Cost Minimizations and Performance Enhancements of Power Systems Using Spherical Prune Differential Evolution Algorithm Including Modal Analysis

Round 1

Reviewer 1 Report

This paper proposed the spherical prune differential evolution algorithm (SpDEA) to solve the

optimal power flow (OPF) problem in electric power systems. Four objectives are adopted to be optimized simultaneously. The effectiveness of the proposed approach was verified in IEEE 30-bus and 118-bus systems.

This paper is well organized and also well written. The reviewer has the following comments to help enhance the quality of this paper further. In particular:

1. How about the computational efficiency of the novel spherical prune differential evolution algorithm? In case studies, there is no any information about how much time are required to solve IEEE 30-bus and 118-bus systems successfully.

2. Since the topic studied in this paper is multi-objective optimal power flow (OPF) problems, there must be many Pareto optimal solutions. Thus, a question for decision-maker is how to choose one solution from these Pareto optimal solutions.

3. The spherical prune differential evolution algorithm (SpDEA) is a stochastic algorithm compared with some traditional mathematical programming approaches. My question is whether such SpDEA algorithm is robust enough (i.e., whether they can provide the same result if running two times).

4. All abbreviations should be defined by their full name in their first appearing place.

5. There are many typos in references which should be double checked and correct with the same format. Also, some of the papers have been presented with incomplete information.

6. The conclusions should be extended for the future directions. For instance, do the authors believe that the proposed Gamma distribution can be further improved?

7. How to address the uncertainty coming from renewable energy generation (such as wind and solar) is also very important. Using stochastic optimization approaches may be very helpful to address this challenge. Some references about stochastic optimization are listed as follows, which are suggested to be included in literature reviews.

[1] Optimal Energy Storage System Positioning and Sizing with Robust Optimization. Energies, vol. 13(3), 2020, 512.

[2] Multi-Period Planning of Multi-Energy Microgrid with Multi-Type Uncertainties Using Chance Constrained Information Gap Decision Method. Applied Energy, vol. 260, Feb. 2020, 114188.

In conclusion, I recommend a revision of the manuscript which takes the above points into account.

Comments for author File: Comments.pdf

Author Response

Authors’ Response Sheet

Manuscript No.: sustainability-1297901R1

Entitled "Cost minimizations and performance enhancements of power systems using Spherical-prune differential evolution algorithm including modal analysis"

The authors are grateful to the anonymous respected Reviewers and esteemed Editor handling the paper for sparing their valuable time and giving constructive comments and suggestions. our thanks should be extended to Prof. Dr. Betsy Qu (Assistant Editor) and the EiC for the kind reconsideration. The revised version has been subjected to a careful proofread by a senior researcher to improve the quality of paper’s presentation. Below is a point by point response to the raised concerns. All constructive suggestions have been incorporated and revised thoroughly and the changes made in original manuscript in this revised copy (The revised text is written in Blue colored text for the convenience of the esteemed reviewers). A number of minor alterations have been made to correct grammatical mistakes and improve expression.

Reviewer #1:

This paper proposed the spherical prune differential evolution algorithm (SpDEA) to solve the optimal power flow (OPF) problem in electric power systems. Four objectives are adopted to be optimized simultaneously. The effectiveness of the proposed approach was verified in IEEE 30-bus and 118-bus systems. This paper is well organized and also well written. The reviewer has the following comments to help enhance the quality of this paper further. In particular:

Authors’ response:  First of all, the authors would like to thank you, sir for sparing time to review the paper and many thanks for your valuable and constructive suggestions. Your thoroughly review is highly appreciated and once again, many thanks. The authors have exerted sincere efforts to answer/amend/clarify your valuable raised criticisms, which indisputable improve the technical quality of the current paper. Nevertheless, any further criticisms are welcome to enable us writing an interesting paper to the readers with the aid of your constructive comments.

1. How about the computational efficiency of the novel spherical prune differential evolution algorithm? In case studies, there is no any information about how much time are required to solve IEEE 30-bus and 118-bus systems successfully.

Authors’ response: Thanks for raising this query. The computational CPU elapsed times are mentioned/reported in Table 4 (last row) for  the IEEE 30-bus system and in Table 7 for the 118-bus system. It might be worth mentioning that all runs are executed on a Laptop with Intel® Core™ i7-7700HQ CPU with 16 GB installed memory.

2. Since the topic studied in this paper is multi-objective optimal power flow (OPF) problems, there must be many Pareto optimal solutions. Thus, a question for decision-maker is how to choose one solution from these Pareto optimal solutions.

Authors’ response: The best answer is chosen carefully among trade-off Pareto points by using the technique of fuzzy Pareto solution. Quote from the paper’s text the following:

In this study, the vector-defined objectives are solved using the SpDEA and are based on the fuzzification of Pareto Fuzzy Optimal (PFO) solutions. In this issue, the objective function  is expressed by a fuzzy membership function  to normalize the values between 0 and 1 as expressed in (11)  [23]:

In addition, for each k-th Pareto solution, the normalized membership  is estimated by the formula depicted in  (12):

where  and M define the number of objectives and the number of PFO solutions, respectively. The best compromise solution is chosen for the minimum value of .

3. The spherical prune differential evolution algorithm (SpDEA) is a stochastic algorithm compared with some traditional mathematical programming approaches. My question is whether such SpDEA algorithm is robust enough (i.e., whether they can provide the same result if running two times).

Authors’ response: Really, thanks for raising this criticism and following your observation. It is well-known that each run of such algorithms gives different feasible answers due the randomness’s nature of heuristic-based algorithms. Therefore, the SpDEA has been implemented 20 times and the best Pareto-set has been picked up and then the best answer is selected carefully among trade-off Pareto points by using the technique of fuzzy Pareto solution. See the answer of comment # 2.

4. All abbreviations should be defined by their full name in their first appearing place.

Authors’ response: Done.

5. There are many typos in references which should be double checked and correct with the same format. Also, some of the papers have been presented with incomplete information.

Authors’ response: All incorporated reference list  has been checked in terms of format style as per the Sustainability Journal and any incomplete information has been corrected/added as necessary.

6. The conclusions should be extended for the future directions. For instance, do the authors believe that the proposed Gamma distribution can be further improved?

Authors’ response: Thanks for this valid comment, future insights of this current are mentioned. In the Conclusion Section the following has been incorporated to guide the readers on the likely extension of this current effort. Quote “Since the shares of renewable power sources including energy storage facilities are booming which rise the uncertainty. So, it is important to extend the existing frameworks/methodologies to address this challenge. The later-mentioned defines the future trend of our current work by incorporating system uncertainties and the variability of different types of renewable power sources and loads”.

7. How to address the uncertainty coming from renewable energy generation (such as wind and solar) is also very important. Using stochastic optimization approaches may be very helpful to address this challenge. Some references about stochastic optimization are listed as follows, which are suggested to be included in literature reviews.

[1] Optimal Energy Storage System Positioning and Sizing with Robust Optimization. Energies, vol. 13(3), 2020, 512.

[2] Multi-Period Planning of Multi-Energy Microgrid with Multi-Type Uncertainties Using Chance Constrained Information Gap Decision Method. Applied Energy, vol. 260, Feb. 2020, 114188.

Authors’ response: Thanks for this valid suggestion, both articles have been incorporated in Reference list, see Refs. [51], [53], as follows:

[51] Chowdhury, N.; Pilo, F.; Pisano, G. Optimal energy storage system positioning and sizing with robust optimization. Energies 2020, 13(3), 512. https://0-doi-org.brum.beds.ac.uk/10.3390/en13030512.

[53] Wei, J.; Zhang, Y.; Wang, J.; Cao, X.; Khan, M.A. Multi-period planning of multi-energy microgrid with multi-type uncertainties using chance constrained information gap decision method. Applied Energy 2020, 260, 114188. https://0-doi-org.brum.beds.ac.uk/10.1016/j.apenergy.2019.114188.

In conclusion, I recommend a revision of the manuscript which takes the above points into account.

Authors’ response: At last, the authors do appreciate your efforts to extract those valuable comments that improved the scientific content of their paper. We hope our respected reviewer will find above have been addressed satisfactory and helpful to come a positive decision.

Kind Regards;

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The authors

Author Response File: Author Response.docx

Reviewer 2 Report

Authors in this work presented a novel application of the spherical prune differential evolution algorithm in order to solve the OPF problem in electric power schemes. The OPF problem is investigated with the IEEE standard  30-bus system. Also authors presented a bus networks as large scale  optimization problem with design control variables. Authors aims at solve multi objective optimization for several fitness functions under various scenarios. In this research PFO solutions are generated, and authors selected optimal settings  by using the technique of normalized fuzzifications. 

In conclusion section more details are needed to justify proposed methods. So in terms of quality of the work more detailed conclusion should be written.  

Comments for author File: Comments.pdf

Author Response

Authors’ Response Sheet

Manuscript No.: sustainability-1297901R1

Entitled "Cost minimizations and performance enhancements of power systems using Spherical-prune differential evolution algorithm including modal analysis"

The authors are grateful to the anonymous respected Reviewers and esteemed Editor handling the paper for sparing their valuable time and giving constructive comments and suggestions. our thanks should be extended to Prof. Dr. Betsy Qu (Assistant Editor) and the EiC for the kind reconsideration. The revised version has been subjected to a careful proofread by a senior researcher to improve the quality of paper’s presentation. Below is a point by point response to the raised concerns. All constructive suggestions have been incorporated and revised thoroughly and the changes made in original manuscript in this revised copy (The revised text is written in Blue colored text for the convenience of the esteemed reviewers). A number of minor alterations have been made to correct grammatical mistakes and improve expression.

Reviewer #2:  

Authors in this work presented a novel application of the spherical prune differential evolution algorithm in order to solve the OPF problem in electric power schemes. The OPF problem is investigated with the IEEE standard  30-bus system. Also, authors presented a bus networks as large-scale  optimization problem with design control variables. Authors aims at solve multi objective optimization for several fitness functions under various scenarios. In this research, PFO solutions are generated, and authors selected optimal settings  by using the technique of normalized fuzzifications. 

Authors’ response: The authors do appreciate your useful comments and suggestions on our work. We have carefully addressed the comments and suggestions from you, sir to enrich the revised manuscript. Once again, the authors also admire your vigilance in finding the oversights. The relevant discussion and many statements have been clearly articulated in the revised version of this article. At last, we hope our respected reviewer will find below concern has been addressed satisfactory and helpful to come a positive decision

In conclusion section more details are needed to justify proposed methods. So, in terms of quality of the work more detailed conclusion should be written.  

Authors’ response: Really, thanks for raising this criticism and following your observation. The Conclusion Section has been amended to give some details in regards to the cropped best results and the future trend is incorporated to guide the readers on the likely extension of this current effort. Kindly refer to the Conclusion Section in this revised version.

Finally, many thanks for highlighting some inaccuracies we didn't realize before submission. We have tried our best to revise the manuscript as suggested by the reviewers and editors and hopefully, the authors explained more clarifications of the research work. Based upon above clarification, the authors look forward to your positive response.

Kind Regards;

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The authors

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Authors have addressed all my comments. Thank you.