A Stackelberg Game-Based Joint Clearing Model for Pumped Storage Participation in Multi-Tier Electricity Markets

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposes a bi-level optimization model based on Stackelberg game theory to address the strategic interactions and constraints faced by pumped storage power stations (PSPSs) participating in joint clearing across multi-level electricity markets amid China’s power market reform. The model aims to guide PSPSs in achieving flexible dispatch and economic operation, enhance their profitability through coordinated market participation, reduce overall system costs, and improve dispatch efficiency. The study provides quantitative decision-making support for PSPSs participation in multi-level spot markets and offers valuable insights for optimal energy storage deployment and market mechanism improvement. However, before this paper can be considered for publication, the following issues should be addressed:

1. Although the IEEE 30-bus system is used as a case study, the simulation environment is relatively simplified. It is recommended to validate the model using real-world electricity market data or specific regional market data in China to enhance its practical relevance and persuasiveness.
2. The current simulation only considers pumped storage and thermal power units, without including intermittent renewable energy sources such as wind and solar. It is suggested that the authors at least discuss the potential for extending the model to such scenarios in future work.
3. Several symbols in the equations lack unit annotations. It is recommended to include unit descriptions for all symbols to improve reader comprehension.
4. While the solution process of the model is clearly illustrated in Figure 2, the discussion on convergence and the uniqueness of the solution is insufficient. The authors are advised to explicitly address these aspects.
5. The English grammar needs improvement. Some sentences are overly wordy; for instance, Lines 19–21 in the Abstract could be simplified to enhance readability. The authors should carefully review and revise the manuscript for clarity and conciseness.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The proposed model study for pumped storage participation in multi-tier electricity markets is an interesting concept to be investigated.

The study presents some good conclusive results.

The model could be extended to include additional services such as spinning reserve, etc., which have already been mentioned by authors as their future work.

The authors have written the paper very well.

However, the novelty and the comparative advantage of the proposed model over existing models should be emphasized in the introduction section and while discussing the results.

Other than that, only proofreading remains to improve the quality of written text.

 

Specific comments

• What is the main question addressed by the research?

To address the limited flexibility of pumped storage power stations (PSPSs) under hierarchical clearing of energy and ancillary service markets.

• Do you consider the topic original or relevant to the field? Does it address a specific gap in the field? Please also explain why this is/ is not the case. It is original, as I did not find implementation of a bi-level Stackelberg game model for PSPSs participating in joint clearing of energy and frequency regulation markets in literature.
• What does it add to the subject area compared with other published
material? They developed the model of the Coordinated Multi-Market Trading Mechanism for PSPSs.   • What specific improvements should the authors consider regarding the
methodology? They do not need to change the methodology. They only need to compare the results with already existing models.
• Are the conclusions consistent with the evidence and arguments presented
and do they address the main question posed? Please also explain why this
is/is not the case. The conclusion is consistent with their arguments discussed in the paper, as they have achieved the results in the case study section. They have presented the conclusion based on those results.
• Any additional comments on the tables and figures. There are no comments on tables and figures.  

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

(1)“Ancillary” is occasionally misspelled as “Ancilary”.

(2) The paper did not explicitly mention the operational costs or penalties for PSPS ramping or switch delay between pump/generation modes.

(3) The current model is deterministic, but real-world market participation involves uncertainty (e.g., renewable forecasts, frequency deviations). This limitation is not discussed.

(4) Figures 4–10 lack uniform axes labels, legends, and sometimes have units missing.

(5)Figures 9 and 10 show negative power for energy market award — needs clarification on whether negative means “pumping”.

(6)In Figure 8, there is a prominent peak, and the authors need to discuss this condition in detail.

(7)In Figures 6 and 7, the non-uniform distribution of power with time should be discussed in detail.

(8)A large peak in Figure 5 should be discussed.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have answered all my questions, and I read the paper without having any further questions.