Comparison and Optimization of Energy Efficiency between Hydropower and Thermal Power in China

Background: As the two main forces of China’s power electricity, the energy generation efficiencies of thermal power and hydropower are important factors affecting the energy conservation, emissions reduction, and green development of the country’s whole power industry. Methods: Considering regional differences and multiple effective decision-making units, this research uses the Meta-SE-SBM undesirable model to comprehensively evaluate the efficiencies of hydropower and thermal power generation in China, taking CO 2 emissions of thermal power generation as the undesirable output. Results: The average group efficiency of thermal power generation in the central region has greatly improved, the eastern and western regions also show an upward trend, but there is a slight downward trend for hydropower in the three regions. The hydropower technological gaps in the three regions have slightly expanded, but their thermal power technology gaps have gradually narrowed. From the perspective of input-output non-efficiency level, the undesirable output CO 2 of thermal power energy efficiency in the eastern, central, and western regions is in a surplus, the redundancy of equipment utilization hours, energy input, and installed capacity in the western region are all high, but generation in the western region is insufficient, leading to relatively low efficiency of thermal power generation there. In the eastern region the redundancy of equipment utilization hours, number of employees, and installed capacity are all high, but the generation of hydropower in the eastern and central regions is insufficient, leading to relatively low hydropower efficiency in these two regions. green regional the efficiencies of hydropower and thermal power. The thermal power industry is relatively mature, but its CO 2 emissions should be reduced and the scale of thermal power cannot be blindly expanded. The hydropower industry needs further policy support to increase market share and to enhance the local power industry’s competitiveness under the condition of its resource endowments.

This is concrete evidence that the power industry plays an important role in both energy consumption and carbon emissions. In 2018, China's power generation increased 7.7% from 2017, accounting for 26.7% of the world's total amount of power generation. China's electricity production clearly occupies an important share of global electricity production.
Thermal power is currently a major part of China's electricity generation, and coal-fired power generation accounts for most of the nation's thermal power generation. Because of the large amount of carbon dioxide produced by coal burning, it is putting huge pressure on the environment in a negative manner. With the greater urbanization and industrialization of China, the demand for electricity is increasing, leading to even more severe pressure on the ecological environment. With the continuous increase in energy consumption and carbon emissions, the country's energy efficiency and structure need to be optimized and adjusted. The positive role of renewable energy such as hydropower cannot be ignored when targeting the green development of the power industry.
China's energy conservation and carbon emissions reduction are a clear focus of the government and its citizens. One of the most important issues throughout the world in the next two decades is how to reduce carbon emissions of the power industry while meeting rapidly growing power demand, especially in developing countries like China. The report of the 19 th National Congress of the Communist Party of China highlighted the development of the production and consumption of electricity energy in order to promote green development. The key point is how to encourage high-quality and efficient power production that helps reduce carbon emissions.
In order to promote the construction of ecological civilization and realize green development, the China government formulated the Environmental Protection Tax Law (Draft) in 2016, proposing to levy environmental protection taxes on air pollutants, water pollutants, solid wastes, and noise. One of the main sources of air pollution is coal, and coal-fired power generation is currently the main form of production in the country's power industry. In 2017, China's total power generation reached 6417.1-billion-kilowatt Hour (KWH), of which thermal power generation and hydropower generation accounted for 70.99% and 18.59%, respectively. In 2017, China's installed power generation capacity hit 1777.08 million kilowatts (kW), an increase of 7.67% over the previous year, whereas installed power generation capacity of thermal power and hydropower accounted for 62.18% and 19.33%, respectively. Although hydropower has received much attention and development, its proportion of power generation and installed capacity is smaller than that of thermal power, meaning that its development scale is currently not as good as thermal power.
Compared to thermal power development, for hydropower development, two questions arise: Is it competitive enough to grow and mature? What is the difference in hydropower efficiency among the various regions of China? Efficiency evaluation is the basis for understand the pathway towards improvement, and whether it is thermal power or hydropower, enhancing generation efficiency can promote the green development of the whole power industry. This research thus conducts an in-depth analysis and comparison of hydropower and thermal power in the three major regions of China from the perspective of technical efficiency in order to provide a reference for improving power generation efficiency and promoting the green development of the country's power industry. As research evaluation and regional comparative analysis on China's thermal power and hydropower energy are of great theoretical value and practical significance, the clean characteristics of hydropower present a good promotion effect on energy conservation and emissions reduction, thus providing a way to improve the energy structure. Scientific and reasonable efficiency evaluation also helps to accurately grasp the current situation of thermal power and hydropower generation.
Regarding the study of energy efficiency, first, most studies use the concept of total energy to perform efficiency calculations. More specifically, it is necessary to examine the industry efficiency issues of thermal power generation and hydropower generation. Some scholars have investigated the efficiency of thermal power generation as a research topic, while others have studied the efficiency of hydropower generation, but they lack a comparative analysis of the power generation efficiency of traditional energy sources like thermal power and new energy sources such as hydropower. Second, in the literature on thermal power generation efficiency, there are more microlevel efficiency calculations for thermal power companies or power plants, with relatively few macro-level thermal power efficiency calculations that consider regional differences. Moreover, the analyses do not solve the problem of distinguishing the effective decision-making unit (DMU). It is thus necessary to incorporate carbon dioxide emissions from thermal power generation in China's provinces as an undesirable output to reflect the energy efficiency of regional thermal power generation more realistically and comprehensively as well as to better compare and observe the efficiency differences between hydropower and thermal power.
The efficiency calculated by considering environmental factors gives a more reasonable understanding of the power industry's operations and offers a measurement for the competitiveness and development of each province's or region's power industry. Further in-depth analyses on efficiency and differences of thermal power and hydropower generation in China's eastern, central, and western regions are of great significance for local governments and power industry managers by providing improvement directions on the input and output of electricity production that can help achieve higher power industry efficiency and less emissions. These three regions face different situations both economically and politically, and so policies to improve the efficiency and the structure of their power industries should not be a "one size fits all". For practical applications, data envelopment analysis (DEA) is increasingly recognized as an effective evaluation tool for policy formulation to promote regional development. The Meta-SE-SBM undesirable model we employ in this paper distinguishes the efficient provinces, includes an undesirable output indicator, and considers regional differences in order to measure the efficiencies of thermal power and hydropower in China's three main regions more accurately and to formulate more beneficial policy recommendations.

Literature Review
With the rapid development of China's economy, the demand for energy continues to increase, and as such green energy development has become an important trend domestically. In recent years, China's clean energy industry, including hydropower, wind power, solar energy, biomass energy, and nuclear energy, has developed quickly and achieved large-scale expansion. In addition, the proportion of clean energy consumption in total energy consumption is still positively rising. This has prompted many scholars to pay greater attention to the country's clean energy and its efficiency.
The energy efficiency literature is mainly divided into efficiency influencing factors research and efficiency measurement evaluation research. Scholars have applied a variety of research methods to study various industries, including different types of energy use and impact issues. The literature on energy efficiency impact factors, on the one hand, often takes the LMDI method to decompose and evaluate the influencing factors of energy or carbon emissions, such as Liu et al. [2] and Wang and Zhou [3]. On the other hand, econometric models have been also adopted to analyze influencing factors, such as Meng et al. [4], who utilized polynomial functions and Partial Least Squares (PLS) algorithms to evaluate the effect of market reforms in China's thermal power industry in 2003. Their results show that the reforms made the thermal industry's "natural" power generation efficiency curve suddenly shift down by 0.142kW h/kg SCE (standard coal equivalent), causing a waste of 555.8 million tons of standard coal during the period 2003-2012. The generation efficiency of China's thermal power industry has decreased since the reform, mainly due to the failure to implement electricity price tendering. Li et al. [5] combined the multiple regression model with the generalized autoregressive conditional heteroscedasticity (GARCH) model to analyze the energy efficiency of thermal power plants in China. The results show that the rate of electricity consumption of power plants has a positive impact on the volatility of energy efficiency. The higher overall energy efficiency index will lead the lower rate of electricity consumption of power plants.
For the literature on efficiency measurement evaluation, the most commonly used methods overall include data envelopment analysis (DEA) and stochastic frontier analysis (SFA). For example, Ghosh and Kathuria [6] employed SFA to investigate the effect of regulatory governance on thermal power generation efficiency in India. The mean technical efficiency of 76.7% indicates there is wide scope for efficiency improvement in the sector, and state-level regulators have positively impacted plant performance. The SFA method requires arbitrary assumptions regarding the functional form or the distributional form of the error terms. However, as a non-parametric method, the DEA model is often used to evaluate the efficiency of power generation, because it does not require any specification of the functional form of the production relationship and has the advantages of avoiding subjective factors and reducing errors. In recent years, the DEA method has been widely applied in various fields to conduct effectiveness analysis. For example, scholars have used DEA to analyze and evaluate energy and environmental efficiency, such as DEA and the Malmquist index by Dyckhoff et al. [7] and Perez et al. [8], SBM-DEA by Choi et al. [9], and metafrontier by Battese et al. [10] and Beltrán-Esteve et al. [11].
The DEA model was originally proposed by Charnes, Cooper and Rhodes in 1978 [12] and has been used by scholars to evaluate energy and environmental efficiencies. However, CCR [12] and BCC [13] set up radial and oriented models to calculate efficiency, but the input (output) model only measures the degree of inefficiency from one aspect of input (output), and the efficiency measurement of the radial model does not consider an input (output) slack variable, which can overestimate a DMU's efficiency. To solve this problem, Tone then proposed the SBM model [14], which is a DEA model that considers input and output slack and an efficiency evaluation method that takes on undesirable output indicators. However, the SBM model also has some limitations. First, it is impossible to effectively identify the efficiency of the decision-making units, and a quantitative comparison and quantitative analysis on this basis may not be accurate. Second, the SBM model assumes that each DMU faces the same technological frontier. However, practically, DMUs are often in different geographical locations or operate under different national policies or socio-economic conditions. The technological frontiers of these DMUs are not the same -that is, there are heterogeneous technologies. If the homogeneity assumption is adopted without considering the difference in their technological frontiers, then the efficiency measurement results may be biased.
For the energy efficiency literature based on DEA methods, the research objects can be divided into regional-/macro-level and company-/micro-level studies. At the company-/micro-level aspect, Shrivastava et al. [15] estimated the efficiency of thermal power plants in India using the DEA method. Their results suggest that 31.67% of power plants are good performers, 35% are moderate performers, and 23.33% are laggards, whereas 10% are poor performers based on a ranking of their variable returns to scale (VRS). Moon et al. [16] used a two-stage DEA model to analyze the efficiency of energy-intensive manufacturing companies in South Korea. Their findings are that pure-energy efficiency is more important to improve overall energy efficiency, and each industry has different possibilities to improve energy efficiency, so governments or policy-makers must be informed of the differences and provide support in realistic ways for each industry. Empirical research on the power industry's efficiency is mainly carried out from the level of power plants and power companies by using DEA methods. Previous research do evaluate the efficiency of power companies, but it is not enough to assist our study in understanding the variations in the efficiency of power generation among different regions.
For regional-/macro-level energy efficiency, Lam and Shiu [17] applied the DEA approach to measure the technical efficiency of China's thermal power. Their results show that municipalities and provinces along the eastern coast and those with rich supplies of coal have the highest levels of technical efficiency, and that the presence of labor slack in many regions indicates that labor redundancy is a serious problem. Mei et al. [18] used the meta-frontier slack-based measure method to conduct an empirical analysis of regional environmental efficiency on China's sulfur dioxide emissions and chemical oxygen demand (COD) from 2000 to 2011. Their results show that excessive emission pollution is the main cause of low environmental efficiency, and there are differences in environmental efficiency in the eastern, central, and western regions. Bi et al. [19] utilized a slack-based measure approach to study the impact of environmental regulations on the energy efficiency of thermal power generation in China, finding that energy efficiency and environmental efficiency are relatively low and have distinct regional characteristics. Song et al. [20] employed the slack-based endogenous directional distance function (SBEDDF) model to evaluate the environmental impact of China's power generation industry, providing results that the environmental efficiency of China's thermal power industry is low, and that the gap between different regions is large. During the period 2006-2012, environmental efficiency increased by 47%, and the best solution to reduce emissions is unique to each region.
When using the directional distance function (DDF) to measure energy efficiency, although the undesirable output of environmental pollution is included, it is assumed that the both undesirable output and the desirable output increase or decrease in the same proportion. Thus, the DDF method has the following shortcomings. First, if the input is slack, then the estimated energy efficiency will be biased [20]. Second, the efficiency of a single input element cannot be measured [22]. Li and Shi [23] thus proposed an improved Super-SBM model with bad output that can reasonably distinguish multiple effective DMUs, make the efficiency ranking more capable, and apply it to measuring the energy efficiency of China's industrial sector. When comparing and analyzing the energy efficiency of thermal power and hydropower, more real and beneficial calculations need to be considered, and attention should focus on the regional differences and rankings of effective DMUs.
With the development of new energy, more attention has been paid to the energy efficiency of hydropower. For example, Barros [24] applied DEA to measure and decompose the efficiency of EDP (Portugal Electricity Company) and its hydroelectric energy generating plants, showing that hydropower stations have improved in terms of technical efficiency and technological progress. Barros et al. [25] employed the Virtual Frontier Dynamic Range Adjusted Model (VDRAM) DEA to evaluate the efficiency of Angolan hydropower plants. The study considered that efficiency analysis is important and can promote the level of energy utilization in order to achieve good management and sustainable development.
Utilizing undesired output when assessing energy efficiency can reflect the requirements for green development of energy and make efficiency measurement more real and effective. Scholars have taken diversified input-output indicators into their energy efficiency calculations, but they have common points, such as [4], [9], [19], [20], [26]. The input indicators mostly are labor and capital, but special input indicators of raw materials and equipment are also counted. In addition, output indicators are typically production volume, GDP, etc. and include an undesirable output that is unfavorable to the environment. Most studies have selected CO 2 emissions, such as [27]- [31].
From the literature review we find scant studies on the calculation of China's hydropower efficiency, yet relatively more research on the efficiency of China's thermal power sector. Research at the micro-level (firms or plants) is more abundant, and thus research at the regional level still needs further exploration. Moreover, there are fewer comparative studies on the energy efficiency of China's hydropower and thermal power industries. Wang et al. [32] believed that although hydropower and thermal power constitute the two pillars of China's electricity supply, the relationship between the two needs more analysis. They aimed to reveal the relationship between the two under the framework of the autoregressive distributed lag (ARDL) model, which provides useful enlightenment to accurately measure regional hydropower and thermal power efficiencies and to compare them.
The various DEA methods chosen by scholars are mainly based on their research purposes and actual conditions. These studies lay a foundation for innovation in our present paper for constructing and using the Meta-SE-SBM undesirable model by considering regional differences in the efficiency calculation of thermal power and hydropower. However, most studies in the literature have the following limitations. (1) Simple analysis and evaluation of thermal power or hydropower efficiency are performed, and most of them are concentrated at the level of power plants or power generation companies. There is a lack of more macro-level regional thermal power and hydropower efficiency calculations and a comparative analysis of the two. Regional development differences are considered so that efficiency values will not be overestimated. (2) A more realistic and effective efficiency measurement of thermal power and hydropower generation methods is needed, and multiple effective DMUs should be ranked. Comparative studies are relatively lacking, and more comprehensive input-output indicators are required.
The academic contributions of this paper are as follows. First, most scholars typically have studied thermal power or hydropower generation efficiency at the company or plant level. Scant studies have conducted a sub-regional analysis of thermal power or hydropower generation industry efficiency, and even fewer studies have comparatively analyzed the generation efficiencies of thermal power and hydropower from a sub-regional basis. It is thus beneficial to carry out a comparative study on China's thermal power and hydropower generation efficiencies in the eastern, central, and western regions to examine efficiency differences and changing trends in these three regions in order to propose specific power industry development initiatives for regional government and power industry managers.
Second, when investigating power efficiency, some scholars have adopted the stochastic frontier model, BCC, CCR, SBM, and other methods. The defect of these models is that they fail to consider the differences in social culture, economic environment, and production structure of various regions, by assuming that all provinces (in China) have the same technical level. They are unable to distinguish multiple efficient provinces, which leads to a large deviation in the evaluation results of power efficiency. The Meta-SE-SBM undesirable model used in this paper considers envelope curves that contain all group production frontiers, enabling different groups to measure efficiency under the same common benchmark, which is more accurate for evaluating the efficiency value. This model also sorts multiple effective provinces in the measurement results of thermal and hydropower energy efficiencies and incorporates undesirable outputs into the measurement system, which can more realistically and comprehensively reflect regional power efficiency.
Third, China's power generation production is maintaining an upward trend and occupies a large share in global power generation, and hence information on the segmentation and effectiveness of the country's power generation is urgently needed. Our study's findings on China's thermal power and hydropower generation efficiencies in the eastern, central, and western regions can help evaluate the current situation of the thermal power and hydropower generation industries and propose relevant countermeasures to promote their efficient operations, providing a reference for local governments and power industry managers to achieve green development. On such a basis, local governments and power industry managers can formulate appropriate policies according to local conditions to adjust the development scale, input elements, and structural proportions of thermal power and hydropower generation to achieve synergy between economic and environmental benefits. The findings also provide useful inspiration for the comparison and improvement of thermal power and hydropower efficiencies in other countries or regions.

SE-SBM model
As a non-parametric research method, DEA evaluates the relative effectiveness of DMUs from the perspective of input and output. The DEA model is often used by scholars to evaluate energy efficiency, because it has no specification for the functional form of the production relationship and has the advantages of avoiding subjective factors and reducing errors. Traditional DEA models include the CCR and BCC models. The use of the CCR model requires that all DMUs are produced at the optimal scale, and so the return to scale of DMUs remains unchanged. When this condition is not met, the efficiency evaluation results by using the CCR model will be biased. In 1984, Banker, Charles and Cooper improved the CCR model and proposed a BCC model with variable returns to scale.
Traditional DEA models only measure the degree of inefficiency from one aspect of input (output), and the efficiency measurement of the radial model does not consider an input (output) slack variable, which will overestimate the efficiency of DMUs. To solve this problem, the SBM model was proposed by Tone [14] and is a DEA approach that considers slack improvement. It is able to solve the problem that the radial model does not include slack variables in non-efficiency measurements. However, the SBM model has the limitation that it is impossible to effectively identify and compare the efficiency of efficient decision-making units, and the quantitative comparison and quantitative analysis on this basis may not be accurate.
The Super-Efficiency SBM model (SE-SBM) solves the problem of differentiating the efficiency of DMUs and at the same time incorporates undesirable outputs into the measurement system [33], thus more realistically and comprehensively reflecting regional energy efficiency. It can accurately assess the efficiencies of thermal power and hydropower of different provinces in the three regions, identify effective provinces, compare the efficiency differences between the two forms of electricity, and provide more scientific and reasonable improvement measures to improve the efficiency and green development of the power industry.
The SE-SBM model (Eq. (1)) assumes that there are n decision-making units, and each decision-making unit has m inputs (x), s 1 desirable output (y g ), and s 2 undesirable output (y b ). We define matrices X, Y g , and Y b as In addition, s is the amount of slack in the input and output, λ is the weight vector, and the objective function is ρ, whose value is between 0 and 1. Here, x ij is the i th input of the j th DMU, and y rj is the r th output of the j th DMU.

Meta-frontier and technology gap ratio
Traditional DEA generally assumes that all producers have the same level of technology, but the assessed DMUs are often in different geographical locations or under different national policies or socio-economic conditions. The technological frontiers of these DMUs are not the same -that is, there are heterogeneous technologies. If the homogeneity assumption is adopted without considering the difference in the technological frontiers, then the efficiency measurement results may be biased. Battese et al. [34] proposed a Meta-frontier Production Function, while O'Donnell et al. [35] further established a meta-frontier framework based on DEA that can accurately calculate the group and meta-frontier technical efficiencies.
Suppose that all DMUs are divided into H groups. DMUs are grouped according to the division of China's eastern, central, and western regions. Group-frontier efficiency is calculated by using the SE-SBM model to measure the efficiency of DMUs in the same group under the group boundary. Meta-frontier efficiency is calculated by using the SE-SBM model to measure the efficiency of DMUs in the total group under the same boundary. Since the meta-frontier contains the group frontier of H groups, the technical efficiency of the meta-frontier (MFE) is less than the technical efficiency of the group frontier (GFE). The calculated value is called the technical efficiency gap ratio (or technology gap ratio, TGR). The formula is: In formula (2), the larger TGR is, the closer is the production technology used by the decisionmaking unit to the frontier of production technology.

Meta-SE-SBM undesirable model
We refer to the Super-Efficiency SBM model proposed by Huang [36], which considers the = . Assume that each DMU has three types of input and output variables: inputs, desirable outputs, and undesirable outputs, which are expressed as: R, and J represent the number of three types of variables in turn. When considering both undesirable output and heterogeneous technologies, the efficiency of the k th group of the o th DMU (o = 1, 2, ..., N k ; k = 1, 2, ..., H) for the non-directed and non-radial SBM of the meta-frontier formed by all groups can be obtained by solving the following: * = ≥ is added to ensure that the denominator of the objective function is not zero. If we assume variable returns-to-scale (VRS), then we need to add the constraint ∑ ∑ ℎ ℎ =1, ≠0 ℎ= ℎ=1 =1 here.

Data sources and description
Due to a lack of statistical data, this study does not consider Hong Kong, Macau, Taiwan, and Tibet as DMUs. In order to consider regional differences, following Liu et al. [27] this study divides 30 provinces and cities in China into three major regions. The eastern region group includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, and Hainan, for a total of 11 provinces; the central region group includes Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei, Hunan, and Guangxi, for a total of 10 provinces; and the western region group includes Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang, for a total of 9 provinces. This study uses the latest data representing China's provinces for measuring thermal power efficiency and takes the latest data from 28 provinces (excluding Shanghai and Tianjin) for measuring hydropower efficiency. Shanghai's hydropower generation has been zero over the years, while Tianjin's hydropower indicators are lacking. Therefore, Shanghai and Tianjin are not considered when calculating hydropower efficiency. The data come from China Statistical Yearbook [37], China Energy Statistical Yearbook [38], and China Electric Power Statistical Yearbook [39], and relevant data for 2013 and 2017 are collected.
The input and output variables are selected based on the comprehensive consideration of previous research experience and data availability. Following Zhou et al. Error! Reference source not found. and Qu et al. Error! Reference source not found., labor, installed capacity, and energy consumption are all selected as input indicators, and power generation is taken as the output indicator to measure power efficiency. In addition, Qu et al. Error! Reference source not found. also chose undesirable output CO 2 emissions, because they were mainly from coal-fired thermal power generation. Bi et al. [19] and Saglam [42] also considered installed capacity as one of the most important input indicators, because of the strong correlation between installed capacity and generated electricity. Zhou and Ang [43] and Bi et al. [19] separated inputs into energy inputs and non-energy inputs, where the former are types of fossil fuel and the latter include capital and labor force. Capital is measured in terms of installed thermal generating capacity.
Input indicators: ① Urban employees in the production and supply industry of electricity, gas, and water are the proxy variable for labor input in the hydropower and thermal power industries; the unit is 10,000 people. ② Installed capacity refers to the sum of the rated active power of generator sets actually installed in the power system. It is used to measure the investment scale in thermal power or hydropower generation equipment in each province; the unit is 10,000 kilowatts (kW). ③ Hours are used to indicate the effective utilization rate of the equipment, which clearly reflect the situation of installed power generation capacity and whether there is any excess; the unit is h. ④ Energy is an important input for the operation of thermal power generation. The energy related input of thermal power generation mainly includes coal, oil, and natural gas. The data of thermal power input are from the fossil fuel data of the thermal power industry provided by China Energy Statistics Yearbook [38], mainly including coal, oil, and natural gas; the unit is 10,000 tons of standard coal. Hydropower energy input data are obtained according to the China Electric Power Yearbook [39]; its unit is also 10,000 tons of standard coal.
Desirable output indicator: Power generation directly reflects the actual production performance level of the power industry. We take the amount of power generation as an important indicator to measure the output of power generation; the unit is 100-million-kilowatt hours (KW H).
Undesirable output indicator: Due to the characteristics of clean energy, hydropower does not consider undesirable output. China's thermal power generation industry is an important sector of energy consumption and carbon emissions. The undesired output brought by thermal power must therefore be fully considered. In the calculation of thermal power efficiency, CO 2 emissions from thermal power generation are selected as the undesirable output, and the unit is 10,000 tons. According to Liu et al. [44] and Qin et al. [31] and based on fossil fuel energy consumption data of the thermal power industry at the provincial level, we estimate the carbon dioxide emissions of thermal power generation in China's provinces in 2013 and 2017. The formula is: Among the variables above, is carbon dioxide emissions caused by the energy consumption of thermal power generation in area i in one year; is the j-type energy consumption consumed by thermal power generation in area i; represents the carbon emission factor; represents the rate of carbon oxidation; and the coefficients of the latter two are from the research of Liu et al. [44] and Qin et al. [31].  Table 1 and Table 2. 0.000 Note: The data are from the authors' collection.
The Kaiser-Meyer-Olkin (KMO) of principal component analysis of input and output indicators of thermal power generation efficiency is 0.731, and the approximate chi-square of Bartlett's sphericity test is large (>0.5) and significant (p-value0.01), indicating that there is a significant correlation between the selected indicators. The KMO of principal component analysis of input and output indicators of hydropower generation efficiency is 0.777, and the approximate chi-square of Bartlett's sphericity test is large (>0.5) and significant (p-value0.01), indicating that there is a significant correlation between the selected indicators. According to the results of principal component analysis of input and output indicators of thermal power generation efficiency, the extraction of the seven variables is greater than 0.70. Thus, these variables are suitable for evaluating the generation efficiency of China's thermal power industry. According to the results of principal component analysis of input and output indicators of hydropower generation efficiency, the extraction of the seven variables is greater than 0.70. Thus, these variables are suitable for evaluating the generation efficiency of China's hydropower industry. Table 3 summarizes the descriptive statistics of the mean, standard deviation, maximum, and minimum of the input variables, desirable output variables, and undesirable output variables used in the model.  Figure 1 illustrates the trend of CO 2 emissions from thermal power generation in China's provinces in 2013 and 2017. We see that CO 2 emissions are on the rise, and thus the issue of CO 2 from thermal power generation requires improvement. The energy efficiency calculation of thermal power generation must also consider CO 2 emissions in order to be more realistic.

Meta-and group efficiency scores and ranks of thermal power and hydropower
This study uses MaxDEA Pro 7.0 software to measure the energy efficiency of thermal power and hydropower in China's provinces and cities in 2013 and 2017 and selects output-oriented and non-radial types in the efficiency measurement. Among them, in the measurement of thermal power energy efficiency, the ratio of desirable output to undesirable output is set to 1: 1; that is, CO 2 emissions and thermal power generation are placed in the same position. Table 4 shows the meta-efficiency scores of thermal power and hydropower in China's provinces in 2013 and 2017. In 2017, thermal power's meta-efficiency scores for Beijing, Jiangsu, Ningxia, Shandong, Hebei, Jiangxi, Zhejiang, and Inner Mongolia are all higher than 1, while hydropower's meta-efficiency scores for Yunnan, Jiangsu, Sichuan, Gansu, Shaanxi, Hubei, and Xinjiang are higher than 1. Moreover, we find that the hydropower and thermal power metaefficiency scores of Jiangsu are both higher than 1 in 2017. The analysis is as follows. The meta-efficiency scores reflect the thermal power efficiency and hydropower efficiency of China's provinces without considering group differences. According to the calculation results in Table 2, the specific analysis runs as follows. Regarding the eastern provinces, thermal power generation meta-efficiencies of Tianjin, Shanghai, Jiangsu, Zhejiang, and Shandong present relatively stable rankings, and Beijing and Hebei have greatly increased their rankings. Compared to 2013, Beijing's meta-efficiency of thermal power increased by 19 places in 2017, as its metaefficiency score rose from 0.2716 to 1.3193. On the contrary, Liaoning has shown a significant decline. The eastern provinces of Hebe, Shandong, and Hainan have maintained a relatively stable ranking of hydropower meta-efficiency, while Jiangsu's ranking has greatly increased. Compared to 2013, the meta-efficiency of Jiangsu's hydropower rose 21 places in 2017, as its efficiency value went from 0.9368 to 1.3506. Jiangsu's hydropower generation efficiency is relatively high, which is similar to Tian et al. [45]. However, they focused on hydropower efficiency in the Yangtze River Economic Belt and adopted the traditional CCR model. Therefore, our study on the hydropower efficiency evaluation of different regions in China is warranted. The hydropower meta-efficiencies of Zhejiang, Guangdong, and Fujian have declined significantly. Conversely, Shandong's thermal power and hydropower meta-efficiency rankings are stable.
Regarding the central region provinces, Jilin, Heilongjiang, and Anhui have maintained relatively stable rankings in terms of thermal power generation meta-efficiency. Compared to 2013, Jiangxi's thermal power meta-efficiency ranking in 2017 increased by 21 places, as its metaefficiency value rose from 0.1917 to 1.0219. By contrast, Guangxi and Shanxi declined significantly. Anhui, Henan, Hubei, Hunan, and Guangxi have maintained relatively stable hydropower generation meta-efficiency rankings, while the rankings of Jilin and Jiangxi have fallen. Anhui's rankings of thermal power and hydropower meta-efficiency have remained stable.
For the western provinces, Yunnan, Shaanxi, Gansu, and Ningxia have all maintained relatively stable rankings in terms of meta-efficiency of thermal power generation. Compared to 2013, Sichuan's thermal power generation meta-efficiency ranking increased by 11 places in 2017, as its efficiency value rose from 0.1721 to 0.8977. However, Guizhou and Xinjiang declined. Yunnan and Gansu have maintained a relatively stable ranking of hydropower generation meta-efficiency, and Xinjiang has risen. Compared to 2013, Xinjiang's ranking increased by 18 places in 2017, as its meta-efficiency score rose from 0.9256 to 1.0156, but Qinghai's ranking dropped. In summary, the hydropower and thermal power generation meta-efficiency rankings of Yunnan and Gansu have remained stable. Figure 2 shows the average meta-efficiency values of hydropower and thermal power generation in the eastern, central, and western provinces in 2013 and 2017. Comparing 2013 and 2017, the average meta-efficiency values of thermal power generation in the three regions all show a significant upward trend, which is similar to Zhou et al. [40], but they adopted a DEA model that uses pollutant gas emissions due to thermal power generation as an input variable. This is inconsistent with the actual situation and cannot accurately measure the generation efficiency of thermal power. Different from them, we incorporate CO 2 emissions from thermal power generation as an undesirable output and consider heterogeneity between regions when measuring the efficiency based on the Meta-SE-SBM undesirable model, which is relatively more accurate.
In 2017 the average thermal power generation meta-efficiency ranking was Eastern > Central > Western. The average meta-efficiency values of hydropower generation in the eastern and central regions show a significant downward trend, while the western region has a slight downward trend. In 2017 the meta-efficiency ranking of hydropower generation was West > Central > East. In summary, the difference in the meta-efficiency value of thermal power generation in all provinces is shrinking, while the difference in the meta-efficiency value of hydropower generation is expanding. In particular, the western region presents large geographical differences, a large river drop, and relatively rich hydropower resources, which make western provinces' hydropower energy efficiency relatively high. Conversely, there is relatively large room for improving hydropower energy efficiency in the eastern and central provinces. Therefore, the development of the hydropower industry should employ measures to suit local conditions, formulate sustainable policies for the power industry, and promote efficient and green development of the two power industries in each province.  of each province in its group, excluding variations caused by group differences. The specific analysis runs as follows. The group efficiencies of Beijing, Jiangsu, and Zhejiang in the eastern region are greater than 1, and the group efficiencies of Chongqing, Shaanxi, Ningxia, and Xinjiang in the western region are also greater than 1, indicating that these provinces are at the efficient production frontier. The thermal power generation group efficiency of Jilin in the central region in 2013 and 2017 is the lowest, but the gap between the thermal power group efficiency and the metaefficiency of each province is gradually narrowing.   [46] and Chen and Zhu [47]. The economically developed eastern region has more advanced technology and more mature market mechanisms, which help improve the efficiency of the thermal power generation industry. There are large regional differences in efficiency values, and there is room for improvement in the thermal power generation efficiency of the central region. By comparison, in 2017 the average group efficiency of thermal power generation was 1.0143, 0.9939, and 1.0279, respectively. The average group efficiency of the central region has greatly improved, and the eastern and western regions are also on the rise. Regarding the average thermal power group efficiency ranking, the western region is currently ranked first, followed by the eastern region, and then the central region. The western region is able to rely on relatively rich coal resources and national energy policies such as "power transmission from west to east" [46] to improve its efficiency. The above results show that the development of the thermal power generation industry in the eastern, central, and western regions is gradually mature and stable.      Table 5 lists the technology gap ratio rankings and technology gap ratio values of the efficiencies of thermal power and hydropower generation in the meta-and group boundaries of China's provinces in 2013 and 2017, respectively. The specific analysis goes as follows.

Technology gap ratio (TGR) scores and ranks of thermal power and hydropower
The thermal power efficiency technology gap ratio values and rankings of the eastern provinces in 2017 were significantly better than those of the central and western regions. In 2017, there were 5 provinces in the eastern region tied for first place with a technology gap ratio of 1: Tianjin, Liaoning, Shanghai, Fujian, and Guangdong. Liaoning rose 20 places in 2017, indicating that its thermal power industry's CO 2 emissions have been effectively controlled and reduced. Compared to 2013, the technology gap ratio values and ranking of the provinces in the central region in 2017 decreased significantly. Among them, Inner Mongolia, Anhui, and Henan dropped by 28, 23, and 19 places, respectively, and thus CO 2 emissions from thermal power generation must be reduced. Compared with 2013, the ranking of Xinjiang in the western region in 2017 dropped by 10 places, and its CO 2 emissions of the thermal power industry also need to be controlled. On the contrary, Yunnan rose by 7 places, indicating that its thermal power industry's CO 2 emissions have improved, while the remaining western provinces have relatively stable ranking changes. In general, the ranking of the western provinces is relatively stable, indicating that there has been no major adjustment in policies on carbon dioxide emissions and treatment in the thermal power industry. Moreover, the rankings of the eastern provinces have risen significantly, while the rankings of the central provinces have fallen significantly. This shows that the technological level of the thermal power generation industry in the eastern provinces has improved. These provinces not only target the economic output of thermal power generation, but also attach importance to energy conservation and emissions reduction in the thermal power industry. The central provinces need to strengthen their technology, energy savings, and emissions reduction of the thermal power industry.  Figure 7 shows the TGR values of the thermal power generation efficiencies of the eastern, central, and western regions in 2013 and 2017. In 2017 the thermal power efficiency technology gap ratio values of the eastern provinces were better than that of the central and western provinces. The TGR values of the eastern and western provinces have a rising trend, while the central provinces have declined. China's central region needs to improve the efficiency level of thermal power generation as well as control and reduce CO 2 emissions. We see that the gap in thermal power technology in the eastern, central, and western regions has gradually narrowed, indicating that technology in the thermal power industry is becoming more mature and CO 2 emissions control and treatment have made some progress.

Note: The data are from the authors' collection
Clustering is a process of classifying and organizing data members that are similar in certain aspects. In order to analyze the characteristics and differences of hydropower's TGR in the three regions, we perform K-means clustering on the TGR values of China's eastern, central and western regions in 2017. Here, we set K to 2, divided into two categories: a group with higher TGR values, and a group with relatively lower TGR values. The clustering results are in Table 6.
From Table 5 and Table 6, according to provincial hydropower efficiency TGR values and rankings in China's three regions, and based on the k-means clustering results of TGR values and ranks of hydropower, we clearly see that the hydropower efficiency TGR values of the western provinces in 2017 were significantly better than those of the eastern and central regions. In 2017, four provinces in the western region tied for first place with a technology gap ratio of 1: Sichuan, Yunnan, Ningxia, and Xinjiang. Moreover, in 2017 Xinjiang and Chongqing increased their rankings by 19 and 17, respectively, indicating that their hydropower industry development has been greatly promoted, and that the technological level of their hydropower industry has greatly improved. Compared to 2013, the technology gap ratio values and rankings of the eastern provinces in 2017 have decreased significantly. Among them, Hebei, Liaoning, Jiangsu, Zhejiang, and Hainan dropped 19,22,16,25, and 23 places, respectively, and efforts must thus be made to improve their efficiency and technology of hydropower generation. Compared with 2013, the rankings of provinces in the central region in 2017 are relatively stable, and the rankings of provinces in the western region have risen relatively. However, the rankings of the provinces in the eastern region have declined significantly, indicating that this region's incentive support policies for hydropower generation are not stable enough.   Table 7 shows the input-output non-efficiency levels of thermal power generation in China's provinces in 2017 and the average input-output non-efficiency levels of thermal power generation in its three major regions. By calculating the input-output redundancy of thermal power generation in China's provinces in 2017, the average non-efficiency levels of the input and output terms of the three regions can be measured. From the perspective of each group, the redundancy of the labor output in each region is relatively high [40], reaching more than 20%, and there is a surplus of undesirable output CO 2 at 8%, 11%, and 20% in the eastern, central, and western regions, respectively. The equipment utilization hours, energy input, and installed capacity of the western region are relatively high, and there is a shortage of thermal power generation output there. In addition, there is a large excess of undesirable output CO 2 , which means that there is a large amount of CO 2 emissions, resulting in relatively low efficiency of thermal power generation in the west.

Improvement analysis of input-output items of thermal power and hydropower
Excessive resource input not only has failed to increase the expected output power generation, but on the contrary it has greatly increased the undesired output of gas pollution emissions [40]. It shows that there is a lack of effective technical management and blindly thinking that more input means more output, which not only leads to a waste of resources, but also higher pollution control costs.
In the eastern region, there is a lot of redundancy in Liaoning's number of employees and energy input, and there is a large excess of undesirable output CO 2 , which places this province's thermal power energy efficiency the last in the group. In the central region, Jilin also has a large amount of redundant inputs, and its input redundancy in the number of employees and energy is 34% and 28%, respectively. There is a large excess of undesirable output CO 2 , and its desirable output is insufficient. This puts Jilin's thermal power efficiency at the bottom of its group. In the western region, Yunnan has a severe surplus of employees and installed capacity, with a redundancy of 68% and 47%, respectively. Moreover, there is a serious shortage in thermal power generation output, placing its thermal power generation efficiency at the bottom of its group.   In the eastern region, Shandong has a large number of employees, with a redundancy of 80%, and the desirable output of hydropower generation is insufficient, reaching 197%, which is the reason why Shandong's hydropower energy efficiency is at the bottom of the group. In the central region, Inner Mongolia also has a large amount of redundancy. The redundancy of the number of employees and installed capacity have reached 34% and 18%, respectively, and the desirable output of hydropower generation is insufficient at 61%. These have led to Inner Mongolia's hydropower energy efficiency being at the bottom of the group. In the western region, Chongqing's equipment utilization hours and installed capacity are excessive, with redundancy reaching 44% and 9%, respectively, and there is insufficient hydropower output, which puts its hydropower energy efficiency in last place of its group. Scant studies have compared thermal power and hydropower generation efficiencies and presented a sub-regional analysis of the eastern, central, and western regions in China at the same time. Different from SFA [6], CCR [12], BCC [13], and SBM methods [19], the Meta-SE-SBM and data availability, we should be able to compare the efficiencies of more types of electricity such as wind power and solar power. Second, based on group boundaries, the energy efficiency of thermal power and hydropower generation in each province is closer to reality than at the meta-frontier. The thermal power group efficiencies of eastern coastal economically developed provinces (municipalities) such as Beijing, Jiangsu, and Zhejiang are greater than 1. By comparison, the hydropower generation group efficiencies of western inland provinces (municipalities) such as Sichuan, Yunnan, and Xinjiang are greater than 1. This shows that China's thermal power generation industry is currently maturing, but its hydropower generation industry needs further development to improve general hydropower efficiency and narrow the regional gap.

Conclusion
Third, there are regional differences in the technology gap ratio values of the thermal power and hydropower industries in the three major regions. In 2017 the thermal power TGR values and rankings of the eastern region were better than that of the central western regions, whereas the central provinces dropped significantly. While the western region's TGR values and rankings of hydropower were better than the eastern and central regions, the eastern provinces dropped significantly. The gap in thermal power technology among the three regions has gradually narrowed, indicating that technology in the thermal power industry is maturing and CO 2 emissions control and treatment have made progress. Conversely, the technological gap for hydropower among the three has slightly expanded, indicating that the hydropower generation industry needs further attention and policy support. Regardless of the development of hydropower and thermal power, both need stable regional policy support to promote technical efficiency and narrow their technological gap.
Fourth, based on the calculation of the input-output non-efficiency level and from the perspective of thermal power generation efficiency, the undesirable output of CO 2 in the eastern, central, and western regions is excessive, reaching 8%, 11%, and 20%, respectively. The equipment utilization hours, energy input, and installed capacity of the western region are relatively high, and there is a shortage of thermal power generation output in the western region. Moreover, there is a large excess of undesirable CO 2 output and a great amount of emissions. This is also the reason for the relatively low efficiency of thermal power generation in the west. From the perspective of hydropower generation efficiency, the equipment utilization hours in the east, the number of employees, and the installed capacity are severely redundant, and the desirable output of hydropower generation in the east and central regions is insufficient, reaching 49% and 28%, respectively. This is why there is relatively low hydropower generation efficiency in the eastern and central regions.

Policy Recommendation
Considering the energy efficiency, technological gaps, and input-output non-efficiency levels of thermal and hydropower generation in China's provinces, strategies should be adopted that meet their actual conditions. Therefore, we offer some policy suggestions.
First, according to the efficiency of the regional thermal power industry, local governments and industry managers should formulate policies that are suitable for the development of local Third, the China government should continue to promote the green and efficient management of regional power industries through reforms of the market-based price mechanism, so that the market can play a better role in resource allocation. In addition to attaching importance to the management and policy support of local governments and power industry managers, it is also necessary to give full play to the role of market mechanisms. The efficiency improvement brought about by technological progress must be reflected in electricity prices to achieve the optimal allocation of resources and the overall improvement of power generation efficiency. In addition, innovation of the power industry's management system should be steadily promoted. At the same time, relevant policies should be implemented effectively to restrain the environmental pollution generated by the thermal power industry as well as to strengthen the competitiveness of clean energy such as hydropower, wind power, and solar power according to local conditions. The end result should help promote the green development of the whole power industry.