For the technical and allocative efficiency evaluation of smart grid, this paper has proposed two methods. One is based on Data Envelopment Analysis and another is based on Stochastic Frontier Model. Among them, the former considered the dynamics of smart grid development and development dynamics is the influence parameter. The latter analyzed self-duality between the Cobb-Douglas production function and cost function; then, it deduced the smart grid resources optimization allocative efficiency evaluation model which can avoid price information needs of input factor in conventional allocative efficiency evaluation. The validity and rationality of the two methods are verified by a case study.
In process of its construction, the advanced technology is the key factor for the development of the grid in the intelligent direction [
In network analysis of technical progress, people have proposed the intelligent technique evaluation method with Cobb-Douglas production function which reflects the level of intelligent power grid development through contribution degree of computing technology to economic benefits [
One of the overall planning objectives for smart grid is to achieve a large range of resource optimization allocation [
Although the smart grid is in the phase of overall construction, the price information of input element is often difficult to get in assessment of technical efficiency. Therefore, according to the analysis of self-dual characteristic between the Cobb-Douglas production function and cost function, this paper has proposed the smart grid efficiency evaluation method based on Data Envelopment Analysis and Stochastic Frontier Model, then compared the two models and verified their usefulness according to the calculation results.
Data envelopment evaluation model is performed to evaluate the efficiency [
The constraints are shown below:
Through the optimization of the model, the parameters are set as follows:
In quantitative assessment of technological progress, the speed of technological progress and the contribution of technology can measure the technological development level of smart grid [
The sketch map of the relationship between technical efficiency and technical progress.
The technology efficiency is a relative concept, which can be understood as the ratio of the actual return output and the maximum output of the smart grid in the case of the given input elements [
Logarithmic form of Cobb-Douglas production function used in this paper is as follows:
The technical efficiency of grid enterprise
Improving the utilization of assets and the operating efficiency is the main characteristic of smart grid. At the same time, high efficiency is the core value of the smart grid for research institutions and power companies at home and abroad. From the point of scientific research, the allocative efficiency of quantitative evaluation for smart grid can not only reflect the grid optimization allocation of resources but also reflect the benefits of efficiency.
Combining production function and cost function is one of the theoretical tools to realize allocative efficiency evaluation. The Cobb-Douglas cost function [
From formula (
In order to avoid the requirement for the input factor price, according to the inherent duality between production function and cost function, the optimization model can be established with formula (
For Cobb-Douglas production function with stochastic frontier characteristic, in the realization of technology efficiency and allocative efficiency evaluation, parameters to be estimated are elastic coefficients (
Based on the observation data of input and output in smart grid, this paper estimates the parameter through least squares which is based on minimum squared residuals [
The model test is determined by statistical theory. The purpose is to evaluate the correctness and reliability of model in the process of setting and estimating parameters [
Set assumptions: null hypothesis: Under the condition of In the given significance level Do the hypothesis test: if
According to the evaluation index system of smart grid with high efficiency characteristic (to optimize asset utilization efficiency and power network operation efficiency) by EPRI, we can select appropriate economic indicators as input and output cells for evaluation model combined with development strategy of smart grid in China [
Data collection.
Order | Power company | Input amount | Output amount | ||||||
---|---|---|---|---|---|---|---|---|---|
(1) Power grid investment (ten thousand yuan) | (2) Infrastructure Investment (ten thousand yuan) | (3) Technological investment (ten thousand yuan) | (4) Marketing investment (ten thousand yuan) | (5) Information technology (ten thousand yuan) | (1) Total profit (ten thousand yuan) | (2) Electricity sales (million kwh) | (3) Purchase price difference (Y/ thousand kwh) | ||
1 | Fujian | 1260422 | 1158031 | 69000 | 153615 | 17139 | 239868 | 1397.80 | 214.16 |
2 | Tianjin | 620911 | 547966 | 22845 | 111471 | 12491 | 95404 | 6078.01 | 237.29 |
3 | Hebei | 912164 | 850828 | 40977 | 118861 | 13541 | 89700 | 13908.74 | 210.08 |
4 | Jiangsu | 2977447 | 2765963 | 121570 | 388372 | 17518 | 686197 | 38488.39 | 152.91 |
5 | Shandong | 2804030 | 2615571 | 107399 | 283868 | 18150 | 595476 | 32978.29 | 123.09 |
6 | Shanghai | 1079683 | 628907 | 128095 | 153731 | 29877 | 110202 | 11174.96 | 224.62 |
7 | Shanxi | 926989 | 807855 | 46466 | 185648 | 13989 | 88613 | 16295.99 | 126.32 |
8 | Zhejiang | 2290509 | 2134974 | 99994 | 239306 | 18355 | 588559 | 28026.15 | 217.98 |
9 | Anhui | 1125446 | 961436 | 107345 | 126241 | 15914 | 75821 | 1250.51 | 191.20 |
10 | Beijing | 643251 | 594054 | 28141 | 132705 | 14041 | 152093 | 7920.60 | 206.48 |
11 | Hubei | 1136556 | 1008999 | 53240 | 171112 | 17442 | 71546 | 1190.21 | 196.62 |
12 | Hunan | 891914 | 776652 | 45236 | 155489 | 16123 | 71723 | 961.89 | 200.39 |
13 | Henan | 1387564 | 1258219 | 87000 | 122140 | 18701 | 126149 | 2399.22 | 112.26 |
14 | Jiangxi | 877297 | 800046 | 22470 | 102954 | 16176 | 65327 | 730.40 | 252.21 |
15 | Sichuan | 2838232 | 2592478 | 157049 | 181748 | 19244 | 99523 | 180.40 | 159.64 |
Data source: Transportation Monitoring Center of State Grid Corporation of China.
Input quantity distributions for power company.
Some data is taken as the reference data set, including inputs 1, 2, 3, 4, and 5 and output of 1, 2, and 3; then, following regression results will be got though software package SPSS Statistics. The regression equation could be explained:
Through regression analysis and the test of parameter and model, the efficiency assessment function of smart grid based on Stochastic Frontier Model is obtained. Substituting reference data into this model can obtain technical efficiency and allocative efficiency index values of each company, as shown in Table
The results of technical efficiency and allocative efficiency.
Order | Technical inefficiency | Technical efficiency | Technical efficiency | Allocative efficiency |
---|---|---|---|---|
|
(SFM) | (DEA) | ||
1 | 0.32 | 0.729 | 0.616 | 0.564 |
2 | 0.17 | 0.846 | 0.752 | 0.743 |
3 | 0.33 | 0.718 | 0.615 | 0.545 |
4 | 0.14 | 0.869 | 0.799 | 0.782 |
5 | 0.17 | 0.841 | 0.733 | 0.733 |
6 | 0.09 | 0.916 | 0.988 | 0.861 |
7 | 0.76 | 0.466 | 0.455 | 0.248 |
8 | 0.06 | 0.944 | 1 | 0.911 |
9 | 0.16 | 0.851 | 0.765 | 0.752 |
10 | 0.07 | 0.929 | 1 | 0.881 |
11 | 0.86 | 0.422 | 0.403 | 0.208 |
12 | 0.82 | 0.439 | 0.431 | 0.218 |
13 | 0.14 | 0.872 | 0.923 | 0.782 |
14 | 0.27 | 0.763 | 0.647 | 0.614 |
15 | 0.56 | 0.573 | 0.52 | 0.366 |
Technical efficiency comparison.
Results are obtained by SFM method in Table
Calculation results of the allocative efficiency show that power companies 6, 8, and 10 have higher technical efficiency, and companies 7, 11, and 12 are lower. The result shows that the distribution law is similar to the technical efficiency, and high technical efficiency can also lead to high allocative efficiency. However, index value among power companies has big difference. For example, the eighth power company has a strong resource optimization allocation in the smart grid construction, while companies 7, 11, are 12 are weak.
As a whole, these companies have high technical efficiency and low allocative efficiency (means are 0.745 and 0.618). This shows that the smart grid can get higher yield with advanced technology in particular year, but it is still in the lower level in optimization allocation of resources.
Sensitivity analysis on efficiency evaluation model was conducted. Data includes input variable 6-Total installed capacity (104 Kw); input variable 7-Electricity (108 Kwh); input variable 8-Unit power distribution cost (yuan/103 Kwh). The following scene is assumed: Scene 1 is a set of basic data; Scene 2 is a set of basic data and new input variable 6; Scene 3 is a set of basic data and all new input variables; Scene 4 is a set of basic data and new input variables 7 and 8. New variable data collection is shown in Table
New variable data collection.
Order | Power company | (6) Total installed capacity |
(7) Electricity |
(8) Unit power distribution cost |
---|---|---|---|---|
1 | Fujian | 3885.4 | 1579.5 | 128.59 |
2 | Tianjin | 1132.1 | 711.9 | 163.48 |
3 | Hebei | 2618.2 | 1621.0 | 160.13 |
4 | Jiangsu | 7531.9 | 4580.9 | 117.41 |
5 | Shandong | 7079.8 | 3794.7 | 131.40 |
6 | Shanghai | 2143.3 | 1353.5 | 180.34 |
7 | Shanxi | 5454.9 | 1765.8 | 98.18 |
8 | Zhejiang | 6170.3 | 3213.4 | 169.96 |
9 | Anhui | 3532.1 | 1361.1 | 161.35 |
10 | Beijing | 765.6 | 874.3 | 163.21 |
11 | Hubei | 5787.6 | 1507.8 | 204.64 |
12 | Hunan | 3311.6 | 1346.5 | 198.45 |
13 | Henan | 5764.7 | 2747.7 | 102.00 |
14 | Jiangxi | 1937.0 | 867.7 | 212.41 |
15 | Sichuan | 5427.0 | 1830.7 | 171.86 |
Data source: Transportation Monitoring Center of State Grid Corporation of China.
Contrast of new investment for each company.
According to the stochastic frontier analysis model, results of technical and allocative efficiency with different scenarios are shown in Tables
The results of technical efficiency in different situation.
Order | Technical efficiency | |||
---|---|---|---|---|
Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |
1 | 0.72864 | 0.75 | 0.816 | 0.837 |
2 | 0.84645 | 0.89 | 0.93 | 0.963 |
3 | 0.71775 | 0.74 | 0.803 | 0.855 |
4 | 0.86922 | 0.87 | 0.923 | 0.944 |
5 | 0.84051 | 0.88 | 0.941 | 0.967 |
6 | 0.91575 | 0.92 | 0.95 | 0.971 |
7 | 0.46629 | 0.61 | 0.63 | 0.651 |
8 | 0.94446 | 0.95 | 0.97 | 0.991 |
9 | 0.8514 | 0.88 | 0.953 | 0.973 |
10 | 0.92862 | 0.92 | 0.935 | 0.956 |
11 | 0.42174 | 0.51 | 0.554 | 0.575 |
12 | 0.43857 | 0.52 | 0.564 | 0.585 |
13 | 0.87219 | 0.85 | 0.912 | 0.933 |
14 | 0.76329 | 0.73 | 0.854 | 0.921 |
15 | 0.57321 | 0.62 | 0.641 | 0.73 |
Results of allocative efficiency in different situation.
Order | Allocative efficiency | |||
---|---|---|---|---|
Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | |
1 | 0.5643 | 0.612 | 0.6487 | 0.701 |
2 | 0.7425 | 0.751 | 0.7961 | 0.821 |
3 | 0.5445 | 0.634 | 0.6720 | 0.731 |
4 | 0.7821 | 0.732 | 0.7759 | 0.838 |
5 | 0.7326 | 0.711 | 0.7537 | 0.814 |
6 | 0.8613 | 0.921 | 0.9531 | 0.966 |
7 | 0.2475 | 0.432 | 0.4579 | 0.632 |
8 | 0.9108 | 0.912 | 0.9550 | 0.977 |
9 | 0.7524 | 0.773 | 0.8194 | 0.885 |
10 | 0.8811 | 0.911 | 0.9234 | 0.934 |
11 | 0.2079 | 0.326 | 0.3456 | 0.543 |
12 | 0.2178 | 0.543 | 0.5756 | 0.632 |
13 | 0.7821 | 0.811 | 0.8597 | 0.928 |
14 | 0.6138 | 0.601 | 0.6371 | 0.688 |
15 | 0.3663 | 0.442 | 0.4685 | 0.654 |
Comparison of results of technical efficiency in different situation.
Comparison of results of allocative efficiency in different situation.
In order to compare the allocation efficiency of different provinces under different situations, the allocation efficiency of four scenarios is sorted, and results are shown in Table
Sort of allocative efficiency.
Order | Power company | Sort | |||
---|---|---|---|---|---|
Scenario 1 | Scenario 2 | Scenario 3 | Scenario 4 | ||
1 | Fujian | 2 | 3 | 3 | 3 |
2 | Tianjin | 7 | 6 | 6 | 7 |
3 | Hebei | 11 | 9 | 9 | 9 |
4 | Jiangsu | 4 | 7 | 7 | 6 |
5 | Shandong | 8 | 8 | 8 | 8 |
6 | Shanghai | 3 | 1 | 2 | 2 |
7 | Shanxi | 13 | 14 | 14 | 13 |
8 | Zhejiang | 1 | 2 | 1 | 1 |
9 | Anhui | 6 | 5 | 5 | 5 |
10 | Beijing | 10 | 10 | 10 | 10 |
11 | Hubei | 15 | 15 | 15 | 15 |
12 | Hunan | 14 | 12 | 12 | 14 |
13 | Henan | 5 | 4 | 4 | 4 |
14 | Jiangxi | 9 | 11 | 11 | 11 |
15 | Sichuan | 12 | 13 | 13 | 12 |
From the results of technical efficiency and allocative efficiency, we can see that the efficiency is approved through new input variable. The results show that the advanced technology and management mechanism make the full use of technology and capital, and the efficiency level of power companies is effectively improved.
From Table
This paper has proposed a new method for evaluating technical and allocative efficiency of smart grid based on Stochastic Frontier Model and Data Envelopment Analysis. In the establishment of efficiency assessment model, it can reflect the technology production capacity and optimal allocation ability for resources of smart grid. The following main conclusions are obtained by example simulation: By establishing the efficiency assessment model of smart grid based on the stochastic frontier function, the effect of input-output relationship on efficiency is analyzed under random factors. Technical efficiency reflects the ability to get the maximum return with fixed investment. The same numerical distribution law can be obtained with the method in this paper. Allocation efficiency reflects the overall capability of optimizing the allocation of resources. The proposed allocation efficiency model can avoid the requirement of the cost function for the price information and provide a reference for smart grid to evaluate resources optimization ability. Results were greatly different with different input variable, which shows the proposed allocation efficiency can be adjusted according to the actual need. Results of contrasting allocative efficiency in 15 regions showed that the efficiency of Zhejiang, Shanghai, and Beijing is much better than others, and it can have the same conclusion considering new variables.
The authors declare that there is no conflict of interests regarding the publication of this paper.