Review of Virtual Inertia Based on Synchronous Generator Characteristic Emulation in Renewable Energy-Dominated Power Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Your article is a review article. The following materials should be added to the article. Given the significant reduction in system inertia observed in regions with higher integration of renewable energy sources, what technical and operational measures are most effective in maintaining frequency stability in low-inertia power systems?

 

The following factors are not taken into account in any way in the work. How cost-effective is the implementation of virtual inertia compared to other methods of frequency support (reserves, battery systems)? A comparison with other means should be given. Also, the work does not show whether virtual inertia can completely compensate for the loss of traditional synchronous inertia, and why does it more often replace it?

Figure 3. How were the results shown in Figure 3 obtained? Was the model or method developed?

What mathematical models (for example, swing equation, VSG) were used in the studies to simulate virtual inertia in single-phase inverters? The above-mentioned questions are related to the fact that the work does not present methods as such.

Author Response

Comments 1:  

Your article is a review article. The following materials should be added to the article. Given the significant reduction in system inertia observed in regions with higher integration of renewable energy sources, what technical and operational measures are most effective in maintaining frequency stability in low-inertia power systems? 

Response 1:   

We thank the reviewer for the suggestion. We have added a clear statement in the Introduction section addressing how to cope with frequency stability problem in low-inertia power systems by implementing virtual inertia. 

“Recent studies have highlighted that maintaining frequency stability in low-inertia power systems requires a coordinated approach that combines both technical and operational measures. Technically, the adoption of grid-forming control in inverter-based resources has been recognized as an effective strategy to provide virtual inertia and enhance system frequency resilience under high renewable penetration [13]. Virtual inertia, aimed at improving system stability, has been a prominent area of research in recent years [14]. As most power systems are still dominated by synchronous generators, which rely on fossil fuels, the early stages of inverter control technology have focused on emulating the characteristics of these generators [15], [16], [17]. As a result, researchers are focusing on controlling on-grid inverter to replicate the behavior of synchronous generators and improve system stability [14].” 

 

Comments 2:   

The following factors are not taken into account in any way in the work. How cost-effective is the implementation of virtual inertia compared to other methods of frequency support (reserves, battery systems)? A comparison with other means should be given. Also, the work does not show whether virtual inertia can completely compensate for the loss of traditional synchronous inertia, and why does it more often replace it? 

Response 2:  

We thank the reviewer for the valuable comment. We have add further explanation regarding the economical challenge of virtual inertia to be considered. 

 “In terms of economical aspect, implementing virtual inertia or frequency regulation system through battery energy storage systems (BESS) and grid-forming inverters requires cost–benefit evaluation. Studies indicate that providing reliable inertia support often demands oversizing of battery capacity, since additional power and energy margins are needed to handle rapid frequency deviations. This design requirement increases both capital expenditure (CAPEX) and system complexity. For example, a study found that when higher reliability levels are targeted, the benefit–cost ratio of virtual inertia from BESS decreases due to growing investment in converter capacity and standby energy reserves [39]. Beyond equipment cost, maintaining headroom for fast frequency response also leads to renewable curtailment, since part of the generation must be withheld to provide inertial power. As a result, while BESS-based inertia emulation improves dynamic performance, it may not always be the most cost-effective standalone option.” 

 

Comments 3:  

Figure 3. How were the results shown in Figure 3 obtained? Was the model or method developed? 

Response 3: 

We thank the reviewer for the comment. The referred figure shows the area of frequency control strategy proposed by the previous research. There is the inertia, primary, secondary, and tertiary control presented by this figure. 

 

Comments 4: What mathematical models (for example, swing equation, VSG) were used in the studies to simulate virtual inertia in single-phase inverters? The above-mentioned questions are related to the fact that the work does not present methods as such. 

Response 4: 

We thank the reviewer for the comment. The mathematical equations provided in the paper is implemented for each balanced-phase for three-phase disturbance. 

Reviewer 2 Report

Comments and Suggestions for Authors

 The topic is relevant and the idea has potential. However, substantial revisions are needed before the work is publishable.

Suggestions (major revision):

1. In the current manuscript the application context is described, but the specific research gap and verifiable contributions are diffuse. Please end the Introduction with a compact “Gap → Goal → Contributions” paragraph listing 3–4 concrete, testable contributions, and map each item to later sections and figures to make the storyline auditable.

2. Symbols and units are not fully aligned across text, equations, and figure labels, and several quantities appear before being defined. Add a short “Notation & Assumptions” box that defines every symbol at first use, enforces one-symbol-one-meaning, and states operating ranges and assumptions that are required by both proofs and experiments.

3. Algorithmic steps are scattered across paragraphs, and boundary conditions are implicit. Provide a clear pipeline/algorithm box with Inputs, Outputs, Steps, and Complexity; list default hyperparameters with brief rationale, and specify any approximations or heuristics so readers can reproduce the behavior.

4. Experimental setup lacks a single source of truth for system/data, sampling rates, controller gains, solver/hardware, runtime, and random seeds. Add a reproducibility table aggregating these items and either release code/data or include pseudocode plus a complete parameter file so third parties can regenerate the main curves within tolerance.

5. Comparisons are limited and not strictly like-for-like. Include at least three strong, recent baselines under identical data splits and tuning budgets; report evaluation metrics up front and provide statistical evidence over 5–10 runs to avoid single-run conclusions.

6. The impact of key design choices and the robustness envelope are unclear. Conduct ablations for principal components (controller terms, loss weights, window sizes) and sensitivity studies over {K, α, τ, noise σ, parameter mismatch ±10–30%}; add stress tests with delays, disturbances, or missing data and plot performance versus stress level to reveal failure modes.

7. Some axes lack units, fonts are small, and captions do not state the takeaway; most plots show single trajectories without uncertainty. Standardize notation, add units, use ≥9-pt fonts, and write self-contained captions ending with the key conclusion; add error bars or shaded confidence intervals, moving crowded auxiliary curves to an appendix.

8. Logical steps in the analysis depend on unstated conditions and jump over intermediate results. For each major claim, explicitly state assumptions and support it with a lemma/theorem, provide a brief proof sketch in the main text with full proof in the appendix, and add a candid “Limitations & Deployment” paragraph covering applicability bounds, complexity O(·), memory/tuning cost, scalability, and potential failure modes.

Comments on the Quality of English Language

The manuscript is readable, but the English needs polishing to clearly convey the results. Common issues include long, multi-clause sentences; inconsistent tense and voice; article and preposition errors; and occasional noun–verb disagreement. Technical terms and symbols are not always introduced on first use, and capitalization of defined terms varies across text, equations, and figure captions. Several captions are descriptive rather than explanatory and should end with the key takeaway. Please shorten and restructure dense sentences, ensure consistent terminology/spelling, and run a careful copy-edit for grammar and punctuation. A professional language edit is recommended before resubmission.

Author Response

Comments

1. In the current manuscript the application context is described, but the specific research gap and verifiable contributions are diffuse. Please end the Introduction with a compact “Gap → Goal → Contributions” paragraph listing 3–4 concrete, testable contributions, and map each item to later sections and figures to make the storyline auditable.
2. Symbols and units are not fully aligned across text, equations, and figure labels, and several quantities appear before being defined. Add a short “Notation & Assumptions” box that defines every symbol at first use, enforces one-symbol-one-meaning, and states operating ranges and assumptions that are required by both proofs and experiments.
3. Algorithmic steps are scattered across paragraphs, and boundary conditions are implicit. Provide a clear pipeline/algorithm box with Inputs, Outputs, Steps, and Complexity; list default hyperparameters with brief rationale, and specify any approximations or heuristics so readers can reproduce the behavior.
4. Experimental setup lacks a single source of truth for system/data, sampling rates, controller gains, solver/hardware, runtime, and random seeds. Add a reproducibility table aggregating these items and either release code/data or include pseudocode plus a complete parameter file so third parties can regenerate the main curves within tolerance.
5. Comparisons are limited and not strictly like-for-like. Include at least three strong, recent baselines under identical data splits and tuning budgets; report evaluation metrics up front and provide statistical evidence over 5–10 runs to avoid single-run conclusions.
6. The impact of key design choices and the robustness envelope are unclear. Conduct ablations for principal components (controller terms, loss weights, window sizes) and sensitivity studies over {K, α, τ, noise σ, parameter mismatch ±10–30%}; add stress tests with delays, disturbances, or missing data and plot performance versus stress level to reveal failure modes.
7. Some axes lack units, fonts are small, and captions do not state the takeaway; most plots show single trajectories without uncertainty. Standardize notation, add units, use ≥9-pt fonts, and write self-contained captions ending with the key conclusion; add error bars or shaded confidence intervals, moving crowded auxiliary curves to an appendix.
8. Logical steps in the analysis depend on unstated conditions and jump over intermediate results. For each major claim, explicitly state assumptions and support it with a lemma/theorem, provide a brief proof sketch in the main text with full proof in the appendix, and add a candid “Limitations & Deployment” paragraph covering applicability bounds, complexity O(·), memory/tuning cost, scalability, and potential failure modes.

 

Comments on the Quality of English Language

The manuscript is readable, but the English needs polishing to clearly convey the results. Common issues include long, multi-clause sentences; inconsistent tense and voice; article and preposition errors; and occasional noun–verb disagreement. Technical terms and symbols are not always introduced on first use, and capitalization of defined terms varies across text, equations, and figure captions. Several captions are descriptive rather than explanatory and should end with the key takeaway. Please shorten and restructure dense sentences, ensure consistent terminology/spelling, and run a careful copy-edit for grammar and punctuation. A professional language edit is recommended before resubmission.

Responses:

Dear Reviewer, 
We sincerely thank you for taking the time to review our manuscript and for providing your comments. After carefully reading your feedback, we noticed that some of the points raised do not appear to relate directly to the topic of our paper, which focuses on virtual inertia control. The comments seem to refer to a different area of research. 
Nevertheless, we have done our best to address the general suggestions, including improving the introduction and refining the English expression throughout the manuscript. We greatly appreciate your effort and time in reviewing our work. 
Sincerely 

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presents a comprehensive and well-structured review of virtual inertia strategies based on the emulation of synchronous generators. The topic is of great relevance and timeliness, given the increasing penetration of renewable energy sources into electrical grids. The manuscript logically addresses the problem of reduced system inertia, explains the concept of virtual inertia, and provides a detailed analysis of three fundamental control methods: the Synchronverter, the Virtual Synchronous Generator (VSG), and the swing equation-based method from Ise Lab. The document is a valuable contribution to the field, particularly for researchers and students new to this topic, owing to its expository clarity and the comparative synthesis it offers. However, the article presents several areas that could be significantly improved to enhance its scientific rigor and impact:

• A thorough review of all figures, captions, and cross-references (to equations, figures, and tables) should be conducted to ensure their accuracy and consistency. For instance:
  • Figure 5 and Figure 7 are identical. The text describes different architectures, yet the diagrams do not reflect this, which could lead to significant reader confusion. A precise and distinct block diagram should be created for each method.
  • In Section 4.2 (page 9), the text states: "These values are used in equation (14) to calculate the power reference...". However, an equation (14) does not exist in the document. This reference must be corrected.
  • In Section 5, the text notes, "The performance comparison across virtual inertia methods was also conducted, as can be seen in Table [7]," which refers to Table 2.
• The authors should expand Table 2 and/or the discussion in Section 5 to include a range of performance values obtained from various research studies. This would provide a more nuanced perspective on the practical performance of each method.
• Section 6, Conclusions, should be broader and more conclusive. For instance, it should propose more specific and novel research directions.

Author Response

Comments 1:

However, the article presents several areas that could be significantly improved to enhance its scientific rigor and impact:

A thorough review of all figures, captions, and cross-references (to equations, figures, and tables) should be conducted to ensure their accuracy and consistency. For instance:

• Figure 5 and Figure 7 are identical. The text describes different architectures, yet the diagrams do not reflect this, which could lead to significant reader confusion. A precise and distinct block diagram should be created for each method.
• In Section 4.2 (page 9), the text states: "These values are used in equation (14) to calculate the power reference...". However, an equation (14) does not exist in the document. This reference must be corrected.
• In Section 5, the text notes, "The performance comparison across virtual inertia methods was also conducted, as can be seen in Table [7]," which refers to Table 2.

Response 1:  

We thank the reviewer for carefully identifying the inconsistencies in figures, captions, and cross-references. We have thoroughly reviewed all figures and references throughout the manuscript to ensure their accuracy and consistency. Specifically, Figure 7 has been replaced with the correct diagram, the incorrect cross-reference to equation (14) has been updated to the correct equation (4), and the missing table number has been added to Table 2. All related text has been revised accordingly to maintain clarity and consistency.

 

Comments 2:

The authors should expand Table 2 and/or the discussion in Section 5 to include a range of performance values obtained from various research studies. This would provide a more nuanced perspective on the practical performance of each method.

Response 2:  

We thank the reviewer for the insightful suggestion. Accordingly, we have added explanatory paragraphs accompanying Table 2 to provide a clearer and more detailed discussion of the performance results. The revised section also highlights key comparative trends and practical implications to enhance the depth and clarity of the analysis.

“The summarized description for the five main virtual inertia methods discussed in this paper can be seen in Table 1 [7]. Starting with the Droop Control approach, this conventional method replicates the governor droop characteristic of synchronous machines. It offers a simple implementation without requiring communication links, making it suitable for basic load-sharing functions. However, it does not provide virtual inertia support, limiting its effectiveness in low-inertia systems with high renewable penetration.

The other method, the synchronous generator model-based approach, is known as the Synchronverter. This method precisely emulates the dynamic behavior of a synchronous generator, allowing seamless integration with conventional grid operations. It does not rely on the frequency derivative, and the PLL is used only for synchronization, making it a robust and realistic control method. However, its implementation can suffer from numerical instability, and it is typically realized as a voltage source without built-in overcurrent protection, which may pose challenges during fault conditions. ...”

 

Comments 3:

Section 6, Conclusions, should be broader and more conclusive. For instance, it should propose more specific and novel research directions.

Response 3:  

We thank the reviewer for the constructive comment. As suggested, we have revised the Conclusion section to provide a broader and more comprehensive summary of the key findings. The revised version now emphasizes comparative insights among the virtual inertia methods and outlines specific and novel future research directions, including integration within grid-forming control frameworks and adaptive parameter tuning strategies.

Reviewer 4 Report

Comments and Suggestions for Authors

In this paper, a review of virtual inertia based on synchronous generator characteristic emulation in renewable energy-dominated power systems is presented. The topic is very importan,t but the contribution of the paper is weak. The comparison is simple and not thorough. Following some comments:

1. The paper compares just three different approaches: the synchroinverter, the VSG, and the swing-equation-based. The comparison is weak, and the content is already widely known in the literature. 

2. The comparison between the approaches is just qualitative. At least a quantitative comparison for a case study (maybe with a simulation) should be carried out.

3. Several comparisons on the topic are already available in the literature, even more detailed. The novelty is not clear.

4. In addition to features and drawbacks, even emerging approaches should be included, for example, the use of AI.

Author Response

Comments 1:

The paper compares just three different approaches: the synchronverter, the VSG, and the swing-equation-based. The comparison is weak, and the content is already widely known in the literature.

Response 1:

We thank the reviewer for the valuable suggestion. To enhance the quality of the comparison, droop control and data-driven grid-forming (GFM) control approaches have been added in the revised manuscript, as presented in Section 4, Virtual Inertia Methods. In addition, several relevant recent references have been included to strengthen the discussion.

 

Comments 2:

The comparison between the approaches is just qualitative. At least a quantitative comparison for a case study (maybe with a simulation) should be carried out.

Response 2:  

We thank the reviewer for this valuable comment. Droop control and data-driven grid-forming (GFM) approaches have been added as additional comparisons in Section 5, Method Comparison. At this stage, the qualitative analysis is considered sufficient to highlight the conceptual differences among the algorithms, as this is the primary focus of the paper. A comprehensive quantitative comparison would require the development and validation of all relevant models, which is beyond the current revision timeline but will be addressed in future work.

 

Comments 3:

Several comparisons on the topic are already available in the literature, even more detailed. The novelty is not clear.

Response 3:  

We thank the reviewer for this important comment. In the revised manuscript, we have clarified the novelty of our work by emphasizing that the paper compares and contrasts five grid-forming (GFM) algorithms, highlighting the advantages and disadvantages of each method in a unified framework. Additionally, the introduction has been restructured to better articulate the specific contributions and distinctive aspects of this study compared to existing literature.

 

Comments 4: In addition to features and drawbacks, even emerging approaches should be included, for example, the use of AI.

Response 4:  

We thank the reviewer for the valuable suggestion. In response, we have included data-driven–based grid-forming (GFM) approaches in the revised manuscript to reflect emerging trends that incorporate artificial intelligence and learning-based methods.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I request that this work be accepted for publication. The authors have taken my comments into account.

Reviewer 3 Report

Comments and Suggestions for Authors

In my opinion, the manuscript is ready forpublication.

Reviewer 4 Report

Comments and Suggestions for Authors

All the concerns have been addressed.