Study of Flexibility Transformation in Thermal Power Enterprises under Multi-Factor Drivers: Application of Complex-Network Evolutionary Game Theory

Abstract

With the increasing share of renewable energy in the grid and the enhanced flexibility of the future power system, it is imperative for thermal power companies to explore alternative strategies. The flexible transformation of thermal power units is an effective strategy to address the previously mentioned challenges; however, the factors influencing the diffusion of this technology merit further investigation, yet they have been seldom examined by scholars. To address this gap, this issue is examined using an evolutionary game model of multi-agent complex networks, and a more realistic group structure is established through heterogeneous group differentiation. With factors such as group relationships, diffusion paths, compensation electricity prices, and subsidy intensities as variables, several diffusion scenarios are developed for research purposes. The results indicate that when upper-level enterprises influence the decision-making of lower-level enterprises, technology diffusion is significantly accelerated, and enhanced communication among thermal power enterprises further promotes diffusion. Among thermal power enterprises, leveraging large and medium-sized enterprises to promote the flexibility transformation of units proves to be an effective strategy. With regard to factors like the compensation price for depth peak shaving, the initial application ratio of groups, and the intensity of government subsidies, the compensation price emerges as the key factor. Only with a high compensation price can the other two factors effectively contribute to promoting technology diffusion.

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 CO₂ 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.

2. Literature Review

2.1. Current Status of Thermal Power-Unit Flexibility Transformation Technology

As the primary units manufactured in China, the controllable output of thermal power units has consistently been their foremost advantage. Flexibility indicators of thermal power units include rapid start–stop capability, swift load changes, and deep peak-shaving capabilities. The utilization of thermal power units for deep peak shaving within current power systems has emerged as a significant industry concern [16,17,18]. To upgrade the unit system, Wang et al. [19] proposed a new system using residual steam to drive rotating equipment, which can reduce the energy consumption of thermal power units and increase the unit’s deep peak-shaving capacity. In the literature [20], authors investigated the electrical and thermal attributes of cogeneration units before and after retrofitting, proposing a retrofit model featuring thermoelectrically decoupled systems. Furthermore, modifications to thermal power-plant boiler systems constitute a prominent research focus. Several studies have demonstrated that preheating pulverized coal enhances the unit’s peak shifting capability [13,21,22]. The focus is on addressing operational control issues in thermal power units; for example, authors in [23] introduced a sliding-mode control strategy for regulating the unit’s boiler temperature during operation. Additionally, some researchers have advocated for a control strategy to integrate the thermal unit with an energy storage system to enhance its flexible output capability [24]. To address steam temperature issues in the boiler subsystem of a thermal unit, Sun et al. [25] suggested employing multi-objective control algorithms for regulation. Presently, the predominant research focus is on optimizing unit operation control, integrating additional resources for peaking purposes, and enhancing unit subsystems (boiler, turbine, etc.).

2.2. Evolutionary Game Theory and Applications

In contrast to traditional game theory, evolutionary game theory posits that the subjects engaged in the game exhibit limited rationality, and delineates the evolution of individual behavioral strategies from a dynamic standpoint. Such limited rationality enables individuals to adapt and learn in response to the environment and the behavior of others during the decision-making process, thereby gradually developing more adaptive strategies. Thus, evolutionary game theory emphasizes the dynamic process of interaction and evolution among individuals, as opposed to merely static strategy selection. A typical evolutionary game model includes four major elements, as shown in

Table 1. Description of the four major elements contained in a typical evolutionary game model.

Major Elements	Descriptions
Game Framework	✓ The structure and rules of a game: conducted under specific techniques and established conditions. Participants do not possess all the knowledge of game structure and rules, a fundamental departure from classical game theory. ✓ Participants typically acquire strategies through transmission mechanisms, such as replicator dynamics (RD), rather than through rational choice.
Fitness Function	✓ Transforming the payoff function in classical games into a fitness function, which describes the reproductive capability of strategies, expressed as the growth rate of strategy adopters after each game round. ✓ The fitness function can be seen as the mapping relationship between strategy and fitness: strategy → fitness.
Replicator Dynamics	✓ Selection/mutation mechanism: Utilizes a systems theory perspective to describe dynamic state changes of systems, specifically the dynamic adjustment process of group behavior. Typical are the deterministic and nonlinear EGT models based on the selection mechanism. ✓ Other behavioral patterns: stimulus response dynamics, approximate adjustment dynamics, etc.
Evolutionarily Stable Strategy (ESS)/Evolutionarily Stable Equilibrium (ESE)	✓ ESS is an equilibrium concept in evolutionary games: if an existing strategy is ESS, there must be a positive invasion barrier that allows the existing strategy to achieve higher returns than the mutated strategy when the frequency of the strategy is lower than this barrier. ✓ A refinement of Nash equilibrium (discussed later).

.

Evolutionary game theory has found widespread application in the energy and power sectors, covering areas such as carbon emission reduction, power markets, and energy economics [26]. A plethora of research outcomes has accumulated, utilizing the theory to guide the transformation of thermal power enterprises towards investment in the CCUS industry. Song et al. [27] employed an evolutionary game model to analyze the interest interaction behavior among alliance organizers, investors, and upstream and downstream operators, revealing that cooperative alliances facilitate the commercial deployment of CCUS technology. Zhao and Liu [28] formulated an evolutionary game model that delineates interactions between the government and power generation enterprises regarding the development of CCS technology, demonstrating that enhanced government regulation and enterprises’ efforts toward cost reduction and efficiency enhancement foster the advancement of CCS technology. Furthermore, it has significant applications in the energy sector, including the exploration of shared energy-storage business models [29] and capacity planning for energy storage in multi-mini-grids using evolutionary game theory [30]. Within the electricity market, the integration of evolutionary game theory with algorithms has been employed to scrutinize the decision-making behavior of electricity distribution companies under the Renewable Portfolio Standard (RPS) [31], examine the decision-making behavior under demand-side dynamic tariffs [32], and explore the behavior of multiple players in demand-side response management (DRM) of electricity [33].

Overall, the research directions of future evolutionary game theoretical methods and models mainly include the following: the study of evolutionary game mechanisms and strategy update rules (such as the pairwise comparison process, Fermi process, Moran process, Wright Fisher process, etc.), the study of evolutionary game paths, evolutionary game relationships, evolutionary game laws, the overall study of evolutionary games, the psychological analysis of game players in the evolutionary process (such as combining belief learning), the optimization and development of evolutionary games (such as combining reinforcement learning), and the design of a panoramic experimental platform for the electricity market, based on evolutionary games.

2.3. Evolutionary Game Theory for Complex Networks and Its Applications

Evolutionary game dynamics on networks have been a significant topic since 1992, when Nowak and May first studied evolutionary games on square lattice networks. Since then, researchers have employed various types of game dynamics to investigate evolutionary games on networks, including the Fermi rule [34], death–birth updating, birth–death updating, imitation updating [35], and pairwise comparison [36]. With the development of complex network science, Watts and Strogatz [37] introduced the concept of “small-world networks” in 1998, demonstrating how these networks exhibit both high clustering and short average path lengths through the reconnection of certain edges. Barabási [38] and Albert introduced the concept of “scale-free networks” and demonstrated that the degree distribution of nodes in many real-world networks (e.g., the Internet, social networks) follows a power-law distribution. Following the introduction of complex network models such as small-world networks and scale-free networks, the study of evolutionary games on complex networks has advanced into a new phase.

Evolutionary game theory for complex networks is a prominent interdisciplinary field that amalgamates complex networks and evolutionary game theory. In this field, researchers view the nodes of complex networks as individuals engaged in the game, with connecting edges representing the topological relationships between individuals. Strategies of each individual are updated via specific dynamics, which facilitates the examination of the relationship between network structure and the evolution of individuals’ strategies within the game. The main elements of the evolutionary game with respect to complex networks are shown in

Table 2. Describe the main elements contained in the complex-network evolutionary game model.

Main Elements	Descriptions
Game Framework	✓ Unlike classical evolutionary game theory, in complex-network evolutionary game theory, the participating populations are structured, and each individual does not play the game with all others. ✓ Examples are random networks, small-world networks, scale-free networks.
Fitness Function	✓ In complex-network evolutionary game theory, the fitness function accounts not only for the individual’s payoff in the game, but also for the network structure and the relationships between individuals. ✓ The network topology can significantly affect the fitness calculation.
Update Mechanism	✓ The mechanism of network evolutionary games leans towards stochastic dynamics, where an individual’s strategy update depends not only on their own and their neighbors’ benefits but also on the network topology. ✓ Update process: Fermi rule, imitation updating, pairwise comparison, etc.
Population Status	✓ The equilibrium state of the network evolutionary game is influenced by the network structure, the distribution of node degrees, and the selection of specific node strategies. ✓ The state of the population is represented by the distribution of strategies.

. By delving deep into the interactions among nodes in complex networks, insights into the emergence patterns of group behavior can be unveiled, thus facilitating exploration of dynamic evolution mechanisms within social systems. Moreover, this approach plays a crucial role in practical applications, including information dissemination in social networks and the evolution of cooperative behaviors in complex networks. Jia et al. [39] analyzed trends in cooperative behavior of social capital through the construction of an evolutionary game model based on a scale-free network. Their findings indicate a correlation between the social network structure, individual strategies, and cooperative-behavior trends of capital. Moreover, they observe a positive correlation between the initial probability of the current strategy in the network and the diffusion evolution of the strategy. Similarly, in the realm of energy and power, the complex-network evolutionary game model significantly contributes to interactions among multi-subject strategies. Fan et al. [40] use the evolutionary game model of small-world networks to investigate the peer effect and government behavior regarding the diffusion of enterprise innovation technology. They ascertain that the degree of diffusion is primarily influenced by the benefits to enterprises during the process. Zhao et al. [41] integrate various stages of research backgrounds with corresponding networks to examine the influence of government subsidies on the diffusion rate of new energy vehicles, offering recommendations grounded in complex network theory. In [42], the authors utilize complex-network evolutionary game theory to analyze the diffusion trend of CCUS technology among groups of thermal power enterprises under multi-factor conditions. In addition, Yue et al. [43] investigate the impact of carbon cap-and-trade (CCT) and RPS on renewable energy using complex-network evolutionary game theory.

Overall, the multi-intelligence complex-network evolutionary game model demonstrates a broad spectrum of applications as an effective research tool for investigating the diffusion and adoption of new technologies and behaviors within groups. In the context of evolutionary games on complex networks, the “diffusion rate” typically refers to the speed or extent to which a behavior, strategy, or information spreads within the network. Specifically, the diffusion rate may indicate the frequency or proportion of a behavior or strategy spreading from one node to others within a given time period. In this paper, the defined diffusion rate refers to the proportion of firms in the network that learn the flexibility transformation technology from an initial firm or a set of initial firms through specific strategy update rules. Based on the above research status, the comprehensive research framework of this article is depicted in Figure 1.

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 $E_1$ is defined as follows:

$$E_1=Q{h}_1{p}_1,$$

(1)

where $Q$ is the installed rated capacity of the thermal power plant and $h_1$ 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. $P_1$ is the feed-in tariff for normal generation.

3.1.2. Deep Peak-Shaving Benefits

The deep peak-shaving benefits includes two parts $E_2$ and $E_3$, which are defined as

$$E_2=\alpha Q{h}_2{p}_2,$$

(2)

$$E_3=\alpha Q{h}_3{p}_2,$$

(3)

where $h_2$ is the annual hours of peaking participation, $P_2$ is the peaking feed-in tariff, $\alpha$ is the depth of peaking, $E_3$ is the current thermal plant’s share of the benefits from neighboring plants that do not participate in peaking, and $h_3$ represents the additional hours of peaking that are shared.

3.1.3. Regular Operation Generation Cost

The regular operation generation cost is denoted by $C_1$, defined as follows:

$$F_1=a{Q}^2+bQ+c,$$

(4)

$$C_1=F_1{h}_1,$$

(5)

where $F_1$ is the hourly generation cost of thermal power plants, and $a$, $b$, and $c$ are the unit generation factors.

3.1.4. Deep Peak-Shaving Cost

The deep peak-shaving costs are defined as follows:

$$F_2=a{(\alpha Q)}^2+b\alpha Q+c,$$

(6)

$$F_3={\displaystyle \frac{\gamma S}{2N_t}},$$

(7)

$$F_4=r(p_d-p_{\mathit{dc}}),$$

(8)

$$C_2=(F_1+F_2+F_3)h_2,$$

(9)

$$C_3=(F_1+F_2+F_3)h_3,$$

(10)

where $F_2$ is the generation cost in the deep peak-shaving stage, $F_3$ is the unit loss cost in the deep peak-shaving stage, $P_d$ is the minimum output of the deep peak regulation without combustion support, $P_{dc}$ is the minimum output of the deep peak regulation with combustion support, $\gamma$ is the loss coefficient, $S$ is the unit purchase cost, which is assumed to be equal to the installed cost in this paper, $N_t$ is the number of weeks of the rotor fracturing cycle, and $F_4$ 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:

$$K=0.3\eta G_{1}Q,$$

(11)

where $\eta$ is the annualized rate (the calculation method is in Appendix A) and $G_1$ 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$x$, while the probability of not adopting it is $1-x$. 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 $h_3$ is computed based on the neighbors of each node in the network. The symbol $\beta$ represents the intensity of government subsidies, while $\theta$ 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. The payoff distribution of the evolutionary game model of thermal power enterprises.

		Group B
		Y (y)	N (1 − y)
Group A	Y (x)	{EA_AYBY, EB_AYBY}	{EA_AYBN, EB_AYBN}
	N (1 − x)	{EA_ANBY, EB_ANBY}	{EA_ANBN, EB_ANBN}

. $E_{\mathrm{A}\_\mathrm{A}\mathrm{Y}\mathrm{B}\mathrm{Y}}=E_{\mathrm{a}1}+E_{\mathrm{a}2}-C_{\mathrm{a}1}-C_{\mathrm{a}2}-(1-\beta )K_{\mathrm{a}}$,$E_{\mathrm{B}\_\mathrm{A}\mathrm{Y}\mathrm{B}\mathrm{Y}}=E_{\mathrm{b}1}+E_{\mathrm{b}2}-C_{\mathrm{b}1}-C_{\mathrm{b}2}-(1-\beta )K_{\mathrm{b}}$, $E_{\mathrm{A}\_\mathrm{A}\mathrm{Y}\mathrm{B}\mathrm{N}}=E_{\mathrm{a}1}+E_{\mathrm{a}2}+E_{\mathrm{a}3}-C_{\mathrm{a}1}-C_{\mathrm{a}2}-C_{\mathrm{a}3}-(1-\beta )K_{\mathrm{a}}$, $E_{\mathrm{B}\_\mathrm{A}\mathrm{Y}\mathrm{B}\mathrm{N}}=E_{\mathrm{b}1}-C_{\mathrm{b}1}$, $E_{\mathrm{A}\_\mathrm{A}\mathrm{N}\mathrm{B}\mathrm{Y}}=E_{\mathrm{a}1}-C_{\mathrm{a}1}$, $E_{\mathrm{B}\_\mathrm{A}\mathrm{N}\mathrm{B}\mathrm{Y}}=E_{\mathrm{b}1}+E_{\mathrm{b}2}+E_{\mathrm{b}3}-C_{\mathrm{b}1}-C_{\mathrm{b}2}-C_{\mathrm{b}3}-(1-\beta )K_{\mathrm{b}}$, $E_{\mathrm{A}\_\mathrm{A}\mathrm{N}\mathrm{B}\mathrm{N}}=\theta (E_{\mathrm{a}1}-C_{\mathrm{a}1})$, and $E_{\mathrm{B}\_\mathrm{A}\mathrm{N}\mathrm{B}\mathrm{N}}=\theta (E_{\mathrm{b}1}-C_{\mathrm{b}1})$.

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):

$$\{\begin{array}{l}{U}_{\mathrm{a}}=E_{\mathrm{a}1}+E_{\mathrm{a}2}-C_{\mathrm{a}1}–C_{\mathrm{a}2}–(1-\beta )K_{\mathrm{a}},\\ U_{\mathrm{b}}=E_{\mathrm{b}1}+E_{\mathrm{b}2}-C_{\mathrm{b}1}–C_{\mathrm{b}2}–(1-\beta )K_{\mathrm{b}}.\end{array}$$

(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):

$$\{\begin{array}{l}{U}_{\mathrm{a}}=E_{\mathrm{a}1}+E_{\mathrm{a}2}+E_{\mathrm{a}3}-C_{\mathrm{a}1}–C_{\mathrm{a}2}–C_{\mathrm{a}3}-(1-\beta )K_{\mathrm{a}},\\ U_{\mathrm{b}}=E_{\mathrm{b}1}-C_{\mathrm{b}1}.\end{array}$$

(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):

$$\{\begin{array}{l}{U}_{\mathrm{a}}=E_{\mathrm{a}1}-C_{\mathrm{a}1},\\ U_{\mathrm{b}}=E_{\mathrm{b}1}+E_{\mathrm{b}2}+E_{\mathrm{b}3}-C_{\mathrm{b}1}–C_{\mathrm{b}2}–C_{\mathrm{b}3}-(1-\beta )K_{\mathrm{b}}.\end{array}$$

(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):

$$\{\begin{array}{l}{U}_{\mathrm{a}}=\theta (E_{\mathrm{a}1}-C_{\mathrm{a}1}),\\ U_{\mathrm{b}}=\theta (E_{\mathrm{b}1}-C_{\mathrm{b}1}).\end{array}$$

(15)

Based on Table 3, the benefits to Group A of choosing to use the flexibility transformation technology are

$$\begin{array}{ll}{U}_{\mathrm{a}1}=& y(E_{\mathrm{a}1}+E_{\mathrm{a}2}-C_{\mathrm{a}1}–C_{\mathrm{a}2}–(1-b)K_{\mathrm{a}})+\\ & (1-y)(E_{\mathrm{a}1}+E_{\mathrm{a}2}+E_{\mathrm{a}3}-C_{\mathrm{a}1}-C_{\mathrm{a}2}-C_{\mathrm{a}3}-(1-\beta )K_{\mathrm{a}}).\end{array}$$

(16)

The benefits to Group A of not using the flexibility modification technology are

$$U_{\mathrm{a}2}=y(E_{\mathrm{a}1}-C_{\mathrm{a}1})+(1-y)\theta (E_{\mathrm{a}1}-C_{\mathrm{a}1}).$$

(17)

The replication dynamic equations for Group A and Group B can be obtained as follows:

$$\begin{array}{ll}{F}_{\mathrm{a}}\left(x\right)& ={\displaystyle \frac{\mathrm{d}x}{\mathrm{d}t}}=x(1-x)(U_{\mathrm{a}1}-U_{\mathrm{a}2})\\ & =x(1-x)(E_{\mathrm{a}2}-C_{\mathrm{a}2}-K_{\mathrm{a}}+(1-y)((1-\theta )(E_{\mathrm{a}1}-C_{\mathrm{a}1})+E_{\mathrm{a}3}-C_{\mathrm{a}3})),\end{array}$$

(18)

$$\begin{array}{ll}{F}_{\mathrm{b}}\left(x\right)& ={\displaystyle \frac{\mathrm{d}y}{\mathrm{d}t}}=y(1-y)(U_{\mathrm{b}1}-U_{\mathrm{b}2})\\ & =y(1-y)(E_{\mathrm{b}2}-C_{\mathrm{b}2}-K_{\mathrm{b}}+(1-x)((1-\theta )(E_{\mathrm{b}1}-C_{\mathrm{b}1})+E_{\mathrm{b}3}-C_{\mathrm{b}3})).\end{array}$$

(19)

The Jacobi matrix formed by the two parties is as follows:

$$\mathit{J}=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),$$

(20)

where $a_{11}=(1-2x)(E_{\mathrm{a}2}-C_{\mathrm{a}2}-(1-\beta )K_{\mathrm{a}}+(1-y\left)\right((1-\theta )(E_{\mathrm{a}1}-C_{\mathrm{a}1})+E_{\mathrm{a}3}-C_{\mathrm{a}3}\left)\right)$, $a_{12}=x(x-1)\left(\right(1-\theta \left)\right(E_{\mathrm{a}1}-C_{\mathrm{a}1})+E_{\mathrm{a}3}-C_{\mathrm{a}3}),a_{21}=y(y-1)\left(\right(1-\theta \left)\right(E_{\mathrm{b}1}-C_{\mathrm{b}1})+E_{\mathrm{b}3}-C_{\mathrm{b}3})$, $a_{22}=(1-2y)(E_{\mathrm{b}2}-C_{\mathrm{b}2}-(1-\beta )K_{\mathrm{a}}+(1-x\left)\right((1-\theta )(E_{\mathrm{b}1}-C_{\mathrm{b}1})+E_{\mathrm{b}3}-C_{\mathrm{b}3}\left)\right).$

As shown in

Table 4. Stabilization conditions at each equilibrium.

	Eig	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$
$(\mathit{x},\mathit{y})$
$x=0,y=0$		$\left(1-\theta \right)E_{\mathrm{a}1}+\left(\theta -1\right)C_{\mathrm{a}1}+E_{\mathrm{a}2}+E_{\mathrm{a}3}-C_{\mathrm{a}2}-C_{\mathrm{a}3}+(\beta -1)K_{\mathrm{a}}$	$\left(1-\theta \right)E_{\mathrm{b}1}+\left(\theta -1\right)C_{\mathrm{b}1}+E_{\mathrm{b}2}+E_{\mathrm{b}3}-C_{\mathrm{b}2}-C_{\mathrm{b}3}+(\beta -1)K_{\mathrm{b}}$
$x=1,y=0$		$E_{\mathrm{a}2}-C_{\mathrm{a}2}+(\beta -1)K_{\mathrm{a}}$	$\left(1-\theta \right)E_{\mathrm{b}1}+\left(\theta -1\right)C_{\mathrm{b}1}+E_{\mathrm{b}2}+E_{\mathrm{b}3}-C_{\mathrm{b}2}-C_{\mathrm{b}3}+\left(\beta -1\right)K_{\mathrm{b}}$
$x=0,y=1$		$\left(1-\theta \right)E_{\mathrm{a}1}+\left(\theta -1\right)C_{\mathrm{a}1}+E_{\mathrm{a}2}+E_{\mathrm{a}3}-C_{\mathrm{a}2}-C_{\mathrm{a}3}+\left(\beta -1\right)K_{\mathrm{a}}$	$E_{\mathrm{b}2}-C_{\mathrm{b}2}+(\beta -1)K_{\mathrm{b}}$
$x=1,y=1$		$C_{\mathrm{a}2}-E_{\mathrm{a}2}+(1-\beta )K_{\mathrm{a}}$	$C_{\mathrm{b}2}-E_{\mathrm{b}2}+(1-\beta )K_{\mathrm{b}}$

, taking the ideal equilibrium state $x=1$, $y=1$ 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,

$$\{\begin{array}{l}{C}_{\mathrm{a}2}-E_{\mathrm{a}2}+(1-\beta )K_{\mathrm{a}}<0,\\ C_{\mathrm{b}2}-E_{\mathrm{b}2}+(1-\beta )K_{\mathrm{b}}<0.\end{array}$$

(21)

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 $G=(V,E)$, where $V$ 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:

$$P\left(S_{\mathrm{A}}\to S_{\mathrm{B}}\right)={\displaystyle \frac{1}{1+\exp \left[\left(f_{\mathrm{A}}(t)-f_{\mathrm{B}}(t)\right)/k\right]}}.$$

(22)

In Formula (22), $f_{\mathrm{A}}\left(t\right)$ and $f_{\mathrm{B}}\left(t\right)$ are the payoffs of the thermal power plants $\mathrm{A}$ and $\mathrm{B}$ at time $t$, $S_{\mathrm{A}}$ and $S_{\mathrm{B}}$ are the strategies of the thermal power plants A and B, respectively, and $P$ is the strategy transfer probability. Here, $k$ is the interference factor, which represents the intensity of irrationality in thermal power enterprises’ decisions.

When$k=0$, 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 $k>0$, the firm is influenced by irrational factors, learning not only strategies with higher payoffs than its own, but also those with lower payoffs.

As $k$ approaches infinity, firms will randomly learn their neighbors’ strategies, irrespective of the payoffs. Considering the practical situation, $k$ 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

$$P_{ij}={\displaystyle \frac{U_j}{{\displaystyle \sum _{j\in G}{U}_j}}},$$

(23)

where $P_{ij}$ is the probability that node $i$ is connected to node $j$, and $U_j$ is the current payoff of node $j$.

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. Parameters settings of the model.

Parameter	Value	Parameter	Value
Q	1500 MW, 1000 MW, 600 MW	h1	4600 H
h2	730 H	p1	400 CNY/MW
p2	600 CNY/MW	α	30%
γ	1	G1	1,000,000 CNY/MW
Nt	500,000	r	2
Pd	45% Q	Pdc	30% Q
S	3,000,000 CNY/MW	η	0.55

(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 $t=5$ 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 $t=40$, 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 $p_2$. Under two different initial application atmospheres, $p_2$ 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 $p_2$ 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 $p_2=400 \mathrm{C}\mathrm{N}\mathrm{Y}/\mathrm{M}\mathrm{W}$, 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 $p_2=600 \mathrm{C}\mathrm{N}\mathrm{Y}/\mathrm{M}\mathrm{W}$, 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 $p_2=400 \mathrm{C}\mathrm{N}\mathrm{Y}/\mathrm{M}\mathrm{W}$, $p_2=400 \mathrm{C}\mathrm{N}\mathrm{Y}/\mathrm{M}\mathrm{W}$), 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.

5. Conclusions and Policy Implications

5.1. Research Conclusions

Promoting the flexibility transformation of thermal power units is crucial for enhancing the flexibility resources of the power grid and fostering the utilization of renewable energy. To promote the dissemination of thermal power-unit flexibility transformation technology within the thermal power enterprise group, this study employs a complex-network-evolution game model for numerical simulation. It analyzes the impact of market type, degree of information dissemination, specific diffusion path, deep peak-shaving compensation tariffs, subsidy level, and initial-application atmosphere on technology diffusion. The findings of this paper are summarized as follows:

(i)

If decision-making by upper-tier enterprises can influence lower-tier enterprises, the dissemination of flexibility transformation technology is more probable. However, if upper-tier enterprises lack influence over lower-tier ones, the diffusion effect of the technology may be limited.

(ii)

Enhancing the level of information exchange among groups of thermal power enterprises can facilitate the widespread adoption of flexibility transformation technology. By improving information exchange, these enterprise groups can gain better insights into power market demand and profitability trends following unit reform, thereby promoting the broader adoption of flexibility transformation technology.

(iii)

Small enterprises lack the capability to independently promote the diffusion and application of technology among groups, making reliance on large and medium-sized enterprises more effective for technology diffusion. Small enterprises often face resource and influence constraints, impeding their ability to drive technology diffusion. Conversely, large and medium-sized enterprises typically possess abundant resources, extensive information sources, and significant influence, making them more effective in promoting technology diffusion.

(iv)

Among the three factors—the deep peak-shaving compensation tariff, initial transformation rate of the group, and subsidy intensity—the deep peak shaving compensation tariff has the most significant impact on the diffusion rate. A deep peak-shaving compensation tariff below 450 CNY/MW fails to attract participation from most thermal power enterprises in unit flexibility transformation, while a tariff exceeding 550 CNY/MW results in a gradual decrease in the final benefit generated.

5.2. Policy Implications

(1)

The deep peak-shaving compensation tariff plays a crucial role in promoting the advancement of technology application. Deep peak-shaving revenue directly influences thermal power enterprises’ decisions to adopt flexibility transformation technology, as it serves as a direct source of revenue. Reasonable and stable compensation tariffs can safeguard the interests of thermal power enterprises and stimulate their active involvement in the peak-shaving market, thereby furthering the application and development of the technology. Effective deep peak-shaving compensation tariffs should not only protect the interests of thermal power enterprises but also foster the optimization and adjustment of energy structures, thereby promoting the development and application of flexibility transformation technology. Additionally, when formulating the deep peak-shaving compensation tariff, regulatory authorities should enhance supervision and control to ensure its rationality and fairness. Simultaneously, they should actively encourage thermal power enterprises to increase investment in peak-shaving capacity and technological transformation to promote the transformation and upgrading of the energy structure, thereby realizing multiple economic, environmental, and social benefits.

(2)

Financial support and the initial application atmosphere of thermal power-unit flexibility transformation-technology diffusion also influence its effect, but they must be combined with the depth of the deep peak-shaving compensation tariff to be effective. With a high deep peak-shaving tariff as the foundation, financial support and a favorable application atmosphere contribute to the process of technology diffusion, providing additional financial backing to enterprises and expediting technology application and diffusion.

(3)

Government and regulatory agencies can promote the widespread adoption of flexibility transformation technologies by encouraging and facilitating information exchange among thermal power enterprise groups. Governments can collaborate with lead enterprises to establish demonstration projects for flexibility transformation technologies, showcasing their practical effects to other enterprises in terms of enhanced productivity, reduced costs, and emissions. For instance, industry organizations or platforms can be established to facilitate information sharing and technology exchange. Policy incentives, such as reward systems or subsidy policies, can encourage enterprises to actively engage in information sharing and technology cooperation, thereby promoting the application of flexibility-transformation technologies in the market.