of civil electric cables, and in accordance with the calculation methods outlined in IEC 60287, the interface between the conductor and insulation layer is assumed to be seamless with negligible gaps; thus, contact thermal resistance is ignored. Furthermore, as heat transfer within the solid cable structure is dominated by conduction, internal radiative heat transfer is considered negligible. The high accuracy of our validation results (Error < 0.148%) supports the feasibility of these assumptions.

Where in the revised manuscript this change can be found [page 3, Lines 117-122].

Comments 2: [The extra space after R_20 should be removed in line 47. An additional unnecessary space is also present in line 85 of the phrase ‘the FEM’.]

Response 2: We apologize for these typos. We have deleted the extra spaces in the revised manuscript to ensure correct formatting.

Where in the revised manuscript this change can be found [Page 2, Line 47; Page 2, Line 85].

Comments 3: [In Figure 1, the letter ‘L’ is positioned too close to the dimension line; The same problem applies to D1 and D2.]

Response 2: Thank you for the detailed observation. We have adjusted Figure 1 to increase the distance between the text labels (L, D1, D2) and the dimension lines, improving the readability of the diagram.

Where in the revised manuscript this change can be found [page 3, Lines 114].

Comments 4: [Commas appear to be missing after several equations (from Equations 1 to Equation 42), and a period is missing at the end of the final equation. In addition, explanations of the parameters introduced in the equations should begin with ‘Here, …’.]

Response 1: We sincerely apologize for the formatting oversight. We have carefully revised all equations (Eq. 1 to Eq. 42).

1.        We have added a period (.) at the end of every equation to ensure they function as complete sentences.

2.        Accordingly, we have standardized the parameter explanations following the equations to begin with "Here, ..." as suggested

Comments 1: [A major point that requires clarification concerns the choice of the Differential Evolution (DE) algorithm for coefficient identification. The manuscript currently states that DE was used to train kr1​, kr2​, and kk, but it does not explain why DE was preferred over common evolutionary optimizers such as Genetic Algorithms or Particle Swarm Optimization. Since the optimization problem here involves real-valued continuous parameters and a non-convex objective derived from FEM-based temperature curves, the authors should briefly justify DE in terms of faster convergence, fewer hyper-parameters, and better robustness to noisy fitness landscapes, as well as its suitability for continuous heat-transfer coefficient inversion. A short justification in Section 3 would resolve this gap.]

Response 1: We appreciate this valuable suggestion. We chose DE primarily because our optimization problem involves estimating real-valued continuous parameters within a specific range. We have added a paragraph in Section 3.3.2 to explicitly justify the choice of DE and cite relevant comparison studies:

"The Differential Evolution (DE) algorithm was selected for parameter identification due to its superior performance in continuous parameter optimization spaces. Compared to other common evolutionary optimizers such as Genetic Algorithms or Particle Swarm Optimization, DE demonstrates faster convergence, fewer control parameters, and better robustness against local minima, making it highly suitable for the continuous heat-transfer coefficient inversion and the non-convex objective function derived from the FEM-based temperature curves in this study."

Where in the revised manuscript this change can be found [page 10, Lines 342-348].

Comments 2: [Several minor issues should also be addressed. Figures would benefit from more informative captions, and variable symbols should be unified upon first appearance (e.g., R1, C1, k1R_1, C_1, k_1R1​, C1​, k1​). Units such as mm² should be formatted consistently, and some English expressions in the Introduction could be streamlined for clarity. In addition, a brief sentence highlighting the physical meaning of the identified coefficients would improve readability.]

Response 2: We thank the reviewer for the detailed attention to detail. We have thoroughly revised the manuscript according to these points:

1. Variable Symbols: All variables (e.g., ) have been unified to use subscript formatting throughout the text and figures.
2. Units: All units involving exponents (e.g., ) have been consistently formatted with superscripts.

3.     Physical Meaning: We added a sentence in Section 3.3 to emphasize the physical significance of the coefficients:

"The identified coefficients possess specific physical interpretations derived from the governing equations. Specifically,  and encapsulate the volumetric heat capacities of the insulation and conductor, determined by their respective densities () and specific heat capacities ().  reflects the thermal resistivity () of the insulation material, while  and  characterize the convective heat transfer capabilities at the cable surface and exposed ends, respectively. "

Where in the revised manuscript this change can be found [page 11, Lines 368-373].

Comments 3: [Finally, the Introduction may cite Journal of Materiomics 10 (3), 748–750 when discussing the broader significance of temperature control for device-level reliability, immediately after noting the sensitivity of electrical resistance to thermal fluctuations.]

Response 2: Thank you for recommending this relevant literature. We agree that highlighting the broader significance of temperature control and device reliability improves the introduction. We have cited this paper in the Introduction, immediately after mentioning the sensitivity of electrical resistance to temperature.