Operational Stress and Degradation of Inverters in Renewable and Industrial Power Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors

Positive points:

Excellent work in tackling the problem by evaluating high-caliber research publications. 
The English quality is ok.

Shortcomings:

What is the main question addressed by the research?
The degradation of inverters with high use of PV and different impacts

Do you consider the topic original or relevant to the field?
yes

Does it address a specific gap in the field?
The authors tried to address but i have suggested for comparative analysis of their research with other research works on inverters degradation
 with more depth on performance, reliability, and efficiency

What does it add to the subject area compared with other published material?
Advanced modeling techniques, particularly Bayesian modeling is employed by authors but they haven't stated the major achievements as compared to other research works

What specific improvements should the authors consider regarding the methodology?
Proper introduction should be there alongwith flowchart of implemented methodology of research should have been included mentioning the research steps taken

Are the conclusions consistent with the evidence and arguments presented and do they address the main question posed?
Framework/modeling presented in figure 5 and subsequent results given in figure 6 are not clear and need to be discussed in more detail to conclude their research

Are the references appropriate?
ok

Any additional comments on the tables and figures.
Figure 5 and 6 needs major improvements

 

Author Response

Thank you very much for your insightful review. We have taken liberty to summarise the comments to make them easier to address:

Comment 1. Main question addressed by the research is unclear.
Response. We now state the central question in the Introduction and reprise it at the start of Results:
“Our central question is: which parsimonious distributional models best characterize degradation-related variability in inverter voltage, current, and active power under operational stress, and how do these patterns compare between PV and induction-motor contexts?”
We also added a one-paragraph outline at the end of the Introduction to guide readers through the IMRaD structure. 
revised

Comment 2. Comparative analysis vs other works on inverter degradation (performance, reliability, efficiency) needs more depth; clearly state major achievements.
Response. We expanded Related Works to emphasize 2020–2025 contributions and positioned our novelty: a unified statistical (AIC/BIC-guided) and Bayesian framing applied across PV and motor contexts, with phase-wise analysis and quantitative model selection. We added an explicit paragraph distinguishing this contribution and the practical implications for monitoring and maintenance strategies. 

Comment 3. Methodology should include a proper introduction and a flowchart of the research steps.
Response. We reorganized the paper into IMRaD and introduced a Methods and Materials section with clearly labeled subsections (data source & preprocessing; modeling families; information criteria; tools; assumptions). At the start of Section 2 we added a stepwise pipeline (enumerated in text) that mirrors a flowchart: data → preprocessing → model fitting (Normal/Log-normal/Gamma/Poisson + linear) → model selection (AIC/BIC) → diagnostics → result synthesis. If the editor prefers a graphical flowchart, we can supply a schematic derived from this stepwise list with the same content. 

Comment 4. Figures 5–6 and subsequent results are unclear; discuss in more detail; conclusions should follow.
Response. Former Figs. 5–6 are now Figures 3–5 (modeling) and Figures 6–7 (microgrid context). We:.

• Regenerated high-resolution vector figures, normalized font sizes, ensured panel labels (a)–(e), and conformed to the MDPI template width.
• Rewrote the captions to be self-contained, stating the model comparison outcome (log-normal best by AIC/BIC; Poisson inapplicable to continuous magnitudes) and the main observation per variable; this makes each figure interpretable on its own. 
• Cross-referenced the AIC/BIC tables (Tables 2–5) to support the narrative. 
  We also tightened the Conclusions to report only study outcomes.

Comment 5. Table/figure caption issues.
Response. We corrected duplicated/over-broad captions and aligned them with MDPI style. For example, Table 2–3 captions were normalized to emphasize the model families and metrics reported. 

As an additional note, because the manuscript was substantially rewritten, tracking changes in red would obscure readability; hence we provide a clean, fully revised version and the above mapping of changes.

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a timely and relevant study on inverter degradation in photovoltaic and induction motor systems, utilizing statistical models—such as log-normal distributions assessed via AIC/BIC—for predictive analysis. The work offers valuable insights, particularly in its practical discussion of degradation mechanisms and its connection to current challenges in renewable energy integration. However, the manuscript would benefit from several improvements in presentation and clarity:

1) Keywords should be revised to better reflect the core contributions of the paper. The current set is overly general and does not adequately capture the unique focus of the study.

2) Table captions, particularly for Table 2 and Table 3, contain duplicated descriptions

3) The authors should provide more detail regarding the datasets used for the statistical modeling, specifically, information on data sources, dataset sizes, sampling frequencies, and preprocessing steps

4) How does this work distinguish itself from the authors’ recent related publications or presentations - for example, Prof. Baranowski’s 2025 webinar on statistical methods in degradation modeling? Additionally, what specific research gaps in the 2024–2025 literature does this manuscript aim to address?

Author Response

Thank you very much for your insightful review. These are responses to individual comments

 

Comment 1. Keywords should be revised to better reflect the core contributions of the paper. The current set is overly general and does not adequately capture the unique focus of the study.

Response. We revised the keywords to reflect our core contributions:
Bayesian Degradation Modeling; PV Inverter Failure; Induction Motor Drives; Voltage Instability; Predictive Maintenance.  
revised

Comment 2.  Table captions, particularly for Table 2 and Table 3, contain duplicated descriptions

Response. Corrected. Captions are now concise and non-duplicative, pointing to AIC/BIC as the selection criteria and to the three-phase scope. 
revised

Comment 3. The authors should provide more detail regarding the datasets used for the statistical modeling, specifically, information on data sources, dataset sizes, sampling frequencies, and preprocessing steps

Response. We added a Data source and preprocessing subsection: 2019-06-25 to 2020-04-14, 15-minute sampling (~294 days), three-phase voltage/current/power/active-power timeseries; outlier removal; normalization; per-phase segmentation. 

Comment 4. How does this work distinguish itself from the authors’ recent related publications or presentations - for example, Prof. Baranowski’s 2025 webinar on statistical methods in degradation modeling? Additionally, what specific research gaps in the 2024–2025 literature does this manuscript aim to address?
Response. Section 2.3 (Information criteria) now explicitly distinguishes this manuscript from prior talks by (i) framing a comparative PV vs motor analysis, (ii) formalizing distributional model selection with AIC/BIC over real operational data, and (iii) linking to Bayesian inference and uncertainty quantification for maintenance insights—thus filling a practical gap. 

As an additional note, because the manuscript was substantially rewritten, tracking changes in red would obscure readability; hence we provide a clean, fully revised version and the above mapping of changes.

Reviewer 3 Report

Comments and Suggestions for Authors

The article submitted for review is devoted to the issues of predicting inverter failures based on Bayesian modeling, as well as planning maintenance of inverters to minimize their failures. Overvoltages and significant voltage fluctuations lead to accelerated degradation and damage of inverters. This is due to the massive introduction of photovoltaic modules. The following are recommendations that the authors should consider when finalizing the article.

1. The authors are recommended to use the standard structure of the sections of the article. It is necessary to enter the sections "Materials and Methods", "Results" and "Discussion" and reformat the article material. This structure is most convenient for the readers of the magazine and has been proven over many years of use.
2. The relevance of the study is poorly substantiated by the authors. Although this problem occurs in the energy sector and industry, it is necessary to provide up-to-date statistical data on the damage of inverters, which are used both in conjunction with photovoltaic systems and in frequency-controlled drives of asynchronous motors, as well as damage and losses from unreliability. Without this information, it is difficult to substantiate the relevance of the study and the significant complication of the inverter maintenance planning process.
3. The review of the research results of other authors on the subject of the article by the authors is insufficient. It is necessary to make a full-fledged review and identify areas that have not been worked out by other authors. Special attention should be paid to publications over the past 5 years.
4. It is recommended to transfer the material from the sections "Overall Inverter Performance" and "Challenges for Induction Motor Inverters" to the "Introduction" section to substantiate the formulation of the research task.
5. At the end of the "Introduction" section, the authors are recommended to present the structure of the article with a brief description of the content (one or two sentences) of each section. This allows readers to easily navigate through the text of the article and quickly find the material they are interested in.
6. Inverters are available from various manufacturers. The authors should clearly indicate which samples of inverters they have studied and for which inverters the results obtained are adequate. Inverters are manufactured in different countries according to different national standards for different industries and have significant differences. Combining all inverters and all manufacturers in all countries of the world is not justified by the authors.
7. On lines 185 and 191, the authors provided square brackets to provide references to the list of references, but they remained empty. You should either provide references or remove the empty brackets.
8. Figures 3, 4, 5, 6 of unsatisfactory quality and size. The signatures on them are not visible at all. Some of the drawings go beyond the right border of the template, which is unacceptable. All of these drawings need to be reworked to be of interest to the readers of the magazine.
9. The authors of the article do not provide any information about the economic side of the implementation of their approach to predicting inverter failures. No technical solution in the field of applied sciences will be implemented if it does not have obvious economic effects and does not pay off within a reasonable time frame for investors. The authors should provide some economic estimates. In most cases, enterprises have backup technological mechanisms driven by asynchronous motors and inverters, so the failure of a single inverter does not lead to significant damage and losses.
10. The "Conclusion" section should be completely redesigned. It should contain only the results obtained by the authors during the conduct of this study, and not general phrases and a repetition of the abstract to the article. The questions of promising research directions from the "Conclusions" section should be moved to the "Discussion" section.
11. Considering that the research was carried out in the field of applied sciences, the authors should, in addition to qualitative assessments, provide quantitative results obtained by the authors in the course of the research. What has been improved and by how much? What technical and economic effects does the implementation of the proposed approach have for the owners of inverters?

Author Response

Thank you very much for your insightful review. We have taken liberty to summarise the comments to make them easier to address:

1) Use standard IMRaD structure, with “Materials and Methods,” “Results,” “Discussion.”
Response. Implemented. The manuscript now follows IMRaD, and the end of the Introduction contains a short “paper structure” paragraph (per your recommendation). 

2) Substantiate relevance with up-to-date statistics on inverter damage and reliability impacts.
Response. We added Section 4.1–4.2 with internationally reported figures on cost/downtime reductions from predictive maintenance and an example of annualized savings, with references. 

3) Expand recent related work (last 5 years) and identify unworked areas.
Response. Related Works was expanded with 2020–2025 items and a summary of what remains insufficiently addressed (comparative, distribution-aware modeling across PV and industrial drives). 

4) Move “Overall Inverter Performance” and “Challenges for Induction Motor Inverters” into the Introduction to motivate the task.
Response. Background text was condensed and moved to the Introduction, supporting the problem framing and the subsequent Methods. 

5) Add a brief article structure at the end of the Introduction.
Response. Added (see lines describing Sections 2–6). 

6) Clarify which inverter samples were studied; avoid over-generalization across all manufacturers.
Response. We explicitly state that the documentation for the analyzed data does not specify models/manufacturers and we delimit applicability accordingly in Section 2.1 (scope/limitations). 

7) Empty citation brackets on lines 185 and 191; remove or supply references.
Response. We corrected these issues in the revision; in particular, the Introduction now contains populated citations where general statements are made. 

8) Figures 3–6 (old numbering) poor quality/oversize; fix fonts/fit; captions unreadable.
Response. We regenerated all figures as vector graphics, standardized font sizes, ensured single-column/2-column compliance, and rewrote captions to be self-contained and MDPI-style, including panel labels and key findings. See Figures 3–5 (modeling) and Figures 6–7 (microgrid). 
 
9) Add economic perspective; quantify effects and payback rationale.
Response. We included a Discussion subsection with internationally reported metrics and a concrete savings example to demonstrate economic relevance for maintenance planning. 

10) Redesign the Conclusions to contain only results; move future-work remarks to Discussion.
Response. The Conclusions were tightened to emphasize empirical findings (model selection outcomes and monitoring implications), with forward-looking statements moved to Discussion.

11) Provide quantitative results (“what improved and by how much?”).
Response. We report AIC/BIC model-selection metrics across variables and phases (Tables 2–5), and summarize the principal outcome (log-normal best among continuous distributions; Poisson inapplicable to quasi-continuous magnitudes). 

As an additional note, because the manuscript was substantially rewritten, tracking changes in red would obscure readability; hence we provide a clean, fully revised version and the above mapping of changes.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors

 

1. The figure 6 of model can be improved in terms of clarity
2. Highlight the obtained results in comparison to other existing works in conclusion section properly with values and parameters in order to enhance your outcome presentation.

Author Response

We appreciate reviewer comments, and we are grateful for the suggestions provided.

Comments 1:The figure 6 of model can be improved in terms of clarity

Response 1: We have increased the size and dpi of the microgrid image, including rotating it by 90 degrees, to fit it better on page. 

Comment 2: Highlight the obtained results in comparison to other existing works in conclusion section properly with values and parameters in order to enhance your outcome presentation.

We have added following paragraphs to the conclusion:

Compared to recent studies, our findings demonstrate improved model selection and interpretability in the context of inverter degradation. For example, Guerra et al. [35] employed Bayesian neural networks to estimate inverter field efficiency, but their approach lacks explainability and provides no direct model selection criteria. In contrast, our statistical modeling yielded the lowest AIC and BIC values using log-normal distributions --- with average AIC values of 134.5 for power signals and 129.2 for current signals, significantly outperforming normal and gamma models (which exceeded 180 in most cases). 

Similarly, Roy et al. [36] identified voltage stress and overtemperature as primary degradation drivers through heuristic analysis; our model quantitatively confirms this by showing that reactive power fluctuations and overvoltages consistently produce heavier-tailed signal distributions, best captured by log-normal fits.

While high-fidelity simulations used by Wang et al. [37] predicted degradation trends under assumed operational profiles, our method uses real operational data and directly extracts statistical parameters (e.g., shape and scale of log-normal models), enabling practical maintenance decisions without requiring extensive simulations. This offers a robust and transferable solution for reliability assessment across both photovoltaic and motor inverter systems.

And we've added additional references to support it. 

Reviewer 3 Report

Comments and Suggestions for Authors

The authors took the comments seriously and answered all the questions and made the necessary changes to the text of the manuscript. I believe that the final version of the manuscript meets the requirements and is recommended for publication.

I would like to draw your attention to Figures 6 and 7. I think that for the convenience of readers, they should be placed on separate pages in a vertical format when editing. You can see general trends in the drawings, but it's almost impossible to read the captions.

Author Response

Thank you very much for your kind words and thorough review. 

Comment 1: I would like to draw your attention to Figures 6 and 7. I think that for the convenience of readers, they should be placed on separate pages in a vertical format when editing. You can see general trends in the drawings, but it's almost impossible to read the captions.

We have done what we could to improve those images, we have replaced microgrid diagram with a one of better quality, and as recommended in vertical form. We have also regenerated figures for the waveforms, to make them more legible and dropped one unnecessary. We have also improved the caption.