A Stackelberg Game-Based Optimal Scheduling Model for Multi-Microgrid Systems Considering Photovoltaic Consumption and Integrated Demand Response
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsReview Evaluation Report
Article Title: A Stackelberg Game Based Optimal Scheduling Model for Multi-microgrid System Considering Photovoltaic Consumption and Integrated Demand Response
Authors: Jie Li, Shengyuan Ji, Xiuli Wang, Hengyuan Zhang, Yafei Li, Xiaojie Qian, Yunpeng Xiao
1. What is the main question addressed by this study?
In this paper, a Stackelberg game model is developed to perform optimal planning of multiple microgrids (multi-microgrid). The energy exchange between microgrids is optimized by considering the photovoltaic (PV) energy consumption and integrated demand response. This study aims to increase the PV consumption. The leader-follower strategy is adopted, while the leader is the microgrid system, the users (followers) adjust their energy demands to maximize their own interests.
2. What is the gap addressed by the article?
· The study calculates the optimization of photovoltaic energy consumption and integrated demand response with an innovative Stackelberg game model.
· In traditional microgrid models, electrical interactions between grids are generally ignored. In this model, electrical interactions between microgrids and individual consumption preferences of users are also taken into account.
· A balance mechanism that considers the interests of both users and microgrid operators is developed using multi-layer game theory.
3. Are the references appropriate?
Yes, the references are generally appropriate. However, it would be beneficial if they were expanded to include the most recent research in the literature.
4. Additional Comments on Tables and Figures and Data Quality
Tables and figures are generally understandable. The variables and units used should be stated more clearly to make the data easier to understand.
What Specific Improvements Should the Authors Consider Regarding the Methodology? What Additional Controls Should Be Considered?
· For the robustness of the model, it should be tested on microgrid networks of different sizes in different geographical regions. This diversity will increase the generalizability of the model and can provide guidance to experts in this field.
· In order to ensure the accuracy of theoretical results, it is very important to validate the model based on experimental data in academic studies. Validation can be achieved by comparing simulation data with real-world conditions.
· Conducting detailed ablation studies that analyse the contribution of each component of the model can increase the contribution and innovation of the study. In particular, the effect of the game theory-based Stackelberg structure on optimization can be examined.
· There are many energy estimation models in the literature. Comparative testing of the proposed Stackelberg model with different energy estimation models such as LSTM, DNN or optimization can reveal the advantages of the method more clearly.
Author Response
Thank you for your constructive comments concerning our manuscript. These comments are all valuable and helpful for improving our article. Point-by-point responses to the comments are listed below.
1. What is the main question addressed by this study?
In this paper, a Stackelberg game model is developed to perform optimal planning of multiple microgrids (multi-microgrid). The energy exchange between microgrids is optimized by considering the photovoltaic (PV) energy consumption and integrated demand response. This study aims to increase the PV consumption. The leader-follower strategy is adopted, while the leader is the microgrid system, the users (followers) adjust their energy demands to maximize their own interests.
2. What is the gap addressed by the article?
The study calculates the optimization of photovoltaic energy consumption and integrated demand response with an innovative Stackelberg game model.
In traditional microgrid models, electrical interactions between grids are generally ignored. In this model, electrical interactions between microgrids and individual consumption preferences of users are also taken into account.
A balance mechanism that considers the interests of both users and microgrid operators is developed using multi-layer game theory.
3. Are the references appropriate?
Yes, the references are generally appropriate. However, it would be beneficial if they were expanded to include the most recent research in the literature.
Response to the comment: Thank you for your kind comments and valuable suggestions. We have included recent research in the introduction:
“In [16], a master-slave game method for energy-sharing management of microgrids with photovoltaic producers and marketers was proposed. Additionally, [17] established a distributed and coordinated optimization model for an integrated energy system featuring one master and multiple slaves, presenting a reasonable pricing strategy for electricity and heat for integrated energy operators. [18] developed a day-master-slave game optimization scheduling model that incorporates stepped car-bon trading and carbon tax. This model effectively guides the output of diverse energy supply equipment, aiming to reduce the total carbon emissions of the system while maintaining economic efficiency. [19] established an optimization method for the Organic Rankine Cycle based on the Stackelberg game framework. [20] proposed an authority transaction model based on a multi-leader multi-follower Stackelberg game, demonstrating the existence of a unique Stackelberg equilibrium to determine optimal bidding prices and allocate authority transactions.”
[16] Nian, L.; Xinghuo, Y.; Cheng, W.; Jinjian, W. Energy Sharing Management for Microgrids with PV Prosumers：a Stackelberg Game Approach. IEEE Transactions on Industrial Informatics 2017, 13(3), 1088-1098.
[17] Haiyang, W.; Ke, L.; Chenghui, Z.; Xin, M. Distributed Coordinative Optimal Operation of Community Integrated Energy System. Proceedings of the CSEE 2020, 40(17), 5435-5445.
[18] Hong, Z.; Ruifang, Z.; Jiancheng, Z.; Fangliang, S.; Delong, J. Low-carbon Economic Dispatch of Integrated Energy System In campus Based on Stackelberg Game and Hybrid Carbon Policy. Acta Energiae Solaris Sinica 2023, 44(9), 9-17.
[19] Hu, Z.; Wu, W.; Si, Y. Optimization of Organic Rankine Cycle for Hot Dry Rock Power System: A Stackelberg Game Approach. Energies 2024, 17, 5151.
[20] Lee, G.H.; Lee, J.; Choi, S.G.; Kim, J. Optimal Community Energy Storage System Operation in a Multi-Power Consumer System: A Stackelberg Game Theory Approach. Energies 2024, 17, 5683.
4. Additional Comments on Tables and Figures and Data Quality
1)Tables and figures are generally understandable. The variables and units used should be stated more clearly to make the data easier to understand.
2)What Specific Improvements Should the Authors Consider Regarding the Methodology? What Additional Controls Should Be Considered?
3)For the robustness of the model, it should be tested on microgrid networks of different sizes in different geographical regions. This diversity will increase the generalizability of the model and can provide guidance to experts in this field.
4)In order to ensure the accuracy of theoretical results, it is very important to validate the model based on experimental data in academic studies. Validation can be achieved by comparing simulation data with real-world conditions.
5)Conducting detailed ablation studies that analyse the contribution of each component of the model can increase the contribution and innovation of the study. In particular, the effect of the game theory-based Stackelberg structure on optimization can be examined.
6)There are many energy estimation models in the literature. Comparative testing of the proposed Stackelberg model with different energy estimation models such as LSTM, DNN or optimization can reveal the advantages of the method more clearly.
Response to the comment:
Thank you for your kind comments and valuable suggestions. The point-by-point responses to the comments are listed below:
1) We have revised Figure.1 and Table.1 to make the operation of the system and the data easier to understand.
2) We have included a discussion addressing the potential limitations of the model and future work in the conclusions:
“This paper focuses exclusively on scenarios in which the microgrids within a multi-microgrid integrated energy system are regarded as a unified entity, provided they cooperate for mutual benefit. It does not take into account the intricate interplay of interests among the microgrids, which encompasses both competitive and cooperative dynamics, and did not analyze the revenue distribution strategy between the microgrids in detail.
Future work should address energy transmission losses and the variability in new energy output. The energy pricing strategy and benefit distribution methods warrant further investigation, particularly as the interaction modes among stakeholders become more complex.”
3) Due to the difficulty in obtaining actual data from microgrids in various regions, we selected one area composed of 3 microgrids for analysis. But some relevant studies in the introduction can demonstrate the generalizability of this method:
“Most of the studies mentioned focused on a single integrated energy microgrid, without considering that multiple microgrids within the same regional distribution network can interact to form a multi-microgrid system with electrical energy exchange [21-22]. In [23], aiming at multiple microgrids belonging to different stakeholders in the same region, an energy interaction framework for multi-microgrid systems was de-signed using multi-agent technology, and an economic optimal scheduling method for multi-microgrid systems based on a master-slave game was proposed. In [24] a coop-erative optimal scheduling strategy considering a integrated demand response and master-slave game for multi-microgrid integrated energy systems with electrical energy interactions was proposed. In [25], an optimal scheduling strategy for multi-agent integrated energy systems based on integrated demand response and electrical energy interaction was proposed. [26] proposed a microgrid group-master-slave game optimization method considering the pricing mechanism, which promoted energy interaction within the microgrids group, effectively improved the net load curve of the regional distribution network, and enhanced the utilization efficiency of distributed energy.”
4) I am sorry that we can only analyze the results through simulation, and cannot conduct experiments in microgrids in the real world. This model aims to identify the optimal equilibrium strategy, thereby providing market and government decision makers with significant reference information that holds practical value. We have made an explanation on how this model works in real world , and illustrated in Figure 1:
“The energy sources within the multi-microgrid system include photovoltaic power (PV), distribution networks, and natural gas networks. The energy coupling and conversion equipment in the microgrid consists of a micro-gas turbine (MT), gas boiler (GB), waste heat boiler (WHB), and heat pump (HP). Energy storage devices encompass both energy storage (ES) and heat storage (HS) systems. There exists a bidirectional electrical energy interaction among the microgrids. The system integrates the advantages of new energy power generation with traditional fuel power generation, operating on the principle of energy cascade utilization to meet diverse user requirements for electricity and heat. The microgrid procures natural gas and electric energy from the natural gas network and distribution network, supplying energy to both electric and thermal loads via energy conversion coupling equipment within the facility. As the micro-gas turbine generates electricity, the heat contained in the cylinder water and flue gas can be recovered and reused through a waste heat boiler. In instances of insufficient heat supply, electric heating is facilitated through a heat pump. Additionally, the battery and thermal storage tank function as energy storage devices, enhancing the system's control, and flexibility.”
5) We have set 4 operation schemes for the multi-microgrid system to analyze the contribution of each part of the model and analyze the effect of Stackelberg game on optimization:
“To verify the rationality of the optimization strategy presented in this paper, the following four schemes are established:
- Scheme 1: This scheme adopts the optimization strategy outlined in this paper, taking into account the electrical energy interactions within the multi-microgrid system, the electrical and heat energy storage devices, as well as the users' integrated demand response.
- Scheme 2: An independent optimization calculation is conducted for each mi-crogrid, without considering the electrical energy interaction among them.
- Scheme 3: This scheme excludes the consideration of electrical and heat energy storage devices in each microgrid, resulting in no energy storage scheduling costs for the multi-microgrid system.
- Scheme 4: The integrated demand response behavior of microgrid users is disregarded. In this case, there is no master-slave game relationship, no iterative solution is required, and the energy prices, along with the fixed electrical and heat loads established in Scheme 1, are utilized for a single optimization calculation.”
6) We have made an explanation in the introduction on how the master-slave game theory is applicable to the problem of energy trading:
“The game theory approach effectively determines the optimal strategies for mul-tiple stakeholders in a rational market, facilitating optimal resource allocation. Various game models, including cooperative games [12], non-cooperative games [13], mas-ter-slave games [14] and evolutionary games [15], have been increasingly applied to the optimal operation of energy systems. In the process of energy trading, energy sellers prioritize pricing strategies according to load demand, while users adjust their consumption in response to price information. The interaction between these two parties occurs in a sequential manner, aligning with the dynamic game framework of a master-slave structure. Therefore, the master-slave game is widely utilized to address energy pricing issues between buyers and sellers.”
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper is interesting. However, I do have some comments:
1. The contributions are obscured in the introduction. Make few bullet points to clearly highlight them.
2. I wonder why only the battery is modeled as a dynamical system. Any rotating machines have dynamics as well as heat pumps. Please justify this decision or consider their dynamical nature in the model and problem formulation.
3. What is even a 'heat storage'? Please provide a concrete real-world example of such device.
4. Provide any reference for all of the equations that model the behavior of each components, from micro-gas turbine to thermal energy storage.
5. Why did the authors consider Stackelberg Game to solve this problem? Is it because of conflicting objectives?
6. Can the problem be posed as a simple optimization problem and/or Model Predictive Control? If no, then why?
7. How does the proposed method scale to thousands/millions of interconnected microgrids?
8. Report computation complexity/time for each scheme considered in the simulation section.
Comments on the Quality of English LanguagePlease check for errors and typos.
Author Response
Thank you for your constructive comments concerning our manuscript. These comments are all valuable and helpful . Point-by-point responses to the comments are listed below.
1.The contributions are obscured in the introduction. Make few bullet points to clearly highlight them.
Response to the comment: Thank you for your positive comments and valuable suggestions to improve the quality of our manuscript. As suggested by the reviewer, we have made bullet points to highlight the contributions in the introduction. The revisions are as follows:
“The main work and contributions are as follows: (1) The establishment of a one-master multi-Slave game equilibrium model, which considers the interests of both parties within the multi-microgrid system, positions the multi-microgrid system as the leader, while each microgrid user functions as a follower[ç›®æ ‡æ˜¯ä»€ä¹ˆ]; (2) It is proved that the Stackelberg game yields a unique Nash equilibrium solution; (3) Through example analysis, the optimal scheduling outcomes for each microgrid under this model are presented; (4)The impact of electrical energy interaction behaviors among microgrids, electrical heating energy storage devices, the master-slave game mechanism, and integrated demand response on the economic performance and photovoltaic energy consumption of the multi-microgrid system and its users is examined, thereby validating the rationality and effectiveness of the proposed model.”
2. I wonder why only the battery is modeled as a dynamical system. Any rotating machines have dynamics as well as heat pumps. Please justify this decision or consider their dynamical nature in the model and problem formulation.
Response to the comment: Thank you for your positive comments. We attempt to provide an explanation for your question: We would like to address the day-ahead optimization scheduling problem during the steady-state operation of the integrated energy microgrid, so we do not focus on the dynamical nature of the devices. Besides, the related references [1-2] have also employed comparable modeling methods, and we have included these references in this paper.
[1]. Shaofeng, F.; Renjun, Z.; Fulu, X.; Jian, F.; Yuanlin, C.; Bin, L. Optimal Operation of Integrated Energy System for Park Micro-grid Considering Comprehensive Demand Response of Power and Thermal Loads. Proceedings of the CSU-EPSA 2020, 32(1)
[2]. Haiyang, W.; Ke, L.; Chenghui, Z.; Xin, M. Distributed Coordinative Optimal Operation of Community Integrated Energy System. Proceedings of the CSEE 2020, 40(17), 5435-5445.
3. What is even a 'heat storage'? Please provide a concrete real-world example of such device.
Response to the comment: Thank you for your positive comments. In this paper, thermal storage tanks are used as “heat storage”, and we have added an explanation in the introduction and in section 2.5:
“Additionally, the battery and thermal storage tank function as energy storage devices, enhancing the system's control, and flexibility.”
“In this study, a storage battery was used for power storage and a thermal storage tank was used for heat storage.”
4. Provide any reference for all of the equations that model the behavior of each components, from micro-gas turbine to thermal energy storage.
Response to the comment: Thank you for your positive comments and valuable suggestions. The mathematical modeling of the aforementioned devices is referred to [1]. We have provided the reference for the model of each component in the section of modeling:
[1]. Shaofeng, F.; Renjun, Z.; Fulu, X.; Jian, F.; Yuanlin, C.; Bin, L. Optimal Operation of Integrated Energy System for Park Micro-grid Considering Comprehensive Demand Response of Power and Thermal Loads. Proceedings of the CSU-EPSA 2020, 32(1)
5. Why did the authors consider Stackelberg Game to solve this problem? Is it because of conflicting objectives?
Response to the comment: Thank you for your positive comments. We attempt to provide an explanation for your question: In this problem, there are two entities: microgrids and users, whose goal is to maximize their own interests. In a Stackelberg Game, the leader possesses a leadership advantage, enabling them to occupy a dominant or advantageous position within the game. Consequently, followers are required to adhere to the leader's direction in order to participate effectively in the game. In the process of energy trading, microgrids prioritize pricing strategies according to load demand, while users adjust their consumption in response to price information. The interaction between these two parties occurs in a sequential manner, aligning with the dynamic game framework of a master-slave hierarchical structure. Therefore, this paper has employed a master-slave game model for analyzing the interactions among the stakeholders involved. And we have added explanation of this issue in the introduction:
“In the process of energy trading, energy sellers prioritize pricing strategies according to load demand, while users adjust their consumption in response to price information. The interaction between these two parties occurs in a sequential manner, aligning with the dynamic game framework of a master-slave structure. Therefore, the master-slave game is widely utilized to address energy pricing issues between buyers and sellers”
6. Can the problem be posed as a simple optimization problem and/or Model Predictive Control? If no, then why?
Response to the comment: Thank you for your positive comments. We attempt to provide an explanation for your question: The problem can’t be posed as a simple optimization problem and/or Model Predictive Control. This problem is a day-ahead optimal schedule which does not run in real-time and does not require rolling optimization. We have employed iterative method to solve this problem. In each iteration step, the problems of maximizing profits for the multi-microgrid system and maximizing user benefits must be calculated separately, and the strategies of the multi-microgrid system and users will evolve, reflecting the dynamic interaction process between the two. If this issue is posed as a simple optimization problem, a fixed energy price and user load must be utilized for a single optimization calculation. And it would be unable to study the evolution of energy pricing strategy and users’ demand response. The reference [1] also provides an explanation for this issue, and we have included this reference.
[1] Peng, L.; Difan, W.; Yuwei, L.; Haitao, L.; Nan, W.; Xichao, Z. Optimal Dispatch of Multi-microgrids Integrated Energy System Based on Integrated Demand Response and Stackelberg Game. Proceedings of the CSEE 2021, 41(04), 1307-1321.
7. How does the proposed method scale to thousands/millions of interconnected microgrids?
Response to the comment: Thank you for your positive comments. If multiple microgrids are considered as the same stakeholder, the proposed method will remain applicable, and the operation of the system is illustrated in fig.1 in this paper. Conversely, if multiple microgrids are regarded as distinct stakeholders, the optimization problem transforms into a master-slave game scenario involving multiple masters and multiple slaves, which should be further studied. And the proposed method is not applicable. We have made revisions to the conclusions, as follows:
“This paper focuses exclusively on scenarios in which the microgrids within a multi-microgrid integrated energy system are regarded as a unified entity, provided they cooperate for mutual benefit. It does not take into account the intricate interplay of interests among the microgrids, which encompasses both competitive and cooperative dynamics, and did not analyze the revenue distribution strategy between the microgrids in detail.
Future work should address energy transmission losses and the variability in new energy output. The energy pricing strategy and benefit distribution methods warrant further investigation, particularly as the interaction modes among stakeholders become more complex.”
8. Report computation complexity/time for each scheme considered in the simulation section.
Response to the comment: Thank you for your positive comments. As suggested, we have reported the software used for the iterative calculations and computation time for each scheme considered in the simulation section:
“The simulation calculations were conducted using MATLAB R2018a software, employing the YALMIP plug-in and utilizing the CPLEX solver for the solution. The computer configuration includes an Intel Core i7-12700H processor.”
“Under the hardware conditions described in this article, the calculation time achieved using the optimized scheduling method is 272.2 seconds, which satisfies the requirements for day-ahead scheduling. With an upgrade in hardware conditions, the calculation speed is expected to increase significantly, resulting in a further reduction in calculation time, thereby demonstrating good practicality.”
“Under the hardware conditions described in this article, the calculation times for Scheme 1 to Scheme 4 are 272.2 seconds, 269.8 seconds, 285.6 seconds, and 4.2 seconds respectively.”
Reviewer 3 Report
Comments and Suggestions for AuthorsThe paper is very interesting and well-written; however, the following corrections are necessary:
1) In the abstract, the most important results should be highlighted more clearly, along with the relevance of the study for a broader audience.
2) Clarify the connection between the objectives of the proposed model and the challenges identified in previous studies to create a smoother transition in the introduction.
3) Figure 1 is not clear; its size and quality should be improved, as it loses resolution when enlarged. Add more descriptive titles to the figures, especially in the system structure diagram, emphasizing how the key components interact.
4) Ensure that all figures and tables are explicitly referenced in the text to facilitate understanding and navigation of the document.
5) Fix formatting throughout the document, particularly in Table 1, where a space should be added after a number and before the unit of measurement (e.g., "900kWh" should have a space after the number).
6) Expand the explanation in the methodology regarding the practical implementation of the model, including the tools or software used for the iterative calculations.
7) Include a more critical discussion addressing the potential limitations of the model, such as its reliance on ideal assumptions (e.g., the exclusion of energy transmission losses).
8) Emphasize the practical and economic benefits of the proposed strategy in the conclusions, highlighting its relevance for real-world applications.
9) Strengthen the conclusions based on the results obtained.
Author Response
Thank you for your constructive comments concerning our manuscript. These comments are all valuable and helpful . Point-by-point responses to the comments are listed below.
1) In the abstract, the most important results should be highlighted more clearly, along with the relevance of the study for a broader audience.
Response to the comment: Thank you for your positive comments and valuable suggestions. As suggested, we have made the following revisions to the abstract:
“To enhance the interests of all stakeholders in the multi-microgrid integrated energy system and to promote photovoltaic consumption, this paper proposes a master-slave game operation optimization strategy for a multi-microgrid system considering photovoltaic consumption and integrated demand response. Initially, a energy interaction model was established to delineate the relationships between each microgrid and the distribution network, as well as the interactions among the microgrids. Additionally, an integrated demand response model for end-users was developed. The above framework leads to the formulation of a one-leader multi-follower inter-action equilibrium model, wherein the multi-microgrid system acts as the leader and the users of the multi-microgrid serve as followers. It is proven that a unique equilibrium solution for the Stackelberg game exists. The upper level iteratively optimizes variables such as energy selling prices, equipment output, and energy interactions among microgrids, subsequently announcing the energy selling prices to the lower level. The lower level is responsible for optimizing energy load and returning the actual load demand to the upper level. Finally, the rationality and effectiveness of the proposed strategy were demonstrated through the case analysis. There is to say, the profitability of the multi-microgrid system is enhanced, along with the overall benefits for each microgrid user, and the amount of photovoltaic curtailment is significantly reduced.”
2) Clarify the connection between the objectives of the proposed model and the challenges identified in previous studies to create a smoother transition in the introduction.
Response to the comment: Thank you for your positive comments and valuable suggestions. As suggested, we have included previous studies and made the following revisions to the introduction:
“Most of the studies mentioned focused on a single integrated energy microgrid, without considering that multiple microgrids within the same regional distribution network can interact to form a multi-microgrid system with electrical energy exchange [21-22]. In [23], aiming at multiple microgrids belonging to different stakeholders in the same region, an energy interaction framework for multi-microgrid systems was de-signed using multi-agent technology, and an economic optimal scheduling method for multi-microgrid systems based on a master-slave game was proposed. In [24] a cooperative optimal scheduling strategy considering a integrated demand response and master-slave game for multi-microgrid integrated energy systems with electrical energy interactions was proposed. In [25], an optimal scheduling strategy for multi-agent integrated energy systems based on integrated demand response and electrical energy interaction was proposed. [26] proposed a microgrid group-master-slave game optimization method considering the pricing mechanism, which promoted energy interaction within the microgrids group, effectively improved the net load curve of the regional distribution network, and enhanced the utilization efficiency of distributed energy.
However, most previous studies have focused on returning unconsumed new energy to the distribution network, neglecting the economic benefits associated with local consumption of distributed photovoltaics. Additionally, there is a scarcity of literature addressing the impact of energy storage equipment on the benefits realized by microgrids and their users.
Therefore, this study proposes a master-slave game operation optimization strategy for a multi-microgrid system, taking into account photovoltaic energy consumption and integrated demand response. The main work and contributions are as follows: (1) The establishment of a one-master multi-Slave game equilibrium model, which con-siders the interests of both parties within the multi-microgrid system, positions the multi-microgrid system as the leader, while each microgrid user functions as a follower; (2) It is proved that the Stackelberg game yields a unique Nash equilibrium solution; (3) Through example analysis, the optimal scheduling outcomes for each microgrid under this model are presented; (4)The impact of electrical energy interaction behaviors among microgrids, electrical heating energy storage devices, the master-slave game mechanism, and integrated demand response on the economic performance and photovoltaic energy consumption of the multi-microgrid system and its users is examined, thereby validating the rationality and effectiveness of the proposed model.”
3) Figure 1 is not clear; its size and quality should be improved, as it loses resolution when enlarged. Add more descriptive titles to the figures, especially in the system structure diagram, emphasizing how the key components interact.
Response to the comment: Thank you for your positive comments and valuable suggestions. We were really sorry for our careless mistakes. Thank you for your reminding. We have replaced Figure 1 and added description of how the key components interact in section 2:
“he system integrates the advantages of new energy power generation with traditional fuel power generation, operating on the principle of energy cascade utilization to meet diverse user requirements for electricity and heat. The microgrid procures natural gas and electric energy from the natural gas network and distribution network, supplying energy to both electric and thermal loads via energy conversion coupling equipment within the facility. As the micro-gas turbine generates electricity, the heat contained in the cylinder water and flue gas can be recovered and reused through a waste heat boiler. In instances of insufficient heat supply, electric heating is facilitated through a heat pump. Additionally, the battery and thermal storage tank function as energy storage devices, enhancing the system's control, and flexibility.”
4) Ensure that all figures and tables are explicitly referenced in the text to facilitate understanding and navigation of the document.
Response to the comment: Thank you for your positive comments and valuable suggestions. We have checked the references of the figures and throughout the paper.
5) Fix formatting throughout the document, particularly in Table 1, where a space should be added after a number and before the unit of measurement (e.g., "900kWh" should have a space after the number).
Response to the comment: We were really sorry for our careless mistakes. Thank you for your reminding. We have checked and fixed these formatting errors.
6) Expand the explanation in the methodology regarding the practical implementation of the model, including the tools or software used for the iterative calculations.
Response to the comment: Thank you for your positive comments and valuable suggestions. We have reported the software used for the iterative calculations and computation time for each scheme considered in the simulation section:
“The simulation calculations were conducted using MATLAB R2018a software, employing the YALMIP plug-in and utilizing the CPLEX solver for the solution. The computer configuration includes an Intel Core i7-12700H processor.”
“Under the hardware conditions described in this article, the calculation time achieved using the optimized scheduling method is 272.2 seconds, which satisfies the requirements for day-ahead scheduling. With an upgrade in hardware conditions, the calculation speed is expected to increase significantly, resulting in a further reduction in calculation time, thereby demonstrating good practicality.”
7) Include a more critical discussion addressing the potential limitations of the model, such as its reliance on ideal assumptions (e.g., the exclusion of energy transmission losses).
Response to the comment: Thank you for your positive comments and valuable suggestions. We have included a discussion addressing the potential limitations of the model and future work in the conclusions:
“This paper focuses exclusively on scenarios in which the microgrids within a multi-microgrid integrated energy system are regarded as a unified entity, provided they cooperate for mutual benefit. It does not take into account the intricate interplay of interests among the microgrids, which encompasses both competitive and cooperative dynamics, and did not analyze the revenue distribution strategy between the microgrids in detail.
Future work should address energy transmission losses and the variability in new energy output. The energy pricing strategy and benefit distribution methods warrant further investigation, particularly as the interaction modes among stakeholders become more complex.”
8) Emphasize the practical and economic benefits of the proposed strategy in the conclusions, highlighting its relevance for real-world applications.
Response to the comment: Thank you for your positive comments and valuable suggestions. As suggested, we have made revisions to the conclusions, as follows:
“As the trend of interactive competition in the energy market becomes increasingly evident, the master-slave game model proposed in this article facilitates the analysis of the interaction process among various decision-making entities. This model aims to identify the optimal equilibrium strategy, thereby providing market and government decision makers with significant reference information that holds practical value.”
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have provided all necessary revisions. I confirm the acceptance of the manuscript. You did a good job.
Reviewer 2 Report
Comments and Suggestions for AuthorsNo further comments.
