Sample Entropy Based Net Load Tracing Dispatch of New Energy Power System

Round 1

Reviewer 1 Report

Requirements to improve the introduction:

- please stress out more the problem you address and sustain it with some quantitative information (e.g. high costs, low MTBF or low efficiency)

- please specify the contribution of the work and describe the scientific progress compared to state of the art

Describe the research methodology:

- please describe the overall picture of the research methodology and the experimental setup you have used, describe the terms used and the parameters and data characteristics. To be more specific, please present the architecture of the setup you use (e.g. a diagram with the power units, consumers, etc.), describe also why you selected the time frame for the data and the specific characteristics of the time frame (e.g. weather conditions, consumers distribution)

- link also these information with the discussion of the results (how general are the date and how particular are the results)

Theoretical model and research methods

- Section 3 describes the mathematical model for the optimization problem, but some of the equations and some of the transformations are not described (e.g. eq. 24-27, 34-37). Please improve the description of this part of the presentation

- The algorithm in section 3.3 is briefly specified. Please describe how the steps are implemented (e.g. how the time series are divided on subsequences? On what basis?)

Results and conclusions:

- I am not convinced, based on one single experiment, that the proposed solution is more cost efficient. The costs you estimate for the two cases you consider are very close each other. The experiment could be a particular solution. You have either to demonstrate the cost of the solution is lower or provide more experiments for that.

- On the other hand I am satisfied with a result in which you obtain similar costs but you improve the stability of the system.

Some other minor changes or clarifications:

- Convention vs. conventional loads (lines 45, 89, 104 etc. vs. lines 14, 320) - please use the same term and explain it.

- Regulation (line 108) - you may use pattern instead

- Lines 225 and 228 - "will at" probably you mean will be at

- Line 55: "assistant" probably should be assist

- Line 118 - caption for Fig. 2 should be placed on the same page with the figure

- Line 134 - "vise verse" should be vice versa

- I would expect to see some references for the affirmations in paragraph at lines 125-131 regarding the values for data loss

Author Response

Dear Editor,

Thank you for your letter and for the comments concerning our manuscript entitled “Sample Entropy Based Net Load Tracing Dispatch of New Energy Power System” (ID: energies-400391). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are highlighted in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Reviewer 1 Comments

Point 1: Requirements to improve the introduction:

- please stress out more the problem you address and sustain it with some quantitative information (e.g. high costs, low MTBF or low efficiency)

- please specify the contribution of the work and describe the scientific progress compared to state of the art

Response 1:

Thank you very much for your comments. We have improved the introduction and highlighted the revisions in the paper on Page1 Line 32-43, Page 2 Line 60-85 and Page 3 Line 95-102 and 109-120.

Point 2: Describe the research methodology:

- please describe the overall picture of the research methodology and the experimental setup you have used, describe the terms used and the parameters and data characteristics. To be more specific, please present the architecture of the setup you use (e.g. a diagram with the power units, consumers, etc.), describe also why you selected the time frame for the data and the specific characteristics of the time frame (e.g. weather conditions, consumers distribution)

- link also these information with the discussion of the results (how general are the date and how particular are the results).

Response 2: Thank you very much for your comments. The diagram of the Ten-Unit system comes from the IEEE 39 system, which can be seen in the follow references [1-2] and the detail data is shown in the paper in Table 2. This study is under a background of transmission grid and day-ahead power dispatch. The day-ahead power dispatch focuses on the power balance between loads and power sources and does not focus on the grid structure of the system. Power dispatch contains different time-scale. The time frame of day-ahead power dispatch is 24 hours, which can be approved by References [3] and the generation dispatching plan on generation side of China [4]. The time frame explanation has been added in the paper on Page 2 Line 71-74. The description of the data and parameters in Table 2 are added and highlighted in the paper on Page 13 Line 378-382.

[1] Fu, Y. M.; Liu, M. B.; Li, L. C. Multiobjective Stochastic Economic Dispatch With Variable Wind Generation Using Scenario-Based Decomposition and Asynchronous Block Iteration. IEEE Trans. Sustainable Energy, 2016, 7, pp. 139-149.

[2] Zhao, B. S.; Hu, Z. C.; Song, Y. H. Robust Optimization of Transmission Topology Considering Renewable Energy Sources Integration and N -1 Security Constraint. Automation of Electric Power Systems. 2018, 42, pp. 1-9.

[3] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[4] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point 3: Theoretical model and research methods:

- Section 3 describes the mathematical model for the optimization problem, but some of the equations and some of the transformations are not described (e.g. eq. 24-27, 34-37). Please improve the description of this part of the presentation

Response 3: Thank you for your comments and we are sorry for the unclear writing.

The spinning reserve chance constraints are formulated by Equation (24) and (25). The up and down reserve should cover the errors between the actual wind power output and the predicted wind power output. In order to avoid the waste of reserve sources, the reserve needs not to cover the whole error range and only to satisfy a certain probability. In addition, the upper limits of up and down reserve are shown in Equation (26) and (27).

                                                                         (24)

                           (25)

                               (26)

                                (27)

where  is the confidence coefficient and  is the actual wind power of wind farm wpi at time t.  and  are the actual up and down reserve of thermal generator pi.

The fractile is used to solve the chance constraints.

                                (33)

where Y is the random variable and  is the fractile of .  In Figure 6, the  is the upper fractile and the  is the lower fractile.  is the density function of Y. Equations (24) and (25) can be transformed into Equations (34) and (35), corresponding to the type of Equation (33).When the  is determined, the  and  can be received by calculating the inverse function through MATLAB. Thus when the function (36) is satisfied, the constraint (34) is ensured. When the function (37) is satisfied, the constraint (35) is ensured.

                      (34)

                      (35)

                          (36)

                         (37)

The descriptions of these equations have been added and highlighted on Page 10 Line 313-317 and Page 11 Line 339-345.

Point 4: Theoretical model and research methods:

- The algorithm in section 3.3 is briefly specified. Please describe how the steps are implemented (e.g. how the time series are divided on subsequences? On what basis?)

Response 4: Thank you for your comments and we are sorry for the unclear writing. The implementation steps of the power dispatch strategy are shown as follows:

1.  Renewable energy is connected to the power grid and consumed by electric loads firstly. Thus the net load time series is generated.

2.  The characteristics and numeric features of the net loads containing the slope of the adjacent points shown in Equation (1), the total number of slope sign changes, ratio of sign changing amount to net load amount shown in Equation (4) and the ratio of   proportion to the valley-to-peak of the net loads shown in Equation (5) are analyzed.

3.  The characteristics of net load mentioned in Step 2 are rolling calculated. According to the results of , the closer results are divied into one subsequence. Thus the net load time series are divided into a few certain subsequences. .

4.  The SampEn of the subsequences are calculated and the time frame are determined according to the point-in-time of the subsequences. Moreover, the generating mode of thermal generators is confirmed according to the SampEn as Equation (13) shows.

5.  The power dispatch strategy based on SampEn is conducted. A prime-dual interior point method is used to solve the optimization problem.

We have made the corrections in the paper and highlighted the revisions on Page 12 Line 355-370.

Point 5:  Results and conclusions:

- I am not convinced, based on one single experiment, that the proposed solution is more cost efficient. The costs you estimate for the two cases you consider are very close each other. The experiment could be a particular solution. You have either to demonstrate the cost of the solution is lower or provide more experiments for that.

- On the other hand I am satisfied with a result in which you obtain similar costs but you improve the stability of the system.

Response 5: Thank you very much for your comments. This dispatch strategy aims at reducing the ramping power of the thermal generators and improve the stability of the system on the basis of the economy of the system is not sacrificed. In order to certify the accuracy of the results and the generally of the conclusion, we added two cases and improved the discussion. The added two cases are shown on Page 16-22. We made accordingly correction and highlighted them in the discussion on Page 22-23.

The adding cases are as follows:

·       Case 3: the power dispatch without SampEn and the wind power reserve confidence degree is 0.95.

·       Case 4: the power dispatch based on SampEn at wind power reserve confidence degree of 0.95.

4.2.3. The results in Case 3

The power outputs of thermal generators in Case 3 are shown in Figure 17. The power outputs of pumped storage are shown in Figure 18, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power..

Figure 17. Power output curves of thermal generators in Case 3

Figure 18. Power output curves of pumped storage generators in Case 3

4.2.4. The results in Case 4

The power outputs of thermal generators based on the SampEn in Case 4 are shown in Figure 19. The power outputs of pumped storage are shown in Figure 20, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power. The power output comparisons of pumped storage in Case 3 and Case 4 are shown in Figure 21.

Figure 19. Power output curves of thermal generators in Case 4

Figure 20. Power output curves of pumped storage in Case 4

Figure 21. Power output comparisons of pumped storage in Case 3 and Case 4

4.2.6. The result comparison of Case 3 and Case 4

The operation costs, total up and down ramping power of thermal generators in Case 3 and Case 4 are shown in Table 5.

Table 5. Results comparison of Case 3 and Case 4

Point 6: Convention vs. conventional loads (lines 45, 89, 104 etc. vs. lines 14, 320) - please use the same term and explain it.

Response 6: Thank you very much for your comments, and we are sorry for the unclearly writing.  We have corrected the mistake in the paper and made them ‘electric loads’ on Page 1 Line 14, Page 2 Line 50, Page 3 Line 112, 129 and 132 and Page 12 Line 356.

Point 7:  Lines 225 and 228 - "will at" probably you mean will be at.

Response 7: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistakes in the paper and highlighted them on Page 8 Line 253 and Page 9 Line 256.

Point 8:  Line 55: "assistant" probably should be assist.

Response 8: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistake in the paper and highlighted it on Page 2 Line 60.

Point 9: Line 118 - caption for Fig. 2 should be placed on the same page with the figure.

Response 9: Thank you very much for your comments. We have corrected the captions of the figures and made them in the same page with the figure.

Point 10: Line 134 - "vise verse" should be vice versa.

Response 10: Thank you very much for your comments and I am very sorry for my spelling mistakes. We have corrected them in the paper and highlighted them on Page 5 Line 159.

Point 11: I would expect to see some references for the affirmations in paragraph at lines 125-131 regarding the values for data loss.

Response 11: Thank you very much for your comments. We are sorry for the citation missing. The related references are listed as follows and cited in the paper as Reference [43] on Page 5 Line 156.

[1]  Xu, W. The Complexity Algorithms Research of Chaotic Sequences Based on Entropy Theory. Heilongjiang University, 2017. (Line 14 on Page 16 )

[2]  Li, J. Analysis on electromagnetically acoustic emission signals using sample entropy and wavelet packet. Hebei University of Technology, 2012. (Line 2-3 on Page 6 )

[3]  Wang, X. P.; Yang, J.; Li Y. Y.; Lu C. C.; Li L. P. Dynamic analysis of heart sound signal with a sample entropy fast algorithm. Journal of Vibration & Shock, 2010, 29, pp. 115-118. (Line 22-24 on Page 2)

[4]  Shen W. H.; Qiao, K. K.; Lu, Z. M. The application of sample entropy in stock stability analysis. Journal of Shandong University, 2014, 49, pp. 50-56. (The second line from the bottom on Page 2)

Reviewer 2 Comments

Point1：The work is interesting and enough well written.

Response 1: Thank you very much for your support.

Point2：However, I have a major concern on the applicability of the method when dealing with real measurement data. In fact, it is known that most dispatch solutions, as well as state estimation approaches, can be negatively affected by the quality in input data, when considering the real case problems of measurements and/or pseudo-measurements uncertainty, meter placement and so on. In my opinion the demonstration of the proposed approach effectiveness should include some considerations on measurement uncertainty which can affect the quality of net load data. Can the authors estimate, even qualitatively, the dispatching uncertainty when considering the uncertainty on input data? I suggest the authors to include these issues in the work, taking into account the measurement uncertainties affecting the net load data and, as a consequence, the network power flows, estimations and dispatching. In this viewpoint reference should be made to some relevant papers in the field, such as those listed below, where the issues on measurement problems are considered.

A. Cataliotti, et al, “An Improved Load Flow Method for MV Networks Based on LV Load Measurements and Estimations”, (2018) IEEE Transactions on Instrumentation and Measurement, DOI: 10.1109/TIM.2018.2847818

A. Cataliotti, et al, “LV Measurement Device Placement for Load Flow Analysis in MV Smart Grids”, (2016) IEEE Transactions on Instrumentation and Measurement, 65 (5), pp. 999-1006. DOI: 10.1109/TIM.2015.2494618

Xygkis, T.C., Korres, G.N., "Optimized Measurement Allocation for Power Distribution Systems Using Mixed Integer SDP”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2967-2976. DOI: 10.1109/TIM.2017.2731019

Xygkis, T.C., Korres, G.N., Manousakis, N.M., “Fisher information-based meter placement in distribution grids via the D-optimal experimental design”, (2018) IEEE Transactions on Smart Grid, 9 (2), pp. 1452-1461. DOI: 10.1109/TSG.2016.2592102

Pegoraro, P.A., et al, “Bayesian Approach for Distribution System State Estimation with Non-Gaussian Uncertainty Models”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2957-2966. DOI: 10.1109/TIM.2017.2728398

Response 2: Thank you very much for your comments. Power dispatch contains different time-scale. The horizon optimization of day-ahead power dispatch is 24 hours [1-2]. The advance dispatch operates in the framework of a short time, such as 30 minutes [1]. The shorter time-scale can be state estimation. We have added explanations in the paper on Page 2 Line 71-74 and added the followed references numbered [17] and [18].

This paper is under the background of day-ahead power dispatch, which means the dispatch strategy should be determined according to the predicted electric load and renewable energy data. The uncertainty of net load in this paper comes from the uncertainty of electric load, photovoltaic and wind power. Usually, the consideration of photovoltaic uncertainty belongs to the frequency modulation category. In addition, in day-ahead power dispatch, the accuracy of electric load prediction can satisfy the demand of the next day power dispatch. Thus the uncertainty of the net load mainly comes from the fluctuation of wind power output. The thermal generators should provide power spinning reserve to supply the errors between the predicted wind power and actual wind power. In this paper, the reserved spare for wind power uncertainty should satisfy a confidence coefficient turn to a chance constraint problem. The spinning reserves for wind power uncertainty are shown in Equation (24) and Equation (25) in Line 318 and 319 on Page 11. The solving process is shown in Equations (28-37).

We have added explanations in the paper according to the comments and highlighted the revisions in red. The recommended references are added in the paper as References [19-23].

[1] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[2] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point3：As ad editing comment, please improve the figure quality; in some of them labels are too small and/or not clearly readable. In some cases measurement units are missing; please add them where needed.

Response 3: Thank you very much for your comments. We have enlarged the format in the figures and made the corrections according to the comments. The measurement units are improved in the paper and the revisions are highlighted in the paper on Page 7 Line 234-246.

Reviewer 3 Comments

Point 1: The improved values or outstandingly data need to show in the sections of ABSTRACT and CONCLUSIONS.

Response 1: Thank you very much for your comments. We have added the improved data in the Abstract section and Conclusions section. The revisions have been highlighted on Page 1 Line 20-24 and Page 24 Line 538-545.

Point 2: In Figs. 4 and 5, the horizontal axis description shows time (15min). This is not clear to present.

Response 2: Thank you very much for your comments. We are sorry for the unclearly writing.  The data on horizontal axis is collected every 15 minutes, and there are 1440minutes in a day. Thus there are 96 data in the horizontal axis. The description of ‘Time (15min)’ in horizontal axis has been corrected to ‘Time (minute*15)’ in Fig. 4 and Fig. 5 on Page 7-8 Line 234-246.

Point 3: The word size and format in all figures need to be revised for clearly presentation.

Response 3: Thank you very much for your comments. We have enlarged the font in the figures and made them clearer.

Point 4: In Figs.12 and 14, they seem to miss out the line of Unit 9.

Response 4: Thank you very much for your comments. Due to the power outputs of Unit 10 and Unit 9 are similar and the power output curve of Unit 9 is covered by the one of Unit 10. We have enlarged the curves of Unit 9 and Unit 10 and corrected the Fig. 12 and Fig. 14 on Page 17 Line 419 and Page 18 Line 432.

Point 5: Some special wind power harvesters can be referred in the description of Introduction for strengthening the content, such as Energies 2015, 8, 7465-7477; doi:10.3390/en8077465 and IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 1, 2014, Pyroelectric-Based Solar and Wind Energy Harvesting System.

Response 5: Thank you very much for your comments. The references have been added and cited.

Point 6: The entropy measurement is also a critical issue. Some references should be useful to enhance the scope for this article, such as Journal of Power Sources 336 (2016) 272-278; IEEE SENSORS JOURNAL, VOL. 15, NO. 12, DECEMBER 2015; Sensors 2018, 18, 3320; doi:10.3390/s18103320.

Response 6: Thank you very much for your comments. The references have been added and cited.

We tried our best to improve the manuscript and made accordingly changes in the manuscript. These changes will not influence the content and framework of the paper. Here we did not list some detailed changes, but highlighted them in the revised paper.

We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper proposes a net load tracing dispatch strategy based on sample entropy (SampEn), which is aimed at maximizing the utilization of renewable energies in power systems.

The work is interesting and enough well written.

However, I have a major concern on the applicability of the method when dealing with real measurement data. In fact, it is known that most dispatch solutions, as well as state estimation approaches, can be negatively affected by the quality in input data, when considering the real case problems of measurements and/or pseudo-measurements uncertainty, meter placement and so on. In my opinion the demonstration of the proposed approach effectiveness should include some considerations on measurement uncertainty which can affect the quality of net load data. Can the authors estimate, even qualitatively, the dispatching uncertainty when considering the uncertainty on input data? I suggest the authors to include these issues in the work, taking into account the measurement uncertainties affecting the net load data and, as a consequence, the network power flows, estimations and dispatching. In this viewpoint reference should be made to some relevant papers in the field, such as those listed below, where the issues on measurement problems are considered.

A. Cataliotti, et al, “An Improved Load Flow Method for MV Networks Based on LV Load Measurements and Estimations”, (2018) IEEE Transactions on Instrumentation and Measurement, DOI: 10.1109/TIM.2018.2847818

A. Cataliotti, et al, “LV Measurement Device Placement for Load Flow Analysis in MV Smart Grids”, (2016) IEEE Transactions on Instrumentation and Measurement, 65 (5), pp. 999-1006. DOI: 10.1109/TIM.2015.2494618

Xygkis, T.C., Korres, G.N., "Optimized Measurement Allocation for Power Distribution Systems Using Mixed Integer SDP”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2967-2976. DOI: 10.1109/TIM.2017.2731019

Xygkis, T.C., Korres, G.N., Manousakis, N.M., “Fisher information-based meter placement in distribution grids via the D-optimal experimental design”, (2018) IEEE Transactions on Smart Grid, 9 (2), pp. 1452-1461. DOI: 10.1109/TSG.2016.2592102

Pegoraro, P.A., et al, “Bayesian Approach for Distribution System State Estimation with Non-Gaussian Uncertainty Models”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2957-2966. DOI: 10.1109/TIM.2017.2728398

As ad editing comment, please improve the figure quality; in some of them labels are too small and/or not clearly readable. In some cases measurement units are missing; please add them where needed.

Author Response

Dear Editor,

Thank you for your letter and for the comments concerning our manuscript entitled “Sample Entropy Based Net Load Tracing Dispatch of New Energy Power System” (ID: energies-400391). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are highlighted in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Reviewer 1 Comments

Point 1: Requirements to improve the introduction:

- please stress out more the problem you address and sustain it with some quantitative information (e.g. high costs, low MTBF or low efficiency)

- please specify the contribution of the work and describe the scientific progress compared to state of the art

Response 1:

Thank you very much for your comments. We have improved the introduction and highlighted the revisions in the paper on Page1 Line 32-43, Page 2 Line 60-85 and Page 3 Line 95-102 and 109-120.

Point 2: Describe the research methodology:

- please describe the overall picture of the research methodology and the experimental setup you have used, describe the terms used and the parameters and data characteristics. To be more specific, please present the architecture of the setup you use (e.g. a diagram with the power units, consumers, etc.), describe also why you selected the time frame for the data and the specific characteristics of the time frame (e.g. weather conditions, consumers distribution)

- link also these information with the discussion of the results (how general are the date and how particular are the results).

Response 2: Thank you very much for your comments. The diagram of the Ten-Unit system comes from the IEEE 39 system, which can be seen in the follow references [1-2] and the detail data is shown in the paper in Table 2. This study is under a background of transmission grid and day-ahead power dispatch. The day-ahead power dispatch focuses on the power balance between loads and power sources and does not focus on the grid structure of the system. Power dispatch contains different time-scale. The time frame of day-ahead power dispatch is 24 hours, which can be approved by References [3] and the generation dispatching plan on generation side of China [4]. The time frame explanation has been added in the paper on Page 2 Line 71-74. The description of the data and parameters in Table 2 are added and highlighted in the paper on Page 13 Line 378-382.

[1] Fu, Y. M.; Liu, M. B.; Li, L. C. Multiobjective Stochastic Economic Dispatch With Variable Wind Generation Using Scenario-Based Decomposition and Asynchronous Block Iteration. IEEE Trans. Sustainable Energy, 2016, 7, pp. 139-149.

[2] Zhao, B. S.; Hu, Z. C.; Song, Y. H. Robust Optimization of Transmission Topology Considering Renewable Energy Sources Integration and N -1 Security Constraint. Automation of Electric Power Systems. 2018, 42, pp. 1-9.

[3] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[4] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point 3: Theoretical model and research methods:

- Section 3 describes the mathematical model for the optimization problem, but some of the equations and some of the transformations are not described (e.g. eq. 24-27, 34-37). Please improve the description of this part of the presentation

Response 3: Thank you for your comments and we are sorry for the unclear writing.

The spinning reserve chance constraints are formulated by Equation (24) and (25). The up and down reserve should cover the errors between the actual wind power output and the predicted wind power output. In order to avoid the waste of reserve sources, the reserve needs not to cover the whole error range and only to satisfy a certain probability. In addition, the upper limits of up and down reserve are shown in Equation (26) and (27).

                                                                         (24)

                           (25)

                               (26)

                                (27)

where  is the confidence coefficient and  is the actual wind power of wind farm wpi at time t.  and  are the actual up and down reserve of thermal generator pi.

The fractile is used to solve the chance constraints.

                                (33)

where Y is the random variable and  is the fractile of .  In Figure 6, the  is the upper fractile and the  is the lower fractile.  is the density function of Y. Equations (24) and (25) can be transformed into Equations (34) and (35), corresponding to the type of Equation (33).When the  is determined, the  and  can be received by calculating the inverse function through MATLAB. Thus when the function (36) is satisfied, the constraint (34) is ensured. When the function (37) is satisfied, the constraint (35) is ensured.

                      (34)

                      (35)

                          (36)

                         (37)

The descriptions of these equations have been added and highlighted on Page 10 Line 313-317 and Page 11 Line 339-345.

Point 4: Theoretical model and research methods:

- The algorithm in section 3.3 is briefly specified. Please describe how the steps are implemented (e.g. how the time series are divided on subsequences? On what basis?)

Response 4: Thank you for your comments and we are sorry for the unclear writing. The implementation steps of the power dispatch strategy are shown as follows:

1.  Renewable energy is connected to the power grid and consumed by electric loads firstly. Thus the net load time series is generated.

2.  The characteristics and numeric features of the net loads containing the slope of the adjacent points shown in Equation (1), the total number of slope sign changes, ratio of sign changing amount to net load amount shown in Equation (4) and the ratio of   proportion to the valley-to-peak of the net loads shown in Equation (5) are analyzed.

3.  The characteristics of net load mentioned in Step 2 are rolling calculated. According to the results of , the closer results are divied into one subsequence. Thus the net load time series are divided into a few certain subsequences. .

4.  The SampEn of the subsequences are calculated and the time frame are determined according to the point-in-time of the subsequences. Moreover, the generating mode of thermal generators is confirmed according to the SampEn as Equation (13) shows.

5.  The power dispatch strategy based on SampEn is conducted. A prime-dual interior point method is used to solve the optimization problem.

We have made the corrections in the paper and highlighted the revisions on Page 12 Line 355-370.

Point 5:  Results and conclusions:

- I am not convinced, based on one single experiment, that the proposed solution is more cost efficient. The costs you estimate for the two cases you consider are very close each other. The experiment could be a particular solution. You have either to demonstrate the cost of the solution is lower or provide more experiments for that.

- On the other hand I am satisfied with a result in which you obtain similar costs but you improve the stability of the system.

Response 5: Thank you very much for your comments. This dispatch strategy aims at reducing the ramping power of the thermal generators and improve the stability of the system on the basis of the economy of the system is not sacrificed. In order to certify the accuracy of the results and the generally of the conclusion, we added two cases and improved the discussion. The added two cases are shown on Page 16-22. We made accordingly correction and highlighted them in the discussion on Page 22-23.

The adding cases are as follows:

·       Case 3: the power dispatch without SampEn and the wind power reserve confidence degree is 0.95.

·       Case 4: the power dispatch based on SampEn at wind power reserve confidence degree of 0.95.

4.2.3. The results in Case 3

The power outputs of thermal generators in Case 3 are shown in Figure 17. The power outputs of pumped storage are shown in Figure 18, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power..

Figure 17. Power output curves of thermal generators in Case 3

Figure 18. Power output curves of pumped storage generators in Case 3

4.2.4. The results in Case 4

The power outputs of thermal generators based on the SampEn in Case 4 are shown in Figure 19. The power outputs of pumped storage are shown in Figure 20, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power. The power output comparisons of pumped storage in Case 3 and Case 4 are shown in Figure 21.

Figure 19. Power output curves of thermal generators in Case 4

Figure 20. Power output curves of pumped storage in Case 4

Figure 21. Power output comparisons of pumped storage in Case 3 and Case 4

4.2.6. The result comparison of Case 3 and Case 4

The operation costs, total up and down ramping power of thermal generators in Case 3 and Case 4 are shown in Table 5.

Table 5. Results comparison of Case 3 and Case 4

Point 6: Convention vs. conventional loads (lines 45, 89, 104 etc. vs. lines 14, 320) - please use the same term and explain it.

Response 6: Thank you very much for your comments, and we are sorry for the unclearly writing.  We have corrected the mistake in the paper and made them ‘electric loads’ on Page 1 Line 14, Page 2 Line 50, Page 3 Line 112, 129 and 132 and Page 12 Line 356.

Point 7:  Lines 225 and 228 - "will at" probably you mean will be at.

Response 7: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistakes in the paper and highlighted them on Page 8 Line 253 and Page 9 Line 256.

Point 8:  Line 55: "assistant" probably should be assist.

Response 8: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistake in the paper and highlighted it on Page 2 Line 60.

Point 9: Line 118 - caption for Fig. 2 should be placed on the same page with the figure.

Response 9: Thank you very much for your comments. We have corrected the captions of the figures and made them in the same page with the figure.

Point 10: Line 134 - "vise verse" should be vice versa.

Response 10: Thank you very much for your comments and I am very sorry for my spelling mistakes. We have corrected them in the paper and highlighted them on Page 5 Line 159.

Point 11: I would expect to see some references for the affirmations in paragraph at lines 125-131 regarding the values for data loss.

Response 11: Thank you very much for your comments. We are sorry for the citation missing. The related references are listed as follows and cited in the paper as Reference [43] on Page 5 Line 156.

[1]  Xu, W. The Complexity Algorithms Research of Chaotic Sequences Based on Entropy Theory. Heilongjiang University, 2017. (Line 14 on Page 16 )

[2]  Li, J. Analysis on electromagnetically acoustic emission signals using sample entropy and wavelet packet. Hebei University of Technology, 2012. (Line 2-3 on Page 6 )

[3]  Wang, X. P.; Yang, J.; Li Y. Y.; Lu C. C.; Li L. P. Dynamic analysis of heart sound signal with a sample entropy fast algorithm. Journal of Vibration & Shock, 2010, 29, pp. 115-118. (Line 22-24 on Page 2)

[4]  Shen W. H.; Qiao, K. K.; Lu, Z. M. The application of sample entropy in stock stability analysis. Journal of Shandong University, 2014, 49, pp. 50-56. (The second line from the bottom on Page 2)

Reviewer 2 Comments

Point1：The work is interesting and enough well written.

Response 1: Thank you very much for your support.

Point2：However, I have a major concern on the applicability of the method when dealing with real measurement data. In fact, it is known that most dispatch solutions, as well as state estimation approaches, can be negatively affected by the quality in input data, when considering the real case problems of measurements and/or pseudo-measurements uncertainty, meter placement and so on. In my opinion the demonstration of the proposed approach effectiveness should include some considerations on measurement uncertainty which can affect the quality of net load data. Can the authors estimate, even qualitatively, the dispatching uncertainty when considering the uncertainty on input data? I suggest the authors to include these issues in the work, taking into account the measurement uncertainties affecting the net load data and, as a consequence, the network power flows, estimations and dispatching. In this viewpoint reference should be made to some relevant papers in the field, such as those listed below, where the issues on measurement problems are considered.

A. Cataliotti, et al, “An Improved Load Flow Method for MV Networks Based on LV Load Measurements and Estimations”, (2018) IEEE Transactions on Instrumentation and Measurement, DOI: 10.1109/TIM.2018.2847818

A. Cataliotti, et al, “LV Measurement Device Placement for Load Flow Analysis in MV Smart Grids”, (2016) IEEE Transactions on Instrumentation and Measurement, 65 (5), pp. 999-1006. DOI: 10.1109/TIM.2015.2494618

Xygkis, T.C., Korres, G.N., "Optimized Measurement Allocation for Power Distribution Systems Using Mixed Integer SDP”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2967-2976. DOI: 10.1109/TIM.2017.2731019

Xygkis, T.C., Korres, G.N., Manousakis, N.M., “Fisher information-based meter placement in distribution grids via the D-optimal experimental design”, (2018) IEEE Transactions on Smart Grid, 9 (2), pp. 1452-1461. DOI: 10.1109/TSG.2016.2592102

Pegoraro, P.A., et al, “Bayesian Approach for Distribution System State Estimation with Non-Gaussian Uncertainty Models”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2957-2966. DOI: 10.1109/TIM.2017.2728398

Response 2: Thank you very much for your comments. Power dispatch contains different time-scale. The horizon optimization of day-ahead power dispatch is 24 hours [1-2]. The advance dispatch operates in the framework of a short time, such as 30 minutes [1]. The shorter time-scale can be state estimation. We have added explanations in the paper on Page 2 Line 71-74 and added the followed references numbered [17] and [18].

This paper is under the background of day-ahead power dispatch, which means the dispatch strategy should be determined according to the predicted electric load and renewable energy data. The uncertainty of net load in this paper comes from the uncertainty of electric load, photovoltaic and wind power. Usually, the consideration of photovoltaic uncertainty belongs to the frequency modulation category. In addition, in day-ahead power dispatch, the accuracy of electric load prediction can satisfy the demand of the next day power dispatch. Thus the uncertainty of the net load mainly comes from the fluctuation of wind power output. The thermal generators should provide power spinning reserve to supply the errors between the predicted wind power and actual wind power. In this paper, the reserved spare for wind power uncertainty should satisfy a confidence coefficient turn to a chance constraint problem. The spinning reserves for wind power uncertainty are shown in Equation (24) and Equation (25) in Line 318 and 319 on Page 11. The solving process is shown in Equations (28-37).

We have added explanations in the paper according to the comments and highlighted the revisions in red. The recommended references are added in the paper as References [19-23].

[1] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[2] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point3：As ad editing comment, please improve the figure quality; in some of them labels are too small and/or not clearly readable. In some cases measurement units are missing; please add them where needed.

Response 3: Thank you very much for your comments. We have enlarged the format in the figures and made the corrections according to the comments. The measurement units are improved in the paper and the revisions are highlighted in the paper on Page 7 Line 234-246.

Reviewer 3 Comments

Point 1: The improved values or outstandingly data need to show in the sections of ABSTRACT and CONCLUSIONS.

Response 1: Thank you very much for your comments. We have added the improved data in the Abstract section and Conclusions section. The revisions have been highlighted on Page 1 Line 20-24 and Page 24 Line 538-545.

Point 2: In Figs. 4 and 5, the horizontal axis description shows time (15min). This is not clear to present.

Response 2: Thank you very much for your comments. We are sorry for the unclearly writing.  The data on horizontal axis is collected every 15 minutes, and there are 1440minutes in a day. Thus there are 96 data in the horizontal axis. The description of ‘Time (15min)’ in horizontal axis has been corrected to ‘Time (minute*15)’ in Fig. 4 and Fig. 5 on Page 7-8 Line 234-246.

Point 3: The word size and format in all figures need to be revised for clearly presentation.

Response 3: Thank you very much for your comments. We have enlarged the font in the figures and made them clearer.

Point 4: In Figs.12 and 14, they seem to miss out the line of Unit 9.

Response 4: Thank you very much for your comments. Due to the power outputs of Unit 10 and Unit 9 are similar and the power output curve of Unit 9 is covered by the one of Unit 10. We have enlarged the curves of Unit 9 and Unit 10 and corrected the Fig. 12 and Fig. 14 on Page 17 Line 419 and Page 18 Line 432.

Point 5: Some special wind power harvesters can be referred in the description of Introduction for strengthening the content, such as Energies 2015, 8, 7465-7477; doi:10.3390/en8077465 and IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 1, 2014, Pyroelectric-Based Solar and Wind Energy Harvesting System.

Response 5: Thank you very much for your comments. The references have been added and cited.

Point 6: The entropy measurement is also a critical issue. Some references should be useful to enhance the scope for this article, such as Journal of Power Sources 336 (2016) 272-278; IEEE SENSORS JOURNAL, VOL. 15, NO. 12, DECEMBER 2015; Sensors 2018, 18, 3320; doi:10.3390/s18103320.

Response 6: Thank you very much for your comments. The references have been added and cited.

We tried our best to improve the manuscript and made accordingly changes in the manuscript. These changes will not influence the content and framework of the paper. Here we did not list some detailed changes, but highlighted them in the revised paper.

We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 3 Report

This article focuses on the dispatch on the net loads with strong uncertainty and large fluctuation. The time series is used to describe the net loads and the SampEn is utilized to evaluate the complexity level of the net loads. In the results of the experiment simulation on the Ten-Unit test system show that the fluctuations of the thermal generators are reduced together with renewable energies fully consumed. The stability and economy of the system operation are improved.

Although the paper is well organized, some problems need to be clarified as follows.

1.The improved values or outstandingly data need to show in the sections of ABSTRACT and CONCLUSIONS.

2.In Figs. 4 and 5, the horizontal axis description shows time (15min). This is not clear to present.

3.The word size and format in all figures need to be revised for clearly presentation.

4. In Figs.12 and 14, they seem to miss out the line of Unit 9.

5. Some special wind power harvesters can be referred in the description of Introduction for strengthening the content, such as Energies 2015, 8, 7465-7477; doi:10.3390/en8077465 and IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 1, 2014, Pyroelectric-Based Solar and Wind Energy Harvesting System.

6.The entropy measurement is also a critical issue. Some references should be useful to enhance the scope for this article, such as Journal of Power Sources 336 (2016) 272-278; IEEE SENSORS JOURNAL, VOL. 15, NO. 12, DECEMBER 2015; Sensors 2018, 18, 3320; doi:10.3390/s18103320.

Author Response

Dear Editor,

Thank you for your letter and for the comments concerning our manuscript entitled “Sample Entropy Based Net Load Tracing Dispatch of New Energy Power System” (ID: energies-400391). Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are highlighted in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Reviewer 1 Comments

Point 1: Requirements to improve the introduction:

- please stress out more the problem you address and sustain it with some quantitative information (e.g. high costs, low MTBF or low efficiency)

- please specify the contribution of the work and describe the scientific progress compared to state of the art

Response 1:

Thank you very much for your comments. We have improved the introduction and highlighted the revisions in the paper on Page1 Line 32-43, Page 2 Line 60-85 and Page 3 Line 95-102 and 109-120.

Point 2: Describe the research methodology:

- please describe the overall picture of the research methodology and the experimental setup you have used, describe the terms used and the parameters and data characteristics. To be more specific, please present the architecture of the setup you use (e.g. a diagram with the power units, consumers, etc.), describe also why you selected the time frame for the data and the specific characteristics of the time frame (e.g. weather conditions, consumers distribution)

- link also these information with the discussion of the results (how general are the date and how particular are the results).

Response 2: Thank you very much for your comments. The diagram of the Ten-Unit system comes from the IEEE 39 system, which can be seen in the follow references [1-2] and the detail data is shown in the paper in Table 2. This study is under a background of transmission grid and day-ahead power dispatch. The day-ahead power dispatch focuses on the power balance between loads and power sources and does not focus on the grid structure of the system. Power dispatch contains different time-scale. The time frame of day-ahead power dispatch is 24 hours, which can be approved by References [3] and the generation dispatching plan on generation side of China [4]. The time frame explanation has been added in the paper on Page 2 Line 71-74. The description of the data and parameters in Table 2 are added and highlighted in the paper on Page 13 Line 378-382.

[1] Fu, Y. M.; Liu, M. B.; Li, L. C. Multiobjective Stochastic Economic Dispatch With Variable Wind Generation Using Scenario-Based Decomposition and Asynchronous Block Iteration. IEEE Trans. Sustainable Energy, 2016, 7, pp. 139-149.

[2] Zhao, B. S.; Hu, Z. C.; Song, Y. H. Robust Optimization of Transmission Topology Considering Renewable Energy Sources Integration and N -1 Security Constraint. Automation of Electric Power Systems. 2018, 42, pp. 1-9.

[3] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[4] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point 3: Theoretical model and research methods:

- Section 3 describes the mathematical model for the optimization problem, but some of the equations and some of the transformations are not described (e.g. eq. 24-27, 34-37). Please improve the description of this part of the presentation

Response 3: Thank you for your comments and we are sorry for the unclear writing.

The spinning reserve chance constraints are formulated by Equation (24) and (25). The up and down reserve should cover the errors between the actual wind power output and the predicted wind power output. In order to avoid the waste of reserve sources, the reserve needs not to cover the whole error range and only to satisfy a certain probability. In addition, the upper limits of up and down reserve are shown in Equation (26) and (27).

                                                                         (24)

                           (25)

                               (26)

                                (27)

where  is the confidence coefficient and  is the actual wind power of wind farm wpi at time t.  and  are the actual up and down reserve of thermal generator pi.

The fractile is used to solve the chance constraints.

                                (33)

where Y is the random variable and  is the fractile of .  In Figure 6, the  is the upper fractile and the  is the lower fractile.  is the density function of Y. Equations (24) and (25) can be transformed into Equations (34) and (35), corresponding to the type of Equation (33).When the  is determined, the  and  can be received by calculating the inverse function through MATLAB. Thus when the function (36) is satisfied, the constraint (34) is ensured. When the function (37) is satisfied, the constraint (35) is ensured.

                      (34)

                      (35)

                          (36)

                         (37)

The descriptions of these equations have been added and highlighted on Page 10 Line 313-317 and Page 11 Line 339-345.

Point 4: Theoretical model and research methods:

- The algorithm in section 3.3 is briefly specified. Please describe how the steps are implemented (e.g. how the time series are divided on subsequences? On what basis?)

Response 4: Thank you for your comments and we are sorry for the unclear writing. The implementation steps of the power dispatch strategy are shown as follows:

1.  Renewable energy is connected to the power grid and consumed by electric loads firstly. Thus the net load time series is generated.

2.  The characteristics and numeric features of the net loads containing the slope of the adjacent points shown in Equation (1), the total number of slope sign changes, ratio of sign changing amount to net load amount shown in Equation (4) and the ratio of   proportion to the valley-to-peak of the net loads shown in Equation (5) are analyzed.

3.  The characteristics of net load mentioned in Step 2 are rolling calculated. According to the results of , the closer results are divied into one subsequence. Thus the net load time series are divided into a few certain subsequences. .

4.  The SampEn of the subsequences are calculated and the time frame are determined according to the point-in-time of the subsequences. Moreover, the generating mode of thermal generators is confirmed according to the SampEn as Equation (13) shows.

5.  The power dispatch strategy based on SampEn is conducted. A prime-dual interior point method is used to solve the optimization problem.

We have made the corrections in the paper and highlighted the revisions on Page 12 Line 355-370.

Point 5:  Results and conclusions:

- I am not convinced, based on one single experiment, that the proposed solution is more cost efficient. The costs you estimate for the two cases you consider are very close each other. The experiment could be a particular solution. You have either to demonstrate the cost of the solution is lower or provide more experiments for that.

- On the other hand I am satisfied with a result in which you obtain similar costs but you improve the stability of the system.

Response 5: Thank you very much for your comments. This dispatch strategy aims at reducing the ramping power of the thermal generators and improve the stability of the system on the basis of the economy of the system is not sacrificed. In order to certify the accuracy of the results and the generally of the conclusion, we added two cases and improved the discussion. The added two cases are shown on Page 16-22. We made accordingly correction and highlighted them in the discussion on Page 22-23.

The adding cases are as follows:

·       Case 3: the power dispatch without SampEn and the wind power reserve confidence degree is 0.95.

·       Case 4: the power dispatch based on SampEn at wind power reserve confidence degree of 0.95.

4.2.3. The results in Case 3

The power outputs of thermal generators in Case 3 are shown in Figure 17. The power outputs of pumped storage are shown in Figure 18, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power..

Figure 17. Power output curves of thermal generators in Case 3

Figure 18. Power output curves of pumped storage generators in Case 3

4.2.4. The results in Case 4

The power outputs of thermal generators based on the SampEn in Case 4 are shown in Figure 19. The power outputs of pumped storage are shown in Figure 20, where the positive power means the operation state is as loads absorbing power from grid and the negative power means the operation state is generating power. The power output comparisons of pumped storage in Case 3 and Case 4 are shown in Figure 21.

Figure 19. Power output curves of thermal generators in Case 4

Figure 20. Power output curves of pumped storage in Case 4

Figure 21. Power output comparisons of pumped storage in Case 3 and Case 4

4.2.6. The result comparison of Case 3 and Case 4

The operation costs, total up and down ramping power of thermal generators in Case 3 and Case 4 are shown in Table 5.

Table 5. Results comparison of Case 3 and Case 4

Point 6: Convention vs. conventional loads (lines 45, 89, 104 etc. vs. lines 14, 320) - please use the same term and explain it.

Response 6: Thank you very much for your comments, and we are sorry for the unclearly writing.  We have corrected the mistake in the paper and made them ‘electric loads’ on Page 1 Line 14, Page 2 Line 50, Page 3 Line 112, 129 and 132 and Page 12 Line 356.

Point 7:  Lines 225 and 228 - "will at" probably you mean will be at.

Response 7: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistakes in the paper and highlighted them on Page 8 Line 253 and Page 9 Line 256.

Point 8:  Line 55: "assistant" probably should be assist.

Response 8: Thank you very much for your comments. We are very sorry for our negligence. We have corrected the mistake in the paper and highlighted it on Page 2 Line 60.

Point 9: Line 118 - caption for Fig. 2 should be placed on the same page with the figure.

Response 9: Thank you very much for your comments. We have corrected the captions of the figures and made them in the same page with the figure.

Point 10: Line 134 - "vise verse" should be vice versa.

Response 10: Thank you very much for your comments and I am very sorry for my spelling mistakes. We have corrected them in the paper and highlighted them on Page 5 Line 159.

Point 11: I would expect to see some references for the affirmations in paragraph at lines 125-131 regarding the values for data loss.

Response 11: Thank you very much for your comments. We are sorry for the citation missing. The related references are listed as follows and cited in the paper as Reference [43] on Page 5 Line 156.

[1]  Xu, W. The Complexity Algorithms Research of Chaotic Sequences Based on Entropy Theory. Heilongjiang University, 2017. (Line 14 on Page 16 )

[2]  Li, J. Analysis on electromagnetically acoustic emission signals using sample entropy and wavelet packet. Hebei University of Technology, 2012. (Line 2-3 on Page 6 )

[3]  Wang, X. P.; Yang, J.; Li Y. Y.; Lu C. C.; Li L. P. Dynamic analysis of heart sound signal with a sample entropy fast algorithm. Journal of Vibration & Shock, 2010, 29, pp. 115-118. (Line 22-24 on Page 2)

[4]  Shen W. H.; Qiao, K. K.; Lu, Z. M. The application of sample entropy in stock stability analysis. Journal of Shandong University, 2014, 49, pp. 50-56. (The second line from the bottom on Page 2)

Reviewer 2 Comments

Point1：The work is interesting and enough well written.

Response 1: Thank you very much for your support.

Point2：However, I have a major concern on the applicability of the method when dealing with real measurement data. In fact, it is known that most dispatch solutions, as well as state estimation approaches, can be negatively affected by the quality in input data, when considering the real case problems of measurements and/or pseudo-measurements uncertainty, meter placement and so on. In my opinion the demonstration of the proposed approach effectiveness should include some considerations on measurement uncertainty which can affect the quality of net load data. Can the authors estimate, even qualitatively, the dispatching uncertainty when considering the uncertainty on input data? I suggest the authors to include these issues in the work, taking into account the measurement uncertainties affecting the net load data and, as a consequence, the network power flows, estimations and dispatching. In this viewpoint reference should be made to some relevant papers in the field, such as those listed below, where the issues on measurement problems are considered.

A. Cataliotti, et al, “An Improved Load Flow Method for MV Networks Based on LV Load Measurements and Estimations”, (2018) IEEE Transactions on Instrumentation and Measurement, DOI: 10.1109/TIM.2018.2847818

A. Cataliotti, et al, “LV Measurement Device Placement for Load Flow Analysis in MV Smart Grids”, (2016) IEEE Transactions on Instrumentation and Measurement, 65 (5), pp. 999-1006. DOI: 10.1109/TIM.2015.2494618

Xygkis, T.C., Korres, G.N., "Optimized Measurement Allocation for Power Distribution Systems Using Mixed Integer SDP”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2967-2976. DOI: 10.1109/TIM.2017.2731019

Xygkis, T.C., Korres, G.N., Manousakis, N.M., “Fisher information-based meter placement in distribution grids via the D-optimal experimental design”, (2018) IEEE Transactions on Smart Grid, 9 (2), pp. 1452-1461. DOI: 10.1109/TSG.2016.2592102

Pegoraro, P.A., et al, “Bayesian Approach for Distribution System State Estimation with Non-Gaussian Uncertainty Models”, (2017) IEEE Transactions on Instrumentation and Measurement, 66 (11), pp. 2957-2966. DOI: 10.1109/TIM.2017.2728398

Response 2: Thank you very much for your comments. Power dispatch contains different time-scale. The horizon optimization of day-ahead power dispatch is 24 hours [1-2]. The advance dispatch operates in the framework of a short time, such as 30 minutes [1]. The shorter time-scale can be state estimation. We have added explanations in the paper on Page 2 Line 71-74 and added the followed references numbered [17] and [18].

This paper is under the background of day-ahead power dispatch, which means the dispatch strategy should be determined according to the predicted electric load and renewable energy data. The uncertainty of net load in this paper comes from the uncertainty of electric load, photovoltaic and wind power. Usually, the consideration of photovoltaic uncertainty belongs to the frequency modulation category. In addition, in day-ahead power dispatch, the accuracy of electric load prediction can satisfy the demand of the next day power dispatch. Thus the uncertainty of the net load mainly comes from the fluctuation of wind power output. The thermal generators should provide power spinning reserve to supply the errors between the predicted wind power and actual wind power. In this paper, the reserved spare for wind power uncertainty should satisfy a confidence coefficient turn to a chance constraint problem. The spinning reserves for wind power uncertainty are shown in Equation (24) and Equation (25) in Line 318 and 319 on Page 11. The solving process is shown in Equations (28-37).

We have added explanations in the paper according to the comments and highlighted the revisions in red. The recommended references are added in the paper as References [19-23].

[1] Marannino, P.; Granelli, G. P.; Montagna, M.; Silvestri, A. Different time-scale approaches to the real power dispatch of thermal units. IEEE Trans. Power Systems, 1990, 5, pp. 169-176.

[2] Generation dispatching plan of Electricity Market on Generation Side. Available online:

http://tech.bjx.com.cn/html/20071227/59347.shtml  (accessed on 25 Dec. 2018).

Point3：As ad editing comment, please improve the figure quality; in some of them labels are too small and/or not clearly readable. In some cases measurement units are missing; please add them where needed.

Response 3: Thank you very much for your comments. We have enlarged the format in the figures and made the corrections according to the comments. The measurement units are improved in the paper and the revisions are highlighted in the paper on Page 7 Line 234-246.

Reviewer 3 Comments

Point 1: The improved values or outstandingly data need to show in the sections of ABSTRACT and CONCLUSIONS.

Response 1: Thank you very much for your comments. We have added the improved data in the Abstract section and Conclusions section. The revisions have been highlighted on Page 1 Line 20-24 and Page 24 Line 538-545.

Point 2: In Figs. 4 and 5, the horizontal axis description shows time (15min). This is not clear to present.

Response 2: Thank you very much for your comments. We are sorry for the unclearly writing.  The data on horizontal axis is collected every 15 minutes, and there are 1440minutes in a day. Thus there are 96 data in the horizontal axis. The description of ‘Time (15min)’ in horizontal axis has been corrected to ‘Time (minute*15)’ in Fig. 4 and Fig. 5 on Page 7-8 Line 234-246.

Point 3: The word size and format in all figures need to be revised for clearly presentation.

Response 3: Thank you very much for your comments. We have enlarged the font in the figures and made them clearer.

Point 4: In Figs.12 and 14, they seem to miss out the line of Unit 9.

Response 4: Thank you very much for your comments. Due to the power outputs of Unit 10 and Unit 9 are similar and the power output curve of Unit 9 is covered by the one of Unit 10. We have enlarged the curves of Unit 9 and Unit 10 and corrected the Fig. 12 and Fig. 14 on Page 17 Line 419 and Page 18 Line 432.

Point 5: Some special wind power harvesters can be referred in the description of Introduction for strengthening the content, such as Energies 2015, 8, 7465-7477; doi:10.3390/en8077465 and IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 5, NO. 1, 2014, Pyroelectric-Based Solar and Wind Energy Harvesting System.

Response 5: Thank you very much for your comments. The references have been added and cited.

Point 6: The entropy measurement is also a critical issue. Some references should be useful to enhance the scope for this article, such as Journal of Power Sources 336 (2016) 272-278; IEEE SENSORS JOURNAL, VOL. 15, NO. 12, DECEMBER 2015; Sensors 2018, 18, 3320; doi:10.3390/s18103320.

Response 6: Thank you very much for your comments. The references have been added and cited.

We tried our best to improve the manuscript and made accordingly changes in the manuscript. These changes will not influence the content and framework of the paper. Here we did not list some detailed changes, but highlighted them in the revised paper.

We appreciate for Editors and Reviewers’ warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

In Ref. [19] and [20] authors names are incorrect; please correct both references as follows:

[19] Cataliotti, A., Cervellera, C., Cosentino, V., Di Cara, D., Gaggero, M., Maccio, D., Marsala, G., Ragusa, A., Tine, G., “An Improved Load Flow Method for MV Networks Based on LV Load Measurements and Estimations”, (2018) IEEE Trans. on Instrumentation and Measurement, Early access available, DOI: 10.1109/TIM.2018.2847818

[20] Cataliotti, A.; Cosentino, V.; Di Cara, D.; Tinè, G. “LV Measurement Device Placement for Load Flow Analysis in MV Smart Grids” IEEE Trans. Instrumentation and Measurement, 2016, 65 (5), pp. 999-1006.