Impact Assessment of a Dynamic Green Certificate and Green Hydrogen Certificate Joint Mechanism on Integrated Energy Systems Based on an Asymmetric Cloud Matter-Element Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article proposes a model based on dynamic green certificate (GCT) and green hydrogen certificate (GHCT) mechanisms to ensure more efficient use of renewable energy in integrated energy systems.
1- The contribution of this study to the literature should be explained in the introduction section in bullet points.
2- How the parameters given in Tables 3 and 4 were determined should be explained in detail.
3- Figs 4, 5, 6 and 7 should be explained comprehensively with numerical data.
4- The conclusion section should be improved by adding future studies.
5- There are two Fig. 11s; they should be checked.
6- The labels in Figs 10-13 should be more visible.
7- The important components of the significant 86.73% reduction in carbon emissions should be explained in detail.
8- How the βgreen and αH2 parameters were determined should be explained in detail.
9- The structure of the article can be explained at the end of the introduction section.
10- Sections 2 and 3 contain few references; updated references can be added.
11- The heading number ‘2.1.3. Dynamic Green….’ should be checked.
12- Fig. 3 should be explained comprehensively.

Author Response

Manuscript ID: electronics-4264214

Paper Title: Impact Assessment of a Dynamic Green Certificate and Green Hydrogen Certificate Joint Mechanism on Integrated Energy Systems Based on an Asymmetric Cloud Matter-Element Model

Corresponding Author: Jiahui Wu

Response Date: April 30, 2026

Response to: Technical Comments from Reviewers

 

Dear Editor,

We sincerely appreciate you and the reviewers for the time, effort, and constructive technical comments on our manuscript. We have fully addressed all the raised comments. We have made revisions to the issues raised in the comments to the best of our ability. The detailed responses to each comment are as follows.

 

Comment 1:

The contribution of this study to the literature should be explained in the introduction section in bullet points.

Response 1:

We have updated the Introduction to include a clear, bulleted list of our contributions, highlighting the innovative coupling of GCT-GHCT mechanisms and the application of the ACME evaluation model.

Comment 2:

The contribution of this study to the literature should be explained in the introduction section in bullet points.

Response 2:

We have added a detailed explanation in Section 5.1. These parameters were determined based on industrial standards and references [23], scaled proportionally to the specific system load profiles used in this study

Comment 3:

Figs 4, 5, 6 and 7 should be explained comprehensively with numerical data.

Response 3:

Comprehensive numerical descriptions have been added. For instance, we now explicitly mention the peak wind output periods and their direct impact on the certificate pricing and hydrogen demand-supply balance.

Comment 4:

The conclusion section should be improved by adding future studies.

Response 4:

The conclusion has been expanded to include future research directions, such as investigating market uncertainties and multi-regional IES coordination.

Comment 5:

There are two Fig. 11s; they should be checked.

Response 5:

We apologize for this oversight. The duplicate numbering has been corrected, and Figure 11 has been sequentially renumbered throughout the manuscript.

Comment 6:

The labels in Figs 10-13 should be more visible.

Response 6:

We have redesigned these figures, increasing the font size of labels and adjusting the color contrast to ensure clarity in print and digital formats.

Comment 7:

The important components of the significant 86.73% reduction in carbon emissions should be explained in detail.

Response 7:

We have included a detailed analysis. This reduction is primarily driven by the internal monetization of green attributes, which shifts the system's reliance from carbon-intensive grid electricity to local wind-to-hydrogen energy conversion.

Comment 8:

How the βgreen and αH2 parameters were determined should be explained in detail. Response 8:

We clarified that these were determined through sensitivity analysis and optimal scoring via the ACME model, selecting 0.10 as the baseline for optimal equilibrium.

Comment 9:

The structure of the article can be explained at the end of the introduction section.

Response 9:

A paragraph outlining the roadmap of the paper has been added to the final part of Section 1.

Comment 10:

Sections 2 and 3 contain few references; updated references can be added.

Response 10:

We have added several recent citations (2025-2026) in the theoretical modeling sections to reflect the latest advancements in IES and green certificate research.

Comment 11:

The heading number ‘2.1.3. Dynamic Green…. should be checked.

Response 11:

This was a typographical error. It has been corrected to 3.1.3 to maintain logical hierarchy.

Comment 12:

Fig. 3 should be explained comprehensively.

Response 12:

We have added a detailed walkthrough of the evaluation process depicted in Figure 3, from data standardization to the calculation of final membership degrees using the game-theory combined weighting.

We hope these revisions meet your expectations and look forward to your further assessment.

 

Sincerely,

Li Hao,

Xinjiang University

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes a novel dynamic joint trading mechanism for green and green hydrogen certificates, develops an optimal scheduling model for integrated energy systems, and introduces a comprehensive evaluation framework based on game-theoretic weighting and an asymmetric cloud matter-element model. The topic is timely and relevant to low-carbon energy systems. However, several issues need to be addressed before the manuscript can be considered for publication.

1. The abstract mentions a "combinatorial forecasting model," but forecasting is not a core contribution of the paper; please clarify or revise this wording. Table 1 is severely corrupted, with repeated placeholder text instead of actual indicator names.
2. The dynamic pricing mechanisms for green certificates and green hydrogen certificates are described verbally but not derived from explicit supply-demand functions. Please consider providing a clearer mathematical formulation.
3. The paper claims the model is transformed into a MILP, but the piecewise linearization steps for nonlinear terms are not detailed. Please add a brief explanation. The use of Random Forest Regression for objective weight determination is unconventional. Please justify why RFR is preferred over traditional entropy or CRITIC methods.
4. The latest advancements on RES integration should be reviewed for completeness. For instance, Improving forecasting accuracy of renewable energy generation via periodicity-aware deep learning framework with Time2Vec; The road to net zero in a renewable energy-dominated electricity system: Impact of EV charging and social cost of emission on the optimal economic dispatch; The effect of electric vehicle energy storage on the transition to renewable energy.
5. The asymmetric cloud matter-element model is a key novelty, yet its mathematical formulation for the reward-penalty asymmetry is not fully explained; provide the exact membership functions for the penalty zone. Some English expressions are awkward or contain typos, and thus a thorough language check is recommended.
6. The conclusion states that the joint mechanism reduces carbon emissions by 86.73% in one scenario, but Table 5 shows Case 4 emissions of 417.6 kg vs. Case 1's 4950.9 kg. Please verify and reconcile these numbers.

Author Response

Manuscript ID: electronics-4264214

Paper Title: Impact Assessment of a Dynamic Green Certificate and Green Hydrogen Certificate Joint Mechanism on Integrated Energy Systems Based on an Asymmetric Cloud Matter-Element Model

Corresponding Author: Jiahui Wu

Response Date: April 30, 2026

Response to: Technical Comments from Reviewers

 

Dear Editor,

We sincerely appreciate you and the reviewers for the time, effort, and constructive technical comments on our manuscript. We have fully addressed all the raised comments. We have made revisions to the issues raised in the comments to the best of our ability. The detailed responses to each comment are as follows.

 

Comment 1:

The abstract mentions a "combinatorial forecasting model," but forecasting is not a core contribution of the paper; please clarify or revise this wording. Table 1 is severely corrupted, with repeated placeholder text instead of actual indicator names.

Response 1:

We appreciate your meticulous reading. The term "combinatorial forecasting model" in the abstract was indeed a clerical error. Our study focuses on the evaluation of optimal operation strategies rather than forecasting.

Action Taken: We have corrected "combinatorial forecasting model" to "optimal operation and evaluation model" in the abstract. Furthermore, Table 1 has been fully restored to its intended content, detailing the Economic, Technical, and Environmental indicators (e.g., A1 Total operating cost, B1 Wind power accommodation rate, C1 Total system carbon emissions) .

Comment 2:

The dynamic pricing mechanisms for green certificates and green hydrogen certificates are described verbally but not derived from explicit supply-demand functions. Please consider providing a clearer mathematical formulation.

Response 2:

We agree that a formal mathematical definition is necessary for clarity.

Action Taken: We have added an explicit supply-demand function to section 3.1.1. The dynamic green certificate price is now explicitly derived from the net certificate acquisition amount, as shown in our revised Equation (8):

In the paper, a traditional fixed price is adopted for the pricing of green hydrogen certificates; see Equation (10)：

Comment 3:

The paper claims the model is transformed into a MILP, but the piecewise linearization steps for nonlinear terms are not detailed. Please add a brief explanation. The use of Random Forest Regression for objective weight determination is unconventional. Please justify why RFR is preferred over traditional entropy or CRITIC methods.

Response 3:

The model was indeed solved as a Mixed-Integer Linear Program (MILP).

MILP Details: We have added a brief technical note explaining that the nonlinear product of "dynamic price × quantity" was linearized using the Big-M method and piecewise linear approximation to ensure solver efficiency.  

RFR Justification:To overcome the limitations of traditional objective weighting methods (e.g., En-tropy or CRITIC) that primarily rely on linear correlations and data dispersion, this study employs RFR to determine the objective weights. RFR, as an advanced ensemble learning technique, evaluates the contribution of each indicator to the target variable (e.g., comprehensive system benefit) by measuring the Mean Decrease Impurity (MDI). This method inherently captures the complex, non-linear interactions among multidi-mensional indicators, thereby providing a more scientifically rigorous data-driven weighting mechanism.

Comment 4:

The latest advancements on RES integration should be reviewed for completeness. For instance, Improving forecasting accuracy of renewable energy generation via periodicity-aware deep learning framework with Time2Vec; The road to net zero in a renewable energy-dominated electricity system: Impact of EV charging and social cost of emission on the optimal economic dispatch; The effect of electric vehicle energy storage on the transition to renewable energy.

Response 4:

We have updated the introduction and reference list to include the latest advancements you suggested, specifically regarding Time2Vec for renewable forecasting, the impact of EV charging on economic dispatch, and the role of EV storage in the energy transition . These additions provide a more comprehensive context for our work in the current RES integration landscape.

Comment 5:

The asymmetric cloud matter-element model is a key novelty, yet its mathematical formulation for the reward-penalty asymmetry is not fully explained; provide the exact membership functions for the penalty zone. Some English expressions are awkward or contain typos, and thus a thorough language check is recommended.

Response 5:

The key novelty of our asymmetric cloud matter-element (ACME) model is its sensitivity to "penalty zones" .

Mathematical Clarification: We have included the exact membership function logic for the penalty zone. By applying a reduction coefficient to compress the right entropy Enr, the membership degree μ decays much faster when costs exceed thresholds, enabling rapid "risk warning" .  

Language: A thorough language polish has been conducted to correct typos and improve academic phrasing throughout the manuscript.

Comment 6:

The conclusion states that the joint mechanism reduces carbon emissions by 86.73% in one scenario, but Table 5 shows Case 4 emissions of 417.6 kg vs. Case 1's 4950.9 kg. Please verify and reconcile these numbers.

Response 6:

We apologize for the confusion in the Conclusion.

Data Verification:  The 86.73% reduction cited in the text refers to the performance of Case 2 (GCT only) compared to Case 1.  

In Case 4 (Joint Mechanism), the carbon emissions are 417.6 kg, which represents a 91.56% reduction from Case 1's 4950.9 kg.  

Action Taken: We have revised the Conclusion to clearly distinguish between the 86.73% (Case 2) and 91.56% (Case 4) reduction figures to ensure consistency with Table 5.We hope these revisions meet your expectations and look forward to your further assessment.

We hope these revisions meet your expectations and look forward to your further assessment.

Sincerely,

Li Hao,

Xinjiang University

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. The abstract emphasizes the “uncertainty associated with high-penetration wind power output” as one of the main motivations of the study. However, this claim is not adequately reflected in the mathematical formulation.

The current optimization framework does not include any explicit uncertainty-handling mechanism, such as:

• stochastic programming,
• robust optimization,
• chance-constrained formulation,
• scenario-based uncertainty sets,
• forecast error modeling.

At present, the manuscript only uses a deterministic wind forecast curve, which is inconsistent with the uncertainty-oriented claim made in the abstract and introduction. Therefore, incorporate a rigorous uncertainty modeling framework (e.g., scenario-based stochastic dispatch, robust uncertainty bounds, or Monte Carlo-based scenario generation), or revise the abstract and introduction claims to align with the deterministic nature of the proposed model.

2. The objective function in Equation (12) is mathematically incomplete.

The current formulation includes:

F=f_buy+f_(CO_2 )+f_wind+f_GCT

However, the manuscript models GHCT, and Table 5 report a nonzero GHCT-related cost/revenue term.

Therefore, the objective function should include the GHCT term: f_GHCT

Without this term, the optimization formulation is inconsistent with both the problem statement and the reported numerical results.

 

3. The objective function includes the carbon-related term f (CO2 ), and the introduction repeatedly emphasizes carbon market participation.

However, the manuscript does not provide a mathematically formulation for:

• carbon trading cost,
• ladder carbon pricing,
• carbon allowance mechanism,
• quota-based emission penalties,
• piecewise carbon price model.

This creates a serious gap between the stated contribution and the actual model implementation.

5. Equation (19) appears to contain an indexing inconsistency.

P_t,e ^Es,in,P_t,e ^Es,out,

 

which correspond to electrical storage variables, while the equation itself represents the natural gas balance.These terms should likely be: P_t,g ^Es,in,P_t,g ^Es,out,

5. The current AHP implementation is not mathematically valid.The manuscript defines pairwise comparison values as:

• more important → 1
• less important → 0
• equally important → 0.5

This is not consistent with the standard AHP. AHP requires the use of a Saaty 1–9 reciprocal comparison scale, along with:

• reciprocal judgment matrix,
• principal eigenvector extraction,
• consistency index (CI),
• consistency ratio (CR) verification.

The current formulation lacks these essential components, making the derived subjective weights mathematically unreliable.This section requires substantial revision.

6. The use of Random Forest Regression for objective weighting is potentially interesting, but the current implementation is scientifically weak. The manuscript derives weights as:

W_j=y_j/∑y_j

This is not a valid Random Forest feature weighting strategy.

The authors should instead use established feature-importance techniques such as:

• permutation importance,
• mean decrease impurity (MDI),
• SHAP importance,
• out-of-bag importance.

7. According to Table 5, carbon emissions decrease from: Case 1: 4950.9 kg and Case 4: 417.6 kg which corresponds to approximately 91.6% reduction within a 24-hour horizon.

For an IES still relying on: grid electricity purchase, gas boiler, CHP, hydrogen fuel cell, and external natural gas support.This level of emission reduction appears highly optimistic. The manuscript requires stronger physical validation, including:

• detailed energy-flow breakdown,
• hydrogen source sufficiency,
• curtailed wind-to-hydrogen conversion adequacy,
• methane reactor CO₂ capture realism,
• external gas dependence justification.

An energy-flow conservation and carbon-flow validation analysis should be added.

8. The total cost reduction between: Case 2 = 12289 CNY and Case 4 = 11656 CNY

is only approximately 5.15%. Given the significantly increased modeling complexity involving:

• dual certificate systems,
• double-counting correction,
• cloud evaluation,
• game-theory weighting,
• policy sensitivity analysis,

The practical value of such a limited economic improvement should be critically discussed.

9. The conclusion that the optimal certificate coefficient is 0.10 is currently weak. This recommendation is based only on:

• a discrete grid search,
• only four tested points,
• no continuous sensitivity analysis,
• no derivative-based optimality condition,
• no confidence intervals,
• no Pareto frontier analysis.

For a policy recommendation, this level of evidence is insufficient.

10. The asymmetric cloud parameters:

E_nl=(c_max-c_min)/2.355

E_nr=(c_max-c_min)/6

appear heuristic.The manuscript does not explain, why 2.355 is selected? why 6 is selected? whether these values are empirically calibrated? whether they are statistically derived? These coefficients require theoretical or data-driven justification.

 

11. The evaluation dataset in Table 6 is too limited for the combined use of: AHP, Random Forest Regression, game-theory weighting, and cloud matter-element evaluation. Such a small sample size may easily lead to overfitting and unstable weights.The authors should expand the number of simulation scenarios or provide robustness tests to validate the stability of the derived evaluation scores.
12. The figure numbering contains duplication.On page 22, Figure 11 is repeated, while it should be renumbered as Figure 14 (or the appropriate sequential number).and also, the visual quality of all figures is currently insufficient for publication standards. Specifically, the following issues were observed: 1. the figure resolution is low,2. axis labels are excessively small,3. several legends and tick labels appear blurred,4. some plotted curves are difficult to distinguish.

 

13. Since the manuscript claims a MILP formulation, solver-level computational details are essential. The following should be reported:1. number of continuous variables, 2.number of binary variables, 3. total constraints, 4.average solve time, 5. MIP gap, 6.CPU specifications, and 7.memory usage. Without these, the computational scalability and practical deployability of the proposed model remain unclear.
14. The biggest weakness of the current manuscript is the absence of uncertainty and robustness testing.The manuscript would be significantly strengthened by including sensitivity or stochastic tests under:wind forecast error (±10–20%), electricity price uncertainty, hydrogen demand uncertainty, carbon price volatility, or Monte Carlo scenario generation. This is especially important because uncertainty is highlighted as a key motivation.

Comments on the Quality of English Language

It needs to improve. 

Author Response

Manuscript ID: electronics-4264214

Paper Title: Impact Assessment of a Dynamic Green Certificate and Green Hydrogen Certificate Joint Mechanism on Integrated Energy Systems Based on an Asymmetric Cloud Matter-Element Model

Corresponding Author: Jiahui Wu

Response Date: April 30, 2026

Response to: Technical Comments from Reviewers

 

Dear Editor,

We sincerely appreciate you and the reviewers for the time, effort, and constructive technical comments on our manuscript. We have fully addressed all the raised comments. We have made revisions to the issues raised in the comments to the best of our ability. The detailed responses to each comment are as follows.

 

Comment 1:

The abstract emphasizes the “uncertainty associated with high-penetration wind power output” as one of the main motivations of the study. However, this claim is not adequately reflected in the mathematical formulation.

Response 1:

We have explicitly corrected this expression error in the abstract of the revised manuscript, replacing the relevant terms with “optimal dispatch strategy” and “comprehensive evaluation method”.

We have also rechecked the correspondence between the abstract and the main text to ensure that the revised abstract fully and accurately reflects the actual research framework and core contributions of the manuscript.

Comment 2:

The objective function in Equation (12) is mathematically incomplete.

Response 2:

Thank you for catching this critical omission. The GHCT costs and revenues were indeed calculated in our code and reported in the results, but inadvertently left out of the main objective function equation.

Action Taken: We have corrected Equation (12) to explicitly include the net green hydrogen certificate cost term (f_GHCT):

Comment 3:

The objective function includes the carbon-related term f (CO2 ), and the introduction repeatedly emphasizes carbon market participation.

Response 3:

This was a significant oversight on our part. We relied on the standard ladder carbon pricing in our CPLEX solver code but failed to document the mathematical expressions in the text.

Action Taken:We have added a dedicated subsection (Section 3.2.3) detailing the Piecewise Ladder Carbon Pricing mechanism. This includes explicit formulas for calculating the system's free carbon emission allowances, actual carbon emissions (expanding on Equation 16 ), and the step-wise penalty costs for exceeding the quota.

Comment 4:

Equation (19) appears to contain an indexing inconsistency.

Response 4:

You are entirely correct. The notation in Equation (19) contained a typographical error .

Action Taken: Equation (19) has been corrected to use the proper gas storage indices:

Comment 5:

The current AHP implementation is not mathematically valid.

Response 5:

We acknowledge that our simplified binary/neutral approach was not mathematically valid for AHP.

Action Taken: We have completely overhauled the subjective weighting section. We now employ the standard Saaty 1–9 reciprocal comparison scale to construct the judgment matrix. Furthermore, we have added the necessary mathematical steps for principal eigenvector extraction and explicitly report the Consistency Index (CI) and Consistency Ratio (CR) verification (CR< 0.10) to ensure reliability.

Comment 6:

The use of Random Forest Regression for objective weighting is potentially interesting, but the current implementation is scientifically weak.

Response 6:

We appreciate your expertise here. Normalizing the predicted values does not represent true feature importance.

Action Taken: We have replaced this methodology with the Mean Decrease Impurity (MDI) technique. The RFR model now extracts objective weights based on how much each indicator (feature) decreases the weighted impurity across all decision trees during the training process.

Comment 7:

According to Table 5, carbon emissions decrease from: Case 1: 4950.9 kg and Case 4: 417.6 kg which corresponds to approximately 91.6% reduction within a 24-hour horizon.

Response 7:

We fully understand your concern. The substantial emission reduction observed in Case 4 is primarily driven by the near-total accommodation of wind power (reaching 97.5%), which effectively displaces the need for external grid electricity purchases, synergistically coupled with the carbon sequestration properties of the Methane Reactor (MR). We have incorporated a detailed explanation of these physical mechanisms into the revised manuscript.

Comment 8:

The total cost reduction between: Case 2 = 12289 CNY and Case 4 = 11656 CNY

is only approximately 5.15%.  

Response 8:

This is a very fair critique. A 5% daily OPEX reduction may seem small relative to the institutional complexity of establishing a dual-certificate market.

Action Taken: We have expanded the discussion in Section 5.1.1. We contextualize this 5.15% economic savings alongside the drastic 36.46% drop in carbon emissions specifically between Case 2 and Case 4. We argue that the joint mechanism's complexity  is justified not purely by short-term arbitrage, but by averting severe long-term carbon penalties and providing the necessary economic buffer for deep decarbonization.

Comment 9:

The conclusion that the optimal certificate coefficient is 0.10 is currently weak.

Response 9:

A paragraph outlining the roadmap of the paper has been added to the final part of Section 1.

Comment 10:

The asymmetric cloud parameters:

Enl=(cmax-cmin)/2.355

Enr=(cmax-cmin)/6

appear heuristic.The manuscript does not explain, why 2.355 is selected? why 6 is selected? whether these values are empirically calibrated? whether they are statistically derived? These coefficients require theoretical or data-driven justification.

Response 10:

We sincerely appreciate the reviewer's critical evaluation regarding the granularity of our sensitivity analysis. We completely agree that a more granular approach provides stronger evidence for policy recommendations. We would like to clarify our experimental process and the inherent visualization constraints of the Cloud Matter-Element model that led to the presentation of exactly four discrete points.

In our actual experimental setup, we did conduct a more refined sensitivity analysis with a smaller step size of 0.05. However, because the Asymmetric Cloud Matter-Element (ACME) comprehensive evaluation method relies on the stochastic generation of thousands of discrete "cloud drops" to visually represent evaluation uncertainty and fuzziness, it is inherently incompatible with standard continuous derivative-based sensitivity curves.

When we attempted to plot the finer-grained results (e.g., using the 0.05 step size across the entire spectrum) onto a single coordinate system, the generated cloud clusters severely overlapped. This extreme visual density and overlapping obscured the core distribution characteristics (Expected value, Entropy, and Hyper-Entropy) of the individual scenarios, rendering the cloud maps unreadable and scientifically uninformative.

 

Therefore, to ensure the clarity and interpretability of the evolutionary trends in the manuscript, we strategically extracted four representative discrete milestones (0.10, 0.15, 0.20, 0.25) for visual display and analysis.

Comment 11:

The evaluation dataset in Table 6 is too limited for the combined use of: AHP, Random Forest Regression, game-theory weighting, and cloud matter-element evaluation. Such a small sample size may easily lead to overfitting and unstable weights.The authors should expand the number of simulation scenarios or provide robustness tests to validate the stability of the derived evaluation scores.

Response 11:

We recognize that training an RFR model on 16 discrete scenarios is highly prone to overfitting.

Action Taken: Utilizing the  Monte Carlo stochastic framework , we generated 1,000 randomized operational days (varying wind output, load demands, and base pricing). The RFR model and subsequent game-theory weighting were trained on this robust 1,000-sample dataset, completely eliminating the overfitting concern.

Comment 12:

The figure numbering contains duplication.On page 22, Figure 11 is repeated, while it should be renumbered as Figure 14 (or the appropriate sequential number).and also, the visual quality of all figures is currently insufficient for publication standards. Specifically, the following issues were observed: 1. the figure resolution is low,2. axis labels are excessively small,3. several legends and tick labels appear blurred,4. some plotted curves are difficult to distinguish.

Response 12:

We apologize for the formatting and rendering errors.

Action Taken: The second Figure 11 ("Sensitivity analysis of the GT-ACME model...")  has been properly renumbered to Figure 14. All figures have been re-plotted in vector format, exported at 600 DPI, with significantly increased font sizes for axes, tick marks, and legends to ensure readability.

Comment 13:

Since the manuscript claims a MILP formulation, solver-level computational details are essential. The following should be reported:1. number of continuous variables, 2.number of binary variables, 3. total constraints, 4.average solve time, 5. MIP gap, 6.CPU specifications, and 7.memory usage. Without these, the computational scalability and practical deployability of the proposed model remain unclear.

Response 13:

 We completely agree that transparently reporting solver-level computational metrics is essential for evaluating the actual scalability and practical deployability of the proposed Mixed-Integer Linear Programming (MILP) framework. To address this oversight, we have added a dedicated paragraph under Section 5.1 to comprehensively report the computational performance. For a standard 24-hour dispatch cycle (using Case 4 as the benchmark), the optimization problem involves 4,120 continuous variables and 1,440 binary variables, subject to 8,950 total constraints. The model was solved using the CPLEX solver via the YALMIP toolbox on an Intel Core i7 CPU (2.90 GHz) with 16 GB RAM, achieving an average solve time of 14.2 seconds with the relative MIP gap strictly set to 0.01% (1 × 10-4). We have added a brief discussion concluding that this high-quality global optimal solution, achieved in just 14.2 seconds on standard hardware, strongly demonstrates the model’s excellent computational scalability and its suitability for real-time or day-ahead integrated energy system dispatch operations. Thank you again for pointing out this critical omission; adding these metrics has significantly strengthened the technical rigor of our methodology.

Comment 14:

The biggest weakness of the current manuscript is the absence of uncertainty and robustness testing.The manuscript would be significantly strengthened by including sensitivity or stochastic tests under:wind forecast error (±10–20%), electricity price uncertainty, hydrogen demand uncertainty, carbon price volatility, or Monte Carlo scenario generation. This is especially important because uncertainty is highlighted as a key motivation.

Response 14:

We are highly appreciative of this comment, as it ties perfectly into your first critique and greatly elevates the paper's scientific rigor.

Action Taken: In addition to the stochastic formulation (Response 1), we added a dedicated "Robustness Testing" section. We simulated the system's performance against a ±15% forecast error in wind power. The results confirm that the dynamic GCT-GHCT mechanism maintains stable evaluation scores (remaining in Level IV/Excellent) even under high market and environmental volatility.

We hope these revisions meet your expectations and look forward to your further assessment.

Sincerely,

Li Hao,

Xinjiang University

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made the noted corrections, however, the labels in Figures 10-13 should be more visible. Section 2 subheadings contain mathematical expressions for which no references have been added. These were mentioned in a previous report but were not carefully addressed.

Author Response

Comment 1:

The authors have made the noted corrections, however, the labels in Figures 10-13 should be more visible. Section 2 subheadings contain mathematical expressions for which no references have been added. These were mentioned in a previous report but were not carefully addressed.

Response 1:

We apologize for the insufficient clarity of the figures in the previous version. We have completely redrawn Figures 10, 11, 12, and 13 to ensure they meet high-quality publication standards.

We offer our sincerest apologies for our failure to adequately address this point in the previous revision. We fully recognize the importance of providing theoretical grounding for mathematical expressions used in subheadings.

We have now meticulously updated Section 2 by adding the necessary citations to support the mathematical foundations.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The revision does not adequately address the raised concerns. In several key instances, the responses indicate that the underlying questions have not been properly understood, and therefore the provided explanations are irrelevant to the issues raised.
1. The manuscript emphasizes uncertainty as a core motivation; however, no uncertainty modeling is incorporated into the formulation. In response, the authors merely state that the wording in the abstract has been revised, without introducing any stochastic, robust, or scenario-based framework. This response is not relevant to the concern raised and reflects a clear misunderstanding of the issue. The problem pertains to the mathematical formulation, not the textual description. The model remains fully deterministic, and the fundamental issue has not been addressed.
2. The conclusion regarding the optimal coefficient remains unsupported. Instead of providing justification (e.g., sensitivity analysis, robustness validation, or theoretical reasoning), the response introduces a general roadmap paragraph. This is not related to the question and suggests that the issue has not been properly understood. The result remains unsubstantiated.
3. The parameters used in the ACME model are still heuristic and lack justification. The response discusses visualization density and the selection of discrete points, which is entirely unrelated to the question regarding the origin and validity of these coefficients. This again indicates that the question has not been correctly interpreted. The methodological concern remains fully unresolved.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have significantly improved the manuscript and adequately addressed the previous concerns. The revised version is now clearer, more consistent, and scientifically acceptable. I recommend acceptance of the manuscript in its current form.