Use of Variable Fuzzy Clustering to Quantify the Vulnerability of a Power Grid to Earthquake Damage
Round 1
Reviewer 1 Report
The article is well written and presents a novelty in the field of power system vulnerability analysis regarding earthquake damage. As the authors state themselves, the problem of choosing the set of indicators remains, nevertheless presented results and adopted methodology establish a clear future research direction.
Author Response
Dear sir/madam:
Thank you for your positive evaluation of our manuscript, which greatly boosts the author's confidence. Thank you very much again.
Yours sincerely, Li Tianhua
Reviewer 2 Report
Identifying nodes in the grid that are highly vulnerable to earthquake damage is significant for effective pre‐earthquake damage prevention, emergency response, and post‐earthquake relief. In this paper, the vulnerability of power grid was estimated by three indicators, the probability of node disconnection, the node hierarchical level, and the node critical threshold, were chosen, and their combined ability to represent node vulnerability to damage from an earthquake event was analyzed.
The idea of the paper is interesting. Reviewer has the following comments:
1) Please test the scalability of the power grid. Often power grid is connected to 100 of nodes. Therefore, testing with 20 nodes network may not reflect the true behavior of a power grid.
2) Also, please provide a list of the variable along with their description at the start of the paper. Many variables are not described in the text.
3) The contribution of the paper is not clear. It is important to specify the main contributions at the end of the first section and support with clear method and discussions on other related work.
4) More references should be added and compared with the proposed algorithm.
5) Please provide the reference for power grid being tested in this paper.
6) Table 3 is broken on two pages. Please adjust it to one page.
Author Response
Dear sir/madam:
We feel great thanks for your professional review work on our article. According to your comments, we have tried best to modify our manuscript to meet with the requirements. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the reviewers are listed in the attached word document.
Yours sincerely, Li Tianhua
Author Response File: 
Author Response.doc
Reviewer 3 Report
This manuscript intends to introduce a methodology to quantify the vulnerability of a power grid to damages resulting from an earthquake. The authors use a combination of three indicators to "measure" the vulnerability of each node in the network, namely: - the probability of node disconnection; - the node hierarchical level; and the node critical threshold. A variable fuzzy clustering model is adopted in order to classify and order the nodes in the grid.
The concept seems to be interesting and it may be one more step forward in order to lead with this important issue.
After reading the paper, this reviewer has the following doubts/concerns/suggestions:
a) I believe that the use of the fuzzy set theory is suitable for the situation. However, I think that the authors should make more clear how this concept is used in their model, namely making clear the adopted membership function.
b) In page 4, lines 164-167, it appears that the authors use a uniform distribution to generate random numbers. Why is this distribution suitable? The authors must make this clear.
c) The authors must make clear how the procedure for the establishment of the hierarchical level may be used in networks that change dynamically their topology. This is even more important when we think in the emergent concept of smartgrids, where the network topology may be frequently changed in order to optimize its behaviour (in terms of reliability, losses, failures, etc.).
d) I believe that the legend of Figure 3 has a mistake (it should be step 2).
e) As long as I under-stood, the methodology proposed by the authors do not consider the impacts of an earthquake on transmission lines. Why is that? Is that a reasonable approach?
f) I can't understand the sentence at lines 221-222 of page 6. How the initial load may "be a product of the node degree and its adjacent node degree"? The load of a node is a product of node degrees? Is not a value in kW or kVA?
g) The approach do not account for technical constraints as the ampacity of the network elements or voltage limits.... Why the authors believe that this is not important when assessing the capacity of the network to supply loads after an earthquake that may affect some of the network elements?
h) Perhaps I missed in understanding the concept, but I can't understand the sentence in lines 229-230 of page 6 of the manuscript. The authors refer that "When the initial node i fails, the load is redistributed to the adjacent nodes, as shown in Figure 5.". This distribution does not account for the technical constraints that rule a power system? The load is distributed among the adjacent nodes in a way that is not supported by the power system constraints? The topology of the network is not accounted for?
i) The authors should apply their methodology in a bigger test network.
j) The authors must justify why the disconnection probability of some elements in table 1 is zero. Is that a practical situation? Why?
Author Response
Dear sir/madam:
We feel great thanks for your professional review work on our article. According to your comments, we have tried best to modify our manuscript to meet with the requirements. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the reviewers are listed in the attached word document.
Yours sincerely, Li Tianhua
Author Response File: 
Author Response.pdf
Round 2
Reviewer 2 Report
Authors have significantly improved the manuscript. However, the reviewer has still some concerns that need to be addressed before accepting it for publication as follows:
1) Proofreading is required. Line 223: it should be "use", not uses. Line 247, why new line starting with 1? It does not make sense.
2) Table 1 and 3 are on two pages. Please place them on a single page, each.
3) Line spacing between 279 and 280, and 286, 287 is different. Please make line spacing equal.
4) Size of equation 10 is bigger than 12 and 13. Please be consistent with sizes.
Author Response
We are really sorry for our careless mistakes. Thank you for your reminding and patience.
Some of the mistakes have been fixed. There seems to be some formatting problems in the other sections. The details are explained in the word.
Author Response File: Author Response.docx
Reviewer 3 Report
Thank you for the answers to my doubts/concerns.
I'm still having some doubts/concerns, mainly because most of the answers the authors gave are not sufficient to clarify the issues I raised in the previous review, mainly in the following items:
c) The authors assume that: "in this study, the hierarchical level is calculated only according to the initial topology of the grid.". I think this is very limiting, particularly in the emerging context of active and intelligent networks. It does not seem sufficient to assess the vulnerability of a power grid for just one of its potential configurations. Note that, by changing the topology os the network, it may be possible to restore the power supply...
e) It's true that to calculate the failure probability of the transmission line is not a easy process. However, it does not make sense for me to have power plants and substations in operation without an operational power grid ... Therefore, the authors should highlight the importance of their work in this context ...
f) / g) / h) I apologize, but I cannot understand how the electrical load may be shared across the resources that remais operacional after the earthquake without taking into account the technical constraints (load, voltage, maximum power transits, etc.) of the system. Here too, the availability of the power grid after the event (possibly reconfigured) is crucial. Thus, in my opinion, authors should improve their methodology to include these aspects.
i) I remain convinced that the methodology, in addition to being completed with the above requirements, should be tested on a larger test network.
Author Response
Thanks a lot for your comments on the manuscript, we have seriously thought about them and provided our response, and listed a few more articles as explanations.
Author Response File: Author Response.pdf
Round 3
Reviewer 3 Report
First of all, I would like to thanks the authors for their answers.
I know that some issues are not easy to account for in the models we develop. However, this should not be a reason to exclude them from a suitable model. I think the authors are right when saying that "In addition, the proponents of pure model believe that when studying the overall behavior of complex systems, refining subsystem information is unscientific and the exhaustive approach to modeling and analysis is inadvisable and incapable. In practical power network analysis, the approximate equivalent or simplified treatment of the model is common.". However, this is a valid situation when the approximations used has no a crucial impact on the results. I believe that this is not the case here.
Therefore, most of my previous questions/doubts remain. I think that the authors should, at least, assume the limitations of their model in the text of the manuscript.
Author Response
We appreciate your professional review work on our article.
According to your nice suggestions, we have listed the shortcomings in the conclusions of the paper (Including neglecting technical constraints, not considering structural changes, and the small scale of grids), and we will make improvements in future work.
Round 4
Reviewer 3 Report
First of all, I woul like to thanks the authors for their work.
I believe that the paper is suitable now.
