Energy and environmental efficiency of China's regional electric power industry by considering renewable energy constraints

Abstract

The renewable electricity quota standard (RES) policy plays an important role in achieving sustainable and green development targets. Thus, it is essential to measure the sustainability of the electric power sectors in the context of RES. In terms of the energy and environmental efficiency (EEE) measurements, few studies divided energy inputs into renewable and non-renewable energy or explored the restricted problem of minimizing resource summation. To fill these gaps, we propose an improved fix-sum energy input data envelopment analysis (FSIDEA) model based on the adjustment strategy of weighted sum minimization of renewable energy inputs. The assurance region (AR) restriction and renewable energy input sum constraint (IC) are, respectively, imposed on the FSIDEA model to achieve the common equilibrium effective frontier (EEF). Finally, this study assesses the EEE of the electric power sectors in China's 30 main regions based on the common EEF. The result reveals that Beijing and Shanghai can be selected as benchmarks after efficiency comparison. In addition, our proposed model can compressively rank all decision-making units (DMUs) compared with traditional efficiency models.

Keywords

Data envelopment analysis energy and environmental efficiency assurance region constraint input constraint electric power sectors

Introduction

Energy is an important material basis for economic and social development. With the continuous deterioration of the ecological environment and the increasingly severe climate change, renewable energy development has gradually become a focus of global attention.^1–3 As an important destination of renewable energy consumption, the proportion of electric energy in China's energy consumption has been increasing, which provides an important driving force for the development of other industries and promotes China's economic growth, social progress, and the improvement of people's living standards.

With the deepening of China's new round of electric power reform, the National Energy Administration issued the third edition of the notice on the implementation of the renewable electricity quota standard (RES) policy in November 2018, which pointed out that the RES policy will be officially implemented from January 1, 2019. The RES policy has set the minimum renewable energy proportion targets for electric power consumption in all regions and forced the stakeholders to consume a certain proportion of renewable electricity.^4,5 By taking the proportion of renewable energy in electricity consumption as a binding index, the RES policy aims to encourage, support, and ensure the priority development and full utilization of renewable electricity, and provide a new strategic choice for promoting the optimization of energy consumption structure and improving energy efficiency.

However, the introduction of the RES policy also brings challenges to the energy efficiency evaluation of traditional electricity power. Under RES, renewable energy electricity consumption in all regions should reach the minimum proportion standards, which means that efficiency cannot be measured by reducing the potential of renewable energy electricity power consumption. To address the new problem caused by the RES policy, it is essential to analyze the energy and environmental efficiency (EEE) of the electric power sectors from the viewpoint of resource constraints.

The main innovations of this study are summarized as follows: (i) We construct the EEE index system to conform to the sustainable development targets based on the existing efficiency evaluation framework. Meanwhile, we apply the common equilibrium effective frontier (EEF) approach to construct the fix-sum energy input data envelopment analysis (FSIDEA) model by imposing the fixed quota input restrictions. (ii) We divide the energy inputs into renewable and non-renewable energy inputs, considering the development goal of green energy transformation. According to the minimum standard that the renewable energy input sum should reach, we add assurance region (AR) constraint and renewable energy input sum constraint (IC), respectively, to optimize the model. (iii) We use our proposed method to calculate and compare regional EEE scores of the electric power industry in China.

The rest of this study is laid out as follows. The “Literature review” section examines the literature. In the section “Methodology,” we introduce the construction of common EEF and propose a new DEA model to measure EEE. In the section “Empirical analysis,” regional EEE scores in China's electric power sectors are analyzed through the proposed method. The section “Conclusions” concludes this study and provides potential research directions. And the full names and abbreviations of some nouns are provided in the Appendix.

Literature review

In response to the global climate crisis, extensive studies have been given to explore the sustainable development from national, regional, and industrial views. For example, Wang and Zhan⁶ assessed the sustainability of renewable energy of EU countries. Wang and Yang⁷ further investigated the factors influencing the sustainability. From the regional and industrial perspectives, Chen et al.⁸ measured the energy efficiency of manufacturing sub-sectors from China and further explored its influencing factors. Recently, more and more scholars have chosen EEE as an indicator to measure sustainability, since improving EEE has become one of the most cost-effective methods to promote China's sustainable development.⁹

Data envelopment analysis (DEA), first introduced by Charnes et al.,¹⁰ is the most commonly used efficiency measurement method.¹¹ In traditional DEA analysis, all evaluated decision-making units (DMUs) are considered to be independent of each other. Nevertheless, the resource change of a DMU is bound to affect the resource adjustments of other DMUs if a certain resource in production activities is limited.^12,13 For example, when evaluating the EEE of each region under the policy of RES in this study, if one region would like to reduce its renewable energy consumption, at least one other region's renewable energy consumption has to increase to achieve the national total consumption target. Furthermore, the existing resource allocation models based on the DEA method have set strong assumptions about the new production of each DMU after allocation, such as keeping the efficiency values unchanged or achieving effective production. Therefore, to deal with these disadvantages of previous studies, it is critical to improve and expand the traditional efficiency evaluation method under input resource constraints and the resource allocation approach under production.

Improving energy efficiency requires reducing energy inputs that provide the same energy services. The intention is to alleviate energy shortages and improve energy utilization performance. In this regard, the existing research considers the construction of an energy efficiency evaluation framework system. Hu and Wang¹⁴ initially proposed the concept of total factor energy efficiency (TFEE), whose core idea is that energy alone cannot produce any output. Therefore, it is essential to combine energy with other input elements to build a multi-input model. One weakness of TFEE is that it regards gross domestic product (GDP) as a single output and ignores the undesirable output (e.g., CO₂ emission). Nevertheless, as the by-product of GDP output, environmental pollution should be integrated into the efficiency index system to reflect the real production process. Hence, to evaluate energy efficiency more accurately, Li and Hu¹⁵ put forward the concept of ecological total factor energy efficiency (ETFEE) and constructed a sustainable framework incorporating environmental impact. Numerous studies have introduced the ETFEE index into their research framework (e.g., Chen et al.,⁸ Chen and Lin,¹⁶ Cheng et al.,¹⁷ and Guo and Yuan¹⁸).

At present, DEA has been widely employed in energy and environmental analysis. For example, Zhao et al.¹⁹ applied a three-stage DEA model to assess the regional energy efficiency from 2008 to 2016 in China. They employed stochastic frontier analysis to exclude the influence of external environmental factors and statistical noise by adjusting the initial inputs so that the calculated efficiency values can better reflect the state of DMUs. Liang et al.²⁰ first used a DEA model to evaluate China's regional energy efficiency from 2006 to 2018, considering the impact of slack variables, and then constructed a Tobit model to identify the factors influencing the efficiency values. The results showed that there are great differences in the energy efficiency level in various regions, and the factors affecting the efficiencies of the three areas are also different. Bian and Yang²¹ proposed a comprehensive efficiency index for measuring resource and environment efficiencies by extending the Shannon-DEA approach. Using an extended DEA model, Wang et al.²² investigated regional energy performance in China. More relevant studies on EEE evaluation can be found in review papers, such as Zhou et al.,²³ Mardani et al.,²⁴ and Song et al.²⁵

Concerning the EEE in the electric power industry, Färe et al.²⁶ first used the DEA method to measure the relative performance of electric utilities. Since then, scholars worldwide started to apply various DEA approaches to assess EEE in the electric power industry. For example, applying a slack-adjusted DEA model which incorporated the influence of slack variables into the efficiency evaluation, Sueyoshi and Goto²⁷ analyzed the performance of the electric power generation industry. Vaninsky²⁸ calculated the environmental scores of the electric sectors in the USA using emission rate, electric power losses, and fossil fuel utilization through the DEA method. Bi et al.²⁹ applied a slack-based DEA approach to investigate the energy efficiency of China's thermal power generation during 2007–2009, and further explored the influence of environmental regulation on the obtained efficiency values using an environmental indicator. Liu et al.³⁰ constructed a comprehensive evaluation model of TFEE in the thermal power industry by combining DEA and Malmquist index approaches.

Under the policy of RES, the minimum proportions of renewable energy use for electricity consumption in all regions are specified. Therefore, it is meaningful to assess energy efficiency by taking resource constraints into account. Lins et al.³¹ first proposed a nonlinear zero-sum gains DEA model to evaluate the efficiency of countries participating in the Olympic Games by taking fixed-sum outputs into account. However, this method can only deal with the fixed-sum output with one dimension. To solve this dilemma, Yang et al.³² proposed a fixed-sum output DEA model based on minimum reduction of fixed-sum output. This model has considered the equal quantity and equal proportion reduction strategies of fixed output. Nevertheless, Yang et al.¹² pointed out that this approach cannot construct a unique equilibrium efficient frontier (EEF), and hence the competition form is memoryless. Then, they proposed an EEFDEA approach to appraise all DMUs' efficiencies on the common EEF with considering fixed-sum outputs. Based on the strategy of minimum adjustment and balanced competition, the EEFDEA model can achieve a common EEF for all DMUs and assess DMUs' original input and output on this platform. Yang et al.³³ further put forward a general EEFDEA model to overcome the drawbacks of the EEFDEA model, such as the possible substantial calculation burden.

Previous studies failed to consider the maximization of energy conservation. Hence, in terms of energy input division, Wang et al.³⁴ denoted that it is critical to separate and save non-renewable energy inputs from energy inputs to enhance energy utilization efficiency and promote emission abatement. Shi et al.³⁵ divided the inputs into energy and non-energy inputs under the existing DEA framework and investigated industrial energy efficiency using an extended DEA model by taking into account fixing non-energy inputs and undesirable outputs. Zhou et al.⁵ considered renewable energy power, non-renewable energy power, and other energy inputs, then applied a zero-sum gains DEA approach to measure the allocation efficiency.

In addition, considering that the state pays different attention to renewable and non-renewable energy, it is necessary to restrict their proportional share, so it is considered to introduce AR constraint. Thompson et al.^36,37 first introduced the AR constraint in the DEA method. Later, this kind of method has been widely used in efficiency measurement to assign weights. For example, treating the deposits as an intermediate variable, Degl’Innocenti et al.³⁸ employed the network DEA method to appraise the bank's efficiencies for new EU members and applied the weight AR approach to determine the weight for each stage. Xu and Zhou³⁹ divided the non-performing loans into three categories for weight setting and then used a two-stage AR-DEA model to analyze the efficiency of 26 commercial banks in China from 2013 to 2017. Several studies have tried to combine AR constraints with the analytic hierarchy process (AHP) method to determine the weights of the AR-DEA model, such as Wang et al.⁴⁰ and Xu and Zhou.³⁹ However, little literature has introduced AR constraints in the energy efficiency evaluation.

Surveying the above research on energy efficiency evaluation, it can be found that there are still several deficiencies. First, most scholars have considered energy and non-energy inputs when constructing energy efficiency evaluation model, but few studies try to divide energy input into renewable and non-renewable energy and further restrict their weights; Second, most of the previous studies on efficiency evaluation under resource constraints are based on the assumption of constant fixed-sum resource, and few studies discuss the problem of resource sum minimization constraints. Therefore, we try to evaluate the EEE of China's electric power industry in the context of RES by considering the constraints of weights and the total use of renewable energy inputs.

Methodology

This section aims to establish an extended DEA model to evaluate regional EEE in the electric power industry of China under the policy of RES by introducing renewable energy input quota and renewable and non-renewable energy input constraints. We first introduce the basic structure of the EEF and propose a DEA model based on fixed-sum inputs. Then, the model is further improved by imposing the AR constraint and IC, respectively. Finally, the improved model is applied to evaluate regional EEE in China.

The foundation of the EEF

In the following analysis, each DMU corresponds to the electric power sectors in a region. Assume that DMU _k ( $k = 1, 2, \dots, g$ ) uses n different renewable energy, represented by ( $a_{k} = (a_{1 k}, a_{2 k}, \dots, a_{n k})^{T}$ ), q different non-renewable energy, denoted by ( $b_{k} = (b_{1 k}, b_{2 k}, \dots, b_{q k})^{T}$ ), and m different non-energy inputs, represented by ( $c_{k} = (c_{1 k}, c_{2 k}, \dots, c_{m k})^{T}$ ) to produce s different desirable outputs, represented by ( $y_{k} = (y_{1 k}, y_{2 k}, \dots, y_{s k})^{T}$ ). Furthermore, undesirable outputs (environmental pollutants) are also produced during the power generation process. With reference to Wang et al.,⁴⁰ they are treated as non-energy inputs in this study.

Considering that energy inputs can be divided into renewable and non-renewable energy inputs, the BCC model⁴¹ can be first constructed to assess the EEE for each DMU _k under the assumption of input orientation and variable return to scale (VRS).

\begin{aligned} θ_{k}^{B C C} = & M a x \frac{\sum_{r = 1}^{s} u_{r} y_{r k} + u_{0}}{\sum_{t = 1}^{n} v_{t} a_{t k} + \sum_{p = 1}^{q} w_{p} b_{p k} + \sum_{d = 1}^{m} q_{d} c_{d k}} \\ s . t . \frac{\sum_{r = 1}^{s} u_{r} y_{r j} + u_{0}}{\sum_{t = 1}^{n} v_{t} a_{t j} + \sum_{p = 1}^{q} w_{p} b_{p j} + \sum_{d = 1}^{m} q_{d} c_{d j}} \leq 1, j = 1, \dots, g \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(1)

where variables

u_{r}

v_{t}

w_{p}

, and

q_{d}

are the corresponding multipliers of desirable outputs, renewable energy inputs, non-renewable energy inputs, and non-energy inputs, respectively. The subscript k denotes the DMU under evaluation.

u_{0}

in the objective function reflects the VRS assumption. The obtained

θ_{k}^{B C C}

denotes the EEE of DMU _k , and its value is between 0 and 1.

However, the traditional BCC method fails to consider that the use of renewable energy should reach a certain level to achieve sustainability. Following Yang et al.,³² model (2) can be constructed to calculate the minimal renewable energy input reduction scale for evaluated DMU by considering the fixed-sum restriction.

\begin{aligned} min \sum_{t = 1}^{n} v_{t} β_{t k} \\ s . t . \frac{\sum_{r = 1}^{s} u_{r} y_{r k} + u_{0}}{\sum_{t = 1}^{n} v_{t} (a_{t k} - β_{t k}) + \sum_{p = 1}^{q} w_{p} b_{p k} + \sum_{d = 1}^{m} q_{d} c_{d k}} = 1 \\ \frac{\sum_{r = 1}^{s} u_{r} y_{r j} + u_{0}}{\sum_{t = 1}^{n} v_{t} (a_{t j} + β_{t j}) + \sum_{p = 1}^{q} w_{p} b_{p j} + \sum_{d = 1}^{m} q_{d} c_{d j}} \leq 1, f o r \forall j \neq k \\ \sum_{j = 1, j \neq k}^{g} β_{t j} - β_{t k} = 0, f o r \forall t \\ 0 \leq β_{t k} \leq a_{t k}, f o r \forall t \\ β_{t j} > 0, f o r \forall t, j \neq k \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(2)

where

β_{t k} (t = 1, \dots, n)

represents the reduction of renewable energy input for DMU _k under evaluation.

β_{t j} (t = 1, \dots, n; j = 1, \dots, g, \neq k)

denotes the increase in renewable energy for DMU _j (

j \neq k

). The constraint,

\sum_{j = 1, j \neq k}^{g} β_{t j} - β_{t k} = 0, f o r \forall t

, indicates that the adjusted total amount of final renewable energy inputs is zero. This method considers the reduction of renewable energy input for DMU _k under the fixed-sum restrictions, and attempts to minimize the weighted sum in the objective function.

A new DEA model can be constructed following the idea of Yang et al.³² Nevertheless, it is worth noting that this strategy evaluates each DMU based on a different frontier, which limits its application. To address this issue, Yang et al.^12,33 and Fang⁴² suggested that a common EEF should be used to replace different effective frontiers when appraising the efficiency. The common EEF aims to make all DMU_s efficient by adjusting their inputs under the fixed-sum restriction. To achieve the common EEF, let us first assume that $β_{t j}$ is a free variable, the positive value means the increase in renewable energy input, and vice versa. Then, to ensure that all DMUs are efficient after adjusting the inputs, the inequality of the second constraint of model (2) is changed into an equation. Considering the unconstrained properties of $β_{t j}$ , we can further merge this equation with the first constraint in model (2) to get the first constraint in model (3). The third and fourth constraints in model (2) also become the corresponding forms in model (3). As a result, model (3) can be developed to obtain the minimized weighted adjustment based on the common EEF.

\begin{aligned} min \sum_{j = 1}^{g} \sum_{t = 1}^{n} v_{t} | β_{t j} | \\ s . t . \frac{\sum_{r = 1}^{s} u_{r} y_{r j} + u_{0}}{\sum_{t = 1}^{n} v_{t} (a_{t j} + β_{t j}) + \sum_{p = 1}^{q} w_{p} b_{p j} + \sum_{d = 1}^{m} q_{d} c_{d j}} = 1, \forall r, t, p, d, j \\ \sum_{j = 1}^{g} β_{t j} = 0, \forall t \\ a_{t j} + β_{t j} \geq 0, f o r \forall t, j \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ β_{t j}, u_{0} f r e e i n s i g n . \end{aligned}

(3)

Considering that

β_{t j}

is a free variable, we take the absolute value of

β_{t j}

in the objective function. Model (3) tries to calculate the minimized weighted adjustment of renewable energy.

Model (3) is difficult to solve owing to its nonlinearity. Thus, we transform it into a linear model as follows:

Step 1: Set $β_{t j}^{'} = v_{t} β_{t j}$ , then model (3) becomes model (4):

\begin{aligned} min \sum_{j = 1}^{g} \sum_{t = 1}^{n} | {β^{'}}_{t j} | \\ s . t . \frac{\sum_{r = 1}^{s} u_{r} y_{r j} + u_{0}}{\sum_{t = 1}^{n} (v_{t} a_{t j} + {β^{'}}_{t j}) + \sum_{p = 1}^{q} w_{p} b_{p j} + \sum_{d = 1}^{m} q_{d} c_{d j}} = 11 \forall r, t, p, d, j \\ \sum_{j = 1}^{g} {β^{'}}_{t j} = 0, \forall t \\ v_{t} a_{t j} + {β^{'}}_{t j} \geq 0, f o r \forall t, j \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0}, {β^{'}}_{t j} f r e e i n s i g n . \end{aligned}

(4)

Step 2: Let $h_{t j} = (1 / 2) (β_{t j}^{'} + | {β^{'}}_{t j} |), l_{t j} = (1 / 2) (| {β^{'}}_{t j} | - β_{t j}^{'})$ ,³³ we have $| {β^{'}}_{t j} | = h_{t j} + l_{t j}, β_{t j}^{'} = h_{t j} - l_{t j}$ . Therefore, model (4) becomes:

\begin{aligned} min \sum_{j = 1}^{g} \sum_{t = 1}^{n} (h_{t j} + l_{t j}) \\ s . t . \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) + \sum_{p = 1}^{q} (w_{p} b_{p j}) + \\ \sum_{d = 1}^{m} q_{d} c_{d j} - \sum_{r = 1}^{s} u_{r} y_{r j} - u_{0} = 0, \forall r, t, p, d, j \\ \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) + \sum_{p = 1}^{q} (w_{p} b_{p j}) + \sum_{d = 1}^{m} q_{d} c_{d j} \geq C \\ \sum_{j = 1}^{g} (h_{t j} - l_{t j}) = 0, \forall t \\ v_{t} a_{t j} + h_{t j} - l_{t j} \geq 0, f o r \forall t, j \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(5)

According to the idea proposed by Yang et al.,³³ the second constraint $\sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) + \sum_{p = 1}^{q} (w_{p} b_{p j}) + \sum_{d = 1}^{m} q_{d} c_{d j} \geq C$ is added to ensure that the value is positive, where C is a given positive number. Furthermore, we can get $β_{t j} = (β_{t j}^{'} / v_{t}) = (h_{t j} * - l_{t j} * / v_{t} *) = ((C^{'} / C) (h_{t j} * - l_{t j} *) / (C^{'} / C) v_{t} *)$ through Theorem 1, indicating that C does not affect the optimal adjustment $β_{t j}$ .³³

Theorem 1.

For the given constant C, if $(u_{r} *, v_{t} *, w_{p} *, q_{d} *, h_{t j} *, l_{t j} * u_{0} *)$ is the optimal solution of model (5), then $(C^{'} / C) (u_{r} *, v_{t} *, w_{p} *, q_{d} *, h_{t j} *, l_{t j} * u_{0} *)$ is also the optimal solution of model (5) with any given $C^{'}$ .

Model extensions

Weight constraints between renewable and non-renewable energy

From the recent development trends of renewable energy, it can be observed that the government has paid different attention to renewable and non-renewable energy. However, the existing studies on the EEE measurement always ignore this discrepancy. As such, the calculated weights may be inconsistent with the actual requirements, which will affect their guiding significance to the actual production.

This study tries to impose the AR constraint on the weight of renewable and non-renewable energy. The common form of multiplier restriction in AR form is to impose upper and lower limits on the ratio of multiplier pairs,⁴³ as shown in the following inequality:

\frac{p_{1}^{l}}{p_{2}^{u}} \leq \frac{v_{t}}{w_{p}} \leq \frac{p_{2}^{l}}{p_{1}^{u}}

(6)

In the foundation of the EEF, we know that

v_{t}

and

w_{p}

in model (1) are the corresponding multipliers of renewable and non-renewable energy inputs. Referring to the study of Yang et al.,³² the weight constraint for renewable and non-renewable energy inputs is imposed by

v_{t} - w_{p} \geq δ_{t p}

, showing that the country focuses more on the development and utilization of renewable energy.

Renewable energy input restrictions

Previous relevant studies are mostly based on the constraint of fixed-sum invariance, that is, assuming that the sum of regional adjustments is zero. However, since the implementation of Thirteenth Five-Year Plan for Renewable Energy Development (13th-FYPRED) and Fourteenth Five-Year Plan for Renewable Energy Development (14th-FYPRED), China has been continuously promoting the green transformation and development of energy. The sum of renewable energy inputs should meet the specified minimum requirements to achieve high-quality development of energy. Hence, we add a constraint, that is, IC on the lower limit of renewable energy input sum. This makes the renewable energy inputs after adjustment greater than those before adjustment and can meet the actual development requirements. The IC is given as follows:

\sum_{j = 1}^{g} \sum_{t = 1}^{n} (a_{t j} + β_{t j}) \geq λ

(7)

Extended results

The linear programming (5) becomes the following model by imposing the AR constraint and IC.

\begin{aligned} min \sum_{j = 1}^{g} \sum_{t = 1}^{n} (h_{t j} + l_{t j}) \\ s . t . \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) + \sum_{p = 1}^{q} (w_{p} b_{p j}) + \\ \sum_{d = 1}^{m} q_{d} c_{d j} - \sum_{r = 1}^{s} u_{r} y_{r j} - u_{0} = 0, \forall r, t, p, d, j \\ \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) + \sum_{p = 1}^{q} (w_{p} b_{p j}) + \sum_{d = 1}^{m} q_{d} c_{d j} \geq C \\ \sum_{j = 1}^{g} (h_{t j} - l_{t j}) = 0, \forall t \\ v_{t} a_{t j} + h_{t j} - l_{t j} \geq 0, f o r \forall t, j \\ v_{t} - w_{p} - δ_{t p} \geq 0 (#) \\ \sum_{j = 1}^{g} \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} - l_{t j}) - v_{t} λ \geq 0 (*) \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(8)

In model (8), constraint condition (#) means that AR constraint is used to limit the weight of renewable and non-renewable energy input, and the model is called as AR-FSIDEA (Assurance Region Fixed-Sum Input DEA); constraints (*) represent restrictions on the sum of renewable energy input, and the resulting model is called IC-FSIDEA (Input Constraint-FSIDEA).

EEE evaluation based on the common EEF

Based on the common EEF constructed above, this subsection employs the following model to calculate the EEE score for each DMU _k $(k = 1, \dots, g)$ .

\begin{aligned} θ_{k}^{E E E} = & M a x \frac{\sum_{r = 1}^{s} u_{r} y_{r k} + u_{0}}{\sum_{t = 1}^{n} v_{t} a_{t k} + \sum_{p = 1}^{p} w_{p} b_{p k} + \sum_{d = 1}^{m} q_{d} c_{d k}} \\ s . t . \frac{\sum_{r = 1}^{s} u_{r} y_{r j} + u_{0}}{\sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} * - l_{t j} *) + \sum_{p = 1}^{q} w_{p} b_{p j} + \sum_{d = 1}^{m} q_{d} c_{d j}} \leq 1, \forall j \\ v_{t} - w_{p} \geq δ_{t p} \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(9)

where the variable

h_{t j} *

and

l_{t j} *

denote the optimal value of model (8),

θ_{k}^{E E F}

is the EEE score for DMU _k based on the common EEF.

Model (9) can be transformed into linear programming (10) following the technique introduced by Charnes and Cooper.⁴⁴

\begin{aligned} θ_{k}^{E E E} = & M a x \sum_{r = 1}^{s} u_{r} y_{r k} + u_{0} \\ s . t . \sum_{r = 1}^{s} u_{r} y_{r j} + u_{0} - \sum_{t = 1}^{n} (v_{t} a_{t j} + h_{t j} * - l_{t j} *) - \sum_{p = 1}^{q} w_{p} b_{p j} - \sum_{d = 1}^{m} q_{d} c_{d j} \leq 0, \forall j \\ \sum_{t = 1}^{n} v_{t} a_{t k} + \sum_{p = 1}^{p} w_{p} b_{p k} + \sum_{d = 1}^{m} q_{d} c_{d k} = 1 \\ v_{t} - w_{p} \geq δ_{t p} \\ u_{r} \geq 0, r = 1, \dots, s; \\ v_{t} \geq 0, t = 1, \dots, n; \\ w_{p} \geq 0, p = 1, \dots, q; \\ q_{d} \geq 0, d = 1, \dots, m; \\ u_{0} f r e e i n s i g n . \end{aligned}

(10)

Empirical analysis

Data sources and description

In the following section, the proposed model is employed to assess the EEE of 30 administrative regions in mainland China. Due to the absence of relevant data on energy use and CO₂ emission, Tibet is excluded from this study.

According to the rule of thumb proposed by Golany and Roll,⁴⁵ the number of DMU_s to be evaluated should not be less than twice the sum of input and output indicators to avoid affecting the model's reliability and validity. Therefore, we have selected seven input and output indicators, as illustrated in Table 1.

Table 1.

Input/output indicator.

Input/output	Variable	Unit
Inputs	Installed capacity of renewable power generation (X1)	10 thousand kilowatts
	Installed capacity of non-renewable power generation (X2)	10 thousand kilowatts
	Labor force in the electric power sector (X3)	10 thousand persons
Desirable outputs	Renewable power generation (Y1)	100 billion kwh
	Non-renewable power generation (Y2)	100 billion kwh
	Industrial value added (Y3)	100 billion RMB
Undesirable output	CO₂ emission (Y4)	10 thousand tons

The reason for selecting the labor force in the electric power sector is that the effective labor time of relevant employees is hard to obtain. Thus, if ignoring the small disparity between regions in the share of employees from the power generation sector in the production and supply of electricity, gas, and water, it can be considered that the average proportion of employees from power generation sector is stable. Following the study of Shi et al.,³⁵ the industrial added value is selected as a desirable output to reflect the economic benefit.

CO₂ emission from the electric power sector is mainly caused by thermal power production, and the relevant statistical data cannot be obtained directly. Thus, this study calculates CO₂ emission using equation (11) with reference to the IPCC national greenhouse gas inventory guidelines and provincial greenhouse gas inventory preparation guidelines.

C O_{2} = \sum_{j = 1} E_{j} \times C A_{j} \times C C_{j} \times O_{j} \times (\frac{44}{12})

(11)

where j denotes the type of fossil energy;

E_{i j}

is the energy consumption;

C A_{j}

and

C C_{j}

represent the average low net calorific value and carbon content of the jth fuel, respectively, and their values can be obtained from Zhao et al.⁴⁶;

O_{j}

is the carbon oxidation rate of the jth fuel, and the value is set to 1, and the factor “44/12” represents the conversion coefficient from carbon to CO₂.

The annual actual energy consumption comes from the regional energy balance table in the China Energy Statistics Yearbook. The installed capacity and power generation of renewable and non-renewable energy are derived from the China Electricity Yearbook. The labor force in the electric power sector comes from the China Statistical Yearbook, and the industrial added value is from the Provincial Statistical Yearbooks.

The descriptive statistics for all indicators are presented in Table 2.

Table 2.

Statistical descriptions of data (5-year average).

Variables	Inputs			Desirable outputs			Undesirable output
Variables	X1	X2	X3	Y1	Y2	Y3	Y4
Mean	1650.82	3314.6	13.1	446.46	1442.5	9348.68	11,976.6
Median	1200.58	2421	12.76	207.22	1030.9	7061.66	7671.64
S.D.	1587.18	2340.36	6.94	617.34	1148.62	7772.6	9812.96
Max.	6836.42	8851.4	30.98	2724.3	4465.4	30,848.18	38,742.6
Min.	58.08	319.2	2.04	8.06	138.2	496.7	1327.48

The initial region EEE analysis with the BCC and FSIDEA models

In this subsection, we apply the traditional BCC and our proposed FSIDEA models to calculate and compare the EEE scores and rankings of DMUs using data from the electric power sectors of China during 2013–2017. The results are presented in Figures 1 and 2.

Figure 1 shows the regional EEE scores based on the BCC model. It can be seen that the efficiency values of more than half of the regions are all one as well as their ranking orders, showing that these regions are on the efficient frontier. However, this causes low discrimination between these efficient regions, thus making it difficult to compare regional efficiencies horizontally. The reason is that the traditional DEA models measure the efficiency through a self-evaluation method, which allows each DMU to select the most favorable weights.^47,48

In terms of the efficiency results in the FSIDEA model, it can be observed from Figure 2 that nearly half of the regions have an efficiency score above 1 in 5 years. In addition, the efficiency ranking of Tianjin and Shanghai has remained in the top two in 5 years, the ranking of Beijing, Fujian, and Chongqing has increased steadily, and the efficiency ranking of Shanxi and Henan presents a declining trend during the study period. The efficiency rankings of the remaining regions are generally stable. Compared with the results calculated by the BCC model, it is clear that the FSIDEA model can rank all DMUs and thus has a higher discrimination, which indicates that it is necessary to take the fixed-sum energy input into account under the framework of EEE evaluation.

The regional EEE analysis under AR constraint

In order to further reflect the country's preference for different renewable and non-renewable energy sources in the context of renewable energy development, this study tries to impose constraints on the weights of renewable and non-renewable energy. Thus, we add the AR restriction to the traditional BCC and FSIDEA models, respectively. The AR constraint indicates that the weights assigned to renewable energy inputs should be higher than non-renewable energy inputs. Here, the value reflecting the AR restriction is set as 0.1 in this study. The results calculated by the BCC and FSIDEA models with AR constraints are shown in Tables 3 and 4.

Table 3.

Regional EEE scores and rankings based on the AR-BCC model.

DMU _s	2013		2014		2015		2016		2017
DMU _s	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank
Liaoning	0.8823	26	0.9232	24	0.8973	24	0.8732	25	0.8855	24
Beijing	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Jiangsu	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Tianjin	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Jiangxi	0.9233	23	0.9861	16	0.9591	23	0.9648	19	1.0000	1
Anhui	0.9680	21	0.9381	22	0.9599	22	0.9539	20	0.9775	23
Shanghai	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Shanxi	0.9148	24	0.9180	25	0.8962	25	0.8753	24	0.8465	25
Heilongjiang	0.7878	29	0.7676	28	0.7901	29	0.7915	28	0.8098	27
Hebei	0.9778	19	0.9527	20	0.9604	21	0.9695	18	1.0000	1
Nei Mongol	1.0000	1	1.0000	1	1.0000	1	0.8974	23	1.0000	1
Zhejiang	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Jilin	0.6740	30	0.7464	30	0.7087	30	0.7591	30	0.7521	30
Fujian	1.0000	1	0.9736	18	1.0000	1	1.0000	1	1.0000	1
Guangxi	0.9430	22	0.9504	21	1.0000	1	0.7972	27	0.8050	28
Chongqing	0.9848	18	0.9767	17	1.0000	1	1.0000	1	1.0000	1
Henan	0.9031	25	0.8603	27	0.8416	27	0.8205	26	0.8421	26
Guizhou	1.0000	1	0.9658	19	1.0000	1	1.0000	1	1.0000	1
Hunan	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Guangdong	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Shandong	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Hubei	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Shaanxi	0.9685	20	0.9381	22	0.8739	26	0.9098	22	0.9828	22
Qinghai	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Sichuan	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Xinjiang	0.8472	27	0.8748	26	1.0000	1	0.9360	21	0.9865	21
Gansu	0.8291	28	0.7644	29	0.8096	28	0.7852	29	0.7844	29
Yunnan	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Ningxia	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1
Hainan	1.0000	1	1.0000	1	1.0000	1	1.0000	1	1.0000	1

Table 4.

Regional EEE scores and rankings based on the AR-FSIDEA model.

DMU _s	2013		2014		2015		2016		2017
DMU _s	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank
Liaoning	0.8883	27	0.9280	27	0.8973	25	0.9674	24	0.9618	28
Beijing	1.2227	7	2.5457	4	1.0002	8	3.5580	3	2.5583	3
Jiangsu	1.4610	5	1.2480	9	1.0008	5	1.5957	5	1.3183	6
Tianjin	6.2914	1	9.0986	1	1.0064	1	5.9509	1	4.9328	1
Jiangxi	1.0785	13	1.2257	10	0.9592	24	1.1245	10	1.0000	17
Anhui	1.2213	8	1.3834	7	0.9599	23	1.2360	9	1.0273	16
Shanghai	6.2453	2	7.3841	2	1.0031	2	5.2206	2	4.6688	2
Shanxi	1.1161	11	1.0351	15	0.8962	27	0.9599	25	1.0343	15
Heilongjiang	0.9136	26	1.0000	18	0.7901	29	0.9409	26	1.0000	17
Hebei	0.9778	24	0.9527	26	0.9604	22	0.9695	23	1.0000	17
Nei Mongol	1.0000	16	1.0000	18	1.0000	13	0.8974	28	1.0000	17
Zhejiang	1.0000	16	1.0000	18	1.0000	13	1.0152	17	1.0000	17
Jilin	0.8271	30	0.7895	29	0.7087	30	0.8610	29	0.8252	29
Fujian	1.0396	14	1.0293	16	1.0001	9	1.4034	7	1.1328	7
Guangxi	0.9535	25	1.1545	12	1.0005	6	1.0619	13	1.0729	9
Chongqing	1.0000	16	1.3495	8	1.0001	9	1.4308	6	1.3343	5
Henan	1.6661	3	1.6208	5	1.0003	7	0.9976	22	1.0575	13
Guizhou	1.0000	16	1.0203	17	1.0001	9	1.0254	16	1.0402	14
Hunan	1.0077	15	1.0000	18	1.0000	13	1.0287	15	0.9997	26
Guangdong	1.0000	16	1.0000	18	1.0000	13	1.0000	18	1.0000	17
Shandong	1.1517	10	1.2230	11	1.0009	4	1.2903	8	1.0729	9
Hubei	1.0000	16	1.0371	14	1.0000	13	1.0315	14	1.0604	12
Shaanxi	1.3694	6	1.5555	6	0.8965	26	1.1114	11	1.0759	8
Qinghai	1.0000	16	1.0000	18	1.0000	13	1.0000	18	1.0000	17
Sichuan	1.1521	9	1.0718	13	1.0001	9	1.0651	12	1.0621	11
Xinjiang	0.8472	29	0.8748	28	1.0000	13	0.9360	27	0.9865	27
Gansu	0.8504	28	0.7644	30	0.8096	28	0.7852	30	0.7844	30
Yunnan	1.0980	12	1.0000	18	1.0000	13	1.0000	18	1.0000	17
Ningxia	1.0000	16	1.0000	18	1.0000	13	1.0000	18	1.0000	17
Hainan	1.5942	4	2.6741	3	1.0020	3	3.3860	4	2.1724	4

Table 3 presents the efficiency scores and rankings of DMUs based on the AR-BCC model. Comparing them with the results based on the BCC model without the AR constraint, it can be seen that the difference in the number of efficient DMUs obtained from these two models, as well as their efficiency rankings, is relatively small. This result indicates that introducing the AR constraint into the BCC model fails to significantly change the efficiency scores and rankings of DMUs. As discussed above, one possible reason is that the EEE evaluation for all DMUs is not on the common EEF.

The EEE results calculated by the AR-FSIDEA model are shown in Table 4. From a longitudinal perspective, Table 4 shows that the EEE scores of Tianjin and Shanghai rank in the top two in 5 years, which is similar to the results from the FSIDEA model. The difference is that the efficiency rankings of Beijing, Fujian, and Chongqing do not present significant increasing trends during the study period compared with the FSIDEA model. Then, from a horizontal view, it is worth noting that the efficiency rankings of Shanxi in 2017, Jiangxi in 2013, and Henan in 2017 after imposing the AR constraint decrease by more than 10 places, while those of Anhui in 2015 and Jiangxi in 2015 jump by more than 10 places. Since the objective of imposing AR constraint is to further clarify the proportion of renewable and non-renewable energy, it can be determined that the reason for the decline of the above efficiency ranking is that the energy consumption structure of electricity use in those provinces in that year is unreasonable and too dependent on renewable energy, while the reason for the rise of the ranking is the opposite. Although AR constraint is effective for the FSIDEA model, the overall effect is not significant.

The regional EEE analysis under IC

Although the AR-FSIDEA model has fully considered the proportion of renewable and non-renewable energy under RES, too much room has been given for the adjustment of renewable energy in the process of adjusting EEF. Considering that China has formulated the 13th-FYPRED and 14th-FYPRED to promote green transformation and development of energy sources, hence, the sum of renewable energy inputs should meet the minimum standards. In this study, we try to limit the total use of renewable energy to narrow the room for adjustment.

China's government has formulated corresponding renewable energy development goals; however, the proportion and trend analysis of the installed capacity of renewable energy power generation issued by the National Energy Administration shows that the installed capacity of renewable energy power generation in that year has not met the national development requirements. Therefore, the renewable energy inputs in all regions should be further increased on this basis. We try to use the installed capacity of renewable energy generation in the current year as the constraint threshold to restrict the lower limit of renewable energy input. Thus, we set the values from 2013 to 2017 as 28,000, 37,000, 48,000, 57,000, and 65,000, respectively, based on the original data. Then, we apply the IC-FSIDEA model to analyze the regional EEE scores.

Table 5 illustrates the efficiency scores and rankings based on the IC-FSIDEA model. Comparing the results of the IC-FSIDEA and FSIDEA models, it can be seen that the EEE scores of Tianjin and Shanghai still rank the first and second positions, respectively. The major difference is that the efficiency rankings of a considerable number of regions changed significantly in 2016 and 2017 after imposing IC. For example, compared with the results from the FSIDEA model, the rankings of Anhui, Guangxi, and Shaanxi in the IC-FSIDEA model decrease by more than 10 places, while those of Henan, Hunan, and Ningxia jump by more than 10 places in the last 2 years. It should be noted that the ranking of Jiangxi fluctuates greatly, which decreases by 10 places in 2016 and rises by 7 places in 2017.

Table 5.

Regional EEE scores and rankings based on the IC-FSIDEA model.

DMU _s	2013		2014		2015		2016		2017
DMU _s	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank	Efficiency	Rank
Liaoning	0.9422	27	0.9295	26	0.9330	27	0.8754	27	0.8958	25
Beijing	2.2200	4	2.5279	4	3.3194	4	1.6789	4	1.7003	3
Jiangsu	1.8101	5	1.6652	5	1.7512	5	1.0637	5	1.0342	6
Tianjin	11.5035	1	11.5525	1	11.4266	1	2.2744	1	2.3380	1
Jiangxi	1.1622	11	1.1196	12	1.1769	12	0.9666	20	1.0115	8
Anhui	1.5061	8	1.4924	8	1.3840	7	0.9575	21	0.9775	23
Shanghai	9.7139	2	9.0044	2	5.9135	2	2.0996	2	2.0468	2
Shanxi	1.1793	10	1.1179	13	0.9793	25	0.8793	26	0.8492	27
Heilongjiang	0.9845	24	0.9074	27	0.8968	28	0.7998	28	0.8429	28
Hebei	0.9778	25	0.9533	25	0.9604	26	0.9695	19	1.0000	11
Nei Mongol	1.0000	17	1.0000	17	1.0000	17	0.8974	24	1.0000	11
Zhejiang	1.0000	17	1.0000	17	1.0000	17	1.0023	12	1.0000	11
Jilin	0.8654	28	0.7839	29	0.7899	30	0.7610	30	0.7554	30
Fujian	1.0306	15	1.0574	15	1.1313	13	1.0212	7	1.0047	10
Guangxi	0.9469	26	1.0859	14	1.2888	10	0.8795	25	0.9021	24
Chongqing	1.0963	13	1.3146	10	1.2929	9	1.0544	6	1.0389	5
Henan	1.7292	6	1.4963	7	1.3173	8	1.0112	10	0.8694	26
Guizhou	1.0000	17	0.9931	24	1.0962	14	1.0000	13	1.0000	11
Hunan	0.9997	23	1.0000	17	1.0000	17	0.9999	18	1.0000	11
Guangdong	1.0000	17	1.0000	17	1.0000	17	1.0000	13	1.0000	11
Shandong	1.2864	9	1.5501	6	1.6311	6	1.0173	8	1.0000	11
Hubei	1.0000	17	1.0000	17	1.0014	16	1.0000	13	1.0000	11
Shaanxi	1.5329	7	1.3728	9	1.2239	11	0.9109	23	0.9891	21
Qinghai	1.0000	17	1.0000	17	1.0000	17	1.0059	11	1.0072	9
Sichuan	1.0549	14	1.0126	16	1.0373	15	1.0000	13	1.0000	11
Xinjiang	0.8472	29	0.8748	28	1.0000	17	0.9360	22	0.9865	22
Gansu	0.8361	30	0.7644	30	0.8096	29	0.7852	29	0.7844	29
Yunnan	1.0099	16	1.0000	17	1.0000	17	1.0000	13	1.0000	11
Ningxia	1.0977	12	1.1486	11	1.0000	17	1.0121	9	1.0179	7
Hainan	2.5381	3	2.8703	3	3.7001	3	1.6887	3	1.5886	4

EEE analysis in the three areas

To analyze the EEE considering fix-sum energy inputs under the AR constraint and IC on a relatively more dimensions. Thirty regions in China are divided into three groups (i.e., eastern area, western area, and central area) on the basis of their geographical characteristics. The eastern area includes Jiangsu, Shanghai, Zhejiang, Fujian, Guangdong, Shandong, Anhui, Jilin, Heilongjiang, Liaoning, Hainan, Hebei, Tianjin, and Beijing. The western area includes Chongqing, Shaanxi, Ningxia, Sichuan, Guizhou, Guangxi, Yunnan, Qinghai, Xinjiang, and Gansu. The central area includes Henan, Hubei, Hunan, Jiangxi, Shanxi, and Nei Mongol. We compare the average EEE scores during the study period in the three areas based on the FSIDEA, AR-FSIDEA, and IC-FSIDEA models. The results are presented in Figure 3.

Overall, the average EEE score of the eastern area is higher than the other two areas. After the implementation of AR constraint and IC, the average EEE score of the central and western areas remains about 1, while that of the eastern area remains almost in the range of 1.7–2.6, which is significantly higher than the other two areas. Furthermore, combining the information from Tables 4 and 5, it can be found that the number of regions, whose EEE scores are >1, in the eastern area is significantly higher than that in the central and western areas. These results indicate that more measures should be taken to narrow the efficiency gap among the three areas.

Another point to note is that imposing the AR constraint and IC has a greater impact on EEE scores for the eastern areas compared to the other two areas. For example, the average EEE of the eastern area in 2015 is 2.47 using the FSIDEA model, and this value is 0.95 after introducing the AR constraint. A similar result can be found while adding the IC; for instance, the average EEE in the eastern area changed from 2.1 to 1.23 in 2016 and from 1.85 to 1.23 in 2017. On the contrary, the effects of AR constraint and IC on EEE in central and western areas are limited during the research period.

EEE analysis at the regional level

From a provincial perspective, Tianjin and Shanghai rank in the top two in terms of EEE scores every year, no matter whether AR constraint and IC are implemented or not. Hence, these two regions can be selected as benchmarks. This result is expected. The reason is that industry is the leading industry in Tianjin, the local government and enterprises have paid more attention to optimizing energy consumption structure, and gradually reducing coal consumption to further promote CO₂ emission abatement in the process of developing industry. Shanghai has focused on formulating more reasonable energy policies to achieve the coordinated development of energy and economy in the process of accelerating the construction of international economic, financial, and trade center. In contrast, Gansu and Jilin perform poorly during the study period due to their backward economic development level and unreasonable energy consumption structure. These two regions still depend mainly on the use of fossil fuels such as coal to achieve their economic growth, thereby resulting in a lower EEE. Overall, most regions perform poorly in terms of EEE. Take the 2017 results from the IC-FSIDEA model as an example, only Beijing (1.7003), Tianjin (2.3380), Shanghai (2.0408), and Hainan (1.5886) have a higher EEE score. Thus, there is great potential for other regions to improve their EEE.

From the perspective of the development trend of EEE, the average efficiency score at the national level and the number of regions with EEE values above 1 are relatively stable; however, it should also be noted that the EEE of about 10 regions presents an upward trend year by year, which indicates that an increasing number of regions have paid more attention to adjusting their energy consumption structure of the electric power sectors and increasing the proportion of renewable energy in total electricity consumption to further improve their EEE levels.

Conclusions

Under the policy of RES, this paper applies the DEA model to evaluate the EEE in 30 administrative regions in China. First, we have set a lower limit of renewable energy inputs in line with the high-quality green development of energy. Then, a common EEF is constructed by minimizing the weighted sum of renewable energy adjustments under fixed-sum restrictions. Furthermore, considering that traditional efficiency evaluation approaches fail to reflect a country's preference for renewable and non-renewable energy and the requirements of national energy green development transformation, we impose AR constraint and IC to adjust the common EEF. Last, the EEE of China's 30 regions is evaluated using the adjusted common EEF.

The empirical analysis reveals that the extended FSIDEA model in this study has a higher discrimination as it can comprehensively rank evaluated DMUs compared with the traditional BCC model. Introducing the AR constraint and IC into the FSIDEA model is reasonable as it can change the rankings of some regions. At the regional level, Shanghai and Tianjin can be selected as benchmarks owing to their outstanding performance no matter whether the AR constraint and IC are imposed, and the EEE of about 10 regions presents an increasing trend year by year, but overall, China's electric power industry in some regions has a poor EEE score. From the perspective of three areas, the eastern area performs better than the other two areas as a whole. Furthermore, adding the AR constraint and IC will exert a greater influence on the EEE scores of the eastern area than those of the western and central areas.

According to the above results, several recommendations are proposed to improve the EEE for China's electric power industry. First, a considerable number of provinces should further increase the proportion of renewable energy in total energy consumption as these provinces perform poorly while considering AR constraint and IC. Compared with fossil fuel, renewable energy use is friendly to the environment and can result in a higher EEE score. Thus, most of the provinces should further improve their renewable energy development policies, such as RES policy, to achieve the sustainable development targets. Second, limiting fossil fuel consumption is also important to promote the development of renewable energy. A feasible approach is to adjust the fossil fuel price to make them reflect market supply and demand. As we all know, a lower price will promote the fossil fuel consumption and pollution emissions and is not conducive to improving the technological innovation level of enterprise. Third, more measures should be taken to narrow the efficiency gaps between the eastern area and the other two areas. It is critical to consider the resource endowment of each area. For example, the western area is rich in renewable energy, but our results indicate that its EEE is not satisfactory. As such, it may be necessary to invest more funds to develop renewable energy technologies. Therefore, the western area can strengthen the technical cooperation with the eastern area, as technical transfer may be more convenient to promote renewable energy development for the western area.

In this study, we have constructed a common EEF by taking into account the weight and input restrictions of renewable energy; however, the unique common EEF still cannot be guaranteed. Therefore, future research can try to apply more strategies to identify the unique platform.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by the National Natural Science Foundation of China, China (Grants 71904084, 72271121, 71934001, 71834003, and 71573121), the Natural Science Foundation for Jiangsu Province, China (Grant BK20190427), the Major Programmer of National Social Science Foundation of China (Grants 20ZDA084 and 21&ZD110), the Postdoctoral Science Foundation of China (Grant 2020TQ0145), and the Innovation and Entrepreneurship Foundation for Doctor of Jiangsu Province, China.

ORCID iDs

Chengzhen Xu

Malin Song

Xifan Chen is a doctor in the College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His study mainly focuses on areas including renewable electricity quota, performance evaluation.

Qingyuan Zhu is a professor in the College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His study mainly focuses on areas including energy and environmental management, performance evaluation, and decision-making modeling. His articles have appeared in European Journal of the Operational Research, Omega, Journal of the Operational Research Society, etc.

Chengzhen Xu is a doctor in the College of Economics and Management, Nanjing University of Aeronautics and Astronautics. His study mainly focuses on areas including energy and environmental management, performance evaluation.

Zhiyang Shen is an associate Professor in IÉSEG School of Management. His study mainly focuses on areas including energy and environment, and economics. His articles have appeared in European Journal of Operational Research, IEEE Transactions on Engineering Management, Journal of Environmental Management, Omega, Energy Economics, Energy Policy, China Economic Review, etc.

Malin Song is a professor in the School of Statistics and Applied Mathematics, Anhui University of Finance and Economics. His study mainly focuses on areas including performance evaluation, and decision-making modeling. His articles have appeared in European Journal of the Operational Research, Omega, Energy Economics, Journal of the Operational Research Society, Annals of Operations Research, Transportation Research Part D: Transport and Environment, International Journal of Production Research, etc.

Appendix

Table A.

Names and abbreviations.

Names	Abbreviations
Renewable electricity quota standard	RES
Energy and environmental efficiency	EEE
Fix-sum energy input data envelopment analysis	FSIDEA
Assurance region	AR
Renewable energy input sum constraint	IC
Equilibrium effective frontier	EEF
Decision-making units	DMUs
Data envelopment analysis	DEA
Total factor energy efficiency	TFEE
Ecological total factor energy efficiency	ETFEE
Variable return to scale	VRS
Assurance Region Fixed-Sum Input DEA	AR-FSIDEA
Input Constraint-FSIDEA	IC-FSIDEA
Five-Year Plan for Renewable Energy Development	FYPRED
Gross Domestic Product	GDP
Analytic Hierarchy Process	AHP

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