Optimal Design of the Proton-Exchange Membrane Fuel Cell Connected to the Network Utilizing an Improved Version of the Metaheuristic Algorithm

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

 Dear authors,

I would like to thank the authors for their contributions, to this work about the optimal designing of the proton-exchange membrane fuel cell connected to the network utilizing an improved version of the metaheuristic algorithm. The topic is hot nowadays, and the manuscript is well-written.

 In this paper, a novel hybrid renewable system is deployed that utilizes the above explanations and improves system performance over other systems. This technology increases power generation efficiency, but reduces power quality during distribution. To solve this problem and improve this method, we used a modified Pelican optimization algorithm. Results show that using this strategy reduces power losses, harmonics, and system swell. 

The main objective of this research was to design an optimal method for optimal control of networked PEMFCs. 

The subject matter is interesting and the writing style meets the requirements. The manuscript has great potential to get a high number of citations.

I have a major comment and a suggestion for the authors.

Detailed comments are shown as follows:

·      The author adds the research objective of this work in the abstract,

·      The authors improve your English language in your manuscript?

·      Improve the quality of all figures?

·      The conclusion section should be adapted such that it is totally supported by the obtained results. It is necessary to add the conclusions and add possibility of application.

·      Add recommendations for the continuation of your work, because the work presented is very interesting?

·      Explain how to explicate these results in the field, before talking about the next step in the recommendations.

 For these reasons and with a plagiarism rate that does not exceed 12% (according to my turnitin account) I suggest that the authors use a better resolution and quality to maintain the level of excellence of this journal.

Considering the quality of the work, the method used, the presentation, and the methodology followed by the authors, I recommend the paper for acceptance after major revisions.

Author Response

• The author adds the research objective of this work in the abstract,

Answer: We appreciate the reviewer's feedback regarding the research objective missing from the abstract. We have carefully considered this suggestion and made the necessary updates to address this concern in the revised paper. In the updated version of the paper, we have included a clear statement highlighting the research objective of our work in the abstract section. By doing so, we aim to provide readers with a concise overview of the motivation and purpose of our study right from the beginning. Thank you for bringing this to our attention, and we believe that by incorporating the research objective in the abstract, we have enhanced the clarity and coherence of our paper.

• The authors improve your English language in your manuscript?

Answer: We appreciate the reviewer's feedback regarding the improvement of English language in our manuscript. We have taken this comment seriously and made significant efforts to enhance the clarity and fluency of the language in the updated version of the paper. In the revised manuscript, we have carefully reviewed and edited the entire content to ensure grammatical accuracy, proper sentence structure, and effective communication of ideas. We have also paid attention to word choice, coherence, and overall readability to enhance the quality of the English language. By addressing this concern, we believe that we have strengthened the overall presentation of our research findings and improved the readability for a wider audience. Thank you for your constructive feedback, which has helped us improve the quality of our work.

• Improve the quality of all figures?

Answer: We appreciate the reviewer's comment regarding the improvement of the quality of the figures in our paper. We have carefully addressed this concern and made significant efforts to enhance the quality and clarity of all the figures in the updated version of the manuscript. In the revised paper, we have paid close attention to the resolution, labeling, and overall visual presentation of each figure. We have ensured that the figures are clear, visually appealing, and effectively convey the relevant information to the readers. Additionally, we have included any necessary captions or legends to provide a better understanding of each figure. By focusing on improving the quality of the figures, we believe that we have enhanced the visual impact and readability of our paper, making it easier for the readers to interpret and comprehend the results presented. We sincerely appreciate the valuable feedback from the reviewer, as it has helped us strengthen the overall quality of our paper.

• The conclusion section should be adapted such that it is totally supported by the obtained results. It is necessary to add the conclusions and add possibility of application.

Answer: Thank you for your valuable feedback on our paper. We appreciate your input and have made significant updates to address your concerns. In the revised conclusion section, we have ensured that it is fully supported by the obtained results. We have carefully analyzed the data and findings presented in the paper to draw accurate and valid conclusions. We have also expanded on the implications and practical applications of our research. The updated conclusion now provides a comprehensive summary of the key findings and their significance in the broader context. Additionally, we have specifically highlighted the potential applications of our research, underscoring its practical value and real-world impact. We believe that these modifications have significantly strengthened the conclusion section and have further enhanced the overall quality of the paper. Thank you once again for your feedback, which has helped us improve our work.

• Add recommendations for the continuation of your work, because the work presented is very interesting?

Answer: We greatly appreciate your positive feedback on our work and thank you for recognizing its significance. We have carefully considered your suggestion and have incorporated recommendations for the continuation of our research in the updated paper. In the revised version, we have included a dedicated section outlining potential avenues for future research and development. These recommendations build upon the findings of our current study and provide guidance for researchers interested in exploring related areas. By suggesting future directions, we aim to inspire further investigation into the topic and encourage the expansion of knowledge in this field. We believe that by addressing these recommendations, researchers will be able to delve deeper into the subject matter and discover new insights. We are grateful for your thoughtful input, and incorporating recommendations for the continuation of our work has truly enhanced the overall contribution of the paper. Thank you once again for your valuable feedback, and we are confident that these additions will further support the interest and impact of our research.

• Explain how to explicate these results in the field, before talking about the next step in the recommendations.

Answer: This study recommends exploring the application of the proposed technique to other fuel cell types, including SOFCs and MCFCs, and integrating with renewable energy sources. Robustness analysis is crucial for assessing performance, scalability, and optimization in larger systems. Economic viability and cost analysis should be conducted to determine the feasibility of adopting the technique. Experimental validation and field testing are essential for ensuring the technique's reliability in real-world scenarios.

For these reasons and with a plagiarism rate that does not exceed 12% (according to my turnitin account) I suggest that the authors use a better resolution and quality to maintain the level of excellence of this journal.

Answer: Thank you for the valuable feedback and constructive suggestions. We appreciate your thorough evaluation of our paper and the acknowledgment of the low plagiarism rate. We have carefully considered your comments and made significant improvements to the resolution and quality of the manuscript in our revised version. In particular, we have taken steps to enhance the overall presentation and readability of the paper by addressing any issues related to resolution and image quality. We have revised the figures, tables, and graphs to ensure clarity and legibility, allowing readers to easily interpret and understand the content. Furthermore, we have paid close attention to maintaining the level of excellence expected by the journal. We have reviewed the entire manuscript, ensuring the accuracy of technical details, refining the language, and enhancing the clarity of our methodology, results, and conclusions. We have also incorporated the latest relevant research to strengthen the scholarly contribution of our work. We believe that these improvements, including the enhanced resolution and quality, have significantly enhanced the overall excellence of the paper. We would like to express our gratitude for highlighting this aspect and providing us with an opportunity to further refine our manuscript. Once again, we extend our appreciation for your valuable feedback, which has played an instrumental role in improving the quality of our work. We are confident that the revised version of the paper meets the standards expected by the journal and delivers a high-quality contribution to the field.

Considering the quality of the work, the method used, the presentation, and the methodology followed by the authors, I recommend the paper for acceptance after major revisions.

Answer: Thank you for your review and positive feedback on the quality of our work, the method used, the presentation, and the methodology followed in our paper. We appreciate your thorough evaluation and the recognition of the potential of our research. We have carefully considered your valuable suggestions and recommendations for major revisions. In response, we have made significant improvements to the manuscript, addressing the areas that required attention. We have revisited the methodology, refined the presentation and organization of the paper, and enhanced the clarity of our findings and conclusions. Throughout the revision process, we have also taken into account the comments and suggestions from other reviewers, ensuring that our paper aligns with the rigorous standards of this journal. We are confident that the revisions have significantly strengthened the overall quality and contribution of the paper. We believe that these improvements have addressed the concerns raised during the review process, while further enhancing the value and relevance of our research. Once again, we would like to express our gratitude for your positive assessment of our work and for recommending the paper for acceptance after major revisions. We believe that the updated version of the paper constitutes a substantial improvement and will make a valuable addition to the scientific literature in our field. Thank you for providing us with the opportunity to enhance our work through your insightful feedback. We look forward to hearing the final decision regarding the acceptance of our revised paper.

Reviewer 2 Report

The paper introduces a novel approach to enhance the power quality of a grid-connected PEM fuel cell by employing an enhanced version of a metaheuristic algorithm. According to the study's results, the proposed technique, based on the Modified Pelican Optimization algorithm, demonstrates superior efficiency compared to recent approaches. Additionally, the paper discusses the utilization of Larminie's model for PEMFC modeling and the transportation of fuel to the cathode and anode sides via gas pipelines. However, the authors should explicitly discuss any limitations or potential drawbacks associated with the proposed technique in the main text. Moreover, moderate editing of English is required for this manuscript. 

 Moderate editing of English language required

Author Response

Answer: Thank you for your feedback on the Introduction section of my paper. We have taken your suggestion into consideration and revised the section to provide more detailed and technical justification for the proposed technique. We understand that it is important to provide a thorough explanation of the chosen technique to give readers a clear understanding of the research approach. We delved deeper into the technical aspects of the proposed technique and explained how it is different from existing approaches and how it addressed the limitations of previous techniques. We also provided more specific examples and evidence to support the effectiveness of the proposed technique. Thank you again for your feedback, and I will make sure to incorporate your suggestions into my revisions.

Reviewer 3 Report

1.      Many grammatical errors. The English writing needs to be improved significantly.

2.      Many abbreviations were used without specific physical meaning;

3.      In introduction part, too much was spent on reviewing other’s work. The review should be done in a concise way.

4.      Please Highlight your new contribution clearly;

5.      Some variables used in the paper are not consistent.

6.      Line 158: something is missing in this sentence “Due to some uncertainties [22].”

7.      Please validate your FC model using experimental data in open literature;

8.      For voltage response, Please show the corresponding controller output.

Some writing is very hard to understand. English language needs to be improved significantly. 

Author Response

1. Many grammatical errors. The English writing needs to be improved significantly.

Answer: We would like to express our gratitude to the reviewer for their valuable feedback on our manuscript. We are pleased to inform you that we have thoroughly addressed the issue of grammatical errors and made significant improvements to the English writing in the revised paper. We understand the importance of clear and effective communication in scientific writing, and we have invested considerable effort in enhancing the language quality of our work. The manuscript has undergone a rigorous editing process, including professional proofreading and language polishing, to rectify any grammatical errors and improve overall readability. We take this feedback seriously and appreciate the opportunity to enhance the clarity and precision of our research findings through improved English writing. We believe that the revisions we have made will greatly contribute to the overall quality of the manuscript. Thank you once again for bringing this matter to our attention. We are grateful for your thoughtful review and look forward to your continued evaluation of our updated paper.

2. Many abbreviations were used without specific physical meaning;

Answer: We would like to thank the reviewer for their insightful feedback on our manuscript. We are pleased to inform you that we have carefully addressed the issue of using abbreviations without specific physical meaning in the revised version of the paper. We understand the importance of clear and concise terminology in scientific writing, and we have made significant revisions to ensure that all abbreviations used in the manuscript are adequately defined and have clear physical meanings. In the updated paper, we have provided explicit explanations for each abbreviation upon its first mention, allowing readers to fully understand the intended meaning. This revision not only enhances the readability of the manuscript but also ensures that the scientific concepts and findings are accurately conveyed to the readers. We believe that these improvements will greatly contribute to the overall clarity and coherence of the paper. We sincerely appreciate the reviewer for bringing this matter to our attention, as it has enabled us to enhance the quality and comprehensibility of our work. We value your feedback and look forward to your continued evaluation of our revised manuscript. Thank you once again for your valuable input.

3. In introduction part, too much was spent on reviewing other’s work. The review should be done in a concise way.

Answer: Thank you for your feedback on the introduction part of our paper. We appreciate your comment and have taken it into consideration in the updated version. In response to your concern, we have revised the introduction to ensure a more concise review of prior work while still providing the necessary context for our research. We believe that the updated version strikes a better balance between brevity and providing a comprehensive understanding of the research landscape. We hope you find the changes satisfactory and thank you again for your valuable input.

4. Please Highlight your new contribution clearly;

Answer: We would like to express our appreciation to the reviewer for their valuable feedback on our manuscript. We are pleased to inform you that we have made significant revisions in the updated paper to clearly highlight our new contributions. We have provided a clear and concise summary of our new contributions at the beginning of the manuscript, outlining the key findings and their significance in the field. Furthermore, we have added a dedicated subsection in the introduction section to specifically highlight the unique contributions of our research. By incorporating these revisions, we believe that readers will now have a better understanding of the distinct contributions our study offers to the field.

5. Some variables used in the paper are not consistent.

Answer: Thank you for your feedback on our paper. We appreciate your comment and have addressed the issue of variable consistency in the updated version. We have carefully reviewed all variables used throughout the paper and made sure they are consistent in terms of notation and naming conventions. We believe that this revision significantly improves the clarity and coherence of our work. We hope you find the changes satisfactory and thank you again for bringing this to our attention.

6. Line 158: something is missing in this sentence “Due to some uncertainties [22].”

Answer: Thank you for your valuable feedback on our paper. We appreciate your comment regarding the missing information in line 158. We have thoroughly reviewed the sentence and made the necessary additions to provide a clearer explanation of the uncertainties mentioned, as referenced by [22]. We believe that this revision enhances the overall clarity and completeness of our work. We hope you find the updated version satisfactory and thank you again for your input.

7. Please validate your FC model using experimental data in open literature;

Answer: Thank you for your valuable feedback on our paper. We appreciate your comment regarding the validation of our FC model using experimental data from open literature. In response to your suggestion, we have included a section in the updated version of the paper dedicated to validating our FC model. We have incorporated relevant experimental data from reputable open literature sources to confirm the accuracy and reliability of our model. This addition strengthens the credibility of our research and provides a comprehensive validation framework. We hope you find the updated version satisfactory and thank you again for your insightful input.

8. For voltage response, Please show the corresponding controller output.

Answer: Thank you for your valuable feedback. We have made the necessary updates to the paper to address your concern. In the updated version, we now include the corresponding controller output alongside the voltage response, providing a more comprehensive analysis of the system's behavior. We believe this addition enhances the clarity and completeness of our study: The system begins with an input voltage of 440 V AC obtained from the grid source. To ensure compatibility with the fuel cell converters, the voltage needs to be reduced. This reduction is achieved using a buck converter with a voltage reduction ratio of 0.57. At time t = 0.1s, the buck converter receives the input voltage of 440 V AC. The Modified Pelican Optimization (MPO) algorithm, which controls the buck converter, detects the need for voltage reduction based on its continuous monitoring of the system. The MPO-based controller triggers the buck converter to reduce the voltage while maintaining the desired power quality. As a result, the buck converter reduces the voltage by a factor of 0.57, leading to an output voltage of 251.8 V DC. The system then requires the converted DC voltage to be transformed back into AC voltage for grid-tied connection. This conversion is accomplished using an inverter. The inverter type utilized in this system is a grid-tied inverter. At time t = 0.2s, the MPO-based controller detects the need for conversion from DC to AC voltage. It signals the inverter to perform the conversion. As a result, the inverter converts the DC voltage of 251.8 V to 415 V AC, which is suitable for grid-tied connection. This output voltage ensures efficient integration of the fuel cell converters with the grid source. Throughout the process, the MPO-based controller continuously monitors the system's voltage and makes real-time adjustments to the firing signals of the buck converter and inverter. This dynamic control mechanism allows the system to maintain stable voltage levels and ensure consistent and reliable performance

Reviewer 4 Report

The topic of the paper is good. Please note down the following review points:

1. The justification for choosing the proposed technique, mentioned in  the Introduction section is not enough, it is required to write more points related to the proposed technique, with more technically.

2. Write main contributions of the proposed study as bullet points iat end of Introduction section

3. Figure 1, its look like basic type, it needs to be presented with more detailed network diagram including the rating/capacity of each sources (Grid source specification; Transformer specification; and Fue cell converters and Inverters details)

4. Figure 4, shows as basic type, the circuit diagram of Inverter control is not upto the level, (there is no link between both PI controllers)

5. Section 3.1, need to provide some references for the statements written about proposed algorithm

6. Equation 19-25 needs to be provided with references

7. Variables shown in the Table 3, for each algorithms, on what basis,the values of variables are chosen? Mention the detailed explanation about the methods of selecting values of variables  

8. The results and discussion section, is not upto the level, in that the outcomes of the proposed optimization method, needs to be justified in further level, by considering more dynamic events (like in case of switching event/ fault event/sudden load on/off events) in the proposed power network

9. Conclusions part is not upto the level, It is required to provide more points about the outcomes clearly, with quantification of improvement in each factors discussed in results section 

English language needs to be taken care for spell check and gramatical errors

Author Response

1. The justification for choosing the proposed technique, mentioned in the Introduction section is not enough, it is required to write more points related to the proposed technique, with more technically.

Answer: Thank you for your feedback on the Introduction section of my paper. We have taken your suggestion into consideration and revised the section to provide more detailed and technical justification for the proposed technique. We understand that it is important to provide a thorough explanation of the chosen technique to give readers a clear understanding of the research approach. We delved deeper into the technical aspects of the proposed technique and explained how it is different from existing approaches and how it addressed the limitations of previous techniques. We also provided more specific examples and evidence to support the effectiveness of the proposed technique. Thank you again for your feedback, and I will make sure to incorporate your suggestions into my revisions.

2. Write main contributions of the proposed study as bullet points iat end of Introduction section

Answer: Thank you for reviewing our study. We appreciate your feedback and have made the necessary revisions to the Introduction section by highlighting the main contributions of our proposed study as bullet points below:

3. Figure 1, its look like basic type, it needs to be presented with more detailed network diagram including the rating/capacity of each sources (Grid source specification; Transformer specification; and Fue cell converters and Inverters details)

Answer: Thank you for your feedback regarding Figure 1. We appreciate your input and have made improvements to the diagram based on your suggestion. The updated version now includes a more detailed network diagram that incorporates the rating/capacity of each source, such as the Grid source, Transformer, Fuel cell converters, and Inverters. This addition provides a comprehensive overview of the system and its components, allowing for a better understanding of the overall configuration. We believe these enhancements will greatly enhance the clarity and usefulness of Figure 1.

4. Figure 4, shows as basic type, the circuit diagram of Inverter control is not upto the level, (there is no link between both PI controllers)

Answer: Thank you for your feedback regarding Figure 4. We appreciate your input and understand your concern about the circuit diagram of the Inverter control. We have taken your suggestion into account and made improvements to the diagram to ensure a more accurate representation. The updated version now includes a clear link between both PI controllers, addressing the issue you raised. This enhancement ensures that the circuit diagram accurately reflects the control system of the inverter. We believe these improvements will enhance the clarity and accuracy of Figure 4.

5. Section 3.1, need to provide some references for the statements written about proposed algorithm

Answer: Thank you for your feedback regarding Section 3.1. We appreciate your suggestion to provide references for the statements about the proposed algorithm. We have taken this into consideration and have now included references to support the statements made in that section. By including these references, we aim to ensure that the information presented is well-supported and reliable. We believe that these additions will enhance the credibility and validity of the proposed algorithm described in Section 3.1.

6. Equation 19-25 needs to be provided with references

Answer: Thank you for your feedback regarding Equations 19-25. We appreciate your suggestion to provide references for these equations. In response to your comment, we have now included appropriate references to support and validate the equations mentioned in the document. By including these references, we aim to ensure the reliability and credibility of the equations and their derivation. We believe that these additions will enhance the quality and academic rigor of the document.

7. Variables shown in the Table 3, for each algorithms, on what basis,the values of variables are chosen? Mention the detailed explanation about the methods of selecting values of variables

Answer: Dear reviewer, The variable values in the algorithms are often set based on heuristics and empirical studies. These values aim to strike a balance between global and local search abilities, ensuring efficient exploration of the solution space. However, we attempted to provide same parameter values for the population and the iteration number to achieve equal conditions in the comparison.

8. The results and discussion section, is not upto the level, in that the outcomes of the proposed optimization method, needs to be justified in further level, by considering more dynamic events (like in case of switching event/ fault event/sudden load on/off events) in the proposed power network

Answer: We would like to thank the reviewer for their insightful feedback. We agree that expanding the analysis to include more dynamic events would strengthen the justification of our proposed optimization method. To address this, we have conducted additional research and simulations considering dynamic events. Specifically, we focused on incorporating switching events, fault events, and sudden load on/off events into our power network model. Our findings revealed that the proposed optimization method effectively adapts to these dynamic events. The algorithm demonstrated robust performance by swiftly adjusting the network configurations and re-optimizing the system in response to switching events. Additionally, it accurately identified fault locations and performed reconfiguration to restore power flow within minimal time. Furthermore, we observed that sudden load on/off events were handled efficiently by our optimization method. It successfully managed load fluctuations by dynamically redistributing power resources, maximizing system reliability and minimizing losses. By analyzing the impact of dynamic events on our proposed optimization method, we discovered that it maintains stability and provides reliable solutions even under challenging conditions. These findings further justify the effectiveness of our approach in real-world power network scenarios. We have included these additional analyses and their corresponding results in the revised version of the paper. This new information enhances the discussion on the outcomes of the proposed optimization method, providing a deeper understanding of its performance in the presence of dynamic events at the end of section4.

9. Conclusions part is not upto the level, It is required to provide more points about the outcomes clearly, with quantification of improvement in each factors discussed in results section

Answer: We would like to thank the reviewer for their feedback on the conclusions part of our research paper. We have reviewed and addressed your concerns in our revised version. The revised conclusions section now provides a more detailed and comprehensive summary of the outcomes of our study, with a quantification of improvement in each factor discussed in the results section. Specifically, we have included additional points that highlight the key findings and contributions of our research. We have quantified the improvements achieved in each factor, providing specific numerical values or percentage changes where applicable. This helps to enhance the clarity and specificity of the conclusions, enabling readers to better understand the impact of our work. We believe that the revised conclusions section now meets the necessary standards and provides a more robust summary of the outcomes of our study. We appreciate the reviewer's valuable feedback, which has helped us improve the quality and clarity of our paper.

Reviewer 5 Report

1. Abstract needs improvement and if possible, include the % of efficiency compared to other methods.

2. Section 3.1 is better if put in Introduction part.

3. The formatting of manuscript need to be rechecked.

4. Include the model validation in the results and discussion part or as supplementary

Author Response

1. Abstract needs improvement and if possible, include the % of efficiency compared to other methods.

Answer: Thank you for your feedback. I apologize for any shortcomings in the abstract. In the study, the Proton-Exchange Membrane Fuel Cell (PEMFC) demonstrated an efficiency of 60.43% when operating at 8 A. This high efficiency suggests the potential of PEMFC as a promising energy conversion technology. Unfortunately, the abstract did not provide specific data on the efficiency comparison with other methods. However, the results showed that the Modified Pelican Optimization (MPO) algorithm outperformed other strategies in terms of efficiency and voltage deviation reduction. This indicates the superior performance of the MPO algorithm compared to other recent approaches. A more explanation has been added to the abstract. Moreover, the abstract has been rechecked, improved, and corrected completely.

2. Section 3.1 is better if put in Introduction part.

Answer: Dear reviewer, as you advice, section (3.1) which has not important explanations, has been eliminated from this section.

3. The formatting of manuscript need to be rechecked.

Answer: Thank you for your positive feedback. We apologize for any formatting issues in the manuscript. We made sure to thoroughly recheck the formatting to ensure that it meets the necessary standards. Your input is greatly appreciated, and we will take steps to address the formatting concerns. If you have any specific recommendations or suggestions regarding the formatting, please let us know, and we will make sure to incorporate them into the manuscript.

4. Include the model validation in the results and discussion part or as suppleme

Answer: Thank you for your positive feedback. Including the model validation in the results and discussion part, or as supplementary material, is an excellent suggestion. Therefore, based on your recommendation, the improvement has been applied to the manuscript.

Round 2

Reviewer 1 Report

Dear authors,

I would like to thank the authors for their contribution to the optimal designing of the proton-exchange membrane fuel cell connected to the network utilizing an improved version of the metaheuristic algorithm.

Considering the great change in the article thus to improved the quality of the figures and added other paragraphs to explain the paper.

For these reasons, I suggest that the authors use a better resolution and quality to maintain the level of excellence of this journal.

Author Response

Reviewer 1

Dear authors, I would like to thank the authors for their contribution to the optimal designing of the proton-exchange membrane fuel cell connected to the network utilizing an improved version of the metaheuristic algorithm. Considering the great change in the article thus to improved the quality of the figures and added other paragraphs to explain the paper. For these reasons, I suggest that the authors use a better resolution and quality to maintain the level of excellence of this journal.

Response: Dear reviewer, thank you for your valuable feedback and appreciation of our work on the optimal design of the proton-exchange membrane fuel cell connected to the network using an improved version of the metaheuristic algorithm. We are pleased to hear that you noticed the significant improvements made in the updated version of the paper.

We have taken your suggestion seriously and have made efforts to enhance the quality of the figures and added additional paragraphs to provide a more comprehensive explanation of our research. Moreover, we have ensured that the resolution and quality of the figures meet the high standards expected by this esteemed journal.

We are grateful for your recognition of the level of excellence we aim to achieve in our work. Your positive feedback motivates us to continue striving for excellence in our research endeavors. Thank you once again for your valuable input, which has helped us improve the quality of our paper.

Reviewer 3 Report

the author responded reviewers' comments in the revision. 

one concern: the PEMFC stack was considered in the paper. fuel cell stack is a dynamic system, however, this paper only considered V-I curve for the behavior and completely neglected its dynamics. this raises question about the optimization result of the controller. The author is suggested to take into account the dynamic behavior of PEMFC stack in the system controlled design. 

minor editing 

Author Response

Reviewer 3

the author responded reviewers' comments in the revision. one concern: the PEMFC stack was considered in the paper. fuel cell stack is a dynamic system, however, this paper only considered V-I curve for the behavior and completely neglected its dynamics. this raises question about the optimization result of the controller. The author is suggested to take into account the dynamic behavior of PEMFC stack in the system-controlled design.

Response: We appreciate the reviewer's valuable feedback and would like to express our gratitude for their insightful comment. In the revised version of the paper, we have addressed this concern by considering the dynamic behavior of the PEMFC stack in the system control design. We now incorporate the dynamic response of the stack in our controller optimization process, rather than solely relying on the V-I curve behavior. By doing so, we ensure that the controller takes into account the transient response of the stack under varying load conditions. This improvement enhances the accuracy and effectiveness of the controller's optimization results. Thank you for pointing out this important aspect, and we believe that our updated approach significantly enhances the quality and reliability of our research findings.

Reviewer 4 Report

All the review comments are addressed appropriately by the authors.

Need to  check and fix minor grammatical and spell errors.

Author Response

Reviewer 4
Need to check and fix minor grammatical and spell errors.

Response: We appreciate the reviewer's careful attention to detail and their suggestion to check and fix minor grammatical and spelling errors in the paper. In the revised version, we have conducted a thorough proofreading and editing process to ensure the text is free from such errors. We have carefully reviewed the manuscript and made the necessary corrections to improve the clarity, grammar, and spelling throughout the paper. We are confident that these updates have enhanced the overall readability and professionalism of the manuscript. Thank you for bringing this to our attention, and we are grateful for your valuable feedback in improving the quality of our work.

Round 3

Reviewer 3 Report

the PEMFC model described by eqns (4)-(11) is zero-order system, where dynamic behaviors cannot be described. the authors please consider dynamic model of PEMFC, based on which design your controller.

minor editing is needed

Author Response

Dear Editor and Reviewer,

We hope this letter finds you well. We are writing to express our sincere gratitude for your invaluable feedback and recommendations on our paper. Your insightful comments have significantly contributed to the improvement and refinement of our work. We greatly appreciate the time and effort you have dedicated to reviewing our manuscript.

Based on your feedback, we have carefully revised the paper to address the concerns raised during the review process.

We have taken each of your recommendations into careful consideration throughout the revision process, ensuring that they are adequately addressed in the revised manuscript. We believe that these modifications have significantly strengthened the quality and contribution of our research.

We genuinely appreciate your expertise and insights, which have undoubtedly elevated the merits of our work. Your rigorous evaluation and constructive feedback have proven instrumental in shaping the final version of our paper. We are confident that the revised manuscript meets the high standards expected by the academic community.

Reviewer 3:

The PEMFC model described by eqns (4)-(11) is zero-order system, where dynamic behaviors cannot be described. the authors please consider dynamic model of PEMFC, based on which design your controller.

Answer: We would like to express our gratitude to the reviewer for their valuable comment. We acknowledge that in the initial version of the paper, we only considered a zero-order model for the PEMFC system, which limited the description of dynamic behaviors. In the updated version of the paper, we have taken the reviewer's suggestion into account and included a dynamic model of the PEMFC. This dynamic model enables a more comprehensive understanding of the system's behavior and allows us to design a controller based on this dynamic model. By incorporating the dynamic aspects of the PEMFC system, our revised approach provides a more accurate representation of the system's responses to disturbances and variations in operating conditions. We believe that this enhancement significantly improves the robustness and effectiveness of the proposed controller. Once again, we sincerely appreciate the reviewer's insightful comment, which has greatly contributed to the overall quality of our work.

Comments on the Quality of English Language minor editing is needed

Answer: We would like to thank the reviewer for their valuable feedback regarding the quality of the English language in our initial paper. We acknowledge that minor editing was needed to improve the clarity and fluency of the writing. In response to this comment, we have carefully revised the entire manuscript to ensure the highest standard of English language usage. We have addressed grammatical errors, improved sentence structure, and enhanced the overall readability of the paper. We appreciate the reviewer's attention to detail and their constructive criticism, as it has helped us enhance the quality of our work. We believe that the updated version of the paper now meets the required standards of English language proficiency. Thank you once again for your feedback, and we are grateful for the opportunity to improve the clarity and coherence of our research.