Modeling Thermal Impedance of IGBT Devices Based on Fractional Calculus Techniques

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, a thermal impedance modeling method based on fractional order is proposed, which is relatively novel, but the related validation analysis is weak, and the following issues need to be further improved:

1. In the introduction section, the literature referenced for the application of IGBT devices in the field of rail transportation is scarce, and it is suggested that the following literature be added to improve the coverage of the literature review.

 (1) D. Xie et al., "Simple Vector Calculation and Constraint-Based Fault-Tolerant Control for a Single-Phase CHBMC," in IEEE Transactions on Power Electronics, doi: 10.1109/TPEL.2024.3437229. 

  (2) X. Li, J. Xu, Z. Chen, S. Xu and K. Liu, "Real-Time Fault Diagnosis of Pulse Rectifier in Traction System Based on Structural Model," in IEEE Transactions on Intelligent Transportation Systems, vol. 23, no. 3, pp. 2130-2143, March 2022, doi: 10.1109/TITS.2020.3033318. 

2. This paper only compares the parameter identification results in the frequency domain. When converted to the time domain, the identification errors for different-order parameters need to be further evaluated.

3. The thermal network model considered in this paper is relatively simple, for multi-chip devices, considering the existence of thermal coupling as well as heat dissipation conditions, the thermal model will be more complex. What is the implementation complexity and identification accuracy of the fractional-order-based thermal modeling approach in this regard?

4. It is suggested to compare the existing thermal impedance modeling methods with the proposed method in a list and highlight the proposed method's advantages in terms of modeling accuracy, complexity, and applicable conditions.

Comments on the Quality of English Language

 The English could be improved to more clearly express the research.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript shows the novel approach to obtaining thermal impedance parameters of IGBT module from measured temperature at certain conditions. The proposed method is based on fractional calculus. I do not see any advantage of the proposed method over the method with a series of exponent functions instead of two parameters. It would be satisfactory if more examples of such calculations were presented. I am not sure if 1-degree precision is important. How is the Bode diagram translated to time Zthjc, where this 1deg discrepancy is observed? In the paper, everything is clearly explained up to Equation 15, and then it looks like the authors ended the article too quickly without a detailed verification of the method. What tools were used in the paper for the calculation of fractional coefficients? Additionally, I have a comment on graph 8b, so I am including the appropriate file.

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors present a fractional-order thermal impedance model for IGBT modules, based on the Foster thermal network model and its parameter extraction methods, along with a parameter identification method using the MOPSO algorithm. Here are a few comments.

1.     The rationale for incorporating fractional calculus in the modeling is inadequately explained. Additional theoretical grounding is needed to help the reader understand the necessity and advantages of using fractional-order models.

2.     The physical significance of the complex frequency “s” is not adequately described. It is important to clarify how “s” relates to the thermal response of the system and how it affects the thermal characteristics of IGBTs in the frequency domain.

3.     The statement that the parameter identification was transformed into a "nonlinear global optimization problem with physical property constraints" is somewhat vague. It would be beneficial to provide details on the constraints applied and their impact on the results

 

4.     The explanation of the parameters of the integer-order four-cell Foster thermal network model is not very clear. Please describe in detail why the time constant of order i, and the thermal resistance value of order trend are so prominent, especially in the third cell of Table 1. If this is not based on the test, please add a note to emphasize that this is just a calculated value.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Thanks for the authors' hard work. Most of the comments have been addressed well. In terms of limitations and future work, the specific description should be illustrated in the Conclusion. If adding this content, I think it can be accepted.

Author Response

Comments 1: Thanks for the authors' hard work. Most of the comments have been addressed well. In terms of limitations and future work, the specific description should be illustrated in the Conclusion. If adding this content, I think it can be accepted.

Response 1: We once again appreciate your kind comments. In response to your comment, we have added the following content in the conclusion part of this paper:

“Currently, the proposed fractional-order equivalent thermal impedance model is applied in the frequency-domain in this paper, in order to further apply the fractional-order equivalent thermal impedance model to the thermal analysis of IGBT devices, it is necessary to transfer the modeling research of fractional-order equivalent thermal impedance to the time-domain in the future.”

For changes, please see lines 344 to 348 on page 12 of this paper.

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for revising the manuscript, now I believe that the manuscript is ready for publication.

Author Response

Comments 1: Thank you for revising the manuscript, now I believe that the manuscript is ready for publication.

Response 1: We once again appreciate your comments about improving the quality of our paper. Wishing you a smooth life and pleasant work.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors addressed all the comments of this reviewer. Now it can be accepted as it is.

Author Response

Comments 1: The authors addressed all the comments of this reviewer. Now it can be accepted as it is.

Response 1: Again, we would like to express our gratitude to you for your help and comments, which improve the quality of our work.