Digital Twin Technology and Energy Sustainability in China: A Regional and Spatial Perspective

Abstract

This study aims to explore the role and impact of digital twin technology in enhancing the sustainable development of the energy industry so as to analyze how digital twin technology facilitates urban sustainability. Using data from 281 prefecture-level cities in China over the twelve-year period from 2013 to 2024, the study employs methods such as the entropy method, kernel density analysis, and spatial econometric models to conduct an in-depth analysis of improvements in energy efficiency. The findings indicate that digital twin technology plays a significant role in promoting the sustainable development of the energy industry. Furthermore, China is divided into four regions—eastern, central, western, and northeastern—for a comparative analysis, revealing regional differences in the relationship between the application level of digital twin technology and sustainable development of the energy industry. To effectively apply digital twin technology in this context, it is recommended to establish comprehensive digital twin models and intelligent decision-making systems for accurate energy monitoring and efficient management decisions. The results reveal that while digital twin technology enhances energy efficiency and promotes sustainable development overall, significant regional imbalances persist. The eastern region shows the highest integration level and performance, while the western and northeastern regions lag behind. In response, the study proposes tailored regional strategies, including the development of scalable digital twin technology, integrated data platforms, and strengthened governance mechanisms to enhance digital coordination and ensure data security. This research provides new empirical evidence and strategic guidance for leveraging digital twin technology in promoting low-carbon and sustainable urban energy systems.

1. Introduction

With the growing global energy shortage and the increasing demand for energy, the enhancement of energy sustainability faces unprecedented challenges, posing significant difficulties for urban sustainable development. The energy system involves multiple stages, including power generation, transmission, distribution, and end-use consumption. However, data standards in these stages are often inconsistent, hindering interoperability and obstructing the achievement of sustainable urban development goals [1]. Traditional energy data processing largely relies on manual meter reading and periodic monitoring, which cannot provide real-time insights into energy consumption dynamics. Furthermore, the lack of visualization and traceability mechanisms in energy consumption processes prevents the accurate identification of anomalies. In cases of sudden load surges or energy waste, the system fails to deliver real-time feedback or implement coordinated control, thereby reducing energy utilization efficiency. To achieve sustainable development in the energy industry, there is an urgent need to explore innovative technological approaches and management models [1].

Digital twin technology, originating in the industrial sector, was initially used for virtual modeling and simulation in manufacturing. It involves the digital replication of physical objects or processes, creating virtual digital twin models that reflect and update the real-time status and behavior of the corresponding physical entities [2]. With the advancement of technology, digital twin applications have gradually extended to the sustainable development of the energy industry, becoming an essential tool for optimizing urban operations and enhancing governance efficiency. In this context, digital twin technology enables the construction of digital replicas of cities, allowing precise monitoring and forecasting of energy elements such as electricity operations, natural gas supply, and energy consumption. These capabilities provide scientific evidence and real-time feedback for urban managers, enabling rapid response and adjustment of sustainable energy development strategies, thereby advancing the goal of urban sustainability [3]. Moreover, the integration of digital twin technology promotes the continuous evolution of urban energy solutions and fosters the deep integration of artificial intelligence, big data analytics, and energy efficiency optimization. This synergy injects new momentum into the sustainable development of the urban energy industry [4]. This study conducts an in-depth investigation into the role and impact of digital twin technology in the sustainable development of the energy industry, aiming to offer theoretical support and practical guidance for urban managers and policymakers and to provide novel insights and strategic recommendations for advancing energy sustainability.

With the acceleration of global urbanization and the rapid development of information technology, the concept of urban sustainable development has gained increasing recognition. As one of the key pillars supporting sustainable urban development, digital twin technology not only represents a breakthrough in technological innovation but also serves as a crucial tool for enhancing the sustainability of urban growth. Originating from the industrial sector’s concept of virtual modeling and simulation, the essence of digital twin technology lies in the creation of virtual replicas of physical objects or processes through digital means—referred to as digital twin models [5]. These models are not merely static copies; they are capable of dynamically reflecting changes in the state and behavior of their physical counterparts in real time, thereby providing decision-makers with a highly accurate simulation environment and real-time data support [6].

In the process of promoting sustainable development in the energy industry, digital twin technology integrates multi-source information such as IoT devices and sensor data to construct a digital mirror of the city, enabling comprehensive monitoring and analysis of energy consumption and other critical parameters [7]. Urban sustainable development faces numerous environmental governance challenges, including urban pollution, resource scarcity, and climate change. Traditional governance methods have become insufficient to address the increasingly complex and rapidly evolving needs of urban environments [8]. Therefore, improving governance efficiency and optimizing resource allocation have become central issues in achieving sustainable urban development. Digital twin technology, with its high-precision environmental simulation and real-time data analysis capabilities, offers new perspectives and tools for addressing these challenges.

Relevant research on the application of digital twin technology in the sustainable development of the energy industry has emerged. Stoeglehner G. (2022) highlighted that digital twin technology can accurately simulate the operational states of various urban elements, including infrastructure and environmental conditions, thus enabling comprehensive monitoring of urban operations [9]. Through data analysis based on digital twin models, urban managers can swiftly respond to the demands of sustainable energy development and adjust their energy strategies accordingly [10]. Intelligent decision support systems not only enhance the accuracy and timeliness of decision-making but also improve the efficiency of resource allocation and utilization, thereby reducing governance costs [11]. The application of digital twin technology has driven continuous upgrades and innovation in smart city solutions. According to Tang J. (2024), the use of technologies such as digital twins in the energy sector has promoted the transformation of energy systems and improved levels of energy sustainability [12].

With decreasing technology costs and increasing data processing capabilities, digital twin technology is expected to be deployed more widely around the world, supporting more cities in achieving their sustainable development goals [13]. Wang Y. J. (2024) affirmed that digital twin technology can precisely simulate the operational states of various urban elements, including infrastructure and environmental conditions, enabling comprehensive monitoring of city operations [14]. Real-time data analysis based on digital twin models allows city managers to respond rapidly to environmental changes and adjust governance strategies accordingly. Wang Q. (2023) summarized that intelligent decision support systems not only improve the accuracy and timeliness of decisions but also optimize resource allocation and efficiency, thereby reducing governance costs [15]. The application of digital twin technology continues to drive the evolution and innovation of smart city solutions. Dang N. (2025) pointed out that the integration of artificial intelligence and big data analytics with digital twin technology can enable the optimization of urban traffic flows and the intelligent management of waste disposal, thereby improving the efficiency of urban operations and the quality of life for residents [16]. As digital twin technology continues to develop and proliferate, its role in urban environmental governance within smart cities will become increasingly prominent. Dang N. (2024) projected that digital twin technology will continue to evolve and expand into broader application areas, such as disaster early warning, urban planning, and resource management [17].

At present, significant gaps remain in the application of digital twin technology within the sustainable energy development field. Yu et al. (2022) emphasized the broad applicability of digital twin technology across the entire industrial energy management process, highlighting its potential for carbon reduction and energy optimization [18]. However, a standardized evaluation framework to assess the current development status of digital twin technology is still lacking, and reliable frameworks supporting its practical deployment remain insufficient. Hashmi et al. (2024) proposed a closed-loop digital twin (CLDT) framework based on the OODA (Observation–Orientation–Decision–Action) system architecture, focusing on renewable energy systems such as wind, solar, and hydrogen energy [19]. Nonetheless, integrated practices combining real-time decision-making loops with security assurances to evaluate the application of digital twin technology in energy sustainability are still missing. Although initial research has addressed their integration, a unified evolution path, maturity assessment, and comprehensive future research roadmap are yet to be developed. To fill these gaps, this study establishes a clear framework linking digital twin technology with sustainable energy development. Additionally, considering the developmental disparities among eastern, central, western, and northeastern China, this research provides an in-depth analysis of digital twin applications in sustainable energy across these regions. This innovative approach offers a theoretical foundation for advancing Digital China, promoting an energy-efficient society, and achieving more balanced regional development.

As both a theoretical foundation and a practical tool for the sustainable development of the energy industry, digital twin technology provides strong support and new development pathways for urban managers through its capabilities in precise modeling, data-driven decision support, and promotion of technological innovation [20]. In future research and practice, further exploration and application of digital twin technology will contribute valuable insights and experience to the sustainable development of the energy industry and the optimization of global urban governance systems.

2. Methodology

2.1. Entropy Method

The global entropy method is a quantitative evaluation technique that captures the degree of variability among multiple indicators across spatial and temporal dimensions. A higher degree of dispersion among indicators reflects their greater informational contribution to the overall assessment. Rooted in the concept of entropy from thermodynamics—originally developed to quantify system uncertainty—this method has been adapted for use in multi-indicator weighting, providing a rigorous alternative to subjective approaches. Compared to techniques such as principal component analysis, the global entropy method offers improved objectivity and sensitivity in assigning indicator weights. Based on the indicator evaluation system of China’s energy industry, this section employs the global entropy method for measurement. As an objective evaluation tool for multivariate weighting, the entropy method effectively eliminates the influence of subjective bias often found in methods such as expert scoring and analytic hierarchy processes, offering significant advantages in studies involving complex indicator systems [21]. Traditional entropy methods are typically suited for static cross-sectional or single time-series analyses and are limited in their ability to process multidimensional dynamic datasets across time and space. To address this limitation, this study improves upon the traditional algorithmic framework by integrating panel data across multiple regions, indicators, and time periods, thereby constructing a spatiotemporally coupled weighting model [19]. The specific steps are as shown in Figure 1.

(1)

Construction of a Global Analysis Matrix.

For the β indicators related to the development of the digital twin technology and energy sustainability, the observed values of α cities over N years are integrated in a time-series manner. The N cross-sectional data tables x^N = (x_ij)_α×β are arranged in chronological order, ensuring both the completeness of the evaluation parameters and the temporal evolution of urban development. This process results in a global-dimensional matrix of size αN × β, which captures the spatiotemporal continuity characteristics of the data.

$$\mathrm{x}=({\mathrm{x}}^1{,\mathrm{x}}^2{,\mathrm{x}}^3,\mathrm{\dots }{,\mathrm{x}}^{\mathrm{N}}{)=({\mathrm{x}}_{\mathrm{ij}})}_{\mathrm{\alpha }\mathrm{N}\times \mathsf{\beta }}$$

(1)

➀

Data Normalization.

Let x_ij denote the value of the j-th indicator for the i-th evaluation unit, where i = 1, 2, 3, …, m and j = 1, 2, 3, …, n.

Positive Indicator:

$$Z_{ij}={\displaystyle \frac{x_{ij}-{\min }_{ij}}{{\max }_{ij}-{\min }_{ij}}}$$

(2)

Negative Indicator:

$$Z_{ij}={\displaystyle \frac{{\max }_{ij}-x_{ij}}{{\max }_{ij}-{\min }_{ij}}}$$

(3)

In Equations (2) and (3), Z_ij represents the normalized value of the j-th indicator for city i, while x_ij denotes the original (raw) value of the j-th indicator for city i. The maximum and minimum values of the j-th indicator are denoted by max x_j and min x_j, respectively.

➁

Quantify the Weight Distribution of Variables. The proportion of city i in the j-th indicator is calculated as follows:

$$y_{ij}={\displaystyle \frac{Z_{ij}}{{\displaystyle \sum _{i=1}^{\alpha N}{Z}_{ij}}}},1\le i\le \alpha N,1\le j\le \beta$$

(4)

➂

Calculate Information Entropy. The information entropy of the j-th indicator is computed as follows:

$$e_j=-k{\displaystyle \sum _{i=1}^{\alpha N}{y}_{ij}I{n}_{ij},1\le i\le }\alpha N,1\le j\le \beta$$

(5)

where

$$k={\displaystyle \frac{1}{In\alpha N}}$$

(6)

➃

Calculate the Information Utility Value. The variation coefficient, dj, of the j-th indicator is defined as

$$d_j=1-e_j$$

(7)

➄

Calculate Indicator Weights, W_j:

$$W_j={\displaystyle \frac{d_j}{{\displaystyle \sum _{i=1}^m{d}_j}}}$$

(8)

➅

Calculate the Comprehensive Score, U:

$$U=\sum _{\mathrm{i}=1}^{\mathrm{m}}{\mathrm{y}}_{\mathrm{i}\mathrm{j}}{\mathrm{W}}_{\mathrm{j}}$$

(9)

2.2. Choropleth Map

A choropleth map, as a type of GIS visualization, is generated based on geospatial databases. Through spatial analysis and graphical rendering, it integrates real-world geographic objects with their associated attribute data and presents them on two-dimensional or three-dimensional maps. This enables decision-makers to intuitively perceive the spatial distribution patterns and temporal trends of the data. The core of a GIS visualization lies in mapping attribute data to variations in color intensity, thereby clearly illustrating regional differences.

➀

Choropleth classification formula:

The attribute value, A_i (the indicator value for region i), is mapped to a color category, C_i.

$$C_{\mathrm{i}}=\left\{\begin{array}{l}{C}_1, A_{\mathrm{i}}\in \left[a_0,a_1\right)\\ C_2, A_{\mathrm{i}}\in \left[a_1,a_2\right)\\ .\\ .\\ .\\ C_n, A_{\mathrm{i}}\in \left[a_{n-1},a_n\right)\end{array}\right.$$

(10)

where A_i is the the indicator value for the i-th administrative unit; [a_j,a_j+1) is the value range of the j-th classification, derived from statistical classification; C_j is the corresponding color fill; and n is the number of classification levels.

➁

Spatial data mapping

Spatial data mapping (based on a fundamental coordinate system) refers to the process of transforming the location attributes of geographic entities into mathematically defined coordinates, typically grounded in a specific map projection and reference system. This coordinate framework provides a unified spatial reference, enabling the integration, analysis, and visualization of spatial data from diverse sources within a consistent mapping environment. The mathematical formula for spatial data mapping is

$${(\mathrm{x}}_{\mathrm{i}}{,\mathrm{y}}_{\mathrm{i}})=\mathrm{Projection}({\lambda }_{\mathrm{i}},{\varphi }_{\mathrm{i}})$$

(11)

The geographic coordinates (${\lambda }_{\mathrm{i}},{\varphi }_{\mathrm{i}}$) of each administrative unit are converted into planar coordinates (x_i, y_i) through a map projection function, enabling accurate rendering on the map. Commonly used projection systems include the World Geodetic System 1984 (WGS84), which provides a standard geographic coordinate framework for global applications; GCJ-02, an encrypted geodetic system required for civilian use in mainland China; and planar projections such as Mercator and Albers, which are frequently employed in cartographic representation and regional-scale spatial visualization.

➂

Data Sources and Normalization for Visualization

In certain cases, to ensure consistency across variables with different units or scales, the attribute values, A_i, must be normalized prior to visualization. The normalized values are then used for choropleth classification and color mapping. The normalization formula is as follows:

$$A_{\mathrm{i}}^{\prime }={\displaystyle \frac{A_{\mathrm{i}}-A_{\min }}{A_{\max }-A_{\min }}}$$

(12)

where $A_{\mathrm{i}}$ is the original attribute value for region i; $A_{\min }$ and $A_{\max }$ are the minimum and maximum values across all regions; and $A_{\mathrm{i}}^{\prime }$ is the normalized value, ranging from 0 to 1.

2.3. Kernel Density Estimation

Kernel density estimation (KDE) is a non-parametric method used to estimate the probability density function of a random variable. In spatial analysis, KDE is employed to evaluate the intensity or concentration of spatial events or values across a continuous surface. By applying a kernel function over each data point, KDE generates a smooth surface that reflects the spatial distribution pattern of the underlying phenomenon.

➀

One-dimensional KDE formula

Assume a set of sample data $x_1,x_2,\mathrm{\dots },x_n$; then, the kernel density estimate at point x is given by

$$f_h(x)={\displaystyle \frac{1}{nh}}{\displaystyle \sum _{i=1}^{n}K\left(\frac{x-x_i}{h}\right)}$$

(13)

where $f_h(x)$ is the density estimate at location x; n is the sample size; h is the bandwidth, controlling the degree of smoothing; and K(·) is the kernel density.

➁

Gaussian kernel

The Gaussian kernel is one of the most widely used kernel functions in non-parametric density estimation. It is defined by a symmetric, bell-shaped curve that follows the form of the standard normal distribution. The kernel function determines how each data point contributes to the estimation at a given location. The Gaussian kernel ensures smooth and continuous density estimates by assigning decreasing weights to observations as their distance from the evaluation point increases. Mathematically, the Gaussian kernel is given by

$$K(u)={\displaystyle \frac{1}{\sqrt{2\pi }}}{e}^{-{\displaystyle \frac{1}{2}}{u}^2}$$

(14)

where u is the standardized distance between the target point and a data point, typically scaled by the bandwidth. The smoothness of the resulting density curve is primarily influenced by the bandwidth parameter rather than the kernel type itself. The larger the bandwidth, the smoother the result; conversely, the smaller the bandwidth, the more peaked or jagged the result.

2.4. Gini Coefficient Theory

The Dagum Gini coefficient, based on the framework of relative disparity measurement, is used to analyze the overall spatial differentiation pattern and dynamic decomposition characteristics of the relationship between digital twin technology and sustainable development in the energy industry. It also quantifies inter-regional and intra-regional heterogeneity [22]. The calculation model is as follows:

In Equation (15), k represents the number of regions, totaling 4; i and r denote the city indices within regions; n_j and n_k represent the number of cities in regions j and h, respectively; n is the total number of cities; y_ij indicates the level of sustainable development of digital twin technology and the energy industry; and $\overline{y_{ij}}$ is the average level of sustainable development of digital twin technology and the energy industry.

$$G={\displaystyle \frac{{\displaystyle \sum _{j=1}^k{\displaystyle \sum _{h=1}^k{\displaystyle \sum _{i=1}^{n_j}{\displaystyle \sum _{r=1}^{n_k}\left|\left.y_{ji}-y_{hr}\right|\right.}}}}}{2n_j^2\overline{y_{\mathrm{ij}}}}}$$

(15)

The Dagum Gini coefficient improves upon the traditional Gini coefficient and the Theil index by overcoming the constraint of non-overlapping group distributions. It allows the overall inequality, G, to be decomposed into intra-group differences (within-region disparities), inter-group differences (between-region disparities), and transvariation intensity effects (the contribution of inter-regional overlap to overall disparities) [23].

The decomposition formula is (16):

$$G=G_w+G_{nb}+G_t$$

(16)

Based on the study of relative differences and their sources, this research employs the kernel density estimation method to identify the absolute differences between digital twin technology and the sustainable development level of the energy industry, thereby conducting an in-depth analysis of their spatial disparities. Kernel density estimation is a non-parametric statistical method that examines the dynamic evolution of characteristic values by analyzing changes in the position, peaks, and tails of the density curve [24]. The horizontal position of the kernel density curve reflects the level of digital twin technology and the sustainable development of the energy industry. The formula is (17):

$$G={\displaystyle \sum _{j-1}^k{G}_{jj}{p}_j{s}_j}+{\displaystyle \sum _{j-1}^k{\displaystyle {\sum }_{h\ne j}{G}_{jh}}}{p}_j{s}_h+{\displaystyle \sum _{j-1}^k{\displaystyle {\sum }_{h\ne j}{G}_{jh}}}{p}_j{s}_h(1-D_{jh})$$

(17)

The height and width of the curve’s peaks indicate the spatial differences between them. The number of peaks can be used to analyze the polarization degree of digital twin technology and energy industry sustainability. The tails of the curve reveal the gap between cities with the highest or lowest levels of digital twin technology and energy industry sustainability compared to other cities—the longer the tail and the wider the coverage, the greater the internal regional disparities. A horizontal comparison of kernel density function curves across different regions can reveal differences in the development trajectories of digital twin technology and energy industry sustainability. A vertical comparison of kernel density curves for a specific region over different time periods can identify the dynamic evolution of their sustainable development levels. Assume that D₁, D₂, …, D_n represent the digital twin technology and energy industry sustainability status of the 1st to the nth cities and that these variables are independently and identically distributed. In Formula (18), f(x) denotes the probability kernel density function of D. The estimated density function for digital twin technology and energy industry sustainability across cities is given by

$$f(x)={\displaystyle \frac{1}{nh}}{\displaystyle \sum _{i=1}^{n}K(\frac{D_i-d}{h})}$$

(18)

In Equation (19), n represents the number of samples, d denotes the mean, h is the bandwidth, and K(·) is the kernel function. The dynamic distribution of digital twin technology and energy industry sustainable development in China and its four major regions is estimated using the Gaussian kernel density function, calculated as follows:

$$K(d)={\displaystyle \frac{1}{\sqrt{2\pi }}}\exp (-{\displaystyle \frac{d^2}{2}})$$

(19)

When investigating the spatial differentiation structure of digital twin technology investment levels and their contributing sources, the Dagum Gini coefficient exhibits certain limitations in characterizing regional development dynamics. Therefore, this study introduces the kernel density estimation method to analyze the evolutionary patterns of digital twin technology investment across China and its four major regions from 2013 to 2024, with a focus on spectral shifts in the density surface, main peak modality, tail extension, and multi-peak characteristics.

2.5. Absolute Convergence Test

To examine whether regional energy sustainability levels tend to converge toward a common steady state under the widespread deployment of digital twin technology, the concept of absolute convergence is employed. The fundamental assumption of absolute convergence posits that, ceteris paribus, regions with lower initial levels tend to grow faster than those with higher initial levels, eventually reaching a similar steady-state level of development.

The functional form of the classical absolute convergence regression model is presented in Equation (20):

$$In\left({\displaystyle \frac{y_{i,t}+T}{y_{i,t}}}\right)=\alpha +\beta In\left(y_{i,t}\right)+{\epsilon }_{i,t}$$

(20)

where y_i,t denotes the energy sustainability level of region i in year t and β is the convergence coefficient. A significantly negative value for β indicates the presence of absolute convergence, suggesting that disparities in development levels across regions are diminishing over time. However, in the actual process of regional development, energy systems may exhibit significant spatial externalities and spillover effects. Moreover, regional heterogeneity and temporal dynamics may jointly influence the convergence process. Therefore, based on the basic model, this study further incorporates spatial fixed effects and temporal fixed effects, while also accounting for potential spatial dependence structures. The extended model is specified as follows (21):

$$In\left({\displaystyle \frac{y_{i,t}+T}{y_{i,t}}}\right)=\alpha +\beta In\left(y_{i,t}\right)+{\mu }_i+{\lambda }_t+{\epsilon }_{i,t}$$

(21)

where ${\mu }_{\mathrm{i}}$ denotes the unobserved region-specific fixed effects and ${\lambda }_t$ represents the time fixed effects, which are introduced to control for the influence of overarching macroeconomic policies, technological diffusion, and energy market dynamics. Building on this foundation, considering the potential spatial interdependence in energy sustainability development, this study further employs spatial econometric models to capture latent spatial autocorrelation. Specifically, Spatial Lag Model forms are adopted. Spatial Lag Model, also known as the spatial autoregressive model, is a type of spatial econometric model that explicitly incorporates spatial dependence in the dependent variable. In this model, the value of the dependent variable in a given region is assumed to be influenced not only by its own characteristics but also by the values of the dependent variable in neighboring regions, as shown in (22):

$$In\left({\displaystyle \frac{y_{i,t}+T}{y_{i,t}}}\right)=\alpha +\beta In\left(y_{i,t}\right)+\rho WIn\left(y_{i,t}\right)+{\mu }_i+{\lambda }_t+{\epsilon }_{i,t}$$

(22)

This specification allows for the estimation of spatial spillover effects, $\rho$ while controlling for both region-specific heterogeneity, ${\mu }_{\mathrm{i}}$, and temporal shocks, ${\lambda }_t$. The spatial weight matrix, $W$, captures the spatial structure or the geographical relationships between regions. The presence of a significant and positive spatial lag coefficient, $\rho$, suggests that regions are not evolving independently but are instead influenced by their spatial neighbors.

To further quantify the speed of the convergence process, the convergence rate is calculated based on the estimated coefficient obtained from the regression results.

$$\mathrm{v}=-{\displaystyle \frac{In(1+\beta )}{T}}\times 100\%$$

(23)

where T represents the length of the observed time period. This indicator reflects the average annual rate (in percentage form) at which the disparities in energy sustainability indicators across regions are diminishing.

The Absolute Convergence Test assumes that spatial correlation primarily exists in the error term, which may arise from unobserved spatial externalities or spatially dependent error structures. To ensure the appropriateness of the model specification and the significance of spatial effects, this study conducts a series of statistical tests as follows in

Table 1. Statistical tests of absolute convergence.

Indicator	Meaning
R2	Goodness of fit
Log-likelihood	A higher value indicates a better model fit
Hausman test	Selects between fixed-effects and random-effects models
LM spatial lag/error	Determines whether spatial effects should be incorporated
Robust LM	Provides a more reliable assessment of spatial dependence
Wald test/LR test	Overall significance test for spatial components in a model
Convergence Speed, v	Indicates how quickly a system approaches a steady state, expressed as % per year

.

The introduction of a multi-level absolute convergence model incorporating spatial and temporal fixed effects, as well as spatial lag and error terms, provides a scientific basis for comprehensively evaluating the impact of digital twin technology on the coordination of regional disparities in the process of energy sustainability.

2.6. Conditional Convergence Test

Conditional convergence refers to the phenomenon where, after controlling for structural factors such as population size, financial development, and educational attainment, economic or system indicators tend to converge toward their respective steady-state levels. In other words, due to inherent regional heterogeneities, different areas may reach different long-term equilibria. However, relative to their own structural characteristics, these regions still exhibit a converging tendency.

$$In(y_{i,t})-In(y_{i,t-1})=\alpha +\beta In(y_{i,t-1})+\gamma X_{i,t}+{\mu }_i+{\lambda }_t+{\epsilon }_i,$$

(24)

where $y_{i,t}$ denotes the economic variable of region i at time t (e.g., per capita GDP or green energy efficiency); $In\left(y_{i,t-1}\right)$ represents the initial level of the variable, which is used to examine whether a “low-to-high” convergence trend exists; $X_{\mathrm{i},t}$ is a vector of control variables, including factors such as population, financial development, and education level; ${\mu }_{\mathrm{i}}$ captures the spatial fixed effects; ${\lambda }_t$ represents the time fixed effects; and a negative coefficient $\beta$ < 0 indicates the presence of conditional convergence. The Meaning of model in Conditional Convergence Test is shown in

Table 2. Meaning of model in Conditional Convergence Test.

Model	Meaning	Characteristic
Two-Way Fixed SDM	Spatial Durbin Model with Two-Way Fixed Effects	Includes both spatially lagged dependent and independent variables, enabling the capture of complex spatial diffusion
Two-Way Fixed SAR	Spatial Autoregressive Model with Two-Way Fixed Effects	Includes the spatial lag of the dependent variable with a relatively simple structure
Spatial Fixed Effects	Regional Fixed Effects	Control for regional heterogeneity
Temporal Fixed Effects	Year Fixed Effects	Account for temporal trends

.

The significance of incorporating control variables in convergence models lies in isolating the effect of initial conditions on convergence by accounting for other structural factors that may influence the growth process. This allows for a more accurate assessment of whether regions converge conditionally, given their unique characteristics, such as population size, financial development, and education levels. The meaning of common control variables used in convergence models is displayed in

Table 3. Common control variables used in convergence models.

Variable Name	Definition	Economic Meaning
lnPOP	Logarithm of population size	Controls for economies of scale or dilution effects caused by population size
Fin	Level of financial development	Reflects the supportive role of financial accessibility in economic growth
Edu	Education level	Represents the promotion of human capital enhancement through education

.

3. Results and Discussion

To ensure temporal consistency in the research data, this study defined the observation period from 2013 to 2024. The target population included all prefecture-level and higher administrative regions. Considering variations in administrative structures and statistical reporting methods across cities, rigorous screening was applied to ensure data completeness and continuity to guarantee the scientific validity and accuracy of the findings: (1) Seven prefecture-level cities established after 2007 were excluded due to insufficient data continuity. (2) An additional six cities were eliminated owing to incomplete data records. After comprehensive screening, 284 prefecture-level and higher cities were ultimately selected as the research sample. The observational data were collected from national and local statistical yearbooks (2013–2024), municipal statistical bulletins, and government open-data systems, with unified statistical coverage across entire municipal administrative boundaries. To better assess governmental digital engagement, this study reviewed 2013–2024 local government work reports, extracting policy indicators related to digital twin technology development to construct a government attention index for digital twin technology.

3.1. Characterization of Fundamental Facts Regarding Digital Twin Technology in Energy Sustainable Development

The application of digital twin technology in the energy sector has enhanced energy utilization efficiency and provided a green blueprint for sustainable urban development [25]. Total electricity consumption across society is a key indicator of urban energy use and directly reflects the demand for electricity driven by economic and social activities [26]. Through smart meters and other devices, digital twin technology collects users’ electricity consumption data in real time, enabling an accurate grasp of trends in total electricity usage. Based on electricity data, digital twin technology can help power departments accurately forecast electricity demand and optimize electricity production and scheduling plans. According to electricity usage patterns across different regions and industries, power generation equipment can be reasonably scheduled, reducing the number of times generators are started or stopped, lowering generation costs and energy loss. Meanwhile, by analyzing users’ electricity consumption behavior, policies such as time-of-use pricing can be implemented to guide users toward rational electricity use, reduce peak loads, and improve the overall operational efficiency of the power system [27]. Therefore, the total electricity consumption of society can be regarded as a representative indicator for assessing the operational scale of digital twin technology within IoT-based power systems, thereby reflecting the efficiency and performance of energy and electricity system operations. To optimize energy use, ensuring the stable supply of clean energy is a key component of sustainable development. Manufactured gas and natural gas, as relatively clean fossil fuels, reflect the capacity and reliability of clean energy supply in cities. Therefore, applying digital twin technology to the supply systems of manufactured gas and natural gas can help optimize urban energy structures, reduce the use of traditional energy sources such as coal, lower pollutant emissions, and improve urban environmental quality [28]. Based on this, the total supply of manufactured gas and natural gas in urban areas can be employed as an indicator to evaluate the coverage of IoT-based gas management systems, thereby facilitating the optimization and upgrading of the energy utilization framework. The total supply of liquefied petroleum gas is an indicator that reflects the diversity and flexibility of urban energy supply. The application of digital twin technology in liquefied petroleum gas (LPG) supply systems helps cities allocate energy resources reasonably according to the characteristics of different regions and users, enhancing the adaptability and coverage of energy supply [29]. Accordingly, the total supply of LPG can be utilized as an indicator to assess the application of digital twin technology in energy supply, thereby providing a clearer representation of the diversity within urban energy systems.

The penetration rate of electronic gas meters is an important indicator of gas service coverage and can thus be used to measure the level of urban energy services for residents, reflecting the degree to which citizens enjoy clean and convenient energy services. The improvement of gas service coverage depends on the application of digital twin technology in urban gas supply infrastructure, thereby enhancing urban energy efficiency, optimizing the energy structure, and promoting sustainable urban development [30]. Therefore, the gas coverage rate can serve as a metric for evaluating the penetration of electronic gas meters, thereby offering valuable insights into the effectiveness of gas utilization in advancing energy sustainability. The evaluation indicators for sustainable development in the energy industry are as shown in

Table 4. Indicator system for improving energy utilization efficiency.

Primary Indicators	Fundamental Indicators	Unit	Weight	Attribute
	Scale of IoT-Based Power System Operation	KW/h	0.193	+
	Coverage of IoT-Based Gas Management	Persons per ton	0.165	+
	Operational Volume of Urban LPG Energy Subsystems	ton	0.195	+
	Penetration Rate of Electronic Gas Meters	%	0.187	+

. Shown in Table 1, the weighting coefficients of the indicators were determined using the entropy method, which objectively captured the degree of information dispersion among the indicators. This approach ensured a more impartial and data-driven evaluation of their relative significance in the context of sustainable energy development. Data sources are shown in Appendix A.

The above indicators are designed to measure the application of digital twin technology in the field of sustainable energy development. The weights of these indicators are determined using the entropy weight method, which offers a scientifically grounded and objective approach to indicator weighting. By analyzing the degree of dispersion or variability within the data, the entropy method assigns higher weights to indicators that carry more information and have greater influence on the sustainable energy evaluation system. This not only avoids subjective bias in the sustainable energy assessment process but also ensures that the composite evaluation accurately reflects the actual contribution of each indicator. Consequently, it enhances the credibility and robustness of sustainable energy evaluation results, providing a reliable basis for analyzing the impact of digital twin technology on energy sustainability.

Specifically, China is divided into four regions according to the official classification standards of the National Bureau of Statistics. The provinces and five representative cities in each region are as follows: (1) Eastern Region: Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan. Representative cities include Beijing, Shanghai, Shenzhen, Hangzhou, Guangzhou, et al. (2) Central Region: Shanxi, Anhui, Jiangxi, Henan, Hubei, and Hunan. Representative cities include Wuhan, Zhengzhou, Changsha, Hefei, Nanchang, et al. (3) Western Region: Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Tibet, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang. Representative cities include Chengdu, Chongqing, Xi’an, Kunming, Urumqi, et al. (4) Northeastern Region: Liaoning, Jilin, and Heilongjiang. Representative Cities include Shenyang, Dalian, Changchun, Harbin, Anshan, and so on.

3.1.1. Evolution Trend of Sustainable Development in the Energy Industry

From Figure 2, it can be seen that the eastern region has the highest overall level of sustainable development in the energy industry, consistently surpassing other regions. This indicates that the eastern region’s energy sustainability is in a stable state, benefiting from industrial structure optimization, technological investment, and the promotion of clean energy. The central region ranks second overall, slightly higher than the western and northeastern regions. However, the sustainable development in the central region exhibits noticeable fluctuations, suggesting that its energy development is influenced by multiple factors, such as the proportion of traditional industries and policy adjustments. The western region shows a trend similar to the central region but slightly lower, indicating that recent investments in renewable energy sectors like wind power and photovoltaics have yielded positive results. The northeastern region has the lowest overall level, demonstrating that structural adjustment and transformation of the energy industry in this region are still ongoing, with a heavy reliance on traditional heavy industries and difficulties in the transition process. Around 2017, China entered a phase of “new normal” economic development, during which the pace of economic restructuring accelerated, and stricter regulations were imposed on high-energy-consuming and heavily polluting industries. The period from 2016 to 2017 marked a critical transition from traditional energy sources—primarily coal—to clean energy sources such as wind and solar power. However, during this transitional phase, the integration of new and old energy systems faced technological lags and institutional bottlenecks, which led to a temporary decline in energy supply efficiency and consequently hindered sustainable development indicators. In addition, the infrastructure for clean energy was not yet fully developed, resulting in a lag in the overall operational efficiency of the energy system. In terms of overall development levels, 2022 marked a general low point, with the central, western, and northeastern regions all reaching their lowest levels, possibly due to the impact of the pandemic, economic slowdown, or energy policy adjustments [25]. In 2023, the energy development levels across all regions in China generally rebounded, reflecting the effective implementation of the new development philosophy during the 14th Five-Year Plan period and the advancement of energy transition strategies.

From the above Figure 3, it can be seen that in 2013, regions with optimized energy efficiency were mainly concentrated in parts of East China, Central China, and South China, such as Jiangsu, Zhejiang, Shandong, and Henan. The data in Figure 3 represent the level of energy sustainability across different regions in China, with data values ranging from 0.000 to 0.005. Different colors indicate the varying levels of sustainable development in the regional energy industry. Darker colors represent higher levels of energy sustainability. The Northwest and Southwest regions had relatively low levels of energy efficiency optimization and development. By 2024, the areas of sustainable development in the energy industry had significantly expanded, especially in the Yangtze River Delta, the Pearl River Delta, and the Beijing–Tianjin–Hebei regions. Some central and western areas, such as Hunan, Jiangxi, and Shaanxi, show deeper colors, indicating an improvement in the level of sustainable development in the energy industry. The overall deepening of color in the northeastern region also reflects an increase in sustainable development levels there. Over time, the imbalance in energy development among regions may have intensified. In 2024, the eastern coastal areas and economically developed regions, such as Guangdong and Shanghai, exhibited a noticeably deeper degree of sustainable development in the energy industry compared to 2013, further widening the gap with the central and western regions. Some resource-rich areas in the west, such as Inner Mongolia, Xinjiang, and Shaanxi, showed slight increases in sustainable development levels, reflecting adjustments in the national energy strategy that promote the shift of the energy industry toward resource-abundant regions. In some parts of Northeast China, the sustainable development level of the energy industry has declined. In some old industrial-based cities, the equipment of traditional energy industries is aging and the technology is backward, making it difficult to meet market demands. Meanwhile, the emerging energy industries lack financial, technical, and talent support, resulting in insufficient development momentum for the energy industry and a decline in the level of sustainable development.

3.1.2. Gini Coefficient

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Inter-group Gini Coefficient

As shown in the Figure 4, the eastern region, relying on its advanced scientific research capabilities and economic foundation, holds a first-mover advantage in the sustainable development of the energy industry. Its Gini coefficient has remained the highest for a long time, reaching a new peak in 2023. This indicates that although the east was the earliest to develop and has the strongest technology in the application of digital twin technology in energy, there are large internal disparities, possibly concentrated in first-tier cities such as Beijing, Shanghai, and Shenzhen, exhibiting an uneven agglomeration effect. The central region’s Gini coefficient shows an “inverted U-shaped” trend, suggesting that there was imbalance in the early stages of technology diffusion, but with strengthened regional coordination policies, the equity of technology diffusion has improved. The western region has consistently maintained a relatively low Gini coefficient, indicating that the overall digital twin technology level there is low, disparities are small, and there is no strong “head-city monopoly effect”, which decentralizes resources in a few major urban centers. The western region has benefited from multiple national strategies, such as the “Western Development Strategy” and regional digital infrastructure investments, which have promoted more balanced development across many second- and third-tier cities. This homogenization effect has helped narrow inter-city gaps and stabilized the overall distribution. The northeastern region started with a low Gini coefficient and showed little change overall, but experienced significant fluctuations between 2018 and 2021, especially with a slight increase after 2021. This was influenced by limitations in technological foundations and resource distribution, which have exacerbated regional development imbalances.

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Intra-group Gini Coefficient

As shown in Figure 5, in the eastern region, the diffusion of technology has shifted from “concentrated leadership” to “regional penetration”, showing a significant trend toward technological equality. From 2012 to 2019, the intra-group Gini coefficient showed an upward trend, with digital twin technology mainly concentrated in first-tier or provincial capital cities, reflecting a “Matthew effect” of digital twin technology in the sustainable development of the energy industry. From 2020 to 2023, the intra-group Gini coefficient rapidly declined, indicating accelerated diffusion of sustainable development in the energy industry and improved efficiency in resource allocation, likely driven by national policies such as the “dual carbon” goals. In the central region, technology diffusion lagged behind the east but a trend toward balanced development has emerged. From 2013 to 2021, the intra-group Gini coefficient rose slowly, indicating an increasing concentration effect of digital twin technology in the early stages of sustainable energy development. From 2022 to 2024, the intra-group Gini coefficient declined as digital twin technology began to spread to small and medium-sized cities, signaling the start of balanced development. In the western region, digital twin technology diffusion also lagged behind the east but a trend toward balanced development has appeared. The intra-group Gini coefficient remained relatively stable with a slight decline, indicating a low starting point for technology application. The diffusion of technology has been constrained by geographical and infrastructural factors and has not yet fully overcome regional barriers, but is gradually penetrating. The west is expected to become a key area for future support. “The 2023 China Digital Twin Industry Development Report” indicates that the application of digital twin technology in sectors such as energy, electricity, and manufacturing still demonstrates a regional pattern characterized by “pilot projects initiated in the eastern region, with gradual diffusion into the central and western regions”. Regional disparities remain pronounced, as the western region faces practical challenges such as high sunk costs and long return cycles for digital twin technology. “The 14th Five-Year Plan for the Development of the Digital Economy” (NDRC High-Tech [2021], No. 201) explicitly calls for “promoting the integration of digital technologies into key industries in the central and western regions” and encourages the adoption of intelligent technologies—such as digital twins—to support the smart transformation of infrastructure in areas such as energy and transportation. The western region is thus identified as a key area for focused policy support. In the northeastern region, the application of digital twin technology in the sustainable development of the energy industry faces a risk of “equal poverty”. Targeted policies are needed to enable leading cities to drive overall development. The Gini coefficient has remained low, with a slight increase after 2019, indicating low technology adoption in the early stages of sustainable energy development, followed by gradual progress but the emergence of new inequalities.

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Main Sources of Differences

From Figure 6, it can be seen that the inter-group Gini coefficient differences in the application of digital twin technology in the sustainable development of the energy industry have remained relatively stable with little fluctuation. Between 2017 and 2024, the contribution of inter-group differences consistently stayed around 0.30, indicating that structural regional disparities persisted with little change, which can be attributed to long-standing imbalances in economic development, digital infrastructure, and institutional capacity among the regions. The intra-group Gini coefficient differences for digital twin technology in the energy industry peaked between 2015 and 2017 (exceeding 0.30), reflecting significant disparities within groups, which are driven by uneven policy implementation and urban heterogeneity. There was a decline in 2020, indicating some alleviation of intra-group technological differences; this was because the effects of intensified national-level support and infrastructure investment temporarily narrowed these gaps. However, from 2021 onward, the intra-group Gini coefficient rose again, showing a fluctuating pattern. The contribution ratio of differences decreased year by year from 2013 to 2017, indicating a reduction in disparities. After 2018, it gradually increased, reaching a peak of about 0.07 in 2020, signaling an expansion of disparities again, followed by a period of steady fluctuations. This suggests that uneven usage in the sustainable development of the energy industry remains the norm. Between 2018 and 2020, digital twin technology entered an accelerated concentration phase, where core regions or main actors began to dominate its application, rapidly widening disparities, especially peaking in 2020. The period from 2021 to 2024 marks the phase of differentiation stabilization for digital twin technology. During this period, regional disparities in its application within the energy sector somewhat receded but remained at a relatively high level. The distribution of digital twin technology use in the energy field has not yet achieved full balance and still requires policy guidance or platform-sharing mechanisms to promote equitable diffusion. The lack of full convergence suggests that the diffusion of digital twin technology in the sustainable energy sector remains uneven, hindered by limited platform-sharing mechanisms, data standardization gaps, and varying regional capacities for technological adoption.

3.1.3. Dynamic Evolution

It can be seen form Figure 7 that, from 2013 to 2024, the kernel density distributions of all regions exhibited dynamic changes, with the overall trend of sustainable development in the energy industry showing steady improvement. The color gradient in Figure 7 represents the magnitude of energy efficiency optimization density, with warmer colors (e.g., yellow, green) indicating higher density values and cooler colors (e.g., blue) representing lower density areas. Between 2013 and 2016, the kernel density distributions fluctuated significantly but gradually stabilized in the later years. At the national level, the kernel density was initially concentrated in regions with lower levels of sustainable energy development. Over time, the areas with high kernel density gradually shifted toward regions with higher degrees of energy efficiency optimization. This indicates a steady nationwide improvement in energy efficiency, with the distribution increasingly concentrated in higher-efficiency intervals. Compared to other regions, the eastern region achieved a higher level of sustainable energy development earlier, with a relatively high kernel density. This suggests that the east began emphasizing sustainable energy development at an earlier stage. With the advancement of digital twin technology, the kernel density distribution of energy sustainability in the east has further shifted toward the high-efficiency range, with relatively small fluctuations—reflecting steady progress and relatively stable outcomes in sustainable energy development. In the western region, kernel density was concentrated in areas with lower levels of sustainable energy development, and the overall distribution skewed to the left. As digital twin technology matured, the kernel density curve gradually shifted to the right, indicating continual improvement in energy efficiency. However, compared to the east, the western region may face a lag in initial conditions and development speed, though it continues to make active progress. The central region’s kernel density distribution trend in sustainable energy development is similar to the national trend. With the ongoing maturation of digital twin technology, the shape of the energy efficiency kernel density curve changed more moderately, suggesting a relatively steady progression in sustainable energy development, though the extent of improvement may be less significant than in the eastern region. In the northeastern region, early kernel density was concentrated in the low-efficiency range and showed notable fluctuations between 2013 and 2016. After 2016, the kernel density curve gradually shifted to the right, indicating that the level of sustainable energy development in the northeast is also improving. However, the overall optimization process may be relatively slow, with certain challenges during implementation, resulting in a more gradual pace of change.

3.1.4. Spatial Convergence Test

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Stock Perspective: Convergence Test

There are significant differences in the application of digital twin technology for achieving sustainable development in the energy industry across different cities and regions. Does this disparity exhibit convergence? Can it trend toward equilibrium? This section uses the coefficient of variation to assess convergence characteristics and explores the spatial convergence trend of sustainable energy industry development from a stock perspective.

Specifically, as shown in Figure 8, the index in the eastern region increased from 0.357 to 0.359, with a relatively small growth margin and values consistently below the national average, indicating that the improvement in sustainable energy industry development in the east has been relatively lagging. The central region’s index rose from 0.359 to 0.389, showing a more significant increase and gradually approaching the national average, suggesting faster progress in sustainable energy development. The western region’s index increased from 0.388 to 0.394, remaining below the national average, indicating that further efforts are needed to enhance sustainable development in the energy industry. The northeastern region’s index grew from 0.395 to 0.405, with a noticeable increase, reflecting substantial progress in sustainable energy industry development.

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Increment Perspective: Convergence Test

To explore the convergence trend of improvements in sustainable energy industry development across the country and the four major regions from an incremental perspective,

Table 5. Absolute Convergence Test for the whole country and four regions.

Region	Full Sample	Eastern Region	Central Region	Western Region	Northeastern Region
Model Type	Two-Way Fixed SEM	Two-Way Fixed SAR	Two-Way Fixed SAR	Two-Way Fixed SAR	Two-Way Fixed SAR
$\beta$(ln egl)	−0.386 ***	−0.284 ***	−0.307 ***	−0.427 ***	−0.374 ***
	(−10.562)	(−13.127)	(−8.251)	(−7.525)	(−7.631)
$\rho$ or $\lambda$	0.327 ***	0.401 ***	−0.285 ***	−0.193	−0.286
	(4.011)	(3.895)	(−3.852)	(−0.285)	(−0.221)
R2	0.301	0.295	0.309	0.254	0.323
Log-likelihood	1320.741	295.741	405.471	33.85	352.8524
Spatial fixed effects	3.214 ***	5.284 ***	6.318 ***	3.894 ***	8.626 ***
Temporal fixed effects	9.634 ***	7.521 ***	9.219 ***	10.322 ***	8.635 ***
Hausman test	21.521 ***	35.214 ***	4.632 ***	28.632 ***	19.363 ***
LM spatial lag	15.633 ***	12.685 ***	7.524 ***	8.697 **	8.633 ***
Robust LM spatial lag	10.879 ***	8.696 ***	0.207	1.186	3.855
LM spatial error	12.879 ***	5.878 **	3.882 **	4.015 **	2.859 **
Robust LM spatial error	8.255 ***	0.527	0.637	0.582	0.416
Wald test spatial lag	0.528	0.396	0.324	0.527	0.481
LR test spatial lag	0.417	0.327	0.205	0.107	0.153
Wald test spatial error	0.294	0.233	1.822	0.274	0.541
LR test spatial lag	0.327	−0.124	3.122	0.157	0.325
Wald test spatial error	0.224	0.048	2.637	0.143	0.144
LR test spatial error	0.211	0.114	0.221	1.235	0.176
Convergence speed, v (%)	0.023	0.032	0.027	0.016	0.028
Number of Observations	284	62	108	27	68

Note: *** and ** indicate significance at the 1% and 5% levels, respectively. Values in parentheses are t-statistics.

presents the results of the absolute β-convergence test. To start with, the improvements in sustainable energy development at both the national and regional levels exhibit absolute β-convergence characteristics, with β coefficients significantly negative at the 1% confidence level. This indicates that, over time, the levels of sustainable energy development across the country and the four major regions will eventually converge toward the same steady state. Additionally, although the convergence speeds of sustainable energy development vary across the four regions, all are lower than the national level. What is more, there are spatial differences in the effects across the country and the four major regions. Specifically, at the national level, the explained variable shows a spatial lag effect, which is significantly positive at the 1% confidence level. This suggests that the sustainable energy development and its growth rate in one city are positively influenced by the spatial spillover effects from other cities. In the eastern region, the spatial lag coefficient of sustainable energy development is significantly positive at the 5% confidence level, indicating that the rate of improvement in sustainable energy development in this region tends to increase as the growth rates in surrounding regions rise. In contrast, the spatial lag coefficient in the central region is significantly negative at the 5% confidence level, indicating that the growth rate of sustainable energy development in the central region tends to decline as the growth rates in other regions increase.

Since conditional convergence only considers the initial value as the testing variable, it may deviate from the actual situation and thus affect the accuracy of the estimation results. Therefore, this section introduces multiple heterogeneity factors as control variables to further conduct the test.

Table 6. Conditional Convergence Test of sustainable development of the energy industry in China and its four major regions.

Region	Full Sample	Eastern Region	Central Region	Western Region	Northeastern Region
Model Type	Two-Way Fixed SDM	Two-Way Fixed SDM	Two-Way Fixed SAR	Two-Way Fixed SDM	Two-Way Fixed SAR
$\beta$(ln egl)	−0.509 ***	−0.483 ***	−0.434 ***	−0.504 ***	−0.357 ***
	(−19.521)	(−12.352)	(−16.339)	(−10.284)	(−11.296)
LnPOP	0.002 ***	0.006 ***	0.003 ***	0.001 ***	0.001 ***
	(7.863)	(2.952)	(4.852)	(5.324)	(3.965)
Fin	−0.089	−1.365 ***	0.018	0.286	0.301
	(−0.385)	(−4.213)	(0.031)	(0.409)	(0.495)
Edu	0.039	−0.141	0.001	−0.896 **	0.214
	(−0.392)	(−0.463)	(0.003)	(−3.142)	(0.015)
$\rho$ or $\lambda$	0.052	0.985 ***	0.629 ***	−0.312	−0.201
	(0.684)	(4.324)	−3.014)	(−1.351)	(−2.634)
R2	0.325	0.385	0.321	0.396	0.322
Log-likelihood	12.254	23.258	61.352	40.252	3.204
Spatial fixed effects	42.126 ***	170.256 ***	259.685 ***	59.638 ***	69.584 ***
Temporal fixed effects	6.286 ***	3.371 ***	2.634 ***	2.682 ***	9.684 ***
Hausman test	75.876 ***	60.851 ***	70.524 ***	61.221 ***	60.333 ***
LM spatial lag	60.285 ***	6.325 **	19.632 ***	6.402 **	7.524 ***
Robust LM spatial lag	3.208 *	4.309 **	8.792 ***	4.211 **	2.124
LM spatial error	6.238 ***	6.125 **	18.205 ***	6.452 **	7.514 ***
Robust LM spatial error	3.247 *	6.314 **	1.238	0.052	0.041
Wald test spatial lag	4.251 ***	5.857 ***	2.596 ***	2.058	9.524
LR test spatial lag	9.627 ***	4.059 ***	9.522 ***	1.529	1.235
Wald test spatial error	5.296 ***	9.521 **	9.388 ***	2.636 *	0.255
LR test spatial lag	50.254 ***	19.524 **	19.574 **	13.964 *	9.614
Convergence speed, v (%)	0.058	0.062	0.058	0.055	0.059
Number of Observations	284	62	108	27	68

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Values in parentheses are t-statistics.

presents the results of the Conditional Convergence Test for the sustainable development of the energy industry nationwide and in the four major regions.

To begin with, the conditional convergence coefficients for the sustainable development of the energy industry at the national level and across the four major regions are all significantly negative at the 1% confidence level. This indicates that conditional convergence exists nationwide and in all four regions. In other words, even when accounting for regional heterogeneity factors such as economic development, fiscal pressure, industrial structure, openness to trade, fiscal decentralization, and attention to energy efficiency, the level of sustainable development in the energy industry continues to converge toward a steady state.

What is more, compared to the speed of absolute convergence, the convergence speed of sustainable development in the energy industry has accelerated under conditional convergence. Specifically, the national convergence speed increased to 0.0596%, and the order of convergence speeds among the four regions remains: eastern region > central region > northeastern region > western region.

Additionally, there are notable differences in spatial effects between the national level and the four regions. These differences are reflected not only in the magnitude of the coefficients but also in the type of spatial effects, which differ from those under absolute convergence. Specifically, the spatial lag coefficient for the national energy industry’s sustainable development remains significantly positive at the 1% confidence level, indicating that improvements in some provinces’ energy sustainability levels can accelerate the overall convergence process. Moreover, for the eastern and central regions, the spatial lag coefficients are also significantly positive at the 1% level, suggesting that there are positive spatial spillover effects in the sustainable development of the energy industry within these regions.

In addition, after incorporating multiple control variables for the conditional convergence analysis, both the R² values and log-likelihood statistics for the national and regional models improve significantly compared to the absolute convergence models. This strongly supports the validity and effectiveness of the selected control variables. From a statistical perspective, the influencing factors of energy industry sustainable development vary significantly across the country and regions. Specifically, economic development accelerates the convergence of sustainable development in the energy industry both nationally and regionally; fiscal pressure significantly hinders convergence in the eastern and northeastern regions; and industrial structure has a significantly negative impact on sustainable development in the eastern region.

3.2. Analysis of the Input Effects of Digital Twin Technology on the Sustainable Development of the Energy Industry

Digital twin technology has a significant impact on the sustainable development of the energy industry. A high level of attention to digital twin technology encourages governments to allocate more funding to energy-related projects, providing strong financial support for energy development. As governments place greater emphasis on the development of digital twin technology, they introduce a series of talent-attracting policies aimed at drawing professionals in the digital twin field into the energy industry [25]. As a complex system integrating physical models, simulation computing, big data, and artificial intelligence, the development trajectory of digital twin technology closely follows the S-shaped diffusion curve typical of technological innovation. Its early-stage accumulation and breakthroughs must rely on scientific and technological investment. Therefore, government funding for science and technology can be used as an indicator to measure the intensity of digital twin-related technological investment. The increased attention from the government also accelerates the formulation and improvement of laws, regulations, and standards related to energy infrastructure, ensuring that the development of urban digital twin technologies operates within a legal framework. This helps safeguard data security, personal privacy, and the safe and stable operation of cities [26]. Emerging fields such as digital twin technology, intelligent power dispatch, carbon monitoring, and smart energy storage are experiencing a surge in demand for specialized talent. The traditional education system urgently needs to update its curriculum content, faculty configuration, and teaching methods through government investment to meet the requirements of the green digital era. Therefore, government educational investment can be used as an indicator to measure Government Investment in Digital Education Development. By enhancing the focus on digital twin technology, the government can effectively promote data sharing and collaboration across different sectors of the energy industry, break down data silos, and eliminate information barriers. This enables various fields within energy development to make decisions and deliver services based on comprehensive and accurate data, thereby improving the operational efficiency and management capacity of cities [27]. Government intervention mechanisms are the key leverage for the widespread promotion and application of digital twin technology from isolated cases to broad implementation. The stronger the institutional intervention, the more favorable the political and institutional environment for the operation of digital twin systems, enhancing the technology’s sustainability. A high degree of digital intervention indicates good coupling between technology and institutions, which facilitates the deep integration of digital twin technology in the energy sector. Therefore, the level of government intervention can be used as an indicator to measure the maturity of multi-stakeholder collaborative governance of digital twin systems in sustainable energy development.

From the perspectives of technological innovation theory and industrial upgrading theory, investment in digital twin technology serves as a core driving force for the sustainable development of the energy industry. Continuous innovation and the integrated application of digital twin technologies provide strong technical support for energy sector growth [28]. Investment by enterprises and research institutions in the research and development of digital twin technologies fosters breakthroughs and innovations in key technologies [29]. The development of digital twin technology is crucial for energy data collection. By capturing changes in energy indicators in real time and with high precision, it offers robust data support for sustainability efforts in the energy sector [30]. Digital twin technology relies on the extensive collection, transmission, processing, and feedback of real-time data. Among these, internet infrastructure is a critical supporting condition. A broad base of internet users reflects strong terminal access capabilities, providing the foundation for deploying user-side sensors (such as home electricity meters and energy usage behavior analysis devices). User terminals within digital twin systems—such as smart electricity usage platforms, carbon footprint visualization platforms, and energy consumption apps—require a large number of connected users for operation and feedback. Whether users have basic internet access capabilities determines if they can connect to energy digital service systems, thereby forming a closed loop of “digital twin–user behavior–energy feedback”, where digital twin systems monitor and simulate user behavior, analyze its impact on energy consumption, and provide real-time feedback to optimize energy use. Therefore, the number of internet users per 100 people and the number of mobile phone users per 100 people can be used as key indicators to measure the role of digital twin technology in sustainable energy development. Digital twin technology is a complex system integrating physical modeling, real-time simulation, data fusion, artificial intelligence, and interactive visualization [31]. It is essentially a highly software-intensive and computation-driven technology platform. For energy sub-sectors such as electricity, coal, and natural gas, customized twin systems need to be developed, which must rely heavily on software engineering talent with interdisciplinary backgrounds. A higher proportion of employees in the computer services and software industry indicates a stronger “human resource foundation” for the technological reserves required by digital twin technology in a region [32]. Based on this, the proportion of employees in the computer services and software industry can serve as an indicator to measure the level of technical talent support for the development of digital twin technology.

The emergence of digital twin technology has significantly enhanced communication speeds between different devices in the energy industry [33]. This facilitates the use of big data and artificial intelligence to deeply analyze vast amounts of urban energy operation data, enabling predictive analysis of urban development trends and the proactive formulation of corresponding policies and measures [34]. In turn, it provides intelligent assistance in urban management and decision-making processes. Based on the above theories, an input indicator system for digital twin technology will be established. The above indicators are sourced from the China City Statistical Yearbook (2013–2024), government work reports, and other related documents.

From the perspectives of technological innovation theory and industrial upgrading theory, investment in digital twin technology serves as a core driving force for the sustainable development of the energy industry. Continuous innovation and the integrated application of digital twin technologies provide strong technical support for energy sector growth [35]. Investment by enterprises and research institutions in the research and development of digital twin technologies fosters breakthroughs and innovations in key technologies [36]. The development of digital twin technology is crucial for energy data collection. By capturing changes in energy indicators in real time and with high precision, it offers robust data support for sustainability efforts in the energy sector [37]. The emergence of digital twin technology has significantly enhanced communication speeds between different devices in the energy industry. This facilitates the use of big data and artificial intelligence to deeply analyze vast amounts of urban energy operation data, enabling predictive analysis of urban development trends and the proactive formulation of corresponding policies and measures. In turn, it provides intelligent assistance in urban management and decision-making processes [38]. Based on the above theories, an input indicator system for digital twin technology will be established.

Based on the digital twin technology investment index system established in

Table 7. Indicator system for investment in digital twin technology.

Primary Indicator	Variable Name
Policy Allocation (PA)	Intensity of Digital Twin-Related Technological Investment
	Government Investment in Digital Education Development
	Government Digital Intervention Mechanism
	Government Attention to Digitalization
Technological Advancement (TA)	Digital Connectivity Capability Index
	Level of Technical Talent Support
	Deployment Capacity of Mobile Sensing Nodes

, the global entropy method was used to analyze the investment in digital twin technology across various regions in China from 2013 to 2024. Data sources are shown in Appendix A. The results for the indicators are shown in Figure 9.

As shown in Figure 9, PA exhibits an overall upward trend with fluctuations. From 2014 to 2017, PA in early-stage digital twin technology experienced some volatility but gradually stabilized thereafter. As a result, policy investment shows a slight decline followed by a slow recovery. Between 2013 and 2024, TA fluctuated more dramatically than policy investment, reflecting a certain degree of instability. Overall, PA remained higher than technological innovation, highlighting the critical role of government funding in the development of digital twin technology. The introduction of national policies supporting the development of digital twin technology has promoted its advancement and laid a technological foundation for the development of the energy sector.

3.2.1. Spatial Distribution of Digital Twin Technology: From “Fragmented Upgrading” to “Integrated Synergy”

To analyze the spatial differentiation characteristics of digital twin technology and its subsystems in China, this study employed the Natural Breaks (Jenks) Classification and Equal Interval Stratification methods in ArcGIS to classify the composite index of digital twin technology input factors by gradient. A comparison of the spatiotemporal patterns was conducted between the base year (2013) and the end of the study period (2024), as shown in Figure 10.

Figure 10(a1,a2) illustrates the changing trend of policy support for digital twin technology. It is evident that cities with significant policy investment effects are mainly concentrated in the eastern coastal regions. In economically advanced areas such as the Yangtze River Delta, the Pearl River Delta, and the Beijing–Tianjin–Hebei region, policy support for digital twin technology is more pronounced.

Figure 10(b1,b2) shows the changing trend of technological innovation in digital twin technology. The figure indicates that the investment effects in digital twin technology are relatively limited in central and western regions, especially in remote western areas. Due to lower levels of economic development and weaker technological foundations, these regions exhibit weaker innovation effects. Cities with the highest levels of digital twin innovation include Shanghai, Beijing, Shenzhen, Hangzhou, and Guangzhou—cities that are not only China’s centers of technological innovation but also key hubs for the digital twin industry. Inland provincial capitals such as Wuhan, Chengdu, and Xi’an also demonstrate relatively high levels of digital twin technology development, reflecting efforts in digital transformation in the central and western regions.

Figure 10(c1,c2) presents the evolution of the coupling effect between policy investment and technological innovation in digital twin technology. From 2013 to 2024, the overall level of digital twin development has increased nationwide. In particular, provinces in the central region—Henan, Hubei, and Hunan—show a deepening of color in the figures over time, indicating an enhancement in digital twin technology development efforts. The eastern coastal regions continue to maintain a leading position, with signs of a diffusion effect emerging to surrounding areas.

3.2.2. Distribution of the Dagum Gini Coefficient

When exploring the spatial differentiation structure and sources of variation in digital twin technology investment levels, the Dagum Gini coefficient presents certain limitations in characterizing regional development dynamics. Therefore, this study introduces the kernel density estimation (KDE) method to analyze the evolution patterns of digital twin technology investment from 2013 to 2024 across the country and within the four major regions. The analysis focuses on the spectral shift, primary mode, tail extension, and multimodal characteristics of the density surfaces (see Figure 11). The color gradient ranging from blue to red reflects the magnitude of kernel density estimates, where warmer colors (e.g., red) denote regions with higher probability density concentrations.

Figure 11a illustrates the spatiotemporal development trajectory of digital twin technology investment levels across 281 sample cities. The kernel density distribution surface exhibits a consistently right-skewed unimodal structure, indicating a relatively concentrated level of investment in digital twin technology and reflecting a general upward trend over time. Although the peak of the curve shows no significant change, its width increases, suggesting a gradual widening of disparities in investment levels. The pronounced tailing on the right side of the curve indicates substantial differences in digital twin investment levels among cities. The progressive extension of the distribution’s right wing demonstrates the growing advantage of high-gradient urban clusters. Figure 11b–d depict the dynamic trajectories of digital twin technology investment in the eastern, central, western, and northeastern regions, respectively. The central positions of the kernel density curves show little fluctuation, reflecting relatively slow improvement in digital twin investment within each region. At the same time, the trend of uneven investment distribution continues to intensify, highlighting persistent imbalances. This pattern of spectral evolution reveals that significant disparities in digital twin technology investment persist across regions, suggesting that achieving balanced regional development remains a long-term challenge.

(1)

Intra-Regional Differences

As shown in Figure 12, due to the significant investment gap between economically developed and less developed areas, the eastern region has the highest Gini coefficient for digital twin technology investment, indicating the greatest imbalance. In the central region, the development of digital twin technology is influenced by industrial development directions and government policies. The Gini coefficient shows a slight increase, reflecting a growing trend of investment concentration. In the western region, affected by policy support and infrastructure investment, the investment level in digital twin technology reached its lowest point in 2015 and gradually recovered thereafter. This indicates that investment balance in the digital twin industry first deteriorated and then improved. The northeastern region has maintained relatively balanced investment in digital twin technology, with a relatively stable Dagum Gini coefficient, suggesting no significant trend of either concentration or dispersion in investment levels.

(2)

Inter-Regional Differences

According to Figure 13, there is a significant difference in the average values of the inter-regional Gini coefficients, ranked as follows: eastern region > central region > western region > northeastern region. Regarding the annual changes in inter-regional differences, in 2013, the inter-regional disparities nationwide, as well as between the eastern and northeastern regions, reached their peak. This indicates a lack of coordination in digital twin technology investment levels across regions, further exacerbating regional imbalances. In contrast, the inter-regional differences between the western and central regions remained relatively stable, reflecting a slower and more consistent pace of development in digital twin technology investment in these two regions, with smaller gaps between them.

(3)

Main Sources of Differences

A further decomposition of the sources of disparity reveals that from 2013 to 2024, the average annual contribution rates of intra-regional differences, inter-regional differences, and transvariation density to overall disparity in the eastern, central, western, and northeastern regions were 37.67%, 33.21%, and 29.12%, respectively (see Figure 14). The contribution of inter-regional transvariation density was significantly higher than that of intra-regional transvariation, indicating that differences between regions are the primary source of imbalance in the development of digital twin technology investment levels. These disparities are also heavily influenced by the COVID-19 pandemic and policy adjustments. The contribution of inter-regional transvariation density fluctuated significantly between 2011 and 2022, ranging from 33.105% to 44.58%, suggesting that disparities in digital twin technology investment between regions contributed substantially—and inconsistently—to the overall difference. The large variation in inter-regional transvariation during 2021–2023 is closely related to the economic and social imbalances caused by the pandemic. Furthermore, the overall trend of transvariation density from 2013 to 2024 shows considerable changes, indicating significant fluctuations in the overall excess variation in digital twin technology investment. The contribution of intra-regional transvariation density shows an upward trend, suggesting that disparities among cities within the same region have been increasing, thereby widening internal regional differences.

3.3. Analysis of the Investment Effect of Digital Twin Technology on Improving Energy Utilization Efficiency

To examine the significance of digital twin technology in enhancing energy utilization efficiency, this study incorporates the following control variables that influence the development of digital twin technology [39]: (1) City Size (LnPOP): represented by the natural logarithm of the total year-end urban population. (2) Level of Economic Development (Fin): measured by the per capita GDP at the end of the year. (3) Education Level (Edu): represented by the natural logarithm of the number of students enrolled in higher education institutions at the end of the year. (4) Economic Density (Des): measured by GDP per square kilometer. (5) Government Intervention (Gov): measured by the general public budget expenditure of local governments. (6) Market Size (Mar): measured by the ratio of total retail sales of consumer goods to GDP. (7) Fixed Asset Investment (Inv): ** measured by the ratio of urban fixed asset investment to GDP.

3.3.1. Baseline Regression

Table 8. Digital twin technology investment and energy development.

Variable	(1)	(2)
PA × TA	0.001 ***
	(7.554)
PA		0.002 ***
		(9.099)
TA			0.003 ***
			(8.383)
LnPOP		0.002 ***	0.000 ***
		(9.494)	(5.304)
Fin		0.000 ***	0.000 ***
		(7.472)	(10.265)
Edu		0.001 **	0.002
		(5.789)	(0.214)
Des		0.563 ***	1.092 ***
		(9.886)	(7.783)
Gov		0.109 **	0.023
		(5.383)	(0.459)
Mar		0.000 ***	0.000
		(7.885)	(0.263)
Inv		0.000 ***	−0.000
		(6.385)	(−0.369)
Constant		0.003 ***	0.006 ***
		(12.482)	(18.356)
City		YES	YES
Year		YES	YES
N		3346	3346
Adj.R2		0.245	0.197

Note: ***, and ** indicate significance at the 1% and 5% levels, respectively. Values in parentheses are t-statistics.

reports the regression analysis results for the effects of digital twin technology investment on the sustainable development of the energy industry. Models (1) and (2) further examine the impact of industrial policy support for digital twin technology (PI) and technological innovation (TI) on energy sustainability.

The results show that both policy support and technological innovation in digital twin technology have a positive effect on the sustainable development of the energy industry, with regression coefficients of 0.0019 and 0.0031, respectively—both statistically significant at the 1% level. These findings suggest that policy support and technological innovation related to digital twin technology contribute to sustainable energy development and play a positive role in optimizing energy efficiency.

3.3.2. Robustness and Endogeneity Tests

Variable Replacement. The growth in the number of AI enterprises and the development of digital twin technology are mutually reinforcing, forming a co-evolutionary process that contributes to the sustainable development of the energy industry [40]. At the same time, advancements in digital twin technology provide AI enterprises with more data, a wider range of application scenarios, and real-world challenges, which in turn drive the development of more sophisticated AI algorithms and models [41]. Through a positive feedback mechanism, digital twin technology and the AI industry promote each other’s progress, accelerating mutual advancement. Therefore, the number of AI enterprises can be used as an alternative proxy to measure the development of digital twin technology.

Exclusion of Direct-Controlled Municipalities. Compared with other prefecture- level cities, direct-controlled municipalities have unique characteristics in terms of administrative level, access to policy resources, and policy influence, which may introduce bias into the empirical results. To address this, Beijing, Tianjin, Shanghai, and Chongqing were excluded from the sample, and regression analysis was re-conducted. The results are presented in models (1)–(4) of

Table 9. Robustness tests: replacing the dependent variable and modifying the sample.

Variable	(1)	(2)	(3)	(4)
	Replace the Dependent Variable	Replace the Dependent Variable	Modify the Sample	Modify the Sample
PA	5.108 ***		1.051 ***
	(18.170)		(36.904)
TA		8.815 ***		0.146 ***
		(22.201)		(5.654)
LnPOP	1.710 ***	2.086 **	0.412 ***	0.232 ***
	(6.009)	(8.528)	(7.432)	(11.377)
Fin	7.416 *	8.936 **	−0.004 **	−0.043 ***
	(1.693)	(0.875)	(8.149)	(5.357)
Edu	1.589 ***	1.735 ***	1.021 ***	0.237 ***
	(7.062)	(15.200)	(5.113)	(6.146)
Des	0.005 *	0.005 **	0.013 ***	0.027 ***
	(1.781)	(2.236)	(1.441)	(9.310)
Gov	−0.003 ***	−0.036 ***	0.003 ***	0.001 **
	(21.573)	(21.408)	(3.069)	(2.380)
Mar	0.138 ***	0.327 ***	0.412 ***	0.001 ***
	(17.305)	(15.195)	(3.596)	(2.381)
Inv	0.003 ***	0.003 ***	1.442 ***	0.851 ***
	(20.563)	(11.223)	(8.210)	(6.483)
Constant	7.020 ***	5.892 ***	0.001 ***	0.001 ***
	(23.931)	(18.455)	(4.872)	(7.049)
City	YES	YES	YES	YES
Year	YES	YES	YES	YES
N	3346	3346	3298	3298
Adj.R2	0.1492	0.1888	0.257	0.152

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Values in parentheses are t-statistics.

. After removing the samples of direct-controlled municipalities, the test results remain consistent with the conclusions of this study.

Considering the lagged effects of policy outcomes, due to the fact that digital twin technology involves processes such as technological development, application, and implementation, its actual impact on the sustainable development of the energy industry may exhibit a time lag. To further account for this influence, this study examines the effect of the development level of digital twin technology in period (t) on the energy optimization utility in periods (t + 1) and (t + 2). The test results are presented in

Table 10. Robustness test: adjusting the lag periods of the dependent variable.

Variable	(1)	(2)	(3)	(4)
	Smc (t + 1)	Smc (t + 1)	Smc (t + 2)	Smc (t + 2)
PA	0.457 ***		0.342 ***
	(36.581)		(33.749)
TA		0.017 *		0.023 **
		(1.783)		(2.509)
LnPOP	0.057 *	−0.028	0.054 *	−0.082
	(1.654)	(−1.166)	(1.658)	(−0.430)
Fin	0.000 ***	−0.000	0.000 ***	0.000
	(10.003)	(−0.117)	(9.277)	(0.664)
Edu	0.000 ***	0.000	0.000 ***	0.000
	(4.515)	(0.887)	(3.981)	(0.819)
Des	−0.000 *	−0.000	−0.000 **	−0.000
	(−1.674)	(−0.683)	(−2.293)	(−0.391)
Gov	0.000 ***	−0.000	0.000 ***	−0.000 **
	(4.542)	(−1.547)	(4.062)	(−2.102)
Mar	−0.000 ***	0.000 ***	−0.000 ***	0.000 ***
	(−13.144)	(3.516)	(−11.641)	(3.027)
Inv	0.000 ***	0.000	0.001 ***	0.000
	(3.573)	(1.130)	(3.898)	(0.861)
Constant	0.000 *	0.004 ***	0.000 *	0.005 ***
	(1.873)	(11.020)	(1.657)	(12.392)
City	YES	YES	YES	YES
Year	YES	YES	YES	YES
N	3074	3074	2798	2798
Adj.R2	0.431	0.913	0.424	0.920

Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Values in parentheses are t-statistics.

. Whether the dependent variable is adjusted to period (t + 1) or (t + 2), the policy support for digital twin technology and the input level of technological innovation synergy both demonstrate a significant positive promoting effect on energy optimization utility, which is consistent with the findings of this study.

3.3.3. Regional Heterogeneity Analysis

The capacity for policy resource integration, technological development levels, and sustainable energy industry development driven by digital twin technology may vary across different regions [42]. Therefore, regional heterogeneity must be considered to further examine whether digital twin technology can effectively promote sustainable energy industry development in different areas. This study first conducts a grouped analysis using city samples from the eastern, central, western, and northeastern regions of China to assess the impact of digital twin technology adoption on sustainable energy industry development across different regions [43]. Second, based on differences in administrative resources and city tiers, municipalities, sub-provincial cities, and provincial capitals are classified as central cities, while others are defined as non-central cities. This classification allows us to examine how digital twin technology adoption affects sustainable energy industry development in different city categories.

First, we conduct LM, Hausman, LR, and Wald tests to determine the optimal model for each regional subsample, followed by spatial econometric regression analysis.

Table 11. Heterogeneity analysis across eastern, central, western, and northeastern regions.

	Eastern		Central	Western	Northeastern
Variable	SDM		SAR	SAR	SDM
	Main	Wx	Main	Main	Main	Wx
Digital Twin	0.904 ***	0.054 ***	0.914 ***	0.536	0.826 ***	0.1127
	(6.342)	(4.166)	(8.658)	(0.137)	(8.874)	(1.779)
LnPOP	−2.258 ***	0.852 ***	0.037 ***	1.242 ***	0.466 ***	0.265 ***
	(−4.528)	(5.104)	(4.887)	(6.375)	(8.372)	(6.093)
Fin	−0.008 ***	0.014	0.464 ***	1.974 ***	0.038 ***	0.462 ***
	(−4.366)	(−1.467)	(8.430)	(6.818)	(4.419)	(7.128)
Edu	0.042	0.087 ***	−0.932 ***	−0.421 ***	−0.592 ***	−0.068 ***
	(0.546)	(5.895)	(−8.852)	(−4.706)	(−6.958)	(−6.540)
Des	0.074 ***	0.092 ***	0.391 ***	0.018 ***	0.050 ***	0.459 ***
	(4.027)	(3.981)	(7.902)	(6.752)	(3.156)	(3.327)
Gov	0.294 ***	0.009 ***	0.026 ***	0.489 ***	0.945 ***	0.006 ***
	(3.689)	(5.066)	(7.651)	(5.387)	(7.461)	(7.112)
Mar	0.289 ***	0.007 ***	0.438 ***	0.079 ***	0.383 ***	0.988 ***
	(3.182)	(3.359)	(5.237)	(7.437)	(1.595)	(7.679)
Inv	−0.051 ***	−0.030	−0.667 ***	−0.419 ***	−0.042 ***	−0.437 ***
	(−5.521)	(−0.312)	(3.006)	(−7.052)	(−6.822)	(−2.615)
Spatial	0.075 ***		0.074 ***	0.054 ***	0.015 ***
	(5.355)		(5.917)	(4.558)	(4.183)
Variance
Б2	0.102 ***		0.001 ***	0.091 ***	0.012 ***
	(6.423)		(7.083)	(6.874)	(7.046)
City	YES		YES	YES	YES
Year	YES		YES	YES	YES
N
R2	0.208		0.252	0.228	0.243

Note: *** indicate significance at the 1% levels, respectively. Values in parentheses are t-statistics.

presents the effects of digital twin technology development on sustainable energy industry development when the sample is divided into the eastern, central, western, and northeastern regions. The spatial correlation coefficients (λ) for the eastern, central, western, and northeastern regions are all statistically significant at the 1% level, indicating strong spatial interdependence among cities within these regions. After accounting for spatial linkages, the regression coefficients for sustainable energy industry development in the central, western, and northeastern regions are significantly positive, suggesting that digital twin technology adoption has a significant promoting effect. However, the coefficient for the western region is positive but statistically insignificant, implying that digital twin technology has not yet effectively driven sustainable energy industry development there. Additionally, the spatial lag coefficient of digital twin technology in the eastern region is significantly positive at the 10% level, indicating a notable spatial spillover effect, where digital twin technology adoption in eastern cities positively influences neighboring cities’ energy sustainability. In contrast, the spatial lag coefficient for the northeastern region is insignificant, suggesting that no such spillover effect exists there.

Regions: Spatial Spillover Effects of Digital Twin Technology.

4. Conclusions

4.1. Research Conclusions

This paper employs the global entropy method to measure the level of digital twin technology application and energy sustainability across 283 prefecture-level and above cities in China from 2013 to 2024. The study further categorizes these cities into four major regions—eastern, central, western, and northeastern—and utilizes spatial econometric models to depict their spatial agglomeration patterns. The Dagum Gini coefficient is adopted to analyze the relative inter-regional disparities, while the non-parametric kernel density estimation method is used to illustrate the dynamic evolution of absolute differences over time. Finally, the coefficient of variation and spatial econometric models are applied to test for spatial convergence. The key findings are as follows:

From 2013 to 2024, the overall level of energy sustainability and the development of digital twin technology in China remained relatively low, although they exhibited a steady upward trend with minor fluctuations, peaking in 2016 and 2019. The spatial distribution of energy sustainability across the four major regions has gradually shifted from a “single-point breakthrough” pattern to one of “systematic coordination,” closely aligned with the distribution of regional growth poles and urban agglomerations. In particular, the central region has seen an increasing number of cities with high and medium levels of energy sustainability, with a noticeable southeastward shift. The eastern region shows a contiguous distribution pattern along the Yangtze River, while the western region exhibits strong spatial stickiness. The eastern region has experienced the most rapid development.

In terms of relative disparities, intra-regional differences in energy sustainability among the four major regions are relatively small, while inter-regional disparities show a clear trend of divergence. The major source of regional disparities is hypervariability density. Specifically, intra-regional disparities follow the pattern of “eastern > northeast > central > western”. The inter-regional disparities have widened significantly during the sample period, especially between the northeastern and central regions. Since 2016, the development trajectories within the eastern region have gradually converged. Between 2013 and 2024, the primary contributor to the overall disparity in energy sustainability levels has been hypervariability density, and its contribution has been increasing. This may be attributed to the existence of numerous overlapping cities not yet covered by official planning documents, where spatial spillover effects associated with smart city development have intensified overall disparities.

Regarding absolute disparities, the dynamic evolution of energy sustainability across the four regions exhibits distinct patterns.

Nationally, absolute differences in energy sustainability have gradually widened, whereas intra-regional disparities have generally narrowed. Within all four regions, there are cities whose levels of energy sustainability are significantly higher than others in the same region. Notably, the probability of extreme values has gradually declined at the national and eastern levels, slightly increased in the central region, and intensified in the northeast, where a “the strong get stronger” pattern is more prominent.

Convergence analysis yields the following insights:

(i)

From stock perspective, energy sustainability across the regions exhibits divergence over the sample period.

(ii)

Between 2013 and 2019, there existed significant spatial autocorrelation in energy sustainability, and this spatial dependence has strengthened over time.

(iii)

From an incremental perspective, absolute and conditional β-convergence can both be observed in all four regions. After incorporating control variables, the speed of β-convergence improves in all regions, with the convergence order remaining as “eastern > northeast > central > western”. Furthermore, population size accelerates the convergence process; however, government governance significantly inhibits the convergence of energy sustainability, while market size exerts a significant negative effect on the improvement of energy sustainability levels.

4.2. Policy Recommendations

(1)

Centralized Planning for the Development of Digital Twin Technology to Narrow Regional Disparities

To achieve balanced regional development of digital twin technology, a national-level “Digital Twin Regional Coordinated Development Strategy” should be formulated. This strategy should implement differentiated application guidance and incorporate the development of digital twin technology into the construction of new infrastructure and regional coordinated development plans. The eastern region should promote high-precision digital twins in industrial and smart city sectors. The central region should focus on intelligent manufacturing and urban safety. The western region should advance applications in energy, water conservancy, and ecological monitoring. The northeast region should leverage the renovation of old industrial bases to upgrade industrial equipment digital twins. To facilitate the promotion of digital twin technology, national-level digital twin pilot zones and joint innovation centers should be established based on the technological development characteristics of different regions. Digital twin collaborative innovation centers should be deployed in the central, western, and northeastern regions, such as the “Digital Twin Yellow River Basin Laboratory”. A computing power coordination center under the “East Data, West Computing” framework should be set up to alleviate the computing power disadvantages in the western region. Additionally, a cross-province (east–central–west) technology sharing platform and standards system should be promoted.

The state should also actively leverage fiscal resources for adjustment by adopting a fiscal transfer payment + industrial guidance fund model to include digital twin technology in the scope of new infrastructure transfer payments. National or local digital twin special guidance funds should be established to focus on supporting project construction and operation in the western and northeastern regions. Local governments are encouraged to introduce social capital into twin system construction through Public–Private Partnership (PPP) models. A “talent enclave” and remote collaboration mechanism should be created. A “Twin Talent Enclave” centered on eastern research institutions should be established to support young scientific researchers in central and western regions through project-based secondments. Universities should co-establish “Regional Digital Twin Research Centers”, adopting mechanisms such as “dual mentors + virtual laboratories”. By leveraging AI collaborative platforms and AR/VR technologies, remote digital model collaborative development should be promoted to lower the threshold for talent aggregation. Application scenarios and a “build first, test first” mechanism should be promoted. Typical demonstration projects such as digital water conservancy, digital forestry and grassland, and digital mining should be prioritized for deployment in the central, western, and northeastern regions. The new model of “Digital Twin as a Service” should be explored to reduce entry barriers for small and medium-sized cities. The “city digital base + industry twin plug-in” development model should be promoted to enhance system portability and adaptability.

(2)

Building a Multi-Level Energy Digital Twin Platform

A four-tier energy digital twin system covering the “national–regional–city–industrial park” levels should be established. This term refers to a multi-level spatial governance or policy implementation framework, ranging from the national level down to specific industrial parks, which highlights the hierarchical structure of policy design, coordination, and execution across different administrative and spatial scales. The government should unify data standards and access protocols to enable real-time data uploads from energy facilities, enterprises, and end-users across regions. By integrating digital models of essential infrastructure such as power grids, gas pipelines, heating networks, energy storage systems, and electric vehicle charging stations, the platform can visualize dynamic energy flows.

Key indicator monitoring models should be developed. The performance of real-time calculations of energy consumption based on industry, region, and GDP per unit to identify abnormal usage or waste will enable the supervision of energy intensity and efficiency. Dynamic tracking of the supply and demand structure of coal, natural gas, and liquefied petroleum gas can be used to assess the substitution potential of clean energy. Electricity load forecasting models that use historical data, weather patterns, and industrial production schedules should be established to predict the spatiotemporal distribution of electricity consumption across society, thereby optimizing power dispatching.

(3)

Digital Twin Technology Drives Optimization of Regional Differentiation Strategies

The eastern region takes on the role of a smart energy utilization pioneer zone, constructing a city-level energy digital twin system to achieve coordinated scheduling of electricity, gas, and heat. Virtual simulation models are established for high-energy-consuming industrial parks to assess technological transformation potential and promote energy conservation and consumption reduction. By integrating energy consumption data from buildings, transportation, and industries, the optimal configuration of distributed energy systems is achieved. AI prediction algorithms are utilized to implement a “virtual power plant” dispatch mechanism during peak periods, enabling peak shaving and load balancing.

As an energy mix optimization hub, the central region can develop a regional simulation platform for coal-to-gas transition, analyzing carbon emissions and economic impacts across different energy scenarios. Simulations will optimize energy infrastructure planning, aiding decisions on gas network expansion and storage site selection. Sector-specific energy consumption models for transportation, buildings, and manufacturing will further accelerate green transformation.

The western region, serving as a clean energy export and storage coordination zone, will establish a new energy-storage-transmission synergy model to optimize the timing and routes of “West-to-East Power Transmission.” Digital twin technology will monitor the operational efficiency of photovoltaic and wind power systems, identifying potential faults or inefficiencies. Simulations will analyze the integration of renewable energy stations with local loads and storage facilities, promoting integrated “generation-grid-load-storage” operations. This will enable real-time cross-regional simulation and coordinated dispatch, ensuring precise allocation of surplus green power to demand centers.

The northeastern region, serving as an aging infrastructure retrofit and heating optimization zone, can develop digital twin models for district heating systems to enhance the synergy efficiency among heat sources, pipeline networks, and end-users while reducing energy losses. Lifecycle simulation assessments will be conducted for coal-to-gas and coal-to-electricity conversion projects to evaluate their energy efficiency improvements and cost-effectiveness. Real-time monitoring of industrial park energy systems will enable the construction of health management models for high-energy-consuming equipment, supporting targeted upgrades. By integrating weather forecasts and building thermal load data, the region will achieve intelligent heating dispatch, driving energy conservation and emission reductions.

(4)

Strengthening Data Governance and Privacy Protection Mechanisms

Establishment of a Tiered Data Governance Framework. A well-defined data management architecture should be built to ensure that governance mechanisms are implemented at every stage—data collection, processing, storage, and application. Permissions and functions can be delineated across perception, transmission, platform, and application layers, enabling full-chain data control. Data can be meticulously categorized (e.g., user-side, device-side, and environment-side) with tiered processing protocols to prevent sensitive data leaks. All stakeholders should adhere to the “minimum necessary” principle for data access, mitigating misuse risks.

Deploy Privacy-Enhancing Technologies for Data Security. Technical solutions should be leveraged to bolster privacy protection during energy data sharing, analysis, and collaboration. Noise injection can be introduced in energy consumption modeling and user behavior analysis to reduce re-identification risks. Decentralized multi-source data training without centralized storage should be enabled to ensure that data remain local. The performance of edge-based preprocessing and encryption at perception-layer nodes can be used to minimize cloud exposure. Privacy-preserving collaborative analytics among entities without raw data decryption should be supported.

4.3. Research Prospects

As the findings of this study demonstrate, digital twin technology holds substantial promise for enhancing the sustainability of energy systems through real-time monitoring, predictive analytics, and optimized resource allocation. However, like any transformative technology, digital twin technology is not without risks. To borrow the words of the English writer Edward G. Bulwer-Lytton, “Every street has two sides, the shady side and the sunny”. While digital twin technology illuminates the path toward smarter and more sustainable energy, it also casts shadows in the form of emerging challenges related to data privacy, structural labor shifts, and ethical governance. The large-scale implementation of digital twin technology systems raises concerns about the security of massive, interconnected data networks, as well as the potential displacement of traditional roles in energy management. Moreover, as algorithm-driven decisions increasingly influence infrastructure planning and public resource distribution, questions about accountability, transparency, and social justice are becoming more urgent. Therefore, in the context of the ongoing digital transformation of the energy sector, future policy efforts must go beyond technical optimization to also address governance capacity, equity, and resilience. Achieving a truly sustainable energy future requires not only technological innovation, but also institutional frameworks that can anticipate risks, safeguard public interests, and ensure that the “sunny side” of digital twin technology benefits society as a whole.

For countries with uneven regional distribution of energy resources—such as Brazil, where hydropower is concentrated in the north while industrial demand is higher in the south, or India, which faces significant east–west energy disparities—China’s experience offers a valuable reference for improving energy flow efficiency and promoting balanced regional energy development. In regions with pronounced urban–rural disparities, such as parts of Africa and South Asia, digital twin technology can be used to identify deficiencies in energy infrastructure, enabling evidence-based rural energy investment planning and enhancing energy accessibility and social equity in remote areas. For countries or regions that are highly dependent on traditional energy resources or are seeking green industrial transformation in the context of deindustrialization, such as the Middle East or parts of Russia, digital twin systems can support the scientific adjustment of industrial structures, reduce carbon dependence, and strengthen green competitiveness. In the face of energy supply instability, such as the European energy crisis or the risk of power outages in the United States, digital twin technology can serve as a critical tool for emergency response and regional coordination, thereby enhancing national energy security and resilience.

The application of digital twin technology in promoting energy sustainability in China provides valuable empirical evidence and policy insights for countries pursuing low-carbon transitions. China’s approach—characterized by the integration of real-time sensing, dynamic modeling, and intelligent control—demonstrates how digital twins can serve as a strategic tool to enhance energy system efficiency, reduce environmental impact, and support data-driven urban governance. The spatial heterogeneity identified across China’s eastern, central, western, and northeastern regions underscores the importance of tailoring digital twin deployment strategies to local conditions, resource endowments, and governance capacities. This regionalized experience suggests that a one-size-fits-all approach is insufficient and that context-specific frameworks are essential for achieving effective and equitable digital transformation in the energy sector.

For developing and emerging economies, China’s experience highlights the importance of establishing scalable and interoperable digital infrastructures and ensuring regulatory safeguards for data privacy and cybersecurity. Furthermore, China’s emphasis on aligning technological innovation with institutional development offers a practical model for balancing progress with resilience. These findings contribute to a broader understanding of how digital twin technologies can be leveraged globally to advance sustainable, inclusive, and adaptive energy systems.