Analysis of the Charge Density Variation Caused by the Physical Properties of the Electrodes of Lithium-Ion Batteries
Round 1
Reviewer 1 Report
Reviewer comments:
The paper presents a fractional order (FO) model that characterizes the charge distribution of lithium-ion batteries and reveals variations in the charge density associated with the physical properties of the electrode. Several experiments at different states of charge (SOCs) and cycle numbers have been carried out to identify the fractional derivative order of the model.
Major comments:
1. In the Introduction, several previous works found in the literature are mentioned regarding the main tests performed (the electromechanical test method, cyclic voltammetry, constant potential intermittent titration and constant current intermittent titration, and electrochemical impedance spectroscopy). However, there is no state of the art of other FO models that characterize the behavior and characteristics of batteries. It could be interesting to make a review of other FO models in order to compare them with the one determined in this paper. For instance, three references about FO models are listed below.
Meijuan Yu, Yan Li, Igor Podlubny, Fengjun Gong, Yue Sun, Qi Zhang, Yunlong Shang, Bin Duan, Chenghui Zhang, “Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion”, Journal of Advanced Research, Volume 25, September 2020, Pages 49-56. https://doi.org/10.1016/j.jare.2020.06.003
Liqiang Zhang, Xiangyu Wang, Mingyi Chen, Fan Yu, Ming Li, “A fractional-order model of lithium-ion batteries and multi-domain parameter identification method”, Journal of Energy Storage, Volume 50, June 2022, 104595. https://doi.org/10.1016/j.est.2022.104595
Yanbo Jia, Lei Dong, Geng Yang, Feng Jin, Languang Lu, Dongxu Guo and Minggao Ouyang, “Parameter Identification Method for a Fractional-Order Model of Lithium-Ion Batteries Considering Electrolyte-Phase Diffusion”, Batteries, Volume 8, 2022. https://doi.org/10.3390/batteries8080090
2. Regarding the references, the reviewer suggests to look for more recent papers, published in the last 3-4 years.
3. A scheme of the test platform described in Section 4.1 could be helpful to readers.
Minor comments:
1. The reviewer suggests defining initials for fractional derivative order, as it is used in many occasions throughout the paper.
2. Last lines of page 3 basically explain the same idea, but twice. The reviewer suggests resuming these lines. These are the following: “Finally, the fractional derivative order is used to explain the capacity of recovery phenomenon caused by the mutation of the charge density. The fractional derivative order can be used to properly characterize the mutation of the charge density and to predict capacity recovery.”.
3. Usually, the magnitude units in figures are indicated within parenthesis, instead of “Voltage/V” as in Fig. 1 of the paper.
4. In last lines of page 12, the first sentence is not finished. May the full stop after “batteries” be a comma?
5. The reviewer suggests revising the whole paper in order to correct some typos, such as:
a. Introduction line 14: “affects the state of charge(SOC),”, please leave a gap between “charge” and the parenthesis.
b. Introduction, third contribution of the paper: in the second line, where it says “physical property”, property should be written in plural?
c. Page 13 point 4, 5 and 7: “battery” should be written in plural.
d. Section 6 line 12: where it is said “… and this process split electrode…”, the verb should end with an “s”.
Comments for author File: 
Comments.pdf
Author Response
Many thanks for the comments of the reviewers and editors. We have learned much from the reviewers’ comments, which are fair, encouraging and constructive. After carefully studying the comments, we have made corresponding changes. Each revisions has been clearly highlighted, and a list of changes can been seen at the end of the new manuscript. A list of answers and changes to the comments is as follows.
Point 1: In the Introduction, several previous works found in the literature are mentioned regarding the main tests performed (the electromechanical test method, cyclic voltammetry, constant potential intermittent titration and constant current intermittent titration, and electrochemical impedance spectroscopy). However, there is no state of the art of other FO models that characterize the behavior and characteristics of batteries. It could be interesting to make a review of other FO models in order to compare them with the one determined in this paper. For instance, three references about FO models are listed below.
Meijuan Yu, Yan Li, Igor Podlubny, Fengjun Gong, Yue Sun, Qi Zhang, Yunlong Shang, Bin Duan, Chenghui Zhang, “Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion”, Journal of Advanced Research, Volume 25, September 2020, Pages 49-56. https://doi.org/10.1016/j.jare.2020.06.003
Liqiang Zhang, Xiangyu Wang, Mingyi Chen, Fan Yu, Ming Li, “A fractional-order model of lithium-ion batteries and multi-domain parameter identification method”, Journal of Energy Storage, Volume 50, June 2022, 104595. https://doi.org/10.1016/j.est.2022.104595
Yanbo Jia, Lei Dong, Geng Yang, Feng Jin, Languang Lu, Dongxu Guo and Minggao Ouyang, “Parameter Identification Method for a Fractional-Order Model of Lithium-Ion Batteries Considering Electrolyte-Phase Diffusion”, Batteries, Volume 8, 2022. https://doi.org/10.3390/batteries8080090
Response 1: According to the comments of reviewers, we have added a review of the fractional modeling methods, which can be seen in the new manuscript.
Point 2: Regarding the references, the reviewer suggests to look for more recent papers, published in the last 3-4 years.
Response 2: According to the comments of reviewers, we have updated some references, which can be seen in the new manuscript.
Point 3: A scheme of the test platform described in Section 4.1 could be helpful to readers.
Response 3: According to the comments of reviewers, we have added the scheme of the experimental platform, which can be seen in the new manuscript.
Point 4: The reviewer suggests defining initials for fractional derivative order, as it is used in many occasions throughout the paper.
Response 4: According to the comments of reviewers, we have made the corresponding modifications, which can be seen in the new manuscript.
Point 5: Last lines of page 3 basically explain the same idea, but twice. The reviewer suggests resuming these lines. These are the following: “Finally, the fractional derivative order is used to explain the capacity of recovery phenomenon caused by the mutation of the charge density. The fractional derivative order can be used to properly characterize the mutation of the charge density and to predict capacity recovery.”.
Response 5: According to the comments of reviewers, we have made the corresponding modifications, which can be seen in the new manuscript.
Point 6: Usually, the magnitude units in figures are indicated within parenthesis, instead of “Voltage/V” as in Fig. 1 of the paper.
Response 6: According to the comments of reviewers, we have made the corresponding modifications, which can be seen in the new manuscript.
Point 7: In last lines of page 12, the first sentence is not finished. May the full stop after “batteries” be a comma?
Response 7: According to the comments of reviewers, we have made the corresponding modifications, which can be seen in the new manuscript.
Point 8: The reviewer suggests revising the whole paper in order to correct some typos, such as:
- Introduction line 14: “affects the state of charge(SOC),”, please leave a gap between “charge” and the parenthesis.
- Introduction, third contribution of the paper: in the second line, where it says “physical property”, property should be written in plural?
- Page 13 point 4, 5 and 7: “battery” should be written in plural.
- Section 6 line 12: where it is said “… and this process split electrode…”, the verb should end with an “s”.
Response 8: According to the comments of reviewers, we have made the corresponding modifications, which can be seen in the new manuscript.
Author Response File: Author Response.pdf
Reviewer 2 Report
Title: “Analysis of the Charge Density Variation Caused by the Physical Properties of the Electrodes of Lithium-ion Batteries”
​My comments:
In this article, the authors a model is presented using fractional derivative order to characterize the charge distribution of the batteries (lithium-ion), and to reveal variations in the charge density associated with the physical properties of the electrode.
It is a very interesting idea and to my knowledge the author presented clearly.
Update some of the references, for instance, the authors should add a paper from M. Yu, et at., Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion. https://doi.org/10.1016/j.jare.2020.06.003
It is an interesting article.
Author Response
Many thanks for the comments of the reviewers and editors. We have learned much from the reviewers’ comments, which are fair, encouraging and constructive. After carefully studying the comments, we have made corresponding changes. Each revisions has been clearly highlighted, and a list of changes can been seen at the end of the new manuscript. A list of answers and changes to the comments is as follows.
Point 1: Update some of the references, for instance, the authors should add a paper from M. Yu, et at., Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion. https://doi.org/10.1016/j.jare.2020.06.003
Response 1: According to the comments of reviewers, we have updated some references, which can be seen in the new manuscript. We also have added a review of the fractional modeling methods.
Author Response File: Author Response.pdf
Reviewer 3 Report
The idea is clear and, to my best knowledge, sufficiently novel.
Mandatory requirement: replace references [37], [38], [39] related to fractional capacitor with the reference to the ORIGINAL paper "Capacitor theory" by S. Westerlund and L. Ekstam (https://doi.org/10.1109/94.326654).
Add a references to the paper "Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion" by Meijuan Yu et al. (https://doi.org/10.1016/j.jare.2020.06.003), which seems to be very close to the conclusions in this manuscript.
Author Response
Many thanks for the comments of the reviewers and editors. We have learned much from the reviewers’ comments, which are fair, encouraging and constructive. After carefully studying the comments, we have made corresponding changes. Each revisions has been clearly highlighted, and a list of changes can been seen at the end of the new manuscript. A list of answers and changes to the comments is as follows.
Point 1: Mandatory requirement: replace references [37], [38], [39] related to fractional capacitor with the reference to the ORIGINAL paper "Capacitor theory" by S. Westerlund and L. Ekstam (https://doi.org/10.1109/94.326654).
Response 1: According to the opinions of the reviewer, we made the corresponding modifications, which can be seen in the new manuscript.
Point 2: Add a references to the paper "Fractional-order modeling of lithium-ion batteries using additive noise assisted modeling and correlative information criterion" by Meijuan Yu et al. (https://doi.org/10.1016/j.jare.2020.06.003), which seems to be very close to the conclusions in this manuscript.
Response 2: According to the comments of reviewers, we have added a review of the fractional modeling methods, which can be seen in the new manuscript.
Author Response File: Author Response.pdf
Reviewer 4 Report
The authors used a fractional derivative model to characterize the fractal distribution of the charges, and the fractional derivative order is also used to study the capacity recovery effect. The authors established a mathematical connection between the internal mechanism of the battery and the external measurable data. This non-destructive testing method is suitable for battery performance detection in actual operation. Overall, it is an interesting and well-argued work. In my opinion, it is suitable for publication as written.
Author Response
Point 1: The authors used a fractional derivative model to characterize the fractal distribution of the charges, and the fractional derivative order is also used to study the capacity recovery effect. The authors established a mathematical connection between the internal mechanism of the battery and the external measurable data. This non-destructive testing method is suitable for battery performance detection in actual operation. Overall, it is an interesting and well-argued work. In my opinion, it is suitable for publication as written.
Response 1: Many thanks for the comments of the reviewers and editors. We have learned much from the reviewers’ comments, which are fair, encouraging and constructive. After carefully studying the comments, we have made corresponding changes. Each revisions has been clearly highlighted, and a list of changes can been seen at the end of the new manuscript.
Author Response File: Author Response.pdf
