Performance efficiency assessment of photovoltaic poverty alleviation projects in China: A three-phase data envelopment analysis model

Energy 159 (2018) 599e610

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Performance efficiency assessment of photovoltaic poverty alleviation projects in China: A three-phase data envelopment analysis model Yunna Wu a, b, Yiming Ke a, b, *, Ting Zhang a, b, Fangtong Liu a, b, Jing Wang a, b a b

School of Economics and Management, North China Electric Power University, Beijing, PR China Beijing Key Laboratory of New Energy and Low-Carbon Development, Beijing, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 March 2018 Accepted 26 June 2018 Available online 27 June 2018

Based on the idea of coordinated and sustainable development, the photovoltaic poverty alleviation project (PPAP) supplies clean electricity and assists poverty-stricken households, which receives widespread attention from the society. However, the existing efficiency assessment models can neither well consider both the economic and social benefits of the PPAP nor provide pertinent site selection suggestions. To accurately evaluate the performance efficiency and explore the influencing factors, a modified three-phase model is proposed: First of all, a two-step approach combining Pearson correlation coefficient and super-efficiency analysis is adopted to screen out unreasonable variables and outliers, which improves the reliability of subsequent calculations; Next, the bootstrapping algorithm is introduced to optimize the data envelopment analysis model, which effectively corrects the bias and guarantee the model accuracy; Finally, the potential environment variables are extracted from both the electricity conversion process and the poverty alleviation procedure, and further verified by Tobit regression, which provides managers with more comprehensive decision support. According to the results, the performance efficiency of PPAPs in China is generally low due to the unreasonable production scale. Most projects are suffering excessive labor input. Moreover, improper site selection is also a cause for low efficiency, and some corresponding suggestions are proposed. © 2018 Elsevier Ltd. All rights reserved.

Keywords: Efficiency assessment Photovoltaic poverty alleviation project Data envelopment analysis Bootstrap Tobit

1. Introduction With the continuous development of social economy, gradually emerging environmental problems and increasingly intensive energy supply and demand contradictions have seriously hindered people from pursuing a better life. Due to the environmentalfriendly, recycling and renewable advantages, photovoltaic power generation is regarded as one of the most promising energy conversion mode and receives great support from all walks of life [1]. According to energy statistics, solar photovoltaic power supply has increased year by year, and the photovoltaic net installed capacity reached 220.2 GW in 2015 [2]. As a developing country with considerable potential in photovoltaic power generation, China manages to reduce the poverty rate while solving the energy crisis. For the reasons above, China combined photovoltaic power generation with the precision poverty alleviation target and formally

* Corresponding author. School of Economics and Management, North China Electric Power University, Beijing, PR China. E-mail address: [email protected] (Y. Ke). https://doi.org/10.1016/j.energy.2018.06.187 0360-5442/© 2018 Elsevier Ltd. All rights reserved.

launched the first PPAP in 2014 [3]. Fig. 1 shows the installed capacity of photovoltaic generation and the poverty-stricken population in China from 2010 to 2016 [4]. During the 7 years, the cumulative installed capacity of solar photovoltaic generation kept increasing, and a remarkable wave of photovoltaic generation in 2013 lays the technical and practical foundation for the proposal of the PPAP. Moreover, as expressed in the picture, it was not until 2014 that the poverty alleviation rate recovered and started to keep increasing, which is in accord with implementation time of PPAPs. PPAPs can be divided into two common modes: one is that with the help of government guarantee and supporting policies, the poor households get a loan from credit cooperatives or banks and then complete installation, operation and maintenance independently; the other is that power enterprises or interest groups take responsibility for the village-level power station and help the poor with a certain electricity sale income. Compared with the household photovoltaic mode, the village-level photovoltaic poverty power station has the advantages of high power quality, grid connected safety, stable income and favorable poverty alleviation efficiency, thus receiving rapid promotion in recent years. However,

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Y. Wu et al. / Energy 159 (2018) 599e610

Fig. 1. Photovoltaic power capacity and poverty-stricken population in China (2010e2016).

since the PPAP started late in China, the corresponding supervision experience and management system has not yet been mature, which brings difficulties in identifying inefficient projects and relieving subsidy pressures. Therefore, it is imminent to make an effective assessment for PPAP operational performance efficiency. This paper aims at exploring a PPAP efficiency assessment method with high precision, so as to identify undesirable projects and figure out potential external influencing factors effectively. The main contributions are as follows: First, since few researches focus on the PPAP performance efficiency assessment, this study can enrich the literature materials and perfect the related theoretical system; Next, the overall ranking and the efficiency score analysis can not only offer government supervision departments a list of troubled projects, but also point out the resource waste situation and the corresponding improvement direction; Last but not least, the potential efficiency influencing factors in both natural and social environment are further analyzed, which may assist policy makers and project managers in making better decisions, such as determining the site selection or the investment scheme. Possible innovations can be summarized in three parts: First, a two-step approach combining Pearson correlation coefficient and superefficiency analysis is adopted to screen out unavailable data and outlier decision making units (DMUs), which can improve the reliability and rationality of the efficiency assessment model; Second, due to the fact that the PPAP started late in China and most project data has not been announced yet, introducing the bootstrap method to optimize the conventional efficiency assessment model can effectively reduce the deviation caused by small samples and guarantee the model accuracy; Third, taking into account the whole life cycle of the PPAP, including the power conversion process and the poverty alleviation process, this paper extracts potential influencing variables from both the natural environment and the social environment so as to provide managers with more comprehensive decision support. The remainder of this study is organized as follows: Section 2 briefly probes the research situation of production efficiency assessment and some relative processing techniques regarding with PPAP features. Section 3 interprets the research framework and main methods. Section 4 explains variable definitions and the data sources. Section 5 carries out the efficiency assessment on 30 PPAPs in China and analyzes the uncontrollable factors on this basis. Finally, Section 6 draws a conclusion. 2. Literature reviews The production efficiency assessment of a power generation project can identify the input redundancy, the output insufficiency

and the influencing factors, and further point out the efficiency improvement direction, which is favored by many decision-makers. At present, mainstream production efficiency models can be divided into two categories: the stochastic frontier analysis based parametric analysis model [5] and the data envelopment analysis based nonparametric assessment model [6]. Compared with stochastic frontier analysis, the latter model can work out efficiency scores under the “multiple inputs and outputs” environment without knowing the production frontier function [7]. And electric power production projects tend to involve many factors and complex interactions, which makes it difficult to determine the specific production function. Therefore, many scholars adopt the DEA-based models to analyze the production efficiency of power generation projects and obtain scientific conclusions: i) Thermal power projects: Using data on generator capacity, operation expenditure, net generation and sulfur dioxide emissions, Liu et al. [8] evaluate cross efficiency of 23 typical coal-fired power plants and effectively deal with the issue of the undesired output calculation. Treating pollutants as the cohesion, Bi et al. [9] divide the coal fired generation system into two subprocesses, including the production subprocess and the pollutant abatement subprocess, and further employ a two-stage network DEA model to realize the performance assessment of 28 observed DMUs, which well satisfies the emission reduction requirements of conventional energy generation projects. ii) Wind power projects: Wu et al. [10] select three inputs and two outputs to evaluate the production efficiency of China’s wind farms and further utilize the Tobit model to figure out the actual impacts of uncontrollable variables, such as age, wind curtailment rate and dummy for group. Similarly, based on the DEA efficiency evaluation and the Tobit regression results of 39 States’ Wind Power, Ümit
lam [11] concludes the current situation of wind power industry Sag in America and explores the improvement direction, which provides a reasonable reference for practitioners and decision-makers.
lam [12] simplifies the input and output variables Later, Ümit Sag and further quantitatively measures the relative operational performance efficiency of 236 large utility-scale wind farms by conducting a multi-criteria decision-making tool. Based on data of 95
lam [13] employs large utility-scale wind farms’ operation, Ümit Sag DEA models to evaluate relative performance efficiency by computing pre-determined variables, and subsequently conducts Tobit regression to figure out the reasons for production inefficiency. iii) Photovoltaic power projects: Toshiyuki and Goto [14] draw a comparison on performance efficiency among 160 photovoltaic power stations in Germany and the United States from the perspective of solar energy and land use and further discuss policy issues regarding cost allocation based on the DEA results. Further, they discuss how to classify the type of Returns to Scale in the DEA production analysis framework and explore the reasons for inefficient operation based on data of large photovoltaic power stations in American and German [15]. Liu, Long and Song [16] incorporate panel data from 2005 to 2015 of China’s photovoltaic power generation into the super-efficient data envelopment analysis model and propose political suggestions on the operation optimization and management improvement. Denoting annual average irradiation, annual average temperature, number of modules, total cost as inputs while capacity and electricity generation as outputs, Wang and Sueyoshi [1] use the nonparametric DEA approach to evaluate the performance efficiency of 855 large commercial rooftop photovoltaic installations in California. Later, they conduct a detailed analysis of operation inefficiency from the perspective of the scale efficiency and returns to scale [17]. Taking nameplate capacity, photovoltaic panel area, insolation, daylight hours and net generation as the basic parameters in the slack based DEA model, Wang et al. [18] provide the objective production performance

Y. Wu et al. / Energy 159 (2018) 599e610

assessment of 70 American photovoltaic power plants considering environmental impacts, including temperature, cloud amount, elevation, wind speed and precipitation. A brief summary of the above studies is listed in Table 1. Unlike the aforementioned power generation projects, the PPAP has the social characteristics of supporting poor households besides the solar electricity conversion. Therefore, the social environment should be considered during the efficiency assessment algorithm. In addition, in view of the late start of PPAPs in China, available data is scattered and the sample size is relatively small, so it is necessary to add the data screening program and the bias correction process to traditional DEA-based models. There are some literature concerning data preprocessing and small sample processing at present: i) Data screening programs: “peer count index” [19] and “superefficiency” [20] are both popular outlier detect programs. Compared to the first method, the “super-efficiency” model, whose principle is computing the adjustable degree of an efficient unit in the case that the efficiency score is kept unchanged, is suitable to act as the pretreatment process of DEA-based models [21]. Besides, since the obvious linear relationship among inputs/outputs will cause assessment bias in DEA models, correlation analysis methods like Pearson correlation coefficient are frequently adopted to identify the unjustified variables [22]. ii) Bias correction processes:

601

the bootstrap method [23], based on the resampling idea, allows researchers to make effective deviation correction without knowing the distribution of data. Jebali, Essid and Khraief [24] employ the double bootstrap algorithm to work out the bias and the confidence interval of efficiency scores, and further examine the energy efficiency determinants according to Mediterranean countries’ data from 2009 to 2012. Fernandes, Stasinakis and Bardarova [25] illustrate that the bootstrapping procedure can effectively weaken the impacts resulting from the high serial correlation in the ordinary DEA model and ensure the statistical interpretability as well as the valid assessment. 3. Methodology To assess the performance efficiency and identify the influencing variables in PPAPs, a three-phase DEA model based on the bootstrap approach is employed. The research framework is shown in Fig. 2 and concrete processes are introduced in the following subsections. 3.1. Phase one: model pretreatments As a vital step in the pretreatment phase, model determination

Table 1 A brief summary of the researches on efficiency assessment of power generation projects. Research objects

Author(s)

Models

Thermal power projects

Liu et al. [8]

Cross-efficiency DEA model

Bi et al. [9]

Two-stage network DEA model

Wu et al. [10]

DEA-Tobit


lam [11] Ümit Sag

DEA-Tobit


lam [12] Ümit Sag

DEA-Tobit


lam [13] Ümit Sag

DEA-Tobit

Sueyoshi and Goto [14,15]

DEA

Liu, Long and Song [16]

Super-efficient DEA model

Sueyoshi and Wang [1,17]

DEA

Wang et al. [18]

DEA

Wind power projects

Photovoltaic power projects

Indicators Inputs Generator capacity Operation expenditure Installed capacity Labor force Coal consumption Operation expense Installed capacity Auxiliary electricity Wind power density Installed capacity Wind turbine quantity Total investment Annual land payment

Outputs Net generation SO2 emissions Power generated SO2 removed

Installed capacity Wind turbines Wind power density Installed power capacity Number of wind turbines Wind power density Insolation Average annual sunshine Photovoltaic modules Land area Installed capacity Utilization hours Power investment Operating cost Covering area Energy replacement rate Production centralization Annual average irradiation Annual average temperature Number of modules Total cost Nameplate capacity PV panel area Insolation Daylight hours

Generated electricity Value of production Homes powered Generated electricity Capacity factor

Electricity generated Availability

Net Generation In-State Production percentage Equivalent U.S. homes powered Industry employment Annual water savings CO2 emissions avoided

Installed capacity Annual power generation

On-grid electricity

Capacity Electricity generation

Net generation

602

Y. Wu et al. / Energy 159 (2018) 599e610

Obtained data

The removals: Redundant indicators; Outlier DMUs

Phase One: Model pretreatments the suitable methods the available data

Phase Two: Bootstrap-DEA efficiency analysis

management inspiration

Efficiency rankings Returns to scale Slacks

Determine the improvement direction

Sensitivity analysis

Acquire the priority strategies

Natural environment effect Social environment effect

Provide reference for project site selection

the efficiency scores External variables

Phase Three: External factors analysis

Fig. 2. A flow chart description of the research framework.

will directly affect the effectiveness and the accuracy of efficiency assessment. Comprehensively considering assessment conditions and requirements, we follow four items to select the assessment model (see Fig. 3): whether the calculation form of production frontier is known; the form of inputs and outputs is single or multiple; the main purpose is to reduce inputs, to increase outputs or both the former two; whether the sample meets the model requirement. Then, we adopt a data screening model which contains two aspects. One t is to pick out suitable inputs/outputs and the other is to detectoutlier DMUs. Since significant linear correlation in the input/output set can reduce assessment accuracy and analysis ability of the model, it is necessary to carry out the correlation analysis. The Pearson correlation coefficient, ranging from
1 to 1, is widely used to measure the correlation degree between two variables in statistics, and its calculation equation is described as follows [26].

rX;Y ¼

covðX; YÞ

sx sy

sx sy

(1)

where X and Y are two data sequences, covðX; YÞ is the covariance and sx is the standard deviation of X: When the absolute value of Pearson correlation coefficient is equal to 1, there is a positive or negative linear correlation between X and Y: When rX;Y ¼ 0; the data sequences are independent. Meanwhile, the DMU outliers will greatly reduce the estimation accuracy and should be eliminated in the subsequent analysis [27]. Due to the limited number of the observed units, we employ the “super-efficiency” method to detect the outlier DMUs based on the convention that the DMUs whose efficiency scores are over 2.5 should be regarded as an outlier [28]. In a “super-efficiency” model, the DMU linear combination excludes the assessing unit during the unit performance assessment, for which the efficiency scores can exceed 1. Hence, its dual model can be defined as follows [29].

Negative or zero value Missing values

¼



E ðX
mx Þ Y
my

Function form

The number of variables Small sample

Model determination Returns to scale Slacks Input-oriented or output-oriented

Fig. 3. A fishbone diagram for model selection.

Y. Wu et al. / Energy 159 (2018) 599e610

m X

minqk
ε

s
ik þ

xij lj þ

s
ik

[35] and ε*k represents a random error from the standard normal distribution.

! sþ rk



r¼1

i¼1

n X

s X

¼ qk xik ; i ¼ 1; 2; ,,,; m

j¼1 jsk

(2)

n subject to X

xrj lj
sþ ¼ yrk ; r ¼ 1; 2; ,,,; s rk

*

þ s
ik  0; srk  0; lj  0

where the subscript k is the index of the assessed DMU; the subscripts i and r are the serial number of inputs and outputs, respectively; q is the performance efficiency and ε is an infinitesimal positive number. x and y stand for the amount of inputs and outputs. 3.2. Phase two: Bootstrap-DEA efficiency analysis The data envelopment analysis method, a linear non-parametric technique for multiple inputs and outputs, can assess the performance efficiency of each unit when the production frontier function is vague [30]. Owing to their simplicity and practicability, the basic DEA models, including the CCR and BCC models, have been widely applied in energy sectors [31]. The dual models of the CCR and BCC models are presented as follows.

minqk
ε n X

i¼1

xij lj þ

j¼1 n X

subject to

s
ik

s
ik

þ

s X

! sþ rk

r¼1

j¼1

d

n X

where qk is a scalar which expresses the performance efficiency of the kth DMU and lk ; indicating the DMU weights, is a set of intensity variables; d is a model coefficient and determines whether the model is in assumption condition of constant returns to scale: when d ¼ 0; the equation is the CCR model; when d ¼ 1; it is the BCC model. However, the efficiency scores in most DEA-based researches may be biased due to the universal existence of random errors [32]. Be capable of distinguishing the efficiency differences and offering confidence intervals for the performance assessment, the bootstrap approach effectively reduces the random error impacts and improves the efficiency evaluation accuracy with a small sample [33]. The bootstrap-DEA algorithm is concluded as follows [34]. Step 1 Estimate the performance efficiency vector b q ¼ ðbq 1 ; bq 2 ; ,,,; b q n Þ of each PPAP fðxk ; yk Þ; k ¼ 1; ,,,; nÞg based on Eq. (3). Step 2 Generate a resample vector b* ¼ ðb*1 ; b*2 ; ,,,; b*n Þ from the original one b q ¼ ðbq 1 ; bq 2 ; ,,,; bq n Þ Step 3 Obtain smoothed estimates through the following formula:

b*k þ hε*k ; * 2
bk
hε*k ;

if b*k þ hε*k  1 otherwise

Step 5 Generate a pseudo-data set fðx*k ; yk Þ; k ¼ 1; ,,,; nÞg by x*k ¼ b q k =*q*k and* further compute the bootstrap replica esti* * mates b q k ¼ ðbq 1 ; bq 2 ; ,,,; bq n Þ by the DEA model. Step 6 Repeat the steps 2e5 several times to obtain a set of boot* strap estimates b q k;b ; and the subscript b refers to the number of bootstrap times. The B value should be over 1000 in general when the q centered confidence interval is estimated [36]. To guarantee the validity of bias correction, we use B ¼ 2000 in this study. ^ * P Step 7 Get the bias from q k ¼ 2b q k
ð1=NÞ Nb¼1 bq k;b and construct the ð1
a%Þ confidence interval by the following equations.

! * b b Prob
ba  q
q 
aa ¼ 1
a ! b Prob
ba  q
q 
aa z1
a

(6)

3.3. Phase three: external factors analysis

lj ¼ d; d ¼ 0; 1

j¼1

(

(5)

(3)

þ s
ik  0; srk  0; lj  0

* ~ qk ¼

*

b q þ aa  q  bq þ ba

¼ qk xik ; i ¼ 1; 2; ,,,; m

xrj lj
sþ ¼ yrk ; r ¼ 1; 2; ,,,; s rk

Step 4 Let b be the mean value of the vector b* ¼ ðb*1 ; b*2 ; ,,,; b*n Þ and b s 2 be the variance of the vector bq ¼ ðbq 1 ; bq 2 ; ,,,; bq n Þ; and then correct the smoothed estimates by the following equation:

~ * qi
b q*k ¼ b þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi 2 1þh sb 2

j¼1 jsk

m X

603

(4)

where h is a bandwidth parameter of the kernel density estimation

To analyze the real effect of external variables, many studies treat the assessed efficiency scores as a dependent variable in a regression [37]. However, the estimates q are censored and ranges from 0 to 1. Therefore, with the feature of handling the censored dependent variables, the Tobit regression model is widely adopted in the DEA-based subsequent analysis [38]. The Tobit model is stated as follows [39].

y*i ¼ b zi þ mi ; i ¼ 1; 2; ,,,; n y*i ; if 0  y*i  1 yi ¼ 0; otherwise

(7)

where y*i is the latent dependent variable and yi is the efficiency estimate from the previous phase for the ith PPAP; zi and b are the vectors of explanatory variables and the estimated parameters, respectively; the symbol mi represents the error term which satisfies the normal distribution. Nð0; s2 Þ: The central limit theorem holds that the error term belongs to a normal distribution when the sample size is large enough [40]. However, restricted to the lack of practical experience or data acquisition capacity, the sample size is often limited. Therefore, the bootstrap regression model is proposed to improve the analysis accuracy in the case of small sample. There are two common bootstrap regression models [41]: one is to resample the units and the other is to resample the residuals. Considering the error structure of the regression model, we use the latter model, and the concrete algorithm is as follows [42].

604

Y. Wu et al. / Energy 159 (2018) 599e610

Step 1 Regress q ¼ ðq1 ; q2 ; ,,,; qn Þ on the explanatory variables Z ¼ ðZ1 ; Z2 ; ,,,; Zp Þ and compute estimates b* and m*ε by Eq. (7). b ¼ b*  Z: Then let Y Step 2 Obtain a resample vector m*b ¼ ðm*1b ; m*2b ; ,,,; m*nb Þ: Step 3 Generate a pseudo-data set fðzi ; y*i Þ; i ¼ 1; ,,,; nÞg by b * by y*i ¼ b y þ m*ib and further compute the replica estimate b i Eq. (7). Step 4 Repeat the steps 2e3 (B ¼ 2000) times and obtain a set of * bootstrap estimates b b i;b ; P * ~ b* Step 5 Get the bias from bi ¼ 2bi
ð1=NÞ N b¼1 b i;b and construct the ð1
a%Þ confidence interval by the following equations.

! b *
b* 
a
ba  b a ¼1
a 
* Prob
ba  b
b 
aa z1
a

Prob

(8)

b* þ aa  b  b* þ ba

Taking into account data availability and previous researches, we treat the following four variables as the independent variable in the regression model from the natural environmental aspect: Annual average temperature (Z1): The variable is based on the mean value of the ambient air temperature at the project site in one year; Annual rainfall (Z2): The variable refers to the total amount of rainfall over a year; Daylight cloud amount (Z3): It describes the cloudiness during the day in a certain area. Moreover, we regard the following three as the independent variable from the social environmental aspect. Power demand (Z4): It indicates the difference between the power generation and the electricity consumption in a region, which determines the quota of on-grid electricity of a project; Poverty-stricken population (Z5): The variable refers to the number of poverty villagers in a region according to the poverty standard that annual income is less than 2800 CNY (equal to 430.35 USD) per year. 4.2. Statistical analysis

4. Variables and data 4.1. Variable description Appropriate selection of the input and output variables is an important prerequisite to assess the PPAP performance with DEA models [43]. Taking the availability and applicability of variables into account, we eventually pick out three input variables and two output variables: Installed capacity (1): This indicator means the total nameplate capacity of photovoltaic modules. As the fundamental attribute of a generation system, the installed capacity largely determines the number of photovoltaic modules, the covered area, auxiliary power consumption and the project cost, which reflects the generating scale and the capital input. Labor quota (2): The parameter represents the total number of operators in a PPAP. With the restriction of the project information level and project experience, it is necessary to employ professional personnel to ensure healthy and stable power generation. However, a large number of operators will increase the burden of domestic waste discharge, water consumption and salary costs. Annual solar radiation (3): This variable refers to the total amount of solar radiation per unit area in one year. As the most important factor in PV generation, the insolation largely determines the actual amount of fuel input in the assumption that all PV arrays are installed with the optimum tilt angle, azimuth and spacing. Annual power generation (Y1): The index stands for the actual amount of electricity provided by a PPAP in one year. The total generated electricity is widely accepted as a desirable output, which expresses the production level and the profit space of a power generation project. Poverty reduction (Y2): The variable describes the number of poverty households supported by a PPAP. Regarded as another desirable output, it reveals the poverty alleviation target achievement and the social value of the project. Besides, some external factors indirectly affect the performance efficiency of PPAPs by limiting optoelectronic conversion or profit. Judging from the variable characteristics, we divide them into two categories: the natural environmental factor and the social environmental factor. Annual mean wind speed, a natural environmental variable which stands for the average value of the instantaneous wind speed within one year, is proved to have no effect on photovoltaic generation performance efficiency [18] and thus is not considered in this study.

Due to data availability and completeness, 42 PPAPs are selected as DMUs in the assessment model, which covers 12 provinces including Inner Mongolia, Anhui, Jilin, Hebei, Shandong, Shanxi, Gansu, Shaanxi, Jiangsu, Hunan, Sichuan and Guangdong. The input-output data of the observed PPAPs originate from publicized environmental impact assessment reports which are audited by Municipal Environmental Protection Ministry. According to the longitude and the latitude of the project location, we look for the natural environment data like environment temperature, precipitation and cloudiness in the NASA database. Moreover, data of energy demand are extracted from China Statistical Yearbook, while data of poverty-stricken population are obtained from county-level government work reports. Table 2 illustrates the descriptive statistics of the observed data in 2016. The sample in this study meets the convention that the number of observed DMUs should not be less than three times of the sum number of input and output variables because 42 > 3  (3 þ 2) [44]. 5. Results and discussion 5.1. Model pretreatments The PPAP efficiency assessment is a typical issue containing multiple inputs and outputs with the unclear defined production frontier. Moreover, limited to the power generation quota and the poverty alleviation requirements, photovoltaic enterprises pay more attention to the project performance efficiency in the case of the given outputs. Therefore, this study applies the radial inputoriented DEA model, in which the inefficiency units are measured

Table 2 Descriptive statistics of inputs, outputs and external variables. Variables

1 2 3 Y1 Y2 Z1 Z2 Z3 Z4 Z5

Descriptive statistics Units

Minimum

Maximum

Mean

Standard deviation

MW

1.25

100.00

28.43

22.29

Person

2.00

20.00

8.76

3.81

MJ/m2$a

4686.00

6404.35

5166.43

323.56

106 kW h Household  C mm % 109 kW h %

1.54 400.00 1.50 59.90 48.20 66.76 0.48

109.80 6772.00 20.70 1768.90 72.60 561.01 38.3

35.51 1928.86 10.31 604.41 56.91 256.12 9.55

27.78 1430.00 4.81 362.24 5.97 166.11 7.48

Y. Wu et al. / Energy 159 (2018) 599e610

by proportionally cutting down inputs under the condition of no output reduction. To ensure appropriate index dimensions and the objective efficiency assessment, we screen the input and output variables according to their correlations. Table 3 lists the Pearson correlation coefficients calculated by Eq. (1). Since there are no significant linear correlations in the selected input/output sets, the variables can satisfy the demands and no additional processing are required. Acting as peers to other units, the outlier DMUs can have an great effect on the assessment accuracy of the DEA model [45]. Fig. 4 shows the super-efficiency scores of the DMUs as well as the alert line for the outliers in the outlier determination process. According to the calculation, the maximum super-efficiency score is 1.66 that is smaller than the alert value of 2.5. The “super-efficiency” approach verifies that no outlier PPAPs exist in the sample, so all the observed DMUs are included in the subsequent analysis.

5.2. Efficiency analysis Table 4 records the efficiency distribution before and after the bootstrap algorithm for the observed DMUs. The overall efficiency (OE) scores of the observed PPAPs range from 0.320 to 0.790 after the bootstrapping, where the mean score is 0.599 and the median score is 0.610. In the bias-corrected model, no PPAPs realize efficient production, and over a quarter of projects operate in the worrying condition where their efficiency scores are all under 0.5. Therefore, electricity generation productivity and poverty alleviation situation are far from satisfactory and it is necessary to explore reasons for inefficiency. OE can be divided into two parts: one is decided by the management and technical level, and the other is reflected by the gap between the actual scale and the optimal productive scale. From the overall point of view, the pure technical efficiency (PTE) scores of most assessed units exceed 0.900, which implies the observed projects possess a favorable management and technical condition. Meanwhile, the scale efficiency (SE) scores are relatively low with a range from 0.358 to 0.914, which indicates the projects do not operate on the optimal scale and there is still a lot of room for the productive scale adjustment. Due to the existence of the inefficient productive scale, the OE scores are unsatisfactory and significantly less than the PTE scores. Therefore, decisionmakers should take measures to narrow the gap between the actual scale and the optimal one for comprehensive production performance improvement. By the contrast of the computing results before and after the bootstrapping, there are differences lying in efficiency scores, rankings and scale returns. First, due to changes in production frontier caused by sample expansion, the bias corrected scores are less than the original efficiency ones. PTE in bias-corrected DEA models varies from 0.809 to 0.983 with a mean score of 0.917, while PTE in the traditional DEA model owns an average efficiency evaluation value of 0.945. Besides, the bias-corrected SE has a mean

Table 3 Correlation coefficients of the input and output variables. 1 1 2 3 Y1 Y2

2

3

Y1

Y2

1.000 0.223

1.000

1.000 0.403

1.000

0.016

0.256

1.000

0.914** 0.241

0.467* 0.084

0.095
0.206

Note: The superscripts ** (*) indicates that the correlation is significant at the 0.01(0.05) level.

605

Fig. 4. The “super-efficiency” scores in the outlier determination process.

score of 0.654, which is about 13% lower than the original SE. According to the original overall efficiency scores, DMU07, DMU14, DMU15, DMU18, DMU32, DMU36, DMU39 and DMU42 are assessed to be efficient and located at the optimal efficiency frontier. However, these projects are proved to be inefficient with the scores of 0.747, 0.775, 0.646, 0.731, 0.734, 0.723, 0.763 and 0.747, respectively. Second, as the ranking is determined based on the score size, the DMU ranking sequence is affected accordingly. Since the bias correction process is to obtain the real optimal frontier, the DMUs near the production frontier, especially the pseudo efficient DMUs, experience dramatical adjustment in their rankings, and the low-ranking DMUs remain basically unchanged. Thirdly, taking into account the relationship between productive scale and marginal revenue from absolute amount, the DEA results which are obtained with the assumption of the variable return to scale (RTS) belong to three forms: constant RTS, the increasing RTS and the decreasing RTS. The efficiency assessment of the original model suggests that except DMU07, DMU14, DMU15, DMU18, DMU32, DMU36, DMU39 and DMU42, the observed projects belong to the increasing RTS, that is, the 4 efficient DMUs do not need to add or reduce the photovoltaic component quantity and the scale of the rest 34 items should be further expanded to increase performance efficiency. However, the revised results do not support this conclusion and express that all projects are not run in the optimal scale, which is more in line with the actual situation. Both the original and bias-corrected results demonstrate that DMU05 performs the worst and ranks the last and its OE scores are 0.380 and 0.320, respectively. Its low efficient operation can be attributed to the following two aspects: One reason is that the energy conversion and utilization level is relatively backward; the other is that serious deviation appears in the size planning due to the inaccuracy of the condition assessment and the actual demand. Therefore, decision makers can replace the photovoltaic module with low conversion rate, introduce the advanced operation technology by recruiting outstanding technicians and adjust the production size based on more accurate planning so as to achieve efficiency improvement. The slack analysis for inputs can draw out the unreasonable parts of each decision unit and prevent excessive investment and waste of resources so as to improve the PPAP performance efficiency. As far as the DMUs whose efficiency scores are equal to 1 are concerned, the slack values emphasize the adjustment direction in the case that the outputs are not reduced and the inputs cannot be reduced proportionally. Meanwhile, for the inefficient DMUs, apart from ð1
qÞ times reduction in all inputs, the amount of each input should be adjusted in detail based on the slack scores to achieve the real efficient status. Table 5 shows the input slacks before and after the bootstrap algorithm for each PPAP. The correction parameters

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Table 4 The computing results of overall efficiency, pure technical efficiency and scale efficiency. DMUs

DMU01 DMU02 DMU03 DMU04 DMU05 DMU06 DMU07 DMU08 DMU09 DMU10 DMU11 DMU12 DMU13 DMU14 DMU15 DMU16 DMU17 DMU18 DMU19 DMU20 DMU21 DMU22 DMU23 DMU24 DMU25 DMU26 DMU27 DMU28 DMU29 DMU30 DMU31 DMU32 DMU33 DMU34 DMU35 DMU36 DMU37 DMU38 DMU39 DMU40 DMU41 DMU42 Mean Scores

Before the bootstrapping

After the bootstrapping

OE

PTE

SE

OE

PTE

SE

0.546(34) 0.514(37) 0.556(31) 0.543(36) 0.38(42) 0.404(41) 1(1) 0.743(18) 0.798(15) 0.592(27) 0.545(35) 0.508(38) 0.561(30) 1(1) 1(1) 0.81(12) 0.614(25) 1(1) 0.841(11) 0.855(10) 0.563(28) 0.743(19) 0.498(39) 0.803(14) 0.553(32) 0.804(13) 0.498(40) 0.769(16) 0.716(21) 0.552(33) 0.658(23) 1(1) 0.755(17) 0.603(26) 0.649(24) 1(1) 0.725(20) 0.711(22) 1(1) 0.927(9) 0.563(29) 1(1) 0.712

0.981(13) 0.975(18) 0.918(29) 0.882(39) 0.904(33) 0.899(35) 1(1) 0.896(37) 0.837(42) 0.936(23) 0.924(27) 0.921(28) 0.908(32) 1(1) 1(1) 1(1) 0.981(14) 1(1) 0.858(41) 0.939(21) 0.894(38) 0.932(24) 0.978(16) 0.938(22) 0.901(34) 0.928(26) 0.875(40) 0.908(31) 0.91(30) 1(1) 1(1) 1(1) 0.977(17) 0.897(36) 0.931(25) 1(1) 0.985(12) 0.978(15) 1(1) 0.964(19) 0.945(20) 1(1) 0.945

0.556(36) 0.528(39) 0.606(32) 0.616(30) 0.421(42) 0.45(41) 1(1) 0.83(16) 0.954(11) 0.632(26) 0.59(34) 0.552(37) 0.618(29) 1(1) 1(1) 0.81(17) 0.626(28) 1(1) 0.98(9) 0.91(12) 0.63(27) 0.797(18) 0.509(40) 0.856(14) 0.613(31) 0.867(13) 0.568(35) 0.847(15) 0.787(19) 0.552(38) 0.658(25) 1(1) 0.773(20) 0.672(24) 0.697(23) 1(1) 0.736(21) 0.726(22) 1(1) 0.962(10) 0.595(33) 1(1) 0.751

0.441(39) 0.474(36) 0.489(34) 0.482(35) 0.32(42) 0.346(41) 0.747(4) 0.653(17) 0.739(7) 0.547(25) 0.496(33) 0.454(38) 0.501(31) 0.775(2) 0.646(19) 0.713(14) 0.541(26) 0.731(11) 0.729(12) 0.74(6) 0.504(30) 0.658(16) 0.457(37) 0.734(9) 0.5(32) 0.736(8) 0.42(40) 0.683(15) 0.619(20) 0.504(29) 0.605(22) 0.734(10) 0.651(18) 0.522(27) 0.571(23) 0.723(13) 0.616(21) 0.549(24) 0.763(3) 0.79(1) 0.513(28) 0.747(5) 0.599

0.968(3) 0.959(7) 0.905(28) 0.872(39) 0.892(32) 0.891(33) 0.937(15) 0.876(37) 0.809(42) 0.914(24) 0.916(22) 0.907(27) 0.897(30) 0.937(13) 0.937(14) 0.936(17) 0.965(5) 0.937(12) 0.825(41) 0.913(25) 0.883(35) 0.917(21) 0.966(4) 0.907(26) 0.892(31) 0.904(29) 0.862(40) 0.888(34) 0.88(36) 0.983(1) 0.974(2) 0.935(18) 0.959(8) 0.872(38) 0.916(23) 0.939(11) 0.961(6) 0.952(9) 0.944(10) 0.933(20) 0.934(19) 0.937(16) 0.917

0.456(40) 0.494(37) 0.541(34) 0.553(31) 0.358(42) 0.388(41) 0.797(9) 0.745(16) 0.914(1) 0.599(24) 0.541(33) 0.501(36) 0.559(30) 0.827(4) 0.69(19) 0.763(15) 0.56(28) 0.779(12) 0.884(2) 0.811(6) 0.571(27) 0.717(17) 0.473(39) 0.809(7) 0.56(29) 0.814(5) 0.487(38) 0.77(14) 0.703(18) 0.513(35) 0.621(23) 0.785(11) 0.679(20) 0.598(25) 0.623(22) 0.771(13) 0.641(21) 0.577(26) 0.808(8) 0.847(3) 0.55(32) 0.797(10) 0.654

Note: The corresponding ranking is present in the parentheses beside the efficiency scores.

are derived from the gap between the original slack and the real redundancy, which is the correction of the deviation caused by the small sample through the bootstrap method. Inefficient units with no slack in inputs such as DMU02, DMU03 and so on need to reduce ð1
qÞ times in all inputs or increase outputs so as to achieve efficient production. It is worth noting that DMU30 and DMU 31 have no input redundancy in the original calculation, but after the bootstrap method, DMU30’s slack value at 2 is 2.482 and DMU31’s slack value at 1 becomes 1.555. Since the efficiency scores of DMU30 and DMU31 are 0.504 and 0.605, the managers of DMU30 should take steps to diminish the inputs by 0.496 times and cut approximately two employees to turn into efficient allocation, while the managers of DMU31 should take steps to diminish the inputs by 0.395 times and further adjust the capacity planning, which reveals problems in personnel recruitment and installed capacity planning. Decision-makers can pay more attention to the issues of cronyism and sinecures in DMU30 and installed capacity planning in DMU31. Since the variable selection has an significant effect on the DEA scores, and the influence degree of each index on the overall results is not the same [46], decision-makers are more concerned about factors with great influence. In order to identify the priority

sequence of the inputs and to verify the robustness of the model, we conduct a sensitivity analysis by removing each input and comparing the corresponding results. Fig. 5 shows the sensitivity analysis results, where Model I represents the original model with all variables, while Model II, Model III and Model IV are the modified models by omitting 1, 2 and 3 respectively. According to the contrast of the trend line of the four models, Model III is the most similar to the original one while Model II displays the lowest similarity, which implies that the priority sequence of the inputs should in general be 1>3>2. Moreover, the sensitivity analysis can be adopted to analyze the influence degree of the inputs in a project. For example, for DMU09, the real score is 0.739, which is much larger than the score 0.164 in Model II and is a bit different from the scores 0.729 and 0.743 in the other two modified models. Since Model II is a modified model by omitting 1, the analysis result shows that the installed capacity of DMU09 is in favorable condition and more concern should be given to personnel recruitment and solar energy utilization. Besides, since the modified models suffer the dimensionality reduction, Model I indisputably owns the highest mean efficiency score of 0.599. Based on the statistical analysis of efficiency scores, Model II owns the largest variance while the smallest one appears in Model IV, which

Y. Wu et al. / Energy 159 (2018) 599e610

607

Table 5 The slack values before and after the bootstrap algorithm for each observed project. DMUs

Before the bootstrapping 1

DMU01 DMU02 DMU03 DMU04 DMU05 DMU06 DMU07 DMU08 DMU09 DMU10 DMU11 DMU12 DMU13 DMU14 DMU15 DMU16 DMU17 DMU18 DMU19 DMU20 DMU21 DMU22 DMU23 DMU24 DMU25 DMU26 DMU27 DMU28 DMU29 DMU30 DMU31 DMU32 DMU33 DMU34 DMU35 DMU36 DMU37 DMU38 DMU39 DMU40 DMU41 DMU42

5.275 0 0 0 18.41 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.803 0 0 0 0 0

After the bootstrapping

2

3

1

2

3

4.675 0 0 0.479 1.661 7.964 0 0.467 4.994 0 3.47 1 2.114 0 0 0 0 0 1.068 0.115 3.785 0.935 0 0 1.089 8.766 0.353 8.527 5.605 0 0 0 1.679 0 0 0 0 1.522 0 0 0 0

0 0 0 0 0 0 0 0 474.634 0 0 0 0 0 0 0 0 0 0 0 0 0 0 194.296 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

2.917(-2.358) 0 0 0 18.307(-0.103) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.555(1.555) 0 0 0 0 0 2.533(0.730) 0 0 0 0 0

7.289(2.614) 0 0 0.724(0.245) 2.856(1.195) 8.812(0.848) 0 0.910(0.443) 7.169(2.175) 0 5.182(1.712) 1.745(0.745) 3.756(1.642) 0 0 0 0 0 1.820(0.752) 0.228(0.113) 6.077(2.292) 1.740(0.805) 0 0 1.887(0.798) 13.085(4.319) 0.381(0.028) 11.906(3.379) 8.331(2.726) 2.482(2.482) 0 0 2.672(0.993) 0 0 0 0 1.785(0.263) 0 0 0 0

0 0 0 0 0 0 0 0 694.293(219.659) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 266.662(72.366) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Note: The corresponding correction parameter is present in the parentheses beside the slack values.

demonstrates that there is a great difference in the efficiency of solar resource utilization in various projects. Finally, the Pearson correlation coefficients between the proposed model and three modified models are 0.711, 0.847 and 0.898, which manifests that there are significant correlations at the 0.01 level. Besides, their performance rankings are roughly the same, proving the stability and robustness of the model. 5.3. External factors analysis PPAPs refers to the projects which convert solar energy into electricity and assist the poor households with the grid-connected profit, so its efficiency is inevitably affected by both the natural and social environment [47]. Taking into account the influencing variables of the solar energy conversion and the poverty alleviation planning, this subsection aims at extracting the key external factors, analyzing the causes and further concluding some effective management suggestions. No definite requirements for the sample size exist in the Tobit regression, but there is a common accepted regulation that the sample quantity needs to exceed 30, otherwise the statistics will no longer obey the normal distribution. Although the sample size in this study meets the requirement in the

convention, we adopt the bootstrap algorithm to correct the bias for the consideration of the reliability of regression analysis under the small sample. Table 6 shows the Tobit regression analysis results before and after the bootstrap algorithm. As is displayed in the table, the regression coefficients keep constant while the standard deviations become larger during the bias correction, which conforms to the situation that the sample size is increasing. Besides, no matter whether the bootstrapping process is used or not, the Z1, Z3 and Z4 variables are proved to have influence on PPAP performance efficiency. The average annual temperature (Z1) variable, whose regression coefficient is
0.008, possesses a negative correlation with the PPAP performance efficiency scores. That is to say, high ambient temperature can reduce the operating inefficiency by affecting the component temperature. Meanwhile, the high working temperature will speed up the loss of photovoltaic cells [48], which may reduce the conversion efficiency and increase the project input. Judging from the coefficients and the significant levels, the larger the daylight cloud amount (Z3), the lower the operating efficiency. After the shielding, scattering, refraction and reflection of the clouds, the intensity of solar radiation suffers a certain attenuation, resulting in a decline of the photovoltaic conversion efficiency. The

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DMU01 DMU42 0.9 DMU02 DMU41 DMU03 DMU40 DMU04 0.8 DMU39 DMU05 0.7 DMU38 DMU06 0.6 DMU37 DMU07 0.5

DMU36

DMU08

0.4

DMU35

DMU09

0.3

DMU34

DMU10

0.2 0.1

DMU33

DMU11

0 DMU32

DMU12

DMU31

DMU13

DMU30

DMU14

DMU29

DMU15

DMU28

DMU16

DMU27 DMU26 DMU25 DMU24 DMU23 Model I

DMU22

Model II

DMU17 DMU18 DMU19 DMU20 DMU21 Model III

Model IV

Fig. 5. Sensitivity analysis of DEA-based efficiency assessment model.

Table 6 The Tobit regression analysis before and after the bootstrap algorithm for each external variable.

Z1 Z2 Z3 Z4 Z5 _cons /sigma

Before the bootstrapping

After the bootstrapping

Coef.

Std. Err.

t-ratio

Coef.

Std. Err.

z-ratio


9.42
0.08
5.82 0.17 5.32 1009.16 61.94

2.84 0.03 2.26 0.07 3.54 121.84 6.76


3.32**
2.58*
2.57* 2.21* 1.51 8.28** e


9.42
0.08
5.82 0.17 5.32 1009.16 61.94

3.13 0.05 2.50 0.08 5.24 132.38 5.69


3.01**
1.60
2.33* 2.07* 1.02 7.62** e

Note. For the sake of better data display, the units of the coefficients and the standard errors are 10
3. The ** and * symbols respectively represent the 1% and 5% significance level.

coefficient of the power demand (Z4) variable is 0.0002 and the Pvalue satisfies the 5% significance level, which implies that regions with large electricity demand are more suitable for PPAP installation. Due to extra cost of the electricity transactions between different regions, power generation projects generally sell electricity to local power grid. PPAPs that are located in an area with a large power gap will gain more support and supervision of the government and the Power Grid Corp, which may easily cause decent feed-in tariffs and full load operation. After the bias correction, Z2 and Z5 do not meet the 5% significant level requirement, which may be due to the data accuracy and the variable noncorrelation. For the annual rainfall amount, it reflects the precipitation in different periods throughout the year while only the daylight precipitation affects the photovoltaic component work. Moreover, the rainfall not only owns the negative

impact of the cloud increase and radiation intensity reduction, but also possesses the positive function of the component surface dust cleaning and the ambient temperature decrease. Since the intensity of its negative and positive influence is not certain in different projects, it is suggested that this factor should not be considered in the project site selection. In terms of poverty-stricken population, the poverty-stricken regions are mostly mountainous areas, and the population statistics, especially the villager income statistics, are extremely difficult, which may lead to some omissions or distortions in the collected data. 5.4. Management inspiration Based on the aforementioned assessment results, some countermeasures are suggested as follows. i) Since most observed DMUs own an unsatisfactory SE score in the performance assessment model which varies from 0.358 to 0.914 with a mean score of 0.654, most PPAPs suffer scale inefficiency. Unreasonable scale of production leads to poor project performance. Besides, most observed units present the increasing return to scales, which indicates that the government should increase the installed capacity of the newly-installed project in the planning stage and the contractor enterprises should expand the investment level in the operating phase. ii) According to slack analysis, about a half of the observed DMUs have slacks in the labor input, which means most projects have overinvestment in the labor employment. Therefore, decision-makers, especially project managers, should pay more attention to the employee recruitment

Y. Wu et al. / Energy 159 (2018) 599e610

issue. Normalizing the staff recruitment process and the personnel assessment system contribute a lot to improving employee quality, which can help prevent the phenomenon of nepotism or sinecures iii) Since Z1 and Z3 have negative correlation with the PPAP performance efficiency scores while Z4 possesses the positive correlation in Tobit regression analysis, PPAPs which locate in the areas with low temperature, little cloud, and large power demand tend to possess high performance efficiency. Therefore, besides the need to select areas with high solar radiation, decision-makers should also consider the factors such as annual average temperature, daylight cloud amount and regional electricity demand in the site selection process. Moreover, the PPAP in hot areas should be equipped with an effective cooling system, and the national Power Grid Corp should spare no effort to settle the electricity gap. 6. Conclusion and future extensions Since the PPAP has a mitigation effect on current hot issues, including environmental pollution, energy shortage and unbalanced social development, it is highly valued and strongly supported by the public. However, due to the late start in China, the imperfect theory system and the conventional supervision regulation make the project performance unsatisfactory. What’s worse, some inefficient projects are wasting national resources and defrauding government subsidies. Therefore, in order to accurately assess the PPAP operation efficiency and explore the improvement direction, this paper propose a modified three-stage DEA-based assessment model: First of all, an improved pretreatment approach combining Pearson correlation coefficient and super-efficiency analysis is developed to identify unreasonable variables and the outlier decision making units; Next, taking into account the small sample, the bootstrap algorithm is introduced into the DEA assessment model. According to the efficiency scores, the PPAP efficiency in China is generally low and the project scale needs to be expanded. Finally, the external influencing factors are verified by the Bootstrap-Tobit regression. The regression results indicate that temperature, cloud amount and power demand have impacts on project efficiency while the precipitation and the poverty incidence need to be further discussed. Because of the late start of the PPAP and very little published data, great barriers lie in efficiency evaluation of project performance. Although the proposed bootstrap based DEA model can make use of the “resampling” idea and reduce the bias to some extent, it fails to deeply analyze the technological progress and related policy promotion due to the lack of years of data. As the PPAP going on, more data can be obtained to support and extend the research. For example, with the promotion of the PPAP practice, core links of PPAPs can be identified. Therefore, integrating the proposed model and the “network” idea can calculate the specific efficiency of each link and make clear reasons for inefficient performance. Besides, some dominating factors for PVs like the smog that may have a disaster impact on the project will be interesting for further research. Moreover, another interesting direction of future extension is that with the help of years of data, the Malmquist index can be computed and Total Factor Productivity of PPAPs can be analyzed. Combined with technological progress rate and annual policy measures, effective policy inspiration will be obtained, which may be an important future research agenda. Acknowledgements This research is supported by the 2017 Special Project of Cultivation and Development of Innovation Base (NO.

609

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