Efficiency Measurement and Factor Analysis of China’s Solar Photovoltaic Power Generation Considering Regional Differences Based on a FAHP–DEA Model

Driven by the transformation of the energy structure, China’s photovoltaic (PV) power generation industry has made remarkable achievements in recent years. However, there are more than 30 regions (cities/provinces) in China, and the economic, policy, technological, and the environmental conditions of each region are significantly different, which leads to a huge discrepancy in PV power generation efficiency. To address the imbalance in the development of PV industry, first, this paper employed the integrated fuzzy analytic hierarchy process–data envelopment analysis (FAHP–DEA) model to evaluate the PV power generation efficiency of 30 regions in China. Second, Tobit regression model was used to examine the effects of 9 potential influencing factors. Third, a concrete analysis was conducted, and discussion based on the efficiency rankings and regression results was made. Additionally, the FAHP–DEA model proposed in this study can also be applied to the efficiency evaluation issues of other types of renewable energy.


Introduction
With the constant change in energy demand, the global energy structure will also undergo major adjustments. Low-carbon and renewable will be the inevitable trend of energy development. Petroleum, coal, and other fossil energy types, which once accounted for a large proportion of the energy structure, will gradually be replaced by cleaner energy. To better cope with the environmental changes and complete the transformation of the energy structure, great efforts have been made worldwide. After the signing of the Paris Agreement in 2016, the United Nations General Assembly passed a resolution on 10 May 2018, which officially opened the negotiation process of the World Environment Convention. The text of the draft convention contains a total of 26 articles, reaffirming the principle of "who pollutes, pays" and the right of citizens to enjoy a healthy environment. The greatest contribution of the World Environment Convention is the introduction of environmental rights, and thus, it is called the enhanced version of the Paris Agreement.
Renewable energy is at the center of the energy transformation process. Driven by the technological progress and environmental concerns, renewables have grown rapidly in several years, accompanied by cost reductions for solar photovoltaic (PV) in particular. The International Energy Agency (IEA) pointed out in the World Energy Outlook 2018 report that flexibility is a new proposition for the power Energies 2020, 13 system. Due to the increasing unique competitiveness of solar PV, its installed capacity will exceed those of wind power by 2025, hydropower by 2030, and coal power by 2040. In addition to large-scale PV power plants, distributed PV will also play an important supporting role. It is estimated that by 2040, the proportion of renewable energy power generation will increase from the current 25% to 40%. Figure 1 shows global ranking of installed PV capacity in 2018.
Energies 2019, 12, x FOR PEER REVIEW 2 of 29 years, accompanied by cost reductions for solar photovoltaic (PV) in particular. The International Energy Agency (IEA) pointed out in the World Energy Outlook 2018 report that flexibility is a new proposition for the power system. Due to the increasing unique competitiveness of solar PV, its installed capacity will exceed those of wind power by 2025, hydropower by 2030, and coal power by 2040. In addition to large-scale PV power plants, distributed PV will also play an important supporting role. It is estimated that by 2040, the proportion of renewable energy power generation will increase from the current 25% to 40%. Figure 1 shows global ranking of installed PV capacity in 2018. As the largest developing country around the world, China has made tremendous contributions to the energy transformation in recent years [1]. The Chinese government attaches great importance to energy transformation, implements structural reforms on the supply side, and promotes a clean and efficient use of energy, thereby promoting the coordinated and comprehensive development of the economy and society [2]. With the support of a series of policies, China's solar PV industry has made remarkable development achievements and its new installed capacity has been ranked first in the world for six consecutive years. By May 2018, China's grid-connected PV installed capacity had exceeded 140 million kilowatts [3]. PV power generation thus plays a vital role in China's energy development and transformation.
However, although China's PV industry has achieved gratifying results, it has also exposed some problems that cannot be ignored in the development process. For example, some regions with abundant solar light resources, such as Gansu and Qinghai, show poor PV industry performance owing to their low installed capacity [4]. Meanwhile, the PV industry in regions with less effective sunshine duration, such as Jiangsu and Anhui, has made rapid progress in recent years, leading the PV installed capacity in China. These problems are largely caused by the unbalanced development of the PV industry in different regions. As a country with a vast territory and special conditions, China has huge regional diversity. The economic status, environmental conditions, and resource endowments in the different regions are significantly different. To promote a sound development and improve the scientific base of the PV industry, it is meaningful and necessary to study the efficiency of the PV power generation in China at the regional level.
It is said that at present, the photoelectric conversion efficiency of most solar cells is about 25%, but the PV power generation efficiency in this paper is considered from the economic level, not the efficiency of photovoltaic modules at the technical level or the photovoltaic conversion efficiency of photovoltaic system. To a certain extent, the PV power generation efficiency in this paper could be defined as performance ratio. Besides, this paper mainly analyzes efficiency from the perspective of input-output and considers it from the economic perspective and we analyze the utilization efficiency between all the input elements and the output power in the PV power generation process  As the largest developing country around the world, China has made tremendous contributions to the energy transformation in recent years [1]. The Chinese government attaches great importance to energy transformation, implements structural reforms on the supply side, and promotes a clean and efficient use of energy, thereby promoting the coordinated and comprehensive development of the economy and society [2]. With the support of a series of policies, China's solar PV industry has made remarkable development achievements and its new installed capacity has been ranked first in the world for six consecutive years. By May 2018, China's grid-connected PV installed capacity had exceeded 140 million kilowatts [3]. PV power generation thus plays a vital role in China's energy development and transformation.
However, although China's PV industry has achieved gratifying results, it has also exposed some problems that cannot be ignored in the development process. For example, some regions with abundant solar light resources, such as Gansu and Qinghai, show poor PV industry performance owing to their low installed capacity [4]. Meanwhile, the PV industry in regions with less effective sunshine duration, such as Jiangsu and Anhui, has made rapid progress in recent years, leading the PV installed capacity in China. These problems are largely caused by the unbalanced development of the PV industry in different regions. As a country with a vast territory and special conditions, China has huge regional diversity. The economic status, environmental conditions, and resource endowments in the different regions are significantly different. To promote a sound development and improve the scientific base of the PV industry, it is meaningful and necessary to study the efficiency of the PV power generation in China at the regional level.
It is said that at present, the photoelectric conversion efficiency of most solar cells is about 25%, but the PV power generation efficiency in this paper is considered from the economic level, not the efficiency of photovoltaic modules at the technical level or the photovoltaic conversion efficiency of photovoltaic system. To a certain extent, the PV power generation efficiency in this paper could be defined as performance ratio. Besides, this paper mainly analyzes efficiency from the perspective of input-output and considers it from the economic perspective and we analyze the utilization efficiency between all the input elements and the output power in the PV power generation process in 30 regions of China under different economic, political, environmental, technological and natural conditions. This paper uses the integrated fuzzy analytic hierarchy process-data envelopment analysis (FAHP-DEA) model to measure the PV power generation efficiency of 30 regions (cities/provinces) in China and analyzes the influencing factors in the PV power generation efficiency.
Energies 2020, 13, 1936 3 of 26 There are two main contributions of this article. From the aspect of method, this study combines objective and subjective methods together so as to make the evaluation results more accurate and comprehensive and uses fuzzy sets to reflect the vagueness of experts' judgments under the uncertain environment. Furthermore, the Tobit model was employed to conduct an outside validation of the measured efficiency, which further prove the reliability and authenticity of the efficiency measurement. From the research problem level, many studies related to PV efficiency are based on the national level, whereas there are few relevant studies on the measurement of PV power generation efficiency in China, especially at the provincial level. Therefore, this article can be regarded as a valuable supplement to related research, which considers the reality of China and its regional differences. Additionally, the evaluation index system and the comprehensive FAHP-DEA model proposed in this article are also applicable to other renewable energy issues.
The remainder of this article is organized as follows: Section 2 briefly introduces the concept of the FAHP and DEA model and its application fields. Section 3 describes the methods and data collection. The application of the FAHP and game cross efficiency DEA model and the obtained results are explained in Section 4. In Section 5, the efficiency ranking results obtained in Section 4 are verified externally and the influencing factors are analyzed. Section 6 presents the discussion and conclusions.

Fuzzy Analytic Hierarchy Process (FAHP)
The analytic hierarchy process (AHP) is a hierarchical weight decision analysis method proposed by Saaty in the early 1970s [5]. However, the AHP cannot reflect the cognitive process of human beings and cannot deal with the uncertainty and fuzziness in the judgment by decision makers [6]. Therefore, it needs to be combined with other techniques, such as the fuzzy set [7].
The FAHP is an evaluation method that combines the traditional AHP with the fuzzy set theory and fully takes the fuzziness of decision makers' thinking in consideration. The linguistic approach is used to solve evaluation problems under an uncertain environment through the use of triangular fuzzy numbers. As a widely used evaluation method, the FAHP has been applied to many fields such as underground metal mining [8], urban traffic [9], highway bridges [10], and energy saving and prediction [11].

Data Envelopment Analysis (DEA)
DEA was proposed by Charnes et al. in 1978 [12]. DEA is a systematic method of analysis based on the concept of relative efficiency, which evaluates the relative effectiveness or benefit of the same type of decision making units (DMU) according to multi-index inputs and outputs. It calculates and compares the relative efficiency of DMU by using a mathematical programming model and evaluates the DMU on this basis. As a widely used objective evaluation method, the DEA has been applied in various fields since it was proposed, such as technical efficiency [13], eco-efficiency [14], productive efficiency [15], performance of the real estate industry [16], and R&D in efficiency measurement [17].
The traditional DEA model has limited ability to distinguish DMUs, especially when the number of DMUs is small and the number of inputs and outputs is relatively large. In order to rank all DMUs completely, it is necessary to combine other methods for further analysis, or to modify the traditional DEA model. For this purpose, scholars at home and abroad have conducted numerous studies and put forward many new models, such as fuzzy DEA, cross efficiency DEA, super efficiency DEA, network DEA models, etc.

Integration of FAHP and DEA
Compared with the traditional AHP method, the FAHP method is based on the use of fuzzy numbers or fuzzy consistency matrices for evaluation. However, the results of the FAHP still depend on subjective judgments and expert experience. The most prominent advantage of the DEA is that no Energies 2020, 13, 1936 4 of 26 weighting assumption is required, and the weight of each input and output is based on the optimal weight obtained from the actual data of the DMU. Therefore, the DEA method which excludes many subjective factors is a highly objective evaluation method. Thus, this study adopts a linear combination weighting model to unify FAHP and DEA in order to achieve the unity of subjectivity and objectivity. Actually, some researchers have applied the FAHP-DEA model to other fields before. Hadi and Mohamadghasemi [18] proposed an integrated FAHP-DEA model for multiple criteria ABC inventory classification. Che [19] used the FAHP and DEA model to make bank loan decisions in Taiwan. Li et al. [20] made efforts to combine the FAHP with DEA for transit operator efficiency assessment.
Although the FAHP-DEA model has been applied in many fields, including energy efficiency evaluation, it is rarely used in the evaluation issues of the PV industry, especially at the regional level. Therefore, the main purpose of this study is to use a more scientific and reliable method to evaluate the PV power generation efficiency of the 30 regions in China. In addition, the influencing factors of efficiency are explored. Considering the resource endowment and economic, technological, and environmental differences between different regions, the countermeasures and suggestions to improve the PV power generation efficiency of each region are put forward. Figure 2 depicts the framework of this article.

Fuzzy Analytic Hierarchy Process
There are two main categories of FAHP, one is based on fuzzy numbers, and the other is based on fuzzy consistent matrix. The method used in this study is the former, which is mainly based on the triangular fuzzy number (Table A1).
The basic steps of the FAHP are as follows [21]:

Fuzzy Analytic Hierarchy Process
There are two main categories of FAHP, one is based on fuzzy numbers, and the other is based on fuzzy consistent matrix. The method used in this study is the former, which is mainly based on the triangular fuzzy number (Table A1).
The basic steps of the FAHP are as follows [21]: Step 1: Analyze the relationship among the factors in the system and construct the hierarchical structure.
Step 2: Determine the weight of each criteria in the hierarchical structure that was constructed in step 1 and establish a pairwise comparison matrix.
Step 3: Construct a fuzzy positive matrix and calculate the fuzzy weights. The scores of pairwise comparisons given by experts are expressed by positive triangular fuzzy numbers, which is listed in Table A1. The definition of the fuzzy positive reciprocal matrix is as follows: where A k is the fuzzy positive reciprocal matrix of expert k, and a ij k is the relative importance of criteria i and j. Then, this article uses the Lambda-Max method to calculate the fuzzy weights: Let α= 1 to obtain the positive matrix of expert k, A k m = a ijm n×n . Let α= 0 to obtain the upper and lower bound positive matrix of expert k, A k u = a iju n×n and A k l = a ijl n×n . And AHP is used to get the weight vector W k m = w k im ,W k l = w k il and W k u = w k iu , i = 1, 2, . . . , n. The lower and upper bound of the weight can be computed by the following equations: and the fuzzy weight matrix of expert k is W k Step 4: Obtain the fuzzy weights of each expert and the final ranking. In this step, use the geometric average to obtain the fuzzy weights of each expert. Define the ranking order of decision units by the following equation, which was proposed by Chen [22]: where S − W i , 0 and S + W i , 1 are the distance measurements between two fuzzy numbers and C i is the weight of criteria i. After that, the linguistic variables (Table A2) of the fuzzy theory were used to reflect the experts' judgments.

Game Cross Efficiency DEA
The CCR-DEA model was proposed by Charnes et al. [12] in 1978, and it is an input-oriented model.
Assuming that there are n DMUs, the input and output vectors of DMU j are X j = x 1 j , x 2 j , . . . , x mj T and Y j = y 1 j , y 2 j , . . . , y sj T , j = 1, 2, . . . , n, U and V are the weight vectors corresponding to the inputs and outputs, respectively, and DMU 0 is the currently evaluated DMU. The CCR-DEA model is as follows: where η represents the efficiency value and λ is a constant vector.
As a traditional DEA model, CCR-DEA has its own defects. It is based on the idea of self-evaluation, and the weight is determined by the DMU itself. In the efficiency evaluation, it maximizes its own efficiency while minimizing the efficiency of others. It means the efficiencies calculated by the CCR-DEA model tend to overestimate owing to its pure self-evaluation process. Moreover, CCR-DEA model can only distinguish the relatively effective and relatively ineffective DMUs, but it can't evaluate the relatively effective DMUs further, and can't effectively rank the efficiency of DMUs. To address this problem, Liang et al. [23] proposed the game cross efficiency DEA model. The definition of game cross efficiency is as follows: here the first m 1 inputs (x ij ) are cost-type indicators (the smaller the value, the better), and the m 1 + 1 to m inputs (z ij ) are fixed indicators (the closer its value is to a fixed value, the better), and v d ij are optimal weights obtained by following model: In Equation (11), η d is a parameter whose initial value can be derived from the average cross efficiency calculated using the cross-efficiency DEA model. The Equation (11) can ensure that the efficiency value of the DMU is not lower than its initial average cross-efficiency value. The optimal solution of Equation (11) is the game cross efficiency value, which is defined by Equation (10). If the Energies 2020, 13,1936 7 of 26 optimal solution of Equation (11) is expressed as u d * rj (η d ), the average game cross efficiency of the j-th DMU is defined as follows: According to the proof of Liang et al. [24], η j calculated by the game cross-efficiency DEA model is convergent and unique, regardless of the average cross efficiency value under which the initial parameters are taken.

The Least Squares Method
As discussed in Sections 3.1 and 3.2, the subjective vector U = (u 1 , u 2 , . . . , u m ) T calculated by FAHP and the objective vector V = (v 1 , v 2 , . . . , v m ) T calculated by game cross efficiency DEA can be obtained. Then, use the least squares method to combine the objective and subjective results into a more comprehensive vector W = (w 1 , w 2 , . . . , w m ) T . The subjective evaluation method (FAHP) reflects the value of variables, while the objective evaluation method (DEA) reflects the information of variables. In this paper, the least squares method is used as a tool to determine the weights of variables by establishing an optimization model, so that the weights can reach the unity of subjective and objective, as well as the unity of value and information.
The least squares method is to minimizes the sum of the squares of errors in calculation results of each data. Thus, the goal is to minimize the deviation between U and V using the combinational weighting method. The objective function is as follows: Subject to: where z ij denotes the normalized criteria value.
To solve the object function of (13), the Lagrange function is introduced as follows: In addition, let: Alternatively, it can be defined by the following matrix Equation (16): where: diag(a 1 , a 2 , . . . , a n ) denotes the diagonal matrix whose diagonal elements are a 1 , a 2 , . . . , a n . Then, the combined weight vector W can be calculated using the following Equation (17):

Variables and Data
Restricted by statistical data availability and consistency, 30 regions are chosen as the basic research units. The data used in this article are mainly derived from the statistical yearbooks (2013-2017) of the National Bureau of Statistics of China (available online: http://www.stats.gov.cn/), the China energy statistical yearbooks (2013-2017) (available online: http://www.nea.gov.cn/), and the International Energy Agency (IEA) (available online: https://www.iea.org/). In addition, the missing data are filled by the average method.
In this paper, three sets of variables were selected. It is worth emphasizing that we consulted a group of experts on the process for selecting variables and fully considered their choices. The 15 experts we consulted include not only scholars and researchers from the field of solar photovoltaic and energy efficiency, but also staff from the listed companies with leading technology in the field of photovoltaic in China. Specifically, the panel included experts from the Research Center of Solar Thermal Conversion (five people), Sungrow (five people), and the Photovoltaic System Engineering Research Center (five people). To a certain extent, this can ensure the professionalism and reliability of experts from the theoretical and practical levels.
These three sets of variables are not only related but also different, which are applicable to FAHP, game cross efficiency DEA and Tobit regression models respectively. All the variables included in this article are presented and described in Table 1. The statistical descriptions of the collected data of all variables are elaborated in Table 2.

Application of FAHP
To measure the PV power generation efficiency of the 30 regions in China, this study sets three basic standards: (i) environmental responsibility (E); (ii) policy and economic support (P); and (iii) technical and natural conditions (T) [25][26][27]. This paper also chooses 12 sub-criteria under the three basic standards, which are constructed from existing literature and public sources. The 12 sub-criteria and their descriptions can be found in Table A3.
The environmental responsibility of local government can be assessed in terms of local pollutant discharge and regional environmental investment [28]. A region with strong environmental responsibility and consciousness tends to have less pollutant discharge and higher environmental investment. Therefore, the sub-criteria within the environmental responsibility goal include SO 2 emissions, NOx emissions, smoke dust emissions and financial expenditure for environmental protection.
To a certain extent, policy and economic support can reflect the ability of a region to develop PV power generation. A bidirectional causal relationship exists between energy development and economic growth. Obviously, the higher the degree of economic development, the greater the degree of policy support and the stronger the ability to develop PV power generation. Therefore, the sub-criteria within the policy and economic support goal include real GDP per capita, general financial revenue, benchmark price, and regional subsidy.
The technical and natural conditions are the external and internal factors affecting the efficiency of PV power generation, respectively. Technical conditions mainly refer to the manpower, material costs, and R&D investment needed to develop PV power generation. The PV power generation industry is a highly resource-dependent industry. Natural conditions mainly refer to the endowment of solar light resources, which is highly related to location factors. Therefore, the sub-criteria within the technical and natural conditions goal include total employment, investment in fixed assets, and R&D in electricity industry and effective sunshine duration.
Then, the hierarchical assessment index system can be constructed (see Figure 3).
Energies 2019, 12, x FOR PEER REVIEW 11 of 29 environmental investment. Therefore, the sub-criteria within the environmental responsibility goal include SO2 emissions, NOx emissions, smoke dust emissions and financial expenditure for environmental protection.
To a certain extent, policy and economic support can reflect the ability of a region to develop PV power generation. A bidirectional causal relationship exists between energy development and economic growth. Obviously, the higher the degree of economic development, the greater the degree of policy support and the stronger the ability to develop PV power generation. Therefore, the sub-criteria within the policy and economic support goal include real GDP per capita, general financial revenue, benchmark price, and regional subsidy.
The technical and natural conditions are the external and internal factors affecting the efficiency of PV power generation, respectively. Technical conditions mainly refer to the manpower, material costs, and R&D investment needed to develop PV power generation. The PV power generation industry is a highly resource-dependent industry. Natural conditions mainly refer to the endowment of solar light resources, which is highly related to location factors. Therefore, the sub-criteria within the technical and natural conditions goal include total employment, investment in fixed assets, and R&D in electricity industry and effective sunshine duration.
Then, the hierarchical assessment index system can be constructed (see Figure 3). According to the steps in Section 3.1, the relative weights of each sub-criteria can be obtained (see Table A4). After that, use the linguistic variables to express the subjective judgments of experts. Experts are required to estimate the PV power generation efficiency of the 30 regions for each criteria. Then, use the geometric average technique to integrate their judgments. The fuzzy estimation of the 30 regions for each sub-criterion is presented in Table A5. After that, this paper uses the following equation to convert the fuzzy numbers into crisp number, which is also called best non-fuzzy performance (BNP) value [29].
where i UR , i LR , and i MR denote the maximum, minimum, and middle values of the fuzzy estimation, which is shown in Table A5. The results are shown in Table A6. Finally, we multiply the BNP values obtained in Table A6 and the aggregated weights of 12 sub-criteria obtained in Table A4. The products are then added to obtain the final efficiency scores According to the steps in Section 3.1, the relative weights of each sub-criteria can be obtained (see Table A4). After that, use the linguistic variables to express the subjective judgments of experts. Experts are required to estimate the PV power generation efficiency of the 30 regions for each criteria. Then, use the geometric average technique to integrate their judgments. The fuzzy estimation of the 30 regions for each sub-criterion is presented in Table A5. After that, this paper uses the following equation to convert the fuzzy numbers into crisp number, which is also called best non-fuzzy performance (BNP) value [29].
Energies 2020, 13, 1936 11 of 26 where UR i , LR i , and MR i denote the maximum, minimum, and middle values of the fuzzy estimation, which is shown in Table A5. The results are shown in Table A6. Finally, we multiply the BNP values obtained in Table A6 and the aggregated weights of 12 sub-criteria obtained in Table A4. The products are then added to obtain the final efficiency scores and rankings of the 30 regions (see Table 3). In addition, normalized scores in Table 3 are the result of processing the scores with a decimal scaling normalization method.

Application of Game Cross Efficiency DEA
In this section, this study uses the game cross efficiency DEA model to measure the PV power generation efficiency in the 30 regions. The indicator system constructed in this section is different from that presented in Section 4.1, because they are applicable to different models. The FAHP method mainly relies on the subjective judgment of experts, while the DEA emphasizes the analysis based on actual data. Thus, this study deliberately selects these different indicators, which are more suitable for the selected DEA model.
Compared with other evaluation methods, the DEA relies more on the actual data itself; hence, the evaluation results are more reliable and objective. Synthetically, considering the relevance of the evaluation indicators, six input indicators and two output indicators were selected (see Figure 4).
The input indicators include total employment, investment in fixed assets in electricity industry, R&D in electricity industry, effective sunshine duration, benchmark price, and regional subsidy [25,26], which represents human and material input, technology and natural conditions, and policy support related to PV power generation efficiency [30]. The output indicators include the new installed and generating capacities [27], which indicate the scale and extent of the development of PV industry [30]. The input indicators include total employment, investment in fixed assets in electricity industry, R&D in electricity industry, effective sunshine duration, benchmark price, and regional subsidy [25,26], which represents human and material input, technology and natural conditions, and policy support related to PV power generation efficiency [30]. The output indicators include the new installed and generating capacities [27], which indicate the scale and extent of the development of PV industry [30].
This paper used R language for programming. The collected input and output data of the 30 regions were put into the CCR-DEA and game cross efficiency DEA models for solving. The PV power generation efficiencies measured by R language are presented in Table 4 and Table 5, respectively. It is more conventional to arrange regions in alphabetical order, but Tables 4-6 arrange regions according to geographical location. On the one hand, it is convenient to see the differences of PV power generation efficiency in different regions. On the other hand, it can be consistent with the order in Table 7, so as to make the article more coherent and consistent.  This paper used R language for programming. The collected input and output data of the 30 regions were put into the CCR-DEA and game cross efficiency DEA models for solving. The PV power generation efficiencies measured by R language are presented in Tables 4 and 5, respectively. It is more conventional to arrange regions in alphabetical order, but Tables 4-6 arrange regions according to geographical location. On the one hand, it is convenient to see the differences of PV power generation efficiency in different regions. On the other hand, it can be consistent with the order in Table 7, so as to make the article more coherent and consistent.  The relative efficiency obtained by CCR-DEA model is the comprehensive efficiency of DMU under specified scale income. If the efficiency value is 1, the input and output of the DMU are relatively effective. If the efficiency value is less than 1, it means that the input and output of the DMU are relatively ineffective, some inputs are not converted into outputs reasonably, and there is a waste of resources. The lower the efficiency value is, the more serious the waste of resources.
The results indicate that the CCR-DEA model overestimates the efficiency value and cannot compare the PV power generation efficiency in different regions. Because many efficiency values calculated by CCR-DEA model are 1, and most efficiency values are basically higher than those calculated by game cross efficiency DEA model. However, the game cross efficiency DEA model can solve this problem appropriately by a more accurate iterative calculation.
In addition, to better study the development situation and changing trend of PV power generation efficiency in recent years, this paper calculated the PV power generation efficiency values of 30 regions from 2013 to 2017 using the game cross efficiency DEA model. The results indicate that the overall PV power generation efficiency of China is increasing year by year, and the development trend is good, but the PV power generation efficiency in few areas has decreased slightly in some years. The calculated game cross efficiency is shown in Figure 5.
Energies 2020, 13,1936 14 of 26 solve this problem appropriately by a more accurate iterative calculation.
In addition, to better study the development situation and changing trend of PV power generation efficiency in recent years, this paper calculated the PV power generation efficiency values of 30 regions from 2013 to 2017 using the game cross efficiency DEA model. The results indicate that the overall PV power generation efficiency of China is increasing year by year, and the development trend is good, but the PV power generation efficiency in few areas has decreased slightly in some years. The calculated game cross efficiency is shown in Figure 5.

Integration Results
In this section, the least squares method was used to integrate the results that were calculated by the FAHP and game cross efficiency DEA methods. The relevant data are obtained from Sections 4.1 and 4.2, and the comprehensive efficiency scores are presented in the following Table 6.

Integration Results
In this section, the least squares method was used to integrate the results that were calculated by the FAHP and game cross efficiency DEA methods. The relevant data are obtained from Sections 4.1 and 4.2, and the comprehensive efficiency scores are presented in the following Table 6.  Figure 6 below presents the comprehensive provincial PV power generation efficiency of the 30 regions in the mainland of China from 2013 to 2017. As illustrated in Figure 6, there are 14 provinces and municipalities with PV power generation efficiency exceeding 0.7, including Xinjiang, Inner Mongolia, Anhui, Zhejiang, Jiangsu, and Shanghai. There are also four provinces and municipalities with PV power generation efficiencies below 0.5, including Heilongjiang, Jilin, Tianjin, and Chongqing. PV power generation efficiency in other regions is at a medium level, with an efficiency value of approximately 0.5 to 0.7.
According to the geographical location, this paper divides the 30 regions and municipalities of China into six major regions, namely: North China (include Beijing, Tianjin, Hebei, Shanxi, and Inner Mongolia), Northeast China (include Liaoning, Jilin, and Heilongjiang), East China (include Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, and Shandong), Central South China (include Henan, Hubei, Hunan, Guangdong, Guangxi, and Hainan), Southwest China (include Chongqing, Sichuan, Guizhou, and Yunnan), and Northwest China (include Shaanxi, Gansu, Qinghai, Ningxia, and Xinjiang). The results are listed in the following Table 7.

Influencing Factors
To externally validate the evaluation results and rankings of Section 4.3 and study the key influencing factors of PV power generation efficiency in different regions, the Tobit regression model is selected for analysis. The model is as follows: where α 0 is a constant term, α i (i = 1, 2, . . . m) denotes a regression coefficient, X i (i = 1, 2, . . . m) denotes an explanatory variable, i denotes different regions, t denotes years, and ε it denotes the random error term.
According to the previous studies, the key influencing factors of PV power generation efficiency are, among others, degree of environmental protection, economic development, policy support, advancement of technology, and natural conditions. This study deployed the Tobit regression model to test the most important influencing factors of PV power generation efficiency. After a comprehensive consideration, nine indicators were selected, which are: real GDP per capita (X 1 ), general financial revenue (X 2 ), electricity consumption (X 3 ), total energy consumption per unit GDP (X 4 ), financial expenditure for environmental protection (X 5 ) [31], NOx emissions (X 6 ), SO 2 emissions (X 7 ), smoke dust emissions (X 8 ) [30], and R&D in electricity industry (X 9 ) [25][26][27][28]. The Tobit regression model is calculated by Stata 13.1 (StataCorp LLC, College Station, TX, USA). The regression results are shown in Table 8. Note: *** Coefficient is significant at the 0.01 level; ** Coefficient is significant at the 0.05 level; * Coefficient is significant at the 0.1 level.
P value is a probability, which can reflect the reliability of the result. α is the significance level. If p value is less than α, it means the coefficient is significant at the α level. For instance, when α is 0.01, if p is less than 0.01, then the coefficient is significant at the level of 0.01.
From the regression results, it can be found that the coefficients of X 1 and X 2 are significant at the level of 0.05, because the p value is less than 0.05; the coefficients of X 4 and X 6 are significant at the level of 0.01, because the p value is less than 0.01; the coefficients of X 5 , X 7 and X 8 are significant at the level of 0.1, because the p value is less than 0.1. In other words, the real GDP per capita (X 1 ), general financial revenue (X 2 ), total energy consumption per unit GDP (X 4 ), financial expenditure for environmental protection (X 5 ), NOx emissions (X 6 ), SO 2 emissions (X 7 ) and smoke dust emissions (X 8 ) are important factors affecting the PV power generation efficiency. Among them, real GDP per capita (X 1 ), general financial revenue (X 2 ) and financial expenditure for environmental protection (X 5 ) have a significant positive correlation with PV power generation efficiency, whereas total energy consumption per unit GDP (X 4 ), NOx emissions (X 6 ), SO 2 emissions (X 7 ), and smoke dust emissions (X 8 ) have a significant negative correlation with PV power generation efficiency. The regression results can just externally verify the reliability and rationality of the evaluation results in Section 4.
Real GDP per capita (X 1 ) and general financial revenue (X 2 ) can reflect the economic development of the region to a certain extent. In general, the more developed regions have sufficient funds for the construction of PV power plants, and the more conditional they are for policy subsidies and support. For example, developed regions in East China, such as Shanghai, Jiangsu, Zhejiang, and Anhui, tend to have higher PV power generation efficiency. Total energy consumption per unit GDP (X 4 ) can reflect the comprehensive energy efficiency of a region. The larger the index value is, the higher the dependent extent of economic development on energy and the lower the comprehensive energy utilization efficiency. Although regions such as Gansu, Qinghai, and Ningxia have abundant resources, the overall energy utilization rate is still low. The phenomenon of light discard is widespread, and the PV power generation efficiency has not reached the ideal state, which is relatively low. In addition, the financial expenditures for environmental protection (X 5 ), NOx emissions (X 6 ), SO 2 emissions (X 7 ), and smoke dust emissions (X 8 ) are all related to the degree of environmental protection. The greater the investment in environmental protection in a region is, the less the emission of pollutants such as NOx, SO 2 , and smoke dust is, and the higher the PV power generation efficiency will be. In areas with severe air pollution, solar radiation and penetration are weak, so the output of solar PV power generation equipment in these areas are low. As shown in Table 5, the efficiency of PV power generation in Heilongjiang, Jilin and Liaoning is relatively low due to serious pollution. As Northeast China is a traditional heavy industry base, its economic development mainly depends on heavy industry, and the transformation and upgrading of the resource structure has not been completed yet.

Discussion and Conclusions
From the calculation and analysis results in Section 4, it can be observed that China's PV power generation industry developed relatively well from 2013 to 2017, with an average efficiency of about 0.6605. From 2013 to 2017, the overall efficiency of PV power generation shows an upward trend, but in 2016 it declined slightly, probably due to the national policy of reducing PV feed-in tariffs.
From the perspective of the six major regions of the country, the PV power generation efficiency in East China is the highest, which is about 0.75. The PV power generation efficiency in the Central South China, Southwest China, North China, and Northwest China ranked from second to fifth respectively, which are in a range from 0.6 to 0.7. The PV power generation in Northeast China has the lowest efficiency, of approximately 0.48, just below 0.5.The results show that the development of China's PV power generation industry has obvious regional differences, which are caused by various factors such as economy, policy, resource endowment, and technical conditions, among others.
From the calculation results of PV power generation efficiency of the 30 regions, this unbalanced development among regions is more obvious. The following Figure 7 shows the categorizations of light intensity and comprehensive efficiency of the 30 regions. The value of effective sunshine duration of each region in the past five years is averaged and then normalized to obtain the light intensity. The efficiency value on the ordinate axes refers to the comprehensive efficiency value, which is calculated by the integrated FAHP−DEA model. Both the horizontal and ordinate axes are chosen to fall at 0.6, which is approximately the mean value.
To further optimize the development layout of China's PV power generation industry and improve the efficiency of PV power generation, several policy suggestions are proposed at the regional level, as follows: To further optimize the development layout of China's PV power generation industry and improve the efficiency of PV power generation, several policy suggestions are proposed at the regional level, as follows: From the classification results of Figure 7, the 30 regions can be divided into four categories, which from the first to the fourth quadrant are high-high (high light intensity, high efficiency), low-high (low light intensity, high efficiency), low-low (low light intensity, low efficiency), and high-low (high light intensity, low efficiency), respectively.
The high-high group includes 10 regions such as Shandong, Inner Mongolia, Shanxi, Hebei, Xinjiang, Shanghai, Yunnan, Henan, Shaanxi, and Ningxia. These areas have abundant light resources and high PV power generation efficiency.
For the high-high group, the abundant light resources in these regions have been fully utilized, and the PV power generation efficiency is high. In the future development process, these regions should continue to use their own advantages and avoid problems such as light discard. At the same time, these regions should rationally control the pace of industrial development, avoid blind scale expanding, and strive to further improve regional PV power generation efficiency from both technical and non-technical perspectives.
The low-high group includes Anhui, Guangdong, Guizhou, Jiangsu, Hubei, Zhejiang, Fujian, From the classification results of Figure 7, the 30 regions can be divided into four categories, which from the first to the fourth quadrant are high-high (high light intensity, high efficiency), low-high (low light intensity, high efficiency), low-low (low light intensity, low efficiency), and high-low (high light intensity, low efficiency), respectively.
The high-high group includes 10 regions such as Shandong, Inner Mongolia, Shanxi, Hebei, Xinjiang, Shanghai, Yunnan, Henan, Shaanxi, and Ningxia. These areas have abundant light resources and high PV power generation efficiency.
Energies 2020, 13, 1936 19 of 26 For the high-high group, the abundant light resources in these regions have been fully utilized, and the PV power generation efficiency is high. In the future development process, these regions should continue to use their own advantages and avoid problems such as light discard. At the same time, these regions should rationally control the pace of industrial development, avoid blind scale expanding, and strive to further improve regional PV power generation efficiency from both technical and non-technical perspectives.
The low-high group includes Anhui, Guangdong, Guizhou, Jiangsu, Hubei, Zhejiang, Fujian, Sichuan, Jiangxi, and Guangxi. Although the light resources in these areas are not abundant enough, PV power generation is highly efficient with economic, technical, and policy support.
For the low-high group, the development of the PV industry in these regions relies mainly on economic and policy support. Therefore, policy makers should continue to give support to these regions at the economic and policy levels, such as local subsidies and tax incentives. Besides, the government should strive to promote technological innovation and effective transformation of technological and scientific achievements in order to be able to further reduce the cost of solar PV power generation.
The low-low group includes Hunan and Chongqing, which have fewer light resources and lower PV power generation efficiency. For the low-low group, the exterior environment of the PV power generation industry should be optimized. The governments should improve the economic development and strengthen the policy support to transform to the low-high group. Because the PV industry is a highly policy-dependent industry, the supporting policies are conducive to stimulating its development.
The high-low group includes Gansu, Liaoning, Beijing, Qinghai, Hainan, Jilin, Heilongjiang, and Tianjin. The sunlight resources in these regions are abundant, but the efficiency of PV power generation is low. For the high-low group, the development of the PV industry in these regions has not reached the ideal level, and several light resources have not been fully utilized as yet. The main reason is that the pollutants such as SO 2 , NOx, and smoke dust are excessively discharged, resulting in insufficient sunlight penetration, which greatly reduces the generation efficiency of the PV power station. Thus, local governments should pay great attention to environment protection and energy utilization so as to transform to the high-high group.
Finally, China should formulate a more scientific and rational development layout of the PV power generation industry, and timely adjust it according to the development trend. The most important aspect is that the government should formulate regionally specific, targeted, and implementable support policies based on the specific conditions of different regions to increase the PV power generation efficiency effectively. Under the dual benefits of national policy dividends and regional support, efforts should be made to improve the local PV power generation efficiency and promote the development of renewable energy, which could finally contribute to the upgrading of the country's energy resources, and the energy structure transformation. This paper adopts the integrated FAHP-DEA model to measure the PV power generation efficiency of the 30 regions in China considering the regional differences, which is a creative solution for PV power generation efficiency measurement. However, we could do more in the future. One limitation of this study is that the interactions among the variables in the FAHP-DEA model haven't been fully considered. It is possible that some variables are correlated, and the analytic network process (ANP) method maybe more appropriate. What's more, the DEA results might be affected by the inputs and outputs included in the model. We leave this to future research and look forward to seeing more extensions.    Table A1. Triangle fuzzy numbers [21].

Sub-Criteria Sub-Criteria Description References
Environmental responsibility SO 2 emissions The quality of SO 2 emitted by power generation. [32,33] NOx emissions The quality of N 2 O, NO, NO 2 , N 2 O 3 , N 2 O 4 and N 2 O 5 emitted by power generation. [21,33] Smoke dust emissions Quantity of particles with certain size emitted by power generation fuel. [21,33] Financial expenditure for environmental protection Local government expenditure for protecting environment which mainly includes expenditure on environmental monitoring, expenditure on pollution control, expenditure on pollution reduction, etc. [34,35] Policy and economic support Real GDP per capita Divide the gross domestic product achieved during the accounting period (usually one year) of a country or region by the number of permanent residents of the country or region. [36,37] General financial revenue Monetary funds collected by a country or region through certain forms and channels, mainly including various taxes, special income, other income, etc. [36,38] Benchmark price Considering the current cost and reasonable profit of PV power generation, PV power plants sell electricity to grid companies at this price. [39,40] Regional subsidy Relevant financial subsidies invested by local governments to support the development of local PV industry. [41,42]

Sub-Criteria Sub-Criteria Description References
Technical and natural conditions Total employment in electricity industry Number of people working in the power industry in a certain region. [1,43] Investment in fixed assets in electricity industry The amount of work and the costs associated with the construction and acquisition of fixed assets in the power industry for a certain period of time in monetary terms. [28,38] R&D in electricity industry Research and experimental development (R&D) personnel full-time equivalent. [17,28] Effective sunshine duration Number of effective hours of annual illumination calculated from optimum angle of incident light and radiation time. [44,45] Appendix C