An Effective Algorithm for MAED Problems with a New Reliability Model at the Microgrid

Round 1

Reviewer 1 Report

The optimization problem presented in the research is very well known and reported in many researches before. The author used an improved algorithm to solve it. The improvement done to the algorithm is also not by the authors. I therefore believe that the contribution of the paper is very marginal 

Author Response

Reviewer 1#

• The optimization problem presented in the research is very well known and reported in many researches before. The author used an improved algorithm to solve it. The improvement done to the algorithm is also not by the authors. I therefore believe that the contribution of the paper is very marginal 

Reply:

We would like to express our most sincere gratitude for your effort and patience in reviewing our manuscript. This paper has been revised according to the relevant comments. The following is provided to outline each change made (point by point) as raised in the reviewer comments. The contribution of this paper is a new framework for multi-area economic dispatch (MAED) in which the cost associated with the reliability consideration is taken into account together with next to the common operational and emission costs using expected energy not supplied (EENS) index. To improve the reliability level, the spinning reserve capacity is considered in the model as well. Furthermore, as the more MAED optimization problem, non-smooth cost functions are taken into account as well as other technical limitations such as tie-line capacity restriction, ramp rate limits, and prohibited operating zones at the microgrid. Considering all the above practical issues do increase the complexity in terms of optimization, which that, in turn, necessitates the use of a powerful optimization tool. A new successful algorithm inspired by the phasor theory in mathematics, which is called phasor particle swarm optimization (PPSO), is used in this paper to address answer this problem.

Reviewer 2 Report

Dear authors the paper proposes a "according to the authors" new framework for multi-area economic dispatch (MAED). The authors also state that to improve the reliability level, the spinning reserve capacity is considered in the model as well. Furthermore, as the more MAED optimization problem, non-smooth cost functions are taken into account as well as other technical limitations such as tie-line capacity restriction, ramp rate limits and prohibited
23 operating zones at the microgrid. The optimal results obtained by the simulations they did reveal that the proposed algorithm finds suitable optimal solutions.

The paper is widely speaking well organized and fits the jounal scope.

Although some improvements may be done in order to improve the readability of the article (specifically cap 2 where some of the formulas in my opinion shall be inserted in an appendix) it follows a logic path.

I would suggest to strenghthen the introduction with some more literature and to expand the conclusion that summarizes the results where it is not clear the added value of this interesting paper.

Author Response

Reviewer 2#

• Comments and Suggestions for Authors
• Dear authors the paper proposes a "according to the authors" new framework for multi-area economic dispatch (MAED). The authors also state that to improve the reliability level, the spinning reserve capacity is considered in the model as well. Furthermore, as the more MAED optimization problem, non-smooth cost functions are taken into account as well as other technical limitations such as tie-line capacity restriction, ramp rate limits and prohibited
  23 operating zones at the microgrid. The optimal results obtained by the simulations they did reveal that the proposed algorithm finds suitable optimal solutions.
• The paper is widely speaking well organized and fits the jounal scope.
• Although some improvements may be done in order to improve the readability of the article (specifically cap 2 where some of the formulas in my opinion shall be inserted in an appendix) it follows a logic path.
• I would suggest to strenghthen the introduction with some more literature.

 

Reply

Thank you very much for your constructive comments. In this revision, it has been endeavoured to precisely address the reviewer’s comments. The below references have been added to the introduction section.

12. Dubey HM, Pandit M, Tyagi N. Wind integrated multi-area economic dispatch using backtracking search algorithm. In: IEEE 6thInter conf on power systems ICPS; 2016. https://doi.org/10.1109/ICPES.2016.7584188.
13. Mokarram MJ, Niknam T, Aghaei J, Kha HMS, Catalao JPS. Hybrid optimization algorithm to solve the nonconvex multiarea economic dispatch problem. IEEE Systems Journal 2019;13(3):3400–9.
14. Vijayaraj S, Santhi RK. Multi-area economic dispatch using flower pollination algorithm. IEEE Inter Conf.ICEEOT 2016. https://doi.org/10.1109/ICEEOT.2016.7755541.
15. Abarghooe RA, Dehghanian P, Terzija V. Practical multi-area bi-objective environmental economic dispatch equipped with a hybrid gradient search method and improved Jaya algorithm. IET Gener, Transm Distrib 2016;10(14):3580–96.
16. Lin J, Wang ZJ. Multi-area economic dispatch using an improved stochastic fractal search algorithm. Energy 2019;166:47–58.
17. Ghasemi M, Davoudkhani IF, Akbari E, Rahimnejad A, Ghavidel S, Li L. A novel and effective optimization algorithm for global optimization and its engineering applications: Turbulent Flow of Water-based Optimization (TFWO). Eng Appl Artif Intel. 2020;92:103666.
18. Nguyen KP, Dinh ND, Fujita G. Multi-area economic dispatch using hybrid cuckoo search algorithm. In: 50th IEEE power engg inter conf UPEC; 2015. https://doi.org/10.1109/UPEC.2015.7339777.
19. Basu M. Artificial bee colony optimization for multi-area economic dispatch. Energy 2013;49:181–7.
20. Chen CL, Chen ZY, Lee TY. Multi-area economic generation and reserve dispatch considering large-scale integration of wind power. Int J Electr Power Energy Syst 2014;55:171–8.
21. Secui DC. The chaotic global best artificial bee colony algorithm for the multi-area economic/emission dispatch. Energy 2015;93(2):2518–45.
22. Ghasemi M, Ghavidel S, Aghaei J, Akbari E, Li L. CFA optimizer: A new and powerful algorithm inspired by Franklin's and Coulomb's laws theory for solving the economic load dispatch problems. Int Trans Electr Energ Syst. 2018;e2536. https://doi.org/10.1002/etep.2536

 

• and to expand the conclusion that summarizes the results where it is not clear the added value of this interesting paper:

Reply:

The authors agree with the comment of the kind reviewer. The conclusion has been revised and more details have been added.

Conclusions

The multi-area economic dispatch (MAED) is a very important issue in power systems in order to transmit electrical energy. In this study, the cost associated with system reliability has been added to the operational cost of the thermal unit in MAED for the first time. The objective function of the problem comprises three main terms including operational cost besides the costs due to reliability and emission factors. Regarding various types of technical limitations as well as spinning reserve capacity, the paper has proposed a new improved particle swarm optimization (PPSO) algorithm to tackle the complex optimization problem. The algorithm uses phasor theory in mathematics to define a new method for creating PSO control parameters and has conducted on optimal MAED problems in the context of different simulation tests. While in the first test, the superiority of the phasor particle swarm optimization (PPSO) algorithm in terms of the quality, reliability and robustness in comparison to the existing algorithms of PSO include adaptive PSO (APSO), Comprehensive learning PSO (CLPSO), fully informed particle swarm (FIPS), Frankenstein’s PSO (FPSO) and the improved standard PSO 2011 (SPSO2011) that is demonstrated, the next tests focus on the impact of reliability considerations on the MAED and RCMAEED.

The obtained optimal results illustrate that the considered algorithm is strong and efficient for optimizing power dispatch in energy systems. Besides, it enjoys a special simplicity compared to its counterparts.

Furthermore, the application of phasor theory in different types of improved PSO algorithms, as well as the proposed PPSO, can be further elaborated in different power system optimization problems for future studies.

 

Reviewer 3 Report

The problem statement is not well introduced. It is suggested to introduce the research gaps then the contribution should be highlighted. The main advantages in addition to the challenges of the proposed method can be added and discussed in a separate section.

Author Response

Reviewer 3#

• The problem statement is not well introduced.

The authors appreciate the comment of the kind reviewer. Kindly to inform you that, the electrical energy generation units are subject to several constraints, including valve-point loading on the objective function of the problem. This constraint leads the objective function to lose its flatness and convert into a sine objective function. There are always several types of fuels with different prices in an energy generation system for feeding electrical energy generation units. Thus, the objective function is transformed into a multi-type objective function. As is shown below, this paper applied these two constraints together to the problem. 

One of the issues with electrical energy generation units is the use of fossil fuels. Several types of gases are emitted into the environment when fossil fuels are burnt; hence, leading to pollution and destruction of nature. To overcome this issue, designers and engineers consider the emission level of these generation units as an objective function that depends on the generation power of the units during the design and optimization phases. This is formulated as follows [9]:

Equation 10 and 11

In an energy generation system, designers and engineers always encounter several constraints that need to be satisfied. These constraints depend on the units, transmission lines, system demand level, and the system total loss level. Each of these constraints is provided and formulated below.

 

3. Phasor Particle Swarm Optimization (PPSO) technique

 

This section introduces the original PSO algorithm and several common and popular versions of it. Then, the proposed and employed method in this study, called Phasor Particle Swarm Optimization (PPSO), is described.

 

• It is suggested to introduce the research gaps then the contribution should be highlighted.
• The main advantages in addition to the challenges of the proposed method can be added and discussed in a separate section.

 

Reply:

Thank you for your valuable suggestion. The gaps have been introduced and the contribution also highlighted.

 

This paper demonstrates that the phasor particle swarm optimization (PPSO) algorithm is straightforward and effective for power flow dispatching in electrical systems. All constraints and limitations of the electrical system, in the present study, are assumed with the emission of pollutant gases. Since PSO is a basic algorithm and has been employed in many papers and research works, this version can be used as a base algorithm for future studied, as this has been proven in the present research. There is always a fast convergence problem with the base algorithm in reaching the optimal solution. This issue has been tackled in the proposed version of the algorithm. On the other hand, selecting the best parameters of the algorithm has always been challenging with the base algorithm. It has been shown in the literature that different parameters need to be selected for different functions of the basic algorithm. However, the present paper overcomes this issue by presenting and selecting a phase angle, in which all control parameters of the algorithm are assigned to sine and cosine functions of the selected phase angle.

Reviewer 4 Report

The authors present an interest work about optimization. As the authors present their work there are points that must be improved. In particular :

1. Table 1 needs further explanation as it is not clear, especially as it concerns the benefits arisen from the authors proposal.
2. The authors must include a table providing the key elements of the power units used in their evaluation. Key point is also the type of the generation unit, especially if the unit is wind or pv, as their production is not easily predicted due to the isuues arisen from wind velocity and solar energy/cloud cover.
3. Implementability and operability including comparison of required calculation resources and time are not presented here. This is of paramount impoertance in case of utilities as the adoption of new approaches is also based on these parameters.
4. The novelty of the presented work is not supported by strong arrguments, even though the results seems to present that the proposed method could have benefits.
5. The discussion session is quite small and poor. I would expect quite extended discussion on the result where the authors should also make a thorough comparison of their proposal against the existing ones, including also a swot analysis of the proposal.
6. The conclusions should be enhanced based on the additional text in introduction and discussion section.
7. the literature used in this paper is rather limitted for a topic that is having significant attention due to the importance it presents.

Author Response

Reviewer 4#

• Comments and Suggestions for Authors
• The authors present an interest work about optimization. As the authors present their work there are points that must be improved. In particular :

 

Reply:

Thank you very much for your time and valuable comments. In this revision, it has been tried to address the reviewer’s comments.

 

• Table 1 needs further explanation as it is not clear, especially as it concerns the benefits arisen from the authors proposal.

Reply

Thank you very much for your constructive comments. In this revision, it has been endeavoured to precisely address the reviewer’s comments.

The best global optimal solution of this test system obtained by each of PSO algorithms in 30 separate runs with a maximum number of iterations equal to 100 and maximum population size equal to N_Pop =80, are given in Table 1 and Table 4. This table represents the results of PPSO, APSO, CLPSO, SPSO2011, FPSO, FIPS, PSO-TVAC [7], Hopfield neural network (HNN) method [33], and direct search method (DSM) [32]. It is obvious from table 4 that the best solutions were obtained using PPSO optimizer. It is obvious from table 4 that performance of PPSO optimizer is better than all other algorithms in reaching to the optimal solutions of the small-scale MAED optimization problem. It can be seen in Table 1 that the minimum operation and fuel cost obtained by PPSO optimizer is 10604.6741 ($/H), which is less than that of HNN [33], DSM [32] and PSO-TVAC [7].

On the other side, referring to Table 4 and Fig. 3, the proposed algorithm has the best standard deviation for the best-obtained solutions. Consequently, it can be claimed that the suggested method is the most reliable method among the methods studied to optimize such problems.

The authors must include a table providing the key elements of the power units used in their evaluation. The key point is also the type of the generation unit, especially if the unit is wind or PV, as their production is not easily predicted due to the issues arisen from wind velocity and solar energy/cloud cover.

Yet, it should be noted that all units in the system under study use fossil fuel. So, we need to consider units emission levels

 

• Implement ability and operability including a comparison of required calculation resources and time are not presented here. This is of paramount importance in case of utilities as the adoption of new approaches is also based on these parameters.

Reply:

Thank you very much for your time and valuable comment. The authors agree with the comment of the kind reviewer. Implement ability and operability have been shown in Table 4.  Furthermore, we will consider this for future study and we intend to improve this method and achieve new algorithms in the near future using new algorithms and fuzzy methods.

Table 4. Comparing the simulation final results for the multi-area power systems.

Test system	Index	FIPS	FPSO	SPSO2011	CLPSO	APSO	PPSO
small-scale system	Best	10604.6742	10604.67	10604.6741	10604.67	10604.67	10604.67
	Mean	10605.3272	10604.92	10604.8543	10604.68	10604.73	10604.67
	Std	1.5275	1.1547	0.5774	0.7022	0.4407	5.75E-05
	Mean time (sec)	4.56	4.78	4	3.16	6.82	2.93
medium-scale system	Best	7341.7942	7340.455	7340.2795	7344.357	7341.714	7337.026
	Mean	7559.7788	7487.087	7637.4443	7486.892	7605.919	7338.115
	Std	74.2674	61.8126	71.271	84.3494	53.07	0.629
	Mean time (sec)	20.95	20.67	19.19	18.31	25.57	17.84
large-scale system	Best	128554.2844	128128.2	127085.5386	127008.9	128514	125100.2
	Mean	130615.4572	129486	129414.4588	128315.4	129495.4	125263.2
	Std	1.19E+03	1.02E+03	9.84E+02	2.16E+02	6.93E+02	85.3092
	Mean time (sec)	54.74	55.85	48.51	48.35	75.3	47.88

 

• The novelty of the presented work is not supported by strong arrguments, even though the results seems to present that the proposed method could have benefits.

Reply:

The authors appreciate the comment of the kind reviewer.  This paper demonstrates that the phasor particle swarm optimization (PPSO) algorithm is straightforward and effective for power flow dispatching in electrical systems. All constraints and limitations of the electrical system, in the present study, are assumed with the emission of pollutant gases. Since PSO is a basic algorithm and has been employed in many papers and research works, this version can be used as a base algorithm for future studied, as this has been proven in the present research. There is always a fast convergence problem with the base algorithm in reaching the optimal solution. This issue has been tackled in the proposed version of the algorithm. On the other hand, selecting the best parameters of the algorithm has always been challenging with the base algorithm. It has been shown in the literature that different parameters need to be selected for different functions of the basic algorithm. However, the present paper overcomes this issue by presenting and selecting a phase angle, in which all control parameters of the algorithm are assigned to sine and cosine functions of the selected phase angle.

• The discussion session is quite small and poor. I would expect quite extended discussion on the result where the authors should also make a thorough comparison of their proposal against the existing ones, including also a swot analysis of the proposal.

Reply:

Thank you very much for your constructive comments. In this revision, it has been endeavoured to precisely address the reviewer’s comments. The discussion session has been revised and more details have been added.

According to the results obtained in this paper, it can be concluded that the proposed algorithm can be a very simple, effective, and widely-used version of the well-known PSO algorithm. Based on the comparisons made between the proposed method and available PSO algorithms including adaptive PSO (APSO), comprehensive learning PSO (CLPSO), fully informed particle swarm (FIPS), Frankenstein’s PSO (FPSO), the improved standard PSO 2011 (SPSO2011), and several algorithms selected from recently published papers, such as HNN [33], DSM [32], PSO-TVAC [32], PSO [9], HHS [12], NFP [37], CEP [36], PS [38], HSLSO [9], and DEC2 [7], it was indicated that the suggested method can be employed by researchers for different problems in the field of energy and engineering optimization. Furthermore, considering the emission of units, reserve load, and system demand, the economic dispatching problem was analyzed practically and comprehensively.

 

• The conclusions should be enhanced based on the additional text in introduction and discussion section.
• the literature used in this paper is rather limitted for a topic that is having significant attention due to the importance it presents.

Reply:

Thank you very much for your constructive comments. In this revision, it has been endeavoured to precisely address the reviewer’s comments. The conclusions has been revised and more details have been added.

 

5. Conclusions

The multi-area economic dispatch (MAED) is a very important issue in power systems, which affects the transmission of electrical energy. In this study, the cost associated with system reliability was added to the operational cost of the thermal unit in MAED for the first time. The objective function of the problem comprises three main terms: operational cost, the costs due to reliability, and emission factors. Regarding various types of technical limitations as well as the spinning reserve capacity, the paper proposed a new improved version of particle swarm optimization (PSO), i.e., the phasor particle swarm optimization (PPSO) algorithm, to tackle the complex optimization problem. The algorithm uses the phasor theory in mathematics to define a new method for creating PSO control parameters and it was applied to optimal MAED problems in the context of different simulation tests. While in the first test, the superiority of the PPSO algorithm was confirmed in terms of the quality, reliability, and robustness in comparison to the existing algorithms of PSO, including adaptive PSO (APSO), comprehensive learning PSO (CLPSO), fully informed particle swarm (FIPS), Frankenstein’s PSO (FPSO), and the improved standard PSO 2011 (SPSO2011), the following tests focused on the impact of reliability considerations on the MAED and RCMAEED.

The obtained optimal results revealed that the proposed algorithm is strong and efficient for optimizing power dispatch in energy systems. In addition, it enjoys a special simplicity compared to its counterparts. Furthermore, the application of the phasor theory in different types of improved PSO algorithms, including the proposed PPSO, can be further elaborated in different power system optimization problems for future studies.

Reviewer 5 Report

The topic is interesting and it is adapt to this journal. The collaboration among several faculties is useful and I think that there is a great work behind the presentation of this work. However, while the presentation is nice in shape, there are few comments and/or suggestions to improve the manuscript.

 

-According to scientific standards, abbreviations cannot be used in the abstract, please correct it in the manuscript.

 

-Clarify better the innovation of this work in the abstract and in the main text.

 

-Read articles to understand the structure of Electronics. The following structure would be preferable based on the Electronics Microsoft Word template file: 1. Introduction (1.1, 1.2, 1.3.), 2. Materials and Methods (2.1, 2.2., 2.3.), 3. Results and Discussion (3.1, 3.2, 3.3), 4. Conclusions. These sections mixed in the text. The introduction section is a literary review of the topic. In the introduction (or where still necessary) all paragraph must be cited because of the risk of plagiarism.

https://www.mdpi.com/journal/electronics/instructions

 

-A short paragraph introducing the problem statement and actions taken (or a description of the study) should be included at the end of the Introduction section.

 

-Equations should always be accurately and clearly referenced.

 

- The conclusion part is short. Extend the conclusion with more general usability. What are the benefits of the results in a global context? Please explain this better in the manuscript.

 

-Put the nomenclature/abbreviations tables after the part of Conflicts of Interest

https://www.mdpi.com/journal/electronics/instructions

 

Author Response

Reviewer 5#

Comments and Suggestions for Authors

The topic is interesting and it is adapt to this journal. The collaboration among several faculties is useful and I think that there is a great work behind the presentation of this work. However, while the presentation is nice in shape, there are few comments and/or suggestions to improve the manuscript.

Reply:

Thank you very much for your time and valuable comments. In this revision, it has

been tried to address the reviewer’s comments.

 

-According to scientific standards, abbreviations cannot be used in the abstract, please correct it in the manuscript.

Reply:

Thank you for your comment. The abbreviation has been moved to the correct place according to the guideline of the journal.

 

-Clarify better the innovation of this work in the abstract and in the main text.

Reply: 

Thank you very much for your constructive comments. In this revision, it has been endeavoured to precisely address the reviewer’s comments. The discussion session has been revised and more details have been added.

According to the results obtained in this paper, it can be concluded that the proposed algorithm can be a very simple, effective, and widely-used version of the well-known PSO algorithm. Based on the comparisons made between the proposed method and available PSO algorithms including adaptive PSO (APSO), comprehensive learning PSO (CLPSO), fully informed particle swarm (FIPS), Frankenstein’s PSO (FPSO), the improved standard PSO 2011 (SPSO2011), and several algorithms selected from recently published papers, such as HNN [33], DSM [32], PSO-TVAC [32], PSO [9], HHS [12], NFP [37], CEP [36], PS [38], HSLSO [9], and DEC2 [7], it was indicated that the suggested method can be employed by researchers for different problems in the field of energy and engineering optimization. Furthermore, considering the emission of units, reserve load, and system demand, the economic dispatching problem was analyzed practically and comprehensively.

This paper demonstrates that the phasor particle swarm optimization (PPSO) algorithm is straightforward and effective for power flow dispatching in electrical systems. All constraints and limitations of the electrical system, in the present study, are assumed with the emission of pollutant gases. Since PSO is a basic algorithm and has been employed in many papers and research works, this version can be used as a base algorithm for future studied, as this has been proven in the present research. There is always a fast convergence problem with the base algorithm in reaching the optimal solution. This issue has been tackled in the proposed version of the algorithm. On the other hand, selecting the best parameters of the algorithm has always been challenging with the base algorithm. It has been shown in the literature that different parameters need to be selected for different functions of the basic algorithm. However, the present paper overcomes this issue by presenting and selecting a phase angle, in which all control parameters of the algorithm are assigned to sine and cosine functions of the selected phase angle.

-Read articles to understand the structure of Electronics. The following structure would be preferable based on the Electronics Microsoft Word template file: 1. Introduction (1.1, 1.2, 1.3.), 2. Materials and Methods (2.1, 2.2., 2.3.), 3. Results and Discussion (3.1, 3.2, 3.3), 4. Conclusions. These sections mixed in the text. The introduction section is a literary review of the topic. In the introduction (or where still necessary) all paragraph must be cited because of the risk of plagiarism.

https://www.mdpi.com/journal/electronics/instructions

Reply:

The authors are grateful for the comments of the reviewer. The structure has been corrected as reviewer suggestion. Furthermore, we tried to cite the references for all paragraphs.

 

-A short paragraph introducing the problem statement and actions taken (or a description of the study) should be included at the end of the Introduction section.

Reply:

The authors appreciate the comment of the kind reviewer. The Below paragraph has been added to the main text.

This paper demonstrates that the phasor particle swarm optimization (PPSO) algorithm is straightforward and effective for power flow dispatching in electrical systems. All constraints and limitations of the electrical system, in the present study, are assumed with the emission of pollutant gases. Since PSO is a basic algorithm and has been employed in many papers and research works, this version can be used as a base algorithm for future studied, as this has been proven in the present research. There is always a fast convergence problem with the base algorithm in reaching the optimal solution. This issue has been tackled in the proposed version of the algorithm. On the other hand, selecting the best parameters of the algorithm has always been challenging with the base algorithm. It has been shown in the literature that different parameters need to be selected for different functions of the basic algorithm. However, the present paper overcomes this issue by presenting and selecting a phase angle, in which all control parameters of the algorithm are assigned to sine and cosine functions of the selected phase angle.

 

-Equations should always be accurately and clearly referenced.

Reply:

Thank you for your evaluate comment. We tried to cite the references for equations as reviewer suggestion.

 

- The conclusion part is short. Extend the conclusion with more general usability. What are the benefits of the results in a global context? Please explain this better in the manuscript.

Reply:

Thank you so much for your comment. The conclusion has been improved as your suggestion.

5. Conclusions

The multi-area economic dispatch (MAED) is a very important issue in power systems, which affects the transmission of electrical energy. In this study, the cost associated with system reliability was added to the operational cost of the thermal unit in MAED for the first time. The objective function of the problem comprises three main terms: operational cost, the costs due to reliability, and emission factors. Regarding various types of technical limitations as well as the spinning reserve capacity, the paper proposed a new improved version of particle swarm optimization (PSO), i.e., the phasor particle swarm optimization (PPSO) algorithm, to tackle the complex optimization problem. The algorithm uses the phasor theory in mathematics to define a new method for creating PSO control parameters and it was applied to optimal MAED problems in the context of different simulation tests. While in the first test, the superiority of the PPSO algorithm was confirmed in terms of the quality, reliability, and robustness in comparison to the existing algorithms of PSO, including adaptive PSO (APSO), comprehensive learning PSO (CLPSO), fully informed particle swarm (FIPS), Frankenstein’s PSO (FPSO), and the improved standard PSO 2011 (SPSO2011), the following tests focused on the impact of reliability considerations on the MAED and RCMAEED.

The obtained optimal results revealed that the proposed algorithm is strong and efficient for optimizing power dispatch in energy systems. In addition, it enjoys a special simplicity compared to its counterparts. Furthermore, the application of the phasor theory in different types of improved PSO algorithms, including the proposed PPSO, can be further elaborated in different power system optimization problems for future studies.

 

-Put the nomenclature/abbreviations tables after the part of Conflicts of Interest

https://www.mdpi.com/journal/electronics/instructions

 

Reply:

Thank you for the suggestion of the kind reviewer. The nomenclature/abbreviations tables have been moved after the part of Conflicts of Interest.

Round 2

Reviewer 1 Report

The paper is fine now