Implementation of Modified Effective Butterfly Optimizer in Solving Multi-Objective Pareto Optimal Power Flow Problem with Renewable Uncertainties

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

• The references cited are relatively outdated. There is no analysis of related studies in the past three years. In the review of the research status, the manuscript mainly lists different algorithms, without discussing the limitations of existing methods.
• The novelty of the paper is weak. Applying the Modified Effective Butterfly Optimizer to the multi-objective optimal power flow problem can only be considered as an application-level contribution, rather than a methodological innovation.
• The experimental design is limited. The study only uses the IEEE 30-bus system, which makes it difficult to demonstrate the applicability of the proposed method in more complex power systems.
• The experimental results seem to be based on a single run, and no statistical results are provided. In addition, it is not clear whether the compared algorithms are reproduced under the same conditions, which raises concerns about fairness. The paper also lacks commonly used multi-objective evaluation metrics, as well as comparisons in computational time and convergence speed, so the conclusion that the proposed method outperforms existing algorithms is not sufficiently supported.

Comments on the Quality of English Language

I have no comments on the Quality of English Language.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes the use of the Modified Effective Butterfly Optimizer (MEBO) to solve the multi-objective optimal power flow (MOOPF) problem in power systems, where operational objectives such as generation cost, power losses, fuel emissions and voltage deviation must be optimized simultaneously under system constraints. Inspired by butterfly foraging behavior, MEBO enhances search efficiency through population reduction and parameter learning mechanisms. The method is tested on the IEEE 30-bus test system using four bi-objective scenarios (cost–loss, cost–voltage, cost–emission, and emission–loss), and the obtained Pareto-optimal solutions are compared with results from the literature. The findings indicate that MEBO outperforms most existing methods and represents a promising new approach for MOOPF applications. The paper is interesting and belongs to the category of studies that draw inspiration from the wisdom with which nature manages and solves complex problems. The manuscript includes a strong Introduction section, where the problem under investigation is clearly described, a comprehensive literature review is presented and the competing methods used later for comparative evaluation are properly identified. In addition, the contribution of the paper is explicitly highlighted, allowing the potential reader to clearly understand its novelty and relevance. As expected, the Authors begin with the mathematical formulation of the problem and the proposed model, and then proceed to the Numerical Results section, where they first perform the optimization process, compare the proposed method with alternative approaches, and finally present results and conclusions regarding the integration of RES. The paper concludes with a sufficiently detailed Conclusions section and is supported by a substantial and relevant list of references. In the Reviewer’s opinion, only a limited number of revisions are required before the paper can be accepted for publication (minor revision), and these are presented in the following list of Reviewer’s comments:

Section 1: In this Section, the Authors introduces their method and analyzes the present situation. At this Section, the Authors present other similar methods from the literature. They achieve to demonstrate their thorough literature study. At the end of the Section, the Authors give the main contribution of this paper. Section 1 does not need any changes.

Section 2: In this Section, the Authors present the mathematical formulation of their method. The mathematics of this Section is well validated knowledge and no significant error is expected in this Section. This Section does not need any changes and renders the basis of the following analysis in Section 3 where the weight methodology that supports the scenario generation is given.

Section 3: This Section is considerably shorter than the other sections. Since Section 3 addresses the solution of the multi-objective problem presented in Section 2, the reviewer suggests that Section 3 should be merged with Section 2. Anyway, the weighting problem is well formulated and Figure 1 supports the justification.

Section 4: The heart of the proposed methodology is given in this Section. MEBO takes inspiration from the biology and the Authors adapt MEBO to solve MO-OPF problems with bound constraints. The required mathematics of MEBO are given in this Section and are linked with the ones of Section 2.

Section 5: In this Section of the numerical results, the Authors are defining the benchmark test case and simulation settings used to evaluate their proposed optimization method. Specifically, they select the IEEE 30-bus test system, which is a widely accepted benchmark for testing optimal power flow algorithms, and then describe its main characteristics (number of buses, branches, generators, shunt capacitors, tap changers, load buses and control variables). They also specify the operational limits and constraints of the system variables, such as voltage magnitude bounds for generator/load buses, capacitor limits, and transformer tap ratio ranges. These constraints define the feasible search space for the optimization algorithm. In Section 5.1, first, the Αuthors are explaining how they transform the multi-objective optimization problem into a compromise optimization problem using weighting factors. It’s OK. Then, they compare their results against well validated models from the literature in Table 3. The analysis of the Table 3 in Section 5.2 is good and there is no need for further justification. In Section 5.3, the Authors are extending the numerical study to a renewable-energy scenario in order to test whether the proposed optimization method remains effective when variable renewable generation is included. Specifically, they modify the IEEE 30-bus test system by replacing two conventional thermal generators with two wind farms (at buses 5 and 11) and adding one photovoltaic (PV) unit at bus 13. This creates a more realistic modern power system with intermittent renewable sources. They then explain how renewable power output is modeled probabilistically and a number of case studies is examined. Here, a paragraph that synopsizes the results is needed. Several figures are not sufficiently clear and need to be redrawn.

Conclusions Section: The Conclusions Section is detailed, perhaps more than necessary, as it presents the full analysis of the model together with the numerical results obtained in the Numerical Results Section 5. The trade-offs that were expected to be discussed are addressed in this Conclusions section, where specific numerical findings are also provided to support them. No changes are required in this section.

References Section: Since this is a classical multi-objective optimization problem, it is expected that several foundational references are relatively old. However, the paper also includes a sufficient number of recent and up-to-date references; therefore, no changes are required in this section.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. It is suggested to include some numerical parameter in the Abstract.

2. The research gap must be discussed properly before starting the main contributions.

3. Equations are not aligned properly. Correct this issue.

4. Algorithm-specific parameters must be provided in a separate Table.

5. Overview/ System architecture is not provided, which must be updated as Fig. 1.

6. The basis of selecting this optimization method must be clearly mentioned. Also, I appreciate the last paragraph provided in the end of Conclusion section. 

7. I suggest that they add box plots and update the related discussion to further strengthen the Result section.

8. A dedicated list of Abbreviations must be added in the Manuscript.

9. I could not see any resulting flowcharts, which is a quintessential aspect of this work. Include the same, and you may refer to a recently published paper, "A Golden Jackal based optimal operation and optimization of a virtual power plant involving renewable resources".

10. Explore the possibility of including some more advanced analysis, like Box plots, to further strengthen the Result section. 

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

1. Caption provided for Figs. 15, 16 and 17 need to be fine-tuned.

2. In Fig. 3, the last block (Pareto_achieve) or archive??? Correct this anomaly.

Good luck!