Correction Control Model of L-Index Based on VSC-OPF and BLS Method

Response to Reviewer 1 Comments

1. Summary

Thank you very much for taking the time to review this manuscript. As you are concerned, there are several problems that need to be solved. According to your nice suggestions, we have made related corrections to our previous manuscript. Please find the detailed responses below and the corresponding revisions in the re-submitted file. Thank you again for your kind work.

2. Point-by-point response to Comments and Suggestions for Authors

Comments 1: This paper used broad learning system to predicts the L-index. It should add some literature review about this in the Introduction.

Response 1: Thank you for reminding us of this important point. In response to your suggestions, we have amended and added the following:

The emergence of BLS provides more possibilities for the combination of AI and power systems. To quickly assess the voltage stability and correct the voltage instability state, re-search [35] established the prediction and linear correction model of L-index based on BLS. Similarly, research [36] used BLS to conduct CCT prediction analysis and correction control of power system. Research [37] proposed a state evaluation method of power system based on BLS, which improved the ability of power system to quickly respond to emergencies.

The revised section is on page 4, line 161 of the manuscript and has been marked with red highlighting.

Comments 2: Please give a detail explanation of sensitivity in the section 5.2.

Response 2: Thank you for bringing this important point to our attention. Based on your suggestion, we have added a detailed explanation about sensitivity in Section 5.2:

The sensitivity of L-index refers to the response degree of L-index to the change of generator output. If only a small adjustment to the output of a generator leads to a huge change in the system L-index, it means that the generator has a high sensitivity to L-index; Similarly, if the output of a generator changes greatly, the L-index of the system only changes slightly, indicating that the generator has a low sensitivity to the L-index. Therefore, in the correction process, it is necessary to determine the adjustment amount of the generator according to the level of sensitivity to ensure the rationality of the correction.

The addition is on page 12, line 390 of the manuscript and has been marked with red highlighting.

Comments 3: In Table 9, the authors should also calculate the relative errors between the predicted value and the actual value.

Response 3: We gratefully appreciate your valuable suggestion. According to your suggestion, we have supplemented the relevant content in Table 9. As shown on page 14 of the manuscript.

Comments 4: In Section 4.1, the authors discuss the time consumption of the Broad Learning System (BLS) versus deep learning. However, they do not provide a comparison of both the time efficiency and the accuracy of the results between BLS and deep learning. Please check it.

Response 4: Thank you very much for carefully reading our manuscript and pointing this out. The focus of our article is on the correction control of the L-index, BLS is only a means, so the comparative results of BLS, deep learning or other machine learning are not presented in Section 4.1. Following your suggestion, we cite reference [35] to prove our point, and a comparison of time efficiency and result accuracy of BLS, deep learning, and other machine learning can be found in its Tables 2 and 3. References can be found at the following:

[35] Online prediction and correction control of static voltage stability index based on Broad Learning System- https://doi.org/10.1016/j.eswa.2022.117184.

Comments 5: The authors should provide the detailed parameters of BLS in section 5.

Response 5: Thank you for your thorough reading of this paper and feedback. According to your suggestion, we give the detailed parameters and related instructions of BLS. The specific content has been marked on page 9 of the manuscript.

Comments 6: The following research can bo compared (not mine):  1: A Two-stage Multi-agent Deep Reinforcement Learning Method for Urban Distribution Network Reconfiguration Considering Switch Contribution  2: The evaluation of the first and second laws of thermodynamics for the pulsating MHD nanofluid flow using CFD and machine learning approach

Response 6: Thank you for carefully reading our paper and for your valuable suggestions. As shown in the fourth reply, we cite reference [35], which includes relevant comparisons, and we hope this is enough to support our point of view, thank you again for your valuable suggestions.

3. Response to Comments on the Quality of English Language

Point 1: can be improved

Response 1: Thank you for bringing this important point to our attention. We apologize for the poor language of our manuscript. We worked on the manuscript for a long time and the repeated addition and removal of sentences and sections obviously led to poor readability.

According to your comments, we have now worked on both the language and readability of the article. We have highlighted in red the sections with significant revisions, such as the abstract, introduction, conclusion, and the first and second paragraphs of page 17 of the article. We really hope that the language level has been substantially improved.

Thank you again for your valuable comments on this article.

Response to Reviewer 2 Comments

1. Summary

Thank you very much for taking the time to review this manuscript. As you are concerned, there are several problems that need to be solved. According to your nice suggestions, we have made related corrections to our previous manuscript. Please find the detailed responses below and the corresponding revisions in the re-submitted file. Thank you again for your kind work.

2. Point-by-point response to Comments and Suggestions for Authors

Comments 1: Please divide the introduction and literature review into two separate sections. In the introduction, explain more precisely what exactly the problem is and what research questions the authors set themselves. It should also be clearer from the literature review why these particular research methods will be used.

Response 1: Thank you very much for your constructive suggestion. Based on your suggestion, we have divided the introduction and the literature review into two separate sections.

In the introduction, we describe in detail the problems facing the current research and the problems we intend to solve, and summarize the contribution of this paper to the field of voltage stability correction control. These revisions can be viewed at line 43 on the first page of the article.

In the literature review, we illustrate in a progressive fashion why these studies were conducted. Please allow me to introduce our thinking and logic in writing this section.

Firstly, we introduce some voltage stability indexes. When the system voltage is unstable, the unstable operation mode needs to be corrected. We then discuss the research predecessors did to correct the unstable state of voltage, such as load shedding and reactive power compensation. However, these methods can result in economic losses and may not provide an optimal solution.

To address these issues, voltage stability constrained optimal power flow is a worthy research direction, which can reduce economic loss and achieve optimal results. Therefore, we next introduce related research on VSC-OPF. However, these studies require building a complete and accurate model and conducting complex simulations to obtain accurate results.

Research shows that artificial intelligence can efficiently solve the problems described above. Therefore, we finally analyze the application of AI in voltage stability analysis and optimal power flow.

Many researches demonstrate that AI is a feasible solution to address the issue in this field. It follows that our study is well-documented. Thank you again for your valuable comments.

Comments 2: The size of all figures should be increased so that the inscriptions on them can be read.

Response 2: Thank you for carefully reading our paper and for your valuable suggestions. Following your suggestion, we have increased the size of all the figures as much as possible, which we hope will be enough to present the figures more clearly.

Comments 3: The conclusions should also be more precise and confirm that all of the research questions were answered.

Response 2: Thank you for reading our paper carefully and providing us with some keen scientific insights. According to your advice, we have improved the conclusion section. We summarized the content of the article and ensured that all of the research questions addressed in the article were answered:

In this paper, a BLS-VSC-OPF model is proposed to improve the voltage stability of the system. The assessment was performed on the IEEE-30, IEEE-118, and 1047 bus systems. First, we use BLS to predict the L-index. The training and testing results show that BLS has 95% or even higher accuracy in different systems, which is sufficient to meet the requirements of practical power systems. Secondly, the BLS is combined with the VSC-OPF model for the first time to solve the problem that the sensitivity derivation process of L-index in the VSC-OPF model is complex and computationally difficult. Finally, we correct the operation mode of the L-index beyond the safe range by the BLS-VSC-OPF model. The results before and after correction show that if the L-index of an operation mode exceeds the threshold, the model can correct the L-index to within the threshold. In addition, we compare the BLS-VSC-OPF model with the BLS-LPC model. For the IEEE-30 bus system, the BLS-VSC-OPF model requires less correction times, has higher correction accuracy and no over-correction phenomenon. For the IEEE-118 bus system and the 1047-bus system, the BLS-LPC model cannot be corrected, while the BLS-VSC-OPF model maintains a good correction ability.

The corrected content can be found on page 17，line550 of the paper and is highlighted in red.

Response to Reviewer 3 Comments

1. Summary

Thank you very much for taking the time to review this manuscript. As you are concerned, there are several problems that need to be solved. According to your nice suggestions, we have made related corrections to our previous manuscript. Please find the detailed responses below and the corresponding revisions in the re-submitted file. Thank you again for your kind work.

2. Point-by-point response to Comments and Suggestions for Authors

Comments 1: It should be explained in more detail why the authors set the accuracy at 10-6 even though they referred to publication [37] and the classic interior point method.

Response 1: Thank you for carefully reading our paper and for your valuable suggestions. The voltage stability constrained optimal power flow is the optimal power flow considering the voltage stability constraint, which is an improved optimal power flow model. In the classical optimal power flow model, the algorithm accuracy is usually set to the power of 10^-6. When the duality gap of the algorithm is less than 10^-6, both inequality and equality constraints will be satisfied. Similarly, in the classical power flow model, the accuracy of the algorithm is also set to 10^-6. When the maximum amount of unbalance of the algorithm is less than 10^-6, the power balance condition is satisfied. Setting the accuracy to 10^-6 is usually able to meet the requirements of most practical power systems. Therefore, we set the accuracy to 10^-6 in the proposed model. For different systems, the convergence accuracy can be adjusted appropriately to balance the computational cost and the accuracy of the solution, but in general 10^-6 is a reasonable default choice.

According to your suggestions, we have improved the relevant content and highlighted it in red on page 7, line 286 of the manuscript.

Comments 2: A few sentences should be added under Fig. 1 to precisely describe the BLS structure

Response 2: Thank you very much for your valuable advice. In the original manuscript, we first described the structure of BLS and only at the end presented the diagram of BLS structure. According to your suggestion, we changed the position of the two and added the relevant description. We hope that such a modification will more accurately describe the structure of BLS.

The revised section is on page 6, line 242 of the manuscript, which has been marked with red highlighting.

Comments 3: BLS-LPC should be further defined by adding a description

Response 3: Thank you very much for critically pointing out this issue to us. In response to your suggestions, we have amended and added the following:

The BLS-LPC model is a linear model. The model mainly includes two parts: prediction and correction. First, BLS is used to predict the L-index of the system. When the L-index of the system is unqualified, the sensitivity of L-index is calculated by BLS and perturbation method, and then the adjustment amount of generator output is obtained by solving linear equations. Finally, the system is corrected to make the voltage return to a reasonable level. To enhance the correction capabilities of the BLS-LPC model, the correction effect of the PV nodes’ voltage with respect to the L-index is additionally considered.

The revised section is on page 15, line 477 of the manuscript and has been marked with red highlighting.

Comments 4: The authors should explain in the manuscript why, in the proposed model for the IEEE-30 bus system, the lower and upper voltage limits were set at 0.8 and 1.1, respectively, and the L-index threshold was set at 0.5

Response 4: Thank you for your careful review of our paper and for providing valuable scientific insights. The value of the L-index ranges from 0 to 1; the closer the L-index is to 1, the lower the voltage stability margin and the higher the probability of voltage collapse. When the system L-index exceeds 0.5, it generally means that the system voltage stability is low, and corrective measures need to be taken in time [35]. The threshold can be chosen based on the analysis of the specific situation. If the threshold is set too low, the economy will decrease. If the threshold is set too high, the risk of voltage collapse increases. Setting the threshold to 0.5 is a reasonable choice. In the classical optimal power flow model, the lower and upper voltage limits are generally set to 0.9 and 1.1. We consider that when L-index is less than the threshold, the system voltage is in the safe range. However, at this time, the voltage of each node in the system does not all exceed 0.9. If the voltage lower limit is set to 0.9, the voltage of all nodes will be increased to more than 0.9, resulting in the occurrence of over-correction phenomenon and the decrease of system economy. Therefore, we relax the voltage lower bound to 0.8.

We have added relevant content and highlighted them in red on page 10 of the article.

Comments 5: A similar situation that should be further explained for the IEEE-18 bus system, the lower and upper voltage limits are set to 0.8 and 1.2 respectively, and the L-index threshold is set to 0.5. Additionally, why the upper limit of the restriction increased to 1.2

Response 5: Thank you for bringing this important point to our attention. We apologize for our oversight. Due to an editing error, we wrote the upper limit of the voltage as 1.2, which is actually 1.1. The specific reason is consistent with the fourth reply. We have corrected the relevant error on page 13 of the manuscript, line 446.

Comments 6: The conclusions should emphasize the results obtained by providing the values resulting from the comparison of the models proposed in the manuscript.

Response 6: We gratefully appreciate your valuable suggestion. According to your comments, we improve the conclusion section to make it more precise. The results obtained by comparing different models are highlighted while ensuring that all research questions are answered:

In this paper, a BLS-VSC-OPF model is proposed to improve the voltage stability of the system. The assessment was performed on the IEEE-30, IEEE-118, and 1047 bus systems. First, we use BLS to predict the L-index. The training and testing results show that BLS has 95% or even higher accuracy in different systems, which is sufficient to meet the requirements of practical power systems. Secondly, the BLS is combined with the VSC-OPF model for the first time to solve the problem that the sensitivity derivation process of L-index in the VSC-OPF model is complex and computationally difficult. Finally, we correct the operation mode of the L-index beyond the safe range by the BLS-VSC-OPF model. The results before and after correction show that if the L-index of an operation mode exceeds the threshold, the model can correct the L-index to within the threshold. In addition, we compare the BLS-VSC-OPF model with the BLS-LPC model. For the IEEE-30 bus system, the BLS-VSC-OPF model requires less correction times, has higher correction accuracy and no over-correction phenomenon. For the IEEE-118 bus system and the 1047-bus system, the BLS-LPC model cannot be corrected, while the BLS-VSC-OPF model maintains a good correction ability.

The corrected content can be found on page 17, line 550 of the paper and is highlighted in red.