Fractional-Order Modeling and Control of HBCS-MG in Off-Grid State

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1) In the abstract, please discuss the demerits of the existing modelling such that it motivates the author to adopt the fractional order characteristics in the model structure.

2) At the end of the abstract, please add the numerical performance index results to justify the effectiveness of the new modelling and control schemes based on the fractional order structure.

3) The organization and content of Section 1 could be improved as follows:

(i) The discussion of modelling and controller structure developments looks mixed. Please discuss them in separate paragraphs.

(ii) The justification of using a fractional order model should be clearly highlighted from the viewpoint of the theoretical aspect (i.e., nonlinearity, frequency bandwidth etc.).

(iii) The justification of using fractional order PI (which is in the class on nonlinear controllers) should be clearly justified, while there are many possible new nonlinear controllers can be applied to the problem such as sigmoid PID controller, BELBIC PID controller, neuroendocrine PID controller and many more. Please provide a gap discussion between the proposed controller and the stated above controllers.

(iv) To justify the selection of fractional order PI, please add several recent applications of fractional order controllers such as A fractional order PID tuning tool for automatic voltage regulator using marine predators algorithm, Fractional-order PID controller for blood pressure regulation using genetic algorithm, Fractional-Order sliding mode control of a 4D memristive chaotic system.

(v) Please add the list of main contributions at the end of Section 1. Note that the statement of contribution must be unique to represent the novelty of the research study.

4) It is better to combine Sections 2 and 3 to represent the comprehensive modelling explanation, Furthermore, it is suggested to show the difference between the proposed model and the existing model of the HBCS-MG system.

5) It is preferable to validate the proposed model with the actual experimental setup of the HBCS-MG system.

6) It is noticed that some of the symbols in equations and figures are not properly defined in text. Please define all symbols carefully or alternatively, the author can add the abbreviation sections.

7) Please make sure the used notation in Figure 6 is consistent with the presented model in the previous section. Secondly, please enlarge the size of symbols in the figure. Thirdly, there are some cross arrows that overlap with other arrows. You should add a proper point junction for the arrow. 

8) How did you fine tune the proposed fractional order controller in this paper? Please provide an appropriate procedure to find those parameters.

9) To clarify the accuracy of the proposed model, please compare its accuracy with the previous model (without fractional order terms).

10) It is suggested to compare the results of the proposed fractional order PI with other conventional or existing control schemes. Please add the numerical results such as time response specifications (i.e., overshoot, rise time, settling time etc.) and integral square error.

Author Response

Please see the response to the comments in the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

1. Clarify the novelty of the proposed fractional-order PI controller compared to existing integer-order or other fractional-order strategies. Explicitly state the practical implications of the findings. 

2. Expand the discussion to include recent advancements in fractional-order control for renewable energy systems, particularly wind energy. The authors should compare their approach with:

   • Hybrid excitation synchronous generators (e.g., "Exploring the Potential of Hybrid Excitation Synchronous Generators in Wind Energy...").

   • Advanced fractional-order control in wind conversion systems (e.g., "Advanced modeling and control of wind conversion systems...").

   • Robust fractional-order strategies (e.g., "Investigation of the Robust Fractional Order Control Approach...").

   • High-efficiency synchronous generators (e.g., "Harnessing the potential of high-efficiency synchronous generators...").

3. Justify the choice of the Oustaloup algorithm over other approximation methods (e.g., Carlson, Matsuda). Compare computational efficiency or accuracy with techniques used in the referenced wind energy papers.
4. Include benchmarks against integer-order controllers or other fractional-order strategies (e.g., from the cited wind energy studies) to quantify performance improvements (e.g., THD reduction, settling time).
5. Evaluate the controller’s performance under extreme parameter variations or external disturbances, as seen in "Investigation of the Robust Fractional Order Control Approach...".
6. Improve resolution and labeling (e.g., axis titles in Figures 8–13).

 

Author Response

Please see the response to the comments in the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The study addresses a gap in fractional-order modeling and control for off-grid microgrids (HBCS-MG), which is less explored compared to grid-connected systems. This is timely given the growing interest in decentralized renewable energy systems. The integration of fractional-order elements into the microgrid model provides a more realistic representation of real-world systems with non-integer dynamics. The authors systematically analyze the impact of varying fractional orders (α₁, β, α₂) on system stability, dynamic response, and power quality (THD). This parameter study offers valuable insights into system optimization. Both theoretical and simulation-based validations are provided, strengthening the credibility of the results. The use of fractional-order PI controllers demonstrates improved flexibility over integer-order controllers, which could enhance microgrid resilience in off-grid scenarios with uncertainties. The article is well-written, however, several shortcomings should be addressed:

1. The abstract is overly technical and could better highlight the practical significance of the work (e.g., how fractional-order control improves off-grid reliability).
2. The proposed equivalent circuits for fractional-order inductors/capacitors (Fig. 4) are not rigorously validated against experimental data or alternative approximation methods. This raises questions about their accuracy in real-world scenarios.
3. The increased model complexity due to fractional elements is acknowledged but not quantified. Practical challenges in real-time implementation are not discussed.
4. The fragmented presentation of figures/tables (Figures 11–24) disrupts the flow. Consolidating these into a dedicated results section would improve readability.
5. The conclusion mentions the need for "optimal configuration" of fractional orders but lacks a roadmap for achieving this.
6. I recommend the authors to include a table summarizing key findings (optimal α/β ranges for stability, THD thresholds).

Author Response

Please see the response to the comments in the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

It can be accepted.

Reviewer 2 Report

Comments and Suggestions for Authors

No further comments