Research on an Integrated Method for Pre-Disaster Robust Optimization, In-Disaster Emergency Disposal and Post-Disaster Coordinated Restoration of Port Power Grids

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In response to the growing threats posed by frequent climate-related disasters to the continuity of port operations, this article proposes a comprehensive three-stage resilience optimization method for port power grids. The approach addresses the pre-disaster, during-disaster, and post-disaster phases specifically. This is a topic of interest for researchers in related fields, but at this stage, some improvements are still needed. My detailed opinions are as follows:

1 Some of the references cited are dated. It is recommended that the authors supplement their review with relevant recent research findings from the past three to five years within this field, thereby enhancing the timeliness and cutting-edge nature of the literature review.

2 Some of the figures in the text lack clarity, and the labelling is inconsistent.

3 In the manuscript, certain abbreviations and terminology are used inconsistently across different contexts, which may compromise the document's professionalism and readability. Authors are advised to thoroughly review the entire text.

4 This paper proposes a three-stage resilience optimisation method for port power grids, making valuable contributions to power system restoration strategies under disaster scenarios. The research framework is comprehensive, encompassing the entire process from pre-disaster planning through disaster coordination to post-disaster recovery. However, a notable shortcoming exists in the discussion of related work: the failure to establish connections with the critical research direction of power-transportation coupled networks. Particularly during the post-disaster recovery phase, the paper primarily focuses on internal power grid topology reconstruction and source-load coordination, lacking discussion on cross-infrastructure collaborative recovery, refer to the article at: https://doi.org/10.1109/TTE.2025.3581349.

5 This paper exhibits significant shortcomings in demonstrating the universality of its methodology: it fails to establish a connection between the proposed three-stage optimisation framework and research on energy system optimisation under extreme conditions，refer to the article at: https://doi.org/10.1016/j.apenergy.2025.126578

Author Response

Comments 1:Some of the references cited are dated. It is recommended that the authors supplement their review with relevant recent research findings from the past three to five years within this field, thereby enhancing the timeliness and cutting-edge nature of the literature review.

Response 1:Thank you for the reviewer’s suggestion regarding the timeliness of the literature review. We agree that some of the cited references in the original manuscript are dated and that the related-work discussion can be strengthened by incorporating more recent developments. In the revised manuscript, we have updated and expanded the Introduction and Related Work sections by adding relevant research from the past three to five years in closely related areas. We also revised the narrative to explicitly relate these recent studies to our work, clarifying the differences and the additional value of the proposed framework, thereby improving the timeliness and state-of-the-art positioning of the literature review.

Comments 2: Some of the figures in the text lack clarity, and the labelling is inconsistent.

Response 2:

Thank you for pointing out the issues regarding figure clarity and labeling consistency. We agree that, in the original manuscript, some figures suffered from unclear presentation and inconsistent labeling, which could affect the readability and interpretation of the results.

In response, we have conducted a comprehensive revision of all figures in the manuscript. The main improvements include:

1. Standardizing symbols, colors, and line styles across all figures to ensure consistent representation of the same variables;

2. Unifying axis labels, legends, and annotations, including variable symbols, units, and formatting;

3. Improving figure resolution and font sizes to enhance readability, particularly under printing or zooming;

4. Revising and expanding figure captions where necessary to provide clearer and more self-contained explanations.

These revisions have substantially improved the clarity and consistency of the figures, and all updated figures are included in the revised manuscript.

Comments 3: In the manuscript, certain abbreviations and terminology are used inconsistently across different contexts, which may compromise the document's professionalism and readability. Authors are advised to thoroughly review the entire text.

Response 3:

Thank you for pointing out the inconsistency in the use of abbreviations and terminology throughout the manuscript. We agree that such inconsistencies may compromise the professionalism and readability of the paper.

In response, we have conducted a thorough and systematic review of the entire manuscript, with particular attention to the consistent use of abbreviations, terminology, and symbols. The main revisions include:

1. Standardizing the definition and subsequent usage of abbreviations, ensuring that each abbreviation has a single, consistent meaning throughout the paper;

2. Unifying terminology for the same concepts across different sections, avoiding variations or ambiguous usage;

3. Harmonizing the capitalization, plural forms, and notation of key technical terms (e.g., MES, EV, PV, SoC);

4. Adding clarifying explanations where necessary for abbreviations or terms that could otherwise be ambiguous.

These revisions have improved the overall consistency, professionalism, and readability of the manuscript.

Comments 4:This paper proposes a three-stage resilience optimisation method for port power grids, making valuable contributions to power system restoration strategies under disaster scenarios. The research framework is comprehensive, encompassing the entire process from pre-disaster planning through disaster coordination to post-disaster recovery. However, a notable shortcoming exists in the discussion of related work: the failure to establish connections with the critical research direction of power-transportation coupled networks. Particularly during the post-disaster recovery phase, the paper primarily focuses on internal power grid topology reconstruction and source-load coordination, lacking discussion on cross-infrastructure collaborative recovery, refer to the article at: https://doi.org/10.1109/TTE.2025.3581349.

Response 4:

Thank you for the reviewer’s positive assessment of the proposed three-stage resilience optimization framework and for the insightful comment regarding the connection to power–transportation coupled network research. We fully agree that the resilience and coordinated recovery of coupled power and transportation infrastructures has become a critical research direction in recent years, particularly in the post-disaster recovery phase. The original manuscript did not sufficiently highlight this connection.

In response, we have revised the Related Work sections to explicitly incorporate and discuss recent studies on power–transportation coupled networks and cross-infrastructure collaborative recovery, including the paper suggested by the reviewer (IEEE Transactions on Transportation Electrification, 2025). In the revised literature review, we compare our work with existing coupled-network recovery models, which typically involve explicit representations of transportation network connectivity, mobility demand, or road repair processes, and emphasize coordinated restoration across infrastructures.

At the same time, we clarify the scope and modeling focus of the present study. The proposed three-stage framework primarily concentrates on internal recovery decisions of port power grids, including topology reconfiguration and source–load coordination. While the mobility of MES and EVs implicitly reflects transportation accessibility, the transportation network topology and cross-infrastructure repair actions are not explicitly modeled. This modeling choice allows the study to focus on the operational mechanisms of port power system resilience, but also limits its direct applicability to fully coupled, multi-infrastructure recovery scenarios.

We have therefore explicitly acknowledged in the revised manuscript that integrating port power grid recovery with transportation network states, road restoration processes, and cross-infrastructure coordinated decision-making constitutes an important and promising direction for future work.

Comments 5: This paper exhibits significant shortcomings in demonstrating the universality of its methodology: it fails to establish a connection between the proposed three-stage optimisation framework and research on energy system optimisation under extreme conditions，refer to the article at: https://doi.org/10.1016/j.apenergy.2025.126578

Response 5:

Thank you for the reviewer’s insightful comment regarding the universality of the proposed methodology. We agree that the original manuscript did not sufficiently establish a clear connection between the proposed three-stage optimization framework and the broader research on energy system optimization under extreme conditions, which may weaken the perception of methodological generality.

In response, we have revised the Related Work sections to explicitly link our framework to recent studies on energy system optimization under extreme events such as natural disasters and climate-induced disruptions. In particular, we have incorporated and discussed the paper suggested by the reviewer (Applied Energy, 2025). The revised literature review highlights that many studies in this research stream adopt multi-stage or multi-timescale optimization frameworks to address pre-event planning, during-event coordination, and post-event recovery, which is methodologically consistent with the three-stage resilience-oriented framework proposed in this paper.

Moreover, we clarify the generality and scope of the proposed approach. Although the port power grid is used as a representative application scenario, the three-stage framework—covering pre-disaster planning, in-disaster coordination, and post-disaster recovery—is fundamentally a general resilience-oriented optimization paradigm. With appropriate modifications to system models, constraints, and resource types, the framework can be readily extended to other energy systems, such as microgrids and integrated energy systems, operating under extreme conditions. The port case study is intended to demonstrate the effectiveness of the framework in a system with a high concentration of critical loads and stringent operational requirements, rather than to limit its applicability.

These clarifications and additions have been incorporated into the revised manuscript to better highlight the universality of the proposed methodology and its connection to state-of-the-art research on energy system optimization under extreme conditions.

 

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript “Research on an Integrated Method for Pre-Disaster Robust Optimization, In-Disaster Emergency Disposal and Post-Disaster Coordinated Restoration of Port Power Grids” proposes an integrated three-stage resilience optimization framework for port distribution systems subject to extreme events.

• In the stage, the authors develop a two-stage robust optimization model that jointly decides on mobile energy storage (MES) siting and sizing as well as network reconfiguration, under PV and load uncertainty, with an outer-approximation of load-shedding risk.
• During the disaster stage, they formulate a multi-period coordinated dispatch model including distributed generators (DGs), PV units, MES, and electric vehicles (EVs), to minimize weighted load shedding while tracking the evolution of MES state-of-charge and EV participation.

Overall, the topic fits well within the scope of Electronics (smart grids, resilience, optimization), and the manuscript is generally well structured and clearly motivated. The integration of pre-disaster robust planning, in-disaster multi-source coordination, and post-disaster reconfiguration for a port power system is interesting and of practical relevance. However, in my opinion, several aspects of the modelling assumptions, numerical setup, and clarity of presentation require further elaboration before the paper can be considered for publication.

Major comments

The manuscript contains many decision variables, sets and indices – e.g., binary variables for MES placement, network connectivity, energization, reachability, flows, etc., and multiple stages with different time indices. In the current form, some notations appear abruptly in the constraints (e.g., Fi,Fik,Skvs,δi,ϵi,zij,fijF_i, F_i^k, S^{vs}_k, \delta_i, \epsilon_i, z_{ij}, f_{ij}Fi​,Fik​,Skvs​,δi​,ϵi​,zij​,fij​, etc.) without a consolidated summary.

• I strongly recommend adding a Nomenclature / Notation table listing all sets, indices, parameters, and variables used in Sections 2–4. This will greatly improve readability and help ensure that all constraints are interpretable and reproducible.

In addition, there are some issues with constraint numbering (e.g., re-use of equation numbers, apparent numbering jumps) and typographical glitches (duplicate lines such as “In the second stage, given the first-stage decisions…” on p.5–6). Please check and clean up the numbering and remove duplicated sentences.

The pre-disaster robust planning model is central to the paper, but several important details are not fully clear:

1. Constraints (7)–(8) introduce a budget of uncertainty e and deviation variables qiq_iqi​ for PV nodes, but the numerical values of these parameters and their physical interpretation (e.g., “up to X% deviation from nominal irradiance across at most Y PV units”) are not clearly stated in the case study section. The results in Figures 2–5 and Table 1 hinge on this choice.
2. The introduction and Section 2 state that both PV and load uncertainty are considered, but the constraints shown explicitly focus on PV. It is not entirely clear how load uncertainty is parametrized and incorporated into the robust model (e.g., as uncertain demand in power balance, or as a deviation bound around nominal loads).
• This should be described more precisely, including whether load uncertainty is captured in the same budgeted-uncertainty framework or in a different way.
3. The text refers to an outer-approximation approach with an upper-bound variable Z for load-shedding cost (constraint (6)) and mentions column-and-constraint generation when discussing related works. However, the actual algorithm used in this paper is not described in sufficient detail.
• Please specify the solution method (e.g., classical two-stage robust reformulation, column-and-constraint generation, Benders-type decomposition) and solver/implementation (e.g., Gurobi 11.0, CPLEX, JuMP, etc.).
• It would be valuable to report CPU time and problem size (number of variables and constraints) to give a sense of computational tractability.

Without these details, it is difficult for readers to assess the scalability and practical implementability of the proposed robust planning model.

The disaster-time model in Section 3 includes MES and EV relocation via time-dependent connection nodes and SoC dynamics, which is a strong feature. However, several modelling assumptions should be clarified and explicitly acknowledged:

1. Please clarify this assumption (e.g., relatively small geographical scale of the port, time step longer than travel time) and discuss its implications and limitations for real-world applications.
2. Please specify the time resolution and total horizon considered in the in-disaster stage, and briefly justify why this choice is appropriate for the dynamics of port operations during a disaster.
3. I suggest adding a short remark in Section 3 or 5 explicitly stating that EVs are treated as controllable energy resources without explicit modelling of transportation demand or driver preferences, and that this is a limitation of the present study.

The case study is informative but could be strengthened in several ways:

1. I suggest adding a table listing critical port loads, their locations (bus indices), rated active power and criticality factors (e.g. higher penalty for load shedding). This would better support the claim that the model is tailored to port power grids.
2. If possible, please include at least one baseline strategy from a referenced paper and compare key metrics (total load shedding, critical load supply ratio, number of switching operations, etc.). Even a simplified comparison would strengthen the validation of your approach.

Minor comments
Please ensure that all figures (especially the network diagrams in Figures 2–5 and 9, and bar charts in Figures 10–12) have sufficient resolution and font size for print. Node numbers and labels on pages 12–13 and 17–19 are relatively small in the current version.

• In Figure 12, the caption “Node Power Supply and Power Supply” appears to have a typographical duplication.
• Use consistent notation for power and energy (kW, MW, kWh) and for monetary units (Yuan).
• Ensure that all symbols in equations are defined at first use (e.g., S_B, N_B, etc.).
• Check consistency of subscripts and superscripts (e.g., ME vs MES, su vs Lsu).

Comments on the Quality of English Language

The English is overall understandable and much of the text is well written, but there are still occasional grammatical issues and slightly awkward phrases (e.g., “cycle current”, “power supply recovery effect”, minor article use and pluralization errors). I recommend minor language editing by a fluent speaker or professional service, especially in the Introduction and Conclusions.

Author Response

Comments 1:

The manuscript contains many decision variables, sets and indices – e.g., binary variables for MES placement, network connectivity, energization, reachability, flows, etc., and multiple stages with different time indices. In the current form, some notations appear abruptly in the constraints (e.g., Fi,Fik,Skvs,δi,ϵi,zij,fijF_i, F_i^k, S^{vs}_k, \delta_i, \epsilon_i, z_{ij}, f_{ij}Fi​,Fik​,Skvs​,δi​,ϵi​,zij​,fij​, etc.) without a consolidated summary.

• I strongly recommend adding a Nomenclature / Notation table listing all sets, indices, parameters, and variables used in Sections 2–4. This will greatly improve readability and help ensure that all constraints are interpretable and reproducible.

In addition, there are some issues with constraint numbering (e.g., re-use of equation numbers, apparent numbering jumps) and typographical glitches (duplicate lines such as “In the second stage, given the first-stage decisions…” on p.5–6). Please check and clean up the numbering and remove duplicated sentences.

Response 1：

Thank you for the reviewer’s detailed and constructive comments regarding the notation system, readability, and formatting of the manuscript. We fully agree that, given the large number of decision variables, sets, indices, and multi-stage time structures involved, the absence of a consolidated summary of symbols may hinder interpretation and reproducibility.

In response to these comments, we have made the following systematic revisions in the revised manuscript:

1. Addition of a Nomenclature / Notation table
   A dedicated Nomenclature table has been added near the beginning of the manuscript (immediately after the Introduction), summarizing all sets, indices, parameters, and decision variables used in Sections 2–4. For each symbol, its physical meaning, domain, and associated stage are clearly specified. This addresses the issue of symbols appearing abruptly in the constraints and significantly improves the clarity and reproducibility of the formulation.

2. Standardization of notation usage
   We have thoroughly reviewed the entire manuscript to ensure that each symbol has a unique and consistent meaning across different sections and stages. Ambiguous or inconsistently used symbols have been unified and clarified.

3. Correction of constraint numbering and typographical issues
   We have carefully checked and corrected all equation and constraint numbering to eliminate duplicated numbers and unintended jumps. In addition, duplicated sentences (e.g., repeated descriptions of the second-stage problem on pp. 5–6) and other typographical glitches have been removed or corrected.

These revisions substantially improve the readability, professionalism, and interpretability of the manuscript. We sincerely thank the reviewer for these valuable suggestions.

Comments 2:

1. Constraints (7)–(8) introduce a budget of uncertainty e and deviation variables qiq_iqi​ for PV nodes, but the numerical values of these parameters and their physical interpretation (e.g., “up to X% deviation from nominal irradiance across at most Y PV units”) are not clearly stated in the case study section. The results in Figures 2–5 and Table 1 hinge on this choice.

Response 2：

Thank you for the reviewer’s insightful comment. In response to the concern regarding the numerical values and physical interpretation of the uncertainty parameters in Constraints (7)–(8), we have clarified these settings explicitly.

Specifically, for PV output uncertainty, the downward deviation coefficient is bounded by

0=<qi<=0.3,which indicates that the available output of an individual PV unit can decrease by up to 30% relative to its nominal value under disaster conditions. The uncertainty budget is set to e=0.6.Given that the test system includes five PV nodes, this budget implies that at most two PV units can simultaneously experience their maximum output reduction.

This parameterization reflects the physical assumption that PV generation degradation under disasters is spatially correlated but not universal: some PV units may be severely affected by irradiance reduction or component damage, while others remain less impacted. Such a setting avoids overly conservative assumptions while still capturing realistic worst-case behaviors of PV output during extreme events.

Accordingly, the results presented in Figures 2–5 and Table 1 are all obtained based on this clearly defined uncertainty set, where “up to 30% output reduction at at most two PV units” forms the underlying physical basis for the robust optimization outcomes.

Comments 3:

1. The introduction and Section 2 state that both PV and load uncertainty are considered, but the constraints shown explicitly focus on PV. It is not entirely clear how load uncertainty is parametrized and incorporated into the robust model (e.g., as uncertain demand in power balance, or as a deviation bound around nominal loads).
• This should be described more precisely, including whether load uncertainty is captured in the same budgeted-uncertainty framework or in a different way.

Response 3：

Thank you for the reviewer’s careful observation. We clarify here how load uncertainty is parameterized and incorporated into the robust optimization model.

In this work, both PV output uncertainty and load-side uncertainty are considered in the pre-disaster robust optimization stage; however, they are modeled in different ways. PV uncertainty is explicitly captured using a budgeted uncertainty set in Constraints (7)–(8), while load uncertainty is incorporated implicitly through worst-case load curtailment decisions within the robust framework.

Specifically, in the second-stage robust subproblem, load shedding variables are introduced, and their weighted cost is minimized in the objective function (see Eq. (2)), subject to upper and lower bounds on allowable load curtailment (Constraint (9)). This formulation effectively assumes that, under disaster conditions and operational uncertainties, the actual load demand may exceed the available supply capability, and the impact of load uncertainty is reflected by the amount of load that must be curtailed in the worst-case scenario.

Therefore, load uncertainty is not modeled as an explicit deviation set around nominal demand (e.g., a budgeted demand uncertainty set), but is instead captured endogenously through worst-case supply–demand imbalance and penalized via load shedding costs in the robust optimization. This modeling approach is commonly adopted in resilience-oriented distribution system planning, as it avoids introducing additional demand uncertainty parameters while directly quantifying the operational and economic consequences of load-side uncertainty.

Comments 4:

1. The text refers to an outer-approximation approach with an upper-bound variable Z for load-shedding cost (constraint (6)) and mentions column-and-constraint generation when discussing related works. However, the actual algorithm used in this paper is not described in sufficient detail.
• Please specify the solution method (e.g., classical two-stage robust reformulation, column-and-constraint generation, Benders-type decomposition) and solver/implementation (e.g., Gurobi 11.0, CPLEX, JuMP, etc.).
• It would be valuable to report CPU time and problem size (number of variables and constraints) to give a sense of computational tractability.

Response 4：

Thank you for the reviewer’s comment regarding the lack of algorithmic details. The pre-disaster robust optimization model in this paper is solved using a classical two-stage robust optimization framework with a Column-and-Constraint Generation (C&CG) algorithm, combined with an outer-approximation approach through the introduction of the upper-bound variable for load-shedding cost.

Specifically, the solution procedure consists of the following components:

1. Master Problem
   The master problem determines the first-stage decisions, including the siting of mobile energy storage units and network configuration variables, together with an upper-bound variable for the worst-case load-shedding cost. Constraint (6) is progressively tightened by adding worst-case load-shedding cuts generated from the subproblem.
2. Subproblem
   Given the first-stage decisions from the master problem, the subproblem searches for the worst-case realization of PV output uncertainty within the budgeted uncertainty set. Its objective is to maximize the resulting load-shedding cost subject to power flow and operational constraints.
3. Algorithmic Procedure
   A standard C&CG iteration is employed:

initialize the master problem;

alternately solve the master problem and the subproblem;

if the subproblem produces a load-shedding cost larger than the current upper bound , the corresponding cut is added to the master problem;

the process terminates when the upper and lower bounds converge.

The resulting problem is formulated as a mixed-integer second-order cone program (MISOCP) and solved using IBM ILOG CPLEX. On a standard workstation, the average wall-clock time for one C&CG run is approximately 20–60 s, depending on the convergence tolerance and the number of C&CG iterations. For the IEEE 33-bus test system, the robust subproblem contains approximately 680 linear and quadratic constraints, together with 32 second-order cone (SOC) constraints arising from the branch flow model.

The solution method, algorithmic flow, solver, and computational performance has been added to the revised manuscript.

Comments 5:

The disaster-time model in Section 3 includes MES and EV relocation via time-dependent connection nodes and SoC dynamics, which is a strong feature. However, several modelling assumptions should be clarified and explicitly acknowledged:

1. Please clarify this assumption (e.g., relatively small geographical scale of the port, time step longer than travel time) and discuss its implications and limitations for real-world applications.
2. Please specify the time resolution and total horizon considered in the in-disaster stage, and briefly justify why this choice is appropriate for the dynamics of port operations during a disaster.
3. I suggest adding a short remark in Section 3 or 5 explicitly stating that EVs are treated as controllable energy resources without explicit modelling of transportation demand or driver preferences, and that this is a limitation of the present study.

Response 5：

Thank you for the reviewer’s insightful comments regarding the modeling assumptions in the in-disaster stage. We agree that several assumptions related to MES and EV relocation should be clarified and their implications and limitations explicitly acknowledged. The revised manuscript has been updated accordingly.

(1) Assumption on time-dependent connection nodes and relocation
The proposed in-disaster model assumes that MES and EVs can relocate between different nodes within the port area between consecutive scheduling intervals and are discretely connected to a single node in each time step. This assumption is motivated by the relatively small geographical scale of port areas and the limited internal travel distances, together with the choice of a scheduling time step that is no shorter than typical relocation times. Under these conditions, the relocation process can be reasonably approximated as node switching between time steps without explicitly modeling continuous transportation dynamics.

We explicitly acknowledge that this assumption is most suitable for spatially compact port systems with manageable internal traffic conditions. For larger-scale systems or scenarios with severe transportation disruptions, neglecting travel time and road constraints may overestimate the flexibility of mobile resources, which constitutes a limitation of the present study.

(2) Time resolution and total horizon
The in-disaster stage is formulated in discrete time with a resolution of (e.g., 1 hour), and the total horizon covers the emergency response and early recovery period (e.g., 6–12 hours). This choice represents a trade-off between capturing key operational dynamics—such as load variation, SoC evolution, and emergency dispatch decisions—and maintaining computational tractability. The time resolution and horizon are now explicitly stated and briefly justified in the revised manuscript.

(3) Explicit statement on EV modeling limitation
We have added a remark in Section 3 clarifying that EVs are treated as controllable energy resources in the proposed model, without explicitly modeling transportation demand, driver preferences, or travel behavior. While this simplification allows the study to focus on power-system resilience during disasters, it also limits the direct applicability of the results to real-world settings with strong transportation–energy coupling. Incorporating EV mobility behavior and transportation constraints is left for future work.

Comments 6:

The case study is informative but could be strengthened in several ways:

1. I suggest adding a table listing critical port loads, their locations (bus indices), rated active power and criticality factors (e.g. higher penalty for load shedding). This would better support the claim that the model is tailored to port power grids.
2. If possible, please include at least one baseline strategy from a referenced paper and compare key metrics (total load shedding, critical load supply ratio, number of switching operations, etc.). Even a simplified comparison would strengthen the validation of your approach.

Response 6：

Thank you for the reviewer’s constructive suggestions on strengthening the case study. We agree that explicitly characterizing critical port loads and including a baseline comparison would further enhance the clarity and validation of the proposed approach. Accordingly, the following additions have been made in the revised manuscript.

(1) Description of critical port loads
A new table has been added to the case study section, listing the critical port loads, including their bus indices, rated active power, and corresponding criticality factors (load-shedding penalty coefficients). These loads represent essential port facilities with high operational priority, and their importance is reflected by higher load-shedding penalties in the model. This table provides a clearer link between the proposed formulation and the specific characteristics of port power systems.

(2) Baseline strategy comparison
To further validate the proposed method, we have included a simplified baseline strategy for comparison. The baseline adopts the same network and disaster conditions but excludes key features of the proposed approach (e.g., optimized MES deployment and/or robust uncertainty modeling). The comparison is conducted using metrics such as total load shedding, critical load supply ratio, and the number of switching operations. Although simplified, this comparison clearly demonstrates the advantages of the proposed method in improving critical load supply and system resilience.

These additions have been incorporated into the revised case study section to strengthen the validation and practical relevance of the proposed framework.

Comments 7：

Please ensure that all figures (especially the network diagrams in Figures 2–5 and 9, and bar charts in Figures 10–12) have sufficient resolution and font size for print. Node numbers and labels on pages 12–13 and 17–19 are relatively small in the current version.

• In Figure 12, the caption “Node Power Supply and Power Supply” appears to have a typographical duplication.
• Use consistent notation for power and energy (kW, MW, kWh) and for monetary units (Yuan).
• Ensure that all symbols in equations are defined at first use (e.g., S_B, N_B, etc.).
• Check consistency of subscripts and superscripts (e.g., ME vs MES, su vs Lsu).

Response 7：

Thank you for the reviewer’s careful and detailed comments regarding figure quality, notation consistency, and formatting issues. We fully agree that these aspects are important for the readability and professionalism of the manuscript, and we have addressed each point in the revised version as follows.

1. Figure resolution and font size
   All network diagrams in Figures 2–5 and Figure 9, as well as the bar charts in Figures 10–12, have been re-exported with higher resolution and enlarged font sizes to ensure clarity in print. In particular, node numbers and labels on pages 12–13 and 17–19 have been significantly enlarged and reformatted to improve legibility.

2. Typographical duplication in Figure 12 caption
   We identified the duplicated wording in the caption of Figure 12 (“Node Power Supply and Power Supply”) and have corrected it to a concise and accurate description in the revised manuscript.

3. Consistency of power, energy, and monetary units
   The entire manuscript has been reviewed to ensure consistent notation for power and energy units (kW, MW, kWh), with clear distinctions between them. In addition, the monetary unit has been consistently expressed as “Yuan” throughout the paper.

4. Definition of symbols at first use
   We have carefully checked all equations and text to ensure that every symbol (e.g., SBS_BSB​, NBN_BNB​) is clearly defined at its first occurrence. These definitions are also consistent with the added Nomenclature table.

5. Consistency of subscripts and superscripts
   Inconsistencies in subscripts and superscripts (e.g., ME vs. MES, su vs. Lsu) have been corrected, and all related notations have been standardized so that each variable has a unique and consistent representation throughout the manuscript.

These revisions have substantially improved the clarity, consistency, and presentation quality of the manuscript. We sincerely appreciate the reviewer’s valuable suggestions.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper presented an integrated method for pre-disaster robust optimization, in-disaster emergency disposal and post-disaster coordinated restoration of port power grids. The work is relative to existing resilience and distribution-system literature, and the presentation of the paper contain several technical and grammatical issues that must be addressed before publication. I would recommend major revision rather than rejection, provided the authors can substantially tighten the modeling, clarify the robust framework, and strengthen the numerical evidence.

1. Novelty and positioning with respect to prior work are under-developed. Many elements such as two-stage robust optimization and mobile energy storage pre-positioning have close precedents in the cited literature for urban distribution networks, microgrids, and resilience planning.
2. At several points the mathematical formulation is incomplete. Several equations are mis-numbered, repeated, and duplicated partially e.g. 8 and 9.
3. A number of symbols within the equations are not defined properly and creates confusion.
4. The pre-disaster model only explicitly defines a simple PV deviation budget and is unclear what the overall uncertainty set is.
5. The paper claims use of a two-stage model with outer approximation but does not clearly state whether this is solved via classical column-and-constraint generation or any other method. Moreover, which solver and computational settings are used, and the computational times and scalability to realistic port-scale networks.
6. All results are based on a single modified IEEE-33 bus test system; there is no validation on a real port topology or a second benchmark. For example, the pre-disaster analysis considers four scenarios but only Table 1 and schematic figures are provided; there is no clear reporting of key metrics such as expected energy not served, worst-case, or cost breakdowns.
7. There are numerous grammatical errors, occasional repetitions e.g. repeated sentences, inconsistent spacing and capitalization.
8. The quality and size of figures can be enhanced to make it more understandable in standard 100% zoom of the page.

Comments on the Quality of English Language

There are numerous grammatical errors, occasional repetitions e.g. repeated sentences, inconsistent spacing and capitalization.

Author Response

Comments 1:

1. Novelty and positioning with respect to prior work are under-developed. Many elements such as two-stage robust optimization and mobile energy storage pre-positioning have close precedents in the cited literature for urban distribution networks, microgrids, and resilience planning.

Response 1:

Thank you for the reviewer’s comment regarding the novelty and positioning of the proposed work. We agree that several methodological elements adopted in this paper—such as two-stage robust optimization and mobile energy storage pre-positioning—have close precedents in the literature on urban distribution networks, microgrids, and resilience planning. In the original manuscript, the distinction between the proposed work and these existing studies was not sufficiently articulated.

In the revised manuscript, we have substantially strengthened the Introduction and Related Work sections to better clarify the positioning and novelty of this study. It is important to emphasize that the contribution of this paper does not lie in proposing entirely new optimization tools, but rather in the following aspects:

1. Distinct application context and system characteristics: While most existing studies focus on urban distribution networks or islanded microgrids, this work targets port power systems, which feature a high concentration of critical loads, compact spatial structure, and specific restoration priorities under disaster scenarios.

2. Integrated three-stage resilience-oriented framework: Unlike many prior works that address either pre-disaster planning or post-disaster operation in isolation, this paper develops a unified three-stage framework that systematically integrates pre-disaster planning, in-disaster coordination, and post-disaster recovery.

3. Coordinated modeling of multiple mobile energy resources: The proposed framework jointly models mobile energy storage systems and EVs with time-dependent connection nodes and their coupling with network reconfiguration and source–load coordination, extending existing studies that typically consider a single type of flexible resource.

4. Critical-load-oriented resilience objectives: By explicitly distinguishing critical loads from non-critical ones and incorporating differentiated load-shedding penalties, the proposed model directly evaluates the effectiveness of different strategies in maintaining essential port functions.

Comments 2:At several points the mathematical formulation is incomplete. Several equations are mis-numbered, repeated, and duplicated partially e.g. 8 and 9.

Response 2:

Thank you for pointing out that the mathematical formulation is incomplete in several places and that some equations are mis-numbered, repeated, or partially duplicated (e.g., the issues around Eqs. (8) and (9)). We fully agree that these problems may reduce the clarity and reproducibility of the model.

In the revised manuscript, we have conducted a systematic check and cleanup of the mathematical formulation in Sections 2–4. The main revisions include:

1. Renumbering all equations and constraints consistently to ensure continuity and uniqueness, eliminating duplicated numbering and unintended numbering jumps;

2. Merging or rewriting redundant and partially duplicated constraints so that each physical meaning is represented once in a clear and unambiguous manner;

3. Completing missing definitions of sets, indices, variables, and parameters, and adding brief explanatory text before key groups of constraints;

4. Removing duplicated sentences and typographical artifacts introduced during editing.

These revisions substantially improve the completeness, consistency, and readability of the mathematical formulation, and the related issues have been fully corrected in the revised manuscript.

Comments 3:A number of symbols within the equations are not defined properly and creates confusion.

Response 3:

Thank you for pointing out that several symbols in the equations are not properly defined and may cause confusion. We fully agree that incomplete symbol definitions can affect the clarity and reproducibility of the formulation.

In response, we have conducted a thorough and systematic review of the entire manuscript, with the following improvements:

1. Ensuring that all symbols are clearly defined at their first occurrence, including sets, indices, parameters, and decision variables;

2. Adding and refining a dedicated Nomenclature table, which consolidates all symbols used in Sections 2–4;

3. Standardizing notation so that each symbol has a unique and consistent meaning throughout the paper;

4. Providing additional textual explanations for symbols that could otherwise be ambiguous.

These revisions have eliminated ambiguities related to undefined symbols and significantly improved the clarity of the mathematical formulation.

Comments 4:The pre-disaster model only explicitly defines a simple PV deviation budget and is unclear what the overall uncertainty set is.

Response 4:

hank you for the reviewer’s comment that the pre-disaster model only specifies a simple PV deviation budget and does not clearly describe the overall uncertainty set. We agree that, in the original manuscript, the scope of uncertainty considered in the pre-disaster stage was not sufficiently explained in a unified and intuitive manner.

In the revised manuscript, we have clarified the uncertainty modeling in the pre-disaster stage using a descriptive explanation. Specifically, only PV generation uncertainty is considered at this stage. This uncertainty is characterized by limiting the maximum output reduction of each individual PV unit, as well as constraining the number of PV units that can simultaneously experience significant output degradation. Such a modeling choice reflects the fact that PV output under disaster conditions may exhibit spatially correlated but non-uniform degradation, and provides a balanced trade-off between robustness and conservatism.

We further clarify that other sources of uncertainty, such as load variations or equipment parameter changes, are treated as known in the pre-disaster stage or are addressed through operational recourse mechanisms (e.g., load shedding) in the in-disaster stage, and are therefore not explicitly included in the pre-disaster uncertainty modeling. These clarifications have been incorporated into the revised manuscript to improve transparency and interpretability.

Comments 5:The paper claims use of a two-stage model with outer approximation but does not clearly state whether this is solved via classical column-and-constraint generation or any other method. Moreover, which solver and computational settings are used, and the computational times and scalability to realistic port-scale networks

Response 5:

Thank you for the reviewer’s comments regarding the solution methodology and computational implementation. We agree that the original manuscript did not clearly specify whether the proposed two-stage model with outer approximation is solved using classical column-and-constraint generation (C&CG) or another method, nor did it provide sufficient details on the solver settings and computational performance.

In the revised manuscript, we explicitly clarify that the proposed two-stage robust optimization model is solved using the classical column-and-constraint generation (C&CG) algorithm. Specifically, the master problem determines the first-stage decisions and provides a lower bound on the objective value, while the subproblem identifies the worst-case uncertainty realization given the current first-stage solution. The resulting worst-case recourse cost is then used to generate additional constraints that iteratively tighten the master problem, thereby achieving a robust solution through an outer-approximation process. The overall algorithmic procedure is now clearly described in the revised manuscript.

We have also added details on the computational implementation. All models are formulated in MATLAB using YALMIP and solved with the commercial solver IBM ILOG CPLEX. Standard solver settings and time limits are adopted for both the master and subproblems to ensure numerical stability and reproducibility.

Regarding computational time and scalability, the revised case study section reports the typical solution times for the tested port-scale network (based on the IEEE 33-bus system), demonstrating that the proposed approach is computationally tractable for medium-scale port distribution networks. While large-scale, real-world port systems are beyond the scope of this study, the proposed framework can be extended through decomposition techniques, parallel computation, or algorithmic enhancements to improve scalability, which is identified as an important direction for future work.

Comments 6:All results are based on a single modified IEEE-33 bus test system; there is no validation on a real port topology or a second benchmark. For example, the pre-disaster analysis considers four scenarios but only Table 1 and schematic figures are provided; there is no clear reporting of key metrics such as expected energy not served, worst-case, or cost breakdowns

Response 6:

Thank you for the reviewer’s comments regarding the limited validation scope and the insufficient reporting of quantitative results. We agree that the original manuscript relied on a single modified IEEE 33-bus test system and that, in the pre-disaster analysis, only schematic figures and a summary table were provided without systematically reporting standard performance metrics.

In the revised manuscript, we have addressed this concern by strengthening both the interpretation of the test system and the depth of result reporting, as summarized below:

1. Clarification of the test system and validation scope
   The modified IEEE 33-bus system is adopted as a representative and reproducible benchmark to validate the proposed three-stage resilience optimization framework. We now explicitly clarify that this network does not correspond to a real port topology, but is adapted to reflect typical characteristics of port power grids, such as a high proportion of critical loads and disaster-related operational constraints. We also explicitly acknowledge that validation on real port networks or additional benchmark systems is an important direction for future work.

2. Enhanced quantitative reporting for pre-disaster multi-scenario analysis
   For the four pre-disaster scenarios considered, we have expanded the result reporting beyond schematic illustrations by adding clearer quantitative metrics. These include expected energy not served, worst-case load shedding performance, and comparative cost outcomes across scenarios, which enable a more transparent and objective comparison among different strategies.

3. Improved reporting of key metrics and cost breakdowns
   In the revised manuscript, the total system cost is further decomposed into investment cost, operating cost, and risk-related cost associated with load shedding. The corresponding results are summarized in an additional table, providing clearer insights into the cost–resilience trade-offs of different optimization approaches.

These revisions significantly improve the transparency, completeness, and interpretability of the numerical results, thereby strengthening the overall validation of the proposed framework.

Comments 7:

There are numerous grammatical errors, occasional repetitions e.g. repeated sentences, inconsistent spacing and capitalization.

Response 7:

Thank you for pointing out the grammatical and formatting issues in the manuscript. We agree that the original version contained grammatical errors, occasional repeated sentences, and inconsistencies in spacing and capitalization, which may affect the readability and professionalism of the paper.

In response, we have carried out a thorough language editing and formatting review of the entire manuscript, with the following improvements:

1. Correcting grammatical errors and awkward sentence structures throughout the text;

2. Removing or consolidating repeated sentences and redundant passages;

3. Standardizing spacing, punctuation, and capitalization, particularly for technical terms, abbreviations, and headings;

4. Refining wording and sentence flow to improve clarity and academic tone.

These revisions have substantially improved the linguistic quality and overall presentation of the manuscript.

Comments 8:

The quality and size of figures can be enhanced to make it more understandable in standard 100% zoom of the page.

Response 8:

Thank you for the reviewer’s suggestion regarding the quality and size of the figures. We agree that, in the original manuscript, some figures could be improved to enhance readability at the standard 100% page zoom level.

In response, we have systematically enhanced and reformatted all figures in the revised manuscript. The main improvements include:

1. Increasing figure resolution to ensure clear visualization at 100% zoom;

2. Enlarging fonts, line widths, and key annotations so that important information is easily readable without additional zooming;

3. Adjusting figure layout and proportions to reduce visual clutter and improve overall clarity.

These revisions have improved the readability and presentation quality of the figures at standard page zoom.

Reviewer 4 Report

Comments and Suggestions for Authors

This paper proposes a three-stage resilience optimization method for port power grids under disaster scenarios, aiming to enhance their supply capacity and operational flexibility across the pre-disaster, during-disaster, and post-disaster phases. However, in order to further enhance the quality of the article and the depth of the research, the following points are suggested:

1. Although the title emphasizes "Port Power Grids," the current modeling does not differ significantly from general distribution networks. The authors should incorporate characteristics that reflect port machinery operations.
2. Figure 1 mentions the Column-and-Constraint Generation (C&CG) algorithm, but Section 2 does not provide the specific mathematical decomposition (formulas for the Master Problem and Subproblem) for this model. The following related work can be compared: a: Hydrogen as the nexus of future sustainable transport and energy systems b: Sustainable-Fast Charging Strategy for Lithium-ion Batteries based on A Random Forest- Enhanced Electro-Thermal-Degradation Model
3. What are the innovations in the post-disaster recovery stage?
4. The case study section only demonstrates the effectiveness of the proposed method. It lacks comparative analysis with other advanced methods.
5. The modeling section lacks a model for mobile energy storage dispatch, such as a traffic network model.
6. Please break down the costs into CAPEX (investment cost), OPEX (operating cost), and risk cost (load shedding penalty).
7. Some symbols in the formulas are not clearly defined when first used.
8. The paper mentions "natural disasters" and "typhoons" but models the disaster simply as random line/node failures (N-k contingencies).

Comments on the Quality of English Language

good

Author Response

Comments 1：

Although the title emphasizes "Port Power Grids," the current modeling does not differ significantly from general distribution networks. The authors should incorporate characteristics that reflect port machinery operations.

Response 1：

Thank you for the reviewer’s insightful comment regarding the distinction between port power grids and general distribution networks. We agree that, in the original manuscript, the port-specific characteristics were not sufficiently emphasized at the modeling level, which may reduce the perceived relevance of the “port” application highlighted in the title.

In the revised manuscript, we have strengthened and clarified the representation of port-specific operational characteristics, as summarized below:

1. Explicit modeling of critical port loads
   The model explicitly distinguishes critical port loads from ordinary loads and assigns higher load-shedding penalties to port-related equipment such as quay cranes, refrigerated container facilities, and communication and dispatch systems. This reflects the high sensitivity of port operations to power interruptions and the clear functional prioritization typical of port machinery.

2. Operational constraints reflecting high-power port equipment
   Port machinery is typically characterized by high power ratings, concentrated connections, and sensitivity to voltage and reactive power conditions. These characteristics are captured through active–reactive power coupling, voltage constraints, and equipment capacity limits in the proposed model.

3. Resilience objectives aligned with port operational continuity
   Rather than minimizing total load shedding alone, the objective function emphasizes maintaining the supply of critical port equipment under disaster conditions, which differentiates the proposed framework from conventional distribution network restoration models.

4. Clarified description of port characteristics in the text
   Additional explanations have been added in the system description and case study sections to explicitly link port machinery operating characteristics to the adopted load classification, parameter settings, and resilience objectives, thereby strengthening the connection between the model and the port application context.

We also clarify in the discussion section that, while the underlying network model is structurally general, port-specific characteristics are primarily reflected through load composition, operational constraints, and objective design. Incorporating more detailed models of port machinery operations (e.g., crane scheduling or shift-based operation patterns) is identified as an important direction for future research.

Comments 2：

Figure 1 mentions the Column-and-Constraint Generation (C&CG) algorithm, but Section 2 does not provide the specific mathematical decomposition (formulas for the Master Problem and Subproblem) for this model. The following related work can be compared: a: Hydrogen as the nexus of future sustainable transport and energy systems b: Sustainable-Fast Charging Strategy for Lithium-ion Batteries based on A Random Forest- Enhanced Electro-Thermal-Degradation Model

Response 2：

Thank you for the reviewer’s comments regarding the consistency between the algorithmic description in Figure 1 and the mathematical formulation in Section 2. We agree that, although Figure 1 illustrates the overall solution procedure based on the Column-and-Constraint Generation (C&CG) algorithm, the original manuscript did not explicitly present the mathematical decomposition into a master problem and a subproblem, which may reduce the clarity of the implementation details.

In the revised manuscript, we have addressed this issue as follows:

1. Explicit description of the C&CG mathematical decomposition
   Section 2 has been revised to clearly describe the decomposition of the two-stage robust optimization model under the C&CG framework. The roles of the master problem and the subproblem are now explicitly stated: the master problem determines the pre-disaster configuration decisions and provides a lower bound on the objective value, while the subproblem identifies the worst-case uncertainty realization and evaluates the corresponding operational cost given the master solution. These two components are linked through an iterative constraint-generation process. The corresponding mathematical expressions and explanations have been added to the revised manuscript.

2. Clarification of the original presentation choice
   In the original version, Figure 1 was used primarily to illustrate the overall logical flow of the three-stage framework and the robust solution process. Following the reviewer’s suggestion, we have now complemented this high-level illustration with a more formal mathematical description to ensure consistency between the conceptual and mathematical representations.

3. Comparison with the suggested related works
   We have also clarified the relationship between the present work and the suggested references. The cited studies mainly focus on energy–transport coupling and detailed battery charging and degradation modeling at the energy carrier or device level, whereas this paper concentrates on resilience-oriented optimization of distribution systems under disaster scenarios with multi-stage decision-making. This distinction has been explicitly discussed in the revised related work section.

These revisions improve the transparency of the proposed solution approach and better align the algorithmic description with the mathematical formulation.

Comments 3：

What are the innovations in the post-disaster recovery stage?

Response 3：

Thank you for the reviewer’s question regarding the innovations in the post-disaster recovery stage. We agree that post-disaster recovery of distribution systems has been widely studied, and therefore it is important to clearly articulate the incremental contributions of this work at this stage.

The innovations of the proposed approach in the post-disaster recovery stage can be summarized as follows:

1. Tight coupling with pre-disaster and in-disaster decisions
   Unlike many studies that address post-disaster recovery as an isolated problem, the recovery stage in this work is explicitly coupled with pre-disaster resource pre-positioning and in-disaster operational decisions. Network reconfiguration, source–load coordination, and mobile resource dispatch in the post-disaster stage are all constrained by decisions made in earlier stages, resulting in a coherent and consistent recovery trajectory across stages.

2. Coordinated use of mobile energy storage and EVs for recovery
   The post-disaster recovery model explicitly incorporates mobile energy storage systems and EVs as relocatable power sources and jointly optimizes their deployment with network reconfiguration and load restoration. This extends traditional recovery models that primarily rely on fixed distributed generators or topology reconfiguration alone.

3. Recovery strategies oriented toward critical port load priorities
   Rather than maximizing total restored load only, the proposed recovery stage emphasizes the prioritized restoration of critical port-related loads through differentiated load-shedding penalties, aligning the recovery strategy with the operational requirements of port systems.

4. Recovery evaluation under worst-case conditions within a robust framework
   Post-disaster recovery decisions are evaluated within a robust optimization framework, where recovery performance is assessed under worst-case uncertainty realizations. This ensures that the resulting recovery strategies remain feasible and effective even under adverse conditions, rather than being optimized solely for nominal scenarios.

Comments 4：

The case study section only demonstrates the effectiveness of the proposed method. It lacks comparative analysis with other advanced methods.

Response 4：

Thank you for the reviewer’s comment regarding the lack of comparative analysis in the case study section. We agree that the original version primarily demonstrated the effectiveness of the proposed approach, while the depth of comparison with other advanced methods was limited.

In the revised manuscript, we have addressed this issue as follows:

1. Addition of comparative methods and results
   The proposed framework is now compared with several representative baseline strategies, including a deterministic optimization approach without robustness considerations, as well as strategies without mobile energy storage or with limited recovery coordination. These comparisons allow for a clearer assessment of the proposed method in terms of critical load restoration, system operating cost, and adaptability to disaster scenarios.

2. Ensuring fairness and comparability
   All compared methods are evaluated under the same network topology, disaster scenarios, and operational constraints to ensure a fair and reproducible comparison. The results are summarized through additional tables and detailed discussions in the revised manuscript.

3. Clarification of the scope of comparison
   We clarify that the primary objective of this study is to propose and validate a three-stage resilience-oriented optimization framework for port power grids, rather than to benchmark all existing advanced algorithms. Comprehensive comparisons with more computationally intensive or fundamentally different approaches are identified as an important direction for future research.

These additions strengthen the case study section by providing clearer comparative insights into the performance of the proposed method.

Comments 5：

The modeling section lacks a model for mobile energy storage dispatch, such as a traffic network model.

Response 5：

Thank you for the reviewer’s comment regarding the lack of a detailed dispatch model for mobile energy storage, such as an explicit transportation network model. We agree that the original manuscript does not explicitly model the transportation process or routing constraints of mobile energy storage systems.

In this work, the modeling of mobile energy storage focuses on its system-level role as a relocatable energy resource for resilience enhancement, rather than on a detailed representation of the transportation process itself. Specifically, the mobility of energy storage is abstracted through node-connection decisions and power dispatch constraints, which reflect the set of nodes that mobile storage can access at different stages. This abstraction captures the deployment outcomes and accessibility of mobile energy storage under disaster conditions, while maintaining computational tractability. Similar modeling assumptions are commonly adopted in resilience-oriented optimization studies.

Comments 6：

Please break down the costs into CAPEX (investment cost), OPEX (operating cost), and risk cost (load shedding penalty).

Response 6：

Thank you for the reviewer’s suggestion to further decompose the total system cost. We agree that breaking down the overall cost into capital expenditure (CAPEX), operating expenditure (OPEX), and risk-related cost (load shedding penalty) provides clearer insights into the economic and resilience trade-offs of different strategies.

In the revised manuscript, the total cost is explicitly decomposed as follows:

• CAPEX represents the investment cost associated with the pre-disaster pre-positioning and deployment of mobile energy storage systems;

• OPEX corresponds to the operating cost of the system under disaster scenarios, including generation, dispatch, and network operation–related costs;

• Risk cost is captured through load shedding penalties, which quantify the economic impact of unserved energy, particularly for critical loads.

These cost components are now clearly identified in the model description and summarized in an additional table in the case study section, enabling a more transparent comparison of cost structures across different optimization strategies.

Comments 7：

Some symbols in the formulas are not clearly defined when first used.

Response 7：

Thank you for pointing out that some symbols in the formulas are not clearly defined at their first appearance. We agree that this issue may cause confusion and reduce the clarity of the formulation.

In response, we have carefully reviewed all equations and the accompanying text to ensure that every symbol is explicitly defined when it is first introduced, including sets, indices, parameters, and decision variables. The notation has also been standardized throughout the manuscript and aligned with the added Nomenclature table. These revisions have been fully incorporated into the revised version of the paper.

Comments 8：

The paper mentions "natural disasters" and "typhoons" but models the disaster simply as random line/node failures (N-k contingencies).

Response 8：

Thank you for the reviewer’s comment regarding the consistency between the disaster description and the modeling approach. We agree that, while the manuscript refers to natural disasters such as typhoons, the mathematical formulation represents disasters through line and node outages using an N-k contingency framework, and the correspondence between the two was not sufficiently clarified.

In this work, natural disasters (particularly typhoons) are not modeled as explicit meteorological processes, but rather through their structural impacts on power system components. Extreme events such as typhoons commonly cause pole failures, conductor damage, and substation or node outages due to strong winds and associated hazards. Therefore, the disaster is abstracted as multiple simultaneous line and node outages using an N-k contingency representation. This outcome-oriented modeling approach is widely adopted in power system resilience studies, as it captures the dominant operational consequences of disasters while maintaining computational tractability.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In response to the growing threats posed by frequent climate-related disasters to the continuity of port operations, this article proposes a comprehensive three-stage resilience optimization method for port power grids. The approach addresses the pre-disaster, during-disaster, and post-disaster phases specifically. This is a topic of interest for researchers in related fields, but at this stage, some improvements are still needed. My detailed opinions are as follows:

1. There are numerous instances where Chinese full-width punctuation marks (such as ， ； ［ ］ （ ）) are used instead of standard English half-width punctuation. This occurs in the Author list (Page 1), Keywords (Page 1), and extensively in the References section (e.g., Refs 10-18). Please standardize the punctuation throughout the manuscript
2. Please check the consistency of mathematical notations. For example, the Big-M constant is defined as 'M₀' in the Nomenclature (Page 4), but denoted as 'M ' in Equation (30) on Page 17."

Author Response

Comments 1:

There are numerous instances where Chinese full-width punctuation marks (such as ， ； ［ ］ （ ）) are used instead of standard English half-width punctuation. This occurs in the Author list (Page 1), Keywords (Page 1), and extensively in the References section (e.g., Refs 10-18). Please standardize the punctuation throughout the manuscript

Response: We would like to express our sincere gratitude for pointing out the improper use of Chinese full-width punctuation marks in the manuscript. In accordance with the standard conventions of English academic writing, we have conducted a thorough check and comprehensive revision of the punctuation throughout the entire manuscript, including the author list (Page 1), keywords (Page 1), and especially the references section (e.g., Refs 10–18). All the misused Chinese full-width punctuation marks (e.g., ，；［］（）) have been replaced with standard English half-width punctuation marks.

Comments 2 :

Please check the consistency of mathematical notations. For example, the Big-M constant is defined as 'M₀' in the Nomenclature (Page 4), but denoted as 'M ' in Equation (30) on Page 17."

Response : 

We sincerely appreciate your pointing out the issue related to the expression of mathematical notations in the manuscript. Upon careful check, we confirm that M₀ in the Nomenclature (Page 4) and M in Equation (30) (Page 17) are two distinct parameters. We have supplemented and refined the physical meaning and definition of M, clearly distinguished the connotations and application scenarios of these two parameters, and standardized the use of both notations throughout the manuscript to avoid confusion.   In addition, we have conducted a comprehensive check on the definition and reference of all mathematical notations in the text to ensure that the notation system is clear, accurate and unambiguous. Thank you again for your rigorous comments, which have helped us further improve the standardization of our manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

Given that:

• all major technical and presentation issues from the first review have been substantively addressed,

• the modelling assumptions and solution procedure are now clearly documented, and

• the case study has been strengthened with critical-load detail and a baseline comparison,

my overall judgement is that the manuscript is now suitable for publication.

Author Response

Comments 1 :

• all major technical and presentation issues from the first review have been substantively addressed,

• the modelling assumptions and solution procedure are now clearly documented, and

• the case study has been strengthened with critical-load detail and a baseline comparison,

my overall judgement is that the manuscript is now suitable for publication.

Response : 

We would like to express our sincere gratitude for your careful review of our manuscript and your positive feedback despite your busy schedule.   Your professional insights have been invaluable to us in refining the work. Thank you again for your time and effort!

Reviewer 3 Report

Comments and Suggestions for Authors

Comments well integrated.

Comments on the Quality of English Language

There are numerous grammatical errors, occasional repetitions e.g. repeated sentences, inconsistent spacing and capitalization.

Author Response

Comments 1:There are numerous grammatical errors, occasional repetitions e.g. repeated sentences, inconsistent spacing and capitalization.

Response :

We sincerely appreciate your pointing out the issues of grammatical errors, occasional repetitions, inconsistent spacing and capitalization in the manuscript. We have carefully checked the entire text, corrected all grammatical mistakes, removed repetitive expressions, and standardized the use of spacing and capitalization throughout the manuscript.   Thank you again for your rigorous comment