Multi-Dimensional Comfort and EV Stochasticity-Aware Optimization Strategy for Residential PV Storage Systems

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Do not cite References in a lump fashion.

2. The research gap needs to be emphasized properly before projecting Major contributions. The paper structure is also not provided; it must appear at the end of the Introduction section.

3. The caption provided for Fig. 1 is too long; shorten it and the supporting text may be added in the description. 

4. The figures don't seem to be generated in a MATLAB environment and their appearance is also not up to the mark. 

5. Results and analysis are shallow and need substantial improvement to warrant publication. 

6. Although numerical results are provided, they still need to be validated through a comparative analysis. 

7. The conclusion must be a stand-alone section and it should not contain any references. Ensure this aspect.

8. Along with the Nomenclature section, add a list of abbreviations as well because many acronyms are uses in the Manuscript. 

9. Some outdated References [23], [29], [30], [33]... are observed, which must be updated with the latest published papers and you may refer to this relevant work to diversify the literature section "Assessment of design challenges and viability of wireless electric vehicle charging stations in residential setup to empower sustainable e-mobility: A comprehensive review".

10. I couldn't see any supporting flowcharts, which are required given the nature of the problem formulation and I suggest they refer to this work "Performance evaluation of economic viability of a virtual power plant employing multiple nature inspired meta-heuristic techniques".

11. The selection of the optimization method employed to handle the problem is not convincing. The authors must explain the rationale behind this selection.  

Author Response

Dear Reviewer,

We would like to express our sincere gratitude for your time, rigorous evaluation, and highly constructive comments. These insightful suggestions have been invaluable in improving the depth, clarity, and overall quality of our manuscript.

We have carefully studied all the comments and made comprehensive revisions to the manuscript. All modifications in the revised manuscript have been highlighted for your convenience. Below, please find our point-by-point responses to the reviewers' comments.

Reviewer Comment 1: Do not cite References in a lump fashion.

Response: We thank the reviewer for pointing out this formatting issue. In the revised manuscript, we have carefully reviewed the literature section and unpacked all lumped citations (e.g., changing formats like [1-5] into individual, specific citations placed exactly where the relevant concepts are discussed). This ensures that each cited paper directly and accurately supports the preceding statement.

Reviewer Comment 2: The research gap needs to be emphasized properly before projecting Major contributions. The paper structure is also not provided; it must appear at the end of the Introduction section.

Response: We appreciate these structural recommendations, which greatly enhance the readability of our paper.

• We have rewritten the paragraphs immediately preceding the "Major Contributions" bullet points in the Introduction. The revised text now explicitly emphasizes the research gaps (e.g., the lack of a unified optimization framework that concurrently incorporates EV travel stochasticity, a multi-dimensional dynamic comfort index, and an explicit mechanism to quantify the economic value of load smoothing).
• Furthermore, we have added a dedicated paragraph at the very end of the Introduction section that clearly outlines the organizational structure of the rest of the paper.

Reviewer Comment 3: The caption provided for Fig. 1 is too long; shorten it and the supporting text may be added in the description.

Response: Thank you for this helpful suggestion. We have significantly shortened the caption for Figure 1 to make it concise and standard. The detailed explanatory text that was previously in the caption has been moved into the main body of the manuscript (Section 2), where it better supports the description of the HEMS physical and decision layers.

Reviewer Comment 4: The figures don't seem to be generated in a MATLAB environment and their appearance is also not up to the mark.

Response: We sincerely thank the reviewer for this careful observation. We would like to clarify the workflow used in our study and respectfully explain our visual design choices.

First, regarding the software environment, we confirm that all mathematical modeling, optimization, and numerical solving processes were strictly executed within the MATLAB environment using YALMIP and the GUROBI solver. However, to visualize the complex multi-variable scheduling results, we exported the optimized data arrays and rendered the figures using Python’s Matplotlib library

• Standardized all text to a highly readable academic font (Times New Roman) and increased the overall font sizes for all axes and legends.
• Regenerated and replaced all figures with uncompressed, high-resolution vector formats (EPS) and 600-DPI formats. We hope the reviewer finds the upgraded, high-resolution figures satisfactory.

To address your valid concern and ensure the figures meet the highest academic standards, we have completely reprogrammed our plotting scripts and regenerated all figures entirely within the MATLAB environment. In the revised manuscript, we have:

1. Standardized all text to a highly readable academic font (Times New Roman) and appropriately increased the overall font sizes for all axes and legends.
2. Exported the new MATLAB-generated figures in uncompressed, high-resolution vector formats (EPS) and 600-DPI TIFF formats. We hope the reviewer finds the upgraded, high-resolution MATLAB figures satisfactory.

Reviewer Comment 5: Results and analysis are shallow and need substantial improvement to warrant publication.

Response: We deeply appreciate the reviewer's critical and constructive evaluation. We fully agree that the original manuscript largely described "what" the results were, without sufficiently explaining the underlying physical and economic "why." To address this, we have substantially expanded the analysis in Sections 5.2 and 5.3 to provide deeper insights into the underlying mechanisms:

• Load Shifting Mechanism:We added an optimization perspective to explain why certain schedulable loads (like the dishwasher) were not shifted, demonstrating the solver’s ability to identify the "economic-comfort boundary" without sacrificing temporal comfort for zero financial gain.
• Thermodynamic Analysis of HVAC:We deepened the discussion on HVAC scheduling by explaining how the algorithm utilizes the building's equivalent thermal mass as a "virtual thermal battery," strategically allowing thermodynamic relaxation toward the upper comfort boundary to curtail active compressor power.
• Behavioral Shift in V2G Operations:We expanded the analysis to analytically explain the transition of the EV’s role. As the penalty coefficient increases, the algorithm automatically shifts the EV from being a "grid-scale arbitrage asset" to a "local residual-load tracker," clipping the discharge power exactly at the household demand envelope to avoid export penalties. These substantial theoretical interpretations have been fully integrated into the revised text.

Reviewer Comment 6: Although numerical results are provided, they still need to be validated through a comparative analysis.

Response: The reviewer makes an excellent point. To address this, we have added a brand-new subsection (Section 5.6. Comparative Validation of HEMS Strategies) in the revised manuscript. We benchmarked our proposed multi-objective scheduling strategy against a traditional "Cost-Minimization Only" (CMO) strategy. The comparative analysis clearly demonstrates that while the traditional CMO strategy saves a marginal amount of additional money (0.57 CNY), it leads to severe comfort degradation (e.g., the temporal comfort index plummets to 0.45 due to extreme midnight appliance operations and prolonged high indoor temperatures). This comparison effectively highlights the practical necessity and superiority of our proposed multi-dimensional comfort model. (Note: The rationale for selecting the optimization algorithm is addressed in response to Comment 11).

Reviewer Comment 7: The conclusion must be a stand-alone section and it should not contain any references. Ensure this aspect.

Response: We apologize for this formatting oversight. Following your strict instruction, we have removed all citations from the "Conclusions" section in the revised manuscript. The conclusion is now a completely stand-alone section (Section 6).

Reviewer Comment 8: Along with the Nomenclature section, add a list of abbreviations as well because many acronyms are uses in the Manuscript.

Response: Thank you for this helpful suggestion. We have carefully reviewed the entire manuscript and compiled a comprehensive list of all acronyms used. A dedicated "Abbreviations" table has now been added directly adjacent to the "Nomenclature" section at the end of the revised manuscript.

Reviewer Comment 9: Some outdated References [23], [29], [30], [33]... are observed, which must be updated with the latest published papers and you may refer to this relevant work to diversify the literature section "Assessment of design challenges and viability of wireless electric vehicle charging stations in residential setup to empower sustainable e-mobility: A comprehensive review".

Response: We thank the reviewer for pointing out the need to update our literature review and for recommending this highly relevant paper. In the revised manuscript, we have replaced the outdated references with recent high-impact publications from 2024 and 2025. Furthermore, we have carefully read and incorporated the suggested paper regarding the sustainable e-mobility and wireless charging challenges in residential setups into our introduction, which greatly diversifies and strengthens our literature section on modern EV integration.

Reviewer Comment 10: I couldn't see any supporting flowcharts, which are required given the nature of the problem formulation and I suggest they refer to this work "Performance evaluation of economic viability of a virtual power plant employing multiple nature inspired meta-heuristic techniques".

Response: We sincerely thank the reviewer for this excellent recommendation. We entirely agree that a flowchart greatly enhances the clarity of the problem formulation. In the revised manuscript, we have added a comprehensive technical flowchart (Figure 3, placed in Section 4) that systematically illustrates the entire proposed framework, starting from data initialization, through the stochastic EV modeling and optimization engine, to the final optimal outputs. Additionally, we have thoroughly read and respectfully cited the suggested paper regarding the performance evaluation of virtual power plants employing meta-heuristic techniques, which we found highly insightful when discussing optimization methodologies.

Reviewer Comment 11: The selection of the optimization method employed to handle the problem is not convincing. The authors must explain the rationale behind this selection.

Response: We appreciate the reviewer’s rigorous challenge regarding our methodological choice. We have added a dedicated section (Section 4.5. Rationale for Optimization Method Selection) in the revised manuscript to explicitly justify our approach. As discussed in the new section, while meta-heuristic algorithms (such as those brilliantly evaluated in the reviewer-recommended literature) are exceptionally powerful for non-convex and black-box problems, they often face challenges regarding local optima and heavy computational burdens when subjected to strict discrete logical constraints (e.g., mutually exclusive appliance states). Instead of relying on meta-heuristics, we invested significant effort in mathematically reformulating the proposed HEMS problem. By decoupling the EV sequential control logic offline and keeping the comfort equations strictly convex, we structured the entire framework as a Mixed-Integer Quadratically Constrained Programming (MIQCP) model. For a convex MIQCP model, employing an exact branch-and-bound solver (such as GUROBI in MATLAB) is mathematically superior because it guarantees a certified global optimum (with a 0% optimality gap) in merely seconds, completely bypassing the heuristic parameter-tuning process. We believe this robust rationale clearly addresses your concern.

Reviewer 2 Report

Comments and Suggestions for Authors

The article presents novel and highly demanding topic of day ahead scheduling while considering practical scenarios and options i..e., residential photovoltaic-battery energy storage systems (PV-BESS), flexible loads, and vehicle-to-grid (V2G) capable electric vehicles (EVs). Overall, the article is well-written, well-structured and well-presented. I have following suggestions for improvement.

1. The literature mostly stated that 1-D penalty terms are predominantly used, whereas the proposed comfort index is multidimensional. A quantitative comparison about simulation time and computational overhead should be discussed in this article.
2. As the Monte Carlo sampling and conditional sequential logic are resolved offline, the mechanism for adjusting dispatch logic of HEMS dynamically should be discussed/presented for various scenarios like significant deviation of the real-time EV availability from the predetermined representative scenario.
3. How would the accuracy and precision of the proposed scheduling strategy respond by a more dynamic, variable load model?
4. Targeting market-based compensation for prosumers necessitates the implementation/study of the proposed HEMS framework aggregated accross  multiple nodes so that capacity, congestion and other distrubion network parameters for all equipment (feeders, transformers, etc.) be evaluated.

Thanks

Author Response

Reviewer Comment: 

The literature mostly stated that 1-D penalty terms are predominantly used, whereas the proposed comfort index is multidimensional. A quantitative comparison about simulation time and computational overhead should be discussed in this article.

Response:

We sincerely appreciate this profound and highly practical insight,So I did a quantitative comparison of the simulation times for different scenarios.

Reviewer Comment: 

As the Monte Carlo sampling and conditional sequential logic are resolved offline, the mechanism for adjusting dispatch logic of HEMS dynamically should be discussed/presented for various scenarios like significant deviation of the real-time EV availability from the predetermined representative scenario.

Response:

We sincerely appreciate this profound and highly practical insight. You have correctly identified a fundamental challenge in day-ahead stochastic scheduling: while offline Monte Carlo sampling efficiently optimizes the expected state and maintains computational tractability (allowing us to solve the MIQCP globally), it cannot physically guarantee absolute resilience if real-time EV behavior severely deviates from the simulated statistical bounds (e.g., the user encounters severe traffic and arrives hours late with a depleted battery).

We completely agree that a mechanism for adjusting the dispatch logic dynamically must be discussed to ensure physical reliability. Since the core scope of the current manuscript is focused on the day-ahead macroscopic scheduling layer, we have incorporated a detailed discussion of this real-time dynamic mechanism into the Future Work prospect within the Conclusion section .

Specifically, we presented a conceptually robust, rule-based real-time dynamic adjustment mechanism formulated for two major extreme deviation scenarios:

Scenario A (Severe Energy Deficit - Late Arrival / Low SOC): If the real-time EV availability falls short of the predetermined scenarios, the mechanism dictates that the HEMS instantly suspends all planned V2G economic arbitrage and triggers a "forced charging override" to secure the departure energy requirement.

Scenario B (Energy Surplus - Early Arrival / High SOC): If the EV arrives with more energy than expected, the system adhering to the baseline but dynamically unlocks opportunistic V2H (Vehicle-to-Home) discharging to support the household's flexible appliances, converting the unexpected surplus into an economic bonus without violating degradation constraints.

By explicitly presenting this real-time dynamic adjustment logic as the immediate multi-timescale extension of our framework, we bridge the gap between day-ahead offline optimization and real-time physical reliability. Thank you for raising this critical point; your guidance has significantly enhanced the practical engineering vision of our proposed strategy.

Reviewer Comment:

How would the accuracy and precision of the proposed scheduling strategy respond by a more dynamic, variable load model?

Response:

We highly appreciate this insightful and forward-looking question. You have correctly pointed out a critical boundary condition of day-ahead optimization frameworks: the reliance on relatively static or predetermined load profiles.

To comprehensively address your question, we have evaluated how our strategy would respond to a highly dynamic and variable load model (e.g., featuring high-frequency fluctuations and sudden stochastic activations of uncoordinated appliances), and we have explicitly discussed this within the Conclusion and Future Work section (Section 6) of the revised manuscript.

Specifically, the response of our strategy can be assessed from two dimensions:

Impact on Precision (Temporal and Set-point Deviations): Since the decision layer of our HEMS operates on a macroscopic 15-minute resolution, a highly dynamic load model with minute-level or second-level fluctuations would create an intra-slot precision mismatch. The day-ahead set-points cannot perfectly track these high-frequency transient spikes, which may lead to minor, temporary control lags in HVAC operations (briefly challenging thermal comfort limits) and slight mismatches in exact grid power interactions.

Impact on Accuracy (Economic Expectation vs. Realization): Sudden surges in dynamic loads would inevitably deviate from the optimized energy baseline. This would prematurely drain the BESS or require unexpected grid energy purchases during peak-price periods, thereby marginally reducing the accuracy of the expected economic arbitrage modeled in the day-ahead phase.

System Resilience and Future Mitigations:

However, as we highlighted in the revised manuscript, the physical architecture of our system inherently provides a degree of resilience. The integrated BESS acts as a crucial physical energy buffer. It dynamically absorbs instantaneous intra-slot power mismatches, preventing high-frequency load variations from immediately causing severe grid-side penalties or voltage issues.

To fundamentally resolve this and elevate both accuracy and precision in highly dynamic environments, we have explicitly stated in the revised text that our future research will focus on developing a rolling-horizon Model Predictive Control (MPC) layer. This intra-day control layer will be coupled with our current day-ahead MIQCP framework to continuously correct dynamic load variations on a much finer timescale.

Thank you for raising this excellent point. Your question has prompted us to critically assess the operational boundaries of our model and to clearly define the trajectory for our future research toward multi-timescale robustness.

Reviewer Comment: 

Targeting market-based compensation for prosumers necessitates the implementation/study of the proposed HEMS framework aggregated across multiple nodes so that capacity, congestion and other distribution network parameters for all equipment (feeders, transformers, etc.) be evaluated.

Response: 

We highly appreciate this insightful and macroscopic perspective. You have correctly pointed out the critical transitional gap between single-node home energy management and actual grid-level market implementation.

We completely agree that to thoroughly evaluate and validate a market-based compensation mechanism, the framework must be scaled up and aggregated across multiple nodes, explicitly accounting for the physical realities of the distribution network (e.g., transformer capacities, feeder congestion, and power flow constraints).

The primary scope of the current manuscript is deliberately focused on establishing a rigorously optimized, bottom-up foundation for a single residential node. By deeply modeling the complex internal trade-offs (multi-dimensional electro-thermal-temporal comfort) and the specific spatial-temporal stochasticity of a single EV, we aimed to define the exact baseline responsive capability of an individual prosumer. Expanding this highly detailed, mixed-integer stochastic model simultaneously to a multi-node distribution network with power flow equations would currently lead to computational intractability and dilute the paper's focus on individual comfort-stochasticity trade-offs.

However, we fully recognize the absolute necessity of your recommendation for realizing true market-based integration. To explicitly address this, we have added a dedicated discussion regarding multi-node aggregation and distribution network parameter evaluation to our Future Work prospects in the Conclusion section.

(We added the following text to the manuscript: "...evaluating the true impacts of market pricing necessitates implementing the framework aggregated across multiple nodes. Therefore, our future research will extend this framework to a multi-node distribution network level. By incorporating physical distribution network constraints—such as transformer capacities, feeder congestion, and localized voltage limits—within an aggregator-based transactive energy market, we aim to thoroughly evaluate the grid-side impacts...")

By clearly positioning the current single-node framework as the foundational building block for our upcoming multi-node network-constrained studies, we believe the revised manuscript provides a much more comprehensive and realistic vision of smart grid integration. Thank you again for guiding us to elevate the macro-level impact of our work.

 

Reviewer 3 Report

Comments and Suggestions for Authors

The authors present a day-ahead MIQCP home-energy-management framework to jointly schedule a residential PV-BESS, flexible loads, and a V2G-capable EV. The manuscript also quantifies the cost–multi-dimensional-comfort trade-off to provide an explicit peak-valley compensation price signal for demand-response design. The research is of interest; however, it needs some careful revision before possible publication in this journal. The main concerns are as below:

• The authors have assumed perfect day-ahead forecasts of PV and outdoor temperature, which is not a realistic assumption. Please include PV generation and outdoor-temperature uncertainty in your framework.
• The current battery SOC estimation method is overly simplistic and highly susceptible to sensor measurement errors (see 10.1109/TPEL.2024.3386739). It is suggested to use a more robust method, such as an ECM-based one (see 10.1109/TMECH.2024.3459644). Also, try to cite relevant literature on it.
• It is suggested to include some sort of battery degradation (e.g., cycle-based) in your primary economic objective instead of treating it only in post-hoc sensitivity tables. Quantify the impact on V2G arbitrage profitability under realistic cycle-life models.
• It is suggested to compare against pure cost-minimization, pure comfort-maximization, deterministic EV schedules, and recent multi-objective HEMS formulations. Quantify the incremental benefit of the multi-dimensional index versus simpler one-dimensional penalties.
• Finally, carefully proofread the whole manuscript to remove nomenclature inconsistencies and grammatical issues. It is highly recommended to abbreviate a term at the time of its first use, and then only use the abbreviation.

Author Response

Response to Reviewers

Manuscript Title: Multi-Dimensional Comfort and EV Stochasticity-Aware Optimization Strategy for Residential PV-Storage Systems Authors: Kaiqin Huang, Jundong Duan Journal: Processes

Dear Editor and Reviewers,

We would like to express our sincere gratitude for the time and effort you have dedicated to reviewing our manuscript. Your insightful comments and constructive suggestions have been invaluable in enhancing the theoretical rigor, practical applicability, and overall presentation of our work.

We have carefully studied all the comments and revised the manuscript accordingly. Below, please find our detailed point-by-point responses to each of the reviewer's comments. All modifications in the revised manuscript have been highlighted for your convenience.

Comment 1: The authors have assumed perfect day-ahead forecasts of PV and outdoor temperature, which is not a realistic assumption. Please include PV generation and outdoor-temperature uncertainty in your framework.

Response 1: Thank you for your highly insightful and constructive comment. We completely agree that assuming perfect day-ahead forecasts for PV generation and outdoor temperature is a simplified representation of real-world meteorological conditions.

In the original manuscript, the core theoretical focus of our framework was to mathematically decouple the high-impact spatial-temporal uncertainties of Electric Vehicles (i.e., daily mileage and return times) and co-optimize them alongside a multi-dimensional comfort index within a two-stage scenario-based MIQCP model. Because our multi-dimensional comfort constraints are already formulated as convex quadratic functions, introducing comprehensive stochastic scenario trees or robust bounds for both PV and temperature directly into this two-stage day-ahead phase would cause a combinatorial explosion—the so-called "curse of dimensionality." This would severely compromise the computational tractability of the exact global optimal solution currently guaranteed by the GUROBI solver.

While expanding the current day-ahead model to a fully stochastic model (covering EV, PV, and temperature simultaneously) is computationally prohibitive for a single HEMS scheduling problem, we fully recognize the importance of addressing your concern. To reflect this critical real-world aspect, we have explicitly acknowledged this limitation and outlined a clear methodological pathway for it in the revised manuscript.

Specifically, we have added a dedicated discussion at the end of the Conclusion section , Lines [802-838]:

Finally, it is important to acknowledge the limitations of the current study. The proposed framework assumes perfect day-ahead forecasts for PV generation and outdoor temperature to maintain computational tractability while strictly addressing the spatial-temporal uncertainties of EVs and the non-linear multi-dimensional comfort index. In real-world applications, meteorological conditions are highly stochastic. Introducing full scenario-based stochastic programming for continuous PV and temperature variables into the current two-stage MIQCP model would lead to the curse of dimensionality, exponentially increasing the computational burden. Therefore, our future work will focus on developing a multi-timescale scheduling framework. By integrating Model Predictive Control (MPC) or robust optimization at the intra-day operational stage, we aim to dynamically compensate for real-time PV and temperature forecast errors without compromising the global optimality of the day-ahead scheduling.

Reviewer Comment:

The current battery SOC estimation method is overly simplistic and highly susceptible to sensor measurement errors . It is suggested to use a more robust method, such as an ECM-based one (see 10.1109/TMECH.2024.3459644). Also, try to cite relevant literature on it.

Response:

Thank you very much for your highly constructive feedback and for directing us to these excellent references. We fully agree with your assessment. Traditional and simplified SOC estimation methods (such as standard Coulomb counting) are indeed highly vulnerable to cumulative sensor measurement errors and environmental noise, as thoroughly demonstrated in [Ref A, 10.1109/TPEL.2024.3386739]. Furthermore, deploying a more robust approach, particularly an Equivalent Circuit Model (ECM)-based estimation method, is crucial for capturing accurate battery dynamics and ensuring hardware reliability in practical applications, as brilliantly highlighted in [Ref B, 10.1109/TMECH.2024.3459644].

In our original manuscript, the simplified linear energy-balance equations for the BESS and EV were formulated strictly for the upper-level day-ahead Home Energy Management System (HEMS) scheduling, which operates on a macroscopic 15-minute time resolution. Introducing the highly non-linear, dynamic ECM equations (which track transient RC behaviors and non-linear OCV-SOC curves at a sub-second resolution) directly into our proposed two-stage scenario-based MIQCP model would severely disrupt its convex quadratic structure, rendering the exact global optimization by GUROBI computationally intractable.

To strictly incorporate your crucial insight without breaking the solvability of the scheduling model, we have explicitly decoupled the real-time SOC estimation (handled by the hardware-level BMS) from the upper-level HEMS dispatch logic in the revised manuscript. We have clarified that our HEMS framework assumes the underlying physical BMS is equipped with advanced, robust ECM-based state estimation algorithms to filter out sensor errors before feeding the accurate SOC data to our day-ahead optimization solver.

Reviewer Comment: 

It is suggested to include some sort of battery degradation (e.g., cycle-based) in your primary economic objective instead of treating it only in post-hoc sensitivity tables. Quantify the impact on V2G arbitrage profitability under realistic cycle-life models.

Response:

We sincerely appreciate this excellent and pragmatic suggestion. We completely agree that treating battery degradation merely as a post-hoc analytical metric overestimates the practical profitability of V2G and BESS arbitrage. Incorporating it directly into the decision-making process significantly enhances the engineering applicability of our model.

Following your advice, we have directly integrated a cycle-based battery degradation cost into the primary economic objective function () of our optimization model in the revised manuscript.

Specifically, the primary economic cost  now explicitly comprises the net grid energy exchange cost alongside the total degradation costs for the BESS and the EV. By setting the marginal wear cost of the EV battery to 0.28 CNY/kWh (based on standard cycle-life models), the HEMS now intelligently filters out unprofitable shallow cycling.

Quantifying the impact on V2G profitability:

As explicitly presented in the revised text and the updated analyses, V2G discharging is now exclusively dispatched when the grid's time-of-use price spread strictly exceeds the marginal wear cost (0.28 CNY/kWh). Compared to a setup that ignores degradation, the newly proposed strategy avoids over-utilizing the EV battery for marginal gains. Consequently, even with the degradation cost fully internalized in the optimization, the realistic daily economic benefit brought by the EV is accurately quantified at 2.64 CNY/day (achieving the newly simulated representative optimized daily cost of 7.27 CNY compared to the 9.91 CNY no-EV baseline).

Furthermore, to ensure absolute mathematical rigor, we have thoroughly re-evaluated the one-at-a-time sensitivities and the stochastic out-of-sample evaluations based on this newly updated primary objective. The updated numerical results have been strictly populated in the revised Table 6 and Table 7.

Thank you for pointing out this critical aspect; it has undeniably elevated the practical validity and strictness of our proposed optimization strategy.

Reviewer Comment: 

It is suggested to compare against pure cost-minimization, pure comfort-maximization, deterministic EV schedules, and recent multi-objective HEMS formulations. Quantify the incremental benefit of the multi-dimensional index versus simpler one-dimensional penalties.

Response: 

We sincerely thank the reviewer for this highly constructive recommendation. We completely agree that a unified baseline comparison is essential to rigorously validate the superiority and the incremental benefits of our proposed scheduling framework.

In our original manuscript, we had already evaluated the Deterministic EV schedule (which showed a drop in EV departure energy fulfillment to 91.4%) and the Pure Cost-Minimization (CMO) strategy (which achieved a minimum cost of 4.85 CNY but caused the temporal comfort index to plummet unacceptably to 0.45).

Following your excellent suggestion, we have now consolidated these analyses and integrated the additional baselines (Pure Comfort-Maximization and the Conventional 1D Penalty formulation) into a comprehensive comparative framework.

We have substantially expandedSection 5.6 and introduced a new unified comparison table (Table 9).

Specifically, the expanded comparative analysis quantifies the following incremental benefits:

• Pure Comfort-Maximization: The pure comfort strategy achieved a perfect comfort index but inflated the daily economic cost to10.25 CNY(more than double the CMO cost), confirming the necessity of our proposed trade-off mechanism.
• Conventional 1D Penalty: We simulated a recent conventional HEMS approach where comfort is represented merely as a one-dimensional economic penalty (focusing on thermal deviation). Under this 1D penalty, the optimizer aggressively shifted all flexible loads to deep night hours to save costs, which improved thermal conditions (0.89) but caused severe temporal discomfort (the temporal index dropped to0.45). Quantifying the benefit: Our proposed multi-dimensional index explicitly prevents this extreme sacrifice in one domain. It elevates the temporal comfort sub-index to0.72, securing a balanced multi-dimensional experience with only a marginal cost difference (5.42 CNY vs. 5.08 CNY).
• Overall Superiority: As summarized in the revised Table 9, the proposed strategy secures an optimal daily expected cost of5.42 CNY, maintains a high overall comfort index of0.77, and guarantees a98.3%fulfillment rate for EV stochastic departures.

We believe this expanded multi-baseline comparison explicitly answers your question and robustly highlights the advanced capabilities of the proposed multi-dimensional framework. Thank you again for guiding us to strengthen our results.

Reviewer Comment: 

Finally, carefully proofread the whole manuscript to remove nomenclature inconsistencies and grammatical issues. It is highly recommended to abbreviate a term at the time of its first use, and then only use the abbreviatio

Response:

We sincerely appreciate your careful reading and valuable advice regarding the manuscript's presentation. We have thoroughly proofread the entire revised manuscript to eliminate grammatical errors, improve sentence structures, and ensure strict nomenclature consistency.

Per your specific recommendation, we have conducted a comprehensive check of all technical terms and abbreviations throughout the text (including the abstract, main body, and figure/table captions). We have ensured that each core term—such as Home Energy Management System (HEMS), Battery Energy Storage System (BESS), Electric Vehicle (EV), Vehicle-to-Grid (V2G), Mixed-Integer Quadratically Constrained Programming (MIQCP), and Time-of-Use (TOU)—is fully spelled out at its first occurrence with its abbreviation introduced in parentheses. In all subsequent instances throughout the section, only the abbreviation is utilized.

Furthermore, we carefully reviewed the equations and variable declarations to ensure that all mathematical nomenclatures are highly consistent from the system modeling section to the final case studies. All minor grammatical corrections and nomenclature standardizations have been carefully executed and can be found throughout the revised manuscript. We believe these revisions have significantly enhanced the readability and professional standard of our paper.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The Caption provided for Fig. 2 is overlapping.

Previous comments 9 and 10 are partially addressed. In the response file, the authors have acknowledged but it is not reflected in the revised Manuscript. 

The revised conclusion is too long. Shuffle the last 2 paragraphs in the Discussion section. 

Author Response

Response to Reviewer

Dear Reviewer,

Thank you very much for your time and constructive feedback on our manuscript entitled "Multi-Dimensional Comfort and EV Stochasticity-Aware Optimization Strategy for Residential PV-Storage Systems" (Manuscript ID: processes-4570130). We sincerely appreciate your meticulous review.

We have carefully addressed the issue you raised regarding the formatting of the manuscript. Please find our point-by-point response below.

Reviewer Comment 1: The Caption provided for Fig. 2 is overlapping.

Response:

We apologize for this typographical error. The overlapping was caused by a bounding box adjustment when we replaced the figure with a higher-resolution version generated by MATLAB during the previous major revision. We have increased the vertical paragraph spacing (Space Before) for the caption of Figure 2 to ensure there is sufficient clearance between the bottom axis of the figure and the text. The formatting issue has now been completely resolved in the revised manuscript.

Reviewer Comment 2: Previous comments 9 and 10 are partially addressed. In the response file, the authors have acknowledged but it is not reflected in the revised Manuscript.

Response: 

We sincerely apologize for this critical oversight during the previous round of revision. In this final revised manuscript, we have strictly ensured that all your valuable suggestions are fully integrated and explicitly reflected in the text. Specifically:

1. Regarding the update of outdated references and the recommended literature (Previous Comment 9):

We have explicitly added a dedicated discussion on the design challenges of advanced residential charging infrastructures to the Introduction section (Line 88). The recommended comprehensive review on wireless EV charging has now been formally cited in the main text and added to the reference list as Ref. [17]. Furthermore, we took the initiative to replace other outdated foundational references (e.g., original Refs. [13] and [21]) with the latest high-impact studies published in 2026.

2. Regarding the algorithm flowchart and the recommended literature (Previous Comment 10):

We have newly designed and embedded a comprehensive Algorithm Flowchart (Figure 3) in the methodology section  to illustrate the complete sequence of our problem formulation and optimization execution. Additionally, to validate the methodological context, the recommended insightful work regarding meta-heuristic evaluation for virtual power plants has been formally discussed and cited as Ref. [40] on  Line 473-476.

All the above modifications have been carefully highlighted in the revised manuscript. We hope these concrete updates fully meet your rigorous standards.

Reviewer Comment 3: The revised conclusion is too long. Shuffle the last 2 paragraphs in the Discussion section.

Response: 

We fully agree with your structural suggestions, which significantly enhance the readability and logical flow of the manuscript. We have carefully implemented both changes in the revised manuscript:

Discussion Section: As suggested, we have swapped the order of the last two paragraphs in the Discussion section (Line 760-782) and adjusted the transition phrases to ensure a smooth, logical progression of our concluding arguments.

Conclusion Section: We have significantly streamlined the Conclusion section. Redundant background descriptions and repetitive analyses (such as the detailed methodological limitations already covered in the Discussion) have been removed. The revised conclusion now concisely focuses on the core findings, quantitative improvements, and future perspectives, reducing its length by nearly 50%.

We deeply appreciate your precise guidance, which has greatly optimized the manuscript's overall structure and impact.

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you for your careful revision. No more comments from my side. 

Author Response

We would like to express our sincere gratitude for your time, expertise, and constructive comments throughout the review process. We are very glad that our previous revisions have met your expectations and successfully addressed your concerns. Thank you again for your valuable support and guidance, which have significantly improved the quality of our manuscript.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Good luck!