Dear Dr. Xu,

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Academic Editor

PLOS One

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

Reviewer #1: Partly

Reviewer #2: Yes

Reviewer #3: Partly

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2. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: The paper addresses the study of the influence of protrusions on the electric field distribution within HVDC cable insulation, by considering various parameters as sizes and shapes of protrusions, activation energy of conductivity for insulation materials and temperature difference across the insulation. The results of a 3D FEM simulation model are shown. The argument is topical. The results may be of industrial interest even if only simulation is proposed. Software is not specified: please, add description of the used software (commercial or not). Some comparison with existing similar experimental results should be added, even if referred to HVDC cables not strictly corresponding to that analysed by the authors, for validating the simulation results of the proposed cable configuration.

Reviewer #2: The detailed comments are as follows:

1. Lines 153–154 contain “Error! Reference source not found.”, indicating a problem with citation format or numbering. Please check and correct all references.

2. Cable geometry and material parameters are provided, but the source of these values (experimental measurement, manufacturer data, or literature) is unclear. Please clarify.

3. Qted in Eq. (5) is described as “thermoelastic damping power,” but the manuscript does not specify which part of heat generation it represents. Clarification is needed.

4. Figures (Fig. 3–Fig. 12) have low resolution; local details are difficult to see. High-resolution or vector images are recommended.

5. In Fig. 6(a) and Fig. 7(a), insulation layer, semiconductive layer, and interface are not labeled. Add clear layer/interface labels and explain the meaning of a/b/c axes in captions.

6. The set temperature field (inner/outer shields, radial gradient) lacks source information. Clarify the origin or calculation basis.

7. What is the practical significance of this study? In engineering practice, a smoother interface—or no protrusions at all—is always preferred. Therefore, the investigation of protrusion height appears to have limited practical relevance. Similarly, it is already known that higher activation energy is detrimental to insulation performance.

Reviewer #3: The manuscript investigates the influence of semiconductive shielding protrusions on electric field distribution in ±500 kV HVDC cables using a 3D finite element model. The topic is relevant to HVDC cable reliability, and the manuscript provides useful parametric analyses regarding protrusion geometry, activation energy, and thermal gradients. However, the work remains largely simulation-based and requires stronger validation, clearer methodological descriptions, and deeper discussion of engineering implications. In its current form, the scientific contribution is somewhat incremental relative to previous studies on HVDC cable interface defects.

1. The authors claim that previous studies mainly focused on 2D analyses while this work employs a 3D FEM model. However, the manuscript does not sufficiently demonstrate the practical advantages of the 3D model over existing 2D studies. It is recommended that to explain, why a 3D model is necessary, which physical phenomena cannot be captured by 2D models, quantitative differences between 2D and 3D results and additional engineering insights obtained from the 3D analysis.

2. The entire study is based on numerical simulations, no experimental measurements, laboratory testing, or comparison with published experimental data are provided to validate the model. It is recommended that to compare the simulated electric field distributions with available literature results. Provide validation against experimental breakdown data or field measurements if available. Discuss model accuracy and limitations.

3. The FEM model description is incomplete, and important information is missing, including, software platform used, number of mesh elements, mesh independence study, convergence criteria, solver settings, and computational accuracy.

4. The protrusion height varies from 50 μm to 300 μm, manuscript does not explain, whether these dimensions are representative of manufacturing defects observed in industrial HVDC cables. The authors should provide references or industrial evidence supporting the selected defect sizes.

5. The authors should clarify what distortion-rate thresholds are considered dangerous. Whether a distortion rate of 9.78 or 102.04 corresponds to insulation failure risk. How these values relate to breakdown strength of XLPE.

6. Activation Energy Analysis Requires Deeper Discussion

The manuscript reports that the distortion rate increases with activation energy.

It is recommended that to explain, the conductivity mechanism responsible for this trend. Whether the activation energy range (0.85–1.00 eV) reflects commercial XLPE materials and practical implications for insulation material selection.

7. In the Conclusion "Field distortions under DC stress are more complex and severe than those under AC conditions" is not directly demonstrated in the manuscript because no AC simulations are presented. Either provide AC simulation results for comparison, or rephrase this statement to avoid unsupported conclusions.

8. Typographical and Language Issues

Several grammatical and wording issues should be corrected, examples include:

i. "insulation system" → "an insulation system"

ii. "the four innermost layers of the cable is considered" → "are considered"

iii. "b increase" → "b increases"

iv. "field strength frops" → "field strength drops"

A thorough English language revision is recommended.

9. Several references appear incomplete or inconsistent. Reference [6] lacks complete bibliographic information, reference [15] appears incomplete, some conference references do not contain page numbers. The reference list should be carefully checked according to journal guidelines.

10. Some symbols are inconsistently defined.

i. Conductivity is denoted using both σ and γ.

ii. Relative permittivity values in Table 2 appear unusual and should be clarified.

iii. Units and notation should be standardized throughout the manuscript.

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what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review?  For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes:  Dr. Muhammad Wahab Hanif

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Influence of semiconductive shielding protrusions on the electric field distribution in ±500 kV HVDC cables

PONE-D-26-17827R1

Dear Dr. Xu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Azim Uddin, Ph.D.

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously? -->?>

Reviewer #1: (No Response)

Reviewer #2: N/A

Reviewer #3: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available??>

The PLOS Data policy

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English??>

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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Reviewer #1: (No Response)

Reviewer #2: The authors have addressed the comments raised in the previous round of review and made the corresponding revisions. I have no further comments on the revised manuscript.

Reviewer #3: (No Response)

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what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review?  For information about this choice, including consent withdrawal, please see our Privacy Policy

Reviewer #1: No

Reviewer #2: No

Reviewer #3: Yes:  Dr. Muhammad Wahab Hanif

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