A Multiobjective Evolutionary Approach for Solving the Multi-Area Dynamic Economic Emission Dispatch Problem Considering Reliability Concerns

Round 1

Reviewer 1 Report

State of presentation of the manuscript is good. I recommend for publication of this manuscript after minor revisions.

1. Please present scientific gap clearly.

2. Authors should discuss main novelty of the present work.

3. Improve introduction section by adding following recent energy paper https://doi.org/10.1016/j.est.2022.105394.

4. Conclusion should be more scientific and powerful.

Author Response

Reviewer: 1

 

State of presentation of the manuscript is good. I recommend for publication of this manuscript after minor revisions

Authors' reply:

Thanks for your positive comment, I have tried to give appropriate answers to all your concerns in the revised paper.

 

1. Please present scientific gap clearly.

Authors' reply:

Thanks for your comment, on pages 2 to 4 in literature review section, past works in the fields of ED, MASDE and MADED are reviewed in 4 paragraphs. In each paragraph, the methods used in each study, the objective functions and the advantages of these studies are presented, and at the end of each paragraph, a part is highlighted in yellow to show that the defects of past works are related to the same paragraph.

 

2. Authors should discuss main novelty of the present work.

Authors' reply:

Thanks for your comment, based on the review of past works, defects have been extracted from past works, which are highlighted in yellow in pages 2 to 4 in each paragraph. In order to resolve these defects on page 4, a paragraph and some bolts are highlighted in green, which shows the innovations of this study.

Also, according to Table 1 and comparing the work of this study with other studies, it shows that the proposed method in this study has considered all the objective functions and also all the limitations in solving the problem. It is also the first study to introduce a reliability objective function.

3. Improve introduction section by adding following recent energy paper https://doi.org/10.1016/j.est.2022.105394.

Authors' reply:

Thanks for your suggestion, this study has reviewed in the introduction section and added in the reference section with red color.

 

4. Conclusion should be more scientific and powerful.

Authors' reply:

Thanks for your suggestion, changes in the conclusion have been applied in order to better present the results and clarify the proposed method, which are marked with green color. Also, the improvement of the results of the proposed method as a percentage has been added in this section.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper focuses on a multi-objective solution for the multi-area dynamic economic dispatch problem. However, some descriptions are not clear. Some revisions are necessary in the manuscript.

1. Please describe Figure 1 in more detail.

2. Please indicate which algorithm in section3 is the author's core innovation.

3. Please describe in detail the relationships and differences among the three algorithms presented in section3.

4. Please explain how the simulation parameters are set.

5. In the paper, authors have focused on the evolution of the economic dispatch. The comparisons of different optimization methods are suggested to supply to indicate advantages of your work, which can refer to：

[a] IEEE Trans. Ind. Inf. vol. 18, no. 2, pp. 835-846. 2022

[b] Journal of Modern Power Systems and Clean Energy, vol. 10, no. 3, pp. 743-754, 2022

[c] IEEE Trans. Power Systems, vol. 37, no. 5, pp. 4067-4077, 2022

Author Response

Reviewer: 2

 

Comments to the Author

This paper focuses on a multi-objective solution for the multi-area dynamic economic dispatch problem. However, some descriptions are not clear. Some revisions are necessary in the manuscript.

Authors' reply:

Thanks for your comment, I have tried to give appropriate answers to all your concerns in the revised paper.

 

1. Please describe Figure 1 in more detail.

Authors' reply:

Thanks for your comment, the optimization problem in this study is the MADED problem. According to Figure 1, four power plants are connected by transmission lines and are supposed to supply load in each region. The objective functions in this study include generation cost, pollution and reliability, which are drawn in the middle of the proposed design. Also, according to Figure 1, the modified grasshopper optimization algorithm using the fuzzy concept has been used to simultaneously optimize all three objective functions. The purpose of presenting this graphic design is to introduce the optimization problem, objective functions, and problem-solving methods in an integrated form.

2. Please indicate which algorithm in section3 is the author's core innovation.

Authors' reply:

Thanks for your comment, in section 3, two conventional grasshopper optimization (GO) and modified grasshopper optimization (MGO) algorithms are presented. The innovation of this study is to present the modified grasshopper optimization (MGO) using chaos theory. Considering that the common conventional GO method is based on the initial random population, it may suffer slow convergence or getting in the local optimum in the optimization process. Therefore, in the MGO method, the logistic mapping as one of the chaos mechanisms is developed to solve the slow convergence problem of the conventional GO method. In this regard, equation (26) has been used to initialize the population. These explanations are shown in blue in the text.

In order to better present the proposed method, the pseudo-code of the MGO is presented in Figure 3 on page 10.

 

3. Please describe in detail the relationships and differences among the three algorithms presented in section3.

Authors' reply:

Thanks for your comment, in section 3, two conventional grasshopper optimization (GO) and modified grasshopper optimization (MGO) algorithms are presented. The difference between the MGO method and the GO algorithm is in the stage of generating the initial population. In conventional GO, the initial population is randomly generated, this issue in the optimization process slows down the speed of convergence, or causes the grasshopper to get stuck in the local optimum. Therefore, in the MGO algorithm, using the chaos mechanism, the initial population is generated according to the equation (25).

In conventional GO and MGO methods, the description of equations is as follows:

According to equation (23), the position of the grasshoppers is updated. ,  and parameters are obtained from equations (19), (21) and (22).  represent the social interactions.  and are the horizontal wind force and force of gravity is on the ith grasshopper, respectively.  is the reduction coefficient to make the comfort zone, the repulsion zone and the gravity zone smaller. The coefficient c reduces the comfort zone, as shown in (24).

As stated in the previous two sections, the difference between the conventional GO and the MGO method is in generating the initial population, in the rest of the steps, the two algorithms are similar. In the conventional algorithm, the location of the initial population is generated completely randomly, while in the improved algorithm, the location of the initial population is generated based on the chaos theory and using equation (25). According to the optimization results in Tables 4, 5, 7, and 8, it is clear that the proposed MGO method has reached a better solution in single and multi-objective optimization than other evolutionary algorithms.

 

4. Please explain how the simulation parameters are set.

Authors' reply:

Thanks for your comment, According to Table (2), the initial population and the number of iterations for all 4 algorithms used in this study, including MGO, GWO, MBHMO and IPSO-MSFLA are the same.

Usually, obtaining these parameters is done by right and wrong method. For example, by increasing the initial population, we check the output of the optimization algorithm. Or by reducing the maximum number of iterations, we check the convergence process of the algorithm.

In this study, we have considered the initial population and the maximum number of iterations as 400 and 100 for all 4 algorithms. With the increase in the number of the initial population in the later tests, we did not converge to better answers, but the software's calculation time became longer. Also, according to the convergence curves, all 4 algorithms have converged at a maximum of 100 iterations.

Some other parameters are also extracted from some other studies and are available in them.

For example, the parameters r₁, r₂ in four evolutionary methods are random number values in the range of 0 to 1. The value of C₁, C₂ parameters in IPSO-MSFLA are considered 2. In many particle swarm optimization studies, including [1,2] the value of these parameters is defined as 2. The number of groups in the IPSO-MSFLA is considered 5, which is set based on right and wrong method. The value of C_min, C_mav parameters in MGO are considered 0.04 and 1, respectively. These parameters are extracted from [3,4].

In general, the optimization parameters used in this study were either obtained from the right and wrong method or extracted from other studies. The parameters obtained from the valid and reliable studies. By examining these studies, it can be found that to a large extent, optimization parameters related to evolutionary algorithms are also determined in a large number of different experiments. The optimization parameters extracted from other studies in the optimization process in this study have also been examined in various experiments.

[1] A. Azizivahed, H. Narimani, E. Naderi, M. Fathi, and M. R. Narimani, “A hybrid evolutionary algorithm for secure multi-objective distribution feeder reconfiguration,” Energy, vol. 138, pp. 355–373, 2017.

[2] Azizivahed, A., Narimani, H., Fathi, M., Naderi, E., Safapour, H., Narimani, M.R. “Multi-objective dynamic distribution feeder reconfiguration in automated distribution systems “. Energy 147, 896– 914, 2018.

[3]   S. Arora and P. Anand, "Chaotic grasshopper optimization algorithm for global optimization," Neural Computing and Applications, vol. 31, no. 8, pp. 4385-4405, 2019.

[4]   M. Ramachandran, S. Mirjalili, M. Nazari-Heris, D. S. Parvathysankar, A. Sundaram, and C. A. R. C. Gnanakkan, "A hybrid grasshopper optimization algorithm and Harris hawks optimizer for combined heat and power economic dispatch problem," Engineering Applications of Artificial Intelligence, vol. 111, p. 104753, 2022.

 

5. In the paper, authors have focused on the evolution of the economic dispatch. The comparisons of different optimization methods are suggested to supply to indicate advantages of your work, which can refer to：

[a] IEEE Trans. Ind. Inf. vol. 18, no. 2, pp. 835-846. 2022

[b] Journal of Modern Power Systems and Clean Energy, vol. 10, no. 3, pp. 743-754, 2022

[c] IEEE Trans. Power Systems, vol. 37, no. 5, pp. 4067-4077, 2022

Authors' reply:

Thanks for your suggestion, these studies have reviewed in the introduction section and added in the reference section with red color.

Author Response File: Author Response.pdf

Reviewer 3 Report

In general, the paper is well-written, and the topic is interesting. Please check and improve the typesetting, such as equations (2), (3), (27), and (28). 

Author Response

Reviewer: 3

 

Comments to the Author

 

In general, the paper is well-written, and the topic is interesting. Please check and improve the typesetting, such as equations (2), (3), (27), and (28). 

 

Authors' reply:

Thanks for your positive comment, the format of all the equations is checked and the previous problems are solved.

Author Response File: Author Response.pdf