Consumer Theory-Based Primary Frequency Regulation in Multi-Microgrid Systems within a P2P Energy Management Framework

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presented a novel primary frequency regulation strategy for multi-microgrid 1 (MMG) systems, utilizing consumer theory within a peer-to-peer (P2P) energy management frame- 2 work. Please address my following comments.

 

1. The illustrations in the article are relatively large. They can be made more compact and beautified to enhance the expression. And the saturation of the pictures should not be too high.

 

2. In ‘6.1. Operational conditions determination’, please explain how the criteria for selecting each parameter were derived.

 

3. In ‘6. Simulations and Results’, some comparative experiments can be added to make the proposed method more obvious, which can improve the experimental effect.

 

4. Some formulas do not need line breaks, such as (44). Some piecewise functions should have domains that include all real numbers, such as (47). The case of ∆f = 0 is not discussed.

 

5. You can appropriately add a description of the contribution of the article and explain its innovation in detail.

 

6：The following market research and related microgrid operation can be compared (not mine): 1: Distributed tri-layer risk-averse stochastic game approach for energy trading among multi-energy microgrids 2: Committed Carbon Emission Operation Region for Integrated Energy Systems: Concepts and Analyses 3: Two-stage robust operation of electricity-gas-heat integrated multi-energy microgrids considering heterogeneous uncertainties

Comments on the Quality of English Language

good

Author Response

We would like to thank for the thoughtful comments and suggestions, which have certainly helped us to improve the paper.  Below is our reply to all comments, explaining in detail the changes made to the paper to address their concerns.  All changes made in response to the comments are highlighted in red text in the revised paper.

Comments 1:

The illustrations in the article are relatively large. They can be made more compact and beautified to enhance the expression. And the saturation of the pictures should not be too high.

Response 1:

We appreciate the reviewer’s feedback regarding the illustrations in the article. In response to your comment, we have made several adjustments to the figures to improve their compactness and overall visual appeal, while also addressing the color saturation issue. Specifically:

1. Figures 4 and 5: These figures have been combined into a single multi-figure (Figure 4) to streamline the presentation.
2. Figure 7 (Now Figure 5): This figure has been redrawn to make it more compact and visually appealing.
3. Figure 9 (Now Figure 8): This figure has been set as a wide figure to better utilize the available space and enhance readability.
4. Figures 10 and 11: These figures have been combined into a single multi-figure (Figure 9) to reduce redundancy and improve clarity.
5. Color Saturation: The colors of all figures have been reviewed and adjusted to ensure they are less saturated, improving readability and visual appeal.

Comment 2:

In ‘6.1. Operational conditions determination’, please explain how the criteria for selecting each parameter were derived.

Response 2:

The parameters in Section 6.1, ‘Operational conditions determination,’ were chosen after a tuning process. This process involved running various simulations under different operational conditions to ensure stable and optimal behavior. Our approach is similar to the methodology used in the paper "Consensus-Based Approach to Peer-to-Peer Electricity Markets With Product Differentiation." Through iterative simulations and adjustments, we were able to identify parameter values that consistently yielded reliable and efficient system performance.

Thank you for highlighting this aspect, and we hope this clarification provides the necessary insights into our parameter selection process. A description of tunning process was added at the beginning of section 6.1. (Lines 500 to 505)

Comment 3:

In ‘6. Simulations and Results’, some comparative experiments can be added to make the proposed method more obvious, which can improve the experimental effect.

Response 3:

Thank you for your suggestion. We would like to clarify that we have already conducted a comprehensive simulation comparing the proposed method with traditional frequency regulation methods, such as conventional droop control and virtual inertia strategy. This comparison is detailed in Section 6 and highlights the advantages of our proposed consumer theory-based primary frequency regulation strategy more effectively. We think that the simulations are comprehensive enough to demonstrate the efficacy of the proposed approach. However, we appreciate your feedback and are open to further suggestions if additional specific comparisons are deemed necessary.

Comment 4:

Some formulas do not need line breaks, such as (44). Some piecewise functions should have domains that include all real numbers, such as (47). The case of ∆f = 0 is not discussed.

Response 4:

We have carefully reviewed the formulas and have rewritten equations (17), (20), and (44) to avoid unnecessary line breaks for improved readability.

Regarding the case of , it is not explicitly discussed as it is inherently included in the broader conditions provided. Specifically:

• The case  in equation (47) (now equation 49) encompasses .
• Similarly, the condition in equation (48) (now equation 50) also includes .

These conditions ensure that the special case where the frequency deviation is zero is adequately covered within our existing framework.

Comments 5:

You can appropriately add a description of the contribution of the article and explain its innovation in detail.

Response 5:

We understand the need to clarify the contributions and advantages of using consumer theory in our proposed primary frequency regulation strategy. To address this, we have made several revisions throughout the manuscript, including the abstract, introduction, and results analysis sections, to better highlight the benefits of our approach.

The abstract now succinctly summarizes the advantages of the proposed method, emphasizing its ability to minimize the curtailment of renewable energy sources, enhance energy efficiency, and achieve faster stabilization compared to conventional strategies. In the introduction, we have added a detailed explanation of how consumer theory provides a simple yet effective modeling approach, leveraging economic principles to improve the response of ESS and PV systems to price signals. This results in a more coordinated and efficient frequency regulation strategy.

In the results analysis section, we have provided a comprehensive comparison of our proposed strategy with conventional droop and virtual inertia control methods. The analysis demonstrates that our approach avoids unnecessary PV power curtailment during over-frequency events, allowing excess energy to charge ESS for later use. This not only improves energy efficiency but also maximizes renewable energy utilization. Additionally, we have highlighted that the local updating of compensation and incentive prices ensures coordinated operation without the need for constant inter-agent communication, thus enhancing system robustness and reliability.

We believe these revisions address the reviewer's concerns by clearly articulating the key insights and advantages of integrating consumer theory-based models into primary frequency regulation strategies. The modifications provide a more detailed explanation of how our approach contributes to a more effective and sustainable power system. Thank you for your constructive comments, which have helped us improve the clarity and impact of our work. (Lines 6 to 7, 115 to 125, 128 to 129, 553 to 559, 561 to 569, 572 to 576)

Comments 6:

The following market research and related microgrid operation can be compared (not mine): 1: Distributed tri-layer risk-averse stochastic game approach for energy trading among multi-energy microgrids 2: Committed Carbon Emission Operation Region for Integrated Energy Systems: Concepts and Analyses 3: Two-stage robust operation of electricity-gas-heat integrated multi-energy microgrids considering heterogeneous uncertainties.

Response 6:

Thank you for your insightful feedback. In response to your suggestions, we have included the work titled "Distributed tri-layer risk-averse stochastic game approach for energy trading among multi-energy microgrids" in the introduction section. This work is relevant as it develops an EMS based on a three-layer market among MMG systems and solves it using game theory in a distributed way.

However, the other two papers, while proposing interesting methods for resource allocation in multi-energy microgrids, do not incorporate market modeling in their optimization processes.

Therefore, we did not include these papers in our discussion. Additionally, we have incorporated more related works in the field of market formulation and distributed optimization for EMS in power systems to provide a comprehensive overview of the current research landscape. (Lines 57 to 61)

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a novel market modeling framework for MMG systems with PVs, ESSs and non-dispatchable loads based on consumer theory models. On top of the market framework, the manuscript proposes a novel primary frequency regulation strategy. Simulation results demonstrate more stable and effective frequency response behavior for the proposed strategy. The manuscript has good novelty with embedding consumer based theory in frequency regulation market models, and is a good match with the special issue. However, there are several major gaps that need to be addressed before the manuscript is ready to be accepted.

 

Below are my general comments:

 

1. Due to the complexity of the modeling, I recommend that the authors put up a table of notations with description for all the variables and parameters used throughout the manuscript. Some of the notations are not well defined (e.g. there is no definition for \delta^k in (24), and the definition of p^{(m)k}_n is hard to interpret), and even if the notations are defined, they tend to be lost in the texts and it’s hard to find out going back and forth in the text.

 

2. Section 2.4.1: the local optimization problem (13)-(16) is derived from the centralized optimization problem (7)-(11) by decomposing over the set of agents \Omega. However, the handling of constraint (9) is missing. From section 2.4 it seems that the authors dualize the reciprocity constraint and enforce a constant dual value \alpha^k for it, but there’s a gap between problem (7)-(11) and problem (13)-(16) which may cause confusion. The authors should consider restructuring the end of section 2.3 with section 2.4 to close the gap and make the handling of constraint (9) a bit more clear.

 

3. Section 2.4.1: For equation (17), the term \alpha^k (p^{k-1}_{nm} + p^{k-1}_{mn}) is somewhat explained from the context. However, I don’t get the term for (\lambda^{k-1}_{nm} - \lambda^{k-1}_{mn}). Lambda are dual variables and thus not primal decision variables of the local optimization problem (13)-(16), and we don’t solve for them from (13)-(16). If it is desired to enforce \lambda^{k-1}_{nm} = \lambda^{k-1}_{mn} for each (m,n) pair, why not enforce \lambda^{k-1}_{nm} = \lambda^{k-1}_{mn} and do dual update (17) for just one of the dual variables? This should also help reduce the dimension of the dual space and in theory improve convergence. 

 

4. Section 2.4.2: what does the weighting factor formula (i.e. equation (24)) come from? What do the p_{nm} and p_{nl} values come from, the previous iteration? And what is \delta^k?

 

5. Is equation (28) a good assumption about ESS systems? Essentially the model implies that the energy injected by an ESS system is proportional to the price difference with respect to a base price / bid price. This doesn’t seem to be consistent with normal stakeholder behavior in an energy market clearing procedure, where stakeholder tend to sell as much energy as possible whenever the price exceeds the bid price.

 

6. Somewhat relevant to the comment above. Overall the contribution of this manuscript is not clear. I agree the manuscript proposes an interesting market scheme for MMS primary frequency response. However, it is still not clear to me the benefits of using consumer theory. I can somewhat infer the benefits by looking at the numerical results, however there’s a lack of key insights on how consumer-theory based modeling contributes to the more effective frequency regulation strategy. The manuscript will benefit from more explanations on this, from either a summary of key advantages of consumer-theory based modeling in the intro, key insights in the modeling part on how consumer-theory models contribute to a more effective strategy, or more detailed analysis in the simulation section (having all three will be very ideal). 

 

7. Sections 3 and 4 will benefit from a good visualization of the overall market scheme / EMS structure, including key stakeholders + their utility / profit functions.

 

8. Section 4.2: the authors need to provide more explanation for modeling MG as non-dispatchable agents. A few unclear parts: why is \lambda taking the max values of all prices? Would that lead to revenue inadequacy issues? Also, if we maintain max and min power values constant across all iterations, wouldn’t the power of each agent n converge to a known value since we already know the max and min bounds from the beginning, and the bounds are the same? The section needs much clarification.

 

9. The model seems much more difficult to solve than the traditional droop and virtual inertia based approach. Since primary frequency response happens in real time, it would be helpful if the authors can comment on the computational performance of the model, i.e. which hardware and software are used to solve the model, what’s the solution time / number of iterations for solving a model of which size etc. This will help evaluate the practicality and applicability of the modeling framework.

Author Response

We would like to thank for the thoughtful comments and suggestions, which have certainly helped us to improve the paper.  Below is our reply to all comments, explaining in detail the changes made to the paper to address their concerns.  All changes made in response to the comments are highlighted in red text in the revised paper.

Comments 1:

Due to the complexity of the modeling, I recommend that the authors put up a table of notations with description for all the variables and parameters used throughout the manuscript. Some of the notations are not well defined (e.g. there is no definition for in (24), and the definition of  is hard to interpret), and even if the notations are defined, they tend to be lost in the texts and it’s hard to find out going back and forth in the text.

Response 1:

Thank you for your insightful suggestion. We agree that a table of notations will significantly enhance the readability and comprehensibility of the manuscript, especially given the complexity of the modeling. We have created a comprehensive table of notations in Apendix A that includes descriptions for all the variables and parameters used throughout the manuscript. This table will help readers easily find and understand the definitions without having to search through the text.

Additionally, we have added definitions for the notations that were previously unclear, such as  in (24) and   We have ensured that these definitions are clearly presented within the context of the equations and are also included in the table of notations.

Comment 2:

Section 2.4.1: the local optimization problem (13)-(16) is derived from the centralized optimization problem (7)-(11) by decomposing over the set of agents  . However, the handling of constraint (9) is missing. From section 2.4 it seems that the authors dualize the reciprocity constraint and enforce a constant dual value  for it, but there’s a gap between problem (7)-(11) and problem (13)-(16) which may cause confusion. The authors should consider restructuring the end of section 2.3 with section 2.4 to close the gap and make the handling of constraint (9) a bit more clear.

Response 2:

Thank you for your insightful comment regarding the handling of constraint (9) in our manuscript. We appreciate the opportunity to clarify and enhance the presentation of our work. To address your concern, we have revised the end of Section 2.3 (now 2.4) and the beginning of Section 2.4 (now 2.5) for a smoother transition and clearer explanation of how the reciprocity constraint is managed by the consensus + innovation algorithm.

We have also included a new subsection on conventional consensus equations to provide foundational context, making the progression to the consensus + innovation algorithm more coherent. This restructuring ensures a better understanding of the derivation from the centralized optimization problem to the local optimization problem, closing the gap between Sections 2.3 and 2.4. (Lines 165 to 173, 205 to 217)

Comment 3:

Section 2.4.1: For equation (17), the term  is somewhat explained from the context. However, I don’t get the term for . Lambda are dual variables and thus not primal decision variables of the local optimization problem (13)-(16), and we don’t solve for them from (13)-(16). If it is desired to enforce  for each (m,n) pair, why not enforce  and do dual update (17) for just one of the dual variables? This should also help reduce the dimension of the dual space and in theory improve convergence. 

Response 3:

Thank you for your insightful comment regarding the dual update process in equation (17) (now equation 19). We appreciate the opportunity to clarify and improve the presentation of our work.

While enforcing   directly could theoretically reduce the dimension of the dual space, it is not feasible to enforce price equality because we are proposing a P2P negotiation market scheme. In this scheme, agents must agree on both the price and the traded power, which can temporarily differ before converging. This is addressed through the consensus algorithm.

With the term  we ensure that prices are negotiated iteratively and is used to promote price convergence among agents through iterations, ensuring that eventually, the negotiation prices equalize. This approach allows agents to adjust their prices independently until a consensus is reached, which is fundamental in a P2P market.

To address this concern, we have revised the text in Section 2.4.1 (now 2.5.1) to provide a clearer explanation of the role of the consensus term and its importance in the negotiation process. Additionally, we have emphasized how the innovation term ensures compliance with the power reciprocity constraint, contributing to the overall stability and accuracy of the power exchange within the multi-agent system. (Lines 232 to 235, 239 to 241)

Comment 4:

Section 2.4.2: what does the weighting factor formula (i.e. equation (24)) come from? What do the  and  values come from, the previous iteration? And what is ?

Response 4:

The weighting factor formula in equation (24) (now equation 26) is designed to ensure proportional updates based on the power exchanged between agents in the previous iteration.

• Weighting Factor Formula: The formula ​ is derived to distribute the adjustment proportionally across all connected agents. This ensures that the update of the power exchanged considers the relative magnitudes of power flows from the previous iteration, thereby reflecting the actual operational conditions more accurately.
• The terms the and  refer to the power values from the previous iteration . We have rewritten equation (24) (now equation 26) to explicitly indicate that these values come from the previous iteration.
• The parameter is a small positive constant introduced to avoid division by zero and to ensure numerical stability in the algorithm. It acts as a stabilizing factor, particularly in the early iterations when power exchanges might be very small or zero, thereby preventing instability or errors in the calculations. We have included the explanation of this parameter in the formulation of the algorithm.

(Lines 250 to 268)

Comment 5:

Is equation (28) a good assumption about ESS systems? Essentially the model implies that the energy injected by an ESS system is proportional to the price difference with respect to a base price / bid price. This doesn’t seem to be consistent with normal stakeholder behavior in an energy market clearing procedure, where stakeholder tend to sell as much energy as possible whenever the price exceeds the bid price.

Response 5:

We appreciate the reviewer's insightful comment regarding equation (28) (now equation 30) and its representation of energy storage systems (ESS) behavior.

The model in equation (28) (now equation 30) represents a simplified approach to capture the dynamic response of ESS systems within the peer-to-peer (P2P) market framework. The proportional relationship between the injected energy and the price difference is designed to reflect the responsiveness of ESS systems to market signals. While it is true that in traditional energy market clearing procedures, stakeholders aim to maximize their energy sales when prices exceed their bid prices, the proposed model accounts for strategic behavior of ESS systems. Stakeholders may not always inject their maximum capacity even when prices are favorable due to factors such as state-of-charge limitations, degradation concerns, the need to reserve capacity for future contingencies, or the opportunity cost of waiting for prices to increase in future time intervals.

Additionally, this modeling approach helps incorporate new incentive prices that can serve as income for stakeholders for the provision of ancillary services, such as primary frequency regulation.

We acknowledge that the model can be further refined to incorporate more detailed stakeholder behaviors and market dynamics. Future work could involve integrating more complex decision-making processes for ESS operators.

However, it is important to note that the behavior of selling as much energy as possible whenever the price exceeds the bid price can be obtained when the elasticity associated with the ESS is high.

Comment 6:

Somewhat relevant to the comment above. Overall the contribution of this manuscript is not clear. I agree the manuscript proposes an interesting market scheme for MMS primary frequency response. However, it is still not clear to me the benefits of using consumer theory. I can somewhat infer the benefits by looking at the numerical results, however there’s a lack of key insights on how consumer-theory based modeling contributes to the more effective frequency regulation strategy. The manuscript will benefit from more explanations on this, from either a summary of key advantages of consumer-theory based modeling in the intro, key insights in the modeling part on how consumer-theory models contribute to a more effective strategy, or more detailed analysis in the simulation section (having all three will be very ideal). 

Response 6:

We understand the need to clarify the contributions and advantages of using consumer theory in our proposed primary frequency regulation strategy. To address this, we have made several revisions throughout the manuscript, including the abstract, introduction, and results analysis sections, to better highlight the benefits of our approach.
The abstract now succinctly summarizes the advantages of the proposed method, emphasizing its ability to minimize the curtailment of renewable energy sources, enhance energy efficiency, and achieve faster stabilization compared to conventional strategies. In the introduction, we have added a detailed explanation of how consumer theory provides a simple yet effective modeling approach, leveraging economic principles to improve the response of ESS and PV systems to price signals. This results in a more coordinated and efficient frequency regulation strategy.

In the results analysis section, we have provided a comprehensive comparison of our proposed strategy with conventional droop and virtual inertia control methods. The analysis demonstrates that our approach avoids unnecessary PV power curtailment during over-frequency events, allowing excess energy to charge ESS for later use. This not only improves energy efficiency but also maximizes renewable energy utilization. Additionally, we have highlighted that the local updating of compensation and incentive prices ensures coordinated operation without the need for constant inter-agent communication, thus enhancing system robustness and reliability.

We believe these revisions address the reviewer's concerns by clearly articulating the key insights and advantages of integrating consumer theory-based models into primary frequency regulation strategies. The modifications provide a more detailed explanation of how our approach contributes to a more effective and sustainable power system. Thank you for your constructive comments, which have helped us improve the clarity and impact of our work. (Lines 6 to 7, 115 to 125, 128 to 129, 553 to 559, 561 to 569, 572 to 576)

Comment 7:

Sections 3 and 4 will benefit from a good visualization of the overall market scheme / EMS structure, including key stakeholders + their utility / profit functions.

Response 7:

Thank you for your constructive feedback regarding the visualization of the overall market scheme and the EMS structure in Sections 3 and 4. We have taken your suggestion into account and have reorganized these sections to enhance clarity. The revised sections now include a detailed description of the EMS and the P2P market, clearly illustrating the roles of key stakeholders, including conventional generators, loads, and microgrids. (Lines 290 to 299, 344 to 358)

Comment 8:

Section 4.2: the authors need to provide more explanation for modeling MG as non-dispatchable agents. A few unclear parts: why is  taking the max values of all prices? Would that lead to revenue inadequacy issues? Also, if we maintain max and min power values constant across all iterations, wouldn’t the power of each agent n converge to a known value since we already know the max and min bounds from the beginning, and the bounds are the same? The section needs much clarification.

Response 8:

Thank you for your valuable feedback on Section 4.2. We have rewritten this section to clarify the process of integrating MGs into the P2P market and to address your concerns regarding the modeling of MGs as non-dispatchable agents, the rationale for using the maximum value of all prices (), and the updates of maximum and minimum power values.

In this revised section, MGs are modeled as must-take agents, meaning their maximum and minimum total power exchanged are the same but vary throughout the negotiation process with their neighbors. This modeling approach captures the internal optimization processes and constraints of MGs, which determine their total power output.

We set to the maximum value of all prices traded with neighboring agents for each iteration. This ensures MGs respond to the highest price signals within their neighborhood, incentivizing them to generate more power or consume less when the market price is high. The rationale for selecting the maximum negotiated price is that it reflects the most favorable market conditions, ensuring the economic viability of MG participation. If an MG is consuming energy, the maximum price represents the price at which it satisfies its total energy demand. Conversely, if it is exporting energy, it corresponds to the most favorable market condition with its neighbors. Additionally, once the market converges, the marketing prices among different agents converge to the same value, making it indistinct to select the maximum marketing price between agents.

Furthermore, for agents that do not belong to the MG set and are dispatchable, the maximum and minimum power values are updated independently and are not required to be the same but remain constant throughout the iterations.

(Lines 378 to 384, 386 to 404, 410 to 411)

Comment 9:

The model seems much more difficult to solve than the traditional droop and virtual inertia-based approach. Since primary frequency response happens in real time, it would be helpful if the authors can comment on the computational performance of the model, i.e. which hardware and software are used to solve the model, what’s the solution time / number of iterations for solving a model of which size etc. This will help evaluate the practicality and applicability of the modeling framework.

Response 9:

We have included in Section 6.1 a detailed description of the hardware used to execute the algorithm and reported the solution time and number of iterations for solving the multiagent system. While the proposed model appears more complex than traditional droop and virtual inertia-based approaches, primary frequency regulation is still performed locally by each component of the MG, ensuring quick and effective response times. The EMS operates as a real-time P2P market, establishing operational conditions and trading prices for primary frequency regulation during each time interval . Once these reference values are determined, the updates to the incentive and compensation prices are performed locally by each system through real-time frequency measurements. This ensures that primary frequency regulation does not impose a significant computational load on the local controllers of the ESS and PV systems, allowing it to operate efficiently within real-time constraints.

(Lines 514 to 520)

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript has significant improved after the first revision and I believe it is in a good form for publication.