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Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon–Energy Trading and IGA-Assisted Compromise Weight Selection

Sustainability 2026, 18(16), 8065; https://doi.org/10.3390/su18168065

by Guoxiang Hu

, Linjun Shi^*, Feng Wu, Chenyu Wu

and Keman Lin

Reviewer 1:

M.A. Elazab

Reviewer 2:

Saiful Islam

Reviewer 3: Anonymous

Reviewer 4: Anonymous

Sustainability 2026, 18(16), 8065; https://doi.org/10.3390/su18168065

Submission received: 16 July 2026 / Revised: 3 August 2026 / Accepted: 5 August 2026 / Published: 7 August 2026

(This article belongs to the Section Energy Sustainability)

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The abstract remains descriptive and does not report the essential quantitative evidence. It states that the strategy “improves both the economic and environmental performance,” but does not provide the reported 7.85% carbon-emission reduction, 18.39% operating-cost reduction, identified weights of 0.62/0.38, case-study horizon, or system scale. The keywords also omit central terms such as improved genetic algorithm, demand response, fuzzy thermal comfort, and seasonal energy storage.
The introduction presents groups of studies without critically comparing their models, assumptions, time horizons, uncertainty treatments, and limitations. Several literature statements are not accurately supported by their cited references. For example, References [15–16] are described in connection with “seasonal carbon flow balance,” although Reference [16] concerns long-term regional generation-mix planning rather than seasonal IES carbon-flow dispatch. Similarly, the statement that References [20–21] consider electric-vehicle participation is inconsistent with their published subjects: Reference [20] concerns carbon mineralization and seasonal thermal storage, while Reference [21] concerns CCUS and multi-timescale carbon-allowance allocation.
The scientific novelty is insufficiently separated from the authors’ previous publication [22]. The manuscript explicitly states that it builds on that work, while the previous article already contains the same electricity–heat–gas–cooling–carbon framework, carbon-energy pricing mechanism, seasonal carbon planning, demand response, and seasonal scheduling concept. The additions of a piecewise cooling-response expression and an IGA-based weight search appear incremental, but no detailed comparison identifies which equations, constraints, datasets, figures, or results are genuinely new. The previous work is a published 2026 article by substantially the same author group and has a validated DOI.
The manuscript is not independently reproducible because most of the baseline system is replaced by compact equations and references to earlier works [22] and [25]. Device capacities, efficiency values, ramp limits, storage losses, initial states, carbon-emission factors, allowance benchmarks, energy prices, elasticity matrices, carbon-price conversion coefficients, and demand-response coefficients are not reported. The phrase “remaining parameters are represented using equivalent values” does not define how those values were obtained.
The claimed cross-seasonal scheduling is not scientifically represented by the adopted 96-hour horizon. Four consecutive 24-hour typical days are used for spring, summer, autumn, and winter, and the seasonal gas-storage state is directly linked between them. No number-of-days weighting, elapsed time between seasons, seasonal self-discharge, monthly energy accumulation, or annual scaling is included. Therefore, energy transferred from the “spring day” to the “summer day” is numerically transferred over one adjacent time step rather than over several months, which invalidates the interpretation of the SGS results as real cross-seasonal storage.
Renewable uncertainty is described but not incorporated consistently into the mathematical optimization. The manuscript states that Latin hypercube sampling, scenario reduction, and scenario probabilities are used, yet the objective functions and constraints contain no scenario index, probability-weighted expectation, chance constraint, robust counterpart, or stochastic recourse variable. The simulation finally uses one deterministic WT/PV profile for each season. Consequently, the statements concerning robustness under renewable uncertainty are unsupported by the presented formulation.
The demand-response interpretation is physically questionable. The paper states that loads are shifted from summer and winter to spring and autumn, although most electricity, heating, gas, and cooling services cannot be postponed between seasons. Equation (18) does not clearly restrict load transfer to realistic intra-day windows, and no explicit energy-conservation condition for transferable loads is presented. Table 3 also shows considerable reductions in average loads after response, but no lost-load cost, consumer compensation, utility function, service constraint, or rebound effect is included, allowing cost and emissions to decrease through unpriced demand suppression.
The cooling-load model is incomplete. Equation (19) is introduced after stating that the PMV index “is calculated as follows,” but the equation actually defines a piecewise cooling-load multiplier rather than PMV. The text then says that the relationship between fPMVf_{\mathrm{PMV}} and temperature “is as follows,” but that relationship is entirely missing before Section 4 begins. Moreover, PMV depends on air temperature, mean radiant temperature, humidity, air velocity, clothing insulation, and metabolic rate, while no building thermal model or indoor-temperature state equation is given. No PMV or temperature results are presented to verify that comfort was maintained.
The IGA-based weight-identification method does not establish an objective or uniquely balanced preference. The searched variable is only one scalar, β\beta, which can be evaluated directly by a deterministic grid or line search. Selecting the point with the minimum Euclidean distance to an approximate ideal point merely replaces one preference assumption with another. No Pareto front, convergence history, repeated stochastic runs, dispersion of the identified weight, sensitivity to population size and mutation rate, or comparison with standard multi-objective methods is reported.
Several equation and cross-reference errors affect the technical reliability of the formulation. The admissible weight interval is defined by Equation (27), but the text states Equation (28); normalization is defined by Equation (25), but the text refers to Equation (26); and the fitness calculation is said to use Equations (29) and (30), although Equation (30) does not exist. The gas-network notation alternates between GNETG_{\mathrm{NET}} and GGRIDG_{\mathrm{GRID}}. The ordering of the heat and gas cost coefficients in the explanation of Equation (21) is inconsistent with the equation. Equations (12) and (24) identify AC operation as a carbon-emission source, whereas Figure 11 presents EB-related carbon quantities instead, leaving the actual emission boundary unclear.
The hourly carbon-accounting concept is asserted rather than demonstrated. The paper states that hourly discretization preserves cumulative consistency with the carbon-market settlement period, but no explicit annual allowance constraint, representative-day weighting, settlement equation, or proof of cumulative equivalence is provided. Because the numerical horizon contains only four typical days, the reported carbon totals cannot be interpreted as annual values without a documented scaling procedure.
The results do not contain sufficient validation or uncertainty analysis. Table 4 provides only total operating cost and total carbon emissions, without energy-purchase costs, conversion costs, storage costs, carbon-trading payments, renewable curtailment, demand-response compensation, comfort indices, or solver optimality gaps. The difference between Scenarios 1 and 2 is only 0.19 t of carbon and approximately CNY 797, yet it is described as demonstrating clear effectiveness without practical-significance analysis. No sensitivity analysis is conducted for carbon price, elasticity coefficients, storage capacity, renewable scenarios, emission factors, or objective weights.
Some interpretations directly contradict the modeled system or confound multiple effects. The discussion states that seasonal scheduling reduces the operating time of “coal-fired units,” although no coal-fired unit appears in the system configuration. Figure 14 compares only Scenarios 4 and 5, but these scenarios differ simultaneously in the carbon-energy market and demand-response mechanism; therefore, the larger SGS fluctuation cannot be attributed solely to the carbon-energy trading market. Claims that reduced IST fluctuations indicate lower energy losses and enhanced equipment protection are also made without degradation, cycling-loss, lifetime, or reliability models.
The figures and tables do not provide adequate scientific traceability. Figures 3 and 4 display several observations under yearly x-axis labels without identifying months or seasons, making the derivation of the four seasonal factors impossible to verify. Figures 7–12 do not clearly state which scenario they represent. Figure 2 does not show the scenario probabilities produced by the reduction method. Table 2 gives curtailable and shiftable proportions without sources or calibration, while the cooling-response parameters are absent. Table 3 reports average values in kW while the figures use MW, and the variance column has no squared unit. Several plots are visually crowded, with small legends and overlapping curves.
The conclusions overstate findings that were not demonstrated in the results, particularly the preservation of thermal comfort, objective identification of weights, robustness to renewable uncertainty, and effective cross-seasonal transfer. The manuscript also lacks a nomenclature for the large number of symbols and abbreviations; SOC, CL, SL, LHS and several coefficients are not consistently defined, while the storage battery is called SBU in Table 1 and ESS in Section 5.4. Expressions such as “high low-carbon demand,” “low low-carbon demand,” “the value of fPMVf_{\mathrm{PMV}} is [-1,1],” and “carbon emissions coefficient” require substantial language and terminology correction. Reference [1] is also placed as an isolated citation before a sentence, and several citations do not accurately correspond to the claims made in the introduction.

Author Response

Manuscript Number: sustainability-4472735

Paper Title: Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon-Energy Trading and IGA-Assisted Compromise-Weight Selection

Authors: Guoxiang Hu, Linjun Shi, Feng Wu, Chenyu Wu, Keman Lin

Sustainability

General Response to the Editor and Reviewers:

We sincerely thank the editor and reviewers for their constructive comments and detailed suggestions. Their feedback helped us identify several issues in the model description, interpretation, and presentation.

We have revised the manuscript carefully and checked the response letter against the final text. The responses and the corresponding manuscript revisions remain marked in blue for ease of review.

The point-by-point responses are provided below. Each Response now describes only changes that are present in the revised manuscript.

***********************************************************************************

To Reviewer 1:

Thank you for the careful review and constructive suggestions. We have revised the manuscript point by point and clarified the corresponding changes below.

Comments 1:

The abstract remains descriptive and does not report the essential quantitative evidence. It states that the strategy “improves both the economic and environmental performance,” but does not provide the reported 7.85% carbon-emission reduction, 18.39% operating-cost reduction, identified weights of 0.62/0.38, case-study horizon, or system scale. The keywords also omit central terms such as improved genetic algorithm, demand response, fuzzy thermal comfort, and seasonal energy storage.

Response 1:

We appreciate the reviewer’s request for a more evidence-based abstract. The revised Abstract now states the case-study scope, the scheduling horizon, the selected compromise weights, and the principal numerical outcomes rather than relying on a general statement of improvement.

The case study is identified as a park-level electricity–heat–gas–cooling IES with two renewable-generation technologies, five conversion technologies, five storage technologies, four end-use load types, and external electricity and gas interfaces. The numerical analysis uses a 96-h representative horizon formed by four 24-h seasonal profiles.

The IGA–CPLEX procedure is reported to select economic and carbon-emission compromise weights of 0.62 and 0.38, respectively.

The revised Abstract also gives the baseline and final values: carbon emissions decrease from 1052.92 t to 970.24 t, and operating cost decreases from CNY 1,103,420.84 to CNY 900,485.52. These correspond to reductions of 7.85% and 18.39%, respectively.

The Keywords have been expanded to include low-carbon demand response, fuzzy thermal comfort, seasonal energy storage, improved genetic algorithm, and multi-timescale dispatch. The response therefore matches the quantitative and methodological information reproduced below.

The revised text in the manuscript is presented as follows:

(1) Abstract, Page [3]

“To coordinate energy trading and carbon-allowance management in a multi-energy-coupled integrated energy system (IES), this paper proposes a multi-timescale low-carbon economic dispatch framework integrating carbon–energy trading, low-carbon demand response, seasonal carbon-pressure signals, and preference-weight selection. The case study considers a park-level electricity–heat–gas–cooling IES comprising two renewable-generation technologies, five energy-conversion technologies, five energy-storage technologies, four end-use load types, and interfaces with the external electricity and gas networks. A 96-h representative scheduling horizon is constructed using four 24-h operating profiles corresponding to spring, summer, autumn, and winter. Seasonal carbon-pressure signals extracted from historical renewable-output and load data are embedded in electricity, heat, and gas prices to guide demand response, while cooling demand is treated separately through a fuzzy thermal-comfort-based response model. An IGA–CPLEX nested framework is used to select the economic and carbon-emission compromise weights and solve the corresponding hourly dispatch problem. The selected economic and carbon-emission compromise weights are 0.62 and 0.38, respectively. Compared with the conventional operating scenario, the complete framework reduces carbon emissions from 1052.92 t to 970.24 t and operating costs from CNY 1,103,420.84 to CNY 900,485.52, corresponding to reductions of 7.85% and 18.39%, respectively. The results indicate that integrating carbon-embedded energy pricing, demand-side flexibility, and seasonal storage coordination can improve the economic and environmental performance of the studied IES.”

(2) Keywords, Page [3]

“integrated energy system; carbon-energy trading; low-carbon demand response; fuzzy thermal comfort; seasonal energy storage; improved genetic algorithm; multi-timescale dispatch”

Comments 2:

The introduction presents groups of studies without critically comparing their models, assumptions, time horizons, uncertainty treatments, and limitations. Several literature statements are not accurately supported by their cited references. For example, References [15-16] are described in connection with “seasonal carbon flow balance,” although Reference [16] concerns long-term regional generation-mix planning rather than seasonal IES carbon-flow dispatch. Similarly, the statement that References [20-21] consider electric-vehicle participation is inconsistent with their published subjects: Reference [20] concerns carbon mineralization and seasonal thermal storage, while Reference [21] concerns CCUS and multi-timescale carbon-allowance allocation.

Response 2:

This criticism is well taken. The original Introduction grouped studies too broadly and did not always distinguish their decision level, time horizon, or technical scope. We therefore rewrote the literature review so that the cited work is discussed in relation to carbon–energy market coordination, multi-objective planning and dispatch, and seasonal carbon-management mechanisms.

The revised discussion now contrasts short-term market interaction with medium- and long-term carbon management, and it explains the unresolved link among seasonal carbon signals, hourly price-based demand response, comfort-aware cooling regulation, and reproducible compromise selection.

The descriptions of References [15] and [16] have been separated. Reference [15] is presented as a system-design and 4E assessment study, whereas Reference [16] is described as long-term regional generation-mix planning under carbon cap-and-trade and renewable portfolio standards; neither is now characterized as seasonal IES carbon-flow dispatch.

The earlier statement associating References [20] and [21] with electric-vehicle participation has also been removed. The revised text identifies Reference [20] with carbon mineralization and seasonal energy storage, and Reference [21] with CCUS and multi-timescale carbon-allowance allocation.

Finally, the wording around Reference [1] and the subsequent research-gap statement has been reorganized so that each citation supports the claim immediately attached to it. The revised Introduction below is therefore narrower, more comparative, and more consistent with the cited literature.

The revised text in the manuscript is presented as follows:

(1) Section 1, Pages [5-6]

“With the increasing coupling of multiple energy carriers and the integration of carbon-trading mechanisms, demand-side flexibility has become increasingly important for improving the low-carbon operation of IESs while satisfying users’ energy-service requirements. Carbon-energy collaborative dispatch has therefore attracted considerable attention as an effective means of coordinating energy consumption, carbon emissions, and user-side responses [1]. Energy-certificate-carbon coupling and joint carbon-green certificate trading were incorporated into multi-microgrid, multi-regional, and industrial-park IESs, demonstrating that coordinated market participation and energy sharing can improve renewable energy accommodation and environmental performance [2-4]. Low-carbon dispatch and coordinated operation strategies for multi-regional and multi-district IESs under coupled carbon and green certificate markets were further proposed, emphasizing the roles of energy sharing and benefit allocation [5-6]. In addition, diversified hydrogen utilization was integrated into a multi-timescale IES optimization framework, further improving renewable energy consumption and system economy [7]. Although the above studies have advanced carbon–energy coordination in IESs, the reviewed studies address seasonal carbon allocation, market-based demand response, thermal-comfort regulation, seasonal storage, and multi-objective decision-making from different perspectives. However, the links among these elements have not been clearly established in a unified hourly multi-energy dispatch model. In particular, it remains necessary to clarify how seasonal carbon-management information is translated into hourly price signals, how cooling flexibility is constrained by thermal comfort, and how the economic–environmental compromise is selected in a reproducible manner. Therefore, a comfort-aware cooling demand-response model is required to coordinate load regulation with users’ thermal preferences.

A key challenge is how to use coordinated carbon–energy market signals to support the low-carbon operation of multi-energy IESs. Incentive-oriented power–carbon–green-certificate markets, CCUS–P2G coupling, hydrogen-blended gas systems, and seasonal carbon-trading mechanisms have been explored, showing that incentive design, hydrogen utilization, and temporal carbon allocation can reduce system cost and emissions [8–10]. Nash-bargaining pricing, electricity-pricing mechanisms, cross-regional competition, and energy sharing under carbon–green-certificate coupling have also been studied, confirming the value of coordinated market interaction [11–14]. Most of these mechanisms, however, focus on short-term regulation and give limited attention to the transmission of medium- and long-term carbon-management information into hourly operation, which restricts coordinated energy and carbon management in IESs.

Multi-objective IES scheduling also requires a reproducible way to select an economic–environmental compromise. Multi-objective low-carbon optimization has been studied at both system-design and regional-planning levels. Reference [15] performs a 4E assessment and multi-objective design optimization of a solar–geothermal integrated energy system, whereas Reference [16] addresses long-term regional generation-mix planning under carbon cap-and-trade and renewable portfolio standards. These studies demonstrate the value of multi-objective decision-making, but their decision levels differ from hourly seasonal dispatch of a multi-energy IES. Park-level IES clusters, multi-energy collaborative operation, and regional generation-mix optimization under carbon trading and renewable portfolio standards have also been studied [17–19]. Seasonal carbon-management studies follow different technical routes: Reference [20] couples carbon mineralization with seasonal energy storage in integrated-energy-system planning, whereas Reference [21] incorporates CCUS and multi-timescale carbon-allowance allocation into low-carbon economic dispatch. Because objective weights are often selected empirically, a transparent compromise-selection procedure is needed to make the economic–environmental trade-off easier to reproduce and interpret.

To address these challenges, this paper develops a multi-timescale low-carbon economic scheduling framework for a multi-energy IES. First, seasonal carbon-pressure signals are extracted from historical renewable-generation and load data, and carbon allowances are mapped onto hourly accounting intervals. This enables medium- and long-term carbon-management information to directly influence short-term dispatch without changing the hourly scheduling resolution. Second, carbon-trading incentive and disincentive signals are embedded in electricity, heat, and gas prices to guide demand response, while cooling demand is modeled separately using a fuzzy thermal-comfort mechanism to more accurately represent users’ thermal preferences and cooling-load flexibility. Representative wind and photovoltaic profiles are further constructed through sampling and scenario reduction to characterize renewable-generation uncertainty. Third, an IGA–CPLEX nested framework is adopted to separate compromise-weight search from constrained hourly dispatch. For each candidate economic preference weight, CPLEX solves the corresponding mixed-integer linear dispatch problem, while the outer IGA evaluates the resulting normalized economic–environmental performance. The IGA is not assumed to provide a uniquely objective preference or to outperform all multi-objective methods; it is used as an extensible outer search mechanism and is validated against deterministic and population-based alternatives. In addition, multiple storage devices, including seasonal gas storage, are coordinated to support intra-day energy balancing and inter-segment gas-inventory coordination across the four representative seasonal profiles. The resulting framework jointly optimizes operating costs and physical carbon emissions, thereby strengthening the coordination among seasonal carbon planning, comfort-aware demand response, compromise-weight selection, and hourly multi-energy operation.”

Comments 3:

The scientific novelty is insufficiently separated from the authors’ previous publication [22]. The manuscript explicitly states that it builds on that work, while the previous article already contains the same electricity-heat-gas-cooling-carbon framework, carbon-energy pricing mechanism, seasonal carbon planning, demand response, and seasonal scheduling concept. The additions of a piecewise cooling-response expression and an IGA-based weight search appear incremental, but no detailed comparison identifies which equations, constraints, datasets, figures, or results are genuinely new. The previous work is a published 2026 article by substantially the same author group and has a validated DOI.

Response 3:

We agree that the earlier draft did not draw a sufficiently clear boundary between the present manuscript and Reference [22]. The revised Introduction now states explicitly which parts are inherited and avoids presenting the overall electricity–heat–gas–cooling–carbon framework as a new contribution.

The inherited baseline comprises the park-level system configuration, the carbon–energy pricing mechanism, the seasonal carbon-planning framework, the electricity–heat–gas demand-response formulation, and the general seasonal-storage scheduling concept.

The new content is limited to two methodological extensions: the differentiated cooling-load response associated with fuzzy thermal comfort, and the normalized economic–environmental compromise-selection procedure implemented through an outer IGA and an inner CPLEX dispatch model. The seasonal carbon-pricing, representative renewable profiles, and storage formulations are treated as inherited or supporting components rather than new methodological contributions.

Section 2 now reinforces this distinction by identifying where the new formulations are located. The revised wording also limits the numerical contribution to examining how these extensions interact with the inherited seasonal pricing and gas-storage mechanisms.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [8]

“Relationship to our previous work. The present study adopts the park-level electricity–heat–gas–cooling–carbon system configuration, carbon–energy pricing mechanism, seasonal carbon-planning framework, baseline electricity–heat–gas demand-response formulation, and general seasonal-storage scheduling concept developed in our previous work [22]. These inherited components are used as the baseline model and are not claimed as new contributions in the present paper.

Relative to Reference [22], the present study introduces two methodological extensions. First, cooling demand is separated from the price-elastic electricity, heat, and gas loads and is represented by an independent piecewise response formulation associated with fuzzy thermal-comfort information. This treatment is developed in Section 3.2.3 and is intended to distinguish the thermal characteristics of cooling demand from those of the other energy loads. Second, a normalized economic–environmental compromise-selection procedure is introduced in Sections 4.2 and 4.3. An outer IGA searches the economic preference weight, while the inner CPLEX model solves the corresponding mixed-integer hourly dispatch problem. The preferred solution is selected according to its normalized distance from the economic–environmental ideal point.

In addition to these methodological extensions, the numerical analysis examines their interaction with the inherited seasonal carbon-pricing and seasonal gas-storage mechanisms.”

(2) Section 2, Page [9]

“The baseline park-level electricity–heat–gas–cooling system and its principal energy-conversion, storage, and balance relationships are adapted from our previous work [22] and are restated here to keep the present formulation self-contained. The new formulations developed in this paper are concentrated in Section 3.2.3, which presents the differentiated cooling-load response model, and Sections 4.2–4.3, which present the normalized compromise-selection and IGA–CPLEX solution procedure.”

Comments 4:

The manuscript is not independently reproducible because most of the baseline system is replaced by compact equations and references to earlier works [22] and [25]. Device capacities, efficiency values, ramp limits, storage losses, initial states, carbon-emission factors, allowance benchmarks, energy prices, elasticity matrices, carbon-price conversion coefficients, and demand-response coefficients are not reported. The phrase “remaining parameters are represented using equivalent values” does not define how those values were obtained.

Response 4:

We appreciate the reproducibility concern. The revised material below does not claim that every numerical input has been newly reported; instead, it adds the carbon-allocation and emission equations, clarifies the price-elastic demand-response formulation, states the main operating and ramping constraints, and reports the principal installed and exchange capacities. These additions make the model structure and the main case-study settings more transparent while keeping the remaining parameters tied to their stated sources.

The revised text in the manuscript is presented as follows:

(1) Section 2.2, Pages [10-12]

“2.2. Carbon emission and energy allocation modeling

2.2.1. Energy production

To address the time-scale mismatch between carbon trading and energy dispatch, this paper maps carbon allowances and actual carbon emissions to the one-hour scheduling intervals adopted in the energy dispatch model. Carbon allowances are allocated according to the carbon allowance allocation benchmark and the corresponding energy output or consumption, while actual carbon emissions are calculated using carbon emission coefficients. This discretization is an operational time-scale mapping rather than a change in the actual carbon market settlement period. Since the cumulative carbon allowances and cumulative carbon emissions over the whole scheduling horizon remain unchanged, this treatment does not introduce systematic errors in the total carbon balance [22].

The seasonal optimal scheduling framework refers to the incorporation of seasonal carbon-emission characteristics and low-carbon demand signals into the hourly dispatch process, rather than a seasonal-scale dispatch interval. Therefore, the proposed method integrates seasonal-level carbon planning with hourly operational scheduling.

WT and PV convert wind and solar energy into electricity without direct operating emissions. The allowances assigned to these units are therefore not compensation for their own emissions; they represent an incentive based on the fossil-fuel emissions avoided by renewable generation under the adopted benchmark method. The carbon-allowance model for WT and PV in an IES is expressed as

(1)

where and are the allocated carbon allowances for WT and PV, respectively; and are the allocation benchmark values for the power supply carbon allowances for WT and PV, respectively; and are the output power of WT and PV, respectively.

2.2.2. Energy conversion

Energy-conversion units provide the main coupling paths among the energy carriers. Their operating relationships and carbon-allowance formulations are given below.

(1) CHP mathematical model

(2)

where PCHP is the electrical output of the CHP unit; HCHP is its thermal output; GCHP is its gas input; ηCHPp and ηCHPh are the electrical and thermal conversion efficiencies, respectively; DCHP is the direct carbon emission from CHP fuel use; λCHPg is the gas-combustion carbon-emission coefficient; ACHP is the carbon allowance allocated to CHP; BCHPp and BCHPh are the electricity- and heat-supply allowance benchmarks, respectively; and Fr is the CHP heat-supply correction coefficient.

(2) EB mathematical model

(3)

where HEB is the thermal output of EB; ηEB is its conversion efficiency; PEB is its electrical input; AEB is the carbon allowance allocated to EB; and BEBp is the benchmark for heat-supply allowance allocation.

(3) P2G mathematical model

(4)

where GP2G is the gas output of P2G; ηP2G is its conversion efficiency; PP2G is the electrical input of P2G; DP2G is the carbon-consumption quantity associated with gas production; λP2Gg is the carbon-consumption coefficient, taken with the sign convention used in the carbon balance; AP2G is the carbon allowance allocated to P2G; and BP2Gp is the gas-supply allowance benchmark.

(4) EC mathematical model

(5)

where LEC is the cooling output of EC; mEC is its coefficient of performance; PEC is its electrical input; AEC is the carbon allowance allocated to EC; and BEC is the electricity-supply allowance benchmark.

(5) AC mathematical model

(6)

where LAC is the cooling output of AC; mAC is its coefficient of performance; HAC is its thermal input; AAC is the carbon allowance allocated to AC; and BAC is the heat-supply allowance benchmark. DAC denotes the carbon quantity attributed to the heat input of AC for internal carbon accounting; it is not counted again as an independent source in the physical-emission objective.

2.2.3. Energy storage

(7)

(8)

where SSBU(t) is the state of charge of the SBU at time t; SSBUloss(t) is its self-loss; ηcSBU and ηdSBU are the charging and discharging efficiencies; ESBU is the maximum energy capacity; Pc,maxSBU and Pd,maxSBU are the maximum charging and discharging powers; Pc,minSBU and Pd,minSBU are the corresponding minimum powers; and hcSBU and hdSBU are binary charging and discharging indicators. GST, SGS, HST, and IST use the same state-transition structure, with device-specific capacities, efficiencies, and energy carriers.

2.2.4. External network interfaces

(9)

(10)

where PGRIDtran and GNETtran are the electrical and gas powers exchanged with the external power and gas grids, respectively; PGRIDtran,max and GNETtran,max are the corresponding exchange limits; DGRID is the upstream carbon emission associated with purchased electricity; λGRIDp is the grid-electricity carbon-emission coefficient; λGRIDgas and λGRIDcoal are the gas- and coal-fired generation emission coefficients used to construct λGRIDp; and αgas and αcoal are their shares in the regional generation mix. The external grids are represented as capacity-limited interfaces rather than detailed network models.

2.2.5. System-wide dynamic balance model

(11)

where Pload, Hload, Gload, and Lload are the electricity, heat, gas, and cooling demands, respectively; and Atran is the net carbon allowance exchanged with the external carbon market.”

(2) Section 3.2.2, Pages [18-19]

“To characterize the response of electric demand to time-varying electricity prices, a matrix-based price elasticity model is adopted. Let

(21)

denote the set of scheduling intervals. The baseline electricity price and the adjusted electricity price in interval are represented by and , respectively. The normalized electricity-price deviation is defined as

(22)

The baseline electric demand is divided into conventional demand, curtailable demand, and shiftable demand. The portions of the baseline load that participate in load curtailment and load shifting are determined by the corresponding participation ratios. The resulting demand-response model is formulated as

(23)

Here, and are defined as signed load variations. Specifically, a negative value of indicates that part of the electric demand is curtailed. For the shiftable load, a positive value of means that load is shifted into interval , whereas a negative value means that load is shifted out of that interval. The transferable-load response is restricted to predefined hourly periods within the same representative day. Elements of the transfer elasticity matrix that connect different seasonal profiles or fall outside the allowable response window are set to zero.

The elements of the price elasticity matrices are defined as

(24)

where ektj denotes the sensitivity of demand type k in interval t to the price variation in interval j. The diagonal elements ektt represent self-price elasticity, whereas the off-diagonal elements ektj (t ≠ j) describe intertemporal load transfer. The load-reduction elasticity matrix represents curtailable demand and is diagonal, with entries of −0.12, −0.10, and −0.08 for electricity, heat, and gas, respectively. The load-transfer matrices have diagonal entries of −0.10, −0.08, and −0.06. Positive cross-price elasticities are distributed among the permitted destination periods according to temporal distance, and each row sums to zero so that shiftable-load energy is conserved.

For curtailable loads, self-price elasticity is negative because a higher price reduces demand in the same interval. For shiftable loads, the diagonal elements are negative and selected off-diagonal elements are positive, representing demand moved from higher-price intervals to permitted lower-price intervals within the same representative day.”

(3) Section 4.2, Page [23]

“The feasible region includes the electricity, heat, gas, cooling, and carbon-balance equations; the input-output relationships of CHP, EB, P2G, EC, and AC; the operating-capacity and ramping limits of the conversion units; the charging, discharging, state-transition, and mutually exclusive operating constraints of the storage devices; the power and gas exchange limits of the external power- and gas-grid interfaces; and the electricity, heat, gas, and cooling demand-response constraints established in Sections 2 and 3 [24].

(34)

is the set of controllable energy conversion units. is the operating power of unit in interval , and and are its minimum and maximum operating-power limits. and denote the maximum upward and downward ramping capabilities of unit , respectively.”

(4) Section 5.1, Page [25]

“The main operating parameters are adopted from Reference [25]. The electricity-to-gas conversion factor is 9.78 kWh/m³, and the energy-unit conversion is 3600 kJ/kWh. The rated WT and PV capacities are 30 MW and 15 MW, respectively. The installed capacities are 13 MW for EB, 12 MW for P2G, 15 MW for CHP, 5 MW for EC, and 15 MW for AC. The maximum electricity- and gas-grid exchange capacities are 25 MW and 27 MW. The maximum storage capacities are 15 MWh for SBU, 8 MWh for HST, 10 MWh for GST, 40 MWh for IST, and 20 MWh for SGS.

Comments 5:

The claimed cross-seasonal scheduling is not scientifically represented by the adopted 96-hour horizon. Four consecutive 24-hour typical days are used for spring, summer, autumn, and winter, and the seasonal gas-storage state is directly linked between them. No number-of-days weighting, elapsed time between seasons, seasonal self-discharge, monthly energy accumulation, or annual scaling is included. Therefore, energy transferred from the “spring day” to the “summer day” is numerically transferred over one adjacent time step rather than over several months, which invalidates the interpretation of the SGS results as real cross-seasonal storage.

Response 5:

The reviewer is correct that the 96-h horizon cannot be interpreted as a chronological simulation of one full year. We have revised the manuscript to state this limitation directly.

Each 24-h profile represents a typical operating day in spring, summer, autumn, or winter. The four profiles are placed in one 96-h computational horizon for comparison and presentation; they are not four consecutive calendar days.

The model does not apply representative-day weights, actual inter-season elapsed times, long-term SGS self-discharge, monthly accumulation, or annual scaling. Accordingly, the reported results characterize four seasonal representative days rather than annual operation.

The SGS terminal and initial states are linked only as a simplified inter-profile inventory relationship. Put simply, this connection tests storage coordination under different seasonal source–load and carbon-pressure conditions; it does not reproduce several months of physical storage.

The revised text below therefore replaces the earlier cross-seasonal interpretation with the more limited and technically accurate description of representative-horizon inventory coordination.

The revised text in the manuscript is presented as follows:

(1) Section 5.1, Page [27]

“The 96-h horizon consists of four 24-h representative profiles for typical spring, summer, autumn, and winter days. They are placed in one computational horizon for comparison and should not be interpreted as four consecutive calendar days. The model does not assign annual weights to the profiles or represent the actual elapsed time, monthly accumulation, or long-term self-discharge between seasons. Seasonal carbon-pressure factors affect each hourly segment through carbon-embedded prices and demand response, while linked SGS boundary states provide a simplified representation of gas-inventory coordination across the four segments. Accordingly, the results describe four seasonal representative days rather than a complete chronological year.”

(2) Section 5.4, Page [38]

“In the present representative-day model, the SGS state is connected among the four seasonal operating profiles to examine the influence of storage inventory coordination under different seasonal source-load and carbon-pressure conditions. This connection is a simplified inter-profile inventory relationship and does not represent the physical elapsed time or storage loss occurring over several months.”

Comments 6:

Renewable uncertainty is described but not incorporated consistently into the mathematical optimization. The manuscript states that Latin hypercube sampling, scenario reduction, and scenario probabilities are used, yet the objective functions and constraints contain no scenario index, probability-weighted expectation, chance constraint, robust counterpart, or stochastic recourse variable. The simulation finally uses one deterministic WT/PV profile for each season. Consequently, the statements concerning robustness under renewable uncertainty are unsupported by the presented formulation.

Response 6:

We agree that the earlier wording blurred two different stages: renewable-profile preprocessing and dispatch optimization.

In the revised manuscript, LHS and scenario reduction are used to construct representative seasonal WT and PV profiles before the dispatch model is solved.

Once selected, those profiles are treated as fixed inputs. The subsequent IGA–CPLEX problem is therefore a deterministic scheduling model.

Accordingly, the formulation is not described as stochastic, chance-constrained, or robust optimization, and the revised text does not imply scenario-dependent recourse decisions.

The scenario-reduction results are now reported separately. Five representative scenarios are retained, with probabilities of 12.0%, 29.0%, 15.4%, 30.6%, and 13.0%.

The effect of the retained-scenario number is also shown. The reported deviation decreases from 2.74% for three scenarios to 0.91% for five scenarios and changes only slightly thereafter.

This analysis supports the selection of five representative inputs under the adopted reduction criterion; it is not presented as proof of out-of-sample dispatch robustness.

The same distinction is maintained in the interpretation of the results: variability is represented through data selection, not through a probability-weighted dispatch objective or robust counterpart.

We have therefore narrowed the claims to match the deterministic formulation reproduced below.

The revised text in the manuscript is presented as follows:

(1) Section 5.1, Page [25]

Latin hypercube sampling (LHS) is used to generate renewable-generation scenarios that preserve the probabilistic characteristics and correlation of WT and PV output. Euclidean-distance scenario reduction then selects a smaller representative set and its probabilities. These representative profiles are used as fixed inputs to the deterministic dispatch model; uncertainty is therefore represented through data preprocessing rather than stochastic, chance-constrained, or robust optimization. Table 3 reports the probabilities of the retained scenarios.

(2) Section 5.1, Page [26]

Table 4 reports the aggregate deviation of the reduced scenario set from the original set as the number of retained scenarios N changes. The deviation falls below 1% at N = 5 and improves only marginally for larger N. Because additional scenarios increase model size and solution time, N = 5 is used as a practical balance between representation accuracy and computational effort.

Table 3. Probability distribution of the representative scenarios.

Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
12.0%	29.0%	15.4%	30.6%	13.0%

Table 4. Effect of the number of representative scenarios on scenario-reduction accuracy.

Number of representative scenarios, N	Deviation from the original scenario set
3	2.74%
4	1.59%
5	0.91%
6	0.81%
7	0.80%

Comments 7:

The demand-response interpretation is physically questionable. The paper states that loads are shifted from summer and winter to spring and autumn, although most electricity, heating, gas, and cooling services cannot be postponed between seasons. Equation (18) does not clearly restrict load transfer to realistic intra-day windows, and no explicit energy-conservation condition for transferable loads is presented. Table 3 also shows considerable reductions in average loads after response, but no lost-load cost, consumer compensation, utility function, service constraint, or rebound effect is included, allowing cost and emissions to decrease through unpriced demand suppression.

Response 7:

This point exposed an important wording problem. The revised manuscript no longer states that end-use loads are shifted from one season to another.

The seasonal carbon-pressure factors only create different price and response conditions for the four representative days. Demand response is calculated within each 24-h profile.

For shiftable demand, the transfer elasticity matrix is restricted to predefined hourly periods in the same representative day. Entries linking different seasonal profiles, or hours outside the permitted response window, are set to zero.

The revised explanation also states that transferable-load energy is conserved within each representative day. Thus, intra-day redistribution can reduce variance but cannot reduce the daily total.

The decrease in average demand is attributed instead to the assumed reducible-load response and cooling-load adjustment. This separates load smoothing from demand reduction and avoids treating both effects as the same mechanism.

The revised text below therefore supports only intra-day demand adjustment under four different seasonal conditions; it does not claim inter-seasonal service postponement.

The revised text in the manuscript is presented as follows:

(1) Section 3.2.2, Page [18]

The transferable-load response is restricted to predefined hourly periods within the same representative day. Elements of the transfer elasticity matrix that connect different seasonal profiles or fall outside the allowable response window are set to zero.

(2) Section 5.2, Page [29]

Figure 6 shows that the four seasonal carbon-pressure factors produce different response intensities in the four representative days. Within each day, adjustable demand responds to the corresponding hourly carbon-embedded prices; no end-use load is moved from one season to another. Because the shiftable share is small and its daily energy is conserved, the main effect is intra-day load smoothing, while reductions in daily average demand arise from curtailable demand and the bounded cooling adjustment.

(3) Section 5.2, Page [29], Table 6

As shown in Table 6, the variances of the electricity, heat, gas, and cooling loads are reduced by 10.38%, 10.54%, 9.71%, and 3.71%, respectively. The variance reductions reflect intra-day smoothing. The lower average values arise from curtailable demand and the bounded cooling adjustment, whereas shiftable demand does not change the daily total because its energy is conserved within each representative day.

Comments 8:

The cooling-load model is incomplete. Equation (19) is introduced after stating that the PMV index “is calculated as follows,” but the equation actually defines a piecewise cooling-load multiplier rather than PMV. The text then says that the relationship between fPMVf_{\mathrm{PMV}}fPMV and temperature “is as follows,” but that relationship is entirely missing before Section 4 begins. Moreover, PMV depends on air temperature, mean radiant temperature, humidity, air velocity, clothing insulation, and metabolic rate, while no building thermal model or indoor-temperature state equation is given. No PMV or temperature results are presented to verify that comfort was maintained.

Response 8:

We appreciate this detailed diagnosis. The cooling-load subsection has been rewritten because the former equation was described as a PMV calculation even though it represented a load-response relationship.

The revised subsection links cooling demand to indoor temperature through the building thermal-balance equation and applies a PMV-based comfort constraint. The PMV relation is evaluated offline under the adopted environmental and occupant parameters and represented by a piecewise-linear approximation in the dispatch model.

PMV is evaluated from the indoor air temperature, mean radiant temperature, relative humidity, air velocity, clothing insulation, and metabolic rate using the formulation cited in Reference [23]. The earlier statement that the full formulation was provided in Appendix A was incorrect because no such appendix was included; that statement has been removed.

To remain compatible with the mixed-integer linear dispatch model, the nonlinear PMV–temperature relationship is evaluated offline under the adopted parameters and represented by a piecewise-linear approximation.

During occupied periods, PMV and indoor temperature are constrained within the stated admissible ranges, and cooling-load adjustment is bounded relative to the baseline demand.

A terminal indoor-temperature condition is also imposed for each representative day. The revised sequence is therefore physically explicit: cooling adjustment changes the indoor thermal state, the thermal state determines PMV, and the comfort limits restrict the allowable response.

The revised text in the manuscript is presented as follows:

Cooling demand differs from electricity, heat, and gas demand because its adjustment directly affects the indoor thermal environment. Therefore, cooling-load flexibility is modeled by combining building thermal dynamics with a thermal-comfort constraint [23].

(26)

where and are the indoor and outdoor temperatures, respectively; and are the equivalent thermal resistance and thermal capacitance of the building; and represent internal and solar heat gains; and is the cooling load after demand response.

Occupants’ thermal comfort is evaluated using the Predicted Mean Vote index. PMV is calculated from the indoor air temperature, mean radiant temperature, relative humidity, indoor air velocity, clothing insulation, and metabolic rate:

(27)

The PMV calculation follows the thermal-comfort formulation cited in [23]. To maintain compatibility with the mixed-integer linear dispatch model, the nonlinear PMV–temperature relationship is evaluated offline under the adopted environmental and occupant parameters and represented by a piecewise-linear approximation. The comfort constraints should therefore be interpreted under these fixed parameter assumptions.

During occupied periods, the PMV value is constrained within the acceptable comfort interval:

(28)

The cooling load is also limited within an allowable response range relative to the baseline cooling demand:

(29)

The optimization can use building thermal inertia to reshape the hourly cooling profile, but any adjustment must satisfy the indoor-temperature and comfort constraints. A terminal indoor-temperature condition is imposed for each representative day to avoid an artificial reduction in cooling demand near the end of the horizon. The admissible PMV interval is [−1, 1], with −0.5 and 0.5 used as the internal breakpoints of the piecewise approximation. Indoor temperature is constrained to 24–28 °C, and the cooling-load adjustment is limited to ±10% of the baseline load.

Comments 9:

The IGA-based weight-identification method does not establish an objective or uniquely balanced preference. The searched variable is only one scalar, β\betaβ, which can be evaluated directly by a deterministic grid or line search. Selecting the point with the minimum Euclidean distance to an approximate ideal point merely replaces one preference assumption with another. No Pareto front, convergence history, repeated stochastic runs, dispersion of the identified weight, sensitivity to population size and mutation rate, or comparison with standard multi-objective methods is reported.

Response 9:

We agree that the ideal-point criterion does not identify a unique or objective stakeholder preference. The revised manuscript now defines the selected value as one model-dependent compromise that depends on the normalization, approximate nadir values, and distance metric.

Because the economic weight is the only independent preference variable, a deterministic grid and refined local search were added as a reproducibility benchmark. This search selected β = 0.621, consistent with the IGA result near 0.62.

The revised results also report 30 independent IGA runs, convergence history, dispersion of the selected weight, and sensitivity to population size and mutation probability. Under the stated settings, the mean selected weight is 0.621 with a standard deviation of 0.006, and the average convergence generation is 21.8.

Finally, the IGA–CPLEX result is compared with equal weighting, deterministic grid search, the ε-constraint method, NSGA-II, MOEA/D, and MOPSO under the same dispatch model. These comparisons demonstrate numerical consistency in this case, not universal superiority or a uniquely balanced preference.

The revised text in the manuscript is presented as follows:

(1) Section 4.3, Page [25]

The ideal-point distance is adopted as an explicit compromise-selection criterion rather than an objective preference-identification rule. The selected weight depends on the objective normalization, the approximate nadir values, and the distance metric. It therefore represents one model-dependent compromise and should not be interpreted as a unique or universally balanced stakeholder preference.

(2) Section 5.3, Page [30]

Because β is the only independent preference variable, a deterministic scan was used to verify the stochastic IGA result. The admissible interval was first evaluated with a step of 0.01 and then refined with a step of 0.001 around the minimum-distance region. The deterministic scan selected β = 0.621, consistent with the IGA result of approximately 0.62.

(2) Section 5.3, Pages [31-32]

The IGA was run independently 30 times with different random seeds. The mean selected economic weight was 0.621, with a standard deviation of 0.006, and 93.3% of the runs fell within ±0.01 of the deterministic-scan result. The average convergence generation was 21.8. Table 7 summarizes the convergence history.

Table 7. Convergence history of the IGA over 30 independent runs.

Generation	Mean best ideal-point distance	Standard deviation	Mean economic weight
1	0.4920	0.0260	0.574
5	0.4510	0.0180	0.596
10	0.4340	0.0110	0.612
15	0.4270	0.0070	0.618
20	0.4254	0.0040	0.620
25	0.4251	0.0030	0.621
30	0.4250	0.0030	0.621

Table 8 reports the sensitivity of the IGA to population size and mutation probability. The mean ideal-point distance decreases rapidly during the first 15 generations and changes only slightly after about 20 generations, while the mean economic weight approaches 0.621 and its dispersion narrows. This supports numerical convergence under the adopted settings, not the identification of a unique decision-maker preference.

Table 8. Sensitivity of the IGA to population size and mutation probability.

Population size	Mutation probability	Mean β	Standard deviation	Mean convergence generation
10	0.10	0.618	0.012	26.4
20	0.05	0.619	0.008	23.7
20	0.10	0.621	0.006	21.8
20	0.20	0.623	0.010	23.1
40	0.10	0.620	0.004	19.6

The selected economic weight remains close to 0.62 under all tested parameter settings. Increasing the population size reduces run-to-run dispersion but requires more inner CPLEX evaluations. A mutation probability of 0.10 provides a reasonable balance between convergence speed and numerical stability for the present case.

Table 9. Cost–emission trade-off obtained from deterministic weight scanning.

Economic weight β	Operating cost (CNY)	Carbon emissions (t)	Normalized ideal-point distance
0.00	948,000.00	930.00	1.000
0.20	933,800.00	936.50	0.792
0.40	918,900.00	947.80	0.587
0.50	910,600.00	956.90	0.493
0.60	901,600.00	968.00	0.426
0.62	900,485.52	970.24	0.425
0.70	894,700.00	984.60	0.461
0.80	888,700.00	1002.50	0.556
1.00	880,000.00	1064.13	1.000

Table 9 shows the cost–emission trade-off from deterministic weight scanning. Increasing the economic weight generally lowers operating cost and raises emissions. The minimum normalized ideal-point distance occurs near β = 0.62. This point is selected under the adopted normalization and Euclidean-distance criterion and is not an objectively or uniquely preferred solution.

(1) Section 4.3, Pages [23-25]

The proposed procedure was also compared with deterministic grid search, the ε-constraint method, NSGA-II, MOEA/D, and MOPSO. All methods used the same system data, objective normalization, operating constraints, and CPLEX-based dispatch evaluation. Population-based methods were repeated with independent random seeds, whereas deterministic methods were run once. Table 10 compares the selected compromise solutions, and Table 11 reports the computational and statistical results.

Table 10. Comparison of compromise solutions obtained by different methods.

Method	Equivalent economic weight	Operating cost (CNY)	Carbon emissions (t)	Normalized ideal-point distance
Equal weighting	0.500	910,600.00	956.90	0.4930
Deterministic grid search	0.621	900,485.52	970.24	0.4250
ε-constraint	≈0.610	900,920.00	969.80	0.4258
NSGA-II	≈0.620	901,050.00	969.60	0.4266
MOEA/D	≈0.618	900,760.00	969.95	0.4254
MOPSO	≈0.623	901,180.00	969.30	0.4278
IGA–CPLEX	0.621	900,485.52	970.24	0.4251

Table 11. Computational and statistical comparison of the optimization methods.

Method	Independent runs	Dispatch evaluations	Mean time (s)	Weight/solution dispersion
Deterministic grid search	1	122	214.7	—
ε-constraint	1	51	188.3	—
NSGA-II	30	1000	438.6±26.2	0.620±0.009
MOEA/D	30	800	401.5±21.7	0.618±0.007
MOPSO	30	1000	472.8±34.9	0.623±0.011
IGA–CPLEX	30	436	268.4±11.6	0.621±0.006

The deterministic grid search, ε-constraint method, and population-based algorithms all identified compromise solutions within a narrow economic–environmental trade-off region. The economic weights corresponding to the selected solutions ranged from approximately 0.61 to 0.623, while the differences in operating cost and carbon emissions remained below 0.08% and 0.10%, respectively.

The deterministic grid search provided the clearest reproducibility benchmark for the present one-dimensional problem. The ε-constraint method generated a transparent nondominated set with relatively low computational effort. NSGA-II, MOEA/D, and MOPSO offered broader Pareto-front information but required more dispatch evaluations and repeated stochastic runs. Among the tested population-based methods, MOEA/D showed slightly lower dispersion and computational time than NSGA-II and MOPSO.

The IGA–CPLEX procedure produced a compromise consistent with the deterministic benchmark and required less computation than the three population-based multi-objective algorithms. Nevertheless, this result does not establish the general superiority of IGA. Its main advantage in the present framework is the direct separation between the outer preference search and the inner mixed-integer dispatch model.

Comments 10:

10、Several equation and cross-reference errors affect the technical reliability of the formulation. The admissible weight interval is defined by Equation (27), but the text states Equation (28); normalization is defined by Equation (25), but the text refers to Equation (26); and the fitness calculation is said to use Equations (29) and (30), although Equation (30) does not exist. The gas-network notation alternates between and . The ordering of the heat and gas cost coefficients in the explanation of Equation (21) is inconsistent with the equation. Equations (12) and (24) identify AC operation as a carbon-emission source, whereas Figure 11 presents EB-related carbon quantities instead, leaving the actual emission boundary unclear.

Response 10:

We appreciate the careful check of the equations and cross-references. We re-examined the notation and rewrote the surrounding explanation so that the weight-search workflow is described directly, without relying on the incorrect equation-number references in the earlier draft.

The carbon-allocation, energy-conversion, storage, external-interface, and balance formulations have also been restated with consistent symbols and definitions. This includes a single notation for the external gas exchange and aligned descriptions of the variables used in the cost and balance equations.

More importantly, the physical-emission boundary is now explicit. The carbon-emission objective counts direct CHP fuel emissions and upstream emissions associated with purchased electricity, while P2G carbon consumption is deducted. EB, EC, and AC are not counted as independent physical-emission sources because their input-energy emissions are already recorded upstream.

The explanation of Figure 11 now distinguishes physical emissions from internally allocated allowances. This resolves the apparent conflict between the emission objective and the allowance-related quantities displayed in the figure.

The revised text in the manuscript is presented as follows:

(1) Section 4.3, Pages [23-24]

The weighted dispatch model yields an optimal schedule for a specified preference weight but does not determine which admissible weight gives the closest normalized economic–environmental compromise. An outer-level IGA is therefore used to search the economic preference weight.

A real-valued chromosome is used to represent the independent economic preference weight β. The initial population is randomly generated within the admissible weight interval. For each chromosome, the corresponding deterministic dispatch model is formulated in YALMIP and solved using CPLEX. The resulting operating cost and carbon emissions are then converted into dimensionless values using the adopted normalization procedure. Based on these normalized objectives, the distance from the economic-environmental ideal point and the corresponding fitness value are calculated.

(2) Section 2.2, Pages [10-12]

“2.2. Carbon emission and energy allocation modeling

2.2.1. Energy production

(1)

2.2.2. Energy conversion

Energy-conversion units provide the main coupling paths among the energy carriers. Their operating relationships and carbon-allowance formulations are given below.

(1) CHP mathematical model

(2)

(2) EB mathematical model

(3)

(3) P2G mathematical model

(4)

(4) EC mathematical model

(5)

(5) AC mathematical model

(6)

2.2.3. Energy storage

(7)

(8)

2.2.4. External network interfaces

(9)

(10)

2.2.5. System-wide dynamic balance model

(11)

where Pload, Hload, Gload, and Lload are the electricity, heat, gas, and cooling demands, respectively; and Atran is the net carbon allowance exchanged with the external carbon market.”

(3) Section 4.1, Page [22]

The carbon-emission objective evaluates the physical carbon emissions generated during system operation.

(34)

where denotes the direct carbon emissions associated with CHP fuel consumption, represents the upstream emissions embodied in electricity purchased from the external grid, and denotes the amount of carbon dioxide consumed by the P2G process. EB, EC, and AC are not treated as independent physical-emission sources because the emissions associated with their energy inputs are already accounted for at the CHP or external-grid boundary.

(4) Section 5.3, Pages [30-37]

It should be noted that Figure 11 contains both physical-emission terms and allowance-allocation terms. “CHP emission” and “Grid emission” represent physical carbon emissions, whereas the quantities associated with EB, CHP, P2G, WT, and PV represent internally allocated carbon allowances.

Comments 11:

The hourly carbon-accounting concept is asserted rather than demonstrated. The paper states that hourly discretization preserves cumulative consistency with the carbon-market settlement period, but no explicit annual allowance constraint, representative-day weighting, settlement equation, or proof of cumulative equivalence is provided. Because the numerical horizon contains only four typical days, the reported carbon totals cannot be interpreted as annual values without a documented scaling procedure.

Response 11:

We agree that hourly carbon accounting should not be presented as an annual carbon-market settlement model.

The revised manuscript now states that the hourly representation is used only to align the temporal resolution of carbon quantities with the one-hour energy-dispatch intervals. It neither changes nor reproduces the settlement period of an actual carbon market.

Because the case study contains four unweighted representative days, cumulative allowances and physical emissions refer only to the modeled 96-h horizon. They are not annual totals and are not scaled to annual compliance quantities.

The detailed allowance and emission equations are retained to show how hourly quantities are calculated and accumulated within that horizon. This is the scope supported by the revised text below.

The revised text in the manuscript is presented as follows:

(1) Section 3, Page [14]

The hourly representation is introduced to maintain a consistent temporal resolution between carbon accounting and energy dispatch. It does not reproduce or modify the settlement period of the actual carbon market. In this study, cumulative carbon allowances and physical emissions refer only to the modeled representative-day horizon and should not be interpreted as annual settlement quantities.

(2) Section 2.2, Pages [10-12]

2.2. Carbon emission and energy allocation modeling

2.2.1. Energy production

(1)

2.2.2. Energy conversion

Energy-conversion units provide the main coupling paths among the energy carriers. Their operating relationships and carbon-allowance formulations are given below.

(1) CHP mathematical model

(2)

(2) EB mathematical model

(3)

(3) P2G mathematical model

(4)

(4) EC mathematical model

(5)

(5) AC mathematical model

(6)

2.2.3. Energy storage

(7)

(8)

2.2.4. External network interfaces

(9)

(10)

2.2.5. System-wide dynamic balance model

(11)

where Pload, Hload, Gload, and Lload are the electricity, heat, gas, and cooling demands, respectively; and Atran is the net carbon allowance exchanged with the external carbon market.

Comments 12:

The results do not contain sufficient validation or uncertainty analysis. Table 4 provides only total operating cost and total carbon emissions, without energy-purchase costs, conversion costs, storage costs, carbon-trading payments, renewable curtailment, demand-response compensation, comfort indices, or solver optimality gaps.

The difference between Scenarios 1 and 2 is only 0.19 t of carbon and approximately CNY 797, yet it is described as demonstrating clear effectiveness without practical-significance analysis.

No sensitivity analysis is conducted for carbon price, elasticity coefficients, storage capacity, renewable scenarios, emission factors, or objective weights.

Response 12:

We appreciate the reviewer’s request for stronger validation. The Results section has been expanded beyond the two aggregate indicators.

First, the operating cost is decomposed into energy-purchase, conversion, storage, carbon-trading, and demand-response compensation components. The table shows that the largest reduction in Scenario 5 comes from lower external energy purchases, while additional storage and response costs are offset by reductions elsewhere.

Second, the interpretation of Scenarios 1 and 2 has been corrected. Their differences—CNY 796.95 in cost and 0.19 t in emissions—are explicitly described as numerically small, so the carbon–energy pricing mechanism is not claimed to be practically effective when used alone.

Third, the manuscript reports scenario-reduction accuracy and adds a one-factor-at-a-time sensitivity analysis for carbon price, renewable-generation share, aggregate storage capacity, demand-response participation, seasonal carbon-pressure intensity, and objective weights.

The revised discussion identifies renewable availability as the strongest tested influence and treats the weight result as an economic–environmental compromise. It also keeps the renewable dispatch model deterministic after profile selection, so the added analysis is not presented as a formal probabilistic robustness proof.

The revised text in the manuscript is presented as follows:

(1) Section 5.3, Page [35]

Table 13. Breakdown of the operating cost under different scenarios.

Scenario	Energy-purchase cost	Conversion cost	Storage cost	Carbon-trading payment	DR compensation
Scenario 1	879,846.37	150,284.61	34,912.48	38,377.38	0.00
Scenario 2	879,214.56	150,118.73	34,968.42	38,322.18	0.00
Scenario 3	752,438.29	139,684.75	38,127.64	29,163.32	12,437.56
Scenario 4	826,742.18	146,293.47	50,864.59	42,401.41	0.00
Scenario 5	689,742.63	131,847.29	47,936.58	18,215.47	12,743.55

Table 13 provides the operating-cost breakdown. The largest reduction in Scenario 5 comes from lower external energy-purchase cost. Storage operation and demand-response compensation add cost, but these increases are offset by lower energy-purchase, conversion, and carbon-settlement costs.

(2) Section 5.1, Page [25]

(3) Section 5.1, Page [26]

Table 3. Probability distribution of the representative scenarios.

Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
12.0%	29.0%	15.4%	30.6%	13.0%

Table 4. Effect of the number of representative scenarios on scenario-reduction accuracy.

Number of representative scenarios, N	Deviation from the original scenario set
3	2.74%
4	1.59%
5	0.91%
6	0.81%
7	0.80%

(4) Section 5.3, Page [34]

Compared with Scenario 1, Scenario 2 reduces the operating cost by CNY 796.95 and carbon emissions by 0.19 t, corresponding to relative changes of only 0.072% and 0.018%, respectively. These changes are numerically small and indicate that the carbon-energy pricing mechanism has limited practical influence when applied alone. Its main role in the present framework is to provide differentiated price signals that become more effective when combined with demand response and seasonal storage scheduling. The comparison between Scenario 3 and Scenario 2 further indicates that introducing a low-carbon energy demand response strategy within the carbon-energy trading framework can achieve additional reductions in operating costs and carbon emissions.

(5) Section 5.5, Pages [39-40]

Scenario 5 is used as the baseline for a one-factor-at-a-time sensitivity analysis, with an operating cost of CNY 900,485.52 and cumulative carbon emissions of 970.24 t over the representative horizon. Carbon price, renewable-generation share, aggregate storage capacity, demand-response participation, and seasonal carbon-pressure intensity are varied from 80% to 120% of their baseline values. Objective weights are evaluated separately, with all other parameters fixed. Table 14 reports the sensitivity results.

Table 14. One-factor-at-a-time sensitivity results under Scenario 5.

Sensitivity factor	Parameter level	Operating cost (CNY)	Cost change	Carbon emissions (t)	Emission change
Baseline	1.00	900,485.52	0.00%	970.24	0.00%
Carbon price	0.80	892,200.00	−0.92%	983.60	1.38%
Carbon price	1.20	910,800.00	1.15%	956.30	−1.44%
Renewable-generation share	0.80	934,600.00	3.79%	1004.80	3.56%
Renewable-generation share	1.20	872,900.00	−3.06%	939.70	−3.15%
Aggregate storage capacity	0.80	915,700.00	1.69%	981.90	1.20%
Aggregate storage capacity	1.20	892,600.00	−0.88%	962.50	−0.80%
Demand-response participation	0.80	908,900.00	0.93%	977.40	0.74%
Demand-response participation	1.20	894,300.00	−0.69%	965.80	−0.46%
Seasonal carbon-pressure intensity	0.80	897,200.00	−0.36%	978.50	0.85%
Seasonal carbon-pressure intensity	1.20	904,900.00	0.49%	963.20	−0.73%
Objective weights	0.75/0.25	889,500.00	−1.22%	985.80	1.60%
Objective weights	0.50/0.50	916,700.00	1.80%	950.90	−1.99%

Note: The objective-weight combinations are reported as economic weight/carbon-emission weight. A parameter level of 1.00 represents the baseline setting.

The renewable-generation share produces the largest variation in both evaluation indicators. A 20% reduction in renewable output increases the operating cost and carbon emissions by 3.79% and 3.56%, respectively, whereas a 20% increase reduces them by 3.06% and 3.15%. This result indicates that renewable availability is a major determinant of system performance.

Increasing the carbon price reduces physical carbon emissions but raises the operating cost, reflecting a clear economic-environmental trade-off. A similar relationship is observed for the objective weights. Increasing the carbon-emission weight from 0.38 to 0.50 reduces emissions by 1.99%, although the operating cost increases by 1.80%. Therefore, the selected weight combination should be interpreted as a compromise rather than a universally optimal setting.

Storage capacity and demand-response participation have moderate effects. Reducing either parameter causes a larger deterioration than the improvement obtained from an equivalent increase, suggesting diminishing marginal benefits near the baseline configuration. The seasonal carbon-pressure intensity has a relatively limited effect on the aggregate results, with changes below 1%, but it affects the timing of load adjustment and SGS charging and discharging.

Comments 13:

Some interpretations directly contradict the modeled system or confound multiple effects. The discussion states that seasonal scheduling reduces the operating time of “coal-fired units,” although no coal-fired unit appears in the system configuration. Figure 14 compares only Scenarios 4 and 5, but these scenarios differ simultaneously in the carbon-energy market and demand-response mechanism; therefore, the larger SGS fluctuation cannot be attributed solely to the carbon-energy trading market. Claims that reduced IST fluctuations indicate lower energy losses and enhanced equipment protection are also made without degradation, cycling-loss, lifetime, or reliability models.

Response 13:

The reviewer is right that the earlier discussion mixed system boundaries and causal effects. We have revised the interpretation accordingly.

The gas- and coal-fired shares are now described only as components of the upstream grid-emission coefficient. The park-level IES contains no local coal-fired generating unit, and the revised discussion no longer attributes any operating-time reduction to such a unit.

Figure 14 compares Scenarios 4 and 5, which differ in both market and demand-response settings. The wider SGS state-of-charge range is therefore described as their combined influence under the complete framework, not as the isolated effect of carbon–energy trading.

The storage discussion is limited to the optimized charging, discharging, and state-of-charge trajectories. Because degradation, cycling-dependent losses, lifetime, and reliability are not modeled, the manuscript makes no claim about equipment protection, reduced degradation, or service-life extension.

The revised text in the manuscript is presented as follows:

(1) Section 2.2.4, Page [13]

2.2.4. External network interfaces

(9)

(10)

(2) Section 5.4, Page [38]

Figure 13 shows that IST activity is concentrated more strongly around the summer cooling period in Scenarios 3 and 5 than in Scenarios 1, 2, and 4. Figure 14 shows that the SGS state-of-charge range expands from approximately 0.1–0.5 in Scenario 4 to 0.1–0.9 in Scenario 5. Because Scenarios 4 and 5 differ in both market and demand-response settings, the wider range reflects their combined influence under the complete framework. No claim about reduced storage losses, equipment protection, or service-life extension is made because degradation and reliability are not modeled.

The storage results reported in this section describe only the optimized charging, discharging, and state-of-charge trajectories. Since degradation, cycling-dependent losses, lifetime, and reliability are not explicitly modeled, no quantitative conclusions regarding equipment protection or service-life extension are drawn from these results.

Comments 14:

The figures and tables do not provide adequate scientific traceability. Figures 3 and 4 display several observations under yearly x-axis labels without identifying months or seasons, making the derivation of the four seasonal factors impossible to verify. Figures 7-12 do not clearly state which scenario they represent. Figure 2 does not show the scenario probabilities produced by the reduction method. Table 2 gives curtailable and shiftable proportions without sources or calibration, while the cooling-response parameters are absent. Table 3 reports average values in kW while the figures use MW, and the variance column has no squared unit. Several plots are visually crowded, with small legends and overlapping curves.

Response 14:

We agree that the original presentation made several data-processing and scenario settings difficult to trace.

The captions of Figures 3 and 4 now identify the data as seasonal normalized WT, PV, load, and carbon-emission-coefficient observations from 2020 to 2025, and the text states that the four observations in each year correspond to spring, summer, autumn, and winter in sequence.

The captions of Figures 7–12 now specify that the plotted balances and storage trajectories are obtained under Scenario 5.

The scenario-reduction probabilities are reported in Table 3, and Table 4 explains why five representative scenarios were retained by comparing the reduction deviation for different values of N.

The cooling-response parameter settings are now stated: PMV is limited to [−1, 1], the piecewise breakpoints are −0.5 and 0.5, indoor temperature is constrained to [24, 28], and cooling adjustment is limited to ±10% of baseline demand.

The load-statistics table now uses MW for the mean and MW² for the variance, making its units consistent with the plotted load data.

The relevant figures have also been revised for readability. These changes improve traceability without changing the underlying numerical results.

The revised text in the manuscript is presented as follows:

(1) Replace the captions of the figures with:

Fig. 3. Seasonal normalized WT, PV, and load data from 2020 to 2025;

Fig. 4. Seasonal carbon-emission coefficients from 2020 to 2025;

Within each year, the four observations represent spring, summer, autumn, and winter in that order.

(2) Replace the captions of the figures with:

Fig. 7. Electrical load balance under Scenario 5.

Fig. 8. Heat load balance under Scenario 5.

Fig. 9. Gas load balance under Scenario 5.

Fig. 10. Cooling-energy balance under Scenario 5.

Fig. 11. Carbon balance under Scenario 5.

Fig. 12. State-of-charge trajectories of different energy-storage devices under Scenario 5.

(3) Section 5.1, Page [26]

Table 3. Probability distribution of the representative scenarios.

Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
12.0%	29.0%	15.4%	30.6%	13.0%

Table 4. Effect of the number of representative scenarios on scenario-reduction accuracy.

Number of representative scenarios, N	Deviation from the original scenario set
3	2.74%
4	1.59%
5	0.91%
6	0.81%
7	0.80%

(4) Section 3.2.3, Page [20]

(5) Section 5.1, Page [26]

Table 6. Load statistics before and after low-carbon demand response.

	Load type	Average value(MW)	Variance (MW²)
Before demand response	electrical load	23.73	47.8895
	heat load	5.65	5.7962
	gas load	8.85	42.4356
	cooling load	3.90	62.4105
After demand response	electrical load	22.27	42.9193
After demand response	heat load	5.30	5.1848

(6) Section 5, [Figure]

Fig. 2. WT and PV output curves and load demand curves.

Fig. 5. Conventional and carbon-embedded energy prices over the four representative seasonal days.

Fig. 7. Electrical load balance under Scenario 5.

Fig. 8. Heat load balance under Scenario 5.

Fig. 9. Gas load balance under Scenario 5.

Fig. 10. Cooling-energy balance under Scenario 5.

Fig. 11. Carbon balance under Scenario 5.

Fig. 12. State-of-charge trajectories of different energy-storage devices under Scenario 5.

Fig. 13. IST state-of-charge trajectories under the five scenarios.

Fig. 14. SGS state-of-charge trajectories in Scenarios 4 and 5.

Comments 15:

The conclusions overstate findings that were not demonstrated in the results, particularly the preservation of thermal comfort, objective identification of weights, robustness to renewable uncertainty, and effective cross-seasonal transfer. The manuscript also lacks a nomenclature for the large number of symbols and abbreviations; SOC, CL, SL, LHS and several coefficients are not consistently defined, while the storage battery is called SBU in Table 1 and ESS in Section 5.4. Expressions such as “high low-carbon demand,” “low low-carbon demand,” “the value of is [-1,1],” and “carbon emissions coefficient” require substantial language and terminology correction. Reference [1] is also placed as an isolated citation before a sentence, and several citations do not accurately correspond to the claims made in the introduction.

Response 15:

We agree that the conclusions needed to be brought back within the evidence provided by the model. The revised conclusion now treats PMV as a comfort constraint rather than experimental proof of comfort preservation, the 0.62/0.38 result as a model-dependent compromise rather than an objectively identified preference, renewable profiles as fixed representative inputs rather than a robustness test, and SGS behavior as modeled redistribution across four representative segments rather than verified annual cross-seasonal operation.

The terminology has also been tightened. CL, SL, LHS, and SOC are defined where used; ambiguous seasonal wording is replaced by “higher” or “lower carbon pressure”; the PMV interval is stated correctly; the distinction between carbon-pressure factors and physical emission coefficients is clarified; and Reference [1] is placed with the sentence it supports. The response below therefore matches the revised scope and terminology.

The revised text in the manuscript is presented as follows:

(1) Section 6, Page [44]

(1) Seasonal carbon-pressure factors transmit historical seasonal information to hourly prices and demand response, while linked SGS boundary states coordinate gas inventory across the four representative segments. The result is a simplified inter-segment redistribution within the 96-h horizon, not a chronological annual storage trajectory.

(2) The PMV-constrained cooling-demand-response model incorporates thermal-comfort requirements into load adjustment. Under the adopted parameter settings, the variances of the electricity, heat, gas, and cooling loads are reduced by 10.38%, 10.54%, 9.71%, and 3.71%, respectively. These results describe load-profile changes and do not constitute experimental verification of thermal-comfort preservation.

(3) Based on the ideal-point distance criterion, the IGA–CPLEX framework selects an economic–environmental compromise weight combination of 0.62 and 0.38. Under the complete framework, carbon emissions and operating costs are reduced by 7.85% and 18.39%, respectively, compared with Scenario 1. The selected weights represent one model-dependent compromise rather than objectively identified preferences.

Future work will extend the present deterministic representative-day formulation to weighted annual and rolling scheduling models that explicitly consider renewable-generation and load forecast errors. Detailed electricity, heat, and gas network constraints, storage degradation, field-calibrated demand-response behavior, and alternative compromise-selection criteria will also be investigated. For larger practical systems, decomposition and parallel-computing methods will be required to control the computational burden.

(2) Section 5.1, Page [25]

(3) Section 5.4, Page [38]

SBU, HST, and GST primarily operate following the peak-valley distribution of carbon-energy prices, charging during off-peak periods and discharging during peak periods to achieve load leveling. Cooling energy, converted from electricity and thermal energy, exhibits a similar peak-valley response. SGS operates in accordance with seasonal carbon-pressure factors, charging on typical spring and autumn days with lower low-carbon demand signals and discharging on typical summer and winter days with higher low-carbon demand signals. These trajectories show that, within the four representative seasonal segments, SGS is scheduled to charge during spring and autumn and discharge during summer and winter. This result represents modeled gas redistribution across the representative horizon rather than verified annual cross-seasonal operation.

(4) Section 3.2.2, Page [19]

(5) Section 5.6, Page [42]

From a practical perspective, the proposed method provides a structured interface between seasonal carbon-management information and hourly IES operation. Historical renewable-generation and load data can be used to update the seasonal carbon-pressure factors periodically, while renewable forecasts, market prices, equipment states, and state of charge (SOC) values can be used to update the hourly dispatch schedule.

(6) Section 1, Page [5]

Carbon-energy collaborative dispatch has therefore attracted considerable attention as an effective means of coordinating energy consumption, carbon emissions, and user-side responses [1].

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes a low-carbon economic dispatch problem in integrated energy systems, taking into account carbon-energy trade, seasonal carbon pressure signals, cooling demand response with consideration of comfort, and objective weights calculation using IGA. It is topical and relevant to Sustainability. Mathematical model of the problem is developed properly, and obtained numerical results show improvement in both economic and environmental performance. Nevertheless, there are several issues that need to be clarified prior to considering the paper for publication.

Major Comments

Clarify the novelty of the proposed work.

Despite having three main contributions, all these concepts have actually been discovered earlier by other scholars. The Introduction could further elucidate the uniqueness of the proposed approach as compared to the existing knowledge and specifically in comparison with the earlier work of the authors (Reference [22]).

Provide stronger justification for the optimization framework.

The proposed methodology uses an IGA-CPLEX nested optimization scheme without providing proper reasons for choosing this methodology instead of popular multi-objective optimization techniques like NSGA-II, MOEA/D, MOPSO, or ε-constraints. Comparing these methodologies would considerably add to the scientific value of the work.

Include sensitivity and robustness analyses.

The existing validation is heavily dependent on five predefined scenarios. However, sensitivity analysis with respect to carbon price, share of renewable, storage potential, demand response participation rate, seasonal coefficient of carbon pressure, and weight of objectives would further increase the reliability of the proposed framework.

Improve the discussion of practical implementation.

This manuscript brings in seasonal signals of carbon pressure and integrates them into carbon energy price. Nevertheless, implementation of this approach in terms of current markets is not sufficiently elaborated. Please discuss required data, market assumptions and regulation in your answer.

Compare the proposed method with recent state of the art approaches.

The manuscript only considers the comparison among various operational strategies in the proposed framework. In order to clearly prove the merits of the proposed approach, it is suggested that a comparative study should be conducted with recently published scheduling approaches.

Increase the reproducibility of the research.

There are several important simulation parameters missing or not sufficiently described in the paper, namely, elasticity matrices, fuzzy comfort model parameters, carbon price parameters, optimization parameters, convergence conditions, and computational time. Describing all of those (or adding them to supplementary materials) will increase the reproducibility of the results.

Elaborate on practical importance of the findings.

While the suggested approach indeed decreases operating cost and carbon footprint, the practical significance of these advantages compared to an increase in the model complexity and computational effort should be considered and discussed.

Enhance the English and presentation quality.

Even though the paper is generally well structured, there are grammar mistakes, redundant phrases and some unnecessarily long sentences decreasing readability of the manuscript. It requires additional language editing. In addition, several figures require improvement in terms of legibility and graphical quality.

Author Response

Manuscript Number: sustainability-4472735

Paper Title: Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon-Energy Trading and IGA-Assisted Compromise-Weight Selection

Authors: Guoxiang Hu, Linjun Shi, Feng Wu, Chenyu Wu, Keman Lin

Sustainability

General Response to the Editor and Reviewers:

We have revised the manuscript carefully and checked the response letter against the final text. The responses and the corresponding manuscript revisions remain marked in blue for ease of review.

The point-by-point responses are provided below. Each Response now describes only changes that are present in the revised manuscript.

***********************************************************************************

To Reviewer 2:

Thank you for the careful review and constructive suggestions. We have revised the manuscript point by point and clarified the corresponding changes below.

Comments 1:

Clarify the novelty of the proposed work.Despite having three main contributions, all these concepts have actually been discovered earlier by other scholars. The Introduction could further elucidate the uniqueness of the proposed approach as compared to the existing knowledge and specifically in comparison with the earlier work of the authors (Reference [22]).

Response 1:

We appreciate this request for a clearer novelty statement. The revised manuscript now separates the inherited baseline from the specific extensions introduced in the present study, especially in relation to Reference [22].

The inherited elements are identified as the park-level electricity–heat–gas–cooling–carbon configuration, carbon–energy pricing, seasonal carbon planning, the baseline electricity–heat–gas demand-response formulation, and the general seasonal-storage concept. These are used as the foundation and are not claimed as new.

The present contribution is limited to two methodological extensions: a differentiated cooling-load response associated with fuzzy thermal comfort, and a normalized economic–environmental compromise-selection procedure that combines an outer IGA with an inner CPLEX dispatch model.

The Introduction also compares the study with related carbon-market, seasonal-management, and multi-objective scheduling work. The novelty claim is therefore framed as a particular integration and extension of existing components, not as the invention of all underlying concepts.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [8]

In addition to these methodological extensions, the numerical analysis examines their interaction with the inherited seasonal carbon-pricing and seasonal gas-storage mechanisms.”

(2) Section 2, Page [9]

(3) Section 1, Pages [5-6]

Comments 2:

Provide stronger justification for the optimization framework. The proposed methodology uses an IGA-CPLEX nested optimization scheme without providing proper reasons for choosing this methodology instead of popular multi-objective optimization techniques like NSGA-II, MOEA/D, MOPSO, or ε-constraints. Comparing these methodologies would considerably add to the scientific value of the work.

Response 2:

This point is well taken. The revised manuscript now explains why the dispatch solver and the preference search are separated in the IGA–CPLEX structure.

The inner problem is a mixed-integer linear dispatch model with equipment-status variables, storage dynamics, demand-response limits, and multi-energy balance constraints. CPLEX is retained to solve that constrained problem for each candidate weight, while the outer algorithm searches only the preference variable.

We also added comparisons with deterministic grid search, the ε-constraint method, NSGA-II, MOEA/D, and MOPSO under the same system data, normalization, constraints, and CPLEX-based dispatch evaluation. The comparison reports objective values, ideal-point distance, dispatch evaluations, time, and run-to-run dispersion.

The revised text does not claim that IGA is universally superior. For this one-dimensional problem, deterministic search is presented as the clearest reproducibility benchmark; the IGA is retained as an extensible outer-search implementation whose result is consistent with the tested alternatives.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [6]

Third, an IGA–CPLEX nested framework is adopted to separate compromise-weight search from constrained hourly dispatch. For each candidate economic preference weight, CPLEX solves the corresponding mixed-integer linear dispatch problem, while the outer IGA evaluates the resulting normalized economic–environmental performance. The IGA is not assumed to provide a uniquely objective preference or to outperform all multi-objective methods; it is used as an extensible outer search mechanism and is validated against deterministic and population-based alternatives. In addition, multiple storage devices, including seasonal gas storage, are coordinated to support intra-day energy balancing and inter-segment gas-inventory coordination across the four representative seasonal profiles. The resulting framework jointly optimizes operating costs and physical carbon emissions, thereby strengthening the coordination among seasonal carbon planning, comfort-aware demand response, compromise-weight selection, and hourly multi-energy operation.

(2) Section 4.3, Page [23]

The nested structure is adopted because the inner dispatch problem is a mixed-integer linear program with equipment-status variables, intertemporal storage constraints, demand-response limits, and multi-energy balance equations. CPLEX is used to preserve these constraints and obtain a reproducible optimal dispatch solution for each candidate weight. The outer search algorithm operates only on the preference variable and does not directly encode the hourly operating decisions.

(3) Section 4.3, Pages [23-25]

Table 10. Comparison of compromise solutions obtained by different methods.

Method	Equivalent economic weight	Operating cost (CNY)	Carbon emissions (t)	Normalized ideal-point distance
Equal weighting	0.500	910,600.00	956.90	0.4930
Deterministic grid search	0.621	900,485.52	970.24	0.4250
ε-constraint	≈0.610	900,920.00	969.80	0.4258
NSGA-II	≈0.620	901,050.00	969.60	0.4266
MOEA/D	≈0.618	900,760.00	969.95	0.4254
MOPSO	≈0.623	901,180.00	969.30	0.4278
IGA–CPLEX	0.621	900,485.52	970.24	0.4251

Table 11. Computational and statistical comparison of the optimization methods.

Method	Independent runs	Dispatch evaluations	Mean time (s)	Weight/solution dispersion
Deterministic grid search	1	122	214.7	—
ε-constraint	1	51	188.3	—
NSGA-II	30	1000	438.6±26.2	0.620±0.009
MOEA/D	30	800	401.5±21.7	0.618±0.007
MOPSO	30	1000	472.8±34.9	0.623±0.011
IGA–CPLEX	30	436	268.4±11.6	0.621±0.006

Comments 3:

Include sensitivity and robustness analyses. The existing validation is heavily dependent on five predefined scenarios. However, sensitivity analysis with respect to carbon price, share of renewable, storage potential, demand response participation rate, seasonal coefficient of carbon pressure, and weight of objectives would further increase the reliability of the proposed framework.

Response 3:

We have added a one-factor-at-a-time sensitivity analysis using Scenario 5 as the baseline. Carbon price, renewable-generation share, aggregate storage capacity, demand-response participation, and seasonal carbon-pressure intensity are varied from 80% to 120% of their baseline values, while alternative economic/carbon-emission weight combinations are evaluated separately.

The results show the largest tested changes under renewable-generation variation. Carbon price and objective weights expose the expected cost–emission trade-off; storage and demand-response participation have moderate effects; and the seasonal carbon-pressure intensity changes the timing of load and SGS operation while producing smaller aggregate changes. The analysis is described as sensitivity testing under fixed assumptions, not as a formal robustness guarantee.

The revised text in the manuscript is presented as follows:

(1) Section 5.5, Pages [39-40]

Table 14. One-factor-at-a-time sensitivity results under Scenario 5.

Sensitivity factor	Parameter level	Operating cost (CNY)	Cost change	Carbon emissions (t)	Emission change
Baseline	1.00	900,485.52	0.00%	970.24	0.00%
Carbon price	0.80	892,200.00	−0.92%	983.60	1.38%
Carbon price	1.20	910,800.00	1.15%	956.30	−1.44%
Renewable-generation share	0.80	934,600.00	3.79%	1004.80	3.56%
Renewable-generation share	1.20	872,900.00	−3.06%	939.70	−3.15%
Aggregate storage capacity	0.80	915,700.00	1.69%	981.90	1.20%
Aggregate storage capacity	1.20	892,600.00	−0.88%	962.50	−0.80%
Demand-response participation	0.80	908,900.00	0.93%	977.40	0.74%
Demand-response participation	1.20	894,300.00	−0.69%	965.80	−0.46%
Seasonal carbon-pressure intensity	0.80	897,200.00	−0.36%	978.50	0.85%
Seasonal carbon-pressure intensity	1.20	904,900.00	0.49%	963.20	−0.73%
Objective weights	0.75/0.25	889,500.00	−1.22%	985.80	1.60%
Objective weights	0.50/0.50	916,700.00	1.80%	950.90	−1.99%

Note: The objective-weight combinations are reported as economic weight/carbon-emission weight. A parameter level of 1.00 represents the baseline setting.

Comments 4:

Improve the discussion of practical implementation. This manuscript brings in seasonal signals of carbon pressure and integrates them into carbon energy price. Nevertheless, implementation of this approach in terms of current markets is not sufficiently elaborated. Please discuss required data, market assumptions and regulation in your answer.

Response 4:

We agree that practical implementation needed more than a mathematical description. A dedicated subsection now identifies the historical and operational data required for deployment, including renewable and load records, forecasts, market and carbon information, equipment states, storage SOC, indoor temperature, and available demand-response capacity.

The proposed workflow is placed within a park-level energy management system or aggregator architecture. The revised text describes smart metering, equipment-state reporting, schedule transmission, two-way communication, time synchronization, data-quality checks, user contracts, comfort limits, opt-out provisions, and carbon measurement, reporting, and verification.

It also states the main limitations: fixed representative renewable inputs, no explicit forecast-error recourse, an aggregated energy-hub model without detailed network constraints, local parameter-calibration needs, regional regulatory differences, cybersecurity, and data privacy. Accordingly, the framework is positioned for day-ahead or periodically updated scheduling rather than second-level control.

The revised text in the manuscript is presented as follows:

(1) Section 5.7, Pages [42-43]

5.7 Practical implementation and deployment limitations

Practical implementation requires both historical and operational data. Historical WT, PV, and multi-energy load records are used to estimate seasonal carbon-pressure factors. Routine scheduling additionally requires short-term renewable and load forecasts, electricity and gas prices, carbon prices and allowance information, equipment availability, conversion efficiencies, SOC values, indoor-temperature measurements, and the available demand-response capacity. The seasonal factors may be recalibrated periodically, whereas the operating inputs should be updated before each scheduling cycle.

The proposed model can be integrated into an energy management system operated by a park-level energy manager or aggregator. Smart meters collect electricity, heat, gas, and cooling data, while equipment controllers report operating states and storage levels. The optimization results are transmitted to local controllers as unit schedules, storage charging or discharging commands, and demand-response instructions. Reliable time synchronization, two-way communication, data-quality checks, and fallback operating rules are required before automatic implementation.

Demand response also depends on contractual arrangements with participating users. The permissible adjustment range, response duration, compensation mechanism, comfort limits, and opt-out conditions should be specified in advance. Carbon settlement requires traceable metering and a measurement, reporting, and verification procedure that distinguishes allocated allowances from physical emissions.

Several limitations remain. The current dispatch model uses fixed representative renewable profiles and does not explicitly optimize forecast-error recourse. It also represents the IES in an aggregated form without detailed electricity, heat, or gas network constraints. In addition, elasticity coefficients and comfort parameters require local calibration, while market access and carbon-settlement rules may differ across regions. Communication failures, cybersecurity risks, and data-privacy requirements may further restrict fully automated deployment. The framework is therefore intended for day-ahead or periodically updated scheduling rather than second-level operational control.

Comments 5:

Compare the proposed method with recent state of the art approaches. The manuscript only considers the comparison among various operational strategies in the proposed framework. In order to clearly prove the merits of the proposed approach, it is suggested that a comparative study should be conducted with recently published scheduling approaches.

Response 5:

We agree that the five internal scenarios alone do not establish a position relative to recent literature. The revised Introduction therefore adds a structured methodological comparison with recent approaches based on carbon and certificate trading, seasonal carbon trading and quota sharing, multi-timescale allowance allocation, and ladder-type carbon trading with CCUS–P2G coupling.

The comparison is deliberately framed around mechanism, emphasis, and scope. It highlights that the present study transmits historical seasonal carbon-pressure information to hourly multi-energy dispatch through differentiated demand response, SGS coordination, and compromise selection; it does not claim general numerical superiority over studies using different systems, horizons, or data.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [7]

The present study focuses on converting historical seasonal carbon-pressure information into carbon-embedded electricity, heat, and gas price signals. These signals are coordinated with comfort-aware cooling demand response, seasonal gas storage, and compromise-weight selection within a unified hourly dispatch framework. The method does not replace carbon-market settlement or reproduce annual allowance allocation; its purpose is to transmit seasonal carbon information to short-term multi-energy operating decisions. Table 1 compares the present framework with recent low-carbon scheduling approaches.

Table 1. Comparison with recent low-carbon scheduling approaches.

Approach	Main mechanism	Main emphasis	Difference from the present study
Carbon and certificate trading	Carbon market, renewable certificates, and energy sharing	Multi-market participation and avoidance of overlapping benefits	Does not introduce a historical seasonal carbon-pressure signal into multi-energy demand response
Seasonal carbon trading	Seasonal carbon trading, hydrogen storage, and quota sharing	Seasonal hydrogen utilization and multi-agent energy sharing	Focuses on hydrogen and quota exchange rather than comfort-aware electricity-heat-gas-cooling response
Multi-timescale allowance allocation	Annual allowance allocation and short-term dispatch	Consistency between annual compliance and operational scheduling	Uses an annual model, whereas the present study is limited to four representative seasonal days
Ladder-type carbon trading	CCUS-P2G coupling and reward-penalty carbon pricing	Detailed low-carbon technology coupling and carbon-price sensitivity	Uses a technology-oriented ladder price rather than data-derived seasonal carbon-pressure factors
Present study	Seasonal carbon-embedded prices, demand response, SGS, and compromise-weight selection	Transmission of seasonal carbon information to hourly multi-energy dispatch	Integrates seasonal signals with differentiated demand response and representative-horizon scheduling

Comments 6:

Increase the reproducibility of the research. There are several important simulation parameters missing or not sufficiently described in the paper, namely, elasticity matrices, fuzzy comfort model parameters, carbon price parameters, optimization parameters, convergence conditions, and computational time. Describing all of those (or adding them to supplementary materials) will increase the reproducibility of the results.

Response 6:

We appreciate this reproducibility request. The revised manuscript now reports the electricity, heat, and gas elasticity settings; the PMV, indoor-temperature, and cooling-adjustment limits; the carbon-embedded price profiles shown in Figure 5; the IGA population, generation, crossover, mutation, stopping, repair, and elitist settings; and the CPLEX optimality-gap and time limits. It also presents the timing values listed in Table 15 and explains the distinction between the complete offline weight-search procedure and the fixed-weight routine dispatch calculation. Together, these additions make the stated simulation setup substantially more explicit.

The revised text in the manuscript is presented as follows:

(1) Section 3.2.1, Pages [15-17]

Elasticity matrices:

(2) Section 3.2.3, Page [20]

Fuzzy comfort model parameters:

(3) Section 5.2, Page [28]

Carbon price parameters:

Fig. 5. Conventional and carbon-embedded energy prices over the four representative seasonal days.

(4) Section 5.3, Page [30]

Optimization parameters and convergence conditions:

The population size was set to 20, and the maximum number of generations was 50. The crossover and mutation probabilities were 0.8 and 0.1, respectively. The outer IGA terminated when the maximum number of generations was reached or when the improvement in the best fitness was below 10−4 for eight consecutive generations. Each inner mixed-integer linear programming problem was solved using CPLEX with a relative optimality gap of 10−4 and a maximum solution time of 300 s. Boundary repair and elitist preservation were applied during each generation.

(5) Section 5.6, Pages [40-41]

Computational time:

5.6. Practical benefits and computational effort

Compared with Scenario 1, Scenario 5 reduces the cumulative operating cost from CNY 1,103,420.84 to CNY 900,485.52 and carbon emissions from 1052.92 t to 970.24 t over the modeled representative horizon. These values correspond to reductions of 18.39% and 7.85%, respectively.

These benefits are accompanied by greater model complexity. The seasonal carbon-pressure factors are calculated before optimization and do not introduce additional decision variables. The main computational increase results from the flexible-load variables, cooling-comfort constraints, inter-segment SGS state equations, and repeated inner optimization during compromise-weight selection.

Across ten runs, the average solution times of Scenario 1, Scenario 5 with fixed weights, and the complete IGA–CPLEX procedure were 9.6 s, 17.8 s, and 268.4 s, respectively. The nested procedure is more computationally demanding because each candidate weight triggers an inner dispatch solve. In practice, the compromise-weight search can be performed offline or repeated only after a material change in market conditions or operating preferences; routine scheduling then uses the fixed-weight dispatch model. Tables 15 and 16 summarize the reported timing results for the solution modes and scheduling horizons.

Table 15. Computational performance of different solution modes.

Solution mode	Average time (s)	Standard deviation (s)
Scenario 1	9.6	0.8
Scenario 5 with fixed weights	17.8	1.4
Complete IGA-CPLEX procedure	268.4	11.6

(6) Section 5.6, Page [42]

Practical importance of the findings:

From a practical perspective, the proposed method provides a structured interface between seasonal carbon-management information and hourly IES operation. Historical renewable-generation and load data can be used to update the seasonal carbon-pressure factors periodically, while renewable forecasts, market prices, equipment states, and storage SOC values can be used to update the hourly dispatch schedule.

For practical deployment, the seasonal carbon-pressure factors and compromise weights can be updated offline or only when market conditions change materially. Routine operation then requires only the fixed-weight dispatch calculation. This separation limits the online computational burden and makes the framework suitable for day-ahead or periodically updated scheduling. Scalability to substantially larger systems with more devices, network constraints, or uncertainty scenarios still requires further testing.

The reported reductions in cost and emissions should nevertheless be interpreted within the adopted representative horizon and parameter settings. Practical deployment would additionally require reliable metering, communication infrastructure, demand-response agreements, and periodic calibration using operational data.

(7) Noun modification

We replace “The comparison between Scenario 5 and Scenario 1 confirms that the proposed integrated model exhibits a significant advantage in improving the economic and environmental performance of the IES.” with “Compared with Scenario 1, Scenario 5 achieves lower operating cost and carbon emissions under the adopted case-study conditions. These improvements are accompanied by additional model constraints and computational effort and should therefore be interpreted within the day-ahead scheduling context.”

Comments 7:

Elaborate on practical importance of the findings. While the suggested approach indeed decreases operating cost and carbon footprint, the practical significance of these advantages compared to an increase in the model complexity and computational effort should be considered and discussed.

Response 7:

We agree that the benefits should be discussed together with the additional computational burden. The revised subsection therefore compares the 18.39% cost reduction and 7.85% emission reduction with the reported solution times for Scenario 1, Scenario 5 with fixed weights, and the complete IGA–CPLEX procedure.

The text identifies the main sources of added complexity as flexible-load variables, cooling-comfort constraints, inter-segment SGS equations, and repeated inner dispatch solves. Seasonal carbon-pressure factors themselves are calculated before optimization and do not add decision variables.

In practical terms, the compromise weights and seasonal factors can be updated offline or only when conditions change materially. Routine scheduling then solves the fixed-weight model, so the proposed use case is day-ahead or periodically updated operation rather than fast real-time control.

The revised text in the manuscript is presented as follows:

(1) Section 5.6, Pages [40-41]

5.6. Practical benefits and computational effort

Table 15. Computational performance of different solution modes.

Solution mode	Average time (s)	Standard deviation (s)
Scenario 1	9.6	0.8
Scenario 5 with fixed weights	17.8	1.4
Complete IGA-CPLEX procedure	268.4	11.6

(2) Noun modification

Comments 8:

Enhance the English and presentation quality. Even though the paper is generally well structured, there are grammar mistakes, redundant phrases and some unnecessarily long sentences decreasing readability of the manuscript. It requires additional language editing. In addition, several figures require improvement in terms of legibility and graphical quality.

Response 8:

We appreciate the presentation comments. The manuscript has been edited to remove redundant wording, shorten several long sentences, and use more precise technical expressions.

The revised text below provides representative examples: the cooling-response description is simplified, the seasonal carbon-pressure procedure is stated in two direct steps, and the four seasonal factors are reported in a concise sentence tied to Section 3.2.1.

The figures listed below have also been revised for legibility. These edits concern language and presentation only and do not change the underlying data or numerical conclusions.

The revised text in the manuscript is presented as follows:

Noun modification

To enhance the readability of the article, we have further polished the language.

We replace “This study also considers a cooling load demand-response model based on a comfort-based piecewise cooling-load response model, further enhancing the flexibility and accuracy of load adjustment.” with “Cooling demand is modeled using a comfort-constrained piecewise response function, which represents cooling-load flexibility while limiting deviations from the prescribed PMV range.”

We replace “In conclusion, the low-carbon energy demand response strategy uses time-series analysis to examine the seasonal characteristics of IES carbon emissions and, by introducing a carbon-energy trading market with low-carbon demand signals, leverages economic means to guide seasonal emission reductions.” with “The proposed demand-response strategy first extracts seasonal carbon-pressure information from historical data. This information is then embedded in the carbon-energy prices to guide user-side load adjustment.”

We replace “Through a series of calculations, the values of the low-carbon demand-response signals for the four seasons were determined to be 0.061, 0.399, 0.241, and 0.301, respectively.” with “Applying the procedure described in Section 3.2.1 yields seasonal carbon-pressure factors of 0.061, 0.399, 0.241, and 0.301 for spring, summer, autumn, and winter, respectively.”

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presents a multi-timescale low-carbon economic dispatch framework for integrated energy systems by integrating carbon-energy trading, seasonal carbon planning, demand response, and IGA-based objective weight identification. The topic is relevant and timely, and the study has potential practical significance. However, several issues should be addressed to improve the scientific quality, clarity, and reproducibility of the manuscript.

The novelty of the proposed framework should be more clearly highlighted, particularly by explicitly distinguishing the current work from the authors' previous publication and emphasizing the new technical contributions.
The proposed IGA-based weight identification method should be validated through comparisons with existing multi-objective optimization or weight determination methods to demonstrate its effectiveness and advantages.
A sensitivity analysis should be included to evaluate the impact of key parameters, such as carbon prices, demand response coefficients, renewable penetration levels, and optimization parameters, on the scheduling results.
The manuscript should report the computational performance of the proposed optimization framework, including convergence behavior, computational time, and scalability, to demonstrate its applicability to practical systems.
More details should be provided regarding the renewable uncertainty modeling, including the scenario generation, scenario reduction process, number of scenarios, and the associated probabilities to improve reproducibility.
The comparative study should be strengthened by including comparisons with recent state-of-the-art approaches rather than limiting the evaluation to the proposed scenarios only.
The practical implementation of the proposed framework should be discussed in greater detail, including data requirements, market assumptions, communication infrastructure, and potential limitations for real-world deployment.
The discussion section should be expanded to better explain the reasons behind the observed improvements and to clearly identify the limitations of the proposed approach and possible future research directions.
The mathematical notation should be improved by ensuring that all variables and symbols are clearly defined when first introduced, and a nomenclature table is recommended.
The manuscript would benefit from careful English language editing, improved figure quality and readability, clearer presentation of equations, and updating the references with more recent literature.

Author Response

Manuscript Number: sustainability-4472735

Paper Title: Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon-Energy Trading and IGA-Assisted Compromise-Weight Selection

Authors: Guoxiang Hu, Linjun Shi, Feng Wu, Chenyu Wu, Keman Lin

Sustainability

General Response to the Editor and Reviewers:

We have revised the manuscript carefully and checked the response letter against the final text. The responses and the corresponding manuscript revisions remain marked in blue for ease of review.

The point-by-point responses are provided below. Each Response now describes only changes that are present in the revised manuscript.

***********************************************************************************

To Reviewer 3:

Thank you for the careful review and constructive suggestions. We have revised the manuscript point by point and clarified the corresponding changes below.

Comments 1:

The novelty of the proposed framework should be more clearly highlighted, particularly by explicitly distinguishing the current work from the authors' previous publication and emphasizing the new technical contributions.

Response 1:

We agree that the novelty boundary needed to be explicit. The revised Introduction now identifies the components inherited from Reference [22] and no longer presents the full park-level carbon–energy framework as newly developed.

The inherited baseline includes the system configuration, carbon–energy pricing, seasonal carbon planning, electricity–heat–gas demand response, and the general seasonal-storage concept.

The new methodological content is stated more narrowly: a differentiated cooling-load response associated with fuzzy thermal comfort, and a normalized compromise-selection procedure in which the outer IGA searches the economic weight and the inner CPLEX model solves the hourly mixed-integer dispatch problem.

Section 2 repeats this boundary and points readers to Sections 3.2.3 and 4.2–4.3 for the new formulations. This makes the relationship with the earlier publication transparent.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [8]

“Relationship to our previous work. The present study adopts the park-level electricity-heat-gas-cooling-carbon system configuration, carbon-energy pricing mechanism, seasonal carbon-planning framework, baseline electricity-heat-gas demand-response formulation, and general seasonal-storage scheduling concept developed in our previous work [22]. These inherited components are used as the baseline model and are not claimed as new contributions in the present paper.

Relative to Reference [22], the present study introduces two methodological extensions. First, cooling demand is separated from the price-elastic electricity, heat, and gas loads and is represented by an independent piecewise response formulation associated with fuzzy thermal-comfort information. This treatment is developed in Section 3.2.3 and is intended to distinguish the thermal characteristics of cooling demand from those of the other energy loads. Second, a normalized economic-environmental compromise-selection procedure is introduced in Sections 4.2 and 4.3. An outer IGA searches the economic preference weight, while the inner CPLEX model solves the corresponding mixed-integer hourly dispatch problem. The preferred solution is selected according to its normalized distance from the economic-environmental ideal point.

In addition to these methodological extensions, the numerical analysis examines their interaction with the inherited seasonal carbon-pricing and seasonal gas-storage mechanisms.”

(2) Section 2, Page [9]

“The baseline park-level electricity-heat-gas-cooling system and its principal energy-conversion, storage, and balance relationships are adapted from our previous work [22] and are restated here to keep the present formulation self-contained. The new formulations developed in this paper are concentrated in Section 3.2.3, which presents the differentiated cooling-load response model, and Sections 4.2-4.3, which present the normalized com-promise-selection and IGA-CPLEX solution procedure.”

Comments 2:

The proposed IGA-based weight identification method should be validated through comparisons with existing multi-objective optimization or weight determination methods to demonstrate its effectiveness and advantages.

Response 2:

We appreciate this suggestion. The revised manuscript now explains the nested architecture and validates the selected compromise against established deterministic and population-based alternatives.

CPLEX is used for the inner mixed-integer linear dispatch problem so that equipment status, intertemporal storage, demand-response, and multi-energy balance constraints are preserved for every candidate weight. The outer IGA operates only on the preference variable.

The comparison includes deterministic grid search, the ε-constraint method, NSGA-II, MOEA/D, and MOPSO under common data, normalization, operating constraints, and CPLEX-based evaluations. Objective values, ideal-point distance, computational effort, and solution dispersion are reported.

The conclusion is deliberately limited: the IGA–CPLEX result is consistent with the alternative methods and separates preference search from dispatch, but it is not claimed to be universally superior or to identify a unique preference.

The revised text in the manuscript is presented as follows:

(1) Section 1, Page [6]

(2) Section 4.3, Page [23]

(3) Section 4.3, Pages [23-25]

Table 10. Comparison of compromise solutions obtained by different methods.

Method	Equivalent economic weight	Operating cost (CNY)	Carbon emissions (t)	Normalized ideal-point distance
Equal weighting	0.500	910,600.00	956.90	0.4930
Deterministic grid search	0.621	900,485.52	970.24	0.4250
ε-constraint	≈0.610	900,920.00	969.80	0.4258
NSGA-II	≈0.620	901,050.00	969.60	0.4266
MOEA/D	≈0.618	900,760.00	969.95	0.4254
MOPSO	≈0.623	901,180.00	969.30	0.4278
IGA–CPLEX	0.621	900,485.52	970.24	0.4251

Table 11. Computational and statistical comparison of the optimization methods.

Method	Independent runs	Dispatch evaluations	Mean time (s)	Weight/solution dispersion
Deterministic grid search	1	122	214.7	—
ε-constraint	1	51	188.3	—
NSGA-II	30	1000	438.6±26.2	0.620±0.009
MOEA/D	30	800	401.5±21.7	0.618±0.007
MOPSO	30	1000	472.8±34.9	0.623±0.011
IGA–CPLEX	30	436	268.4±11.6	0.621±0.006

Comments 3:

A sensitivity analysis should be included to evaluate the impact of key parameters, such as carbon prices, demand response coefficients, renewable penetration levels, and optimization parameters, on the scheduling results.

Response 3:

A one-factor-at-a-time sensitivity analysis has now been added around the Scenario 5 baseline. The tested factors are carbon price, renewable-generation share, aggregate storage capacity, demand-response participation, seasonal carbon-pressure intensity, and alternative objective-weight combinations.

The revised discussion quantifies the resulting cost and emission changes. Renewable availability produces the largest variation; carbon price and weights expose the cost–emission trade-off; storage and demand-response changes have moderate effects; and seasonal carbon-pressure intensity has a smaller aggregate effect but changes the timing of load and SGS operation.

The revised text in the manuscript is presented as follows:

(1) Section 5.5, Pages [39-40]

Table 14. One-factor-at-a-time sensitivity results under Scenario 5.

Sensitivity factor	Parameter level	Operating cost (CNY)	Cost change	Carbon emissions (t)	Emission change
Baseline	1.00	900,485.52	0.00%	970.24	0.00%
Carbon price	0.80	892,200.00	−0.92%	983.60	1.38%
Carbon price	1.20	910,800.00	1.15%	956.30	−1.44%
Renewable-generation share	0.80	934,600.00	3.79%	1004.80	3.56%
Renewable-generation share	1.20	872,900.00	−3.06%	939.70	−3.15%
Aggregate storage capacity	0.80	915,700.00	1.69%	981.90	1.20%
Aggregate storage capacity	1.20	892,600.00	−0.88%	962.50	−0.80%
Demand-response participation	0.80	908,900.00	0.93%	977.40	0.74%
Demand-response participation	1.20	894,300.00	−0.69%	965.80	−0.46%
Seasonal carbon-pressure intensity	0.80	897,200.00	−0.36%	978.50	0.85%
Seasonal carbon-pressure intensity	1.20	904,900.00	0.49%	963.20	−0.73%
Objective weights	0.75/0.25	889,500.00	−1.22%	985.80	1.60%
Objective weights	0.50/0.50	916,700.00	1.80%	950.90	−1.99%

Note: The objective-weight combinations are reported as economic weight/carbon-emission weight. A parameter level of 1.00 represents the baseline setting.

Comments 4:

The manuscript should report the computational performance of the proposed optimization framework, including convergence behavior, computational time, and scalability, to demonstrate its applicability to practical systems.

Response 4:

We agree that practical applicability cannot be assessed without computational evidence. The revised manuscript now reports the IGA and CPLEX convergence settings, the average solution times and standard deviations for the baseline, fixed-weight, and complete nested procedures, and a scalability test for 24-, 48-, 96-, and 192-h horizons. The results show approximately linear growth for the fixed-weight dispatch and higher cost for the nested search; the manuscript therefore recommends offline or infrequent weight updates and limits the practical claim to day-ahead or periodically updated scheduling.

The revised text in the manuscript is presented as follows:

(1) Section 5.3, Page [30]

Convergence conditions:

(2) Section 5.6, Pages [40-41]

Computational time:

5.6. Practical benefits and computational effort

Table 15. Computational performance of different solution modes.

Solution mode	Average time (s)	Standard deviation (s)
Scenario 1	9.6	0.8
Scenario 5 with fixed weights	17.8	1.4
Complete IGA-CPLEX procedure	268.4	11.6

(3) Section 5.6, Pages [41-42]

Scalability:

Table 16. Computational performance for different scheduling horizons.

Scheduling horizon	Fixed-weight dispatch time	Complete IGA–CPLEX time
24 h	5.1 s	79.4 s
48 h	9.2 s	145.7 s
96 h	17.8 s	268.4 s
192 h	36.9 s	553.6 s

The fixed-weight dispatch time increases approximately linearly with the scheduling horizon. The complete nested procedure requires substantially more time because each IGA candidate invokes an inner mixed-integer optimization. Nevertheless, even the 192-h case can be solved within approximately 10 min under the tested configuration.

Comments 5:

More details should be provided regarding the renewable uncertainty modeling, including the scenario generation, scenario reduction process, number of scenarios, and the associated probabilities to improve reproducibility.

Response 5:

We agree that the renewable-profile construction needed a clearer and reproducible description. The revised manuscript now separates LHS and scenario reduction from the deterministic dispatch stage.

Five representative scenarios are retained, with probabilities of 12.0%, 29.0%, 15.4%, 30.6%, and 13.0%. The effect of retaining three to seven scenarios is reported, and N = 5 is selected because the stated deviation falls below 1% and changes only slightly for larger N.

These scenarios are used to construct fixed seasonal renewable inputs. The revised wording therefore does not describe the subsequent dispatch as stochastic or robust and does not claim scenario-dependent recourse.

The revised text in the manuscript is presented as follows:

(1) Section 5.1, Page [25]

(2) Section 5.1, Page [26]

Table 3. Probability distribution of the representative scenarios.

Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
12.0%	29.0%	15.4%	30.6%	13.0%

Table 4. Effect of the number of representative scenarios on scenario-reduction accuracy.

Number of representative scenarios, N	Deviation from the original scenario set
3	2.74%
4	1.59%
5	0.91%
6	0.81%
7	0.80%

Comments 6:

The comparative study should be strengthened by including comparisons with recent state-of-the-art approaches rather than limiting the evaluation to the proposed scenarios only.

Response 6:

We have strengthened the comparison by evaluating the compromise-selection procedure against deterministic grid search, the ε-constraint method, NSGA-II, MOEA/D, and MOPSO under identical dispatch data and constraints.

The added tables compare the selected economic weight, operating cost, carbon emissions, normalized ideal-point distance, number of dispatch evaluations, computational time, and dispersion. The methods converge to a narrow trade-off region; the revised text presents this as cross-method consistency and explicitly avoids a general superiority claim.

The revised text in the manuscript is presented as follows:

(1) Section 4.3, Pages [23-25]

Table 10. Comparison of compromise solutions obtained by different methods.

Method	Equivalent economic weight	Operating cost (CNY)	Carbon emissions (t)	Normalized ideal-point distance
Equal weighting	0.500	910,600.00	956.90	0.4930
Deterministic grid search	0.621	900,485.52	970.24	0.4250
ε-constraint	≈0.610	900,920.00	969.80	0.4258
NSGA-II	≈0.620	901,050.00	969.60	0.4266
MOEA/D	≈0.618	900,760.00	969.95	0.4254
MOPSO	≈0.623	901,180.00	969.30	0.4278
IGA–CPLEX	0.621	900,485.52	970.24	0.4251

Table 11. Computational and statistical comparison of the optimization methods.

Method	Independent runs	Dispatch evaluations	Mean time (s)	Weight/solution dispersion
Deterministic grid search	1	122	214.7	—
ε-constraint	1	51	188.3	—
NSGA-II	30	1000	438.6±26.2	0.620±0.009
MOEA/D	30	800	401.5±21.7	0.618±0.007
MOPSO	30	1000	472.8±34.9	0.623±0.011
IGA–CPLEX	30	436	268.4±11.6	0.621±0.006

Comments 7:

The practical implementation of the proposed framework should be discussed in greater detail, including data requirements, market assumptions, communication infrastructure, and potential limitations for real-world deployment.

Response 7:

We agree that the earlier manuscript did not provide enough deployment detail. The new implementation subsection specifies the required historical records, forecasts, prices, allowance information, equipment states, storage SOC, indoor-temperature data, and demand-response capacity.

It also describes a park-level energy-management architecture with smart meters, equipment controllers, two-way communications, data-quality checks, fallback rules, user agreements, comfort limits, opt-out conditions, and carbon measurement, reporting, and verification.

The limitations are stated directly: deterministic representative inputs, no forecast-error recourse, aggregated network representation, site-specific calibration, regional market and regulatory differences, cybersecurity, and privacy. The proposed application is therefore day-ahead or periodically updated scheduling.

The revised text in the manuscript is presented as follows:

(1) Section 5.7, Pages [42-43]

5.7 Practical implementation and deployment limitations

Comments 8:

The discussion section should be expanded to better explain the reasons behind the observed improvements and to clearly identify the limitations of the proposed approach and possible future research directions.

Response 8:

We appreciate this request. The revised discussion now explains that the improvements arise jointly from carbon-embedded price signals, flexible electricity–heat–gas demand, short-term storage, SGS coordination across the four representative segments, and comfort-constrained cooling response.

The interpretation is also bounded more carefully. The reported values cover four unweighted representative days; renewable inputs are fixed after preprocessing; detailed multi-energy network constraints, forecast-error recourse, storage degradation, and field-calibrated response behavior are not included; and the selected weight is criterion-dependent.

The future-work paragraph follows directly from these limitations and identifies weighted annual and rolling horizons, stochastic scheduling, detailed network models, degradation, field calibration, alternative compromise criteria, and decomposition or parallel computation for larger systems.

The revised text in the manuscript is presented as follows:

(1) Section 5.8, Page [43]

5.8 Discussion of performance mechanisms and limitations

The improvements obtained under the complete framework cannot be attributed to a single model component. Carbon-embedded prices provide temporal signals for flexible electricity, heat, and gas loads, causing part of the demand to move away from periods with higher energy costs and carbon pressure. Meanwhile, SBU, HST, GST, and IST coordinate hourly supply and demand, whereas SGS provides additional flexibility between the four seasonal segments. The comfort-constrained cooling model further allows the cooling load to participate in scheduling within the prescribed PMV and load-adjustment limits. These mechanisms jointly reduce unfavorable external energy purchases and improve the coordination of renewable generation, conversion units, and storage devices.

The results should nevertheless be interpreted within the adopted modeling boundary. The study uses four unweighted seasonal representative days, and the re-ported cost and emission values are cumulative results over the 96-h horizon rather than annual estimates. Renewable profiles are treated as fixed inputs after scenario preprocessing, so forecast errors and recourse decisions are not explicitly modeled. The IES is represented as an aggregated energy hub without detailed electricity, heat, or gas network constraints. In addition, the elasticity coefficients, comfort parameters, and equipment characteristics require calibration before application to a specific site.

The compromise weight selected by the ideal-point criterion is model-dependent and should not be regarded as a unique stakeholder preference. The complete IGA–CPLEX procedure also introduces additional computational effort, although the com-promise-weight search can be performed offline. Future research will consider weighted annual representative periods, rolling and stochastic scheduling, detailed multi-energy network constraints, storage degradation, field-calibrated de-mand-response parameters, and decomposition or parallel solution methods for larger systems.

(2) Section 6, Page [44]

Comments 9:

The mathematical notation should be improved by ensuring that all variables and symbols are clearly defined when first introduced, and a nomenclature table is recommended.

Response 9:

We agree that the notation was too dispersed. The revised manuscript now includes a consolidated classification table for the IES entities and their abbreviations, covering generation, conversion, storage, external interfaces, and end-use loads.

A separate symbol-definition table groups the principal indices, multi-energy variables, equipment inputs and outputs, storage states and powers, carbon-allocation and emission quantities, demand-response variables, thermal-comfort variables, objectives, the preference weight, and the feasible region. This provides readers with one consistent reference point for the mathematical notation.

The revised text in the manuscript is presented as follows:

Table 2. Classification of IES entities.

Category	Main entities	Abbreviation
Energy production	Wind turbine	WT
Energy production	Photovoltaic	PV
Energy storage	Storage battery unit	SBU
	Gas storage tank	GST
	Heat storage tank	HST
	Ice storage tank	IST
	Seasonal gas storage tank	SGS
Energy conversion	Combined heat and power unit	CHP
	Electric boiler	EB
	Power to gas	P2G
	Electric chiller	EC
	Absorption chiller	AC
Upper-level network	Power grid	—
Upper-level network	Gas grid	—
End-user load	Electrical load	—
	Heat load	—
	Cooling load	—
	Gas load	—

*Symbol*	*Definition*
	Hourly interval and set of scheduling intervals
	Equipment or controllable-unit index
	Electricity, heat, gas, and cooling power
	WT and PV electrical outputs
	CHP electrical output, thermal output, and gas input
	EB electrical input and thermal output
	P2G electrical input and gas output
	EC electrical input and cooling output
	AC thermal input and cooling output
	State of charge or stored-energy state of storage device
	Charging and discharging power
	Carbon allowance allocated to unit
	Physical carbon emission or carbon-consumption quantity
	Purchased and sold carbon allowances
	External carbon-market price
	Baseline and post-response demand of energy type
	Self- or cross-price elasticity coefficient
	Indoor and outdoor temperatures
	Predicted Mean Vote index
	Economic and physical carbon-emission objectives
	Economic preference weight
	Feasible region of the dispatch model

Comments 10:

The manuscript would benefit from careful English language editing, improved figure quality and readability, clearer presentation of equations, and updating the references with more recent literature.

Response 10:

We appreciate the language and presentation recommendations. The manuscript has been edited to replace repetitive or overly long constructions with direct technical statements; several representative revisions are reproduced below.

The figures listed in the response have also been revised to improve their readability and consistency. The equations and surrounding explanations were checked during the same revision so that notation is presented more clearly.

The material reproduced below documents the language and figure changes. No separate reference update is claimed in this response because the revised excerpt does not list one.

The revised text in the manuscript is presented as follows:

Noun modification

To enhance the readability of the article, we have further polished the language.

Reviewer 4 Report

Comments and Suggestions for Authors

1. The core innovation of this article is the discretization of carbon accounting and the matching of temporal consistency, as well as the embedding of seasonal carbon pressure signals into price mechanisms. However, there is insufficient explanation of the multi time scale coupling logic.
2. The details of the carbon quota management model are missing. Only mentioning carbon allocation and carbon trading mechanisms, but without specifying the accounting method for systematic carbon quotas, penalties for excess carbon emissions, temporal characteristics of carbon trading prices, and constraints, the model corresponding to Figure 1 lacks rigor.
3. The paper mentions that the model covers the upper layer network, but does not specify the modeling methods for the power grid, heat network, and gas network. Whether key factors such as network flow constraints, pipeline delay, and loss characteristics are considered, and the simplification and rationality of network constraints need to be demonstrated.
4. The paper generates typical wind and solar profiles through sampling and scenario simplification, but does not explain the sampling method, scenario reduction rules, or verify the fitting accuracy of typical scenarios to the original wind and solar uncertainties. At the same time, it does not consider multiple uncertainties such as load forecasting errors and carbon price fluctuations, and the robustness of the scenarios needs to be verified.

Author Response

Manuscript Number: sustainability-4472735

Paper Title: Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon-Energy Trading and IGA-Assisted Compromise-Weight Selection

Authors: Guoxiang Hu, Linjun Shi, Feng Wu, Chenyu Wu, Keman Lin

Sustainability

General Response to the Editor and Reviewers:

We have revised the manuscript carefully and checked the response letter against the final text. The responses and the corresponding manuscript revisions remain marked in blue for ease of review.

The point-by-point responses are provided below. Each Response now describes only changes that are present in the revised manuscript.

***********************************************************************************

To Reviewer 4:

Thank you for the careful review and constructive suggestions. We have revised the manuscript point by point and clarified the corresponding changes below.

Comments 1:

The core innovation of this article is the discretization of carbon accounting and the matching of temporal consistency, as well as the embedding of seasonal carbon pressure signals into price mechanisms. However, there is insufficient explanation of the multi time scale coupling logic.

Response 1:

We agree that the previous draft named the seasonal and hourly components without showing the actual coupling path. The revised manuscript now explains the information flow step by step.

Historical WT, PV, and multi-energy load data are first processed into one carbon-pressure factor for each season. Each factor is assigned as a fixed parameter to its corresponding 24-h representative segment and modifies the hourly carbon-embedded electricity, heat, and gas prices.

Those prices enter the demand-response model, and the updated loads then enter the hourly energy-balance, equipment-operation, storage-state, and carbon-accounting constraints. This is the information channel linking seasonal data to hourly dispatch.

A second, physical-state channel transfers the terminal SGS state of one representative segment to the initial state of the next. Carbon quantities are accumulated over the modeled 96-h horizon; the revision does not interpret this coupling as an annual settlement or a chronological annual simulation.

The revised text in the manuscript is presented as follows:

(1) Section 3.2.1, Page [15]

The multi-timescale coupling is implemented through a sequential information-transfer mechanism. Historical renewable-generation and multi-energy load data are first processed to obtain one carbon-pressure factor for each season. These factors are not optimized again in the hourly dispatch model; instead, they are assigned as fixed parameters to the corresponding spring, summer, autumn, and winter representative segments.

For each hourly interval, the seasonal carbon-pressure factor adjusts the carbon-embedded electricity, heat, and gas prices. The adjusted prices are passed to the demand-response model, which determines the curtailable and shiftable portions of the corresponding loads. The updated load profiles then enter the hourly energy-balance, equipment-operation, storage-state, and carbon-accounting constraints. Thus, the medium- to long-term information affects hourly operation through the price–demand–dispatch chain without changing the one-hour scheduling resolution.

(2) Section 5.1, Pages [26-27]

The multi-timescale coupling contains two complementary channels. The first is an information channel. Historical WT, PV, and multi-energy load data are used to de-termine seasonal carbon-pressure factors, which are then mapped to the corresponding 24-h representative segments. Within each segment, the assigned factor modifies the hourly carbon-embedded energy prices, and these prices influence the de-mand-response loads and subsequent dispatch decisions.

The second is a physical state channel. The terminal SGS state of each seasonal segment is transferred to the following segment as its initial state, thereby linking gas-storage decisions across spring, summer, autumn, and winter. Carbon allowances and physical emissions are calculated at the same hourly resolution as the energy dis-patch and accumulated over the modeled 96-h horizon.

Comments 2:

The details of the carbon quota management model are missing. Only mentioning carbon allocation and carbon trading mechanisms, but without specifying the accounting method for systematic carbon quotas, penalties for excess carbon emissions, temporal characteristics of carbon trading prices, and constraints, the model corresponding to Figure 1 lacks rigor.

Response 2:

We appreciate the reviewer’s concern. The revised Section 2.2 now makes the allowance and physical-emission accounting explicit for renewable generation, conversion units, storage, external energy exchange, and the system carbon balance, all at the hourly dispatch resolution. This revision specifically clarifies how allowances and emissions are calculated and connected within the model; it does not claim to introduce a separate market-wide excess-emission penalty schedule or a new temporal carbon-price formation model beyond the carbon-trading inputs already used in the objective.

The revised text in the manuscript is presented as follows:

(1) Section 2.2, Pages [10-12]

“2.2. Carbon emission and energy allocation modeling

2.2.1. Energy production

(1)

2.2.2. Energy conversion

Energy-conversion units provide the main coupling paths among the energy carriers. Their operating relationships and carbon-allowance formulations are given below.

(1) CHP mathematical model

(2)

(2) EB mathematical model

(3)

(3) P2G mathematical model

(4)

(4) EC mathematical model

(5)

(5) AC mathematical model

(6)

2.2.3. Energy storage

(7)

(8)

2.2.4. External network interfaces

(9)

(10)

2.2.5. System-wide dynamic balance model

(11)

where Pload, Hload, Gload, and Lload are the electricity, heat, gas, and cooling demands, respectively; and Atran is the net carbon allowance exchanged with the external carbon market.”

Comments 3:

The paper mentions that the model covers the upper layer network, but does not specify the modeling methods for the power grid, heat network, and gas network. Whether key factors such as network flow constraints, pipeline delay, and loss characteristics are considered, and the simplification and rationality of network constraints need to be demonstrated.

Response 3:

Thank you for identifying the ambiguity in the phrase “upper-level network.” The revised equations show that the external power grid and gas grid are represented as capacity-limited exchange interfaces, not as detailed network models.

Electricity, heat, gas, and cooling are balanced at the aggregated IES level in each hour. A separate external heat network is not included in the reproduced formulation.

Consequently, power-flow constraints, gas-pipeline pressure and delay, thermal-hydraulic transport, and network-specific losses are outside the present model boundary. The revised response therefore characterizes the study as an aggregated energy-hub dispatch model rather than a network-constrained optimization.

The revised text in the manuscript is presented as follows:

(1) Section 2.2, Pages [13-14]

2.2.4. External network interfaces

(9)

(10)

2.2.5. System-wide dynamic balance model

(11)

where Pload, Hload, Gload, and Lload are the electricity, heat, gas, and cooling demands, respectively; and Atran is the net carbon allowance exchanged with the external carbon market.”

Comments 4:

The paper generates typical wind and solar profiles through sampling and scenario simplification, but does not explain the sampling method, scenario reduction rules, or verify the fitting accuracy of typical scenarios to the original wind and solar uncertainties. At the same time, it does not consider multiple uncertainties such as load forecasting errors and carbon price fluctuations, and the robustness of the scenarios needs to be verified.

Response 4:

We agree that the earlier uncertainty wording was broader than the implemented model. The revised manuscript now states that LHS and scenario reduction are preprocessing tools for constructing fixed representative WT and PV profiles; the subsequent dispatch problem remains deterministic.

LHS and scenario reduction are used to obtain representative seasonal WT and PV inputs. Five scenarios are retained with probabilities of 12.0%, 29.0%, 15.4%, 30.6%, and 13.0%, and the reduction-deviation table supports the choice of N = 5 because the reported error falls below 1%.

After preprocessing, the selected profiles are fixed inputs to the IGA–CPLEX scheduling model. The formulation therefore contains no scenario-dependent recourse, chance constraints, or robust counterpart.

Load forecast errors and carbon-price fluctuations are not included in this renewable scenario set. Accordingly, the revised text treats the table as a scenario-reduction accuracy check, not as proof of multi-source uncertainty robustness.

The revised text in the manuscript is presented as follows:

(1) Section 5.1, Page [25]

(2) Section 5.1, Page [26]

Table 3. Probability distribution of the representative scenarios.

Scenario A	Scenario B	Scenario C	Scenario D	Scenario E
12.0%	29.0%	15.4%	30.6%	13.0%

Table 4. Effect of the number of representative scenarios on scenario-reduction accuracy.

Number of representative scenarios, N	Deviation from the original scenario set
3	2.74%
4	1.59%
5	0.91%
6	0.81%
7	0.80%

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer 2 Report

Comments and Suggestions for Authors

Authors addressed all of comments carefully and revise the manuscript accordingly. I appricriate authors effort to improve the quality of the manuscript. This revised manuscript can be accepted at its currents form.

Reviewer 3 Report

Comments and Suggestions for Authors

I thank the authors for their efforts in revising the manuscript. The paper has been significantly improved. No further comments are required.

Reviewer 4 Report

Comments and Suggestions for Authors

The author has completed the response to the revision question.

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Low-Carbon Economic Dispatch of Integrated Energy Systems Considering Carbon–Energy Trading and IGA-Assisted Compromise Weight Selection

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