Data-Driven Reliability Assessment of PV Inverters Using SCADA Measurements

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper titled "Data-Driven Reliability Assessment of PV Inverters Using SCADA Measurements" proposes a framework for assessing the reliability of photovoltaic inverters by comprehensively utilizing correlation analysis, machine learning models (XGBoost, LSTM), and hidden Markov models (HMM).

Revision suggestions:

1. There is confusion in the numbering of formulas (the article has two formulas numbered 4 and 11). It is recommended to re-arrange the numbering and correctly cite them in the text; at the same time, there are some garbled characters in formulas 4 and subsequent formulas. It is suggested to rewrite the corresponding formulas.
2. The role of Chapter 3.1.3 is not clear.
3. The hyperparameter settings of LSTM and XGBoost in the paper have not been detailed in the text. It is recommended to supplement the basis for parameter selection or refer to the tuning methods in the text.
4. In the HMM model, the state definitions, including the discrimination thresholds for normal, abnormal, and error conditions, should have a basis and should not be set subjectively. It is recommended to set them according to relevant literature.

Author Response

Reviewer 1

Comments and Suggestions for Authors

The paper titled “Data-Driven Reliability Assessment of PV Inverters Using SCADA Measurements” proposes a framework for assessing the reliability of photovoltaic inverters by comprehensively utilizing correlation analysis, machine learning models (XGBoost, LSTM), and hidden Markov models (HMM).

Revision suggestions:

Comment 1

There is confusion in the numbering of formulas (the article has two formulas numbered 4 and 11). It is recommended to re-arrange the numbering and correctly cite them in the text; at the same time, there are some garbled characters in formulas 4 and subsequent formulas. It is suggested to rewrite the corresponding formulas.

Response:
Thank you for pointing out this issue. We have carefully revised all mathematical expressions in the manuscript. Specifically:

• all equations have been renumbered sequentially and consistently throughout the paper;

• incorrect or ambiguous references to equations in the text have been corrected;

• formulas that contained garbled characters or formatting issues have been rewritten, reformatted, and displayed with improved font size and consistent notation.

These changes ensure clarity, correct citation, and proper rendering of all mathematical expressions.

Comment 2

The role of Chapter 3.1.3 is not clear.

Response:
We appreciate this remark and have clarified the role of Section 3.1.3 in the revised manuscript. The following changes were made:

• Section 3.1.3 has been renamed to
  “Random Forest for incident typology (supporting module, not contributing to RS)”.

• We added an introductory paragraph titled “Role and position in the framework”, where we explicitly state that the Random Forest (RF) model is used only for post-hoc incident typology and interpretability validation.

• We clearly emphasize that RF does not participate in the computation of the Reliability Score (RS), which is formed solely from the XGBoost, LSTM, and HMM components.

• The figure caption presenting RF feature importance has been updated with the note
  “supporting module; does not affect RS”.

These clarifications remove ambiguity and clearly position Section 3.1.3 as a diagnostic and interpretability support module.

Comment 3

The hyperparameter settings of LSTM and XGBoost in the paper have not been detailed in the text. It is recommended to supplement the basis for parameter selection or refer to the tuning methods in the text.

Response:
Thank you for this important suggestion. We have substantially expanded the methodological description in Section 3 to include detailed information on model configuration and tuning. In particular:

• we added the hyperparameter search ranges for XGBoost (e.g., number of estimators, tree depth, learning rate, subsampling, regularization terms) and for LSTM (window length, number of units, dropout, learning rate, batch size);

• we described the tuning strategy, including random search with successive halving, followed by focused grid search around the best-performing regions;

• we specified the time-aware validation protocol (rolling-origin cross-validation) to avoid temporal leakage;

• we reported the final selected hyperparameter values, together with justification regarding generalization ability, stability, and performance on highly imbalanced SCADA data.

These additions improve transparency and ensure full reproducibility of the ML models.

Comment 4

In the HMM model, the state definitions, including the discrimination thresholds for normal, abnormal, and error conditions, should have a basis and should not be set subjectively. It is recommended to set them according to relevant literature.

Response:
We fully agree with this remark and have significantly revised and expanded Section 3.2 (Stochastic modeling using HMM). In the revised version, we:

• clearly define the three HMM states (Normal, Anomaly, Error) based on engineering practice, SCADA monitoring conventions, and relevant literature;

• justify the discrimination thresholds using:

  • power-quality standards for frequency and voltage,

  • percentile-based temperature thresholds (T95, T99),

  • efficiency residuals relative to reference performance,

  • correlation-drift indicators derived from rolling correlation matrices;

• describe the calibration procedure for these thresholds using grid/Bayesian search and cross-validation, with constraints on false-alarm rate and alarm persistence;

• include literature references supporting the use of HMMs for degradation and reliability modeling in PV inverters and power electronics.

As a result, the HMM state definitions and thresholds are now data-driven, literature-grounded, and reproducible, rather than subjective.

We once again thank the Reviewer for the constructive and insightful comments. The suggested revisions have significantly improved the clarity, rigor, and reproducibility of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes an integrated framework for evaluating the reliability of photovoltaic inverters using SCADA data, combining correlation analysis, XGBoost, LSTM, and HMM, and synthesizing the information into two aggregate metrics: the Health Index (HI) and the Reliability Score (RS). The approach is ambitious, technically competent, and well-aligned with the current predictive maintenance agenda. However, the work is overly descriptive, methodologically weak, and the narrative suggests more than it actually demonstrates.

The paper presents HI and RS as methodological contributions, but in practice, they are ad-hoc combinations of probabilities and scores derived from existing models. It remains unclear what makes them conceptually novel compared to standard composite indices used in reliability engineering or PHM.

The entire analysis is exploratory. There are no explicit hypotheses, no statistical tests, and no formal comparison against benchmarks (e.g., classical MTBF, a single ML model, or a score based solely on temperature/efficiency).

The study uses a single short period (Feb–Apr 2025) and apparently a single system. There is no real cross-temporal validation or out-of-sample testing on another inverter or wind farm. The conclusions are presented as general when they are case-specific.

The HMM is interpreted strongly (transitions, anomaly scaling), but:

The initial probabilities are clearly biased by the time order.
The sensitivity of the number of states is not evaluated.
The assumption of a near-absorbing "Error" state is not critically discussed.

There are a large number of correlation, voltage, and frequency figures that confirm expected behaviors, but they contribute little to the scientific argument. The paper gains length, but not analytical depth.

The κ values ​​and thresholds are justified by expert judgment, but no sensitivity analysis is performed. This weakens reproducibility.

Phrases like "confirms," ​​"demonstrates," and "proves reliability" should be softened: the results suggest, they do not confirm.

There is talk of degradation and escalation, but the entire approach is correlational/predictive. This should be explicitly clarified.

Author Response

Reviewer 2

Comments and Suggestions for Authors

The paper proposes an integrated framework for evaluating the reliability of photovoltaic inverters using SCADA data, combining correlation analysis, XGBoost, LSTM, and HMM, and synthesizing the information into two aggregate metrics: the Health Index (HI) and the Reliability Score (RS). The approach is ambitious, technically competent, and well-aligned with the current predictive maintenance agenda. However, the work is overly descriptive, methodologically weak, and the narrative suggests more than it actually demonstrates.

Comment 1

The work is overly descriptive and suggests more than it demonstrates.

Response:
We appreciate this critical remark. In the revised manuscript, we have repositioned the study explicitly as a case study based on a single inverter and a limited observation horizon (February–April 2025). To reduce the exploratory nature and strengthen methodological rigor, we introduced:

• a structured evaluation protocol with explicit hypotheses (H1–H3);

• a time-aware validation design to mitigate temporal leakage;

• benchmark and ablation comparisons against simpler baselines (rule-based indicators, single-model predictors, and partial integrations).

All conclusions are now explicitly framed as dataset-specific evidence, and claims of generality have been removed or deferred to future work.

Comment 2

HI and RS appear to be ad-hoc combinations without conceptual novelty compared to existing composite indices.

Response:
We agree that HI and RS should not be interpreted as fundamentally new reliability metrics. In the revised manuscript, we explicitly clarify that:

• HI and RS are interpretable, operational composite indicators (risk summaries), not new physical or theoretical reliability measures;

• their novelty lies in the structured integration of calibrated probabilities, correlation-based drift, and temporal consistency, rather than in the invention of a new reliability definition.

This clarification is reflected in the Abstract, Methodology, and Discussion sections, where HI and RS are consistently positioned as decision-support summaries within a SCADA-only monitoring context.

Comment 3

The analysis is exploratory: no hypotheses, no statistical tests, and no benchmark comparisons.

Response:
Thank you for this important observation. To address it, we introduced an explicit hypothesis-driven evaluation structure:

• H1: Separation of HI/RS distributions between pre-error and normal windows;

• H2: Elevated correlation drift prior to error events;

• H3: Improved rare-event detection performance of the integrated framework compared to simpler baselines.

Non-parametric statistical tests (Mann–Whitney U, Wilcoxon signed-rank) and effect-size measures (Cliff’s delta, median differences) are specified, together with a benchmark/ablation design. These additions provide a formal analytical structure, while maintaining appropriate caution given the limited dataset.

Comment 4

The study uses a single short period and a single system, but conclusions are presented as general.

Response:
We fully agree. In the revised version:

• the scope of conclusions has been strictly limited to the analyzed inverter and time period;

• limitations regarding sample size, observation horizon, and lack of cross-site validation are explicitly stated;

• generalization to other inverters, sites, or climates is framed as future validation, not as an established result.

This clarification is emphasized in the Abstract, Discussion, and Conclusion.

Comment 5

The HMM is interpreted too strongly.

Response:
We have softened the interpretation of the HMM throughout the manuscript. The HMM is now explicitly described as:

• a supporting component that provides temporal structure and consistency;

• not a standalone proof of degradation, failure progression, or physical causality.

All HMM-derived results are now presented as contextual, probabilistic summaries, rather than definitive indicators of degradation mechanisms.

Comment 6

The initial probabilities are biased by the time order.

Response:
This issue is now explicitly acknowledged. We added a discussion of start-of-record bias and introduced a sensitivity framework comparing:

• empirical initialization of initial probabilities π;

• weakly informative or stationary initializations.

This allows a more cautious interpretation of early-state dominance and bounds the influence of data ordering.

Comment 7

The sensitivity of the number of states is not evaluated.

Response:
We have introduced a sensitivity design for the HMM state cardinality, considering alternative configurations (K = 2, 3, 4). The goal is not optimization, but to verify that qualitative patterns of state persistence and transitions remain stable across reasonable modeling choices. This limits over-interpretation tied to a single arbitrary configuration.

Comment 8

The near-absorbing “Error” state assumption is not critically discussed.

Response:
We clarified that the absorbing-state formulation is included only as a conceptual extension for catastrophic or long-term failure scenarios. For the analyzed dataset, the “Error” state is treated as transient, consistent with frequent transitions back to “Normal.” The manuscript now explicitly states that no absorbing-failure assumption is applied in this case study.

Comment 9

Many correlation, voltage, and frequency figures add length but little analytical depth.

Response:
We agree that these figures should not be interpreted as independent scientific contributions. Accordingly:

• they are now explicitly framed as contextual and exploratory diagnostics;

• their role is limited to motivating feature selection, drift detection, and interpretability;

• claims of standalone novelty or confirmation have been removed.

The analytical focus has been shifted toward model-based indicators, hypothesis-driven evaluation, and composite behavior.

Comment 10

κ values and thresholds are based on expert judgment, without sensitivity analysis.

Response:
To improve reproducibility, we added a sensitivity analysis framework for κ-thresholds. Rather than identifying a single optimal value, the analysis examines:

• bounded variations around nominal thresholds;

• resulting trade-offs between sensitivity and false-alarm rates.

This positions κ not as a fixed truth, but as a tunable parameter whose qualitative impact is explicitly bounded within the case-study scope.

Comment 11

Strong language (“confirms”, “demonstrates”, “proves”) should be softened.

Response:
We performed a global tone revision of the manuscript. Strong confirmatory language has been systematically replaced with more appropriate formulations such as “suggests,” “indicates,” “is consistent with”. Claims are now explicitly limited to the analyzed dataset and framed as evidence rather than proof.

Comment 12

The approach is correlational/predictive, but degradation and escalation are discussed.

Response:
We explicitly clarified that terms such as “degradation” and “escalation” are used in an operational risk-level sense, not as statements of physical causality. The approach is now clearly described as predictive and correlational screening, and does not claim causal inference about underlying failure mechanisms.

 

We thank the Reviewer for the thorough and critical assessment. The manuscript has been substantially revised to improve methodological clarity, analytical rigor, interpretative caution, and reproducibility. We believe that the revised version now presents a well-bounded, transparent case study that can serve as a practical reference point for future multi-inverter validation studies.

Reviewer 3 Report

Comments and Suggestions for Authors

This paper is devoted to assessing the reliability of photovoltaic converters. To this end, it proposes a comprehensive model based on machine learning algorithms and a Hidden Markov Model. The material is structured logically and consistently, but the quality of its presentation requires improvement. A number of suggestions and comments regarding the paper are in order:

1) References to sources should be removed from the title in subsections 3.1.1 and 3.1.2 and included in the text.

2) Formula 5 is a repetition of Formula 4. The formatting is distorted. This should be adjusted accordingly.

3) The abbreviations EWMA, CUSUM, RNN, and MTTF are repeated no more than twice or not at all. They should be excluded from the paper.

4) Figures 2 and 8 should be revised. Figure 1 seems questionable. Perhaps the O-y axis in this figure should be displayed on a logarithmic scale?

5) The same abbreviation is used multiple times in the paper. For example, the Health Index (HI) is entered in the abstract, in section 3 in line 178, in subsection 3.3 in line 253; in section 5 in line 578 and section 6 in line 628. This reduces the quality of the presentation of the material.

6) The formula numbering is incorrect. This must be provided in the co-defendant.

7) All formulas must be captioned with explanations of each operand.

8) The formatting of formulas 4–6 and 11 and the character indices in lines 261 and 263 is incorrect. This must be corrected.

The work is in dire need of revision.

Author Response

Reviewer 3

Comments and Suggestions for Authors

This paper is devoted to assessing the reliability of photovoltaic converters. To this end, it proposes a comprehensive model based on machine learning algorithms and a Hidden Markov Model. The material is structured logically and consistently, but the quality of its presentation requires improvement. A number of suggestions and comments regarding the paper are in order:

Comment 1

References to sources should be removed from the title in subsections 3.1.1 and 3.1.2 and included in the text.

Response:
Thank you for this remark. The references previously included in the subsection titles of Sections 3.1.1 and 3.1.2 have been removed from the headings and relocated into the body text of the respective subsections. This ensures compliance with standard academic formatting practices and improves the readability and consistency of the manuscript.

Comment 2

Formula 5 is a repetition of Formula 4. The formatting is distorted. This should be adjusted accordingly.

Response:
We agree with this observation. Formula 5 has been corrected, reformulated where necessary, and clearly distinguished from Formula 4. Additionally, the formatting distortion has been resolved, ensuring that both formulas now have correct mathematical structure, notation, and consistent numbering.

Comment 3

The abbreviations EWMA, CUSUM, RNN, and MTTF are repeated no more than twice or not at all. They should be excluded from the paper.

Response:
Thank you for pointing this out. The abbreviations EWMA, CUSUM, RNN, and MTTF have been removed from the manuscript where they were redundant or insufficiently used. Where the underlying concepts remain relevant, they are now described explicitly in text without introducing unnecessary abbreviations. This improves clarity and presentation quality.

Comment 4

Figures 2 and 8 should be revised. Figure 1 seems questionable. Perhaps the O-y axis in this figure should be displayed on a logarithmic scale?

Response:
We appreciate this suggestion. All mentioned figures have been revised and regenerated with improved resolution, clearer labeling, and consistent visual style. Figures 2 and 8 were redrawn to enhance readability. Figure 1 was carefully reviewed, and its scaling and axis representation were adjusted where appropriate to ensure correct interpretation of the presented data. Overall, the graphical presentation quality has been significantly improved.

Comment 5

The same abbreviation is used multiple times in the paper. For example, the Health Index (HI) is entered in the abstract, in section 3, in subsection 3.3, in section 5 and section 6. This reduces the quality of the presentation of the material.

Response:
We understand this concern and have carefully reviewed the manuscript for abbreviation usage. All abbreviations, including Health Index (HI), are now:

• defined only at first occurrence;

• used consistently thereafter without redundant redefinitions.

This revision improves readability and aligns the manuscript with standard editorial conventions.

Comment 6

The formula numbering is incorrect. This must be provided in the co-defendant.

Response:
Thank you for identifying this issue. All formulas have been systematically corrected and renumbered in sequential order throughout the manuscript. Cross-references in the text have been updated accordingly to ensure full consistency between equations and their citations.

Comment 7

All formulas must be captioned with explanations of each operand.

Response:
We agree with this recommendation. In the revised manuscript, all mathematical formulas are now accompanied by explicit explanations of each operand and parameter, either directly below the equation or immediately in the surrounding text. This improves transparency and ensures that the methodology is fully understandable and reproducible.

Comment 8

The formatting of formulas 4–6 and 11 and the character indices in lines 261 and 263 is incorrect. This must be corrected.

Response:
We have carefully revised the formatting of Formulas 4–6 and 11. All character indices, subscripts, and superscripts have been corrected and unified. The formulas were rewritten using consistent mathematical notation, ensuring proper alignment, indexing, and typographical correctness.

Final remark by Reviewer:
The work is in dire need of revision.

Response:
We appreciate the Reviewer’s candid assessment. The manuscript has undergone a comprehensive revision, addressing all presentation, formatting, and clarity issues raised. We believe that these corrections substantially improve the overall quality, readability, and academic rigor of the work.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

accept in present form

Author Response

Dear Reviewer,

We sincerely thank you for your positive evaluation of our manuscript and for recommending acceptance in its present form. We highly appreciate your time and consideration.

Warmest regards,
Nikolay Hinov

Reviewer 3 Report

Comments and Suggestions for Authors

1) Lines 155 and 156: “Here, unsupervised ML and HMM are used to evaluate failure mechanisms in PV inverters”. Is “evaluate” in the sentence unnecessary?

2) lines 249: “We form sequences with window L:[x_τ-L+1,…,x_τ] and target y_τ+δ at horizon…”. Is L is width or sliding step of window? What do the indices at x and y mean?

3) Figure 1. The unit of X-axis are seconds or minutes?

Author Response

Response to Reviewer 3

Round 2

Comment 1

Lines 155–156:
“Here, unsupervised ML and HMM are used to evaluate failure mechanisms in PV inverters”. Is “evaluate” in the sentence unnecessary?

Response:
Thank you for this observation. We agree that the wording could be improved for clarity. The sentence has been revised to remove the potentially ambiguous term “evaluate” and to better reflect the methodological role of the models.

The revised sentence now reads:

“Here, unsupervised ML and HMM are used to identify and model failure mechanisms in PV inverters by capturing the transitions between healthy, degraded, and failed operating states.”

Comment 2

Line 249:
“We form sequences with window L:[xτ−L+1,…,xτ] and target yτ+δ at horizon…”. Is L the width or the sliding step of the window? What do the indices at x and y mean?

Response:
Thank you for pointing out the need for clarification. We have revised the manuscript to explicitly define all symbols and indices used in the sequence formulation.

In the revised text, we clarify that:

• L denotes the temporal lookback window length (i.e., the number of past time steps included in the input sequence), not the sliding step;

• the window advances with a unit stride;

• the index τ corresponds to the last time step of the input sequence;

• δ defines the prediction horizon between the input window and the target output y.

The following explanatory sentence has been added to the manuscript:

“Here, L denotes the temporal lookback window length (number of past time steps), while the window is advanced with a unit stride. The index τ corresponds to the last time step of the input sequence, and δ defines the prediction horizon between the input window and the target.”

Comment 3

Figure 1:
The unit of the X-axis: are they seconds or minutes?

Response:
Thank you for highlighting this ambiguity. We have clarified the x-axis labeling in Figure 1.

The revised figure caption and axis description now explicitly state that the x-axis represents calendar time derived from SCADA timestamps, with a fixed sampling resolution of five minutes.