Review Reports - A Demand Response Transaction Method for Integrated Energy Systems with a Trigonometric Membership Function-Based Uncertainty Model of Costumers’ Responsive Behaviors

Round 1

Reviewer 1 Report

The article “A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based Uncertainty Model of Costumers’ Responsive Behaviors s” proposed a demand response transaction model for integrated energy systems considering the uncertainty of customer demand response. The study is an interesting research topic, and it also has some practical significance. I’m in general satisfied with the paper.

In the following, I describe some major and minor issues that need to be addressed by the authors:

1) The overall presentation of the paper is weak. There are several bulk sentences throughout the paper which should be shortened. Please enhance the English level and grammar of the manuscript.

2) The first section should include four parts: motivation, literature survey, contributions, and the organization of the manuscript. The main organization of the article should be presented in the introduction.

3) The conclusion can be revised. This reviewer suggests improving the flow of the conclusion section. Start with a brief explanation of the paper goal (like the abstract), but make sure that the conclusion should be different from the abstract. Provide the main findings/ claims. Then finalize your conclusion by providing one or two suggestions for future work.

4) Some mistakes in the template of references should be corrected. Please consider the template of the journal significantly and modify the form and title of the table according to the template.

5) The abstract requires revisions to reflect the key ideas of this paper as well as the details of the proposed approach. The main contributions of the paper are not clearly expressed. The authors should give a detailed statement to highlight the novelty in section I

Author Response

Response to Reviewer#1

Reviewer#1: The article “A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based Uncertainty Model of Costumers’ Responsive Behaviors s” proposed a demand response transaction model for integrated energy systems considering the uncertainty of customer demand response. The study is an interesting research topic, and it also has some practical significance. I’m in general satisfied with the paper. In the following, I describe some major and minor issues that need to be addressed by the authors:

Thanks to the reviewer for the comments and the valuable suggestions on the overall manuscript. Based on your comments, we have made corresponding amendments to the paper. Kindly find our responses to each of your comments and related modifications below.

Reviewer#1, Concern # 1: The overall presentation of the paper is weak. There are several bulk sentences throughout the paper which should be shortened. Please enhance the English level and grammar of the manuscript.

Author response:

Thanks to the reviewer for the comment. We checked the paper carefully and shorten all bulk sentences throughout the paper. Also, all grammatical errors have been revised. Long single sentences and complex sentence structures are revised and concise and the active voice has been used.

Details of the revision are available in Author action.

Author action:

All the authors proofread the manuscript to shorten the bulk sentences throughout the paper.

Reviewer#1, Concern # 2: The first section should include four parts: motivation, literature survey, contributions, and the organization of the manuscript. The main organization of the article should be presented in the introduction.

Author response:

Thanks to the reviewer for the comment.

The development of an integrated energy system (IES) should consider the safety, economy, and cleanliness. It integrates various energy resources such as natural gas and photovoltaic power in the region, and meets the multiple energy requirements of users. Thus the IES is becoming a hot spot for research in the energy field.

With the development of IES, the technological advances in demand response (DR) have become a key solution to achieve this energy transition. DR can effectively increase the active participation of consumers in the IES.

Incentive-based DR strategies are a very effective way of involving flexible loads in the grid DR process. Yet, for IESs that aggregate a large number of flexible loads, there exists uncertainty in the response volume they provide to the grid because of the specificity of the way it aggregates resources.

In our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potential and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

In response to your valuable advice, we added the main organization in the end of the introduction.

Details of the revision are available in Author action.

Author action:

The contributions of this paper are threefold：

1) We introduce the analysis of demand respond uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load and replaceable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

3) We point out the relationship between the uncertainty level of user response and the incentive level and utilize the trigonometric membership fuzzy function to construct the uncertainty model of flexible load response. Therefore, the transaction model containing fuzzy variables is transformed into a deterministic model for a solution.

The remainder of this paper is arranged as follow. Section Ⅰ introduces the DR load uncertainty analysis and modeling. In Section Ⅱ, a DR transaction model that considers uncertainty of flexible loads is given. Section Ⅲ elaborates on the process of the model uncertainty. Case study is given in Section Ⅳ to evaluate the impact of the uncertainty of user response volume and the fuzzy chance constraints confidence level on the transaction results of transaction stake-holders. Conclusions are presented in Section Ⅴ.

Reviewer#1, Concern # 3: The conclusion can be revised. This reviewer suggests improving the flow of the conclusion section. Start with a brief explanation of the paper goal (like the abstract), but make sure that the conclusion should be different from the abstract. Provide the main findings/ claims. Then finalize your conclusion by providing one or two suggestions for future work.

Author response:

Thanks to the reviewer for the comment.

In this paper, the impact of uncertainty in flexible load response on DR transactions is considered. First, the uncertainty problem of incentive-based DR is analyzed, and the relationship between the level of incentive and the range of fluctuations in the user response volume is investigated. Subsequently, the treatment of uncertainty is introduced, and this paper uses fuzzy variables to represent the user response volume. Based on this, a trigonometric membership function is used to represent the uncertainty level of user response quantity for different types of flexible loads. Finally, for the objective function and chance constraints containing fuzzy variables, they are converted into explicit equivalence classes and then solved. The case study section examines the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraints confidence level on the response revenue. The results demonstrate that the revenue of each transaction entity decreases to a certain extent when the uncertainty of user response volume is considered, and the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

We revised the conclusion carefully. Both the main findings and future work were added to the conclusion.

Details of the revision are available in Author action.

Author action:

In this paper, the impact of uncertainty in flexible loads response on DR transaction is considered. First, the uncertainty problem of incentive-based DR is analyzed, and the relationship between the level of incentive and the range of fluctuations in the user response volume is investigated. Subsequently, the treatment of uncertainty is introduced, and this paper uses fuzzy variables to represent the user response volume. Based on this, a trigonometric membership function is used to represent the uncertainty level of user response quantity for different types of flexible loads. Finally, for the objective function and chance constraints containing fuzzy variables, they are converted into an explicit equivalence classes and then solved. The case study section examines the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraints confidence level on the response revenue. The results demonstrate that the revenue of each transaction entity decreases to a certain extent when the uncertainty of user response volume is considered, and the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

The proposed method of dealing with user response uncertainty in this paper provides some ideas and suggestions to solve the problems faced by flexible loads when participating in DR, but it can still be extended in the following two aspects. Firstly, the study of flexible loads response strategy under multiple time scales. The research conducted in this paper does not consider the time scale, and does not study the regulation of flexible loads in multiple time scales such as day-ahead, intra-day and real-time. In fact, in the case of approaching time scale, the types of flexible users that can participate in grid DR will be reduced continuously, and the uncertainty of user response will also be reduced continuously, even in the real-time stage is possible without considering the problem of user response uncertainty. Secondly, the study of user uncertainty under multiple response mechanisms. In this paper, we only consider the problem of response uncertainty of flexible loads under contract constraints, but in fact, some flexible loads can also participate in the DR of the grid under tariff guidance, and their response uncertainty cannot be ignored.

Reviewer#1, Concern # 4: Some mistakes in the template of references should be corrected. Please consider the template of the journal significantly and modify the form and title of the table according to the template.

Author response:

First of all, we appreciate your comments. By comparing the template, we found that there are definitely some mistakes in the format, including references and title. Your suggestions were extremely helpful to us. We then systematically corrected the formatting errors that appeared in the paper according to the template. The form and title of the table were also modified according to the template.

Details of the revision are available in Author action.

Author action:

All the authors proofread the manuscript to correct the mistake in the template of references carefully.

Reviewer#1, Concern # 5: The abstract requires revisions to reflect the key ideas of this paper as well as the details of the proposed approach. The main contributions of the paper are not clearly expressed. The authors should give a detailed statement to highlight the novelty in section I

Author response:

Thanks to the reviewer for the comment.

To reflect the key ideas of this paper as well as the details of the proposed approach. We revised the abstract according to you comment. Also, the main contributions of the paper were clearly expressed and the novelty was given in section I.

Details of the revision are available in Author action.

Author action:

Abstract revision:

As an important regulation tool for power systems, demand response can greatly improve system flexibility and economy. However, when an integrated energy system with a large number of flexible loads is aggregated for DR transaction, the uncertainty in the amount of load response should be taken into account. Therefore, a DR transaction model for an integrated energy system that considers the uncertainty of customer DR is proposed in this paper. At first, the uncertainty of incentive-based DR is analyzed, and the relationship between the incentive level and the fluctuation of customer response volume is investigated. The flexible loads are classified into curtailable loads, translatable loads, and replaceable loads. Secondly, fuzzy variables are used to represent the response volume of users. After that, a trigonometric membership function is used to represent the degree of uncertainty in the response volume of different flexible loads. Finally, the objective functions and chance constraints containing fuzzy variables are converted into explicit equivalence classes for solving. In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low

Revision in section I

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution [1], [2]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem [3], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

Based on the above problems, this paper focuses on the uncertainty of the excitation-type flexible load response and proposed a DR transaction model for the customers to actively interact with the IES. Firstly, the uncertainty problem of the incentive-based DR method is studied. The relationship between the uncertainty level of user response and the incentive level has been pointed out. Secondly, fuzzy variables are used to represent user response; then, the trigonometric membership fuzzy function is used to construct the uncertainty model of flexible load response. Finally, the transaction model containing fuzzy variables is transformed into a deterministic model for a solution.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and replaceable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

The remainder of this paper is arranged as follows. Section Ⅰ introduces the DR load uncertainty analysis and modeling. In Section Ⅱ, a DR transaction model that considers the uncertainty of flexible loads is given. Section Ⅲ elaborates on the process of the model uncertainty. The case study is given in Section Ⅳ to evaluate the impact of the uncertainty of user response volume and the fuzzy chance constraints confidence level on the transaction results of transaction stakeholders. Conclusions are presented in Section Ⅴ.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper is dealing with A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based 3 Uncertainty Model of Costumers’ Responsive Behaviors. The man concept is related to the demand response and the transaction methods within the IESs. The topic is timely and interesting, however, there are some comments before more consideration in this journal.

1- Please provide some quantitative achievements in the Abstract.

2- Regarding the Translatable loads, how do the Authors guarantee the consumption during the operating horizon? Please refer to 'A two-stage joint operation and planning model for sizing and siting of electrical energy storage devices considering demand response programs, Equations 26-29 can be helpful.

3- The Literature Review can be extended. There are some good Review Papers that can help the Authors to conduct a comprehensive literature review. Please see Demand response programs in multi-energy systems: A review, which is recently published by the same publisher.

4- Term '6. Patents' is not applicable to this work.

5- To highlight the transactions, please clarify whether the concept is centralized or decentralized. In this case, a comprehensive comparison is performed in the Transactive energy framework in multi-carrier energy hubs: A fully decentralized model.

Author Response

Response to Reviewer#2

Reviewer#2: This paper is dealing with A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based 3 Uncertainty Model of Costumers’ Responsive Behaviors. The man concept is related to the demand response and the transaction methods within the IESs. The topic is timely and interesting, however, there are some comments before more consideration in this journal.

Reviewer#2, Concern # 1: Please provide some quantitative achievements in the Abstract.

Author response:

Thanks to the reviewer for the comments and valuable suggestions.

This paper focuses on the uncertainty of the excitation-type flexible load response and proposed a decentralized DR transaction model for the customers to actively interact with the IES. Firstly, the uncertainty problem of the incentive-based DR method is studied. The relationship between the uncertainty level of user response and the incentive level has been pointed out. Secondly, fuzzy variables are used to represent user response; then, the trigonometric membership fuzzy function is used to construct the uncertainty model of flexible load response. Finally, the transaction model containing fuzzy variables is trans-formed into a deterministic model for a solution. In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint chang-es from high to low.

In line with the recommendations, we have listed some quantifiable achievements analysis in the Abstract.

Details of the revision are available in Author action.

Author action:

The Abstract is modified as follows:

As an important regulation tool for power systems, demand response can greatly improve system flexibility and economy. However, when an integrated energy system with a large number of flexible loads is aggregated for demand response transaction, the uncertainty in the amount of load response should be taken into account. Therefore, a demand response transaction model for an integrated energy system that considers the uncertainty of customer demand response is proposed in this paper. At first, the uncertainty of incentive-based demand response is analyzed, and the relationship between the incentive level and the fluctuation of customer response volume is investigated. The flexible loads are classified into curtailable loads, translatable loads, and replaceable loads. Secondly, fuzzy variables are used to represent the response volume of users. After that, a trigonometric membership function is used to represent the degree of uncertainty in the response volume of different flexible loads. Finally, the objective functions and chance constraints containing fuzzy variables are converted into explicit equivalence classes for solving. In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low

Reviewer#2, Concern # 2: Regarding the Translatable loads, how do the Authors guarantee the consumption during the operating horizon? Please refer to 'A two-stage joint operation and planning model for sizing and siting of electrical energy storage devices considering demand response programs, Equations 26-29 can be helpful.

Author response:

Thanks to the reviewer for the valuable comment. In our previous manuscript, the constraints to guarantee the consumption of the translatable loads during the operating horizon are neglected due to our poor understanding of this type of load. Through deeply reading the reference [1], we added these constraints to our model.

where the parameter, γ, in represents the inclination of aggregators to alter their demand from one hour to another.

Details of the revision are available in Author action.

Involved references:

[1] M. S. Javadi et al., “A two-stage joint operation and planning model for sizing and siting of electrical energy storage devices considering demand response programs,” International Journal of Electrical Power & Energy Systems, vol. 138, p. 107912, Jun. 2022, doi: 10.1016/j.ijepes.2021.107912.

Author action:

2.2. Constraints

This section uses a fuzzy chance constraint to represent the constraint [23], allowing the established constraint to be unsatisfied to some extent, but the confidence that the constraint holds should be no less than a pre-given confidence level.

Based on the above theory, the expressions for the load reserve constraint, the maximum customer response constraint, and the common constraint for different loads are shown below. The load reserve constraint indicates that the grid needs to allow sufficient standby capacity to solve the customer's uncertain response problem and ensure stable system operation.

where Cr{} is the expression for the confidence level; δ_dr represents the standby capacity factor of the grid and satisfies δ_dr ∈ [0,1], β₁ represents the confidence level that the system standby constraint holds; and β₂ represents the confidence level that the maximum user response volume constraint holds. The confidence levels that should be satisfied for multiple fuzzy chance constraints are generally considered to be the same.

For curtailable loads, the following constraints shall be met

where εcu i,min(t) represents the minimum cut rate of the curtailable load; tcu min represents the minimum continuous cut response time; tcu max represents the maximum continuous cut response time; Nmax c,i represents the maximum time of load cuts allowed in a dispatch cycle; vl max represents the maximum load cut rate allowed by the curtailable load; T represents the entire response time. Equation limits the response volume of the curtailable load. Equation limits the maximum number of participants in the DR. Equations represent continuous load response constraint, and the equation is the load response speed constraint.

For translatable loads, the following constraints shall be met

where λtran i,min(t), λtran i,max(t) represents the minimum load translate rate and maximum load translate rate respectively; Ttran,i min,du represents the minimum duration of translatable load; ΔPtran i,a(t) represents transferable load power after response. Equation limits the load translate rate, Equation limits the duration of translatable load, Equation ensures the balance of the response volumes.

For replaceable loads, the electrical energy substitution rates should satisfy the following constraints:

where μre i,min(t) and μre i,max(t) represent the minimum and maximum electrical energy substitution rates for replaceable loads, respectively.

The grid operator transaction model constraints are shown below:

where Pdr min(t) represents the minimum DR capacity required by the grid at time t; Cn price,min(t), Cn price,max(t) are the minimum and maximum unit response capacity offered by the grid operator to the VPP at time t, respectively. Equation limits the minimum of DR volumes, Equation limits the transaction cost of different loads.

VPP operator transaction model constraints:

where Cvpp max(t) represents the maximum transaction cost of the VPP operator; Padlo dr(t) is the DR capacity provided by the user; and Padlo dr,max(t) represents the maximum DR capacity that can be provided by the user. Equation limits the maximum transaction cost of the VPP operator. Equations - ensure the balance of the transaction volumes. Equation limits the maximum DR volumes of the VPP operator. The parameter, γ, in represents the inclination of aggregators to alter their demand from one period to another [24].

Reviewer#2, Concern # 3: The Literature Review can be extended. There are some good Review Papers that can help the Authors to conduct a comprehensive literature review. Please see Demand response programs in multi-energy systems: A review, which is recently published by the same publisher.

Author response:

Thank you for your valuable comments. According to your suggestion, we have extended the content of the literature review, especially including the DR in the IES and the uncertainty modeling methods. Importantly, we added the reference [1] to emphasize the role of DR in the IES.

The development of an IES should consider safety, economy, and cleanliness. It integrates various energy resources such as natural gas and photovoltaic power in the region and meets the multiple energy requirements of users. Thus the IES is becoming a hot spot for research in the energy field.

With the development of IES, technological advances in DR have become a key solution to achieve this energy transition. DR can effectively increase the active participation of consumers in the IES [1].

In our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potentials and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

Involved references:

[1] M. Vahid-Ghavidel, M. S. Javadi, M. Gough, S. F. Santos, M. Shafie-khah, and J. P. S. Catalão, “Demand Response Programs in Multi-Energy Systems: A Review,” Energies, vol. 13, no. 17, p. 4332, Aug. 2020, doi: 10.3390/en13174332.

Details of the revision are available in Author action.

Author action:

The development of an integrated energy system (IES) should consider the safety, economy, and cleanliness. It integrates various energy resources such as natural gas and photovoltaic power in the region, and meets the multiple energy requirements of users [1,2]. Thus the IES is becoming a hot spot for research in the energy field[3,4].

With the development of IES, technological advances in demand response (DR) have become a key solution to achieve this energy transition. DR can effectively increase the active participation of consumers in the IES [5]. Flexible loads in IESs have a strong DR capability. Flexible loads on the customer side can adjust their electricity consumption behavior according to the price-based DR mechanism [6][7] and the incentive-based DR mechanism [8], relieving the electricity supply tensions of the IES. Based on multiple types of low carbon factors and price-based DR mechanisms, Ma et al [9] construct an energy efficiency improvement scheduling model with abandoned wind penalty costs, power purchase costs, equipment operation and maintenance costs, and carbon transaction costs as optimization targets, improving the comprehensive energy efficiency of the IES. Yang et al [10] proposed the rolling optimization planning framework and model of IES considering CAES and sliding time window-based electric and heating integrated demand response (IDR), improving the economy and flexibility of the IES. Based on the DR potential and consumer’s consumption characteristics, as well as the coupling characteristics of the energy flows in the regionally integrated energy system (RIES), Hu et al.[11] establish a RIES optimization model that considers the DR of cooling, heating and electricity consumption of flexible loads. The synergistic optimization of the supply side and the consumer side is realized.

Incentive-based DR strategies are a very effective way of involving flexible loads in the grid DR process [12]. Du et al. [13] provide an in-depth analysis of incentive-based IDR in an IES model. A customer-side IDR service architecture based on electric heating multi-energy interconnection is designed. Wang et al [14] designed an IDR scheme that takes different types of consumers into account. By designing a price-based mechanism that implements various prices for different consumers, the total cost of user participation in IDR can be reduced. Jiang et al.[15] incorporates consumers' heating and cooling demand into IDR scheduling, then proposes an IDR mechanism with three effective load shedding incentive models. The incentive methods are used to increase heating and cooling loads and increase consumers’ motivation. However, in all of the above incentive-based DR studies, the response volume of the flexible load during the transaction is default certain. Yet, for IESs that aggregate a large number of flexible loads, there exists uncertainty in the response volume they provide to the grid because of the specificity of the way it aggregates resources. Also, there are inherent uncertainties such as communication delays, coupled with the fact that the response capacity provided by the user is also highly subjective [16][17]. The response volume is susceptible to a variety of factors such as unexpected next-day conditions, subjective and objective negligence, and changes in consumption behavior [18].

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution[19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem[21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and replaceable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

Reviewer#2, Concern # 4: Term '6. Patents' is not applicable to this work.

Author response:

Thanks to the reviewer for the comment. We carefully check the template of the sustainability and find the mistake we make. we have already deleted Term 6. Patents' in the paper.

Author action:

All the authors proofread the manuscript to correct the mistake exists in the paper.

Reviewer#2, Concern # 5: To highlight the transactions, please clarify whether the concept is centralized or decentralized. In this case, a comprehensive comparison is performed in the Transactive energy framework in multi-carrier energy hubs: A fully decentralized model.

Author response:

Thanks to the reviewer for the comments. In our paper, a DR transaction model for the customers to actively interact with the IES is proposed.

The transaction mode of the proposed method is platform-dominated centralized. In this mode, there are two stakeholders: 1) the grid operator minimizes the operation cost of purchasing DR services from the VPP; 2) the VPP minimizes the total cost for aggregating the flexible loads to participate in the DR transaction. In response to the reviewer’s suggestion, we added a paragraph to highlight the transaction mode of our proposed method. In addition, considering the development of the decentralized model in the transaction, we will further study the transformation of our proposed model into a decentralized model in the future.

Details of the revision are available in Author action.

Author action:

DR is increasingly used as an essential regulation tool in power systems, however, when an IES with a large number of flexible loads is aggregated for DR transaction, uncertainty in the amount of load response can have an impact on the process and outcome of the transaction. In this paper, the impact of uncertainty in flexible load response on DR transactions is considered. First, the uncertainty problem of incentive-based DR is analyzed, and the relationship between the level of incentive and the range of fluctuations in the user response volume is investigated. Subsequently, the treatment of uncertainty is introduced, and this paper uses fuzzy variables to represent the user response volume. Based on this, a trigonometric membership function is used to represent the uncertainty level of user response quantity for different types of flexible loads. Finally, for the objective function and chance constraints containing fuzzy variables, they are converted into explicit equivalence classes and then solved. The case study section examines the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraints confidence level on the response revenue. The results demonstrate that the revenue of each transaction entity decreases to a certain extent when the uncertainty of user response volume is considered, and the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

The proposed method of dealing with user response uncertainty in this paper provides some ideas and suggestions to solve the problems faced by flexible loads when participating in DR, but it can still be extended in the following two aspects. Firstly, the study of flexible loads response strategy under multiple time scales. The research conducted in this paper does not consider the time scale and does not study the regulation of flexible loads in multiple time scales such as day-ahead, intra-day and real-time. In fact, in the case of approaching time scale, the types of flexible users that can participate in grid DR will be reduced continuously, and the uncertainty of us-er response will also be reduced continuously, even in the real-time stage is possible without considering the problem of user response uncertainty. Secondly, the study of user uncertainty under multiple response mechanisms. In this paper, we only consider the problem of response uncertainty of flexible loads under contract constraints, but in fact, some flexible loads can also participate in the DR of the grid under tariff guidance, and their response uncertainty cannot be ignored.

Author Response File: Author Response.docx

Reviewer 3 Report

This manuscript aims to develop a demand response (DR) transaction model for integrated energy systems considering the uncertainty of customer DR. After the introduction section, the authors started with DR Load Uncertainty Analysis and Modeling. Then, they built the problem's objective function and constraints before starting the phase of model uncertainty processing. And they finished their study with a case study of an industrial park.

I can say that the topic of considering uncertainties while modeling a process is a mandatory step to confirm its reliability and its generalisability. Unfortunately, the authors fail to clearly address this serious problem of quantifying and analyzing the uncertainty related to the load response, due to the following points:

1- The novelty of the article must be emphasized. It is necessary to have accurate results to validate the novelty of the study.

2- An comprehensive and full literature review should be undertaken to provide the state-of-the-art shortcomings of the studies with strong relevance to the topic of the paper.

3- The authors must place their study in line with existing literature.

4- The DR load uncertainty analysis and modeling subsections are not well explained and all equations are parachuted without explanations and without physical interpretation (Even those of the objective function and of the constraints).

5- The choice of a Trigonometric membership function (MF) is not justified. What happened if other MFs types are used?

6- The process of optimizing the MFs parameters is not performed, where the authors chose unoptimized values of them in specific intervals. Even the interval boundaries are neither justified nor discussed. I suggest authors apply an effective optimizer for this purpose.

7- The presented case study should be presented clearly with more results and diagrams to clarify things for the scientific audience.

8- The authors must ensure the fluidity of the passages between sections and subsections. I recommend the authors reorganize their paper as follows: Abstract; Introduction; Related works; Materials and methods; Results and discussions; Conclusion; References.

9- A comparison study with recently published papers is required in order to prove the accuracy and performance of the current study.

10- Proofreading is required to improve the organization and the language of the article.

Author Response

Response to Reviewer#3

Reviewer#3: This manuscript aims to develop a demand response (DR) transaction model for integrated energy systems considering the uncertainty of customer DR. After the introduction section, the authors started with DR Load Uncertainty Analysis and Modeling. Then, they built the problem's objective function and constraints before starting the phase of model uncertainty processing. And they finished their study with a case study of an industrial park.

Thanks to the reviewer for the comments and the valuable suggestions on the overall manuscript. Based on your comments, we have made corresponding amendments to the paper.

In our paper, we propose a DR transaction model for electric customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potentials and uncertainty in the electric customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

Here, we would like to emphasize the reasons why we select this theory to cope with the problem of load uncertainty. Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem, yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

Reviewer#3, Concern # 1: The novelty of the article must be emphasized. It is necessary to have accurate results to validate the novelty of the study.

Author response:

In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint chang-es from high to low.

To emphasize the contribution and novelty of our paper. We first revise the abstract to show more quantity results. Then, we add a Contribution part in Section I. Furthermore, we add a comparison of different methods in the case study to show a more accurate result. Finally, we also revise the conclusion. A summary of our paper and a vision of future work has been added.

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Abstract

As an important regulation tool for power systems, demand response can greatly improve system flexibility and economy. However, when an integrated energy system with a large number of flexible loads is aggregated for demand response transaction, the uncertainty in the amount of load response should be taken into account. Therefore, a demand response transaction model for an integrated energy system that considers the uncertainty of customer demand response is proposed in this paper. At first, the uncertainty of incentive-based demand response is analyzed, and the relationship between the incentive level and the fluctuation of customer response volume is investigated. The flexible loads are classified into curtailable loads, translatable loads, and replaceable loads. Secondly, fuzzy variables are used to represent the response volume of users. After that, a trigonometric membership function is used to represent the degree of uncertainty in the response volume of different flexible loads. Finally, the objective functions and chance constraints containing fuzzy variables are converted into explicit equivalence classes for solving. In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

Section I

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution [19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem [21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and replaceable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

Case study

4.1.2 Consider the change of returns of each transaction entity in response to uncertainty

To fully compare the impact of users' uncertain responses on the returns of each transaction entity, two scenarios are set up in this section:

Scenario 1: Considering the incentive flexible load to participate in the transaction of the power grid, but not considering the uncertainty of the response volume of the flexible load;

Scenario 2: When the flexible load is encouraged to participate in the grid transaction, the uncertainty of the response volume of the flexible load is considered.

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 6.

Figure 6. The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

1）With flexible users participating in the grid DR, the peak-to-valley differences in their load curves are reduced to some extent both with and without accounting for uncertainty in the response volume. However, the peak-to-valley difference of the system load curve is higher when the uncertainty of the user response is taken into account than the peak-to-valley difference in the case where the uncertainty of the response is not considered.

2）The load curve accounting for response uncertainty is obtained with a confidence level of 0.95 for the opportunity constraint and a pessimistic confidence level of 0.9 for the transaction cost. And when the confidence level takes different values, the load curve is actually a band of varying intervals. In other words, the ambiguity of the amount of customer response introduces certain ambiguous properties into the transaction decisions of the grid operator.

(2) Accordingly, the income comparison results of each transaction entity to the two scenarios can be obtained, as shown in Figure 7.

Figure 7. (a) The income comparison of VPP operator; (b)The income comparison of the power grid operator

As seen from the analysis of the above, During the period of the user response, The revenue of scenario 1 is higher than that of scenario 2 in each period, thus it can be seen that when considering the motivational flexible load response volume of uncertainty, the transaction entity yields have a certain degree of decline, it shows that because of the uncertainty about the user's response volume, Grid operators need to increase the investment cost of the spare capacity to mitigate the user response to the impact of uncertainty, the rise in the cost of power grid operation, income is reduced, and the decrease of the volume at the same time will also lead to a decline in the benefits of VPP operators, so each transaction earnings compared to not consider the response under the condition of uncertainty is reduced. At the same time, it can be seen from the figure that the income of each transaction entity reaches the maximum at 12:00 and 19:00, because the DR of the power grid is the largest at these two times, and the response volume provided by users is also the largest, so the income of each transaction entity is also the largest.

In order to demonstrate the advantages of our proposed method, we further compare it with three other methods for solving the uncertainty as follow:

M1: Our proposed method

M2: Distributionally robust optimization-based method

M3: Robust optimization-based method

M4: Stochastic programming-based method

Accordingly, the income comparison results of each transaction entity with the above four methods can be obtained, as shown in Figure 8. It is easy to notice that the benefits of the power grid operator and VPP operator for participating in the DR transaction rank first among these methods. Thus, the fuzzy theory utilized in our model with Trigonometric Membership Function can effectively cope with the uncertainty brought by flexible loads.

Figure 8. Income comparison.

Reviewer#3, Concern # 2: An comprehensive and full literature review should be undertaken to provide the state-of-the-art shortcomings of the studies with strong relevance to the topic of the paper.

Author response:

Thank you for your valuable comments.

In our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potentials and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

Details of the revision are available in Author action.

Author action:

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution [19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem [21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

Based on the above problems, this paper focuses on the uncertainty of the excita-tion-type flexible load response and proposed a DR transaction model for the custom-ers to actively interact with the IES. Firstly, the uncertainty problem of the incentive-based DR method is studied. The relationship between the uncertainty level of user response and the incentive level has been pointed out. Secondly, fuzzy variables are used to represent user response; then, the trigonometric membership fuzzy function is used to construct the uncertainty model of flexible load response. Finally, the transaction model containing fuzzy variables is transformed into a deterministic model for a solution.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and re-placeable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

Reviewer#3, Concern # 3: The authors must place their study in line with existing literature.

Author response:

Thank you for your valuable comments. Currently, the development of an IES should consider the safety, economy, and cleanliness. It integrates various energy resources such as natural gas and photovoltaic power in the region, and meets the multiple energy requirements of users. Thus the IES is becoming a hot spot for research in the energy field.

With the development of IES, the technological advances in DR have become a key solution to achieve this energy transition. DR can effectively in-crease the active participation of consumers in the IES. Yet, for IESs that aggregate a large number of flexible loads, there exists uncertainty in the response volume they provide to the grid because of the specificity of the way it aggregate resources.

Thus, in our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potentials and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

The main contribution of the paper is as follows：

A DR transaction model for the customers to actively interact with the IES is proposed in this paper.
Considering that various types of flexible loads with different responsive potentials and uncertainty in the customers may influence the transaction results, the fuzzy theory with trigonometric membership-function is applied to describe the uncertainty of these flexible loads.

In order to place our work in line with existing literature, we add an extended literature review to introduce the development of IES, while focusing on comparing current uncertainty handling methods with trigonometric membership-function to reflect the superiority of our work.

Details of the revision are available in Author action.

Author action:

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution [19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem [21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

Based on the above problems, this paper focuses on the uncertainty of the excita-tion-type flexible load response and proposed a DR transaction model for the custom-ers to actively interact with the IES. Firstly, the uncertainty problem of the incentive-based DR method is studied. The relationship between the uncertainty level of user response and the incentive level has been pointed out. Sec-ondly, fuzzy variables are used to represent user response; then, the trigonometric membership fuzzy function is used to construct the uncertainty model of flexible load response. Finally, the transaction model containing fuzzy variables is transformed into a deterministic model for a solution.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and re-placeable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

Reviewer#3, Concern # 4: The DR load uncertainty analysis and modeling subsections are not well explained and all equations are parachuted without explanations and without physical interpretation (Even those of the objective function and of the constraints).

Author response:

Thank you to the reviewers for those comments on the interpretation of equations.

In our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potentials and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

The flexible resources that respond to the grid demand can be divided into two types: peak-staggered and peak-avoiding. The response characteristics of different types of flexible loads are generally different. Peak-avoiding flexible loads are mainly translatable loads, which can transfer part of the load from peak hours to low hours to reduce peak-to-valley differences; peak-avoiding flexible loads mainly include curtailable loads and replaceable loads, which respond to grid demand by reducing electricity consumption.

The objective function of the grid operator's participation in DR transaction consists mainly of the cost of the DR services purchased by the grid operator from the VPP, and the equivalent benefit to the grid of the increased stability and reliability of its own operations through DR.

The objective function of the VPP's participation in DR transaction consists of two main terms, i.e., the cost of purchasing the DR services of the grid operator and the compensation cost provided to the flexible customers it aggregates.

For curtailable loads, the constrains limit the response volume of the curtailable load. the maximum number of participants in the DR. represent continuous load response constraint, and the load response speed.

For translatable loads, the constraints limit the load translate rate, the duration of translatable load, and ensure the balance of the response volumes.

For replaceable loads, the electrical energy substitution rates should be satisfied.

The grid operator transaction model constraints limit the minimum of DR volumes and the transaction cost of different loads.

VPP operator transaction model constraints limit the maximum transaction cost of the VPP operator, the maximum DR volumes of the VPP operator and ensure the balance of the transaction volumes. The parameter, γ, represents the inclination of aggregators to alter their demand from one period to another.

Details of the revision are available in Author action.

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The objective function of the grid operator's participation in DR transaction is shown in . It consists mainly of the cost of the DR services purchased by the grid operator from the VPP, and the equivalent benefit to the grid of the increased stability and reliability of its own operations through DR.

where is a fuzzy expression for the transaction costs of the grid operator at time t; is a fuzzy expression for the response costs paid by the grid operator to the VPP operator at time t; represents a fuzzy expression for the equivalent benefits to the grid by DR at time t.

The objective function of the VPP's participation in DR transaction is shown in . It consists of two main terms, i.e., the cost of purchasing the DR services of the grid operator and the compensation cost provided to the flexible customers it aggregates. The compensation cost represents compensation for the customer's response capacity.

where represents a fuzzy expression for the transaction cost of the VPP operator at time t; represents a fuzzy expression for the compensation cost provided by the VPP to the customer at time t; represents a fuzzy expression for the response capacity compensation provided by the VPP operator to the customer at time t.

For curtailable loads, the following constraints shall be met

For translatable loads, the following constraints shall be met

For replaceable loads, the electrical energy substitution rates should satisfy the following constraints:

where μre i,min(t) and μre i,max(t) represent the minimum and maximum electrical energy substitution rates for replaceable loads, respectively.

The grid operator transaction model constraints are shown below:

VPP operator transaction model constraints:

Reviewer#3, Concern # 5: The choice of a Trigonometric membership function (MF) is not justified. What happened if other MFs types are used?

Author response:

Thanks to the reviewer for the valuable comments. In our paper, we aim to utilize the fuzzy theory to cope with the uncertainty of flexible loads in the DR transactions. We firstly analysis the reason why the uncertainty generates in the DR transactions and then construct the uncertainty model for three different loads, i.e., curtailable loads, translatable loads, and replaceable loads, considering their characteristics of electricity consumption. We forget to introduce some basic information about the fuzzy theory, especially the membership function, and thus we added a subsection to introduce the fuzzy theory and the description of the relative membership function.

In classical set theory, a set S in universe Q is composed of multiple elements. Each element has only two states for the set, belonging to or not belonging to. There are many expressions derived from this. However, this membership relationship is sometimes difficult to express with an accurate expression, which requires the introduction of fuzzy concepts. Fuzzy means that the extension of a property is not clear, and there is no way to use the above theory to describe it. The membership function represents the degree of membership of a fuzzy concept. It extends the value range of the characteristic function in set theory from {0,1} to [0,1], and measures fuzziness through [0,1] intervals. At present, membership functions widely used include trigonometric functions, trapezoidal functions, S-type functions, etc.

Triangular and trapezoidal membership functions are frequently used in problems involving fuzzy variables, and their function expressions are shown below. They can be depicted in Fig. 1.

Figure 1. The membership function diagram

In order to analyze the impact of the types of member ship function on the transaction results, the pessimism confidence of each transaction cost is unchanged at 0.9, and fuzzy chance constraint selects different confidence levels to analyze the income changes of each transaction entity under different confidence levels. In addition, the fuzzy parameters describing the response volume are represented by different types of membership functions for comparison. The trigonometric membership function and trapezoidal membership function are selected in this section. Accordingly, the trend of the social welfare of transactions with the confidence level of fuzzy chance constraint can be obtained, as shown in Figure 2.

Figure 2. The impact of confidence level on social welfare

It can be seen from Figure 2 that as the confidence level of opportunity constraint changes from high to low, the social welfare of the whole transaction is constantly in-creasing. All transaction entities participate in the transaction in response to the demand at different confidence levels, and the results reflect different attitudes towards the transaction risk. Chance constrained the confidence level is lower, generated by the exchange of social welfare will be higher, but lower confidence level will lead to an in-crease of the system risk, and when the chance-constrained confidence level increases, the risk of response uncertainty to the system is reduced, although the social welfare is reduced, the risk of system operation is decreased greatly.

To reflect the merits of the method in our paper, we have added a new review of the literature on the application of fuzzy theory in the introduction

Details of the revision are available in Author action.

Author action:

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution[19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem[21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and re-placeable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

××Reviewer#3, Concern # 6: The process of optimizing the MFs parameters is not performed, where the authors chose unoptimized values of them in specific intervals. Even the interval boundaries are neither justified nor discussed. I suggest authors apply an effective optimizer for this purpose.

Author response:

Thanks to the reviewer for the comments. Considering that the size of the confidence level reflects the level of risk taken by the system operation, the lower the confidence level, the higher the risk of the grid operation. Therefore, for the consideration of conservative grid operation, in general, the confidence level of the fuzzy chance constraint is chosen as a number greater than 0.5. and the latter is that considering that the cost of transaction stakeholders has a negative impact on the DR transactions, we set MFs parameters to its maximum limit of 0.9.

To verify the impact of different confidence levels of fuzzy chance constraint on the transaction, based on scenario 2 in the previous subsection, the pessimism confidence of each transaction cost is unchanged at 0.9, and fuzzy chance constraint selects different confidence levels to analyze the income changes of each transaction entity under different confidence levels. In addition, the fuzzy parameters describing the response volume are represented by different types of membership functions for comparison. The trigonometric membership function and trapezoidal membership function are selected in this section. Accordingly, the trend of the social welfare of transactions with the confidence level of fuzzy chance constraint can be obtained

Details of the revision are available in Author action.

Author action:

It can be seen from Figure 9 that as the confidence level of opportunity constraint changes from high to low, the social welfare of the whole transaction is constantly increasing. All transaction entities participate in the transaction in response to the demand at different confidence levels, and the results reflect different attitudes towards the transaction risk. Chance constrained the confidence level is lower, generated by the exchange of social welfare will be higher, but lower confidence level will lead to an increase of the system risk, and when the chance-constrained confidence level increases, the risk of response uncertainty to the system is reduced, although the social welfare is reduced, the risk of system operation is decreased greatly.

Figure 9. The impact of confidence level on social welfare

In addition, the above also compares the trapezoidal membership functions and trigonometric membership functions about social welfare under different confidence levels, As can be seen from the figure, compared to the trapezoidal membership function, the use of the trigonometric membership function to describe the uncertainty of customer response volumes is more likely to be trusted by the grid operator in its prediction of response demand volumes, and therefore has higher social welfare than the trapezoidal membership function when the chance constraint confidence level is certain.

Reviewer#3, Concern # 7: The presented case study should be presented clearly with more results and diagrams to clarify things for the scientific audience.

Author response:

Thanks to the reviewer for the comments. According to your suggestion, we added a case to compare the load curves based on the model with and without the consideration of the DR uncertainty in flexible loads.

Scenario 1: Considering the incentive flexible load to participate in the transaction of the power grid, but not considering the uncertainty of the response volume of the flexible load;

Scenario 2: When the flexible load is encouraged to participate in the grid transac-tion, the uncertainty of the response volume of the flexible load is considered.

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 4.5.3.

Fig. 4.5.3 The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

Furthermore, we have also added new comparison of the validity of article methods

Details of the revision are available in Author action.

Author action:

4.1.2 Consider the change of returns of each transaction entity in response to uncertainty

To fully compare the impact of users' uncertain responses on the returns of each transaction entity, two scenarios are set up in this section:

Scenario 1: Considering the incentive flexible load to participate in the transaction of the power grid, but not considering the uncertainty of the response volume of the flexible load;

Scenario 2: When the flexible load is encouraged to participate in the grid transaction, the uncertainty of the response volume of the flexible load is considered.

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 6.

Figure 6. The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

(2) Accordingly, the income comparison results of each transaction entity to the two scenarios can be obtained, as shown in Figure 7.

Figure 7. (a) The income comparison of VPP operator; (b)The income comparison of the power grid operator

In order to demonstrate the advantages of our proposed method, we further compare it with three other methods for solving the uncertainty as follow:

M1: Our proposed method

M2: Distributionally robust optimization-based method

M3: Robust optimization-based method

M4: Stochastic programming-based method

Figure 8. Income comparison.

Reviewer#3, Concern # 8: The authors must ensure the fluidity of the passages between sections and subsections. I recommend the authors reorganize their paper as follows: Abstract; Introduction; Related works; Materials and methods; Results and discussions; Conclusion; References.

Author response:

Thanks for the valuable comments. According to your comments. We have reviewed the titles, sub-titles and content of the articles and found that some titles appeared too simple or did not correspond. We try to structure our articles in a logical way as: Abstract; Introduction; Related works; Materials and methods; Results and discussions; Conclusion; References.

Section	Title
0	Introduction
1	Demand Response Load Uncertainty Analysis and Modeling
2	A demand response transaction model that considers uncertainty
3	Materials and methods
4	Results and discussions
5	Conclusion
6	References

Details of the revision are available in Author action.

Author action:

Section	Title
0	Introduction
1	Demand Response Load Uncertainty Analysis and Modeling
2	A demand response transaction model that considers uncertainty
3	Materials and methods
4	Results and discussions
5	Conclusion
6	References

Reviewer#3, Concern # 9: A comparison study with recently published papers is required in order to prove the accuracy and performance of the current study.

Author response:

Scenario 1: Considering the incentive flexible load to participate in the transaction of the power grid, but not considering the uncertainty of the response volume of the flexible load;

Scenario 2: When the flexible load is encouraged to participate in the grid transaction, the uncertainty of the response volume of the flexible load is considered.

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 4.5.3.

Fig. 4.5.3 The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

In order to demonstrate the advantages of our proposed method, we further compare it with three other methods for solving the uncertainty as follow:

M1: our proposed method

M2: distributionally robust optimization-based method

M3: robust optimization-based method

M4: stochastic programming-based method

Accordingly, the income comparison results of each transaction entity with the above four methods can be obtained, as shown in Figure 6. It is easy to notice that the benefits of power grid operator and VPP operator for participating in the DR transaction rank the first among these methods. Thus, the fuzzy theory utilized in our model with Trigonometric Membership Function can effectively cope with the uncertainty brought by flexible loads.

Figure 8. Income comparison.

Details of the revision are available in Author action.

Author action:

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 6.

Figure 6. The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

In order to demonstrate the advantages of our proposed method, we further compare it with three other methods for solving the uncertainty as follow:

M1: Our proposed method

M2: Distributionally robust optimization-based method

M3: Robust optimization-based method

M4: Stochastic programming-based method

Figure 8. Income comparison.

Reviewer#3, Concern # 10: Proofreading is required to improve the organization and the language of the article.

Author response:

Thank you for the valuable comment. We have revised extensive modifications to our manuscript. Firstly, we went through the whole text and fixed the grammatical, spelling, and formatting errors. Then we have reorganized the subheadings of the article to make a better overall structure of the article. Finally, we have adjusted the abbreviations in the article, removing the uncommon ones and keeping the common ones, so that the reader can read them more fluently.

Details of the revision are available in Author action.

Author action:

All the authors proofread the manuscript to shorten the bulk sentences throughout the paper.

Author Response File: Author Response.docx

Reviewer 4 Report

The paper "A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based

Uncertainty Model of Customers’ Responsive Behaviors" is interesting. However, the authors need to improve several points.

1. I consider the abstract to be improved. It could be reduced. Also briefly add elements such as the main results and implications. The objective of the work is not clear.

2. In the introduction the authors must improve the contribution of the article. Clearly establish what has been done in the literature and what is the difference with this paper. Expand the justification of the paper. Why are the results of this research important?

3. The authors must improve the specification of the case study. What industrial park? date and place.

4. Improve the presentation and interpretation of the results.

5. The conclusions are poor. Most of this section is repeated from the introductory section. The authors should highlight their contribution and the main results and implications. Limitations of the paper and future lines of research.

Author Response

Response to Reviewer#4

Reviewer#4: The paper "A Demand Response Transaction Method for Integrated Energy Systems with Trigonometric Membership Function Based

Uncertainty Model of Customers’ Responsive Behaviors" is interesting. However, the authors need to improve several points.

Reviewer#4, Concern # 1: I consider the abstract to be improved. It could be reduced. Also briefly add elements such as the main results and implications. The objective of the work is not clear.

Author response:

Thanks to the reviewer for the comments and the valuable suggestions. We have made appropriate changes to the summary as suggested. Some redundant elements were deleted while some main findings and significance were added.

Details of the revision are available in Author action.

Author action:

As an important regulation tool for power systems, demand response can greatly improve system flexibility and economy. However, when an integrated energy system with a large number of flexible loads is aggregated for demand response transaction, the uncertainty in the amount of load response should be taken into account. Therefore, a demand response transaction model for an integrated energy system that considers the uncertainty of customer demand response is proposed in this paper. At first, the uncertainty of incentive-based demand response is analyzed, and the relationship between the incentive level and the fluctuation of customer response volume is investigated. The flexible loads are classified into curtailable loads, translatable loads, and replaceable loads. Secondly, fuzzy variables are used to represent the response volume of users. After that, a trigonometric membership function is used to represent the degree of uncertainty in the response volume of different flexible loads. Finally, the objective functions and chance constraints containing fuzzy variables are converted into explicit equivalence classes for solving. In the case study, the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraint confidence level on the response revenue are investigated. The results show that the revenue of each transaction entity decreases to a certain extent under the consideration of the uncertainty of user response volume; the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

Reviewer#4, Concern # 2: In the introduction the authors must improve the contribution of the article. Clearly establish what has been done in the literature and what is the difference with this paper. Expand the justification of the paper. Why are the results of this research important?

Author response:

Thank you for the comments. In our paper, we propose a DR transaction model for the customers to actively interact with the IES. Considering that various types of flexible loads with different responsive potential and uncertainty in the customers may influence the transaction results, we apply the fuzzy theory with trigonometric membership-function to describe the uncertainty of these flexible loads.

In the current incentive-based DR studies, the response volume of the flexible load during the transaction is default certain. Yet, for IESs that aggregate a large number of flexible loads, there exists uncertainty in the response volume they provide to the grid because of the specificity of the way it aggregates resources. Also, there are inherent uncertainties such as communication delays, coupled with the fact that the response capacity provided by the user is also highly subjective. The response volume is susceptible to a variety of factors such as unexpected next-day conditions, subjective and objective negligence, and changes in consumption behavior.

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding the random variables with a bounded interval or a certain probability distribution. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem, yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by expert system when fuzzy number lacks historical information, so this method is of low dependence on historical data and good description on the uncertainty.

Based on the above problems, this paper focuses on the uncertainty of the excitation-type flexible load response, and proposed a decentralized DR transaction model for the customers to actively interact with the IES. Firstly, the uncertainty problem of the incentive-based DR method is studied. The relationship between the uncertainty level of user response and the incentive level has been pointed out. Secondly, fuzzy variables are used to represent user response; then, the trigonometric membership fuzzy function is used to construct the uncertainty model of flexible load response. Finally, the transaction model containing fuzzy variables is trans-formed into a deterministic model for a solution.

The main contribution of the paper is as follows：

A DR transaction model for the customers to actively interact with the inte-grated energy system is proposed in this paper.
Considering that various types of flexible loads with different responsive poten-tial and uncertainty in the customers may influence the transaction results, the fuzzy theory with trigonometric membership-function is applied to describe the uncertainty of these flexible loads.

Details of the revision are available in Author action.

Author action:

The development of an integrated energy system (IES) should consider the safety, economy, and cleanliness. It integrates various energy resources such as natural gas and photovoltaic power in the region, and meets the multiple energy requirements of users[1,2]. Thus the IES is becoming a hot spot for research in the energy field[3,4].

With the development of IES, technological advances in demand response (DR) have become a key solution to achieve this energy transition. DR can effectively in-crease the active participation of consumers in the IES [5]. Flexible loads in IESs have a strong DR capability. Flexible loads on the customer side can adjust their electricity consumption behavior according to the price-based DR mechanism [6][7] and the incentive-based DR mechanism[8], relieving the electricity supply tensions of the IES. Based on multiple types of low carbon factors and price-based DR mechanisms, Ma et al [9] construct an energy efficiency improvement scheduling model with abandoned wind penalty costs, power purchase costs, equipment operation and maintenance costs, and carbon transaction costs as optimization targets, improving the comprehensive energy efficiency of the IES. Yang et al [10] proposed the rolling optimization planning framework and model of IES considering CAES and sliding time window-based electric and heating integrated demand response (IDR), improving the economy and flexibility of the IES. Based on the DR potential and consumer’s consumption characteristics, as well as the coupling characteristics of the energy flows in the regionally integrated energy system (RIES), Hu et al.[11] establish a RIES optimization model that considers the DR of cooling, heating and electricity consumption of flexible loads. The synergistic optimization of the supply side and the consumer side is realized.

Traditional methods usually transform a certain optimization model into a stochastic optimization via adding random variables with a bounded interval or a certain probability distribution[19,20]. These methods are required to form the accurate probability distribution of every random variable, while there are numerous flexible loads participating in the DR and it is unfeasible to confirm their accurate probability. Thus, a robust-based optimization model is proposed to tackle this problem[21], yet the results solved by this model could be quite conservative along with the poor economy of the system. Considering both the characteristics of flexible loads and the economy of the system, we eventually utilize the fuzzy theory with trigonometric membership-function. Trigonometric membership-functions of uncertain parameters can be obtained by an expert system when a fuzzy number lacks historical information, so this method is of low dependence on historical data and a good description of the uncertainty.

The contributions of this paper are threefold：

1) We introduce the analysis of DR uncertainty. Additionally, the DR load uncertainty models of curtailable load, translated load, and replaceable load are proposed respectively.

2) A DR transaction model is investigated. In this model, various types of flexible load response volume uncertainty are taken into consideration.

Reviewer#4, Concern # 3: The authors must improve the specification of the case study. What industrial park? date and place.

Author response:

Thanks for your valuable advice. The simulated data in this paper comes from an international low-carbon park in eastern China in 2005, which integrates various forms of energy supply, including new and renewable energy sources, to achieve self-sufficient recycling.

To improve the specification of the case study, we add the data source of our work in the case study.

Details of the revision are available in Author action.

Author action:

Taking an international low-carbon park in eastern China as an example, the park contains a variety of load resources, mainly consisting of flexible loads as well as base loads that are not responsive, where the flexible loads consist of shiftable loads, transferable loads, curtailable loads, and replaceable loads. The load data for flexible users are shown in Table 2, Table 3, Table 4, and Table 5.

Considering that the value of the confidence reflects the level of risk taken by the sys-tem operation, the lower the confidence level, the higher the risk of the grid operation.The confidence of opportunity constraint is set as β₁=β₂=β₃=0.95, the pessimistic confidence of each transaction cost is set as α₁=α₂=0.9, and the reserve capacity coefficient of the power grid is set as 0.05. The allowable fluctuation range of the response rate of various flexible loads is shown in Table 6.

Reviewer#4, Concern # 4: Improve the presentation and interpretation of the results.

Author response:

Thank you for your valuable advice.

The case study section examines the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraints confidence level on the response revenue. The results demonstrate that the revenue of each transaction entity decreases to a certain extent when the uncertainty of user response volume is considered, and the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

According to your advice, firstly, we checked the paper carefully and shorten all bulk sentences throughout the paper. Also, all grammatical errors have been revised. Long single sentences and complex sentence structures are revised and concise and the active voice has been used. Then we add an extra comparison study to Improve the presentation and interpretation of the results.

Details of the revision are available in Author action.

Author action:

(1) After analyzing the results of the load response, the results of the combined comparison of the optimized load profiles for Scenario 1 and Scenario 2 are shown in Figure 6.

Figure 6. The comparison of load curve

Comparing the three load curves shown above, the following conclusions can be drawn.：

In order to demonstrate the advantages of our proposed method, we further compare it with three other methods for solving the uncertainty as follow:

M1: Our proposed method

M2: Distributionally robust optimization-based method

M3: Robust optimization-based method

M4: Stochastic programming-based method

Figure 8. Income comparison.

Reviewer#4, Concern # 5: The conclusions are poor. Most of this section is repeated from the introductory section. The authors should highlight their contribution and the main results and implications. Limitations of the paper and future lines of research.

Author response:

Thanks to the reviewer for the comments and the valuable suggestions. To emphasized the contribution and novelty of our paper. We first revise the conclusion to show more quantity result. Furthermore, the contributions are emphasized in the last part. Finally, A summary of our paper and a vision of future work have been added to highlight the contribution of our article and the main results and impact.

Details of the revision are available in Author action.

Author action:

DR is increasingly used as an essential regulation tool in power systems, however, when an integrated energy system with a large number of flexible loads is aggregated for DR transaction, uncertainty in the amount of load response can have an impact on the process and outcome of the transaction. In this paper, the impact of uncertainty in flexible load response on DR transactions is considered. First, the uncertainty problem of incentive-based DR is analyzed, and the relationship between the level of incentive and the range of fluctuations in the user response volume is investigated. Subsequently, the treatment of uncertainty is introduced, and this paper uses fuzzy variables to represent the user response volume. Based on this, a trigonometric membership function is used to represent the uncertainty level of user response quantity for different types of flexible loads. Finally, for the objective function and chance constraints containing fuzzy variables, they are converted into explicit equivalence classes and then solved. The case study section examines the impact of the uncertainty of user response volume on the revenue of each transaction entity and the impact of the fuzzy chance constraints confidence level on the response revenue. The results demonstrate that the revenue of each transaction entity decreases to a certain extent when the uncertainty of user response volume is considered, and the social welfare of the whole transaction increases as the confidence level of the chance constraint changes from high to low.

The proposed method of dealing with user response uncertainty in this paper pro-vides some ideas and suggestions to solve the problems faced by flexible loads when participating in DR, but it can still be extended in the following two aspects. Firstly, the study of flexible loads response strategy under multiple time scales. The research con-ducted in this paper does not consider the time scale, and does not study the regulation of flexible loads in multiple time scales such as day-ahead, intra-day and real-time. In fact, in the case of approaching time scale, the types of flexible users that can participate in grid DR will be reduced continuously, and the uncertainty of user response will also be reduced continuously, even in the real-time stage is possible without considering the problem of user response uncertainty. Secondly, the study of user uncertainty under multiple response mechanisms. In this paper, we only consider the problem of response uncertainty of flexible loads under contract constraints, but in fact, some flexible loads can also participate in the DR of the grid under tariff guidance, and their response uncertainty cannot be ignored.

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

The authors have reviewed their research paper and have taken into account all the points indicated. The paper can be considered for publication.

Reviewer 4 Report

The authors have improved the paper sufficiently and I consider that it can be accepted.