Supercapacitors in Constant-Power Applications: Mathematical Analysis for the Calculation of Temperature

Round 1

Reviewer 1 Report

The proposed manuscript developed a mathematical analysis method with incomplete gamma function to simulate the temperature change while a supercapacitor is operating at constant power. The method could provide good estimation of the temperature and avoided differential equations without any unnecessary simplifications. The authors provided a comprehensive background of the research, and presented the work clearly. I would suggest to accept the manuscript.

Author Response

Please find the manuscript in the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear Authors,

Thank you for your submission to this journal.

There is only a point for final consideration, in sections 3.1 and 3.2, where you are showing the effect of SC charging and discharging in low and high power on temperature, please highlight the differences too. I mean Tables 2 and 3 also Figures 5 and 6.

 

Best Regards

Reviewer

Author Response

The authors wish to thank the reviewer for their valuable time and useful contribution to the revision of the manuscript, whose quality has undoubtedly improved.

Author Response File: Author Response.docx

Reviewer 3 Report

It is better not to use “novel” and “precise” to define your work. If you want this work to survive the test of time address broader issues. The idea of novelty vanishes with time and the paper will appear to be less important in the future. Instead of “Novel” and “Exact” in the title, use phrases that can help search your paper more effectively.

The paper uses one assumed R and C without tolerance and provides exact solutions based on that. What is the chance that a user’s supercapacitor will match those values? Equation 40 is not easy to implement, even if it is exact analytical solution. To make the paper useful, please generate a family of curves to cover reasonable range of variables that are used in the industry.

Following are my comments to improve the manuscript:

1. Use a nomenclature section to define the symbols used.
2. Line 227: temperature difference instead of “thermal jump”
3. Where do you measure Tcell? Is it average cell temperature? If so, do not use the word exact-as that can be confusing and not measurable as easily as suggested in the paper.
4. Line 231: do not use “easily” – use “can be calculated”. Search “easily” and “easy” words in the document and remove. What is easy for you may not be so with others.
5. Line 232. Give a name for g1- what is it?
6. Equation 14 has several new variables like R.C and W- what are they?
7. Line 294: Reference Gamma Function with equation 32.
8. Figure 6, how do we know which one is correct? Is there any experimental evidence? Yours and numerical model assumed several things and how do we make an informed decision? For example, how do you know the R and C stay the same during the entire discharge/charge process?
9. If possible, add sensitivity analysis. Exact solution needs exact assumptions and can be problematic. Vary the variables by reasonable tolerance and show the behavior and explain your observations.

Author Response

The authors wish to thank the reviewer for their valuable time and useful contribution to the revision of the manuscript, whose quality has undoubtedly improved.

Author Response File: Author Response.docx