Exploring Clean Energy Technology Diffusion and Development in the Yellow River Basin Amid Water Resource Constraints

Abstract

Clean energy serves as a crucial means to alleviate water resource shortages and ensure power production safety. This study delves into clean energy diffusion and development within the confines of the Yellow River Basin, considering water resource constraints. It examines the dynamic evolution of the strategic choices made by local governments and the expansion of clean energy businesses among power generation groups using an evolutionary game model. Additionally, the study employs the L-V model to elucidate the diffusion and competition dynamics between fossil fuel power generation technology (FFGT) and clean energy generation technology (CEGT). To provide a more scientific elucidation of this process, actual values are utilized for simulation. The findings indicate that: (1) The strategic decisions of power generation groups are influenced not only by local government guidance but also by advancement in clean energy technology and cost reduction efforts; (2) the implementation of water resource tax guidance strategies yields noticeable effects, with higher taxes correlating to increased willingness among power generation groups to expand clean energy businesses; (3) in contrast to diffusion speed, the final state of equilibrium attained by the two technologies is more closely tied to the competition coefficient. A higher competition coefficient leads clean energy generation technology to gain a competitive advantage in the market, potentially dominating it entirely. Based on these conclusions, pertinent policy suggestions are proposed to drive the advancement of clean energy and facilitate energy structure transformation in the Yellow River Basin.

1. Introduction

As the second longest river, the Yellow River functions as a vital water source for northwest and north China. Despite accounting for only 2% of China’s water resources, the Yellow River sustains approximately 12% of the country’s population, 15% of its cultivated land, 14% of its total economic output, and in excess of 50 medium-sized and large cities [1]. Consequently, the Yellow River plays a pivotal role in China’s economic development landscape. However, due to its geographical location and the East Asian monsoon climate, a significant portion of the basin demonstrates arid and semi-arid characteristics, and its average annual precipitation fluctuates between 200 and 600 mm. This situation has led to a severe shortage in respect to the water resources all over the region [2]. Despite efforts to implement unified management and allocation of water resources in the Yellow River basin, the region continues to face a stark contrast between the increasing regional demand for water and the limited supply available. This challenge has been exacerbated by ongoing social and economic development and population growth [3]. Currently, the water resource exploitation rate in the Yellow River basin stands at an astonishing 80%, which is far beyond the ecological warning threshold of 40% designated for the sustainable development of river basins. If not effectively addressed, this situation poses a significant risk to the region’s sustainable social and economic development [4]. The shortage of water resources in the Yellow River Basin significantly restricts the development of traditional energy. With an annual average water resource volume of only about 58 billion cubic meters and per capita water resources of less than 500 cubic meters—just 20% of the national average—it starkly contrasts with the Yangtze River Basin, which has an annual water resource volume of 961.6 billion cubic meters and per capita water resources of over 2200 cubic meters, more than four times that of the Yellow River Basin. This disparity directly impacts the layout and production efficiency of traditional energy sources such as coal power, which requires 2.5–3.0 L of water per kilowatt-hour. The Yellow River Basin’s water resource utilization rate has already exceeded 70%, approaching the ecological warning threshold, making further coal power expansion unsustainable. Meanwhile, the development of clean energy is also constrained by water scarcity; for instance, the periodic cleaning of photovoltaic panels requires water, which adds pressure to an already tight water supply–demand balance. In contrast, the Yangtze River Basin, with its abundant water resources, faces fewer constraints on coal power and achieves energy structure optimization through diversified layouts of hydropower, solar, and wind energy, showcasing a significant regional advantage.

Traditional coal power plays a predominant role in China’s power generation structure, with large enterprise groups contributing the largest share. The production of traditional coal power necessitates a reliable supply of water resources, leading to the power industry’s top ranking among the largest consumers of water. Here, water consumption refers to the amount of water that cannot be recovered during the power generation process, as opposed to water usage, which refers to water that can be treated and reused. Between 2010 and 2015, total water consumption and water usage by the thermal power industry within the eight provinces along the Yellow River basin increased from 9.265 billion cubic meters and 8.995 billion cubic meters to 13.313 billion cubic meters and 13.227 billion cubic meters, respectively. Notably, 6.1% of the total water use quota within the eight provinces along the Yellow River basin was allocated to the cooling process of coal power production [5]. In line with the Outline of National Land Planning (2016–2030) and the Strategic Action Plan for Energy Development (2014–2020), six out of the nine large-scale coal power bases of China are located within the Yellow River basin, including Ordos, middle Shanxi, northern Shanxi, northern Shaanxi, eastern Shanxi, and eastern Ningxia [6]. The development of large-scale coal power bases is expected to exacerbate the water stress in the basin further. The scarcity of water resources can precipitate a crisis in the power industry, as exhibited by the severe drought experienced by Kenya in 2017, which led to the shutdown of power plants. On that occasion, Kenya’s energy reserve rate plummeted to 4.4%, well below the required 15% threshold necessary to avert the risk of power outages.

In contrast, clean energy boasts minimal water consumption. The application of clean energy can significantly conserve water resources. Compared to traditional coal power, wind and solar energy consume much less water. For example, wind power almost does not require water resources, with the main consumption being for equipment cleaning and maintenance. In contrast, it can save between 50 million and 100 million cubic meters of water annually. Solar photovoltaic power generation almost does not consume water, with the main water consumption focused on panel cleaning. On average, about 0.01 L of water is needed to generate 1 kilowatt-hour, which is far lower than the 2.5–3.0 L required by coal power. It is estimated that solar power generation can save approximately 350 million to 400 million cubic meters of water annually. One hundred million cubic meters of water can meet the annual water needs of about 500,000 people, which is the annual water supply of a medium-sized city and can irrigate about 10,000 hectares of farmland. According to estimates by the International Energy Agency (IEA), if the global energy transition fully adopts clean energy by 2030, especially water-efficient energy sources such as wind and solar, about 300 billion cubic meters of water will be saved annually. If wind and solar energy become globally widespread, it is expected that around 1 billion people’s annual water usage could be saved, enough to meet the water supply needs of large cities. Moreover, the Yellow River Basin commands abundant wind, solar, and hydropower resources, laying down a solid foundation for the development of the clean energy power industry [7]. Therefore, the transformation from an energy structure dominated by traditional coal power to an expanded clean energy mix is imperative for restructuring the power sector and mitigating the water stress in the Yellow River Basin. Such measures hold paramount significance for both water resource security and power security in the region.

Unlike the current research, the contributions of this paper can be summarized in the following three aspects: (1) Innovation in research perspective: From the “human” perspective, we construct an evolutionary game model involving the government and energy enterprises to explore the impact of policy guidance and corporate transformation on the diffusion and development of clean energy technologies, providing valuable references for government energy policy formulation. (2) Innovation in research methodology: From the “population” competition and cooperation perspective, we construct a Lotka–Volterra (L-V) model to examine the impact of competition and cooperation between two biological populations—clean energy technologies and traditional coal power technologies—on the diffusion and development of clean energy technologies. (3) Expansion of research scope: From the “water–energy” nexus perspective, we explore the constraints of water issues in the Yellow River Basin on energy development, as well as the role of energy transition in alleviating water problems in the region, providing evidence for collaborative management of natural resources.

2. Literature Review

According to the theories of public goods and externalities, water resources of rivers, lakes, and seas fall into the category of public goods. The shortage of water resources of the Yellow River Basin determines that the consumption behavior of coal power enterprises in the Yellow River Basin has significant negative externalities and thus results in the “tragedy of the commons” [8]. According to the hypothesis of “economic man”, individuals will seize every opportunity to maximize the utility when conditions permit. Therefore, the governance of the “tragedy of the commons” requires the intervention of a powerful central government [9]. Therefore, promoting the transformation of power structure in the Yellow River Basin and raising water use efficiency is not only a technical problem but also a realistic problem arising from different interest demands and behavioral conflicts of multiple stakeholders. Classical game theory has been widely used to reveal the interests and behaviors of different subjects in the power industry and achieved fruitful results. Pingkuo (2020) showed the process of interest trade-off and collaborative development between coal power and clean energy by the evolutionary game method [10]. Banaei Mohsen et al. analyzed the strategic game between wind power producers and thermal power generators in the power market and determined the optimal behavior of power generation enterprises [11]. On the basis of game analysis and market equilibrium, Aryani Morteza designed a regulatory tool for coordinated investment between renewable energy power generation and traditional coal power generation [12].

The current research about the power production and intensive utilization of water resources mainly focuses on the following two aspects: The first one is to realize intensive water use through technological improvement. Daniel proposed that using air-cooling technology instead of water-cooling technology in coal power generation could reduce the demand for cooling water effectively [13]. Actually, many other processes in coal power generation still require huge water consumption, such as ash removal, discharge control and purification, boiler feeding water, etc. [14]. At the same time, air cooling technology will also lead to the loss of efficiency [12], and the efficiency loss is even as high as 10–11% [15]. The second one is to realize intensive water use through adopting clean energy. According to the statistics on water consumption of wind power in China, each 1 million kilowatts of wind power could save 400 million m³ of water use, as compared to coal power generation, which shall effectively alleviate the potential water crisis [16]. The power industry represents the second largest water consumer in China. Compared with traditional coal power, the wind power generation process uses 50% less water [17], while not emitting carbon dioxide [18]. Traditional energy sources are major contributors to carbon emissions. China’s transportation system, which mainly uses oil as fuel, emits large amounts of carbon dioxide [19], which also affects air quality and sustainable urban development in the Yangtze River Delta [19].

Clean energy, as a key solution to the global energy crisis and environmental pollution, has garnered widespread attention in recent years. Clean energy includes solar energy, wind energy, hydropower, biomass energy, geothermal energy, and others, all of which originate from renewable natural resources. These energy sources not only effectively reduce greenhouse gas emissions but also contribute to the transformation of the energy structure. First, in terms of clean energy technology advancements, solar and wind energy, as some of the most promising clean energy sources, can be developed in synergy with renewable microgrids [20,21].

In recent years, significant progress has been made in these technologies. Solar photovoltaic technology has evolved from traditional materials to new photovoltaic materials such as perovskite solar cells and quantum dot solar cells, with continuous improvements in conversion efficiency and cost-effectiveness [22]. In wind energy, with advancements in wind turbine technology, both installed capacity and generation efficiency have steadily increased. Especially in offshore wind power, with the progress of large-scale projects, the cost of wind power is expected to decrease further [23]. Moreover, biomass energy can not only be used for direct combustion to generate energy but also be converted into biogas or bioliquid fuels, providing diversified solutions for energy supply [24]. The utilization of geothermal energy has also received increasing attention, particularly in regions rich in geothermal resources, where geothermal power generation has become a stable and reliable clean energy source [25]. Secondly, in terms of policy support, many countries have implemented a range of policy measures to promote the development of clean energy. For example, the EU and China have introduced renewable energy feed-in tariff policies to encourage businesses to invest in clean energy projects [26]. Additionally, the establishment of carbon trading markets and the introduction of carbon tax policies have provided clearer market signals and incentive mechanisms for the clean energy industry [27].

Building upon the preceding research on power generation and water resource constraints, this study establishes an evolutionary game model involving local governments and power generation entities. It delves into the analysis of how the power structure evolves under the constraints of water resources and adopts the bionic Lotka–Volterra model to elucidate the dynamics of competition and diffusion between traditional coal power and clean energy alternatives. Utilizing basic power data from 2019, simulations are conducted to empirically assess the impact of government regulations, input costs, diffusion rates, and competition coefficients on the expansion of clean energy business by these entities. The simulation outcomes offer valuable insights and suggestions to local governments within the Yellow River Basin, in terms of making informed decisions and guiding the transformation of power structures.

3. Construction of Evolutionary Game Model and Lotka–Volterra Model

The coal power sector within power generation groups has remained a significant consumer of water resources for many decades. As per the 2020 Water Resources Bulletin released by Ministry of Water Resources of China, coal power generation accounted for 8% of China’s total water consumption and a substantial 46% share of total industrial water usage in that year. Given the pronounced water scarcity in the Yellow River Basin, the substantial water demand of the power industry brings about significant challenges to both energy and water resource security in the region. Due to the complexity and publicity of water resources and the property of “economic man” of power enterprises, the transformation of power generation structure calls for intervention and incentives from local governments urgently.

The power system studied in this paper primarily relies on combustible materials (such as coal) as fuel to generate electricity, while also engaging in other business activities. It is a highly water-consuming entity, mainly consisting of coal-fired power enterprise groups. These groups often engage in other energy-related activities. Since the power industry reform launched in 2003, five major state-owned power generation entities have been established in China, including State Power Investment Group Corporation, State Energy Investment Group, China Datang Power Group Corporation, China Huaneng Group, and China Huadian Group. Furthermore, along with the progress of reform, local energy conglomerates such as Shanxi Jinneng Group, Shanxi Coking Coal Group, Shandong Luneng Group, and Sichuan Energy Investment Group have emerged in the Yellow River Basin.

3.1. Construction of Evolutionary Game Model

3.1.1. Hypotheses of Evolutionary Game Model

This paper thus addresses two key stakeholders: Local governments and power generation groups, both characterized as bounded rational entities. The local governments under study are provincial and municipal administrative bodies within the Yellow River Basin, tasked with devising specific policies, guided by the central government’s strategies, with the aim of promoting water-efficient and locally tailored power generation practices. Friedman (1998) suggested that three or more participants can be considered as groups within evolutionary games [28]. Therefore, local governments are included in the group behavior category within the evolutionary game model.

Moreover, the power generation groups examined in this study predominantly utilize coal as fuel for electricity production, a process known for its high water consumption. In addition, these groups often engage in other energy-related activities. Since the power industry reform launched in 2003, five major state-owned power generation entities have been established in China, including State Power Investment Group Corporation (SPIC), State Energy Investment Group, China Datang Power Group Corporation, China Huaneng Group, and China Huadian Group. Furthermore, along with the progress of reform, local energy conglomerates such as Shanxi Jinneng Group, Shanxi Coking Coal Group, Shandong Luneng Group, and Sichuan Energy Investment Group have emerged in the Yellow River Basin. According to Friedman’s theory, these power generation groups also fall within the realm of group behavioral patterns in the evolutionary game model.

In order to provide a lucid explanation of the model, a series of assumptions are made by us in line with the actual circumstances.

Hypothesis 1:

As participants in the game, municipal governments and power generation enterprise groups compose the relatively stable complete system. Both municipal governments and power generation enterprise groups are individuals with the capability of learning from practice and dynamically adjusting their behavior and strategies in response to central government policies and external market conditions. Local governments could make the strategic choice in guiding power generation groups to expand the clean energy business, whereas power generation groups could also consider strategic options related to their clean energy business. In this hypothesis, t, x, and y stand for the probability of making the corresponding strategy choices (x,y ∈ [0,1]).

Hypothesis 2:

Under the direction of the local government, if the power generation group decides to expand the clean energy business, S + J − C is the income of the power generation group, where J denotes the subsidy that the local government grants to those power enterprises choosing to expand the clean energy business, S is the income for expanded clean energy business, and C is the cost input for expanding the clean energy business. At present, the income of the local government is V − J − L₁ − L₂, in which V represents the positive externality brought about by the improvement of water resources and environment conditions of the basin as contributed by the expansion and progress of clean energy business under the guidance of the local government. L₁ is the loss caused by the instability of clean energy, and L₂ is the waste of resources accrued to various regions in the basin by the consumption of clean energy. If the power generation group fails to expand its clean energy business, the revenue of the power generation group is −D₁ − D₂, and the income of the local government is −W + D₂, where W is regarded as the negative externality existing in the clean energy business for the water resources and the associated environment within the basin. For power enterprises that refrain from expanding their clean energy business, D1 represents the loss of development opportunities and market share, D₂ is the fee of resource and environment charged by local governments for power enterprises that do not expand clean energy business.

Hypothesis 3:

Without the guidance of the local government, if the power-producing group expands the business of clean energy, the income of the power generation group is S − C, and the income of the local government is V − L₁ − L₂; if the power-producing group chooses fossil fuels to generate electricity, the income of the power generation group is -D1, while the income of the local government is −W. The parameters and their description are shown in

Table 1. Parameters and their Description.

Parameter	Variable Name	Description
J	Government Subsidy	Subsidy provided by the local government to power generation groups expanding into clean energy
S	Income from Expansion	Income generated from expanding the clean energy business
C	Expansion Cost	Cost of expanding the clean energy business
V	Positive Externality	Positive externality from improved water resources and environmental conditions due to clean energy development
L1	Instability Loss	Losses caused by the instability of clean energy
L2	Resource Wastage	Resource wastage resulting from the consumption of clean energy
D1	Lost Market Share	Loss of market share and development opportunities for power companies not expanding into clean energy
D2	Environmental Resource Fee	Fees charged by local governments for power companies not expanding clean energy business
W	Negative Externality	Negative externality caused by clean energy development on water resources and the environment

.

According to the abovementioned hypothesis about the power generation structure of the local governments and power generation groups, we build the income matrix of the game behavior for each participant, which is presented in

Table 2. The Game income matrix of power generation and local government groups.

Game Players		Power Generation Group
		Expanding Clean Energy Business y	Not Expanding Clean Generation Business 1 − y
Local Governments	Guidance x	−J + V − L1 − L2	−W + D2
		J + S − C	−D1 − D2
	No Guidance 1 − x	V − L1 − L2	−W
		S − C	−D1

. The strategy choices of both parties in the game are shown in Figure 1.

3.1.2. The Evolution Process’s Balance Point

During the evolutionary game, participants assess the strategies of other players and determine their own strategies through ongoing trial-and-error learning and historical experience. The dynamic adjustment of strategies entails a process akin to dynamic copying. When the dynamic replication equation reaches 0, both sides of the game reach a local equilibrium state, thereby obtaining the evolutionary process’s balance point for the game participants.

(1) Based on the income matrix of game, local governments’ expected incomes when choosing to support or not support clean strategy are

$$\begin{array}{l}{U}_{11}=y(-J+V-L_1-L_2)+\left(1-y\right)(-W+D_2)\\ U_{12}=y(V-L_1-L_2)+\left(1-y\right)(-W)\end{array}$$

(1)

Consequently, the average revenue of the local government is $\overline{U_1}=x{U}_{11}+\left(1-x\right)U_{12}$.

Based on the Malthusian equation, the copying dynamic equation of the local government can be derived as

$$F\left(x\right)={\displaystyle \frac{dx}{dt}}=x(U_{11}-\overline{U_1})=x\left(1-x\right)\left[D_2-(J+D_2\right)y]$$

(2)

(2) The expected incomes of power generation groups choosing to expand or not expand the business of clean energy are

$$\begin{array}{l}{U}_{21}=x(J+S-C)+\left(1-x\right)(S-C)\hfill \\ U_{22}=x(-D_1-D_2)+\left(1-x\right)(-D_1)\hfill \end{array}$$

(3)

The average income of the power generation group is $\overline{U_2}=y{U}_{21}+\left(1-y\right)U_{22}$.

In accordance with the Malthusian equation, the copying dynamic equation of the power generation group can be derived as

$$F\left(y\right)={\displaystyle \frac{dy}{dt}}=y(U_{21}-\overline{U_2})=y\left(1-y\right)[(J+D_2)x+S-C+D_1]$$

(4)

During the evolutionary game process between local governments and power generation groups, the above dynamic copying process depicts the dynamic process of continuous learning of bounded rational groups. When both participants arrive at the stable state, it implies that they have discovered an effective Nash equilibrium by means of constant trials. Defining that $F\left(x\right)\mathrm{and}F\left(y\right)$ are equal to 0, respectively, two sets of stable solutions can be obtained by

$${\mathrm{x}}_1=0,{\mathrm{x}}_2=1,\mathrm{y}*={\displaystyle \frac{D_2}{J+D_2}}$$

(5)

$${\mathrm{y}}_1=0,{\mathrm{y}}_2=1,\mathrm{x}*={\displaystyle \frac{C-S-D_1}{J+D_2}}$$

According to the above formulas, it can be verified that five balance points exist in the system: E₁(0,0), E₂(0,1), E₃(1,0), E₄(1,1), and E₅(${\displaystyle \frac{C-S-D_1}{J+D_2}}$,${\displaystyle \frac{D_2}{J+D_2}}$).

3.2. Process and Stability Analysis of the CEGT in Yellow River Basin

3.2.1. Lotka–Volterra Model of the CEGT

The Lotka–Volterra model, originally developed to describe predator–prey interactions in ecological systems, is particularly well-suited for studying the dynamic relationship between fossil fuel generation technologies (FFGTs) and clean energy generation technologies (CEGTs). This model captures the competitive and cooperative nature of two interacting entities over time, making it an effective tool for understanding how FFGT and CEGT evolve in response to technological, market, and policy changes. In the context of energy transition, FFGT and CEGT can be seen as competitors for market share, with the growth of clean energy technologies potentially reducing the dominance of fossil-fuel-based power generation. The model’s non-linear dynamics are reflective of how the market share of FFGT may shrink as CEGT becomes more cost-competitive and technologically advanced. Similarly, the relationship between the two technologies can also exhibit elements of cooperation, particularly in transitional energy systems where hybrid solutions, such as natural gas supporting intermittent renewable energy, play a crucial role in grid stability. The ability of the Lotka–Volterra model to illustrate both competitive and symbiotic dynamics in a simple yet powerful framework makes it an ideal choice for studying this interplay.

However, despite its utility, the Lotka–Volterra model has notable limitations. Its assumptions of simple competition and mutual dependency between two entities may overlook the complexity of the energy sector. The model does not account for the multifaceted drivers of energy technology adoption, such as policy interventions (e.g., subsidies for renewables or carbon pricing), technological breakthroughs, and social factors like public acceptance. The use of the game theory model effectively compensates for the limitations of the Lotka–Volterra model. By constructing an evolutionary game model involving government and energy companies, we can simulate and analyze the impact of policy interventions (such as reward and punishment policies, fiscal and tax policies, etc.) on the diffusion and development of clean energy technologies. Therefore, this paper makes comprehensive use of both the evolutionary game model and the Lotka–Volterra model (Figure 2).

The game model depicts a decision-making process in which “people” are the main body [29], while the Lotka–Volterra model turns out to be a dynamic system model of differential equations developed from the biological population theory, which can be used in quantitative research on the cooperation and competition between populations [30,31]. The Lotka–Volterra model has been extensively utilized to conduct research on the symbiosis and diffusion of wind and solar energy [32] and to predict the fuel consumption of clean energy [33]. Drawing on prior research, this paper incorporates the L-V model to investigate the competition and diffusion among fossil fuel power generation technology (FFGT) and clean energy generation technology (CEGT) assuming that there are two groups specialized in the FFGT and the CEGT in the same power market. With the aim of acquiring more profits and market share, there exists competition between them in the power market. Based on the L-V model, the survival and evolution of fossil fuel power generation technology (FFGT) E₁ and clean energy generation technology (CEGT) E₂ at time t are

$$\left\{\begin{array}{l}{\displaystyle \frac{d{E}_1(t)}{dt}}=r_1{E}_1(1-{\displaystyle \frac{E_1}{N_1}}-{\partial }_{12}{\displaystyle \frac{E_2}{N_2}})\\ {\displaystyle \frac{d{E}_2(t)}{dt}}=r_2{E}_2(1-{\displaystyle \frac{E_2}{N_2}}-{\partial }_{21}{\displaystyle \frac{E_1}{N_1}})\end{array}\right.$$

(6)

For the power market, fossil fuel power generation technology (FFGT) and clean energy generation technology (CEGT) are dependent on each other and mutually influenced. From Equation (1), E₁ denotes the quantity of enterprises opting for the FFGT; E₂ denotes the quantity of enterprises opting for CEGT; r₁ and r₂ represent the diffusion rates of the FFGT and the CEGT, respectively; N₁ and N₂ respectively denote the maximum values of the FFGT and the CEGT; ${\partial }_{12}\mathrm{and}{\partial }_{21}$ are the competition coefficients; ${\partial }_{12}=N_1/N_2$ stands for the CEGT’s coefficient replacing FFGT, which demonstrates the support by local governments and markets to the clean energy power. ${\partial }_{21}=N_2/N_1$ is the FFGT’s coefficient inhibiting to the CEGT, which mainly reflects the stability of the FFGT and the dependence of local government and market on the FFGT. Both the FFGT and the CEGT are affected by blocking benefits, where ${\displaystyle \frac{E_i}{N_i}}(i=1,2)$ represents the inherent blocking benefit, ${\partial }_{ij}{\displaystyle \frac{E_j}{N_j}}(i,j=1,2,\mathrm{and}i\ne j)$ is the external influence’s blocking benefits.

3.2.2. Analysis of Evolutionary Stability of Clean Energy Generation Technology (CEGT)

For the purpose of probing into the equilibrium state of the dynamic evolution between the FFGT and the CEGT in the power market, ${\displaystyle \frac{d{E}_1(t)}{dt}}={\displaystyle \frac{d{E}_2(t)}{dt}}=0$ is defined and four evolutionary balance points, A₁(0,0), A₂(N₁,0), A₃(0,N₂), $A_4({\displaystyle \frac{N_1(1-{\partial }_{12})}{1-{\partial }_{12}{\partial }_{21}}},{\displaystyle \frac{N_2(1-{\partial }_{21})}{1-{\partial }_{12}{\partial }_{21}}})$, are achieved. In the initial development stage of clean energy power, a substantial amount of capital investment is required. Meanwhile, clean energy is likely to be suppressed by traditional coal power. As the CEGT’s market share gradually attains equilibrium, the acceptability of clean energy within the power market will also approach saturation. The linear relationship between the FFGT and the CEGT can be expressed as

$$\left\{\begin{array}{l}P:1-{\displaystyle \frac{E_1}{N_1}}-{\partial }_{12}{\displaystyle \frac{E_2}{N_2}}=0\\ Q:1-{\displaystyle \frac{E_2}{N_2}}-{\partial }_{21}{\displaystyle \frac{E_1}{N_1}}=0\end{array}\right.$$

(7)

The intersection of lines’ point P and E₁ = 0 is $(0,N_2/{\partial }_{12})$, the intersection of lines’ point P and E₂ = 0 is $(N_1,0)$; the intersection of lines’ point Q and E₁ = 0 is $(0,N_2)$; the intersection of lines’ point Q and E₂ = 0 is $(N_1/{\partial }_{21},0)$.

When ${\partial }_{21}>1$ and ${\partial }_{12}<1$, the balance point A₂(N₁,0) is stable. The two populations’ dynamic evolution trend is illustrated in Figure 3a. At this moment, the power production comes entirely from the FFGT, and the CEGT is completely suppressed.

When ${\partial }_{21}<1$ and ${\partial }_{12}>1$, the balance point A₃(0,N₂) is stable. The dynamic evolution trend of the two populations is shown in Figure 3b. At this time, the power production comes entirely from the CEGT, and the FFGT is completely replaced.

When ${\partial }_{12}<1$ and ${\partial }_{21}<1$, the balance point $A_4({\displaystyle \frac{N_1(1-{\partial }_{12})}{1-{\partial }_{12}{\partial }_{21}}},{\displaystyle \frac{N_2(1-{\partial }_{21})}{1-{\partial }_{12}{\partial }_{21}}})$ is stable. Two populations coexist within the market environment, and the dynamic evolution trend is shown in Figure 3c. At this time, the proportion of the FFGT and the CEGT in the power market is ${\displaystyle \frac{N_1(1-{\partial }_{12})}{N_2(1-{\partial }_{21})}}$.

When ${\partial }_{21}>1$ and ${\partial }_{12}>1$, the balance point $A_4({\displaystyle \frac{N_1(1-{\partial }_{12})}{1-{\partial }_{12}{\partial }_{21}}},{\displaystyle \frac{N_2(1-{\partial }_{21})}{1-{\partial }_{12}{\partial }_{21}}})$ is a saddle point. The two populations’ dynamic evolution trend is illustrated in Figure 3d. On the right-hand side of the OS curve, the influence of the CEGT on the FFGT is higher than the internal influence of the traditional one. Therefore, with the passage of time t, the FFGT tends to the point $({\displaystyle \frac{N_1}{{\partial }_{21}}},0)$. On the left-hand side of the OS curve, the influence of the FFGT on the CEGT is higher than the internal influence of the clean energy. Therefore, the CEGT tends to the point $(0,{\displaystyle \frac{N_2}{{\partial }_{12}}})$.

When ${\partial }_{21}=1$ and ${\partial }_{12}=1$, the straight lines of the FFGT and the CEGT are coincident. Every point on the line serves as the balance point.

4. Results of Evolutionary Game Model and Lotka–Volterra Model Simulation

According to the game analysis, we can see that government subsidies, water taxes, and cost inputs will affect the development of clean energy generation technology (CEGT) in power generation groups. In addition to the above factors, the speed and competitiveness of clean energy generation technology (CEGT) itself will also affect its diffusion. In order to mirror the dynamic diffusion process of the clean energy generation technology (CEGT) more intuitively and clearly, the Lotka–Volterra model is simulated and analyzed using Matlab software 2016a numerically.

4.1. Results of the Simulation Analysis of the Evolutionary Game Model

Based on the above analysis, within the dynamic copying system of local governments and power generation groups, it was found by us that the evolutionary game’s balance state of behavior strategies of the participants is influenced by numerous factors. In order to mirror the dynamic evolutionary process of the strategic choices made by local governments and to present power generation groups more clearly and intuitively, the game model under changing constraints is numerically simulated and analyzed using Matlab software.

The strategic choice of the power generation groups is not only affected by the subsidy of the local government J but also affected by the cost input of clean energy C, the income S, the loss of market share D₁, and the cost of resource and environment D₂. According to the statistics of Chinese Financial Yearbook 2020 released by the Ministry of Finance, the subsidy expenditure on renewable energy such as wind power, solar power, and biomass power in 2019 is CNY 86.61 billion. Referring to the water resources tax of the pilot city of Hebei Province, when the water consumption of the traditional coal power within the Yellow River Basin exceeds the planned quota by 20%, the price of industrial water consumption will rise to 4.1 yuan/m, while the average water consumption of thermal power units with cooling towers is 2 kg/Kw·h. China Energy Statistical Yearbook 2020 shows that the total output of the coal power reached 4.56 trillion kilowatt-hours at 2019, and the average water consumption of thermal power units with cooling towers is 2 kg/Kw·h. It can be calculated that thermal power will increase the cost of water resources to 45,600 × 2 × 0.001 × 4 × 2 × 20% = CNY 14.6 billion. It is assumed that the market share is the proportion of the sales income in the total income or target product income, and the market share is expressed by the sales income. If the power generation of renewable energy reaches 2.04 trillion kW·h in 2019, and the unit price of renewable clean energy is CNY 1 per kilowatt hour, the traditional coal power sector will lose CNY 20,400 million × 0.4 = CNY 816 billion due to the loss of the market share, and the income from the clean energy business amounts to CNY 2.04 trillion. It is supposed that the cost of expanding the clean energy business is CNY 3 trillion. According to the analysis of the above parameters, for simplified calculation, the values of the parameters at the initial stage are J = 0.08, S = 2, C = 3, D₁ = 0.8, D₂ = 0.01, the starting point of evolution is set as x = 0.5, y = 0.5, z = 0.5, where the vertical axis stands for the local government (x), the horizontal axis stands for time (t), and the power generation group is y.

A series of external shocks that occurred after 2020, such as the COVID-19 pandemic and the Russia–Ukraine war, caused sudden and uncertain changes in many areas, which may lead to fluctuations in energy markets across different regions. Therefore, using 2019 data provides a relatively independent context for the study. Future research can comprehensively consider various external shocks and use updated data for comparative analysis.

4.1.1. The Influence of Different Subsidies of Local Governments on the Evolution Path of Participants of Game Model

When the other parameters mentioned above remain constant, the amount of subsidy provided by the local government varies, and the subsidies J are 0.01, 0.08, and 0.20, respectively. The evolutionary stability strategy of the game subjects is shown in Figure 4. In Figure 1, the three blue lines corresponding to the power generation groups represent the strategy choices of energy enterprises regarding whether to expand clean energy business when the subsidy amounts are 0.01, 0.11, and 0.21. The blue line represents the strategy choices of energy enterprises, while the red line represents the strategy choices of the government. By plotting both the blue and red lines on the same graph, we can compare the strategy choices of both parties at the same time.

As revealed by Figure 4, during the evolution cycle, the impact of government subsidies on strategic choices of power generation groups is limited. The probability of local government choosing to support clean energy strategy will decrease with the increase in the subsidy at the initial stage. The probability curve will firstly fall to the lowest point, and thereafter rise, demonstrating a U shape. In the long run, the probability will be stabilized in the support strategy of y = 1. The amount of government subsidy is positively correlated with the evolution cycle, namely, the higher the amount of subsidy, the lower the enthusiasm of local government in choosing the support strategy and the longer it takes to reach the stable strategy. Therefore, the government subsidy amount is a coefficient in the evolutionary game model. By varying the subsidy amount, we obtain different strategy choices for both the government and enterprises. When the subsidy amount is low, the government is more willing to provide subsidies, but enterprises are less motivated to expand their clean energy business because the subsidy is insufficient to cover costs.

4.1.2. The Influence of Different Taxes and Fees of Water Resources on the Evolution Behaviors of Game Subjects

When other parameters remain unchanged, the tax and fee of water resource usage are changed for the game simulation. When the tax and fee D₂ is set at 0.01, 0.11, and 0.21, respectively, the evolutionarily stable strategy of game subjects is shown in Figure 5.

As revealed in Figure 5, whether or not power generation groups choose to expand their clean energy business is correlated to water resources’ tax and fee. The higher the water resource tax is, the stronger the willingness of power generation groups to expand their clean energy business will be. Specifically, when the tax and fee of water resources D₂ is 0.01 or 0.11, the strategic choice of power generation groups is basically consistent. It will finally stabilize on the strategy of not expanding clean energy business of y = 0. The higher the tax and fee of water resources is, the shorter the time to reaching the stable equilibrium state. It indicates that the strategic choice of power generation groups is constrained by the tax and fee of water resource usage. However, a low tax and fee on water resources alone are insufficient to prompt strategic adjustments by power generation groups. Instead, as the likelihood of local governments adopting guiding strategies increases, it will eventually stabilize at y = 1. When the tax and fee of water resources D₂ is 0.21, the incentive impacts of water resource tax and fee on the willingness of power generation groups to expand their clean energy business are more prominent. Although the probability of power generation groups choosing to expand clean energy business declines in the early stage of game evolution, it will increase in the long term and even exceed 0.9. Correspondingly, the probability curve of policy intervention by local governments demonstrates an inverted U shape, demonstrating that as the strategies of power generation groups change, the probability of local governments leveraging the tax and fee of water resource usage to guide energy structure transformation will increase at first and then decrease gradually after reaching the peak.

4.1.3. The Influence of Different Cost Inputs of Clean Energy Power on the Behavior of the Evolution of Game Subjects

With other parameters remaining unchanged, the cost inputs of clean energy power are changed. In Figure 6, the evolutionarily stable strategy of the game subjects when the cost input C is 2.5, 2.8, and 3.1, respectively, is shown.

As revealed in Figure 6, the cost input of clean energy business directly affects the strategic choice of power generation groups. When C = 3.1, C > S + D₁, the cost–benefit rate of power generation groups is less than 0, and the probability of the power generation groups expanding clean energy business continues to decline before stabilizing at y = 0, which indicates that the associated capital investment and construction costs are relatively high and therefore denting the motivation of power generation groups to expand their clean energy business. Under this scenario, local governments gradually adopt the strategy of not guiding energy transformation. Compared with the power generation groups, the time taken by local governments in reaching the strategy of evolutionary stability is longer, which indicates that the cost of expanding clean energy is too high and the subsidies of local governments are not enough to cushion the deficit incurred by power generation groups. Therefore, local governments will return to a rationality position and finally stabilize in the strategy of not guiding energy transformation. When C is 2.8, C < S + D₁ and the cost–benefit rate of power generation groups is equal to zero, the probability of local government choosing the guiding strategy exhibits a U-shaped gentle upward curve. Correspondingly, the probability of power generation groups choosing to expand their clean energy business continues to increase, with the probability always being higher than 0.5 and even more than 0.8. It proves that the guiding strategy of local governments can effectively stimulate power generation groups to expand their clean energy businesses. As a result, game subjects will move from the strategies of not guiding and not expanding clean energy businesses to those of guiding and expanding clean energy businesses. When C = 2.5, C < S + D₁, the cost–benefit rate of the power generation groups is higher than 0, and the probability of the power generation groups expanding clean energy businesses continues to rise and quickly stabilizes at y = 1, which indicates that when it is profitable to expand new business, no matter whether local governments provide incentives or not, the enthusiasm of the power generation groups to develop their clean energy business is high. The likelihood of local governments opting for the strategy of guidance gradually decreases and finally stabilizes at y = 0. It shows that with the increasing willingness and scale effect of the power generation groups in expanding clean energy businesses, the technology of clean power generation already boasts a cost advantage, and the mission of the government to guide the energy structure transition has been fulfilled. Under this scenario, the policy of government subsidy will be gradually phased out, and all game participants will return to rationality. Finally, it will achieve the evolution equilibrium state of not guiding clean energy transformation.

4.2. Results of the Simulation Analysis of the Lotka–Volterra Model

From the perspective of “people”, the above section analyzes the evolution of the power generation group’s choices regarding their clean energy business and reveals the effects of different strategies of government intervention and different cost inputs on the strategic choice of power generation groups. Based on the theory of the competition of populations in nature, this section makes use of the L-V model for the purpose of analyzing the cooperation and competition that exists between the FFGT and the CEGT in the market. At the beginning, the two technologies’ maximum capacity within the market is designated as N = 1000, and the effects of factors such as diffusion speed and competition coefficient in the model are discussed respectively. The diffusion’s inflection points of the two technologies (that is, the maximum market share) and the time to reaching the equilibrium are both analyzed, and the influencing factors of the technologies’ diffusion are revealed.

4.2.1. The Effect of Diffusion Velocity r on the Diffusion of Clean Energy Generation Technology (CEGT)

To examine the impact of diffusion velocity on the diffusion process, Figure 7 illustrates the diffusion dynamics of the CEGT under varying diffusion velocities. The simulation results indicate that, in the long run, the final equilibrium of both the FFGT and CEGT diffusion processes is independent of the diffusion velocity r. However, in the short term, both the inflection points of the diffusion curves and the time t required to reach equilibrium are influenced by the diffusion speed r. Initially, the diffusion rate of the FFGT in the market is significantly higher than that of the CEGT, causing the FFGT to spread rapidly and reach its peak. As the CEGT gradually enters the market, the market share of the FFGT begins to decline, leading to an inflection point (Figure 7a). Once the growth rate of the CEGT matches that of the FFGT, the market share of the CEGT increases, eventually surpassing that of the FFGT (Figure 7b). When the growth rate of the CEGT exceeds that of the FFGT, the market share of the CEGT grows quickly, significantly surpassing the FFGT (Figure 7c). From Figure 7a–c, it is evident that the larger the difference in diffusion velocities |r1 − r2|, the greater the market share of the technology with the comparative advantage.

From the evolutionary game model in Equation (4), the power generation group’s strategy choice is strongly influenced by both the cost of the CEGT and the cost of resource use. When the cost of the CEGT is lower than the amount of water it saves, enterprises are more likely to opt for the CEGT. The evolutionary game model emphasizes the innovation of the CEGT, whereas the Lotka–Volterra model is more focused on the diffusion of the CEGT. As discussed in Section 4.2.1, the growth rate r₁ represents the resistance of water cost to the diffusion of the FFGT, while the growth rate r₂ reflects the resistance of innovation costs to the diffusion of the CEGT. The greater the resistance, the slower the diffusion rate. In other words, the higher the innovation cost, the slower the diffusion of the CEGT will be.

4.2.2. The Effect of Competition Coefficient on the Diffusion of Clean Energy Generation Technology (CEGT)

To investigate the effect of the competition coefficient in the diffusion process, we suppose that r₁ = r₂ = 0.5. Figure 8 is the diffusion dynamics of the CEGT and FFGT under different competition coefficients. The simulation results suggest that the final equilibrium of the diffusion process is strongly influenced by the competition coefficient. While the competition coefficient for both technologies is below 1 and ${\partial }_{12}<{\partial }_{21}$, that is, the substitution of the CEGT to the FFGT is less than the inhibition of the FFGT to the CEGT, the final equilibrium state is realized with two populations occupying the market together, while the share of the FFGT is absolutely dominant. When both technologies’ competition coefficient is below 1 and ${\partial }_{12}>{\partial }_{21}$, namely, the substitution of the CEGT to the FFGT surpasses the inhibition of the FFGT on the CEGT, the ultimate equilibrium still is the market occupied by two technologies together, but the share of the CEGT becomes absolutely dominant. Once ${\partial }_{12}$ exceeds 1, following intense competition between the FFGT and the CEGT, the CEGT achieves the market and competitive advantage monopoly, whereas the FFGT is squeezed out of the market.

According to Section 3.2.1 and Section 3.2.2, the competition coefficient primarily manifests in the subsidy support from governments for clean energy generation technology (CEGT) and the tax penalties for fossil fuel generation technology (FFGT). The simulation results of the Lotka–Volterra model indicate that the CEGT will establish dominance in the competition under strong government backing. Similarly, the evolutionary model’s outcomes reveal that within a specific subsidy coefficient range, enterprises show heightened enthusiasm for innovating the CEGT. This implies that government subsidies amplify enterprise support for the CEGT, thereby elevating its competition coefficient. The heightened competition coefficient enables the CEGT to secure a dominant position. The analysis underscores the alignment between the evolutionary model results and those of the Lotka–Volterra model.

5. Discussion

Due to the public nature and complexity of water resources, as well as the “economic man” attributes of enterprises, the power structure transformation of coal power companies cannot be achieved without intervention and regulation by local governments. Through the analysis using the evolutionary game model, this study finds that when the government subsidy coefficient is low, government regulation is insufficient to motivate enterprises to expand their clean energy business. In contrast, the water resource tax policy has a more significant incentive effect on coal power companies’ expansion into clean energy. In the long run, the probability of enterprises expanding into clean energy business even exceeds 0.9, which is consistent with other findings [11], although that study specifically focused on wind energy as a form of clean energy. Additionally, through the Lotka–Volterra model analysis, we find that, in the long term, the extent of clean energy technology diffusion is unrelated to its diffusion speed but is closely related to the competition coefficient. A larger competition coefficient will enable clean energy technology to gain an advantageous position in market competition. This conclusion aligns with the study [33], which used the Lotka–Volterra model to analyze the competition and cooperation between low-carbon energy and fossil fuels from the perspective of carbon dioxide emissions.

Regarding energy enterprises in the Yellow River Basin, it is worth noting that the main energy companies in this region are predominantly state-owned. For example, in the coal power sector, large state-owned enterprises such as the State Power Investment Corporation and China Huaneng Group dominate the market. Therefore, the energy enterprises mentioned in the paper are mostly state-owned, which reflects the actual situation in the Yellow River Basin. However, with the development of the clean energy market, some private enterprises have gradually entered the clean energy sector and have experienced rapid growth. This has made collaboration between the government and private enterprises an important pathway for promoting the adoption of clean energy technologies. For example, the Ningxia government has actively guided private enterprises to invest in solar photovoltaic power projects, providing tax incentives and financial subsidies, which has promoted the utilization of clean energy in the region and reduced dependence on traditional fossil fuels. This is also an important direction for our future research.

The Yellow River Basin has particularities compared to other regions with water scarcity, both in China and globally. Its clean energy development exhibits some distinct differences when compared to other regions with similar constraints. These differences are mainly reflected in the types of clean energy diffusion and the direction of government-led clean energy development. For example, compared to Middle Eastern countries such as Saudi Arabia and the UAE, although both the Middle East and the Yellow River Basin face water scarcity issues, the former, with its excellent sunlight conditions, focuses more on solar energy development. In contrast, the Yellow River Basin, with superior wind and solar resources, primarily relies on wind power and photovoltaic generation for clean energy development. Additionally, the clean energy development in the Middle East emphasizes technology importation and innovation, such as large-scale solar power and seawater desalination projects. Government policies in the region tend to focus on attracting foreign investment and technological cooperation. Meanwhile, the Yellow River Basin places greater emphasis on the efficient use of local resources and the construction of a water-saving society. Its government policies also focus on providing transitional support for stakeholders in traditional energy sectors, ensuring a smooth transition in energy structure transformation. Therefore, despite having similar constraints, the diffusion of clean energy development in different regions is unique. It is essential to adopt region-specific, differentiated policies to support the local energy transition.

6. Conclusions and Political Suggestions

Recently, with the accelerating pace of urbanization and industrialization, social and economic development increasingly depends on the support of natural resources. Water resources, as fundamental natural resources and strategic economic resources, are crucial for the national economy, people’s livelihoods, and energy production. However, the Yellow River Basin is situated in an arid region. The high concentration of power enterprises in the basin brings about significant challenges to the balance between water sustainability and economic development. This conflict represents a typical game situation between power generation groups and local governments.

Therefore, this paper utilizes game theory to construct an evolutionary game model involving power generation groups and local governments. It explores the asymptotic stability of the equilibrium point and the evolutionary stability strategies of the participants. Additionally, a bionic L-V model is introduced to study the process of diffusion and competition between traditional coal power and clean energy power. The following are the key conclusions: First, low subsidies from local governments are insufficient to encourage power generation groups to expand their clean energy business. The expansion of clean energy business by power generation groups is influenced by water resource taxes and fees. Higher taxes and fees lead to stronger willingness among power generation groups to expand their clean energy business. Second, the cost input of the clean energy business directly affects the strategic choices of power generation groups. As costs and incomes increase, both local governments and power generation groups will transition from strategies of no guidance and no expansion to those of guidance and expansion. Eventually, the situation reaches an equilibrium of no guidance and expansion. Third, the ultimate equilibrium of the diffusion process of the FFGT and the CEGT is independent of the diffusion speed. However, in the short term, larger differences in diffusion speeds between the two technologies will lead to a longer time to reach equilibrium. Fourth, the ultimate equilibrium of the diffusion process of the FFGT and the CEGT has a close correlation with the competition coefficient. A higher competition coefficient results in the CEGT achieving dominance in the market competition until it monopolizes the market.

In light of these conclusions, the subsequent policy recommendations are put forward: First, local governments should consider the policy of increasing the rate of water resource tax to encourage water-saving behaviors among large water consumers. The study of this paper shows that power generation groups will choose to expand their clean energy business more actively when the water resource tax is higher. In addition, higher tax revenues can help make up for the cost of guidance incentives offered by local governments. Therefore, we suggest that local governments increase taxes and fees of water resource usage so as to harvest the double dividends of boosting tax revenues and speeding up water resource tax reform. Furthermore, we suggest that local governments utilize the income of water resource taxes and fees to build up a special water fund for promoting intensive use and ecological protection of local natural resources. Second, local governments should support technological innovation in clean energy development with a view to reducing the cost input and enhancing competitiveness. The analysis in this paper suggests that the expansion of clean energy business by power generation groups depends more on cost input than government subsidies. Technological innovation is the primary driver for improving quality, increasing efficiency, and reducing cost. Therefore, we suggest that local governments should support and encourage the technological innovation of clean energy when they decide to provide incentives. As a major water consumer, the power industry ought to be incorporated into the annual technological transformation and upgrading plan formulated by the local Industry and Information Technology Departments. Additionally, the financial backing for energy transformation projects needs to be enhanced through industrial funds, bond financing, and revenues from water resource taxes. Third, local governments should increase subsidies to improve the competition coefficient of clean energy and promote its development. The bionic model in this paper indicates that the competition coefficient plays a bigger role than the diffusion coefficient in determining the market share, with the level of local government support figuring high in the game. Therefore, we suggest that local governments should increase subsidies for clean energy power generation and establish special funds for clean energy development. In addition, government subsidies should be allocated according to the principle of proportioning financial support to the size of expanded clean energy business.

Fourth, water resource tax revenue should be effectively allocated for the development of clean energy. Local governments should establish a dedicated “Water Resources Tax Clean Energy Development Fund”. The fund’s revenue primarily comes from the collection of water resource tax, and it should be earmarked exclusively for the research, construction, and promotion of clean energy projects. A sound auditing and supervision mechanism should be established to ensure that funds are allocated in accordance with project needs, preventing misuse of funds or resource wastage.

Fifth, the potential resistance of the fossil fuel industry to clean energy should be mitigated. The government should set a clear transition period to ensure that companies and workers in the coal power industry can smoothly transition to the clean energy sector. During the transition period, the government can provide subsidies or financial compensation to assist coal power companies with equipment upgrades, modifications, or industrial transformation. A fair carbon pricing system should be promoted, where the government allows the fossil fuel industry to bear its environmental costs, while also creating a fair competitive environment for the clean energy industry.

The promotion of clean energy is not only a technical and policy challenge but also involves profound socio-economic impacts. The interaction between social equity, urban development, and the diffusion of clean energy may influence policy formulation and the effectiveness of technology implementation. Therefore, future research could focus on the following areas: (1) The relationship between clean energy and social equity: Exploring how the promotion of clean energy affects the interests of different social groups, particularly low-income groups and remote areas. (2) The interaction between clean energy and urban development: Analyzing the role of clean energy in the urbanization process, especially in rapidly urbanizing regions, and how to balance energy demand with environmental protection to promote green urban development. (3) The social effects of policies: Further studying how governments, when promoting clean energy policies, consider the needs of social equity and urban sustainability to create more balanced and comprehensive policies.