Joint Optimal Scheduling of Power Grid and Internet Data Centers Considering Time-of-Use Electricity Price and Adjustable Tasks for Renewable Power Integration

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I want to say that the article is interesting. The authors consider a rather interesting problem.

The internet data center (IDC) has experienced rapid growth recently. Computing power tasks have the characteristic of flexible adjustment and can participate in demand-side response. Existing studies lack research on the joint optimization between the IDC and power grid. This paper proposes a joint optimization scheduling approach for IDC and power systems, focusing on the response of computing tasks. Based on the adjustment characteristics of computing tasks, tasks are categorized, and operational constraints for each category are defined. The bi-level optimization model for the IDC and power grid is established, taking into account the task constraints, as well as the operational limits of power generation units and the IDC. A novel elasticity coefficient matrix for time-of-use (TOU) electricity pricing is proposed, considering the load characteristics of IDC tasks. The IDC's demand response volume is determined using the elasticity coefficient matrix. The enhanced Benders decomposition method is then employed, incorporating the IDC's demand response capacity and the constraints of the bi-level optimization model, to solve the optimal planning problem. To achieve scenario reduction, the K-means algorithm is utilized to derive the typical daily load profiles of the IDC.  The results show that the approach effectively reduces the operational costs of IDC- power system and enhances the integration of renewable energy

Remarks:

1.The current state of the problem overview needs to be improved. It would be desirable to describe the current state of the problem in more detail. Not enough sources

2. Clarify the task statement and the purpose of the work.
3. The authors use Benders decomposition method. It is necessary to provide a brief description of it and how it is applied in this study. A reference to the original source is required, For example: Benders, J.F. Partitioning procedures for solving mixed-variable programming problems. Numerische mathematic.- 1962.- Vol. 4. - №1. - P.238–252.
4. The figures are very small
5. It is not clear how to interpret the results presented in Fig. 10.

Author Response

To Reviewer 1

I want to say that the article is interesting. The authors consider a rather interesting problem. The internet data center (IDC) has experienced rapid growth recently. Computing power tasks have the characteristic of flexible adjustment and can participate in demand-side response. Existing studies lack research on the joint optimization between the IDC and power grid. This paper proposes a joint optimization scheduling approach for IDC and power systems, focusing on the response of computing tasks. Based on the adjustment characteristics of computing tasks, tasks are categorized, and operational constraints for each category are defined. The bi-level optimization model for the IDC and power grid is established, taking into account the task constraints, as well as the operational limits of power generation units and the IDC. A novel elasticity coefficient matrix for time-of-use (TOU) electricity pricing is proposed, considering the load characteristics of IDC tasks. The IDC's demand response volume is determined using the elasticity coefficient matrix. The enhanced Benders decomposition method is then employed, incorporating the IDC's demand response capacity and the constraints of the bi-level optimization model, to solve the optimal planning problem. To achieve scenario reduction, the K-means algorithm is utilized to derive the typical daily load profiles of the IDC.  The results show that the approach effectively reduces the operational costs of IDC- power system and enhances the integration of renewable energy

Thank you for your confirmation and valuable suggestions.

 

1. The current state of the problem overview needs to be improved. It would be desirable to describe the current state of the problem in more detail. Not enough sources

With the development of digital economy, the IDC loads increase quickly in recent years. For example in a Province in China, the daily electricity demand of the IDC increases from 13.3 MWh in Jan. 1^st 2024 to 83.3 MWh in Dec. 18^th 2024. The IDC loads have the characteristics of spatiotemporal mobility and reducibility, thus are high-quality resource of demand-side response for power systems, which can increase the profit of the IDCs, alleviate the pressure of peak-value dispatch, and allow more integration of stochastic renewable energies e.g. wind and solar powers.

The revise is made in Section 1, the first paragraph of Section 1.

 

2. Clarify the task statement and the purpose of the work.

The motivation of this paper is to find the optimal solution of the coordinated scheduling of the power grid and the IDCs with demand-side response. We describe the adjustable characteristics of the computing power tasks, solve the elasticity coefficient matrix of the IDCs, and consider the impact of the time-of-use electricity price on the IDCs’ load.

Figure 3. Joint optimization to power grid with IDC using Benders decomposition.

 

3. The authors use Benders decomposition method. It is necessary to provide a brief description of it and how it is applied in this study. A reference to the original source is required, For example: Benders, J.F. Partitioning procedures for solving mixed-variable programming problems. Numerische mathematic. 1962.- Vol. 4. – No.1. P.238–252.

The most important contribution of this this paper is the bi-level optimal scheduling model to the power systems with the IDC loads having demand-side response. For comparison, the existing studies either focus on the IDC while ignoring the power grid, or consider the power grid and the IDC but ignore the response of the IDC load to the electricity price.

Based on bi-level optimization model, the master problem, the subproblems, and the decision variables are found to obtain the problems with discrete 0-1 variables. Then the problem is solved with the enhanced Benders decomposition method.

Now as suggested, more references about the Benders decomposition are added.

[A1] Benders, J.F. Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252 (1962). doi.10.1007/BF01386316

[A2] Huang, Q. Zhao, L. and Wu, C. Benders decomposition for multimodal facility location allocation problem considering capacity levels and uncertainty. IEEE Transactions on Intelligent Transportation Systems, doi: 10.1109/TITS.2025.3552599.

[A3] Pecci,F. and Jenkins, J. D. Regularized Benders decomposition for high performance capacity expansion models. IEEE Transactions on Power Systems, doi: 10.1109/TPWRS.2025.3526413.

 

4. The figures are very small.

As suggested, the size of all the Figures is increased to show clearly.

 

5. It is not clear how to interpret the results presented in Fig. 10.

Fig. 10 shows the convergence process to verify the effectiveness of the proposed model. The convergence error ε is defined as |C₁-C₂|/C₂, where C₁ and C₂ are the optimal scheduling values to the IDC-power grid using the Benders decomposition and the centralized method respectively.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes a coordinated optimal scheduling method for Internet Data Centers (IDCs) and the power system, considering the response of computational tasks, based on demand-side response of the power grid. The study analyzes the adjustable characteristics of different types of computational tasks by constructing a bi-level optimization model and proposes a price elasticity coefficient matrix based on time-of-use electricity prices. The paper employs an enhanced Benders decomposition method to solve the mixed-integer linear programming problem and uses the K-means clustering algorithm to simplify scenarios for the IDC load curve.

The following are suggestions for revisions aimed at improving the clarity, accuracy, and readability of the document:

1. The manuscript is based on existing methods, but does not adequately explain how this work represents a significant advance in the field. It would have been preferable for the authors to have articulated their unique contribution more clearly.
2. It is suggested to add Benders decomposition algorithm with traditional algorithm comparison test to prove its superiority.
3. It is proposed to add a robustness analysis to demonstrate the stability of the algorithm in an uncertain environment.
4. Add an explanation for Equation 12.
5. Provide a more detailed explanation of the charts mentioned in the text (such as Figure 2, Figure 3, etc.) to help readers understand their significance.
6. If the authors create a table at the end of the paper listing all abbreviations in alphabetical order, it may help readers understand the content more easily.

Comments on the Quality of English Language

Moderate editing of English language required.

Author Response

Reviewer 2

This paper proposes a coordinated optimal scheduling method for Internet Data Centers (IDCs) and the power system, considering the response of computational tasks, based on demand-side response of the power grid. The study analyzes the adjustable characteristics of different types of computational tasks by constructing a bi-level optimization model and proposes a price elasticity coefficient matrix based on time-of-use electricity prices. The paper employs an enhanced Benders decomposition method to solve the mixed-integer linear programming problem and uses the K-means clustering algorithm to simplify scenarios for the IDC load curve.

Thank you for your confirmation and valuable suggestions.

 

The following are suggestions for revisions aimed at improving the clarity, accuracy, and readability of the document:

1. The manuscript is based on existing methods, but does not adequately explain how this work represents a significant advance in the field. It would have been preferable for the authors to have articulated their unique contribution more clearly.

The motivation of this paper is to derive the price elasticity of the IDC loads with demand-side response, then the operational costs of the IDC and the power grid are minimized using a bi-level optimization model and solved with Benders decomposition method. The contributions lie in, 1) Based on the task flexibility of the IDC, its price elasticity coefficient matrix is newly quantified; 2) A bi-level optimization model for the power grid with the IDC is proposed and solved with Benders composition method. Finally, the simulation results for an actual power system are then given to validate the feasibility and effectiveness of the proposed model. We hope now the paper is easier to read and understand.

The above explanations are given in Section 1, the last paragraph.

 

2. It is suggested to add Benders decomposition algorithm with traditional algorithm comparison test to prove its superiority.

As suggested, comparison to the optimization results using the method proposed in this paper and those using the existing methods such as individual optimization [B1-B2], or branch and bound [B3-B5], is newly made in Table 2. Compared with the existing methods, the method proposed in this paper considers the demand-side response capacity of IDC and the adjustable characteristics of tasks, and ensures system economics. It is found that the total cost using the proposed method is decreased by 7.356%.

The corresponding revise is made in Tab.2 and the paragraph before it in Section 4.1.

Table 2. Cost comparison of system in different scheduling methods.

cost/$	individual optimization [B1-B2]	branch and bound [B3-B5]	joint optimization in this paper
operation cost of power grid	11389.66	11078.46↓	10965.94↓
operation cost of IDC	5888.25	5518.71↓	5040.95↓
total cost	17277.91	16597.17↓	16006.89↓

[B1] Yu, L. Jiang, T. and Zou, Y. Distributed real-time energy management in data center microgrids, IEEE Transactions on Smart Grid, 2018, 9(4): 3748-3762 doi: 10.1109/TSG.2016.2640453.

[B2] Cheng, Y. Anwar, A. and Duan, X. Analyzing Alibaba's co-located datecenter workloads, Proceedings of 2018 IEEE International Conference on Big Data. 2018, 292-297.

[B3] Xu, M. Wang, J. Wang, K. and Chen, Z. Hierarchical and validated branch-and-bound method for global point cloud registration, IEEE Transactions on Industrial Informatics, 2025, 21(1): 940-949. doi: 10.1109/TII.2024.3470893.

[B4] Wang, Z. Zeng, Q. Liu, B. Qu, C. and Wang, H. A Tailored two-stage algorithm for quay crane and automated guided vehicle scheduling problems, IEEE Transactions on Intelligent Transportation Systems, 2025, 26(4): 5049-5066. doi: 10.1109/TITS.2025.3545433.

[B5] Wang, H. Huang, J. Lin, X. and Mohsenian-Rad, H. Proactive Demand Response for Data Centers: A Win-Win Solution, IEEE Transactions on Smart Grid, 2016, 7(3): 1584-1596. doi: 10.1109/TSG.2015.2501808.

 

3. It is proposed to add a robustness analysis to demonstrate the stability of the algorithm in an uncertain environment.

To validate the robustness of the joint optimization model proposed in this paper, different daily load curves of the IDC are applied, with the results shown in Fig.11. It is found that the method proposed in this paper can effectively shift adjustable loads of IDC from peak to off-peak hours, and reduce the operating cost of the IDC.

The corresponding revise is made in Fig.11 and the paragraph before it in Section 4.1.

(a) Daily load curves of IDC before adjustment

(b) Daily load curves of IDC after adjustment

Figure 11. Optimal scheduling result under different daily load curves of IDC

 

4. Add an explanation for Equation 12.

Eq. 12 defines the total system cost of coordinated optimization scheduling to the IDC and the power grid. It has two components, (1) the operational cost of the IDC, including the IT service cost, server startup cost, and task transmission cost, and (2) the operational cost of the grid, including startup, shutdown cost of generation units, and operation cost of generations.

 

5. Provide a more detailed explanation of the charts mentioned in the text (such as Figure 2, Figure 3, etc.) to help readers understand their significance.

The authors are sorry for the concise explanations to the Figures. Now more discussion is given to the Figures. For example,

Figure 2 shows the correlation of the elasticity coefficient matrix among the computing power tasks in the IDC. Firstly, the tasks are classified according to the adjustable characteristics of the IDC tasks. Secondly, the influence of each type of task on the price elasticity is analyzed. The rigid tasks are important loads that do not participate in scheduling. They are almost fixed and do not change with the electricity price. The transferable tasks affect the autocorrelation coefficient. The shiftable and reducible tasks affect the cross-correlation coefficient. The revise is made …

Figure 3 gives the solution procedure using the enhanced Benders decomposition method. The master problem, the sub-problems, the corresponding decision variables, as well as the operational constraints, are decided to find the optimal solution of the bi-level optimization model for power system with the IDC participating in demand-side response. For the transferrable load, at first, the master problem is solved, and the solution is sent to the subproblems. Then, each subproblem is solved to generate the Benders cut. When the solutions do not change, the process converges.

 

6. If the authors create a table at the end of the paper listing all abbreviations in alphabetical order, it may help readers understand the content more easily.

Thank you for your kind advice.

Now the Notations are added to define the variables used in the paper. The corresponding revise is given in Section 1.

Notations

A,B,C,D,E,F,H,I,J,K,L,M                     Constant coefficient matrix

a, b, c, d, e, f, g, h                                 Constant coefficient

C                                                         Economics cost

E, e                                                     Elasticity coefficient matrix, elasticity coefficient

I                                                         Operational status decision variables

P                                                         Active powers

T                                                         Working hours of IDC tasks

x, y, m, z, u                                           Variables

λ                                                         Linearized generators output cost of IDC

The corresponding revise is given in Section 1.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

There is no clear implementation of the maths in the system case analysis. There are two separate sections with loosely related information between theory and implementation. Some maths, a plot image displayed in figure 3 not correctly related to the maths below and then some images not generally readable and the final remark is the paper is so hard to read and understand if you must give a positive or negative review. There is no evidence of the maths in the implementation. Also, which is the software package by which the plots are derived?

Comments on the Quality of English Language

it can be improved

Author Response

To Reviewer 3

There is no clear implementation of the maths in the system case analysis. There are two separate sections with loosely related information between theory and implementation. Some maths, a plot image displayed in figure 3 not correctly related to the maths below and then some images not generally readable and the final remark is the paper is so hard to read and understand if you must give a positive or negative review. There is no evidence of the maths in the implementation. Also, which is the software package by which the plots are derived?

Thank you for your valuable suggestions. Your comments are classified in to 4 questions.

 

1. There are two separate sections with loosely related information between theory and implementation.

The authors are sorry for the structure of the paper not clear to the readers.

The motivation of this paper is to derive the price elasticity of the IDC loads with demand-side response, then the operational costs of the IDC and the power grid are minimized using a bi-level optimization model and solved with Benders decomposition method. The contributions lie in, 1) Based on the task flexibility of the IDC, its price elasticity coefficient matrix is newly quantified; 2) A bi-level optimization model for the power grid with the IDC is proposed and solved with Benders composition method. Finally, the simulation results for an actual power system are then given to validate the feasibility and effectiveness of the proposed model. We hope now the paper is easier to read and understand.

The revise is given in Section 1, the last paragraph. The reviewer may also see Fig.3 to find the logic of the paper.

 

2. A plot image displayed in figure 3 not correctly related to the maths below and then some images not generally readable.

The authors realized that Fig.3 contains too much information, thus is difficult to understand.

Now as suggested, it is redrawn to show the main procedure and contribution of this paper. Its relation with the equations is now labelled in several blocks.

The revise is made in Fig.3 and the paragraph before it.

Figure 3. Joint optimization to power grid with IDC using Benders decomposition.

 

3. The final remark to the paper is so hard to read and understand if you must give a positive or negative review.

The authors are sorry for the ambiguous expression of the Conclusion. Now as suggested, the logic of the conclusion is revised as follows,

This paper newly quantifies the price elasticity of the IDC loads, and proposes a bi-level optimization model for the power grid with the IDC responded to the time-of-use electricity price. Based on mathematical modeling and simulation results, some conclusions are found,

(1) The IDC-power grid bi-level optimization model proposed in this paper can effectively express the collaborative optimization relationship between the two entities, achieving optimized planning while ensuring reasonable economic benefits for both systems. Compared with individual optimization, the proposed optimization model can reduce the operational costs of IDC and power grid systems by 7.356%.

(2) Time-of-use electricity price can guide IDC to adjust computing task scheduling strategies. Through the adjustable characteristics of computing tasks IDC can participate in demand-side response. This mechanism facilitates peak shaving and valley filling in power systems while enhancing renewable energy integration.

(3) A 39 nodes distribution system is selected as a simulation case, and the solution effects of the method proposed in this paper and conventional methods are compared. The simulation results prove the effectiveness and good convergence of the proposed method.

3.3 Discussions

(1) The price elasticity is related to time-of-use electricity price and quantified with historical load-price data. But it changes with the time instead of being constant, hence the price-elasticity coefficient matrix is to be checked and updated with time, especially when the load components and characteristics change notably.

(2) The time-of-use electricity price in this paper does not change with the system conditions. However, the power grid may change the time-of-use time curve to provide better service to the IDC while not increase the burden of the peak-load scheduling.

(3) This paper optimizes one IDC with several load components with different responses to the change of electricity price. With increasing capacity, the IDCs may located at different locations, thus may be optimized in a coordinated manner. Furthermore, if the distance of the IDCs is large enough, the peak-valley loads of the power grids occur at different time. Such spatial feature of multiple IDCs may be applied to reduce the cost of the power grid with the IDCs.

Therefore, the optimal scheduling method for IDC loads considering the response of computing power tasks proposed in this paper provides an effective approach for the optimal scheduling of the IDC - power system. In the future, online optimal scheduling of IDC loads will be taken as a key research direction.

The revise of conclusion is made in Section 5. and the discussion is newly added to Section 3.3.

 

4. Also, which is the software package by which the plots are derived?

The proposed optimization model is implemented with the Matlab software, and run on the PC computer with Intel i5-12400 2.5 GHz. The Matlab provides the optimization toolbox and the plot function which may be applied. But detailed objective function and the constraints of the IDC and power gird are not available, and to be provided by the authors according to demand-side response characteristics of the IDC, and the corresponding program is written by the authors, which have not been studied yet.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The paper presents a study on Joint Optimal Scheduling of Power Grid and Internet Data Centers Considering Time-of-Use Electricity Price and Adjustable Task Characteristics, the paper is written well overall, here are my comments:
-add a highlight section where you mention your main contribution 
-in you abstracts better to add specific results
-add a literature review sections and use more recent references
-at the end of your literature review specify the research gaps and define how are you gonna tackle them in your research
-at the end of your intro/literature review, add a paragraph illustrating the flow of rest of the paper
-it's better to add a numnenclarure and define all variables and abbreviations 
-add a comparison between recent literature methods and your method
-your conclusions is divided to points which is good, add to it limitations and future work
-add DOI for all references used for easy locating 
-more discussion in the discussion section for the results would be good

Author Response

To Reviewer 4

The paper presents a study on Joint Optimal Scheduling of Power Grid and Internet Data Centers Considering Time-of-Use Electricity Price and Adjustable Task Characteristics, the paper is written well overall, here are my comments:

Thank you for your confirmation and valuable suggestions.

 

1. Add a highlight section where you mention your main contribution in you abstracts better to add specific results.

The highlight of this paper lies in tasks are classified according to the adjustable characteristics of them in the IDC and the corresponding task operation constraints are constructed. Taking into account the above constraints of the IDC and the operational constraints of power grid, a bi-level optimization model is proposed. Considering the adjustable characteristics of IDC tasks, the elasticity coefficient matrix of the IDC is constructed, which is used to solve the demand-side response volume of the IDC. Based on the bi-level optimization model and the demand response volume of the IDC, this paper adopts the enhanced Benders decomposition method to solve the nonlinear programming problem.

 

2. Add a literature review sections and use more recent references.

There are some studies about the participation of the IDC in the demand-side response. Considering the privacy issue of the DCOs, Ref. [6] proposes a two-level distributed scheduling algorithm based on the alternating direction multiplier method which is applied to privacy protection and distributed autonomy. Ref. [7] decomposes the joint optimization problem into two sub-problems and proposes a two-timescale optimization framework. In order to characterize the graph-structured states of connected data centers, it gives a directed graph convolutional network based global state representation model. Ref. [8] proposes a spatiotemporal task scheduling (STTS) algorithm to minimize energy cost to all tasks to meet their delay bound constraints.

Table D1. Literature review and comparison

Literature	Methods
[6]	Alternating direction multiplier method
[7]	Two-timescale multi-agent deep reinforcement learning algorithm
[8]	Spatiotemporal task scheduling algorithm
[13]	Adaptive scheduling algorithm
[15]	The coordination of multiple coupled regulation methods

However, the existing studies on joint optimization of distribution networks and IDC mainly focus on operational aspects, lack the interrelationship between IDC and power gird, and have not simultaneously considered their joint layout strategies from the planning perspective.

As suggested, some of the recent studies are discussed in Section 1.

 

3. At the end of your literature review specify the research gaps and define how are you gonna tackle them in your research.

This paper classifies the IDC loads based on adjustable characteristics to yield their operational constraints, which is then combined with the operational constraints of the generators in the power system to propose a bi-level optimization model to the power systems with the IDC loads. The contributions lie in, 1) Based on the task flexibility of the IDC, its price elasticity coefficient matrix is newly quantified; 2) A bi-level optimization model for the power grid with the IDC is proposed and solved with Benders composition method. Finally, the simulation results for an actual power system are then given to validate the feasibility and effectiveness of the proposed model. We hope now the paper is easier to read and understand.

 

4. At the end of your intro/literature review, add a paragraph illustrating the flow of rest of the paper.

As suggested, a paragraph about the flow of rest of the paper is discussed in the last paragraph of Section 1.

 

5. It's better to add a numnenclarure and define all variables and abbreviations

In accordance with expert advice, a table listing all abbreviations in alphabetical order is added. The corresponding revise is given in Section 1.

Notations

A,B,C,D,E,F,H,I,J,K,L,M                     Constant coefficient matrix

a, b, c, d, e, f, g, h                                 Constant coefficient

C                                                         Economics cost

E, e                                                     Elasticity coefficient matrix, elasticity coefficient

I                                                         Operational status decision variables

P                                                         Active powers

T                                                         Working hours of IDC tasks

x, y, m, z, u                                           Variables

λ                                                         Linearized generators output cost of IDC

 

6. Add a comparison between recent literature methods and your method

Please see the response to Comment 2. Thank you.

 

7. Your conclusions is divided to points which is good, add to it limitations and future work

In the future research direction, the coordinated optimal scheduling of multiple IDC in multiple regions and the site selection of IDC will be considered. Since the time-of-use electricity price policies of power grids in different regions are different, IDC can achieve large-scale load transfer, which is convenient for them to participate in the demand-side response of power grids in different regions. The limitation of this paper lies in the fact that the operation constraints of the power grid are simplified, and the influence of climate factors such as temperature on the cooling power is not taken into account in the modeling of IDC.

The corresponding revise is given in Section 5.

 

8. Add doi for all references used for easy locating

In accordance with expert advice, the doi of the corresponding reference has been added.

The corresponding revise is given in references.

 

9. More discussion in the discussion section for the results would be good

In accordance with expert advice, the discussion is added to the section of conclusion.

(1) The IDC-power grid bi-level optimization model proposed in this paper can effectively express the collaborative optimization relationship between the two entities, achieving optimized planning while ensuring reasonable economic benefits for both systems. Compared with individual optimization, the proposed optimization model can reduce the operational costs of IDC and power grid systems by 7.356%.

(2) Time-of-use electricity price can guide IDC to adjust computing task scheduling strategies. Through the adjustable characteristics of computing tasks IDC can participate in demand-side response. This mechanism facilitates peak shaving and valley filling in power systems while enhancing renewable energy integration.

(3) A 39 nodes distribution system is selected as a simulation case, and the solution effects of the method proposed in this paper and conventional methods are compared. The simulation results prove the effectiveness and good convergence of the proposed method.

The corresponding revise is given in Section 5.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Accept in present form

Reviewer 2 Report

Comments and Suggestions for Authors

The author has addressed all my concerns, and I have no further questions.

Reviewer 3 Report

Comments and Suggestions for Authors

accept as it is

Reviewer 4 Report

Comments and Suggestions for Authors

The paper is revised. Thanks and good luck