Unified Efficiency Measurement of Electric Power Supply Companies in China

This paper measured the economic and unified efficiency of 24 electric power supply companies in China. With the development of a low carbon economy, further requirements for energy-saving and emission-reducing have been put forward for electric power supply companies. In this case, we considered the desirable (good) outputs (e.g., electricity sale amount) and undesirable (bad) outputs (e.g., line loss) in evaluating the performance of power supply companies. We combined the unified efficiency data envelopment analysis (DEA) model and the super-efficiency DEA model to create tge USDEA model, calculating companies' unified efficiency. The unified efficiency DEA model can easily incorporate both desirable and undesirable outputs in a unified analytical structure. The super-efficiency data envelopment analysis model can make a comparison among various efficient decision making units (DMUs). Our results showed that the electric power supply companies of Hebei, Qinghai, Ningxia, Beijing and Shanghai achieved the highest levels of unified efficiency during the observed period (2003–2010), which differed from the economic efficiency results. The results meant that using unified efficiency to evaluate power supply companies will motivate them to care more about social and environmental benefit besides economic benefit.


Introduction
With rapid growth of the economy and support from foreign countries, China's electric power industry has entered a new stage.China has achieved second in the world in electric power generation capacity and first in transmission line and transformation capacity.At the end of 2011, the national power generation capacity was 1,055.76gigawatts (GW), the total transformation capacity above 110(66) kilovoltage (kV) was 239,162 × 10 4 kVA, the total length of transmission lines above 35 kV was 135 × 10 4 km.If these amounts of resources could not be used well or oversupplied, lots of labor force, materials and money could be consumed in vain.In order to avoid blind investment, we should pay more attention to the performance of electric power supply companies.However, the economic benefits, such as investment revenue rate and total production value, are usually used as the targets of performance evaluation of Chinese electric power supply companies.In fact, with the voice of "sustainable development" continuing to soar, Chinese electric power supply companies should also consider the environmental benefit and social benefit as well.In order to achieve this, we need to measure the unified performance of electric power supply companies, which is also important for comparing traditional economic performance.
The data envelopment analysis (DEA) method is a common method to measure the efficiency scores.The DEA method was proposed by Charnes et al. [1] for evaluating the relative efficiency of the decision making units (DMUs).Now, the DEA method has been used to measure the efficiency of the electric power supply companies around the world, such as Turkey [2], Sweden [3], Australia, New Zealand [4], Philippines [5], UK [6], Taiwan [7], and Scandinavian Electricity Distribution [8].However, research about Chinese electric power supply companies' unified efficiency is rare.
In this paper, we measured the performance of Chinese electric power supply companies with the consideration of energy saving by a proposed DEA approach, the unified super data envelopment analysis (USDEA) approach, which is a combination of unified efficiency data envelopment analysis (DEA) model and the super-efficiency DEA model.The remaining structure of this study is organized as follows: In section 2, the current structure of the electric power supply industry in China was outlined.Section 3 described previous DEA approaches and introduces a modified DEA approach methodology, which is a combination of unified DEA and super DEA.Section 4 described the efficiency measurement of the electric power supply companies in China.The last section made conclusions and discussed the implications of our empirical results.

The Current Structure of the Electric Power Supply Industry in China
In China, 90% of generating companies are owned by the state, and transmission is 100% government-owned.In order to accelerate the development of the electric power industry, the Chinese government implemented reforms in 2002 to dismantle the State Power Corporation into 11 new companies including two electric power supply companies, five electric power generation companies and four other companies, in order to end the power corporation's monopoly.However, until now, the grid corporation is still a central enterprise belonging to state monopoly management.The two electric power supply companies are the State Power Grid (SGCC) and China South Power Grid.The SGCC is the largest electric power supply company including 26 provinces' electric power supply subsidiary companies such as Beijing electric power supply company, Tianjin electric power supply company, and Hebei electric power supply company, which are shown in Figure 1.The length of the transmission lines above 35 kV operated by SGCC was 316,770 km at the end of 1997 and increased to 727,820 km until 2010.The average growth rate is 6.63%.Detailed data are shown in Figure 2. The voltage degrees of the transmission lines are 750 kV, 500 kV, 330 kV, 220 kV, 110 kV, and 35 kV.The percentage of voltage degrees of the transmission lines in 1997 and 2010 are shown respectively in Figure 3.It shows that the proportion of high voltage degree transmission lines has increased, with the proportion of transmission lines above 330kV being about 17% in 2010.Transformer capacity above 35kV operated by the SGCC was 449.81 GVA at the end of 1997, and it increased to 2,308.99 GVA at the end of 2010.The average growth rate is 13.33%.The detailed data are shown in Figure 4. Similar with the transmission lines' voltage degree structure, there was a trend in the percentage of transformer capacity to a high voltage degree as shown in Figure 5.The proportion of transformer capacity above 330kV was nearly 30% in 2010.

Literature Survey
Since the early 1990s, DEA has gradually become a popular benchmarking tool for studying the efficiency of electricity distribution utilities (Weyman-Jones [9]).Until now, much research has appeared in the literature and the study scope has also expanded from a single country case to an international one.Such published papers are shown in Table 1.It is an important step in the DEA method to choose the inputoutput variables.As shown in Table 1, the most frequently used outputs are units of energy delivered, number of customers, and size of the service area.The most widely used inputs are the number of employees, transformer capacity, and network length.In some papers, the transmission line loss was also taken as an input (Raul Perez-Reyes, Beatriz Tovar [10], and Ramos-Real et al. [11]) or output variable (Tooraj Jamasb and Michael Pollitt [12]).There are altogether four efficiency analysis methodologies used in these papers, including DEA, Malmquist index, DEA-PCA and DEA-COLS-SFA.

Data Envelopment Analysis
Data envelopment analysis (DEA) is a non-parametric technique to assess the relative efficiencies of multi-input and multi-output production units.DEA uses linear programming methodology to define a production frontier for decision-making units (DMUs), then like Stochastic Frontier Analysis (SFA), DEA identifies a "frontier" on which the relative performance of all utilities in the sample can be compared: DEA benchmarks DMU only against the best producers.It can be characterized as an extreme point method which assumes that if a DMU can produce a certain level of output utilizing specific input levels, another DMU of equal scale could be capable of doing the same [22].
Since the introduction of DEA by Charnes et al., several alternative models that preserve the upper bound of one for efficiency scores have been proposed.The main differences among these models are whether they are input or output oriented and whether they stipulate a constant or a variable return to scale.The original output-oriented DEA model which introduced by Adler, Friedman, and Sinuany-Stern [23] and Cook and Seiford [24] is as follows:  ).Also, the score of the DMU under consideration is o  .The DMUs cannot be ranked exactly since there are several DMUs which take score 1 by Model (1).To overcome this problem, Andersen and Petersen [25] proposed a new approach which leads to a concept called -super-efficiency‖.

Super-Efficiency DEA (SDEA) Model
In the super-efficiency DEA model, the efficiency scores from the model are obtained by eliminating the data of the DMU to be evaluated from the solution set.The super-efficiency model is defined as follows: Model ( 2) computes the score of the DMU by removing it from constraints.Although Model ( 2) is introduced to rank efficient DMUs obtained by the model (1), we can use it to evaluate and rank all DMUs.

Unified Efficiency DEA Model
To deal with the undesirable (bad) outputs in assessing the operational and environmental performance of energy firms, Fare et al. [26] (pp.473-474) proposed the following directional distance function: Here, P(X) = {(G, B): X can produce (G, B)}.The P(X) indicates a production possibility set, which has a column vector of inputs (X) that can produce not only a column vector of desirable outputs (G) but also a column vector of undesirable outputs (B).In Equation ( 3), represents a directional vector for desirable and undesirable outputs,  is a magnitude of how much each DMU can simultaneously increase its desirable outputs and decrease its undesirable outputs within the production possibility set.The directional vector Here, the value  represents technical inefficiency.The direction vector ( , , ) x y b g g g g  = (0, , ) yb  determines the direction in which efficiency is measured.Given the technology and direction vector, the directional distance function measures the maximum feasible expansion of desirable output and contraction of undesirable output.For an efficient firm, which operates on the frontier, the value of the directional distance function  is zero.The directional distance function  is obtained by solving the maximization problem in model ( 5).Here, the outputs regarding the jth DMU are separated into desirable outputs ( rk g ) and undesirable outputs ( fk b ).This model can measure the efficiency by 1   , where  is obtained from optimality of Model (5).
In addition to Model (5), Zhou and Ang [28] proposed the following model to measure the unified efficiency of the energy firms:  ).Model ( 6) can be considered as an extension of CCR (Charnes-Cooper-Rhodes) and the production possibility set of Model ( 6) is shaped by constant RTS (returns to scale).The USDEA model we proposed in this paper is on the basis of Model ( 6), which is illustrated in Section 4.4 of the paper.

The Unified Super DEA Model
The Model ( 6 Here, unified super DEA Model ( 7) computes the score of the DMU by removing itself from constraints, which is realized by letting the j ≠ k in the formula.s  is the slack variable related to desirable output.s  is the slack variable related to undesirable output.

The Efficiency Analysis Indexes of the Electric Power Supply Company
At the point of production, the input efficiency indexes of electric power supply companies were chosen based on human input (e.g., input 3), cost of production (e.g., input 4) and material resources (e.g., inputs 1 and 2).The output indexes were chosen based on the considerations of economic benefit (e.g., output 1), social benefit (e.g., outputs 2 and 3) and environmental benefit (e.g., output 4).Among the four outputs, outputs1, 2, and 3 are the desirable outputs, while output 4 (line loss) is an undesirable output.In this paper, four variables were used as inputs and four variables were used as outputs.The variables were listed as below. Inputs:

Data Collection
We studied the data of 24 electric power supply subsidiary companies of SGCC except East Inner Mongolia and Tibet Electric Power Supply Companies.Table 2 showed the raw data of 24 companies from 2003-2010.This study combined the data sets in the eight annual periods together into a single panel data set for our DEA application.Data have been gathered from China Electric Power Yearbooks, China Statistical Yearbooks and other various sources.

The Unified Efficiency of 24 Electric Power Supply Subsidiary Companies of SGCC
We studied the unified efficiency by USDEA and the economic efficiency through SDEA, respectively, in order to explore the difference between them.We used inputs (x1, x2, x3, and x4) and outputs (y1, y2, y3, and y4) to calculate the unified efficiency.We used inputs (x1, x2, x3, and x4) and output (y1) to calculate the economic efficiency.We presented the unified efficiency scores and the economic efficiency scores of 24 electric power supply subsidiary companies in Table 3 and Table 4, separately.The ranking of the efficiency was based on the average of eight years' efficiency.What we found from comparing unified efficiency with economic efficiency was listed as below: (i) The ranking of unified efficiency and economic efficiency was different based solely on outputs.The unified efficiency took into consideration environmental and social benefit, whereas the economic efficiency did not.(ii) Tianjin, Qinghai, Jiangxi and Chongqing power supply companies had a great improvement in ranking, their achievements in the social and environmental outputs were reflected.(iii) The unified efficiencies of 24 electric power supply companies did not show a clear trend but all displayed a fluctuation during the observed periods (2003-2010).In order to analyze the changes in the unified efficiency dynamically for each company during our research period, we selected four time points with an interval of one or two years between them-2003, 2005, 2008 and 2010-to illustrate 24 province electric power supply subsidiary companies' unified efficiencies.The result was displayed in Figure 6.It could be seen that: (i) The unified efficiency of Hebei electric power supply company showed the biggest deviation among the four time points, which standard deviation (S.D.) was 0.2535 (Table 3).(ii) The unified efficiency of 24 electric power supply companies in 2003, 2005 and 2008 did not change a lot, but the unified efficiency in 2010 showed a significant change.This result implied that 24 province electric power supply subsidiary companies experienced a great improvement in their social and environmental performance in 2010.This is due to the optimization of the grid structure and grid operation.We will collect and use related data to realize quantitative analysis of the unified efficiency.

Conclusions
This study discussed a new DEA approach to measure the economic and unified efficiency of electric power supply companies.Since the former unified DEA models did not realize the comparison among the efficient DMUs, we modified the unified DEA model taking into account super DEA.Then, we used the unified super DEA (USDEA) model to measure the performance of the 24 electric power supply subsidiary companies of SGCC.The results indicated that the combination of a unified efficiency model and applying a robust super-efficiency data envelopment analysis model can be more reliable for unified efficiency estimating and ranking strategies.
The results showed that although the subsidiary companies of SGCC have made great progress in the grid scale, such as in transmission line and transformer capacity, their overall performance is poor.There are only five subsidiary companies with unified efficiencies above 1 among the 24 subsidiary companies.Meanwhile, it is possible that electric power supply companies will not only pay attention to improving economic outputs but will also place more emphasis on the social and environmental outputs after learning of our unified efficiency measure method.This is an embodiment of sustainable development in electric power supply companies.
Future studies are encouraged to gain more insight into the companies in this study in order to draw more generalized conclusions.Meanwhile, a greater amount of data might also be needed.

Figure 1 .
Figure 1.The organization of the State Power Grid (SGCC).

Figure 2 .
Figure 2. The total length of the transmission lines above 35 kV of the SGCC and its growth rate.

Figure 3 .
Figure 3.The voltage degrees percentage of the transmission lines of the SGCC in 1997 and 2010.

Figure 4 .
Figure 4.The total transformer capacity above 35 kV of the SGCC and its growth rate.

Figure 5 .
Figure 5.The voltage degrees percentage of transformer capacity of the SGCC in 1997 and 2010.
Model (1) evaluates the relative efficiencies of n DMUs, with each DMU using m inputs x ij ( 1, , im  ) and generating s outputs rj y ( 1, , rs  is suggested as (1, 1, …, 1, −1, −1, … ,−1) T which contains s + h components.Mandal and Madheswaran[27] assumed that if the firm's objective is to simultaneously expand the desirable output and reduce the undesirable one by same proportion without increasing the inputs, the directional technology distance function becomes: ( , , ;0, , ) sup[ :[(1 ) ,(1 regarding the jth DMU are separated into non-energy ( : 1, , ) cannot realize the comparison of the efficient DMUs.In order to solve this problem, we proposed a new model: the unified super DEA (USDEA) model, which is a combination of unified efficiency DEA model (Model (6)) and the super-efficiency DEA model (Model (2)).The USDEA model has the following formulation:

Figure 6 .
Figure 6.The radar map of the 24 provinces' electric power supply subsidiary companies.

Table 1 .
Information on input-output variables and methods in related papers.

Table 3 .
Unified efficiency scores of the 24 distribution units.

Table 4 .
Economic efficiency scores of the 24 distribution units.