Evaluation and Prediction of Comprehensive Efficiency of Wind Power System in China Based on Two-Stage EBM Model and FNN Model
Abstract
1. Introduction
2. Methods
2.1. Two-Stage EBM Model Setting
- : the output of the DMU,
- : the input of the DMU,
- : Slack variable,
- : Surplus variable,
- : Weight of the input i,
- : Weight of output S,
- : the key parameter that combines the input radial θ and the non-radial slack terms.
- : the key parameter that combines the output radial θ and the non-radial slack terms.
- (k, h): the link from Division k to Division h.
2.2. Tobit Regression Model Setting
2.3. Prediction Model
3. Data
3.1. Data Overview
3.1.1. Two-Stage EBM Model
3.1.2. Tobit Regression Model
- Dependent variable: The dependent variable is the comprehensive efficiency of wind power systems in various regions of China, measured using the two-stage EBM model.
- Independent variables: This study examines the factors influencing the comprehensive efficiency of wind power systems, comprehensively considering natural resource factors, technical factors, and economic factors. Uncertainty factors, such as weather, temperature, and humidity, can impact the actual data of wind power generation [53,54]. Few studies have thoroughly explored the impact of extreme natural conditions. Therefore, this paper selects the extreme low-temperature index, extreme rainfall index, and extreme drought index to investigate the influence of extreme weather on wind power system efficiency. Technical and economic factors, such as green finance, technological progress, and price policies, have also been shown to impact the development of wind power [55,56,57]. Unlike previous studies, this paper selects the level of wind power technological innovation, human resources in the power industry, and electricity demand to explore the impact of technical and economic factors on wind power system efficiency. The independent variables are described in detail as follows:
- LTD, ERD, and EDD: Extreme low-temperature index, extreme rainfall index, and extreme drought index. Extreme weather events threaten economic development and energy supply, potentially affecting wind power systems, which are highly reliant on wind resources. The occurrence of extreme weather events also represents disturbances in the resource subsystem. The extreme low-temperature index, extreme rainfall index, and extreme drought index used in this study are sourced from the extreme climate index data constructed by Guo, Ji, and Zhang (2024) [58]. The higher the index, the more frequent the corresponding extreme weather events in the region during that year, and the more unstable the resource subsystem becomes.
- Technology: The level of technological innovation in wind power. The level of wind power technology innovation is the key element of the technology subsystem. The improvement of technological innovation in wind power demonstrates the transformation of the technology subsystem. Wind turbines are the key equipment for wind power generation. The IPC classification number F03D [59] specifically identifies wind turbine technology, covering patents related to wind power generation equipment and associated technologies. Due to the lag in patent authorization, the number of patent applications better reflects the technological innovation vitality of wind power in each province compared to the number of granted patents. In this study, the total number of invention and utility model patent applications for wind power technology in each province during the current year, with the restriction of “IPC = F03D”, was manually collected. The logarithm of the total number of wind power technology patent applications + 1 was used to measure the innovation level of wind power technology. Patent data is sourced from the China National Intellectual Property Administration.
- HR: Human resources. Professional technical personnel are essential for the efficient operation of wind power equipment and the proper maintenance of the power transmission network. Human resources are part of the operation and maintenance capabilities of the technology subsystem, while reflecting the cost burden of the economy subsystem. A shortage of human resources can limit the construction and operational efficiency of wind power systems, while an overinvestment in human resources may lead to resource waste and increased costs, resulting in lower efficiency. Given the available data, this study collects employment figures for the electricity, gas, and water production and supply industry. These values are then transformed using logarithms to measure the human resource situation. Data on the number of employees in this industry is sourced from the CSMAR database.
- Electricity: Electricity demand. Insufficient electricity demand may result in inadequate accommodation capacity of regional power grids, leading to the abandonment of wind power and a loss of comprehensive efficiency. Electricity demand reflects the market demand in the economic subsystem and is the main driving force for the change of the economic subsystem. This study collects data on electricity consumption and logarithmically measures the electricity demand of each province for the current year. The electricity consumption data is sourced from the China Statistical Yearbook.
3.2. Descriptive Statistics
Input and Output Variables
4. Results
4.1. Overall Efficiency Analysis
4.2. Stage Efficiency Analysis
4.3. Sub-Index Efficiency Analysis
4.4. Tobit Regression Analysis
4.5. Statistical Testing of Metrics
4.6. Prediction Analysis
5. Discussion
6. Conclusions and Suggestions
6.1. Conclusions
- The national average efficiency of wind power systems remains low (0.284), but exhibits a steady upward trend over time, particularly after 2020. Spatial disparities are pronounced: Northeast and Western regions show higher efficiency, reflecting more effective subsystem coordination, while resource-limited Eastern and Central regions lag behind.
- The efficiency of both development and operation stages has improved over time, though the drivers differ. In the development stage, PTE dominates, underscoring the role of technological optimization in siting and construction. In contrast, SE is more influential in the operation stage, indicating shortcomings in maintenance and management practices that limit technological effectiveness.
- Subsystem coordination remains insufficient. While strong resource conditions enhance development efficiency in certain regions, there is limited synergy between the development and operation stages. This suggests that the resource–technology–economy triadic framework has not yet achieved integrated optimization.
- Influencing factors vary across subsystems. Within the resource subsystem, extreme rainfall and drought positively affect efficiency, whereas extreme cold conditions reduce it, exposing its volatility and vulnerability. Technological innovation promotes efficiency, while inefficient human resources constrain it. Electricity demand positively drives efficiency, revealing the economy subsystem’s market-pull effect.
- Projections indicate that overall efficiency will continue to rise under technological support, though regional imbalances are expected to persist. This underscores the need for targeted interventions in low-efficiency regions and a shift from scale expansion to quality-focused, technology-led development.
6.2. Suggestions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
EBM | Epsilon-Based Measure |
DEA | Data Envelopment Analysis |
ANN | Artificial Neural Network |
LSTM | Long Short-Term Memory network |
CCR | Charnes-Cooper-Rhodes model |
BCC | Banker-Charnes-Cooper Model |
SBM | Slacks-Based Measure Model |
APPHE | AFSA-PSO-parallel-hybrid evolutionary |
IPC | International Patent Classification |
CSMAR | China Stock Market and Accounting Research Database |
FNN | Feedforward neural network |
DMU | Decision-making unit |
S1 | Development stage |
S2 | Operation stage |
TE | Technical efficiency |
PTE | Pure technical efficiency |
SE | Scale efficiency |
AWS | Average wind speed |
PD | Population density |
ULA | Unutilized land area |
WPIC | Wind power installed capacity |
OAMC | Operation and maintenance cost |
WPG | Wind power generation |
ESI | Energy substitution income |
LTD | Extreme low-temperature index |
ERD | Extreme rainfall index |
EDD | Extreme drought index |
HR | Human resources |
KMO | Kaiser-Meyer-Olkin Measure of Sampling Adequacy |
Appendix A
Region | Province |
---|---|
Eastern region | Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan |
Central region | Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan |
Western region | Gansu, Guangxi, Guizhou, Inner Mongolia, Ningxia, Qinghai, Shaanxi, Sichuan, Xinjiang, Xizang, Yunnan, Chongqing |
Northeast region | Heilongjiang, Jilin, Liaoning |
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Stage | Indicator Attribute | Variable | Meaning | Unit | Literature Support |
---|---|---|---|---|---|
Development stage (S1) | Input | Average wind speed | The main indicators for evaluating wind energy resources | m/s | Latinopoulos and Kechagia (2015) [52]; Hua et al. (2024) [19] |
Population density | Population/land area | person/km2 | Hua et al. (2024) [19] | ||
Unutilized land area | The area of grassland and bare land suitable for a wind power system | km2 | Hua et al. (2024) [19] | ||
Output | Wind power installed capacity | The main indicators for evaluating the construction achievements and power generation capacity of the wind power system | 10 MW | Dong and Shi (2019) [7] | |
Operation stage (S2) | Input | Operation and maintenance cost | The annual cost for the operation and maintenance of the wind power system | 104 yuan | Dong and Shi (2019) [7] |
Output | Wind power generation | The annual electricity generated by the regional wind power system | 105 MWh | Dong and Shi (2019) [7] | |
Energy substitution income | The cost of carbon emissions is saved by wind power generation, replacing coal-fired power generation to produce clean electricity | 104 yuan | Dong and Shi (2019) [7] |
Variable | Subsystem | Unit (of Measure) | Coefficient | z | p > |z| |
---|---|---|---|---|---|
LTD | Resource subsystem | / | −0.0008681 ** | −2.36 | 0.018 |
ERD | Resource subsystem | / | 0.0009972 *** | 3.12 | 0.002 |
EDD | Resource subsystem | / | 0.0012309 ** | 2.41 | 0.016 |
Technology | Technology subsystem | pieces | 0.0973076 *** | 7.05 | 0.000 |
HR | Technology-economy subsystem | 104 persons | −0.1738902 *** | −3.96 | 0.000 |
Electricity | Economy subsystem | 108 kWh | 0.3447305 *** | 8.82 | 0.000 |
KMO Value | 0.602 | |
---|---|---|
Bartlett’s Test of Sphericity | Approximate chi-square | 1452.807 |
df | 36 | |
p value | 0.000 |
Province | R2 | MSE | Value | 2012 | 2015 | 2018 | 2021 | Trend |
---|---|---|---|---|---|---|---|---|
Anhui | 0.9736 | 0.0189 | pre | 0.057 | 0.093 | 0.135 | 0.335 | |
true | 0.06 | 0.104 | 0.189 | 0.377 | ||||
Beijing | 0.9755 | 0.0057 | pre | 0.044 | 0.054 | 0.085 | 0.129 | |
true | 0.044 | 0.054 | 0.085 | 0.129 | ||||
Fujian | 0.9958 | 0.0117 | pre | 0.292 | 0.401 | 0.551 | 0.694 | |
true | 0.119 | 0.201 | 0.269 | 0.532 | ||||
Gansu | 0.9499 | 0.0336 | pre | 0.1 | 0.16 | 0.228 | 0.451 | |
true | 0.25 | 0.401 | 0.551 | 0.694 | ||||
Guangdong | 0.9952 | 0.0105 | pre | 0.117 | 0.161 | 0.205 | 0.471 | |
true | 0.114 | 0.161 | 0.204 | 0.438 | ||||
Guangxi | 0.9247 | 0.0718 | pre | 0.023 | 0.025 | 0.094 | 0.749 | |
true | 0.048 | 0.071 | 0.239 | 0.679 | ||||
Guizhou | 0.9710 | 0.0292 | pre | 0.098 | 0.256 | 0.351 | 0.442 | |
true | 0.098 | 0.256 | 0.348 | 0.544 | ||||
Hainan | 0.9032 | 0.0107 | pre | 0.095 | 0.092 | 0.118 | 0.173 | |
true | 0.095 | 0.129 | 0.118 | 0.172 | ||||
Hebei | 0.9989 | 0.0073 | pre | 0.262 | 0.52 | 0.511 | 0.823 | |
true | 0.259 | 0.52 | 0.511 | 0.823 | ||||
Henan | 0.9601 | 0.0489 | pre | 0.058 | 0.08 | 0.199 | 0.69 | |
true | 0.054 | 0.069 | 0.198 | 0.691 | ||||
Heilongjiang | 0.9929 | 0.0178 | pre | 0.291 | 0.495 | 0.627 | 0.822 | |
true | 0.355 | 0.495 | 0.627 | 0.822 | ||||
Hubei | 0.9853 | 0.0201 | pre | 0.044 | 0.1 | 0.242 | 0.495 | |
true | 0.043 | 0.114 | 0.242 | 0.496 | ||||
Hunan | 0.9543 | 0.0375 | pre | 0.046 | 0.133 | 0.238 | 0.52 | |
true | 0.046 | 0.133 | 0.238 | 0.52 | ||||
Jilin | 0.9735 | 0.0294 | pre | 0.278 | 0.368 | 0.484 | 0.678 | |
true | 0.278 | 0.368 | 0.484 | 0.656 | ||||
Jiangsu | 0.9983 | 0.0107 | pre | 0.12 | 0.197 | 0.405 | 0.814 | |
true | 0.12 | 0.197 | 0.371 | 0.814 | ||||
Jiangxi | 0.9537 | 0.0342 | pre | 0.075 | 0.081 | 0.188 | 0.404 | |
true | 0.053 | 0.085 | 0.213 | 0.46 | ||||
Liaoning | 0.9815 | 0.0259 | pre | 0.283 | 0.414 | 0.513 | 0.73 | |
true | 0.283 | 0.408 | 0.566 | 0.744 | ||||
Inner Mongolia | 0.9278 | 0.061 | pre | 0.482 | 0.731 | 0.714 | 0.936 | |
true | 0.364 | 0.545 | 0.714 | 0.936 | ||||
Ningxia | 0.9872 | 0.0317 | pre | 0.272 | 0.473 | 0.719 | 1 | |
true | 0.272 | 0.474 | 0.717 | 0.997 | ||||
Qinghai | 0.9341 | 0.0442 | pre | 0.168 | 0.104 | 0.262 | 0.509 | |
true | 0.08 | 0.104 | 0.262 | 0.509 | ||||
Shandong | 0.9927 | 0.0175 | pre | 0.216 | 0.315 | 0.423 | 0.727 | |
true | 0.216 | 0.321 | 0.423 | 0.727 | ||||
Shanxi | 0.9446 | 0.0636 | pre | 0.168 | 0.33 | 0.548 | 0.728 | |
true | 0.168 | 0.33 | 0.548 | 0.902 | ||||
Shaanxi | 0.9674 | 0.0306 | pre | 0.08 | 0.138 | 0.362 | 0.535 | |
true | 0.082 | 0.146 | 0.253 | 0.536 | ||||
Shanghai | 0.9565 | 0.0337 | pre | 0.093 | 0.109 | 0.371 | 0.502 | |
true | 0.092 | 0.176 | 0.371 | 0.502 | ||||
Sichuan | 0.9856 | 0.0155 | pre | 0.036 | 0.058 | 0.243 | 0.362 | |
true | 0.038 | 0.058 | 0.194 | 0.362 | ||||
Tianjin | 0.9933 | 0.0049 | pre | 0.054 | 0.085 | 0.091 | 0.18 | |
true | 0.055 | 0.09 | 0.089 | 0.176 | ||||
Xizang | 0.9982 | 0.0024 | pre | 0.036 | 0.005 | 0.061 | 0.036 | |
true | 0.036 | 0.005 | 0.061 | 0.036 | ||||
Xinjiang | 0.9378 | 0.0600 | pre | 0.16 | 0.371 | 0.732 | 0.782 | |
true | 0.16 | 0.371 | 0.568 | 0.782 | ||||
Yunnan | 0.9575 | 0.0519 | pre | 0.226 | 0.42 | 0.636 | 0.764 | |
true | 0.167 | 0.411 | 0.64 | 0.772 | ||||
Zhejiang | 0.9962 | 0.0052 | pre | 0.055 | 0.078 | 0.134 | 0.224 | |
true | 0.055 | 0.078 | 0.134 | 0.224 | ||||
Chongqing | 0.9807 | 0.0089 | pre | 0.045 | 0.046 | 0.081 | 0.179 | |
true | 0.041 | 0.043 | 0.09 | 0.177 |
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Ren, F.-R.; Liu, H.-L.; Liu, X.-Y. Evaluation and Prediction of Comprehensive Efficiency of Wind Power System in China Based on Two-Stage EBM Model and FNN Model. Systems 2025, 13, 579. https://doi.org/10.3390/systems13070579
Ren F-R, Liu H-L, Liu X-Y. Evaluation and Prediction of Comprehensive Efficiency of Wind Power System in China Based on Two-Stage EBM Model and FNN Model. Systems. 2025; 13(7):579. https://doi.org/10.3390/systems13070579
Chicago/Turabian StyleRen, Fang-Rong, Hui-Lin Liu, and Xiao-Yan Liu. 2025. "Evaluation and Prediction of Comprehensive Efficiency of Wind Power System in China Based on Two-Stage EBM Model and FNN Model" Systems 13, no. 7: 579. https://doi.org/10.3390/systems13070579
APA StyleRen, F.-R., Liu, H.-L., & Liu, X.-Y. (2025). Evaluation and Prediction of Comprehensive Efficiency of Wind Power System in China Based on Two-Stage EBM Model and FNN Model. Systems, 13(7), 579. https://doi.org/10.3390/systems13070579