Review Reports - The Use of a Complex Network with NetworkX and Neplan Software for the Analysis of a Power Transmission System

Round 1

Reviewer 1 Report (New Reviewer)

Comments and Suggestions for Authors

The manuscript addresses the combination of topological analysis (NetworkX) and classical load-flow simulation (Neplan) to assess the reliability of the power transmission system in a selected region of Kosovo. The topic is timely and relevant, and the general idea of combining functional and structural analysis is appreciated. However, several issues must be addressed to improve the scientific contribution, clarity, and technical rigor of the work.

Please consider the following suggestions for improvement:

1. The manuscript presents a set of substations and transmission lines but does not provide essential technical details (e.g., voltage levels, line impedances, transformer ratings). It is also unclear whether the presented diagram reflects a real segment of the Kosovo transmission network, a simplified abstraction, or a custom model created for this study. Please describe the origin of the model and justify its representativeness.

2. Although fault counts are presented, the manuscript does not specify what types of faults occurred, how they were classified, or what technical characteristics the affected components have. Temperature data are shown, but no analytical link to the fault occurrence is provided. Including even basic correlation or trend analysis would significantly strengthen this section.

3. The two considered scenarios (one line under maintenance and one line outage) are too limited to draw meaningful conclusions about grid reliability. Although the manuscript mentions the N‑1 criterion, the proposed cases do not reflect a systematic application of N‑1 or N‑1‑1 contingency analysis. Please justify why these scenarios were selected and consider expanding the study to include more realistic and critical operating conditions (e.g., overloads, voltage collapse risk, or heavy-load scenarios).

4. Table 6 presents a correlation value (R² = 0.76) without explaining how ΔP and ΔV were computed or which statistical method was applied. Please provide the formula, dataset description, and calculation procedure. A visualization (scatter plot) would also help make the result more transparent.

5. Incorporating more advanced indicators (e.g., algebraic connectivity, effective graph resistance, vulnerability indices, edge betweenness, line criticality metrics) would enrich the methodological contribution and help justify the novelty claimed in the manuscript.

6. Figures—especially Figure 8—contain small or unclear elements and should be enhanced in resolution, font clarity, and labeling. Ensure uniform style across all figures.

7. The manuscript contains multiple grammatical issues, awkward phrasing, and inconsistencies. A full language proofreading is recommended. Try to use Grammarly to improve your English. Additionally, some references lack complete bibliographic information (e.g., missing DOIs or volume data), and several URLs are too generic to be acceptable as scientific references. The title may also benefit from greater precision and a stronger focus on the methodological contribution.

I encourage the authors to revise the manuscript in line with these suggestions and wish them success in improving their work.

Author Response

Comments and Suggestions for Authors

Please consider the following suggestions for improvement:

The manuscript presents a set of substations and transmission lines but does not provide essential technical details (e.g., voltage levels, line impedances, transformer ratings). It is also unclear whether the presented diagram reflects a real segment of the Kosovo transmission network, a simplified abstraction, or a custom model created for this study. Please describe the origin of the model and justify its representativeness.

Response:

We appreciate you bringing attention to this, and thank you for your recommendations. The presented diagram is real part of Kosovo Transmission System; we have putted the exact path under the reference no 31 (text line 834). We agree that Figure 7 a) and b) does not include all of the technical details and the certain parameters have been abstracted. We have revised the figure 7 a) by adding the voltages at 400 kV & 220 kV levels, and rate for power transformers. The power transformer at electrical substations at 110kV have been abstracted with load L. The Figures 8 a&b have been enhanced in order to show more electrical parameters and to have a clearer picture. To avoid overloading the Figure 7a) with additional parameters, such as impedance lines and line’s distance, we excluded these parameters from the display. Neplan configurations are used to establish these parameters, as well as during developing the code in Python. Since the Figure 8 is zoomed in, the text lines 516-519 are moved in 536-538, and the text lines 565-573 have been moved beneath the text lines 579-587 in order to adjust the spaces better, close to the Figures.

Although fault counts are presented, the manuscript does not specify what types of faults occurred, how they were classified, or what technical characteristics the affected components have. Temperature data are shown, but no analytical link to the fault occurrence is provided. Including even basic correlation or trend analysis would significantly strengthen this section.

Response:

Thank you very much for highlighting this and your recommendation. Although the focus of the study was not to analyze deeply the cause of faults, we have added the mainly causes of fault regarding the transmission lines and power transformers, text lines 397-399. By understanding the fault frequency, we tried to improve the reliability and security of overall power transmission system.

We have shown the temperature data, and we fully agree that the temperature and weather conditions have a direct influence on the failure frequency of overhead lines and transformers. The reader would be able to see primarily the temperature range at which the system was operated. As mentioned in text lines 422-428, we attempted to demonstrate that a further investigation and a new study is necessary to include such analysis.

The two considered scenarios (one line under maintenance and one line outage) are too limited to draw meaningful conclusions about grid reliability. Although the manuscript mentions the N‑1 criterion, the proposed cases do not reflect a systematic application of N‑1 or N‑1‑1 contingency analysis. Please justify why these scenarios were selected and consider expanding the study to include more realistic and critical operating conditions (e.g., overloads, voltage collapse risk, or heavy-load scenarios).

Response:

Thank you for the recommendation. This part of the system has some specifics. As we can see from scenarios, when there is a line under maintenance on that part (first line between SS2-SS9) and at the same time there is a trip of line SS1-SS3 (of any type like overloads, any damages etc.), the N-1 or N-1-1 security criteria can be violated (in case there is another trip: line SS5-SS6 or the second line between SS2-SS9). We agree that number of system elements (substations, overhead lines, power transformers etc.) are small. Under such circumstances, the whole idea of the study was to get the results about this case using both software’s: Neplan tool, and calculating the metrics by running the code, developed using the Python’s library NetworkX.

We agree that number of system elements (substations, overhead lines, power transformers etc.) are small one, but there is a need for a new study to get as a case whole power transmission system or more widely, the South East Europe transmission systems, for further analyses. We tried explain that on the Conclusion part text lines 733-739.

Table 6 presents a correlation value (R² = 0.76) without explaining how ΔP and ΔV were computed or which statistical method was applied. Please provide the formula, dataset description, and calculation procedure. A visualization (scatter plot) would also help make the result more transparent.

Response:

Thank you for the recommendation. We revised the manuscript and added the explanation of correlation value R² and calculated formula, text lines 673-681. We have not visualized these results; on the Table 6 we have included and shown only substations (nodes) with high correlation value.

Incorporating more advanced indicators (e.g., algebraic connectivity, effective graph resistance, vulnerability indices, edge betweenness, line criticality metrics) would enrich the methodological contribution and help justify the novelty claimed in the manuscript.

Response:

Thank you for bringing this to our attention and for the suggestion, which we wholeheartedly concur with. The degree, closeness, and betweenness were incorporated into the Python code and the manuscript that was presented. Taking into consideration the structure of the research, we are concerned that we may lose study inconsistency, experience computational complexity, have trouble interpreting the findings, and get poor correlation values by including additional indicators (algebraic connectivity, effective graph resistance, vulnerability indices, edge betweenness, line criticality metrics).

Figures—especially Figure 8—contain small or unclear elements and should be enhanced in resolution, font clarity, and labeling. Ensure uniform style across all figures.

Response:

Thank you for the recommendation. For clarity and to view the values of all technical parameters, the resolution of the Figure 8 (a and b) has been increased and Figure 8 is zoomed in.

The manuscript contains multiple grammatical issues, awkward phrasing, and inconsistencies. A full language proofreading is recommended. Try to use Grammarly to improve your English. Additionally, some references lack complete bibliographic information (e.g., missing DOIs or volume data), and several URLs are too generic to be acceptable as scientific references. The title may also benefit from greater precision and a stronger focus on the methodological contribution.

Response:

Thank you very much for highlighting this and the recommendation.

We have added the CrossRef (including DOI hyperlink) for all references, text lines 774-879.

I encourage the authors to revise the manuscript in line with these suggestions and wish them success in improving their work.

Response:

We sincerely thank the reviewer for the constructive and detailed feedback, which has significantly helped strengthen the scientific quality, clarity, and methodological rigor of our manuscript. All suggestions have been carefully addressed in the revised version, including improvements to the figures, clarification of model details, additions to the methodological description, corrections of references, and extensive proofreading of the text.

We appreciate the reviewer’s positive closing remarks and the encouragement to further improve our work. We believe that the revised manuscript now meets a substantially higher standard of clarity and technical completeness.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Fig.1 Delete one of the drawings.
Eq(2): Change the multiplication symbol. The symbol "x" in eq(3) has a different meaning.
Fig.4 Delete one of the drawings.
Fig.5 Delete one of the drawings.
Fig.5a Illegible drawing
Fig.6 Delete one of the drawings.
Fig.9 Delete one of the drawings.
Fig.10 Delete one of the drawings.

To determine the reliability of the entire power grid, it is necessary to know the elementary reliability of individual elements of this grid against various external and internal factors.
These aspects are very poorly covered in this article. Therefore, it is difficult to assess its value at this time.
Relying solely on active and reactive power values is not a valid measure for determining failure rates. High power values for one branch may be negligibly low for another branch.
There are no cognitive conclusions from the simulations. The reader may be interested in the details of the simulation and how the simulation parameters were determined, or the cognitive results for this specific network. It is difficult to find elements in this article that would be of interest to such a reader.

Author Response

Response to Reviewer 2

Comment 1.
Fig.1 Delete one of the drawings.
Eq(2): Change the multiplication symbol. The symbol "x" in eq(3) has a different meaning.
Fig.4 Delete one of the drawings.
Fig.5 Delete one of the drawings.
Fig.5a Illegible drawing
Fig.6 Delete one of the drawings.
Fig.9 Delete one of the drawings.
Fig.10 Delete one of the drawings.

Response:
We thank the Reviewer for these precise and practical comments.

Equation (2) has been corrected by replacing the ambiguous symbol “x” with the multiplication symbol “*”, in order to avoid confusion with variable notation in Eq. (3).
The apparent duplication of Figures (Fig. 1, 4, 5, 6, 9, 10) is due to the manuscript being in Track Changes mode, where both the original and revised versions are shown for transparency. In the final clean version of the manuscript, only one instance of each figure will remain, and all redundant drawings will be removed.
Figure 5a has been improved in resolution and labeling. It uses hourly data over a four-year period, which naturally results in a dense plot. Its purpose is to illustrate the temporal scope and variability of temperature conditions relevant for the grid. After the revision, the figure is more legible and its explanatory role is clarified in the caption and text.

We appreciate the Reviewer’s attention to these details, which has helped us improve the presentation quality.

Comment 2.
To determine the reliability of the entire power grid, it is necessary to know the elementary reliability of individual elements of this grid against various external and internal factors. These aspects are very poorly covered in this article. Therefore, it is difficult to assess its value at this time.
Relying solely on active and reactive power values is not a valid measure for determining failure rates. High power values for one branch may be negligibly low for another branch.
There are no cognitive conclusions from the simulations. The reader may be interested in the details of the simulation and how the simulation parameters were determined, or the cognitive results for this specific network. It is difficult to find elements in this article that would be of interest to such a reader.

Response:
We are very grateful for this detailed and critical comment, which raises important points about scope, reliability modeling, and interpretability.

We fully agree that a complete reliability assessment of a power grid requires detailed modeling of the elementary reliability of each component (lines, transformers, substations, etc.) under various external and internal factors, including environmental influences, equipment condition, and protection schemes. Relying solely on active and reactive power is indeed not sufficient to derive failure rates.

The primary objective of the present article, however, is more specific and limited in scope:

to demonstrate how combining a classical engineering tool (Neplan) for power-flow and contingency studies with complex network concepts (NetworkX) can reveal critical nodes and lines in a regional transmission subsystem, by jointly considering functional (P/Q flows, voltages) and structural (centrality, connectivity) information.

We now emphasize this more clearly in the Introduction and Conclusions, to avoid any misunderstanding that we claim to perform a full probabilistic reliability study.

In response to the Reviewer’s comments, we have:

Clarified the simulation setup and parameter sources:
- All technical parameters (line impedances, transformer ratings, voltage levels, etc.) are taken from the Neplan model of the western Kosovo transmission subsystem.
- The same data are exported via CSV and imported into Python to construct the NetworkX graph, ensuring one-to-one consistency between the Neplan and NetworkX representations. This is now explained in Section 3.3.
Explained more explicitly what the simulations show:
- The Neplan simulations under the two scenarios highlight operational stress points (e.g., increased loading on lines SS5–SS6 and substations such as SS8 and SS7).
- The NetworkX analysis identifies topologically critical nodes via centrality metrics.
- Table 6 and the associated discussion make explicit the correlation between high centrality and high ΔP/ΔV, indicating that the hybrid approach can identify elements that are both structurally and operationally critical.
Clarified the limits of the methodology:
- We explicitly state that active/reactive power and voltage deviations are used as indicators of operational stress, not as direct proxies for failure rates.
- We acknowledge that modeling failure rates requires additional statistical and probabilistic data, which are beyond the scope of this case study and will be addressed in future work on larger network models.

We believe that, with these clarifications and additions, the cognitive value and interest of the paper become more apparent, especially for readers interested in integrating complex network theory with conventional power system tools.

Closing remark

We once again thank both Reviewers for their time, constructive criticism, and helpful suggestions. We hope that the revisions and clarifications we have made adequately address the raised concerns and that the improved manuscript will now be suitable for publication in Technologies.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

This article is to address the challenges associated with the modern grid by evaluating the 662 reliability and security of the power transmission system using a combination of engineer- 663 ing Neplan software, and complex network concepts with Python NetworkX.The following are my comments:

1 Please explain the discrepancy where the main text only describes steady-state power flow analysis without any simulation results or analytical procedures, yet the conclusion claims that transient stability analysis was conducted.

2 Please explain the role of presenting temperature data in the current study for the assessment of power grid reliability and security.

3 Please clarify how the combined approach improves reliability assessment over using either Neplan or NetworkX alone, as no quantitative comparison is provided.

4 Please elaborate in detail on the physical quantities and definitions of the symbols introduced by multiple formulas (e.g., Eq. (1)–(3), (7)–(11)).

This paper focuses on proposing a hybrid analysis method for evaluating the reliability and security of power transmission systems by integrating Neplan engineering software with Python NetworkX complex network theory. However, the research should deepen the following analyses: clarify the specific methodological and result-based connections and differences between steady-state analysis (power flow calculation) and transient analysis (such as transient stability mentioned in the conclusions) to address inconsistencies in the presentation pointed out by users; quantitatively evaluate the added value of the proposed hybrid method compared to single tools (e.g., using only Neplan or only NetworkX), such as by comparing key node identification accuracy or risk assessment efficiency; Systematically elaborate quantitative correlation models linking environmental data (e.g., temperature) to component failure rates and network topology metrics to demonstrate their practical utility in reliability assessment; and provide detailed explanations of the physical significance, parameter definitions, and specific computational processes for introduced formulas (e.g., efficiency vulnerability, centrality metrics) within the case studies to ensure methodological transparency and reproducibility. By supplementing these analyses, the paper will elevate from a tool demonstration to a methodological innovation with clear validation criteria and quantifiable advantages.For reference：

[a] IEEE Transactions on Industrial Informatics, DOI: 10.1109/TII.2024.3390595

[b] IEEE Transactions on Smart Grid, vol. 16, no. 1, pp. 330-343, Jan. 2025, doi: 10.1109/TSG.2024.3445113

Author Response

Response to Reviewer 3

Comment 1.
Please explain the discrepancy where the main text only describes steady-state power flow analysis without any simulation results or analytical procedures, yet the conclusion claims that transient stability analysis was conducted.

Response:
We thank the Reviewer for pointing out this inconsistency. You are correct that the manuscript only presents steady-state (load flow) analysis, and that transient stability analysis was neither performed nor intended as part of this study.

We have now removed the incorrect reference to transient stability analysis from the Conclusions section (former line 718) and clarified that the proposed hybrid framework is, in its current form, restricted to steady-state conditions. Any extension to dynamic and transient stability analysis is explicitly mentioned as future work in the revised text.

Comment 2.
Please explain the role of presenting temperature data in the current study for the assessment of power grid reliability and security.

Response:
We appreciate this insightful question. Temperature and weather conditions have a well-known impact on the failure rates of overhead lines and transformers. Our intention in including the temperature data was to provide context for the operating environment of the studied subsystem and to show the range of climatic conditions in which the recorded failures occurred.

In the revised manuscript, we have clarified that:

The temperature time series in Figure 5 illustrate the extreme and typical operating conditions of the network over the period 2020–2023.
The number of failures per year and per component type is presented together with this meteorological context, indicating that there may be a relationship between extreme temperature events and increased outage rates.

However, we also explicitly state that the current paper focuses on structural (topological) and operational (P/Q, voltage) parameters, and does not yet perform a full statistical correlation analysis between temperature and failure rates. The revised text (around lines 422–428) now emphasizes that establishing such quantitative relationships is an important direction for future work, where regression models will be used to assess whether temperature and other meteorological variables can be integrated as probabilistic modifiers of component reliability.

Comment 3.
Please clarify how the combined approach improves reliability assessment over using either Neplan or NetworkX alone, as no quantitative comparison is provided.

Response:
Thank you for this important point. We agree that the added value of the hybrid approach should be clearly explained.

In the revised manuscript, we clarify that:

Neplan alone provides detailed functional/operational information, such as voltages, active and reactive power flows, and the impact of contingencies on specific lines and buses under steady-state conditions. It is well suited to identify overloaded elements, voltage deviations, and violations of operational limits.
NetworkX alone provides structural/topological information via complex network metrics (degree, closeness, betweenness, eigenvector centrality, etc.), identifying nodes and lines that are topologically critical within the network graph, but without directly incorporating electrical parameters or load-flow results.

The proposed hybrid method combines these two perspectives by:

Performing Neplan simulations for two scenarios and quantifying ΔP and ΔV for each monitored element;
Computing centrality metrics for the same elements using NetworkX;
Cross-mapping the results to identify elements that are both structurally central and operationally stressed.

This is summarized in Table 6, where substations such as SS8 and SS7 exhibit simultaneously:

high centrality measures (especially betweenness); and
significant active power and voltage variations between the two scenarios.

The correlation analysis (R² ≈ 0.76) reported in the revised manuscript indicates a strong alignment between structural criticality and operational stress under the considered contingencies. While this is not a full benchmark against individual tools, it demonstrates that the hybrid approach provides additional insight: it highlights elements where topological importance and operational loading coincide, which neither Neplan-only nor NetworkX-only analysis would reveal as clearly on its own.

We have expanded the explanation of this added value in the discussion around Table 6.

Comment 4.
Please elaborate in detail on the physical quantities and definitions of the symbols introduced by multiple formulas (e.g., Eq. (1)–(3), (7)–(11)).

Response:
Thank you for this recommendation. We agree that clear definitions of all variables and symbols are essential for transparency and reproducibility.

In the revised manuscript, we have:

Expanded the descriptions around Equations (1)–(3), explicitly defining all physical quantities, including normal efficiency, post-damage efficiency, vulnerability index, and the parameters used in the reliability-related formulas.
Similarly, for Equations (7)–(11) (centrality and correlation measures), we now provide explicit definitions of each symbol, including adjacency matrix entries, degree, eigenvector components, shortest path lengths, betweenness centrality terms, and the definitions of SST, SSR, and R² in the correlation analysis.

These clarifications are embedded directly in the text where the formulas are introduced, so that readers can follow the derivations and computations without ambiguity.

Comment 5.
This paper focuses on proposing a hybrid analysis method for evaluating the reliability and security of power transmission systems by integrating Neplan engineering software with Python NetworkX complex network theory. However, the research should deepen the following analyses:
(a) clarify the specific methodological and result-based connections and differences between steady-state analysis (power flow calculation) and transient analysis (such as transient stability mentioned in the conclusions) to address inconsistencies;
(b) quantitatively evaluate the added value of the proposed hybrid method compared to single tools;
(c) systematically elaborate quantitative correlation models linking environmental data (e.g., temperature) to component failure rates and network topology metrics;
(d) provide detailed explanations of the physical significance, parameter definitions, and specific computational processes for introduced formulas…
By supplementing these analyses, the paper will elevate from a tool demonstration to a methodological innovation with clear validation criteria and quantifiable advantages. For reference: [a], [b].

Response:
We are very grateful for this comprehensive and forward-looking comment, as well as for the suggested references [a] and [b]. We address the points (a)–(d) as follows:

(a) Steady-state vs. transient analysis
We fully agree that there was an inconsistency between the steady-state nature of the simulations and the mention of transient stability in the conclusions. As noted in our response to Comment 1, we have:

Removed the reference to transient stability analysis from the Conclusions;
Clarified that the current work is restricted to steady-state (load flow) conditions;
Indicated that extending the hybrid framework to dynamic and transient stability studies would require time-domain models and is considered future work, in line with the more advanced methodologies reported in [a] and [b].

(b) Quantitative evaluation of the hybrid method’s added value
Within the scope of the current case study, we have strengthened the quantitative aspect by:

Presenting the combined analysis of Neplan-based ΔP/ΔV and NetworkX centrality metrics,
Highlighting in Table 6 that nodes such as SS8 and SS7 are identified as critical by both functional and structural criteria, and
Reporting a correlation coefficient R² ≈ 0.76 between centrality metrics and power-flow variations, showing strong alignment between topological and operational criticality.

We acknowledge that a full quantitative benchmark against single-tool approaches (e.g., systematic comparison of detection rates for critical nodes, or risk assessment metrics) would require a broader set of scenarios and performance indicators, similar in spirit to the validation protocols discussed in [a] and [b]. We explicitly mention this as an important direction for future research and position the present work as a methodological demonstration on a real regional system, rather than a complete benchmarking study.

(c) Correlation models between environmental data and reliability
As discussed in our response to Comment 2, the current paper uses temperature data mainly to provide context and to illustrate the range of operating conditions. We agree that building quantitative correlation models that link environmental variables (temperature, weather extremes) to component failure rates and possibly to topological metrics would significantly enhance the practical utility of the framework.

In the revised manuscript, we now explicitly state that this is beyond the present scope but planned as future work, where statistical regression or machine-learning based methods will be applied in a manner similar to the approaches proposed in [a] and [b].

(d) Physical significance and computational details for formulas
In line with this recommendation and with Comment 4, we have:

Extended the explanations of all key formulas (efficiency/vulnerability, centrality metrics, correlation measures),
Provided clear definitions of variables and parameters, and
Described, at a high level, the computational process (e.g., how centralities are computed in NetworkX, how R² is obtained from the Neplan/NetworkX results).

These additions improve methodological transparency and reproducibility, even though the full extension to multi-scenario, probabilistic reliability modeling is left for future work.

We again thank the Reviewer for these thoughtful suggestions and for pointing us to relevant literature. We believe that the revised manuscript now has a clearer scope, better methodological transparency, and a more explicit positioning as a hybrid, real-data-based framework that can be further expanded towards the richer analyses exemplified in [a] and [b].

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

in general, in whole text, there are a lot repeating in content, such as table and figure, or expression in text. if the authors can give some explicit information how to evaluate the security and reliability of power system, not the basic theory, it is better.

1：if figure 1 has the same data in table 1, there is no need to repeat table with figure

2：please give the full expression at first appearance of abbreviation, such ash RESs in line 113

3：figure 3， the black word can not be seen in blue background

4：in section 2.2, these are the basic concept in complex networks, maybe, there is no need to introduce so such in detail.

5:figure 4 is totally same with those data in table 2, please delete the table or figure, just keep one is enough.

6: actually, figure 8 was hard to see clearly, as well as other figures

7: line 560, please give more detail explanation, why SS8 is more important, as well as SS5-SS6, with which index to get this finding.

8:figure 9 was repeated with table 5, please choose table or figure.

9: table 6, it is better to give the correlation equation in the text, which will helpful to reader to understand the relationship.

Author Response

General Comment:

In general, in whole text, there are a lot repeating in content, such as table and figure, or expression in text. If the authors can give some explicit information on how to evaluate the security and reliability of the power system, not basic theory, it is better.

Response:
We thank the Reviewer for this valuable recommendation. In the revised manuscript, we have:

Removed unnecessary repetitions in tables, figures, and explanatory text;
Streamlined the methodological descriptions to focus more explicitly on how the combined Neplan + NetworkX approach supports security and reliability assessment;
Added clearer cross-references between operational (power-flow) and structural (centrality-based) results to highlight practical evaluation criteria.

We appreciate this comment, which helped us improve the clarity and conciseness of the paper.

1. Comment:

If Figure 1 has the same data as Table 1, there is no need to repeat both.

Response:
Thank you for this observation. Indeed, Figure 1 and Table 1 present the same underlying dataset. We retain both formats because:

Table 1 provides precise numeric comparison;
Figure 1 provides a visual overview, highlighting trends and yearly patterns.

This dual presentation improves interpretability for different types of readers. We have revised the captions to clarify their complementary roles and removed redundant descriptive text.

2. Comment:

Please give the full expression at first appearance of abbreviations, such as RESs in line 113.

Response:
Thank you. We now provide the full expanded form—Renewable Energy Sources (RES)—upon its first appearance. We also ensured consistency across the entire manuscript and confirmed that all abbreviations appear in the Abbreviations List (around line 771).

3. Comment:

Figure 3: the black words cannot be seen on the blue background.

Response:
Thank you for noting this. We have improved the resolution and adjusted the color contrast and labeling of Figure 3 so that all text is now clearly visible.

4. Comment:

In Section 2.2, these are basic concepts in complex networks. Maybe there is no need to introduce them in such detail.

Response:
We appreciate this suggestion. Our aim was to ensure that the methodology section is self-contained for readers without a background in complex network theory. Nevertheless, we have now shortened several explanations and streamlined the section to improve readability while keeping essential definitions required for reproducing the analysis.

5. Comment:

Figure 4 is totally the same as Table 2; please delete one.

Response:
Thank you for this recommendation. While Figure 4 and Table 2 present the same core dataset, we intentionally include both because:

Table 2 presents exact numeric fault counts;
Figure 4 visually emphasizes temporal comparisons and distributions.

We clarified this in the text and removed redundant narrative descriptions to avoid repetition.

6. Comment:

Figure 8 is hard to see clearly, as well as other figures.

Response:
Thank you for pointing this out. We have substantially enhanced the resolution, zoom level, and labeling of Figure 8 and other figures identified as unclear. Font sizes and color contrasts have been standardized across all figures in the revised manuscript.

7. Comment:

Line 560: please give more detailed explanation why SS8 is more important, as well as SS5–SS6, and with which index this finding was obtained.

Response:
Thank you for this request for clarification. We have now expanded the explanation in the text:

Substation SS8 has the highest values in Degree, Closeness, and Betweenness Centrality in the NetworkX analysis (Table 5), indicating strong structural importance.
The SS5–SS6 transmission line becomes critical under the simulated contingency because Neplan’s security analysis shows significant increases in power flow and altered voltage conditions when this line is out of service.

This explanation has been added to the revised text to clearly connect which indices (centrality metrics and ΔP/ΔV values) support the identification of these critical elements.

8. Comment:

Figure 9 is repeated with Table 5; please choose table or figure.

Response:
Thank you. As in earlier cases, Table 5 provides numeric centrality values while Figure 9 provides a visual comparison across scenarios. The combination improves interpretability, especially when comparing scenario 1 vs. scenario 2. We have removed repetitive text to avoid redundancy while keeping both representations due to their complementary value.

9. Comment:

Table 6: It is better to give the correlation equation in the text.

Response:
Thank you for this helpful recommendation. In the revised manuscript (lines 673–681), we now include:

The full definition of R²,
The formulas for SST and SSR,
A short explanation of how ΔP and ΔV were used in the correlation analysis.

This provides a clearer understanding of how the relationship between centrality and operational variations was quantified.

Round 2

Reviewer 4 Report (New Reviewer)

Comments and Suggestions for Authors

after the revision, some information were added, I think it can be accepted for publication.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

To address the reliability and security issues of power transmission systems, this paper encourages the combination of traditional power system analysis methods with complex network-based methods. However, this idea is not new, and it was proposed. Moreover, the reviewer has the following concerns regarding the work presented in this paper:

* The motivation of the work in this paper is not clear. While this paper focuses on the reliability and security issues of power transmission systems, it does not specify what issues traditional power system analysis methods cannot address, so that the complex network-based methods are needed.

* The contribution is weak. The major contribution of this paper is the method described in subsection 3.3. This method is not novel and simply compares the results of traditional power system analysis methods and those from centrality metrics from complex network analysis.

* In this proposed method, the centrality metrics from complex network analysis can only provide insights into the topology of the transmission system, but they ignore the functionality of the transmission system. Thus, the centrality metrics may not provide useful insights for system operators and planners. For instance, a generator bus may connect to a power system only via a line, but losing the generator may cause a power imbalance and even cascading failures. The purely topological metrics cannot identify such critical generators.

* According to the proposed method, the evaluation results of centrality metrics from complex network analysis need to be compared with power flow analysis and transient stability analysis. However, such a comparison is not presented in Section 4. Thus, the conclusions of this paper are concerned.

Author Response

Reviewer 1:

Comments and Suggestions for Authors

Response to Reviewer 1

We sincerely thank the reviewer for their careful reading, constructive comments, and insightful feedback, which have significantly helped us improve the clarity, motivation, and scientific contribution of the paper.
Below we address each comment point by point and indicate the corresponding revisions in the manuscript (highlighted in the revised version).

Comment:

“The motivation of the work in this paper is not clear. While this paper focuses on the reliability and security issues of power transmission systems, it does not specify what issues traditional power system analysis methods cannot address, so that the complex network-based methods are needed.”

Response:
We thank the reviewer for this important observation.
We have clarified the motivation in the Introduction by explicitly identifying the limitations of traditional power flow and contingency analyses and explaining why complex network theory provides additional value.
A new paragraph was added (text lines 180-186):

“Traditional power flow and contingency analyses, while effective for steady-state studies, are limited in capturing the topological vulnerabilities and interdependencies of grid components. These approaches cannot quantify how the failure of a non-critical component (in power terms) may trigger cascading effects through the network’s structure. Therefore, this paper addresses the gap by combining power system modeling (functional analysis) with complex network metrics (structural analysis), providing a dual perspective that links grid functionality and topology.”

This modification clarifies the research gap and provides a stronger rationale for combining both approaches.

Comment:

“The contribution is weak. The major contribution of this paper is the method described in subsection 3.3. This method is not novel and simply compares the results of traditional power system analysis methods and those from centrality metrics from complex network analysis.”

Response:
We have strengthened the novelty and contribution of the paper in Section 3.3 (The methodology used) by highlighting that the proposed method introduces a cross-validation framework that integrates both topological and operational data, allowing quantitative ranking of nodes not only by connectivity but also by operational sensitivity.
The new paragraph now reads (text lines 187-190):

“Unlike previous works that use network metrics in isolation, our approach systematically integrates these metrics with engineering simulation data from Neplan. The novelty lies in the cross-validation framework between the topological centrality indices and power flow parameters (active/reactive power, voltage deviation). This integration enables quantitative ranking of nodes not only by connectivity but also by operational sensitivity.”

This clarification makes the methodological contribution more explicit and highlights its added value over existing studies.

Comment:

“In this proposed method, the centrality metrics from complex network analysis can only provide insights into the topology of the transmission system, but they ignore the functionality of the transmission system. Thus, the centrality metrics may not provide useful insights for system operators and planners.”

Response:
We fully agree with the reviewer that the functional aspects of the grid must be addressed.
Therefore, a new paragraph was added to Section 4.2 to bridge the topological and functional domains. The paragraph states (text lines 584-589):

“While centrality metrics provide a purely topological view, we introduce an interpretive mapping between network measures and physical system parameters. For example, nodes with high betweenness centrality that also exhibit significant active/reactive power exchange in Neplan simulations are classified as functionally critical. This cross-mapping allows the identification of elements whose failure could lead to instability or imbalance, even if their topological degree is moderate.”

This addition directly addresses the reviewer’s concern by demonstrating that functional significance is explicitly considered in the proposed analysis.

Comment:

“According to the proposed method, the evaluation results of centrality metrics from complex network analysis need to be compared with power flow analysis and transient stability analysis. However, such a comparison is not presented in Section 4. Thus, the conclusions of this paper are concerned.”

Response:
We appreciate this valuable comment.
To address it, a new subsection and comparison were added at the end of Section 4 (page 32–33), including a new Table 6 that correlates the centrality metrics from NetworkX with the operational results from Neplan simulations. The new text reads (text lines 625-630).

“To validate the topological analysis, the results of the centrality ranking were compared with the outcomes from the Neplan power flow simulations. Table 6 summarizes the correlation between high-centrality substations and those exhibiting significant power flow variations or voltage deviations in both simulated scenarios. The correlation coefficient (R² = 0.76) indicates strong alignment between topological criticality and operational stress points, confirming the complementary nature of the two analyses.”

and the accompanying table (Table 6) provides detailed comparative results.

This directly addresses the reviewer’s concern by providing the requested quantitative comparison between both analyses.

Overall Revisions in the Conclusion

Finally, the Conclusion section was expanded to emphasize the hybrid character of the framework and its practical relevance (text lines 665-669).

“The proposed framework represents an advancement over existing studies by coupling graph-theoretical measures with conventional simulation tools, creating a bridge between topology-driven insights and functional system responses. This hybrid evaluation scheme can be extended for early warning systems and reliability planning in future smart grids. … Future work will focus on extending the framework to dynamic simulations, integrating transient stability and cascading failure modeling, to further link topological indicators with time-domain performance.”

This strengthens the significance of the contribution and highlights the practical implications.

Summary of Revisions:

Reviewer Concern	Location of Revision	Type of Change
Motivation unclear	Introduction, end	Added explicit research gap and rationale
Weak contribution	Section 3.3	Clarified novelty and integration of methods
Centrality ignores functionality	Section 4.2	Added cross-mapping between topology and physical performance
No comparison between analyses	Section 4 (new Table 6)	Added correlation analysis and interpretation
Weak conclusions	Section 5	Expanded contribution and future work

We sincerely thank the reviewer again for their constructive feedback, which has led to substantial improvements in both clarity and technical depth of the manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Although the term transient stability is emphasized in the conclusions section of the article, the study generally addresses load flow. Why were transient stability or frequency deviations excluded from consideration?
The article does not address the statistical dependence of the temperature criterion on failure frequency. What are your thoughts on addressing the impact of temperature or other meteorological parameters on outages?
To what extent can regional data from the Kosovo transmission system be generalized to national or international transmission lines?

Author Response

Reviewer 2:

Comments and Suggestions for Authors

Although the term transient stability is emphasized in the conclusions section of the article, the study generally addresses load flow. Why were transient stability or frequency deviations excluded from consideration?
The article does not address the statistical dependence of the temperature criterion on failure frequency. What are your thoughts on addressing the impact of temperature or other meteorological parameters on outages?
To what extent can regional data from the Kosovo transmission system be generalized to national or international transmission lines?

Response to Reviewer 2

We sincerely thank Reviewer 2 for the constructive comments and valuable feedback, which have helped us improve the clarity, completeness, and scope of the paper. All suggestions were carefully considered, and corresponding revisions have been made in the manuscript (highlighted in the revised version). A detailed response to each comment is provided below.

Comment 1:

“Although the term transient stability is emphasized in the conclusions section of the article, the study generally addresses load flow. Why were transient stability or frequency deviations excluded from consideration?”

Response:
We appreciate the reviewer’s observation. The present study focuses primarily on steady-state (load flow) conditions, as the main objective is to validate the integration between Neplan power flow simulations and complex network metrics as part of the proposed hybrid evaluation framework.
To clarify this point, an explanatory paragraph has been added in Section 3.3 (The methodology used) and reinforced in Section 5 (Conclusions) (text lines 491-496):

“This study focuses on steady-state (load flow) conditions, where the integration between Neplan simulations and complex network metrics is validated. Transient stability and frequency deviation analyses were intentionally excluded from the present scope, as they require dynamic time-domain modeling and a different data structure. These aspects will be incorporated in future work to extend the proposed hybrid framework toward dynamic and cascading failure analysis.”

This modification clarifies the scope and justifies why transient stability and frequency aspects were excluded from the current phase of the research.

Comment 2:

“The article does not address the statistical dependence of the temperature criterion on failure frequency. What are your thoughts on addressing the impact of temperature or other meteorological parameters on outages?”

Response:
We fully agree with the reviewer that temperature and weather-related parameters have a significant impact on the frequency of component failures and network reliability.
To address this, a new paragraph has been inserted in Section 3.2 (The analyses of data retrieved) immediately after the discussion of Figure 5 (temperature profile), (text lines 409-415):

“Temperature and weather conditions have a direct influence on the failure frequency of overhead lines and transformers. Although the present work primarily focuses on structural and operational parameters, the recorded temperature profiles (Figure 5) suggest a potential correlation between extreme temperature events and increased outage rates. Future work will incorporate statistical regression analysis to quantify this dependence and to evaluate whether temperature and other meteorological parameters can be integrated as probabilistic modifiers of component reliability.”

This addition demonstrates the authors’ acknowledgment of the issue and outlines a clear plan for integrating meteorological dependencies into future reliability modeling.

Comment 3:

“To what extent can regional data from the Kosovo transmission system be generalized to national or international transmission lines?”

Response:
We thank the reviewer for raising this important question. The Kosovo regional transmission grid was selected as a representative case study due to its mixed characteristics—multiple voltage levels, a balance of generation and load, and structural complexity that resembles larger interconnected grids.
A clarifying paragraph has been added in Section 3.4 (The system understudied): text lines 516-521.

“Although the analyzed case corresponds to the western regional segment of the Kosovo transmission network, its topology—comprising multiple voltage levels, interconnected substations, and mixed generation sources—is representative of many medium-scale European grids. Therefore, the proposed methodology is scalable and can be generalized to national or cross-border transmission systems by adjusting the input data and network dimensions.”

This clarification explains that the chosen system is not unique, and that the methodology can be extended to broader contexts with minimal adaptation.

Summary of Revisions:

Reviewer Concern	Location in Revised Manuscript	Type of Revision
Missing justification for excluding transient stability/frequency deviations	Section 3.3 and Section 5	Added clarification of study scope and future extension
No discussion of temperature–failure correlation	Section 3.2	Added paragraph on meteorological influence and planned regression analysis
Generalization of Kosovo data	Section 3.4	Added explanation of representativeness and scalability

We thank Reviewer 2 once again for these constructive comments, which have helped us improve the manuscript’s scope, completeness, and interpretability. We believe that the revised version now clearly communicates the study’s focus, limitations, and future research directions.

Reviewer 3 Report

Comments and Suggestions for Authors

In this paper the use of complex network with NetworkX and Neplan Software for the analysis of power transmission system is presented.

The topic has already been widely studied. The literature overview is poor, and the novelty of the paper is not well stated. Following some comments:
1. Please clarify how the datasets were integrated between Neplan and Python NetworkX. Is it an automated process?

2. In the workflow (Figure 6), could you explain how validation between Neplan and NetworkX outputs was performed (e.g., error tolerance, consistency checks)?

3. Figure 5 (temperature data) lacks clear axis labelling and units.

4. Fi. 3 is difficult to read, and it is not useful for the paper. Even Figures 9 and 10 could be improved by adding clearer captions.

5. Table 2 has some zero or missing values for some years. Please clarify.

Author Response

Reviewer 3:

Comments and Suggestions for Authors

In this paper the use of complex network with NetworkX and Neplan Software for the analysis of power transmission system is presented.

In the workflow (Figure 6), could you explain how validation between Neplan and NetworkX outputs was performed (e.g., error tolerance, consistency checks)?
Figure 5 (temperature data) lacks clear axis labelling and units.
Fi. 3 is difficult to read, and it is not useful for the paper. Even Figures 9 and 10 could be improved by adding clearer captions.
Table 2 has some zero or missing values for some years. Please clarify.

Response to Reviewer 3

We sincerely thank Reviewer 3 for the valuable and constructive comments that helped us improve the clarity, quality, and scientific rigor of our manuscript.
Below we provide detailed responses to each comment, together with corresponding revisions made in the manuscript.

Comment 1:

Please clarify how the datasets were integrated between Neplan and Python NetworkX. Is it an automated process?

Response:
We appreciate this important comment. The data integration between Neplan and Python NetworkX has been clarified in Section 3.3 (The methodology used, page 13).
We explicitly state that the process is automated through a CSV-based export/import pipeline, ensuring identical topological and parametric consistency between both environments (text lines 467-471).

Added text:

“The data exchange between Neplan and Python was automated through a CSV-based export/import routine. The Neplan data files containing node, branch, and impedance parameters were parsed using a custom Python script that directly generates NetworkX graph objects. This ensures consistency of topology and attributes between both environments without manual editing.”

Comment 2:

In the workflow (Figure 6), could you explain how validation between Neplan and NetworkX outputs was performed (e.g., error tolerance, consistency checks)?

Response:
Thank you for pointing out this aspect. We have expanded Section 3.3 (page 13–14) to include the validation procedure between the Neplan and NetworkX results.
The comparison was performed at the level of node–branch connectivity matrices and impedance parameters. Deviations in impedance values remained within ±1 %, confirming numerical consistency between both datasets (text lines 472-475).

Added text:

“Validation between Neplan and NetworkX outputs was performed by comparing the node–branch connectivity matrices and impedance parameters. The number of nodes, lines, and connectivity relations were identical in both datasets, and differences in impedance values remained below ±1 %.”

Comment 3:

Figure 5 (temperature data) lacks clear axis labeling and units.

Response:
We agree with the reviewer. Figure 5 has been redrawn with clearly defined axes and units (°C). Furthermore, descriptive text has been added in Section 3.2 (page 12) specifying temperature ranges and their yearly variation (text lines 389-392).

Added explanation:

“Figure 5 shows that in 2020, the highest temperature is 32 °C and the lowest is −9 °C… The highest and minimum temperatures in 2023 are 38 °C and −10 °C, respectively.”

This enhancement ensures full clarity of the meteorological dataset.

Comment 4:

Figure 3 is difficult to read, and it is not useful for the paper. Even Figures 9 and 10 could be improved by adding clearer captions.

Response:
We appreciate this observation. Figure 3 was simplified and retained only as a conceptual illustration of a simple graph, directly referenced in the theoretical part on complex networks. Its caption and explanatory text were rewritten for clarity.
Figures 9 and 10 were significantly improved with detailed captions that now describe the variables (degree, closeness, betweenness, eigenvalue centralities), color coding, and comparative scenarios (Scenario 1 vs. Scenario 2).

Comment 5:

Table 2 has some zero or missing values for some years. Please clarify.

Response:
We thank the reviewer for highlighting this point. We have clarified the reason for the zero entries in Section 3.2 (page 11) immediately below Table 2 (text line 385-385).

Added clarification:

“Zero values mean that we had not any faults on network elements.”

This ensures full transparency of the dataset and prevents misinterpretation.

The literature overview is poor:

Thank you for recommendation, and we agree with this suggestion. We have reviewed many research papers and we have added some of them, revised text lines 558-559, and 781-797.

Summary of Revisions:

Added explicit explanation of automated data exchange and validation procedure between Neplan and NetworkX.
Improved figures (5, 9, 10) with labeled axes, units, and detailed captions.
Clarified the interpretation of Table 2 values.
Enhanced methodological section with reproducible workflow and error tolerance description.
The overall novelty and reproducibility of the study are now clearly demonstrated.

We are grateful for the reviewer’s careful evaluation and believe that these revisions fully address all concerns, resulting in a stronger and more transparent manuscript.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The reviewer thanks the one-by-one response to the comments. However, the reviewer's concerns in the comments are addressed.

In the literature from around year 2000, many works have tried to modify the centrality metrics from complex network theory in different ways for vulnerability analysis in power systems by introducing the unique engineering features of power systems. The reason for this is that these purely topological centrality metrics cannot provide insightful and correct results which are consistent with those obtained from power system planning and operation analysis.

The conclusions are different from those in this paper, showing that these purely topological centrality metrics can provide insightful and correct results that are consistent with those obtained from power system planning and operation analysis.

Reviewer 3 Report

Comments and Suggestions for Authors

All the concerns have been addressed.