Spatial network analysis of green electricity efficiency dynamics in the Yellow River Basin cities

Abstract

Improving the green electricity efficiency (GEE), is an important issue for China's high-quality economic development. This study presents a spatial correlation network of urban GEE in the Yellow River Basin from 2012 to 2021, constructed using an improved gravity model. Social network analysis and the quadratic assignment procedure method are employed to analyze the spatial correlation characteristics and influencing factors. The findings indicate that urban GEE in the Yellow River Basin exhibits complex and stable network characteristics. The spatial network analysis reveals that Jiayuguan City, Dongying City, Dingxi City, Zibo City, and Shizuishan City occupy central positions within the network. The results indicate that spatial adjacency, GDP per capita, industrial structure, and the level of science and technology expenditure are positively related to urban GEE, while environmental regulation and average temperature are negatively related. The findings of the study have led to policy recommendations aimed at enhancing urban GEE in the Yellow River Basin.

Introduction

Countries around the world are facing environmental problems such as climate change¹, land desertification², and resource scarcity³, which pose serious challenges to ecological health and sustainable development. As a countermeasure, the concept of green development has been widely recognized⁴, emphasizing the harmonious symbiosis between social progress and the natural environment. The thermal power generation sector is the largest source of carbon emissions in the industrial sector, accounting for more than 40% of total emissions⁵. Therefore, the power sector's greening transformation should have a significant impact on climate change mitigation^6,7. China, as a responsible developing country, has already taken such measures. For example, the National Energy Administration (NEA) has proposed prioritizing clean energy in grid access, the National Development and Reform Commission (NDRC) has proposed increasing the share of clean energy in inter-provincial and regional power transmission and reception, and the State Grid has continued to promote large-scale grid integration of clean energy and large-scale trading of clean power across regions and provinces. With strong support from policy, science and technology, capital, and other factors, the world's first dedicated clean energy channel, the "Qinghai-Tibet Electricity Transmission," has rapidly developed, providing an example of inter-provincial cooperation in the development of clean energy. The momentum of green energy use across provinces is gaining traction. In this context, realizing green development, especially improving the green electricity efficiency (GEE), is an important issue for China's high-quality economic development.

Most of the available studies on GEE focus on the carbon emission performance of the power sector⁸, integrated green energy efficiency⁹, green innovation efficiency of the energy sector¹⁰, and the electricity price market¹¹. These studies often concentrate on the relationship between a single factor and GEE, and there is a lack of analysis on the relationships and drivers of GEE. Since the realization of the "double carbon" goal on schedule requires provinces to cooperate in greening the power industry, it is necessary to explore the spatial relationships and drivers of GEE. Therefore, this study explores the spatial dynamic correlations and driving mechanisms of urban GEE in the Yellow River Basin. Specifically, the overall network structure characteristics, centrality, and block model of GEE are analyzed using social network analysis (SNA). Additionally, the driving factors of the spatial dynamic correlation network of urban GEE in the Yellow River Basin and its practical application effects are explored, with a view to supporting the inter-provincial and inter-regional connection and interaction of greening the electric power industry.

With the implementation of China's 'north to south coal transportation' and 'west to east power transmission' policies, it is of great practical significance to thoroughly analyze the overall network structure of urban GEE in the Yellow River Basin, and clarify the roles of each region in the spatial network of green development of the electric power industry, to promote emission reduction and sustainable development of the power sector. Although existing studies have revealed significant spatial effects of green development in the electric power sector¹², the following limitations remain: First, most studies rely on traditional spatial econometrics⁶, which tend to ignore spatial network effects. In addition, traditional spatial econometric methods usually study 'quantity' effects, but not 'relationship' effects. Second, most studies use attribute data rather than relationship data, making it difficult to characterize the whole network structure of the spatial correlation of GEE. Finally, most studies on GEE are conducted from the perspective of the whole country, the Yangtze River Economic Belt, or major provinces, lacking exploration of the Yellow River Basin. However, the Yellow River Basin has a long history of power industry development. The coal reserves in the basin account for more than half of China's total reserves, there are six 10-million-kilowatt large-scale coal power bases, and more than half of the 19 photovoltaic power generation leading bases are located in or immediately adjacent to the Yellow River Basin. Therefore, the importance of green power development in the Yellow River Basin is evident both regionally and nationally.

In this study, relational data and network analysis methods are used to deeply explore and elucidate the spatial network characteristics of urban GEE and its dynamic changes in the Yellow River Basin. First, an extended gravity model is introduced to more accurately quantify and explain the intensity of interactions among prefecture-level cities in the Yellow River Basin. Then, SNA is applied to reveal the spatial network structure, evolutionary trend, and regional agglomeration characteristics of GEE, and to explore the roles and influences of each city in this network. In addition, the study further investigates the driving factors behind the formation of the spatial network of urban GEE in the Yellow River Basin using the quadratic assignment procedure (QAP) analysis method. This approach provides a new perspective and empirical basis for understanding resource flows and promoting the coordinated development of regional green power.

In summary, this study has the following three contributions. In terms of research perspective, the concept of green development is integrated into the electric power industry, and the analysis of GEE provides countermeasures and suggestions for developing countries to solve the dilemma of energy inefficiency and achieve green economic and social transformation and sustainable development. In terms of research methodology, SNA is used to analyze the network space of urban GEE in the Yellow River Basin. The constructed social relationship matrix serves as the basis to describe the network space association and structural attribute characteristics. In terms of research objects, this study focuses on 69 cities in the Yellow River Basin of a specific region, rather than a macro-region. As the most important ecological barrier and economic zone in China, the Yellow River Basin holds a crucial strategic position in ecological protection and socio-economic development. Exploring the spatial correlation network of urban ecosystems at a specific geographical level is significant in proposing differentiated green development paths for local governments. The rest of the study is organized as follows: Section "Method model and data" introduces the research design, detailing the full model used in this study and the reasons for its selection. Section "Results and analysis" presents the study's results, explaining the characteristics of the spatial correlation network and the drivers of urban GEE in the Yellow River Basin. Section "Discussion" discusses the findings. Section "Conclusions and policy implications" provides the conclusion and policy recommendations.

Method model and data

Study area

The Yellow River Basin is an important agricultural production area and ecological security barrier. Referring to the division of the natural catchment area of the Yellow River by the Yellow River Commission of the Ministry of Water Resources, and considering the natural resources and socio-economic conditions of agricultural production, 69 prefecture-level administrative counties in Qinghai, Sichuan, Gansu, Ningxia, Inner Mongolia, Shanxi, Shaanxi, Henan, and Shandong were included in this study. The Yellow River Basin is rich in energy and minerals, wind, solar, and hydro energy, and has a strong foundation for the development of the electric power industry. According to the National Land Planning Outline (2016–2030) and the Strategic Action Plan for Energy Development (2014–2020), eightofthe14-billion-ton large-scale coal bases that China is focusing on building are located in the Yellow River Basin and nearby areas, with the basin's coal reserves accounting for more than half of the country's total reserves. Additionally, six of the nine ten-million-kilowatt large-scale coal power bases that China is focusing on building are situated in the Yellow River Basin. Besides coal power, the western part of Inner Mongolia is one of China's nine large-scale modern wind power bases with associated transmission projects. More than half of China's 19 photovoltaic power generation bases are located in or near the Yellow River Basin. Furthermore, in the 1980s, the Upper Yellow River Hydropower Base and the Middle Yellow River Hydropower Base were listed among China's thirteen major hydropower bases. The Yellow River Basin has a long history of development in the electric power industry, underscoring its importance both regionally and nationally.

Method model

Super-SBM method

The super-SBM method overcomes the problem of overestimation of production efficiency caused by ignoring non-desired outputs in energy production in traditional DEA models¹³, and at the same time performs the sorting of decision units at the frontier, which is widely used in natural resource efficiency measurement¹⁴, and sets $n$、$m$、${r}_{1}$ and ${r}_{2}$ as the number of decision units, input indicators, desired output indicators and undesired output indicators, respectively, in the process of GEE. be the number of decision units, input indicators, desired output indicators and undesired output indicators, respectively, in the process of GEE, and $x$、${y}^{g}$、${y}^{b}$ be the inputs, desired outputs and undesired outputs, respectively. Where, $x\in {R}^{m}$,${y}^{g}\in {R}^{{r}_{1}}$,${y}^{b}\in {R}^{{r}_{2}}$, and define the matrix $X=\left[{x}_{1},\cdot \cdot \cdot ,{x}_{n}\right]\in {R}^{m-n}$, ${Y}^{g}=\left[{y}_{1}^{g},\cdot \cdot \cdot ,{y}_{n}^{g}\right]\in {R}^{{r}_{1}-n}$, ${Y}^{b}=\left[{y}_{1}^{b},\cdot \cdot \cdot ,{y}_{n}^{db}\right]\in {R}^{{r}_{2}-n}$. The model is built as follows:

$$ \min \rho = \frac{{\frac{1}{m}\sum\limits_{i = 1}^{m} {({{\overline{x}} \mathord{\left/ {\vphantom {{\overline{x}} {x_{ik} )}}} \right. \kern-0pt} {x_{ik} )}}} }}{{\frac{1}{{r_{1} + r_{2} }}\left[ {\sum\limits_{r = 1}^{{r_{1} }} {({{\overline{y}^{g} } \mathord{\left/ {\vphantom {{\overline{y}^{g} } {y_{{{\text{sk}}}}^{g} }}} \right. \kern-0pt} {y_{{{\text{sk}}}}^{g} }}) + \sum\limits_{q = 1}^{{r_{2} }} {({{\overline{y}^{b} } \mathord{\left/ {\vphantom {{\overline{y}^{b} } {y_{{{\text{sk}}}}^{b} }}} \right. \kern-0pt} {y_{{{\text{sk}}}}^{b} }})} } } \right]}} $$

(1)

$$ s.t.\left\{ \begin{gathered} \overline{x} \ge \sum\limits_{j = 1, \ne k}^{n} {x_{ij} \lambda_{j} ;{\overline{\text{y}}}^{{\text{g}}} \le \sum\limits_{j = 1, \ne k}^{n} {y_{sj}^{g} \lambda_{j} ;{\overline{\text{y}}}^{{\text{b}}} \ge \sum\limits_{j = 1, \ne k}^{n} {y_{qj}^{{\text{b}}} \lambda_{j} ;} } } \\ \overline{x} \ge x_{k} ;{\overline{\text{y}}}^{{\text{g}}} \ge y_{k}^{g} ;{\overline{\text{y}}}^{b} \ge y_{k}^{b} \\ \lambda_{j} \ge 0,i = 1,...,m;j = 1,...,n; \\ {\text{j}} \ne 0,s = 1,...,r1;q = 1,...,r2 \\ \end{gathered} \right. $$

(2)

In Eq. (1)-Eq. (2), $\rho$ is the GEE value of the evaluation unit. If $\rho \ge 1$, the evaluation unit is efficient; if $\rho <1$, there is an efficiency loss. $\overline{x }$、$\overline{y}^{g}$、${\overline{\text{y}}}^{b}$ are the redundancy of inputs, desired outputs, and undesired outputs, respectively. $\lambda_{{\text{j}}}$ is the weight vector.

In order to measure the GEE, this study selects the input–output panel data of 69 prefecture-level cities from 2012 to 2021 for the relevant measurements, and constructs the relevant input–output indicators as the amount of capital input, labor input and energy input, as well as the desired outputs and non-desired outputs, and the relevant indicators are set up as follows with reference to the research results of Meng and Qu¹⁵and Liu et al.⁹:

(1) Relevant Input Indicators.

Capital input (K). Introducing the perpetual inventory method adopted by Shan(2008)¹⁶, the capital input is expressed as follows:

$${K}_{it}={I}_{it}/{P}_{it}+\left(1-\sigma \right){K}_{i,t-1}$$

(3)

In the above equation, ${K}_{it}$、${I}_{it}$、${P}_{it}$ and $\sigma$ respectively denote the capital stock, gross fixed asset formation and fixed asset price deflator, as well as the asset depreciation rate of the $i$th prefecture-level city in the $t$th year.

Labor input (L). Considering the effective labor force actually involved in the production process, this study selects the number of employees at the end of the year in each prefecture-level city to measure the amount of labor input.

Energy input (E). Energy input is measured by the total social electricity consumption of each prefecture-level city.

(2) Related Output Indicators.

Expected Output (GDP). This study treats GDP at 2012 constant prices to eliminate the effects of inflation and other factors.

Unwanted Output (Poll). The 12th Five-Year Plan for Energy Conservation and Emission Reduction states that the key indicators for environmental regulation are industrial sulfur dioxide and wastewater emissions¹⁷. In addition, soot (particulate matter) emissions are solid wastes from fossil fuel combustion, which also pollute the environment. Therefore, this study converts the three pollutant indicators of SO₂ emissions, soot (particulate matter) emissions, and total wastewater discharges of each prefecture-level city to synthesize an environmental pollution indicator that can comprehensively reflect the undesirable outputs, and defines it as the environmental pollution composite index, which serves as a proxy for the undesirable outputs, i.e., environmental pollution. In summary, by combining the availability, scientific and accuracy of data, the evaluation index system of GEE is constructed, as shown in Table 1.

Table 1 GEE input–output indicator system.

Social network analysis (SNA)

Social network analysis (SNA) is a method for studying phenomena such as network structure, organizational relationships, and resource factor flows. It is widely used in the fields of economics, management, and sociology¹⁸. This study employs SNA to examine the correlation between GEE among the cities in the Yellow River Basin. The cities interact and conduct business with each other in geospatial space, gradually forming a network-type correlation relationship¹⁹. The cities in the Yellow River Basin serve as the "points" in the spatial correlation network structure, while the mutual transmission is the "line" in the spatial correlation network structure. These points and lines collectively constitute the spatial correlation network of GEE among the cities in the Yellow River Basin. Currently, the trade gravity model primarily uses the perspective of "spatial distance" to assess the interaction relationship between various elements, subsequently determining the "relationship" between elements. Nevertheless, the limitations of the trade gravity model preclude its ability to accurately and effectively assess the efficiency relationship between regions. Referring to the study by Liu and Song²⁰, a modified gravity model considering economic geographic distance is introduced, constructing the gravity coefficient using GDP to measure the spatial correlation strength of urban GEE in the Yellow River Basin, as shown in Eq. (4):

$${F}_{ij}={k}_{ij}\frac{{N}_{i}{N}_{j}}{{D}_{ij}^{2}},{K}_{ij}=\frac{{G}_{i}}{{G}_{i}+{G}_{j}},{D}_{ij}^{2}={\left(\frac{{d}_{ij}}{{g}_{i}-{g}_{j}}\right)}^{2}$$

(4)

where ${F}_{ij}$ is the linkage intensity, ${K}_{ij}$ is the gravity coefficient, $N$ is the GEE, ${d}_{ij}$ is the spherical distance between cities, and $G$ and $g$ denote the city GDP and GDP per capita, respectively.To better compare the degree of linkage between cities, based on Liu et al.²¹, the mean of the data in the rows of the matrix is used as the threshold, and the matrix is binarized. If the linkage intensity is greater than the threshold value, a value of 1 is assigned to indicate the existence of GEE linkage between cities, and vice versa, a value of 0 is assigned to indicate the absence of linkage²².

Based on the spatial correlation matrix, this study analyzes the overall, individual, and local structural characteristics of the spatial correlation network of urban GEE in the Yellow River Basin. The overall network structure is analyzed in terms of network density, network relevance, network efficiency, and network hierarchy. Individual network characteristics are analyzed in terms of degree centrality, betweenness centrality, and closeness centrality, with degree centrality further divided into in-degree and out-degree. The block model is an important method for measuring clustering within spatially correlated networks and draws on related studies by Faust et al.²³and Sweet et al.²² to analyze clustering according to "brokers," "net spillovers," "two-way spillovers," and "net benefits." See Appendix A for the detailed formulas, block model analysis, and segment definitions for the overall network structure and individual network structure indicators.

Quadratic assignment process method (QAP)

The QAP is a nonparametric method for identifying the influencing factors of the spatial correlation network of independent variables based on 'relational data.' It does not require assumptions of independence and normal distribution, and can effectively address the problem of multicollinearity that may exist in relational data, thereby obtaining robust and effective estimation results^24,25. Following an analysis of the structural characteristics of the GEE spatial correlation network, it is necessary to further examine the factors that drive change in this network. These factors can alter the network, resulting in different structural features. Therefore, this study adopts the QAP method to explore the driving factors of the spatial correlation network of urban GEE in the Yellow River Basin. Referring to existing studies^26,27,28, the driving factors selected in this study are shown in Table 2.

Table 2 List of variables of QAP method.

The driving econometric model to construct the spatial correlation network of urban GEE in the Yellow River Basin is as follows:

$${N}_{t}=f\left(Geo,Pgdp,Ind,Env,Tech,Tem\right)$$

(5)

In the equation, ${N}_{t}$ represents the spatial correlation matrix of urban GEE within the Yellow River Basin region in the year $t$; Geo represents the geographical adjacency matrix; $Pgdp$, $Ind$, $Env$, $Tech$ and $Tem$ represent the network matrices of the differences in each factor.

Data sources

The data for urban GEE evaluation indicators, the gravity model, and driving variables in the Yellow River Basin were obtained from the China Statistical Yearbook, the China Rural Statistical Yearbook, China Population, and provincial statistical yearbooks and statistical bulletins. The vector administrative boundary map of Chinese cities is based on 1:500,000 geographic information provided by the National Geographic Information Center of China (http://www.ngcc.cn/ngcc/), the most authoritative published database in China that integrates geographic information storage, data management, map production, and data application, and is capable of spatial analysis and manipulation of the vector administrative boundaries of the study samples. In case of missing data for some regional variables, linear interpolation was used to supplement the data.

Results and analysis

Characterization of the spatial correlation network structure of urban GEE in the Yellow River Basin

In this study, the spatial correlation of urban GEE in the Yellow River Basin is determined, and the relationship matrix is constructed according to the modified gravity model. To illustrate the spatial correlation network structure of urban GEE in the Yellow River Basin, this study creates a network diagram of urban GEE in the Yellow River Basin for 2021, as shown in Fig. 1. Figure 1 was drawn using the Netdraw tool in Ucinet 6.0. The spatial correlation of urban GEE in the Yellow River Basin presents a typical network structure. The improvement of GEE in this region is influenced by other regions, and this influence transcends the limitation of spatial proximity distance, forming a cross-regional spatial network correlation. Therefore, it is necessary to further analyze the characteristics of the spatial network structure of urban GEE in the Yellow River Basin.

Figure 1

Spatial correlation network map of urban GEE in the Yellow River Basin in 2021.

Characterizing the overall network structure

The overall characteristics of the spatial correlation network of urban GEE in the Yellow River Basin were measured using Ucinet 6.0 from 2001 to 2021. The spatial correlation network of urban GEE in the Yellow River Basin exhibited low correlation and strong stability. Furthermore, there were significant spatial correlation and spillover effects of GEE among cities. Figure 2 illustrates the temporal trends of the spatial correlation network density, the number of network connections, and the network correlation degree of urban GEE in the Yellow River Basin between 2012 and 2021. During the study period, the network density of urban GEE in the Yellow River Basin showed an overall fluctuating upward trend, with the network density peaking in 2020. The average network density during the study period was 0.248, indicating that the spatial connection of urban GEE was established and the closeness of the spatial correlation of urban GEE in the Yellow River Basin was constantly increasing. Nevertheless, considering the absolute value, the communication and cooperation intensity of urban GEE in the Yellow River Basin is average, and the cohesion level is generally satisfactory. The highest network density value during the study period is 0.273, which is not significantly different from the theoretical maximum value, but there is still room for improvement. Consequently, it is imperative to intensify the collaborative advancement of green power utilization among cities in the Yellow River Basin, thereby collectively establishing a spatial correlation network of GEE.

Figure 2

Spatial correlations and network density.

During the sample period, the number of urban GEE network correlations in the Yellow River Basin exhibited a fluctuating downward and then upward trend, essentially consistent with the trajectory of the network density value. This fluctuation is primarily attributable to the impact of energy conservation and emission reduction policies, which improved the environmental performance of coal and thermal power in the Yellow River Basin. Consequently, the number of associations in the GEE spatial correlation network decreased from 2012 to 2014. Furthermore, the value of the urban GEE network correlation in the Yellow River Basin remained consistently at 1 from 2012 to 2021. This indicates that although the density of urban GEE networks and the number of network associations fluctuated yearly, the overall network structure maintained a certain degree of stability and accessibility. Additionally, it can be observed that most cities have already established a robust green electricity cooperative relationship with one another.

Figure 3 depicts the trends of spatial correlation network efficiency and network hierarchy of urban GEE in the Yellow River Basin between 2012 and 2021. The network efficiency values range from 0.749 to 0.795, indicating low redundancy in the spatial correlation network and relatively stable urban GEE. However, there is still room for improvement. The network ranking degree demonstrates a fluctuating and then stabilizing trend, stabilizing at 0.057 in most years. This indicates that the spatial correlation network lacks a strict hierarchical order and that there are no barriers to network linkages. Additionally, it suggests that the linkage level of GEE between cities continues to improve, allowing changes in GEE in one city to be rapidly transmitted to other cities. Improvements in the spatial association network of cities with lower GEE levels can significantly enhance network function, emphasizing the need for inter-provincial and inter-regional cooperation in green electricity development. The northwestern part of the Yellow River Basin, rich in wind and solar energy resources and vast land, is ideal for large-scale wind and solar power generation facilities. However, the population size and technology level in this region are not as advanced as those in the eastern part of the basin. Consequently, cooperative development between the western and eastern parts of the Yellow River Basin can enhance overall GEE. Therefore, cities within the Yellow River Basin must leverage the region's energy resources to minimize enterprise energy costs and facilitate regional economic growth.

Figure 3

Network level and network efficiency.

Characterizing the individual network structure

By analyzing the overall network characteristics, this study has preliminarily clarified the overall spatial correlation network of urban GEE in the Yellow River Basin but failed to explore the specifics of network node centrality. Therefore, it is necessary to further measure and analyze the individual network characteristics. Ucinet 6.0 is used to measure the centrality indicators of the spatial correlation network of urban GEE in the Yellow River Basin from 2001 to 2021, revealing the position and role of each region in the network. Taking 2021 as an example, ArcGIS was used to draw the centrality distribution map for analysis.

The point-in degree represents the influence exerted by other cities, while the point-out degree represents a city's capacity to influence other cities. If the point-in degree exceeds the point-out degree, there is a net benefit effect; otherwise, there is a net spillover effect. Figure 4 illustrates the degree centrality, point-in-degree, and point-out-degree of urban GEE in the Yellow River Basin in 2021. Figure 4a indicates that 34.783% of cities have a degree centrality that exceeds the average value of 16.261. The top five cities in this regard are Jiayuguan City, Dongying City, Dingxi City, Zibo City, and Shizuishan City. This indicates that cities with high centrality can play a pivotal role in the spatial correlation network of GEE. These cities are situated at the core of the network and can significantly enhance GEE, which generates positive externalities of green electricity use. Among them, Jiayuguan and Dingxi are located in Gansu Province, Dongying and Zibo are situated in Shandong Province, and Shizuishan is situated in Ningxia Hui Autonomous Region. The reason these cities can play a role in the positive externality of GEE is due to the better growth momentum of hydropower installation in Gansu Province after 2017, and the higher increment of wind power installation in Shandong Province and Ningxia Hui Autonomous Region. Moreover, the growth of installed solar power in the Ningxia Hui Autonomous Region exhibited a more pronounced acceleration after 2010²⁹.

Figure 4

Point degree centrality.

Figure 4b illustrates that the top five cities in terms of in-degree are Yulin City, Jiayuguan City, Jinchang City, Dongying City, and Shizuishan City. This indicates that, in comparison to other cities in the Yellow River Basin, the aforementioned five cities are more susceptible to the influence of other cities in obtaining the benefits from the improvement of GEE. This is consistent with the actual situation that cities in Gansu and Shandong provinces, which are adjacent to many resource-based cities, may benefit from the improvement of GEE levels in neighboring cities due to their geographic proximity.

Figure 4c depicts the top five cities in terms of out-degree, namely Yulin, Luohe, Xuchang, Shangqiu, and Heze. These cities are primarily located in Henan Province, indicating that the GEE level of the aforementioned cities is more likely to generate spillover effects and assist other cities in improving their GEE. The reason for this is that Yulin, Luohe, Xuchang, Shangqiu, and Heze are geographically located in the middle of the Yellow River Basin, and their natural geographic advantages provide convenient conditions for the radiation of electricity consumption efficiency. From a development perspective, these five cities also belong to the latecomers, mainly relying on new infrastructure, new technology development, and a non-polluting industrial structure, which greatly improves the efficiency of electricity consumption. Furthermore, Yulin City is strategically situated with regard to the country's mineral resources, serving as a pivotal component of the national energy and chemical base in northern Shaanxi. Additionally, it has been designated as a national new energy demonstration city. These factors collectively justify the elevated ranking of the aforementioned five cities in terms of GEE out-degree.

This study presents a comprehensive analysis of the intermediary centrality degree of urban GEE within the Yellow River Basin. The aim is to elucidate the roles played by these cities in advancing the transition to green energy and optimizing the power system. Intermediary centrality degree measures a city's capacity to function as a pivotal node in transmitting information, resources, or influence within a network. Figure 5 depicts the intermediary centrality degree of GEE in Yellow River Basin cities as of 2021. The average mediated centrality degree of GEE in these cities was calculated at 1.076, providing a baseline for assessing city network influence. Only 10.140% of cities exceed this average, indicating that most cities play relatively minor roles in the network. This disparity underscores significant variations in the potential for GEE enhancement among Yellow River Basin cities. Such disparities highlight unequal network status among cities, revealing disparities in GEE improvement across the basin. Further analysis reveals that the maximum intermediary centrality value reaches 14.955, significantly above the average, indicating substantial advantages for certain cities in the network. These stark differences underscore inequality in network status among cities and offer valuable insights for governmental identification of key node cities and optimization of resource allocation.

Figure 5

Intermediary centrality.

It is notable that the five cities of Yulin, Jiayuguan, Jinchang, Dongying, and Shizuishan exhibit a high degree of intermediary centrality. These cities play a pivotal role in the network, acting as key nodes for regional exchanges and possessing unique geographic locations or resource advantages that make them vital hubs in the GEE network. As evidenced by the literature, the spatial pattern of power production in the Yellow River Basin is gradually evolving from monocentric to bicentric and even polycentric. Yulin City, a representative city of polycentricity, has a combined urban power generation capacity of close to 50 billion kilowatt-hours in both cases. Additionally, the main contributing regions to the growth of renewable energy installed capacity are Qinghai Province and Gansu Province. These findings establish the significant role of Yulin, Jiayuguan, Jinchang, Dongying, and Shizuishan cities in the spatial network of GEE. In summary, the network structure of urban GEE in the Yellow River Basin demonstrates a clear hierarchy and unevenness. This status quo not only reveals the imbalance of development within the region, but also provides an important reference for policy formulation and urban planning to realize the overall improvement of GEE and the goal of sustainable development.

Figure 6 illustrates the proximity centrality degree of urban GEE in the Yellow River Basin in 2021. The mean value of proximity centrality, which is a key indicator of a city's geographic centrality in the network, is 54.139, reflecting the average connectivity distance between cities and other cities. The study indicates that approximately 17.392% of the cities have a proximity centrality that exceeds the mean value. This indicates that these cities occupy a more central position in the network and are able to connect efficiently with other cities through shorter paths. This centrality confers a significant advantage on these cities in acquiring and disseminating technologies and knowledge related to GEE, thus playing a pivotal role in promoting regional green development. In particular, the proximity centrality of Yulin, Jiayuguan, Jinchang, Shizuishan, and Dongying ranked among the top five of all cities, which further highlights the centrality of these cities in the spatial network. The location advantages of these cities not only facilitate the improvement of their own GEE, but also have a positive radiation effect on neighboring cities through their central role in the network, which promotes the improvement of GEE in the whole region. As "central actors," the central position of these cities in the spatial network confers upon them a leading role in regional green development. They are not only able to respond promptly to the demand for GEE, but also to transfer advanced technology and management experience to other cities through their network connections, thus promoting the overall improvement of GEE at the regional level. From an empirical standpoint, Yulin City and other cities are situated in proximity to regions that are rich in power resources. This is conducive to the promotion of cross-provincial and cross-regional power transmission, and the formation of a pattern of west-to-east and north-to-south power transmission within the North China Power Grid.

Figure 6

Approximate centrality.

Cluster characterization of spatial association networks

This study examines the clustering characteristics of the spatial correlation network of urban GEE in the Yellow River Basin using the block modeling method in the year 2021 as a case study^30,31. The CONCOR program in Ucinet6.0 is employed to set the maximum segmentation depth to 2 and the convergence criterion to 0.2. Given the limitations of the CONCOR method, which typically involves no more than 50 running samples, this study screens the observation samples of 69 prefecture-level cities through correlation analysis. It is well established that the industrial sector uses electricity intensively, and cities with large-scale industrial enterprises have the largest electricity consumption. Therefore, it is crucial to visualize the level of GEE. In this study, 24 cities with a greater number of industrial enterprises than the annual average are selected to reflect the actual level of GEE and its interaction with the scale of industrialization development in typical cities.

Figure 7 illustrates the spatial clustering characteristics of the GEE of cities in the Yellow River Basin. Plate I includes six cities, namely Jinan, Qingdao, and Zibo. Within the region, Shandong, China's most populous province, has Jinan, Qingdao, and Zibo at the forefront of its economic development. Consequently, as significant economic and consumption hubs, these cities import clean electricity from other regions while exporting resources such as technology, capital, and information, demonstrating a two-way flow of resources. Plate II includes the four cities of Luoyang, Zhengzhou, Xuchang, and Xi'an. Henan and other provinces possess natural and market advantages in green power development and have a robust foundation for industrial advancement. These provinces have high levels of production technology, management, and industry standards, and have attracted and acquired resources for green power development from other regions. The amount of external resources attracted and absorbed by these provinces significantly exceeds the amount of external resources released, and they also belong to the "net benefit zone." Plate III includes six cities, including Tai'an, Weifang, and Dezhou. Situated in the lower reaches of the Yellow River Basin, Shandong Province serves as a pivotal node for China's south-to-north and east-to-west opening strategies, as well as a crucial bridge between the eastern and western regions. Plate IV encompasses eight cities, including Heze, Xinxiang, and Nanyang. As an inland region of China, Henan Province is constrained by the regional industrial structure and power infrastructure conditions, and the development potential of the green power industry is extremely limited. This has led to an outflow of capital, technology, and market resources for power development.

Figure 7

Interaction of the four segments.

Table 3 illustrates that in the spatial network of GEE of 24 typical cities in the Yellow River Basin, there are 149 spatial correlation relationships, including 21 intra-plate relationships and 128 inter-plate relationships. This indicates that the spatial correlation paths of GEE of cities are predominantly concentrated in inter-plates, with sparse intra-plate connections. In particular, there are 11 intra-plate relationships in Plate I, and the number of relationships outside the receiving plate (52) is significantly higher than the number of relationships outside the overflow plate (17). The number of intra-plate relationships is smaller than the sum of the number of relationships outside the receiving plate and the overflow. The proportion of actual intra-plate relationships (39.296%) is larger than the proportion of desired intra-plate relationships (21.749%), indicating that Plate I benefits from the improvement of the level of GEE of the other plates. This is a "net benefit." This indicates that Segment I benefits from the improvement of GEE in other segments and belongs to the "net benefit" segment. The number of internal relations in Block II is 2, the number of receiving relations in the block is 21, and the number of overflow relations in the block is 31, thus demonstrating that the number of receiving relations and overflow relations among the blocks is equal, and it is a "broker block." All members of Plate III are located in Shandong Province, in the middle and lower reaches of the Yellow River. There are 7 internal relations, 23 plate receiving relations, and 24 plate overflow relations. This generates spillover effects both within and outside the plate, and it is a "two-way spillover" plate. The members of Plate IV are primarily situated in the middle and lower reaches of the Yellow River. They exhibit 1 internal relationship, 28 plate receiving relationships, and 52 plate overflow relationships. Notably, the number of plate overflow relationships is considerably greater than the number of plate receiving relationships, indicating a net overflow pattern.

Table 3 Segmentation of spatial association networks.

In order to examine the correlation relationship and spillover path of GEE between the plates, the density matrix of the network between the plates is calculated in greater detail. The density matrix between the four main plates was calculated using Ucinet6.0 and combined with the correlation relationship between the plates. The density matrix obtained for the plate densities is compared with the overall network density value of 0.266. If the density of the plate is greater than 0.266, the value of 1 is assigned to the image matrix; otherwise, the value is 0. The results of the specific image matrix are shown in Table 4. From the image matrix, it can be seen that Plate I exhibits a high level of "activity." There is a correlation between the GEE within Plate I and with Plates III and IV, with a significant spillover effect. This activity is primarily attributable to the inclusion of Jinan, Qingdao, Zibo, and other cities with higher levels of economic development within Plate I. In addition to their economic advantages, these cities also possess notable green development capabilities. The so-called "siphon effect" has enabled these cities to effectively absorb green innovation resources from Plates III and IV. The "siphon effect" refers to the attraction of resources, technologies, and talents from neighboring or distant regions by cities with stronger economic and technological innovation capabilities. This effect enables cities in Plate I to enhance their GEE, thereby exerting a positive influence on Plate III through technology transfer and knowledge sharing. Furthermore, Plate I also benefits from spillover effects from Plates III and IV, indicating that this plate not only exerts influence externally but also is positively influenced by other plates in the process of GEE improvement. This two-way interaction promotes the overall improvement of GEE. This two-way interaction contributes to the overall improvement of GEE in the region. In summary, the analysis in this study reveals the correlations and spillover paths of GEE among the Yellow River Basin segments, with particular emphasis on the central role of Plate I in regional green development. These findings provide an important theoretical basis and practical guidance for formulating regional green development strategies, optimizing resource allocation, and promoting regional synergistic development.

Table 4 Density matrix and pixel matrix of each segment.

Analysis of QAP regression results of urban GEE in the Yellow River Basin

The constructed QAP regression model was employed to obtain the QAP regression results for 2012, 2015, 2018, and 2021 through 6000 random permutations. Table 5 presents the QAP regression results for the spatial correlation network drivers of urban GEE in the Yellow River Basin.

• (1) The regression coefficients of geographical adjacency are consistently significant and positive. This indicates that cities with geographical adjacency are more likely to collaborate in enhancing GEE, reducing energy consumption levels, and forming a spatial correlation network of GEE. The phenomenon of 'electricity borrowing' exists between neighboring cities, thereby facilitating the formation of spatial relationships in GEE through the external network structure of geographical proximity. The acceleration of regional integration promotes mutual dependence and penetration of economic activities among different regions³². The spatial correlation network of GEE at the regional level, as a manifestation of the spatial linkage effects in economic activities, does not operate solely within its internal network space but inevitably experiences influences from relevant external environmental factors.

• (2) The differences in economic growth are significantly positive in most years, suggesting that greater differences in economic growth between cities contribute to the formation of the spatial correlation network of GEE. This is mainly because cities with differences in economic development levels are more likely to achieve division of labor and cooperation in the supply chain and production chain under normal circumstances, optimizing the allocation of production factors and thus promoting the development of the spatial correlation network.

• (3) The coefficient of differences in industrial structure is significantly positive, indicating that higher similarity in industrial structure is advantageous for the formation of spatial correlation relationships. According to the factor endowment theory, the industrial structure is endogenous to the factor endowment structure³³. Regions with abundant natural resources, especially energy, tend to develop resource-intensive industries with a 'comparative advantage'³⁴. For example, cities rich in coal resources are inclined to develop electricity-intensive industries and export electricity-intensive products to other regions.

• (4) The coefficient of differences in environmental regulation intensity in 2021 is -0.092, significant at the 1% level. This suggests that consistency in the formulation standards of environmental protection policies can reduce the cost of green economic cooperation between cities, facilitate collaboration in green technology, and enhance the correlation between regions' GEE.

• (5) The coefficients of differences in technological expenditure levels are mostly significantly positive. This implies that the greater the difference in technological expenditure input, the greater the differences in electricity infrastructure and equipment configuration between regions. This increases the possibility of the flow of resources such as funds, technology, and talent, leading to higher transmission and spillover effects of electricity technology innovation and, consequently, a stronger spatial correlation in GEE.

• (6) The regression coefficients of differences in average temperatures are consistently significant and negative. This indicates that smaller differences in average temperatures between cities are conducive to the formation of the spatial correlation network of urban GEE in the Yellow River Basin. The correlation between urban electricity consumption and temperature is strong, and abnormal temperature values can lead to a decrease in GEE, hindering the formation of the spatial network of GEE.

Table 5 QAP regression results.

Discussion

This study assesses the GEE of 69 cities in nine provinces in the Yellow River Basin from 2012 to 2021. It employs the SNA method to analyze the spatial distribution of urban GEE in the Yellow River Basin. Furthermore, it uses the QAP method to explore the role of six factors, including geographic proximity, in driving the spatial network of urban GEE in the Yellow River Basin.

This study differs from previous academic studies on green power development in that it analyzes in detail the spatial correlation network and drivers of urban GEE in the Yellow River Basin^35,36. It reveals the formation and dynamic evolution of the spatial correlation network and provides a new perspective for understanding the spatial layout of urban GEE in the Yellow River Basin. In addition, it examines in detail the structure and evolution of the urban GEE network in the Yellow River Basin. The construction of the spatial correlation network enables the dynamic changes in the network structure to be revealed, thereby providing a new perspective for understanding the spatial pattern of urban GEE in the Yellow River Basin. The study also highlights the changing roles of regions within the network, noting in particular that Gansu, Shaanxi, and Shandong have long been at the center due to their natural conditions and market advantages. Consequently, it is imperative to consider regional characteristics and optimize the allocation of electricity resources when formulating relevant policies.

Furthermore, it was determined that the network of urban GEE spatial linkages in the Yellow River Basin is highly interconnected, with no isolated entities. This indicates that the development of GEE is intricately intertwined and interdependent within the Yellow River Basin, exhibiting considerable spatial spillover effects. Rita and Alessandro (2022)³⁷ examined the spatial value ordering effect of renewable energy on the Italian power exchange and discovered that the Apennine region between Campania and Apulia belongs to a distinct region or market area. They further demonstrated that wind power facilities at the region's borders can be spatially connected by establishing a correlation between renewable energy outputs within the region or between regions. In Germany, Ruth et al.³⁸ discovered a correlation between renewable energy inputs and outputs between geographic neighborhoods, demonstrating that the spatial concentration of climatic conditions can facilitate the deployment of renewable energy technologies. Wen et al.³⁹ reached a similar conclusion through an analysis of data related to New Zealand's power exchange. Nevertheless, there is still considerable scope for enhancement in the connectivity and resilience of urban GEE development networks in the Yellow River Basin, indicating the necessity for further regional collaboration and resource sharing in the future.

This study examines the internal structure of the urban GEE network in the Yellow River Basin and divides it into four distinct functional blocks, thereby enhancing our comprehension of the interregional interaction patterns in the context of green agricultural development. Finally, the study of the drivers of the spatial correlation network of green development in the power sector reveals that geographic proximity and the level of economic development exert a significant influence on the formation of this network, in accordance with the findings of other scholars. These insights provide a foundation for the formulation of policies designed to enhance regional collaboration and facilitate coordinated growth.

In conclusion, this study contributes to the existing body of knowledge by systematically analyzing and discussing the spatial correlation network of urban GEE and its drivers in the Yellow River Basin. Furthermore, it provides valuable insights for the formulation of policies to promote green electricity development. Future studies may wish to explore the characteristics and changes of spatial correlation networks in different geographic and socio-economic contexts in greater depth, with a view to providing more detailed strategies and recommendations for the electric power industry in the Yellow River Basin with a view to achieving the goal of sustainable development.

Conclusions and policy implications

Conclusions

This study employs a panel data set comprising 69 prefecture-level cities in the Yellow River Basin from 2012 to 2021. SNA and QAP regression methods were employed to investigate the spatial correlation network structure and its evolution of urban GEE in the Yellow River Basin. Additionally, the factors driving the changes in these networks are analyzed. The primary findings are as follows: (1) There is a significant spatial correlation effect on the urban GEE in the Yellow River Basin. There are no isolated cities in the spatial network of GEE, and each city is directly or indirectly connected to other cities, indicating good connectivity and accessibility. The network is hierarchical, although this hierarchy is on a downward trend. (2) From the perspective of individual network characteristics. Prefecture-level cities such as Yulin, Luohe, Xuchang, Shangqiu, and Heze are primarily situated within the province of Henan. Among these cities, Yulin holds a prominent position in the country's mineral resources, serves as a vital component of the national energy and chemical base in northern Shaanxi, and is also designated as a national new energy demonstration city. Consequently, the superior clean energy development conditions, advanced green power technology, and substantial consumer market have a profound impact on the green development of the power industry in other regions, and have enabled the network to maintain its core position for an extended period. (3) From the perspective of spatial clustering characteristics, the urban GEE network in the Yellow River Basin can be divided into four blocks. Block I, which is dominated by Jinan and Qingdao, is a "net beneficiary" block and is the primary beneficiary in the spatial correlation network of GEE. Block II, which is dominated by Luoyang and Zhengzhou, has a comparable number of receiving relationships with spillover relationships and is a "broker block." The third plate, which encompasses Taian and Weifang and other cities in the eastern part of the Yellow River Basin, generates spillover effects both within and outside the plate. This is a "two-way spillover" plate. Plate IV, which encompasses Heze and Xinxiang and other cities in the central and western regions of the Yellow River Basin, exhibits a considerably greater degree of overflow than the number of plate receipts, indicating a "net overflow" pattern. Furthermore, the spatial correlation network spillover effect of GEE in the Yellow River Basin cities exhibits a pronounced "centripetal" spatial transmission characteristic. (4) Geographic proximity, differences in economic growth, differences in industrial structure, and differences in the level of scientific and technological expenditures have a significant positive effect on the formation of the spatial correlation network of GEE in the Yellow River Basin municipalities. In contrast, differences in the intensity of environmental regulations and differences in the average temperature have a negative effect.

Policy implications

This study presents a series of countermeasure suggestions based on the study of the spatial correlation network of urban GEE and its functioning mechanism in the Yellow River Basin. In particular, it suggests the establishment of a regional green electricity collaborative innovation platform. Cities in the Yellow River Basin should establish demonstration zones for green power technologies to showcase the practical application effects of green power technologies by sharing successful cases and experiences with other cities within the platform. Such demonstration zones could encompass solar farms, wind power bases, smart grids, and energy efficiency management projects, thereby providing models for neighboring cities to emulate. Furthermore, cities in the Yellow River Basin should enhance collaboration with other cities on green power consumption, thereby augmenting the proportion of green power in the region's overall energy consumption. This may be achieved by establishing a green power trading market, which would facilitate the circulation and trading of green power within the region.

The promotion of optimization of the energy structure and cross-regional allocation of clean energy is also recommended. In accordance with the energy endowments of each city in the Yellow River Basin, the energy structure should be optimized and the proportion of clean energy increased. This may be achieved through the development of hydropower in water resource-rich areas and the development of wind power and photovoltaic power generation in wind and solar resource-rich areas. The establishment of a regional energy Internet will facilitate the effective allocation and complementary use of clean energy, thereby reducing the loss in the transmission of electricity across the region.

It is recommended that environmental regulation and incentive policies be integrated more effectively. The current status of environmental regulations in cities within the Yellow River Basin should be combined, the coordination and consistency of environmental regulation policies should be strengthened, and the compliance costs of green transformation for enterprises should be reduced. Financial subsidies, tax incentives, and other incentives should be utilized to encourage enterprises to adopt green power and improve the efficiency of electricity consumption, particularly for energy-intensive sectors such as industry, construction, and transportation.

Limitations and outlooks

Although this study provides insights for a deeper understanding of the structure and development of the spatial correlation network of urban GEE in the Yellow River Basin, it also has its limitations. First, due to the limitation of data availability, this study does not include data for all prefecture-level cities in the Yellow River Basin, which could improve the accuracy of future analysis. Additionally, GEE is influenced by many complex factors, and this study focuses on specific influencing factors; future research should consider a wider range of potential influencing factors to gain a more comprehensive understanding. In conclusion, by systematically analyzing and exploring the spatial correlation network of urban GEE and its driving factors in the Yellow River Basin, this study not only enriches existing research but also provides valuable insights for formulating green development policies in the power industry. Future studies can delve into the characteristics of the spatial correlation network of the power sector and its changes in different geographical and socio-economic contexts, and provide more detailed strategies and suggestions for developing countries to achieve sustainable development goals.