1. Introduction
Approximately two years following the announcement of China’s 14th Five-Year Plan for a Modernized Energy System, the transition to low-carbon energy in the sector has accelerated. In 2023, for the first time, the total installed capacity of non-fossil energy units surpassed that of traditional fossil energy units, signifying the Chinese government’s commitment to an orderly transition to a low-carbon power sector, with renewable energy generation assuming a pivotal role. With the growing prioritization of renewable energy consumption, traditional power generators, especially thermal power plants within the industry, are actively exploring alternative pathways [
1,
2,
3].
Currently, three prevalent approaches are recognized for the transformation of thermal power plants: investment in carbon capture, utilization, and storage (CCUS) technologies, adoption of energy storage services, and retrofitting of existing thermal units for enhanced flexibility [
4]. The predominant focus of the current literature is on CCUS for the transformation of thermal power enterprises [
5,
6]. In China, the industrial implementation of CCUS incurs significant costs due to its delayed initiation, requiring mature business models and policy incentives for its favorable development [
7]. Geographical location poses an additional constraint to the large-scale industrialization of CCUS. Regions that have substantial potential for advancing CCUS technology include Northeast China, North China, and Northwest China [
5,
8]. Regarding transformation and investment in the energy storage sector, the conversion of coal-fired power plants into thermal storage facilities has garnered significant attention within the industry [
9,
10]; however, their power losses present a notable challenge [
11]. In comparison to the aforementioned technologies, the flexibility conversion of coal-fired power plants features mature technology, a brief construction period, and minimal investment costs. Research indicates that retrofitting the fuel supply system, boiler, flue gas treatment system, and thermo-electrolytic coupling system of coal-fired power units represents an effective approach for enhancing unit flexibility [
12,
13,
14]. Enhanced flexibility in coal-fired power units can bolster renewable energy consumption, indirectly mitigate CO
2 emissions, and foster the sustainable growth of the renewable energy sector.
However, a significant proportion of renewable energy consumption within the power system is poised to reduce the revenue of thermal power enterprises in the power market. Modifying the units can enhance the influence of thermal power enterprises in the capacity and standby markets, thereby bolstering their competitiveness in the power market. Nevertheless, ongoing research on the flexibility of thermal power plants predominantly focuses on process enhancement and optimal control. Given that China’s existing power trading operates under a market model, its benefits depend not only on the decisions made by individual companies but also on the strategic actions of peers. Currently, there is a lack of income assessment and prediction for the application diffusion of this technology in the competitive multiplayer environment of the power market, following the flexible transformation of thermal power enterprises.
Evolutionary gaming in complex networks is a research domain that combines complex network theory and evolutionary game theory (EGT) to investigate the dynamics of individual interactions and evolution within network structures [
15]. Studies in this field aim to elucidate the influence of network topology on individual strategic decisions, game outcomes, and the evolution of node connections. The significant advantage of complex network evolutionary games lies in their ability to analyze how changes in individual strategies affect the propensity of the current strategy to diffuse throughout the group, making it a pivotal tool for modeling multiple intelligences.
Drawing upon the identified limitations of current research, this paper integrates the complex network evolutionary game model with the emerging trend of enhanced power system flexibility to investigate the potential diffusion of thermal power-unit flexibility transformation technology among supply-side thermal power enterprises. This study aims to address the gap in the literature by examining how the adoption of flexibility transformation technology among thermal power enterprises is influenced by network dynamics and the evolving landscape of power system flexibility. This paper is innovative in the following three aspects:
- (1)
Initially, there exists a dearth of research within the industry concerning the extent to which thermal unit-flexibility technologies can penetrate among groups of thermal power enterprises. Through investigating these matters, it becomes feasible to conduct an anticipated evaluation of the thermal power enterprises poised for transformation and to offer guidance for the development of the enterprise group.
- (2)
Diverging from previous approaches that employ evolutionary game models to explore multi-body interest interaction issues in the power industry, this paper integrates complex network theory and evolutionary game theory for modeling research. Additionally, utilizing complex network theory, the thermal power enterprise group is characterized by heterogeneity, and dynamic network modeling is employed to simulate the evolving game processes.
- (3)
Building upon the examination of thermal power-unit flexibility transformation technology, this paper explores the diffusion trajectory of this technology among thermal power enterprises. Through the establishment of varied initial strategies for the nodes, the paper simulates the initial distribution of the technology among the thermal power enterprise group and investigates the dynamic diffusion trend of flexibility transformation technology throughout the entire group under this scenario.
The rest of this article is organized as follows:
Section 2 reviews the literature.
Section 3 analyzes the income composition of thermal power-generation enterprises and establishes both the evolutionary game model and the complex network evolutionary game model. In
Section 4, initial parameters are set, and numerical simulations are conducted to discuss the factors affecting technology diffusion from the perspectives of thermal power-generation enterprises and the power market, respectively. Conclusions and policy recommendations are presented in
Section 5.
3. Methodology
3.1. Revenue and Cost of Thermal Power Enterprises
This paper assumes that each thermal power plant treats one unit as an individual unit. The minimum output of all units is set at 60 percent of the unit’s rated capacity before the implementation of flexibility modification technology, and this minimum output decreases to 30 percent after the implementation of this technology. Moreover, due to challenges in estimating the output of thermal units, it is presumed that unit output remains fixed at 30 percent of the unit’s rated capacity during deep peak-shaving periods, while the unit operates at full load during non-deep peak-shaving periods.
3.1.1. Regular Operation Generation of Income
Generally, the regular operation generation of income
is defined as follows:
where
is the installed rated capacity of the thermal power plant and
is the annual generation utilization hour, representing the equivalent hours of operation of the generating unit in a year based on the unit’s rated capacity.
is the feed-in tariff for normal generation.
3.1.2. Deep Peak-Shaving Benefits
The deep peak-shaving benefits includes two parts
and
, which are defined as
where
is the annual hours of peaking participation,
is the peaking feed-in tariff,
is the depth of peaking,
is the current thermal plant’s share of the benefits from neighboring plants that do not participate in peaking, and
represents the additional hours of peaking that are shared.
3.1.3. Regular Operation Generation Cost
The regular operation generation cost is denoted by
, defined as follows:
where
is the hourly generation cost of thermal power plants, and
,
, and
are the unit generation factors.
3.1.4. Deep Peak-Shaving Cost
The deep peak-shaving costs are defined as follows:
where
is the generation cost in the deep peak-shaving stage,
is the unit loss cost in the deep peak-shaving stage,
is the minimum output of the deep peak regulation without combustion support,
is the minimum output of the deep peak regulation with combustion support,
is the loss coefficient,
is the unit purchase cost, which is assumed to be equal to the installed cost in this paper,
is the number of weeks of the rotor fracturing cycle, and
is the cost of oil injection in the deep peaking stage.
3.1.5. Annual Upgrade Cost of Thermal Power Units
According to the literature [
44], the cost of flexible transformation of thermal power units is related to the minimum output levels before and after the transformation. In this paper, the minimum output before the transformation of the unit is set at 60% of the rated capacity, and the minimum output after the transformation is set at 30%. Based on this, the annual upgrade cost of thermal power units is defined as follows:
where
is the annualized rate (the calculation method is in
Appendix A) and
is the cost per MW of upgrade.
3.2. Assumptions
In the research process, the following three model assumptions are established, based on actual scenarios.
Assumption 1. Thermal power enterprises in the market are categorized into three groups: large enterprises with a small number but significant influence, medium-sized enterprises with a moderate number and volume, and small enterprises with the largest number but limited influence. During the game process, two enterprises are randomly selected from these groups to engage in the game.
Assumption 2. Thermal power firms have two strategic options: to either implement flexible transformation of the unit or not. The probability of implementing this technology is denoted as, while the probability of not adopting it is . Revenue sources for firms opting not to implement flexibility transformation technology include standard revenue from electricity sales, along with revenue from participation in peaking services. Conversely, revenue for firms choosing not to employ flexibility transformation technology solely comprises revenue from electricity sales.
Assumption 3. The escalating demand for deep peak shaving is spurred by China’s persistent growth in electricity demand and renewable energy power. This paper postulates a 1.5% annual increase in the duration of thermal power generation units engaged in deep peak shaving. The parameter is computed based on the neighbors of each node in the network. The symbol represents the intensity of government subsidies, while signifies the penalty factor.
3.3. Evolutionary Game Model
The evolutionary game model of thermal power enterprises is established based on the payoff distribution matrix, which is demonstrated in
Table 3.
,
,
,
,
,
,
, and
.
In Scenario 1, both Thermal Power Company A (defined and abbreviated as Group A) and Thermal Power Company B (defined and abbreviated as Group B) opt to carry out the flexibility transformation of the unit. As a result, both players receive the benefits of normal power sales, along with additional benefits from participation in peaking services, as detailed in Formula (12):
In Scenario 2, Group A decides to implement the flexibility transformation technology, whereas Group B opts not to implement it. Consequently, Group A receives normal revenue from electricity sales and revenue from participation in peaking services. Furthermore, A will share a portion of the peaking share borne by Group B, as detailed in
Appendix B. On the other hand, Group B solely receives normal revenue from electricity generation, as shown in Formula (13):
In Scenario 3, Group A chooses not to carry out the flexibility transformation of the unit, while Group B decides to implement it. Consequently, Group A receives only normal generation revenues. Conversely, Group B obtains normal revenues from electricity sales and participation in peaking services. Additionally, Group B will share a portion of Group A’s peaking share, as outlined in
Appendix B, as shown in Formula (14):
In Scenario 4, if both playing parties, Group A and Group B, opt not to implement the flexibility transformation of the unit, they will earn solely normal power generation revenue. However, neither party will cooperate in promoting the consumption of renewable energy, leading to a certain degree of penalty for both, as shown in Formula (15):
Based on
Table 3, the benefits to Group A of choosing to use the flexibility transformation technology are
The benefits to Group A of not using the flexibility modification technology are
The replication dynamic equations for Group A and Group B can be obtained as follows:
The Jacobi matrix formed by the two parties is as follows:
where
As shown in
Table 4, taking the ideal equilibrium state
,
as an example, according to the stability of equilibrium points [
45], at this time the Jacobi matrix
J must satisfy det (
J) > 0, tr (
J) < 0,
From Formula (21), it can be seen that thermal power plants will use flexibility transformation technology when the benefits of participating in deep peak shaving are greater than the costs.
3.4. Complex-Network Evolutionary Game Model
The group network of thermal utilities is represented by an undirected network , where is the set of nodes of G representing the thermal utilities and E is the set of edges of G representing the network of relationships among the thermal utilities. Two strategies are randomly assigned on the network G: one employing the flexibility transformation technique and the other not. It is important to note that in practice, the payoffs of enterprises are not necessarily related to the number of neighbors. Therefore, in this model, the payoffs of thermal power enterprises are calculated using a group interaction mode.
In each game, each firm first calculates its own payoff and then randomly selects a neighbor from whom to learn a strategy. The strategy update rules are applied using the Fermi rule [
46], as demonstrated below:
In Formula (22), and are the payoffs of the thermal power plants and at time , and are the strategies of the thermal power plants A and B, respectively, and is the strategy transfer probability. Here, is the interference factor, which represents the intensity of irrationality in thermal power enterprises’ decisions.
When, the Fermi rule mirrors dynamic replication equations, wherein a firm only learns a neighbor’s strategy if that strategy’s payoff is higher than its own.
When , the firm is influenced by irrational factors, learning not only strategies with higher payoffs than its own, but also those with lower payoffs.
As approaches infinity, firms will randomly learn their neighbors’ strategies, irrespective of the payoffs. Considering the practical situation, is 0.1 in this paper.
In the process of flexibility transformation-technology diffusion, the relationships between thermal power companies will also evolve. To simulate this evolution process, this paper introduces a dynamic network-update mechanism where a pair of nodes is first randomly selected, the connection between them is severed, and subsequently, one of the nodes from this pair is randomly chosen to reconnect with other nodes, excluding itself, with a certain probability. Here, the probability of reconnecting severed edges is
where
is the probability that node
is connected to node
, and
is the current payoff of node
.
4. Simulation and Discussion
4.1. Data and Parameters
In this section, we analyze the impacts of various factors on the diffusion of flexibility transformation technologies from the perspectives of thermal power enterprise groups and power markets. The experimental simulation software used is Python version 3.9. Some of the experimental parameters are listed in
Table 5 (thermal power-unit parameters are demonstrated in
Appendix C), and the data sources include the
China Electric Power Statistical Yearbook 2022 and the National Bureau of Statistics of China.
When differentiating the heterogeneity of thermal power enterprise groups, this paper employs complex network theory. Nodes in the network are sorted based on their degrees. Those with node degree values in the top 10% are defined as large-sized enterprises (denoted by “L”), those with values between the top 10% and top 40% are defined as medium-sized enterprises (denoted by “M”), and the rest are considered small enterprises (denoted by “S”). Additionally, this paper sets the iteration step of the evolutionary game as
and the total number of iterations as 100. Considering the potential impact of random factors on each simulation experiment, 500 experiments were conducted for each part of the experimental results, and the average value was calculated as the final result. The evolutionary game flow of complex networks discussed in this paper is shown in
Appendix D.
4.2. The Effect of Network Structure on Diffusion
Firstly, to investigate the impact of market environment diversity and complexity on thermal power enterprises’ implementation of unit flexibility reform, we establish two market scenarios for simulation experiments.
Scenario I: In a situation of information asymmetry, the leading enterprise exerts significant influence and can impact the decisions of lower-level enterprises. The simulation experiment is conducted based on a scale-free network with a degree of 2.
Scenario II: In this scenario, individual differences are minimal, and the flow of information is high. Head firms are unable to influence lower-level firms. The experiment is conducted based on a small-world network with a degree of 2.
The simulation results are shown in
Figure 2: in Scenario I, the circulation path of information dissemination is relatively linear. The strategic decisions of the leading firms profoundly influence the behavior of the following firms, resulting in a consistently high growth rate during the initial 80 times of iterations. By the 100th iteration, the diffusion rate of thermal power-unit flexibility transformation technology approaches 100%. This suggests that in an oligopolistic market with asymmetric information, where firms’ decisions are dominated by the leading firms, technology transformations are more likely to diffuse. In contrast, in Scenario II, the diffusion of this technology is relatively slow, with a consistently low diffusion rate. The final diffusion rate is 76.6%, which is comparable to the results observed during the middle iterations of Scenario I but significantly lower than the final results of Scenario I.
After the reform of China’s electricity system, the flow of information among different enterprises has significantly accelerated. Therefore, this will better reflect the effects of technology diffusion in the actual market environment and provide valuable guidance for future policy and market strategies.
4.3. The Influence of Network Average Degree on Diffusion
In our previous experiments, we conducted simulations using a network with an average degree of 2. To further investigate the impact of the network’s average degree on diffusion effects, we conducted additional analyses using small-world networks. We generated small-world networks with average degrees of 2, 4, 6, and 8 for our game experiments. The simulation results are shown in
Figure 3, with an average degree of 2; the diffusion process is slow, due to the network’s low connectivity, resulting in a final diffusion rate of the thermal power-unit flexibility transformation technology of approximately 76.6%, indicating a limited diffusion effect. With an average degree increased to 4, the connectivity between network nodes improves. By the 60th iteration step, the overall diffusion rate reaches a level comparable to the final result observed at an average degree of 2, with a final diffusion rate of 86.6%. With average degrees of 6 and 8, respectively, the iterations required to reach a 70% diffusion rate are
, resulting in final diffusion rates of 94.5% and 96.4%, respectively. These results demonstrate that as the connectivity of the small-world network increases, the number of neighboring nodes also increases, enhancing the degree of information flow. Consequently, more thermal power companies observe and actively adopt flexibility transformation technology, leading to broader diffusion of the technology.
Therefore, we conclude that enhancing the degree of information dissemination and technology exchange among thermal power enterprises will facilitate the application and development of flexibility transformation technology for thermal power units. Governments and related departments should encourage and support information exchange and technology cooperation among thermal power enterprises to foster industry development and progress.
4.4. The Influence of Different Initial Application Groups on Diffusion
In the preceding section, thermal power enterprises initially adopting flexible transformation technology were randomly selected, and the distribution of enterprises choosing to implement unit flexibility transformation remained relatively stable across different stages. To investigate the impact of a specific propagation path on diffusion rate, we conducted a comparative study in this section by setting a designated node at the initial moment. The adoption target for the flexible transformation-technology strategy includes the entire small enterprise group, the entire medium-sized enterprise group, the entire large enterprise group, and a mixed group of large and medium-sized enterprises with an initial adoption ratio of 30%.
The experiment reveals that technology diffusion driven by different types of enterprise groups at the initial moment results in varying final diffusion effects. As illustrated in
Figure 4, when small enterprises are initially targeted for adopting flexible transformation technology, the final diffusion rate decreases to 41.7%. Conversely, when the initial adoption target includes the entire group of medium-sized enterprises, all large enterprises, and the mixed group of large and medium-sized enterprises with an initial adoption ratio of 30%, the diffusion effect significantly improves to 95.2%, 89.9%, and 99.5%, respectively. The research demonstrates that the differential impact of various types of enterprise groups on promoting technology diffusion at the initial moment can be attributed to their specific roles and influence within the group structure.
Despite the relatively large scale of small enterprises, their limited risk tolerance and uncertain outcomes lead to a cautious, wait-and-see approach toward the benefits of flexible transformation technology. Consequently, they are unable to drive widespread adoption of flexible transformation technology throughout the thermal power enterprise group, resulting in a relatively poor overall final diffusion rate. When targeting the entire group of medium-sized enterprises for flexible transformation-technology adoption, their scale and resource advantages contribute to a more stable technology diffusion process.
Therefore, in a controlled experiment, when the initial adoption proportion is 30% for the mixed group of large and medium-sized enterprises, the diffusion effect is optimal, achieving a diffusion depth of 98%. In developing future flexible technology-diffusion strategies for thermal power units, we recommend comprehensive consideration of the characteristics of different types of enterprise groups. Large and medium-sized thermal power enterprises should take the lead in promoting technology diffusion to achieve more optimal outcomes. Such meticulous strategy formulation will effectively promote the dissemination and application of technology in thermal power enterprises.
4.5. Sensitivity Analysis
4.5.1. The Impact of the Deep Peak-Shaving Compensation Electricity Tariff on Diffusion
The deep peak-shaving compensation tariff holds a crucial position in the current power market, as the primary source of income for thermal power enterprises engaging in deep peaking. This compensation mechanism not only ensures a stable income for thermal power enterprises, but also incentivizes them to invest in the construction and enhancement of their peaking capacity. Numerical simulation verification is conducted in this section to examine the impact of deep peak-shaving compensation tariffs on the flexibility transformation of thermal power units. The parameter settings remain unchanged, except for
. Under two different initial application atmospheres,
is set to 400 CNY/MW, 450 CNY/MW, 500 CNY/MW, 550 CNY/MW, 600 CNY/MW, 750 CNY/MW, and 900 CNY/MW, respectively, to conduct a sensitivity analysis of the deep-peaking tariff.
Figure 5 indicates that at a deep-peaking compensation tariff of 400 CNY/MW, thermal power enterprises in the low initial application atmosphere maintain a conservative approach to unit flexibility transformation, resulting in a low overall application diffusion level. In the high initial-application atmosphere, the total diffusion rate drops to 39.1%. With the compensation tariff increasing to 450 CNY/MW, the overall diffusion rate rises to 34.8% in the low initial-application atmosphere and 59.6% in the high initial-application atmosphere, yet it remains insufficient to prompt most enterprises in the group to undertake the transformation. With
increasing to 500 CNY/MW, the final total diffusion rates in the two scenarios are 81.5% and 88.0%, respectively, both significantly higher than the initial period. Beyond a compensation tariff of 550 CNY/MW, its increase has a more substantial impact on the overall diffusion level in the medium term than in the late period, with the final marginal benefit gradually diminishing. Thus, the increase in the deep-peaking compensation tariff is likely to incentivize thermal power enterprises to prioritize the reform in flexibility of their units. As the deep-peaking compensation tariff increases, the overall diffusion rate increases, albeit at a diminishing rate once the tariff surpasses a certain threshold.
4.5.2. The Impact of Varying Initial-Application Ratios on Diffusion
The initial transformation ratio of thermal power-unit flexibility transformation represents the level of acceptance of this technology within the thermal power enterprise community. Investigating the initial transformation ratio that can promote the diffusion of thermal unit flexibility-transformation technology is the objective of this inquiry. This section builds upon the findings of the previous section to separately examine the impacts of varying initial transformation ratios on the incentive of the thermal power enterprise group to undertake unit flexibility transformation under two distinct degrees of deep peak-shaving compensation tariffs. As shown in
Figure 6, with the deep peak compensation tariff set at
, the final diffusion rates corresponding to initial transformation ratios ranging from 10% to 50% are 11.3%, 22.6%, 27.8%, 31.6%, and 34.8%, respectively. The total diffusion change consistently exhibits a decreasing trend, regardless of the initial transformation ratio, as depicted in
Figure 6. Under the high compensation tariff
, as the group transformation ratio increases in the initial stage of the flexibility transformation technology, the final diffusion percentages are 78.7%, 85.8%, 89.7%, 91.7%, and 96.1%, respectively, with a notable increase in diffusion rate in the middle stage. In the low-depth peak-compensation-tariff environment, enhancing the adoption atmosphere of flexibility transformation technology within the group of thermal power enterprises does not improve the technology’s diffusion rate; instead, the overall trend is decreasing. In the high-depth peak-compensation-tariff environment, fostering an atmosphere of applying flexibility transformation technology within the group of thermal power enterprises can facilitate the widespread adoption of this technology. Furthermore, the influence of the deep peak-shaving compensation tariff on the diffusion of flexibility transformation within the thermal power enterprise group surpasses the impact of the group’s initial transformation percentage on the diffusion of the technology.
4.5.3. The Impact of the Level of Government Subsidies on the Spread of Something
The financial subsidy intensity indicates the level of government support for flexibility transformation technologies. Building on the findings of the previous two sections, we examine the impacts of various financial subsidy intensities on incentivizing thermal power enterprises to undertake unit flexibility transformation under two distinct levels of deep peak-shaving compensation tariffs. In two distinct compensation-tariff scenarios (where
,
), numerical simulations consider three subsidy-intensity levels:
β = 0, 0.2, and 0.5, representing no financial support, medium subsidy intensity, and high subsidy intensity, respectively. As shown in
Figure 7, in the low-compensation-tariff scenario, the diffusion rate of flexibility transformation technology increases with the rise in subsidy intensity; however, the proportion of the group finally adopting the technology under high subsidy intensity is 30% of the total. With the deep peak-shaving compensation tariff set at 600 CNY/MW, the flexibility transformation technology exhibits a favorable diffusion rate, irrespective of the subsidy-intensity type, achieving diffusion rates of 81%, 86.1%, and 93.3% under the three subsidy intensities, respectively. Despite the positive diffusion rate of flexibility transformation technology for thermal power units under a high deep peak-shaving compensation tariff, the final outcomes vary significantly across different subsidy intensities. For instance, achieving a diffusion rate of 80% requires iterations up to
t = 100, 75, and 60 under the three subsidy intensities, respectively. Hence, in the case of a low compensation tariff, increasing the subsidy intensity fails to counterbalance the adverse effects of the tariff, thus hindering the widespread adoption of the technology. Conversely, in a market environment characterized by a high deep peak-shaving compensation tariff, enhancing the subsidy intensity can expedite the diffusion of flexibility transformation-technology application.