Study on the Effect of Sampling Frequency on Power Quality Parameters in a Real Low-Voltage DC Microgrid
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript addresses the importance and algorithm to improve the power quality of DC grid systems. Work is interesting and following concerns needs to be addressed.
1) authors should provide a brief introduction on similar studies that have been done in literature. Provide a sound background on algorithm derived.
2) what are potential problems expected with this algorithm when the authors plan to validate with real DC grid system?
3) the assumptions and parameters considered in the algorithm, is it feasible in real system. If so, how does the author plan to validate this model.
4) Overall interesting study.
Author Response
Comment 1: authors should provide a brief introduction on similar studies that have been done in literature. Provide a sound background on algorithm derived.
Response 1:
Actually we have not found any study in which a similar sampling frequency analysis is presented. As it is stated in Introduction, in all mentioned articles the initially selected sampling rate remained fixed during all the study. Anyway, two new papers are added as references, both corresponding to theorical tests, comprising generated and measured signals in laboratory or synthetic signals with three levels of white Gaussian noise: [11], [12].
Comment 2: what are potential problems expected with this algorithm when the authors plan to validate with real DC grid system?
Response 2:
This algorithm has been already implemented in a real DC microgrid, whose characteristics are described in 3.1 (see new Figure 1).
Comment 3: the assumptions and parameters considered in the algorithm, is it feasible in real system. If so, how does the author plan to validate this model.
Response 3:
The implementation of this algorithms has been done in a real DC microgrid, but might be applied to other measured data in real LV DC grids in order to check the validity and extension for any different topology and condition, as it is stated in ‘Conclusions and future work’.
Reviewer 2 Report
Comments and Suggestions for Authors(1)The article lacks cutting-edge research analysis related to the topic of the paper, about the effect of Sampling Frequency in Power Quality parameters in a Real Low Voltage DC Microgrid.
(2) The specific experimental circuit should be designed out in the third part of the article.
(3) The coordinate axesshould be annotated with coordinate axis units in Figures 1 and 2.
(4) It is necessary to demonstrate these reasons why the middle section of the curve shown in Figure 3 is always 0, and the same problem also occurs in Figures 4, 5, and 6.Meanwhile, it is necessary to analyze why the voltage value fluctuates so much?
(5) Why choose sampling frequencies such as 5K, 10K, 25K, 50K, etc. in Table 3, instead of continuous sampling frequencies, or why not consider sampling frequencies such as 6K, 7K, 7.8K?
(6) Why was the maximum voltage value shown in Table 5 not compared under the same accuracy?
(7) Could the author consider whether the suggested sampling frequency should be 25KHz or within a certain range?
Author Response
Comment 1: The article lacks cutting-edge research analysis related to the topic of the paper, about the effect of Sampling Frequency in Power Quality parameters in a Real Low Voltage DC Microgrid.
Response 1:
Actually we have not found any study in which a similar sampling frequency analysis is presented. As it is stated in Introduction, in all mentioned articles the initially selected sampling rate remained fixed during all the study. Anyway, two new papers are added as references, both corresponding to theorical tests, comprising generated and measured signals in laboratory or synthetic signals with three levels of white Gaussian noise: [11], [12].
Comment 2: The specific experimental circuit should be designed out in the third part of the article.
Response 2:
New Figure 1 shows a simplified schematic diagram of the monitored DC microgrid (see subsection 3.1).
Comment 3: The coordinate axes should be annotated with coordinate axis units in Figures 1 and 2
Response 3: Both figures have been modified to include coordinate axis units.
Comment 4: It is necessary to demonstrate these reasons why the middle section of the curve shown in Figure 3 is always 0, and the same problem also occurs in Figures 4, 5, and 6. Meanwhile, it is necessary to analyze why the voltage value fluctuates so much?
Response 4:
Those Figures (now, renumbered as #4 to #7 due to the addition of new Figure 1) are replotted to change Y-axis from linear to logarithmic, so it can be shown that curve data actually never reach zero, but get drastically reduced in centered hours. Anyway, the aim of those representations is not knowing the exact value of DTW areas at each hour, but the evolution of them along the day.
As it is stated in subsequent paragraphs, it can be concluded that DTW correlation among frequencies presents a more scattered behaviour at night than daylight hours. This may be explained under the assumption of white noise presence during the period in which solar panels and DC/AC inverters do not work due to the lack of PV generation.
Comment 5: Why choose sampling frequencies such as 5K, 10K, 25K, 50K, etc. in Table 3, instead of continuous sampling frequencies, or why not consider sampling frequencies such as 6K, 7K, 7.8K?
Response 5:
9 frequencies were studied (1, 2, 4, 5, 10, 25, 50 and 100 kHz, against 200 kHz). Indeed, the first 8 values were selected to be integer submultiples of 200 kHz. Surely a continuous series of sampling frequencies, ranging an interval from 1 to 200 kHz, would constitute a more extensive and accurate study, but it would require a huge effort as well. Anyway, we consider our study as a first finding to later deepen in detail covering a more specific interval, e.g. from 20 to 30 kHz in steps of 1 kHz.
Comment 6: Why was the maximum voltage value shown in Table 5 not compared under the same accuracy?
Response 6: The reviwer is right, there were inconsistent resolutions in some tables. Tables #4, #5 and #6 (note that a new Table 1 is added in section 2) were modified in order to establish a consistent resolution in all of them: 3 decimals for maximum voltage and 2 decimals for duration.
Comment 7: Could the author consider whether the suggested sampling frequency should be 25 kHz or within a certain range?
Response 7:
As it is stated in ‘Conclusions and future work’, we consider that the same approach might be applied to other measured data in real LV DC grids in order to check the validity and extension for any different topology and condition. Anyway, at least for the monitored DC grid, using a sampling frequency higher than 25 kHz seems to be a good choice.
Reviewer 3 Report
Comments and Suggestions for AuthorsThis manuscript studys the time window on how sampling frequency affects power quality parameters in DC systems. Its innovative use of the DTW algorithm for comparing time-series data, along with empirical data from a real microgrid, strengthens the study's reliability. However, the presentation of some content, technical details, and discussions need further improvement.
1. The selection of the 20-ms time window directly adopts the AC system standard without discussion on its applicability in DC systems, and the impact of the time window on measurement accuracy needs further study. Though the definition of voltage ripple is meaningful, its relation to sampling frequency isn't deeply studied in this section.
2. The section 3 doesn't explain why it only measures the DC bus voltage and one inverter's current, ignoring parameters like current ripple and power flow. This could weaken the assessment of microgrid power quality.
3. The explanation of DTW is rather technical, which may be hard for readers unfamiliar with the algorithm to understand. The rationale for choosing a one - hour time series (3600 values) for DTW analysis is computational complexity. But it's not convincing that this choice can represent the typical behavior or events of a microgrid. Moreover, Figure 1 and Figure 2 are mentioned but not described in detail.
4. The discussion of errors in Tables 3 to 5 is relatively brief, especially for the duration error of event 2 at 1 kHz (lasting 5.47 seconds). The causes of this error have not been explored.
Author Response
Comment 1: The selection of the 20-ms time window directly adopts the AC system standard without discussion on its applicability in DC systems, and the impact of the time window on measurement accuracy needs further study. Though the definition of voltage ripple is meaningful, its relation to sampling frequency isn't deeply studied in this section.
Response 1:
As it is stated in Section 2, 20-ms time window was selected in accordance with 50 Hz systems measurements according to IEC 61000-4-30. Ripple phenomenon is not part of this study, so we didn’t see it necessary to include its definition, but some related references ([1], [14]) were added in that section
Comment 2: The section 3 doesn't explain why it only measures the DC bus voltage and one inverter's current, ignoring parameters like current ripple and power flow. This could weaken the assessment of microgrid power quality.
Response 2:
The aim of this work was only focused in DC voltage, not current, power or other magnitudes. So, the results and conclusions presented there are just related to the calculation of mean or RMS voltage values and the process of detecting voltage events.
As stated in ‘Conclusions and future work’, we consider that the same approach might be extended to other parameters, such as ripple, transients or voltage fluctuations.
Comment 3: The explanation of DTW is rather technical, which may be hard for readers unfamiliar with the algorithm to understand. The rationale for choosing a one - hour time series (3600 values) for DTW analysis is computational complexity. But it's not convincing that this choice can represent the typical behavior or events of a microgrid. Moreover, Figure 1 and Figure 2 are mentioned but not described in detail.
Response 3:
The response times of the effects observed in the events of the microgrid (see Figure 10, Figure 11 and Figure 12) are of the order of seconds. For this reason, a time series with values every second is considered representative enough to not lose information for the DTW algorithm to be able to reconstruct the temporal sequence. This has been clarified in the text.
A larger explanation of examples shown in Figure 2 and Figure 3 is included (note that a new Figure 1 is added in section 3.1), highlighting the differences between them.
Comment 4: The discussion of errors in Tables 3 to 5 is relatively brief, especially for the duration error of event 2 at 1 kHz (lasting 5.47 seconds). The causes of this error have not been explored.
Response 4: A larger discussion of obtained errors, analysing separately results in each event, is included, in particular addresing the event 2.
Reviewer 4 Report
Comments and Suggestions for AuthorsDear authors, below you will find a review of your work structured by sections.
Abstract:
The abstract should be strengthened by including numerical findings or recommendations based on the work, such as the 25 kHz frequency found to be optimal for sampling.
Introduction:
This is redundant with the abstract; the motivation for the work is already written in the abstract and should not be repeated. The state-of-the-art review focuses almost exclusively on previous EMPIR work; more international studies, such as DC PQ, should be included.
Definition of DC PQ parameters
The authors assume that readers are familiar with AC standards, such as IEC 61000-4-30, without first summarizing the important points of these standards for new readers.
This section would benefit from a table summarizing DC vs. AC PQ parameters.
Microgrid Setup
This is focused on a single microgrid; more case studies should be included.
The choice of 200 kHz as the reference frequency is based solely on practical analysis; a theoretical background for this choice should be indicated.
DTW Analysis
Statistical validation of the DTW output should be included.
Figures are not always referenced in the text.
Some figures contain labels such as "anaylisis"
Voltage Event Detection
No dips were detected, and this is not further analyzed. Why is this? Authors should detail this
The hysteresis ranges are defined arbitrarily; these must be justified
Results and sampling frequency
Would benefit from statistical quantification of errors (mean absolute error, % deviation).
Discussion lacks implications for real-time monitoring systems or economic trade-offs.
Conclusions
It could be better emphasized that the importance of considering storage, ripple, and transients should be considered in future work.
The authors mention the impact of the Nyquist limit (12.5 kHz for 25 kHz sampling) but this is underexplored in the context of harmonic distortion, which sloud be expanded
Author Response
Comment 1:
Abstract: The abstract should be strengthened by including numerical findings or recommendations based on the work, such as the 25 kHz frequency found to be optimal for sampling.
Response 1: Abstract has been rewritten and a new final sentence added.
Comment 2:
Introduction: This is redundant with the abstract; the motivation for the work is already written in the abstract and should not be repeated. The state-of-the-art review focuses almost exclusively on previous EMPIR work; more international studies, such as DC PQ, should be included.
Response 2:
Actually we have not find any study in which a similar sampling frequency analysis is presented. As it is stated in Introduction, in all mentioned articles the initially selected sampling rate remained fixed during all the study. Anyway, two new papers are added as references, both corresponding to theorical tests, comprising generated and measured signals in laboratory or synthetic signals with three levels of white Gaussian noise: ([11,12]).
Comment 3: Definition of DC PQ parameters. The authors assume that readers are familiar with AC standards, such as IEC 61000-4-30, without first summarizing the important points of these standards for new readers. This section would benefit from a table summarizing DC vs. AC PQ parameters.
Response 3: New Table 1 has been added in Section 2, to present that correspondence among DC and AC PQ parameters.
Comment 4: Microgrid Setup. This is focused on a single microgrid; more case studies should be included. The choice of 200 kHz as the reference frequency is based solely on practical analysis; a theoretical background for this choice should be indicated.
Response 4:
As it is stated in ‘Conclusions and future work’, we consider that the same approach might be applied to other measured data in real LV DC grids in order to check the validity and extension for any different topology and condition. Indeed, this first study may be understood as a part of an exploratory process that might be followed by further analysis.
As mentioned in a new paragraph added before the last one in the "Introduction" section, using a sampling frequency of 200 kHz, the finally obtained database for a whole period of two weeks measurements occupies 507 Gb compressed, which represents a huge memory space close to the available limit.
Comment 5: DTW Analysis. Statistical validation of the DTW output should be included. Figures are not always referenced in the text. Some figures contain labels such as "anaylisis"
Response 5:
Thank you for pointing out the statistical validation of the DTW method. It is indeed important to validate accuracy and replicability. As the analysis presented in this work is exploratory using real microgrid data, we think DTW results are promising given the fact that are consistent in two different data days, and they are also consistent with the event analysis. We also think that further data gathering and analysis coming from other microgrids would be beneficial to that validation. We have mentioned this topic in ‘Conclusions and future work’.
It was checked that all figures are referenced in the text. Spelling errors were corrected.
Comment 6: Voltage Event Detection. No dips were detected, and this is not further analyzed. Why is this? Authors should detail this
Response 6: It is included in the text a little explanation for those results: during the measurement period mean voltage data ranges from 47.340 V (minimum) to 53.059 V (maximum), presenting an average of 49.439 V and a standard deviation of 1.524 V.
Comment 7: Voltage Event Detection. The hysteresis ranges are defined arbitrarily; these must be justified
Response 7: As it is stated in the paragraph above Table 2 (note new Table 1 is added in clause 2), voltage detection limits (including swell, dip and hysteresis thresholds) were set in accordance to usual values considered in IEC 61000-4-30. In addition, they are exactly the same that were previously used in referred paper [29].
Comment 8: Results and sampling frequency. Would benefit from statistical quantification of errors (mean absolute error, % deviation). Discussion lacks implications for real-time monitoring systems or economic trade-offs.
Response 8:
6 new tables are added to show maximum voltage and duration errors for each sampling frequency in each recorded event (see Table 7, Table 8, Table 9, Table 10, Table 11 and Table 12).
A DC analyzer should be able to follow 25 kHz, performing periodical tasks every 40 µs to calculate the PQ parameters presented in this work. This does not seem a very stringent requirement for current hardware. On the other hand, 25 kHz could require more computational resources if frequency spectrum is calculated.
Comment 9: Conclusions. It could be better emphasized that the importance of considering storage, ripple, and transients should be considered in future work. The authors mention the impact of the Nyquist limit (12.5 kHz for 25 kHz sampling) but this is underexplored in the context of harmonic distortion, which should be expanded
Response 9:
It has been clarified in ‘Conclusions and future work’ section that we consider that the same approach might be applied to other measured data in real LV DC grids in order to check the validity and extension for any different topology and condition, as well as its extension to other parameters, such as ripple, transients or voltage fluctuations.
Concerning to the sampling rate selection, at least for the monitored DC grid, using a sampling frequency higher than 25 kHz seems to be a good choice. Indeed, this first study may be understood as a part of an exploratory process that might be followed by further analysis. Regarding frequency analysis, some results were already presented in referred articles [8,10] (see Section 2).
Reviewer 5 Report
Comments and Suggestions for Authors- Abstract is very weak. The abstract requires significant revision to better reflect the study's objectives, methods, and findings. Author can follow following pattern: “Background (1 sentence), Aim (1 sentence), Method (2-3 sentences), Results (1-2 sentences), significance of findings (1 sentence).
- The introduction does not explicitly state the research objectives or hypotheses. While the study's focus is evident. Clearly articulate the research questions or hypotheses at the end of the introduction.
- Include more recent references on PQ assessment in DC grids to contextualize the study within the broader field.
- Several aspects of the methodology lack clarity: (i) There is no mention of whether an anti-aliasing filter was used during data acquisition. (ii) No information is provided about the calibration of measurement instruments. (iii) The manuscript does not discuss measurement uncertainties or error margins.
- The manuscript relies heavily on DTW but does not explore other statistical methods for comparing signals. Additionally, there is no discussion of statistical significance or confidence intervals for the results.
- Typographical errors in figure captions (e.g., "anaylisis" instead of "analysis") detract from professionalism. Ensure all figures are included and properly labeled and correct typographical errors.
- It is recommended that the author discuss the smooth and uninterrupted operation of DC microgrids. Author can read following article: Smooth and uninterrupted operation of standalone microgrid under high and low penetration of RESs.
- The manuscript does not discuss negative results, such as why no voltage dips were detected despite lowering the threshold.
- The conclusions are somewhat repetitive and do not strongly tie back to the initial research questions.
- Why was 200 kHz chosen as the reference sampling frequency? Was this based on theoretical considerations or empirical evidence? How does the Nyquist theorem apply to the selected sampling frequencies, particularly for capturing high-frequency distortions?
- Why was DTW chosen over other similarity measures? How were the warp area thresholds determined, and what is their physical significance? What was the computational complexity of the DTW analysis, and how was it managed for large datasets?
- Include all referenced figures and ensure they are high-quality and clearly labeled.
Need improvemens
Author Response
Comment 1: Abstract is very weak. The abstract requires significant revision to better reflect the study's objectives, methods, and findings. Author can follow following pattern: “Background (1 sentence), Aim (1 sentence), Method (2-3 sentences), Results (1-2 sentences), significance of findings (1 sentence).
Response 1: The abstract has been sigficantly rewritten and a new final sentence added following the reviewer recommendations.
Comment 2: The introduction does not explicitly state the research objectives or hypotheses. While the study's focus is evident. Clearly articulate the research questions or hypotheses at the end of the introduction.
Response 2: A new paragraph has been added at the end of the Introduction following the reviewer suggestions.
Comment 3: Include more recent references on PQ assessment in DC grids to contextualize the study within the broader field.
Response 3: Two new papers are added as references, both corresponding to theorical tests, comprising generated and measured signals in laboratory or synthetic signals with three levels of white Gaussian noise: ([11,12]).
Comment 4: Several aspects of the methodology lack clarity: (i) There is no mention of whether an anti-aliasing filter was used during data acquisition. (ii) No information is provided about the calibration of measurement instruments. (iii) The manuscript does not discuss measurement uncertainties or error margins.
Response 4: Thanks for pointing out the room of improvement in the text explaining the methodology. We have modified some issues following the specific issues you mention:
i) New paragraph added in Introduction (see also answer in point 2)
ii)) Added text related to the calibration of measurement instruments in Appendix A
ii) Added text related to measurement uncertainties in Appendix A
Comment 5: The manuscript relies heavily on DTW but does not explore other statistical methods for comparing signals. Additionally, there is no discussion of statistical significance or confidence intervals for the results.
Response 5: This first study may be understood as a part of an exploratory process that might be followed by further analysis. The use of DTW algorithm revealed promising and interesting results that might be corroborated on other measured data in real LV DC grids to check the validity and extension for any different topology and condition.
Comment 6: Typographical errors in figure captions (e.g., "anaylisis" instead of "analysis") detract from professionalism. Ensure all figures are included and properly labeled and correct typographical errors.
Response 6: Thank for reporting those issues. It was checked that all figures are referenced in the text. The Spelling errors pointed out have been corrected.
Comment 7: It is recommended that the author discuss the smooth and uninterrupted operation of DC microgrids. Author can read following article: Smooth and uninterrupted operation of standalone microgrid under high and low penetration of RESs.
Response 7: This topic has been raised when discussing the behaviour of this specific microgrid. A new reference to the paper [19] has been included in section 3.1.
Comment 8: The manuscript does not discuss negative results, such as why no voltage dips were detected despite lowering the threshold
Response 8: A little explanation for those results has been included in the text : during the measurement period mean voltage data ranges from 47.340 V (minimum) to 53.059 V (maximum), presenting an average of 49.439 V and a standard deviation of 1.524 V. For this reason, no dip was detected.
Comment 9: The conclusions are somewhat repetitive and do not strongly tie back to the initial research questions.
Response 9: Thank you for pointing out this. This text is written for a clearer and more comprehensive presentation.
Comment 10: Why was 200 kHz chosen as the reference sampling frequency? Was this based on theoretical considerations or empirical evidence? How does the Nyquist theorem apply to the selected sampling frequencies, particularly for capturing high-frequency distortions?
Response 10:
As mentioned in a new paragraph added at the end of the Introduction, using a sampling frequency of 200 kHz, the finally obtained database for a whole period of two weeks measurements occupies 507 Gb compressed, which represents a huge memory space close to the available limit. Indeed, this first study may be understood as a part of an exploratory process that might be followed by further analysis. Regarding frequency analysis, some results were already presented in referred articles [8,10] (see Section 2).
Comment 11: Why was DTW chosen over other similarity measures? How were the warp area thresholds determined, and what is their physical significance? What was the computational complexity of the DTW analysis, and how was it managed for large datasets?
Response 11: We consider that the same approach might be extended on other measured data in real LV DC grids in order to check the validity and extension for any different topology and condition. Trying to clarify that, the text of the conclusion have been rewritten.
Comment 12: Include all referenced figures and ensure they are high-quality and clearly labeled.
Response 12: We have reviewed all figures following the reviwers suggestion. All figures have been enlarged to facilitate its visualization. It was checked that all figures are referenced in the text.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsAll review comments have been revised, and it is agreed that the article will be accepted.
Comments on the Quality of English LanguageAll review comments have been revised, and it is agreed that the article will be accepted.
Author Response
Thank you very much for your comments
Reviewer 3 Report
Comments and Suggestions for Authors
The manuscript fails to adequately address the four reviewer comments; therefore, the comments are restated in detail below, together with the reasons why the authors’ replies are unsatisfactory.
1. Comment 1: The authors provide no justification for the 20 ms time window’s applicability to DC systems, fail to explore the relationship between ripple and sampling frequency, and do not clarify how references [1] and [14] support the choice of window length. The authors should justify the 20 ms window through frequency-component analysis, clarify the limitations of their ripple analysis with supporting data, and specify how references [1] and [14] validate the adopted approach.
2. Comment 2: While the authors state that the study focuses exclusively on DC voltage measurements and therefore excludes current ripple and power flow, they offer no rationale for selecting only the DC-bus voltage and the current of a single inverter. Moreover, they omit any discussion of the microgrid’s operational context (e.g., daily voltage and power distributions). The authors should explain parameter selection in terms of microgrid topology or hardware limitations and include a figure or table illustrating daily voltage and power distributions to support analyses of daytime and nighttime behaviour.
3. Comment 3: The authors justify the use of a one-hour time series (3 600 values) for DTW analysis by noting that microgrid events exhibit response times on the order of seconds; they also claim to have improved the descriptions of Figures 2 and 3. However, they provide no data demonstrating that a one-hour series is representative, nor do they specify the enhancements to the figure descriptions (e.g., quantitative warping-path analysis). The authors should add event-frequency or voltage-fluctuation statistics to justify the one-hour interval and include a table summarising DTW results and the differences in warping paths.
4. Comment 4: The authors do not present a specific analysis of the error associated with Event 2, such as the influence of sampling rate or the characteristics of the voltage curve. A detailed error analysis for Event 2 should be provided, accompanied by a figure comparing the loss of sampling points at 1 kHz and the accuracy of event-boundary detection across different sampling rates.
Author Response
Comment 1: The authors provide no justification for the 20 ms time window’s applicability to DC systems, fail to explore the relationship between ripple and sampling frequency, and do not clarify how references [1] and [14] support the choice of window length. The authors should justify the 20 ms window through frequency-component analysis, clarify the limitations of their ripple analysis with supporting data, and specify how references [1] and [14] validate the adopted approach.
Response 1:
The reviewer points out an interesting question about the behavior of the PQ parameters as a function of the window width and a parallel frequency analysis in order to understand and justify the results. This may be a very complementary study, and it is reserved for future work.
Concerning the voltage ripple, DTW analysis was also tried for voltage ripple, but the obtained results were not significant to draw conclusions. A lower variation of this parameter along the day made more difficult the use of this algorithm. This was reflected in the text adding the following phase: ”The same analysis was also tried for voltage ripple, but the obtained results applying this technique were not significant to draw conclusions. A lower variation of this PQ parameter along the day made more difficult the use of this algorithm” In Addition, a new equation (2) was added in Section 2 to present the way in which voltage ripple was calculated.
The relationship between ripple and sampling frequency could be explored also by varying the computation width. These points have been highlighted in the “conclusion and future work” section. We have added the following text:
“As future work, the behavior of the PQ parameters as a function of the temporal window width could be explored. Additionally, a parallel frequential analysis could be carried out in order to understand and justify the results.”
Additionally, we have tried to clarify our choice of window. The text in Section 2 was improved and a new sentence is added in Section 5 to mention that 20-ms time windows were applied in accordance with IEC 61000-4-30, as previously stated in Section 2 and also done in Section 4. The relevant phrase in Section 2 now reads:
“In accordance with the prescription of IEC 61000-4-30 [13] regarding AC measurements for 50 Hz systems, time window for these calculations should be established in 20 ms (for events detection), being refreshed every 10 ms (if class A requirements are applied).”
Comment 2: While the authors state that the study focuses exclusively on DC voltage measurements and therefore excludes current ripple and power flow, they offer no rationale for selecting only the DC-bus voltage and the current of a single inverter. Moreover, they omit any discussion of the microgrid’s operational context (e.g., daily voltage and power distributions). The authors should explain parameter selection in terms of microgrid topology or hardware limitations and include a figure or table illustrating daily voltage and power distributions to support analyses of daytime and nighttime behaviour.
Response 2:
The reviewer highlights some points that require clarity in the text, such as the use of only voltage data, the choice of the point of measurement and the lack of operation information.
Concerning the Voltage only analysis, we agree with the reviewer that the previous text was misleading, stating that current was measured and stored. In the measurement campaign presented in this paper, only the voltage was stored in order to maximize the amount of acquired data. This has been clarified in the text and modified the experimental setup figure (Figure 1). Given the fact that the system only stored voltage, the point of measurement is less crucial.
The description of the experimental setup is now:
“The data acquisition chain was designed to digitize the voltage of the bus. It was also able to get the voltage of AC side of the same inverter in order to study a possible correlation between AC PQ parameters and DC PQ indices [7], but the AC side was not digitized for this work.
[…]
First, continuous mode was configured. […] The higher Sampling Rate was selected to be 200 kHz due to technical limitations: the hard disk size, the objective of taking data for two weeks […] The acquisition system stored only DC voltage in order to save space. […]”
Concerning the operational context, we have added Voltage mean, standard deviation and min/max per hour in order to support the statements of the different behavior and the selection of this parameter. A new appendix (Appendix A) has been added to present its behavior and statistics. In Figure A1, the stability of the night hours can be seen in contrast with the activity in the hours with PV generation. This effect is more evident at the beginning and end of the generation, with a good agreement with DTW findings.
On the other hand, DTW analysis was also tried for voltage ripple, as mentioned in the response to comment 1.
Comment 3: The authors justify the use of a one-hour time series (3 600 values) for DTW analysis by noting that microgrid events exhibit response times on the order of seconds; they also claim to have improved the descriptions of Figures 2 and 3. However, they provide no data demonstrating that a one-hour series is representative, nor do they specify the enhancements to the figure descriptions (e.g., quantitative warping-path analysis). The authors should add event-frequency or voltage-fluctuation statistics to justify the one-hour interval and include a table summarising DTW results and the differences in warping paths.
Response 3:
The reviewer is right, the text lacked clarity in some points and additional data help to give more context. The one-hour interval is selected to have enough variations in the signal to be temporally reconstructed with the DTW algorithm. To support that statement, the statistical analysis presented in the new appendix (Appendix A) commented earlier.
The text describing Figures 2 and 3 and has been improved, now pointing to the “Appendix A” in order to justify the selection of both intervals:
“To illustrate this technique, two examples of DTW results are presented for 1 kHz (’query index’) against 200 kHz (’reference index’) at two different hours that present quite different trends. In Figure 2, obtained at 7 am UTC, DTW analysis shows a very good correspondence between frequencies; while in Figure 3, obtained at 12 pm UTC, DTW analysis shows a clearly worse correspondence between both. Consequently, the resulting warp area in Figure 2 is smaller than the area in Figure 3. These two different intervals were selected taking into account the temporal grid behavior described in Appendix A.”
Additionally, a new appendix (Appendix C) is added to present the numerical results of applying DTW algorithm on mean and RMS voltage.
Comment 4: The authors do not present a specific analysis of the error associated with Event 2, such as the influence of sampling rate or the characteristics of the voltage curve. A detailed error analysis for Event 2 should be provided, accompanied by a figure comparing the loss of sampling points at 1 kHz and the accuracy of event-boundary detection across different sampling rates.
We have added two different sampling frequencies data (1 kHz, 2 kHz) to the recorded event figures (Figures 10, 11 and 12). This is especially remarkable in the detection of event 2. The produced effect of sampling frequency in the event detection is due to the use of less points to calculate the value of mean voltage, increasing that way the statistical fluctuation and affecting especially the duration of the event. This effect has been reflected in the text, in the discussion on the event 2. We have added the following text:
“In case of event 2, the maximum errors at 1 kHz are even higher than those obtained in event 1, resulting in 83 mV and 5.47 s. This clear inconsistency, especially in duration, is caused by the specific profile of this swell, in which there is a rapid recovery curve described by an asymptote bordering the hysteresis level.
This can be observed in Figure 11, showing the effect of sampling frequency in the event detection, due to the use of less points to calculate the value of mean voltage, increasing in that way the statistical fluctuation and exceeding the hysteresis level which causes a significant reduction in the obtained event duration."
Reviewer 4 Report
Comments and Suggestions for AuthorsDear authors, thank you for taking the time to improve your manuscript. The present version can be published as it is
Author Response
Thank you very much for your comments
Reviewer 5 Report
Comments and Suggestions for AuthorsI am satisfied with author's response. In my opinion, this article is ready for publication.
Author Response
Thank you very much for your comments
Round 3
Reviewer 3 Report
Comments and Suggestions for AuthorsThe revisions, including the clarification of the 20 ms window per IEC 61000-4-30, the addition of statistical data in Appendix A, and the enhanced DTW analysis with new appendices, adequately address the concerns raised. The inclusion of sampling frequency effects for Event 2 and the operational context via voltage statistics strengthens the manuscript. The manuscript is now suitable for acceptance. Overall, the revised article is now essentially in acceptable condition for publication.
While some suggestions (e.g., ripple-sampling frequency relationship) are complex and theoretical development that lie beyond the scope of a single revision. I therefore encourage the authors to treat them as a valuable work for future research.
