Research on Resource Utilization of Bi-Level Non-Cooperative Game Systems Based on Unit Resource Return

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The study addresses a critical issue in power market optimization, particularly resource utilization and profitability of generation units. The game-theoretic approach aligns well with real-world challenges in energy market competition. This game-theoretic model for power market optimization is well-formulated and innovative. For that reason, I recommend publishing this paper with with minor revisions to improve clarity.

1. Please in abstract include information about scientific and practical contributions of the paper
2. Address how the model fits into existing market regulations (e.g., carbon pricing, renewable energy targets, capacity markets, demand response programs). It can be part of chapter 4 or 5.
3. Discuss potential limitations such as gaming the system, strategic bidding, or market power concentration. It can be in part Conclusion where you state limitation of the model.
4. Strengthen the conclusion by summarizing key takeaways and better outlining potential extensions of the model.
5. Please in the Conclusion clearly state scientific and practical contribution of the paper.

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents a bi-level non-cooperative game model for resource utilization in electricity markets. The model is based on Unit Resource Return (URR) and aims to balance the competing interests of different power generation units (wind, thermal, and photovoltaic) with the Independent System Operator (ISO). The bi-level structure consists of: Upper-level game (The ISO, acting as a leader, determines power allocation and pricing to maximize system-wide efficiency and fair competition); and the Lower-level game (Generation units act as self-interested followers, optimizing their bidding strategies to maximize their own profit). The model incorporates Nash equilibrium and employs Particle Swarm Optimization (PSO) and CPLEX solvers to achieve an optimal balance between cost reduction and resource efficiency.

The game-theoretic framework is well delineated, with an appropriate structure, Nash equilibrium conditions, and fairness considerations. However, two key aspects could be addressed by the authors:

- Could there be room for partial cooperation or mixed strategies?

- The model assumes static bidding strategies, but real markets are subject to external shocks (e.g., fuel price fluctuations, policy changes) that influence decisions dynamically. A sensitivity analysis could enhance the model's robustness.

Other points:

- The model's assumptions require further discussion. Choices such as treating all units as price-takers, ignoring transmission constraints and congestion effects, and the absence of regulatory frameworks should be explicitly justified.

- The weighting mechanism in the ISO's objective function lacks proper justification.

- The simulation does not explicitly mention real-world data calibration. The chosen values are vaguely justified. A table listing all data used in the model, with a column indicating data sources, would improve transparency.

- Captions for tables and figures need improvement.

- In Figure 6, how do the different rates translate into economic or operational benefits?

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Optimal allocation of the amounts of electricity to generate to distributed generation units has been a classical problem and is still an interesting issue. To determine an appropriate amount of electricity that each generation unit supplies as well as the price for purchasing a unit amount of electricity to pay to the generation unit, it seems that this paper tried to construct a non-cooperative game and find a Nash equilibrium. The topic of this paper is interesting. For the publication of this paper, however, major revisions should be made in a large scale.

A game was not properly built in the paper. Players (or participants) and strategies should be clearly specified. Payoff (or profit) should be clearly stated when each player uses a certain strategy.

One of the important measures in the paper is the unit resource return, which was defined as (M_i - I_i)/D_i in Equation (2). What is M_i? What is I_i? What is D_i? To use the unit resource return, it should be clearly defined.

In Equations (3) and (4), three types of the unit resource return were given without explanation. How did you get it?

Another important measure is the overall system resource utilization function given in Equation (5), which was defined as the sum of unit resource returns of generation units. Why was it defined as the sum of unit resource returns?

URR_i is polysemous in the paper. It means either URR of generation unit i or URR of generation unit of type i. The notation should be changed not to invoke such a confusion.

Equation (6) says "max x_i = ...". What is x_i? With respect to what do you maximize x_i?

Equation (11) says "max F_ISO = ...". What is F_ISO? With respect to what do you maximize F_ISO?

Mathematical notations are confusing and unfriendly to readers.

In Section 5, an algorithm to find a Nash equilibrium is given. You should reveal the condition for the existence of a Nash equilibrium. Also, you should prove that the proposed algorithm definitely finds a Nash equilibrium, if exists.

In Section 6, Tables 1 and 2 show that the values of some parameters used in case studies. How did you get the values?

The references were not cited in order. References [24] and [26] were not referred in the main body of the paper.

In writing references, initialization, capitalization, etc should be consistently kept.          

Comments on the Quality of English Language

Writing should be improved.

Author Response

Please see the attachment.

Author Response File: Author Response.docx