Abstract
Accurate wind power prediction can scientifically arrange wind power output and timely adjust power system dispatching plans. Wind power is associated with its uncertainty, multi-frequency and nonlinearity for it is susceptible to climatic factors such as temperature, air pressure and wind speed. Therefore, this paper proposes a wind power prediction model combining multi-frequency combination and feature selection. Firstly, the variational mode decomposition (VMD) is used to decompose the wind power data, and the sub-components with different fluctuation characteristics are obtained and divided into high-, intermediate-, and low-frequency components according to their fluctuation characteristics. Then, a feature set including historical data of wind power and meteorological factors is established, which chooses the feature sets of each component by using the max-relevance and min-redundancy (mRMR) feature selection method based on mutual information selected from the above set. Each component and its corresponding feature set are used as an input set for prediction afterwards. Thereafter, the high-frequency input set is predicted using back propagation neural network (BPNN), and the intermediate- and low-frequency input sets are predicted using least squares support vector machine (LS-SVM). After obtaining the prediction results of each component, BPNN is used for integration to obtain the final predicted value of wind power, and the ramping rate is verified. Finally, through the comparison, it is found that the proposed model has higher prediction accuracy.
WIND power has the characteristics of instability, which may lead to cascaded failure and certain shock in the power system. This brings severe challenges to the safe and stable operation of power system [
At present, wind power prediction methods commonly used at home and abroad are mainly machine learning methods such as neural network method [
For example, [
In recent years, some researchers have considered the influence of some factors in the wind power prediction process. For example, [
Based on the above discussion, this paper improves wind power prediction on the basis of [
The rest of this paper is organized as follows. Section II briefly introduces the prediction model and prediction performance evaluation indicators. Section III conducts case studies and analyzes the results. The research conclusions are given in Section IV.
According to the above discussion, the flow chart of the prediction method proposed in this paper is shown in

Fig. 1 Flowchart of prediction process.
It can be seen from
For the prediction methods of various frequencies, BPNN and LS-SVM are the mature methods that have been used in various fields including wind power prediction [
When evaluating the proposed model, this paper uses the MAPE to evaluate the prediction accuracy of intrinsic mode functions (IMFs). For comparison with other models, this paper uses three evaluation indicators including MAE, MSE, and RMSE. The calculation formulas of each indicator are as follows:
(1) |
(2) |
(3) |
(4) |
where is the actual value; is the predicted value; and M is the sample capacity.
The wind power data in this paper is collected every 10 minutes, and each wind farm has 144 data points per day. In this paper, the data in October, 2009 in northern Shaanxi, China and the data of wind farm in July, 2010 in Yunnan, China will be selected for analysis. For the division of the training set and test set, this paper uses a variety of divisions. Considering the influencing factors, the training data is used to train the model and make predictions on the test set, and the final prediction result is evaluated by MAE. The comparison results are shown in

Fig. 2 Wind power data for wind farm in northern Shaanxi, China in October, 2009.
The basic information of the wind power value is shown in
The wind power values of the two wind farms are highly random. In addition, the difference between the average and standard deviation of data of wind farm in Yunnan in July, 2010 is 0.88 MW, and the difference between the average and standard deviation of data of wind farm in northen Shannxi in October, 2009 is 4.56 MW. The greater the difference between the average and the standard deviation is, the greater the dispersion of the data will be. Therefore, by comparison, the wind power fluctuation of wind farm in northern Shaanxi in October, 2009 is stronger. In the following analysis, a specific explanation is conducted on the data of the wind farm in northern Shaanxi in October, 2009. The prediction process of the wind farm in Yunnan is consistent with that in northern Shaanxi. First, VMD is used to decompose the wind power data of the wind farm in northern Shaanxi in October, 2009 to better utilize its multi-frequency characteristics. The wind power data is decomposed by VMD, and the result is shown in
Each component, which is obtained by decomposing wind power data by the VMD, is shown in

Fig. 3 Decomposition map and spectrogram. (a) IMF1. (b) IMF2. (c) IMF3. (d) IMF4. (e) IMF5. (f) IMF6. (g) IMF7. (h) IMF8. (i) IMF9. (j) IMF10.
The wind power is affected by characteristic factors such as wind speed, temperature, and wind direction. Therefore, each sub-component obtained by decomposing the wind power using VMD is also affected by different characteristics. This sub-section will use mRMR to select the feature set of each component. The specific process is shown in

Fig. 4 Flowchart of component feature selection.
This paper first establishes a feature set. The features and representation variables contained in the set are shown in
The time scale of wind power in this paper is 10 minutes. Therefore, the time in
After the feature matrix is established, the candidate feature set J is established for each component, respectively, by using the incremental search method. The size of the mRMR value of each feature in the candidate feature set J is calculated, and the features are arranged in descending order according to the magnitude of the mRMR value. The descending sorting results of candidate feature sets of each feature component are shown in
After obtaining the candidate feature sets of the respective components, the features are input into the prediction model one by one to calculate the prediction error, and the number of input features with the smallest error is taken as the final input feature set . The MAPE is used for evaluation. The relationship between the error of each component and the number of input features is shown in

Fig. 5 Relationship between number of each component feature and error. (a) IMF1. (b) IMF2. (c) IMF3. (d) IMF4. (e) IMF5. (f) IMF6. (g) IMF7. (h) IMF8. (i) IMF9. (j) IMF10.
It can be seen from
1) Continuous fluctuation. We will get a minimum error in the fluctuation finally, for example,
2) Small fluctuation. The error first decreases and then undergoes a period of smooth fluctuation such as
Through the above analysis, the input feature set of each modal component is selected out, as shown in
It can be seen from
As described above, BPNN is used to predict high-frequency components, and LS-SVM is used to predict intermediate- and low-frequency components. Before adding the influencing factors, BPNN and LS-SVM are used to directly predict various frequency components of VMD decomposition, and MAPE is used to represent the error. The results are shown in
It can be seen from
To sum up, the prediction performance of BPNN is better than LS-SVM for high-frequency components, and the prediction performance of LS-SVM is better than BPNN for low- and intermediate-frequency components.
In the training model, the input data is extracted from the new matrix composed of the frequency components and the corresponding . When the input quantity of BPNN is trained, three points of high-frequency components and their corresponding features are used as the input of the neural network, which is also called the input layer. For example, the number of input layer nodes of IMF5 is 15. In addition, the number of iterations is set to be 1000, the learning speed is set to be 0.1, and the expected error is set to be 0.0004. When LS-SVM is trained, the kernel function is the radial basis function (RBF), and the particle swarm optimization (PSO) algorithm is used to optimize the kernel parameters and regularization parameters. After the model of each frequency component is trained, and the wind power prediction is done, the prediction results of the various frequency components are integrated using BPNN to obtain the final predicted values. The results and distribution map of predicted points are shown in

Fig. 6 Wind power prediction results. (a) Prediction and actual wind power. (b) Distribution of predicted points.
It can be seen from
In
Wind power ramping is likely to cause imbalances to the active power of the system, disrupt the frequency stability, and even lead to large-scale load shedding, which severely threatens the safe, stable, and economic operation of power system. Therefore, after predicting the wind power value, the wind power ramping rate still needs to be predicted. Wind power ramping rate refers to the rate of change of wind farm power caused by the random nature of wind, i.e., the power ramping rate (PRR), which is calculated as:
(5) |
where is the amplitude change value of wind power; and is the duration of power fluctuation. The key to the definition of wind power ramping rate is the selection of . Generally, has 3 reference values, 15 min, 30 min, and 60 min [

Fig. 7 Prediction results of wind power ramping rate. (a) Predicted and actual PRR. (b) Distribution of predicted points.
It can be seen from
In order to visually analyze the proposed prediction model, we compare the predicted point distribution maps of LS-SVM, BPNN, long short-term memory (LSTM), deep belief network (DBN), EMD combination prediction model, EEMD combination prediction model, and VMD combination prediction model considering influencing factors by using MI with the model proposed in this paper. Among them, the EMD combination prediction model, the EEMD combination prediction model, and the VMD combination prediction model firstly use EMD, EEMD, or VMD to decompose wind power data, and then use BPNN to predict high-frequency components and LS-SVM to predict intermediate- and low-frequency components, and finally, use BPNN for integration. For the VMD combination prediction model considering the influencing factors by using MI, after using VMD to decompose the wind power data, we use MI to consider the influencing characteristics of each modal component, BPNN to predict the high-frequency components, and LS-SVM to predict the intermediate- and low-frequency components. Finally, BPNN is used for integration.
In order to analyze the above model prediction results more intuitively, we compare each model using the evaluation indicators mentioned above. The calculation results are shown in
It can be clearly seen from
The combination prediction model proposed in this paper has the highest accuracy. For example, for MAE, the prediction accuracy in this paper is higher than those of the EMD combination model, EEMD combination model, and VMD combination model by 60.3%, 54.8%, and 22.5%, respectively. It can be seen that the wind power prediction accuracy is significantly improved considering the influencing factors such as meteorology.
Similarly, the prediction situation of wind farm in Yunnan is basically consistent with that of wind farm in northern Shaanxi. It can be seen from
In this paper, the combination of decomposition method and feature selection method considers not only the multi-frequency of wind power data, but also the influence of wind speed and temperature on wind power. In order to avoid the modal aliasing and false components of EMD and EEMD when decomposing wind power data, this paper uses VMD to decompose wind power, whose principle is completely different from those of EMD and EEMD, aiming to make better use of the multi-frequency of wind power and improve the prediction accuracy. In addition, wind power data is affected by wind speed, direction, and other characteristics, so the components of various frequencies contain the above information. To this end, this paper uses mRMR for feature selection, which aims to select the features that have a greater impact on the component of various frequencies. When selecting features, a feature matrix composed of wind speed, wind direction, temperature and other features is firstly established, and the incremental search method is used to establish candidate feature sets of each component. The features are then arranged in the candidate feature set in descending order of mRMR, and are input into the prediction model one by one to calculate the error. Finally, the number of features is taken with the smallest error as the input feature of the component. It can be seen from the case study that after considering the influence of features on each component, the model prediction accuracy is significantly improved. It turns out that the prediction model proposed in this paper has higher accuracy.
In addition, when the input feature set is selected after the candidate feature set is established, the features of the candidate feature set are input into the prediction model one by one, and the calculated error is taken as the decisive factor. The workload is relatively large although this will greatly improve the prediction accuracy of each component and reduce the input dimension. Therefore, it is the next research direction of this paper to find a better way to choose the input feature set or develop a better feature selection method.
REFERENCES
M. F Tahir, H. Y. Chen, A. Khan et al., “Optimizing size of variable renewable energy sources by incorporating energy storage and demand response,” IEEE Access, vol. 7, pp. 103115-103126, Sept. 2019. [Baidu Scholar]
M. F Tahir, H. T. Hassan, K. Mehmood et al., “Optimal load shedding using an ensemble of artificial neural networks,” International Journal of Electrical and Computer Engineering Systems, vol. 7, no. 2, pp. 39-46, Aug. 2016. [Baidu Scholar]
L. Zhang, J. Lu, Y. Mei et al., “Wind power prediction based on different optimization criteria,” Electric Power Automation Equipment, vol. 35, no. 5, pp. 139-145, May 2015. [Baidu Scholar]
Y. Ju, L. Qi, and S. Liu, “Short-term wind power forecasting based on improved crow search algorithm and ESN neural network,” Power System Protection and Control, vol. 47, no. 4, pp. 58-64, Feb. 2019. [Baidu Scholar]
Y. Ju, G. Sun, Q. Chen et al., “A model combining convolutional neural network and lightGBM algorithm for ultra-short-term wind power forecasting,” IEEE Access, vol. 7, pp. 28309-28318, Apr. 2019. [Baidu Scholar]
J. Cao, R. Zhou, X. Deng et al., “Wind power forecast considering differential times of optimal ARIMA model,” Proceedings of the CSU-EPSA, vol. 31, no. 1, pp. 105-111, Jan. 2019. [Baidu Scholar]
X. Zhu and Y. Liu, “Wind power forecasting using time series model based on robust estimation,” Proceedings of the CSU-EPSA, vol. 24, no. 3, pp. 107-110, Jun. 2012. [Baidu Scholar]
D. Wu and C. Gao, “Short-term wind power generation forecasting based on the SVM-GM approach,” Electric Power Components and Systems, vol. 46, pp. 1250-1264, Jul. 2018. [Baidu Scholar]
A. Liu, Y. Xue, J. Hu et al., “Ultra-short-term wind power forecasting based on SVM optimized by GA,” Power System Protection and Control, vol. 43, no. 2, pp. 90-95, Jan. 2015. [Baidu Scholar]
P. Salgado, G. Igrejas, and P. Afonso, “Multi-Kalman filter to wind power forecasting,” in Proceedings of 2018 13th APCA International Conference on Automatic Control and Soft Computing (CONTROLO), Ponta Delgada, Portugal, Jun. 2018, pp. 110-114. [Baidu Scholar]
Y. Jiang, X. Yang, L. Chen et al., “Super-short-term wind power combination forecasting based on support vector machine optimized by EMD-SC and AGSA,” Chinese Journal of Engineering Design, vol. 24, no. 2, pp. 187-195, Apr. 2017. [Baidu Scholar]
Z. Zhang, C. Ma, J. Xu et al., “Novel total-power combinational forecasting method of wind farm based on EMD and NARX neural network,” Computer Engineering and Applications, vol. 52, no. 2, pp. 265-270. Apr. 2016. [Baidu Scholar]
Q. Cheng, L. Chen, Y, Cheng et al., “Short-term wind power forecasting method based on EEMD and LS-SVM model,” Electric Power Automation Equipment, vol. 38, no. 5, pp. 27-35, May 2018. [Baidu Scholar]
B. Tian, Z. L. Park, and D. Guo et al., “Wind power ultra short-term model based on improved EEMD-SE-ARMA,” Power System Protection and Control, vol. 45, no. 4, pp. 72-79, Feb. 2017. [Baidu Scholar]
A. A. Abdoos, “A new intelligent method based on combination of VMD and ELM for short term wind power forecasting,” Neurocomputing, vol. 203, pp. 111-120, Aug. 2016. [Baidu Scholar]
G. Zhang, H. Liu, J. Zhang et al., “Wind power prediction based on variational mode decomposition multi-frequency combinations,” Journal of Modern Power Systems and Clean Energy, vol. 7, no. 2, pp. 281-288, Mar. 2019. [Baidu Scholar]
Y. Xue, C. Yu, K. Li et al., “Adaptive ultra-short-term wind power prediction based on risk assessment,” CSEE Journal of Power and Energy Systems, vol. 2, no. 3, pp. 59-64, Feb. 2016. [Baidu Scholar]
J. Wang, X. Han, Y. Ma et al., “Short-term wind power probabilistic forecasting considering spatial correlation,” in Proceedings of 2017 IEEE Conference on Energy Internet and Energy System Integration, Beijing, China, Nov. 2017, pp. 1-6. [Baidu Scholar]
S. Buhan and I. Çadırcı, “Multistage wind-electric power forecast by using a combination of advanced statistical methods,” IEEE Transactions on Industrial Informatics, vol. 11, no. 5, pp. 1231-1242, Oct. 2015. [Baidu Scholar]
A. Sharma, K. K. Paliwal, S. Imoto et al., “A feature selection method using improved regularized linear discriminant analysis,” Machine Vision & Applications, vol. 25, pp. 775-786, Apr. 2014. [Baidu Scholar]
H. Zhao and F. Magoulès, “Feature selection for predicting building energy consumption based on statistical learning method,” Journal of Algorithms and Computational Technology, vol. 6, no. 1, pp. 59-78, Mar. 2012. [Baidu Scholar]
K. Dragomiretskiy and D. Zosso, “Variational mode decomposition,” IEEE Transactions on Signal Processing, vol. 62, no. 3, pp. 531-544, Mar. 2014. [Baidu Scholar]
X. He, J. Luo, G. Zuo et al., “Daily runoff forecasting using a hybrid model based on variational mode decomposition and deep neural networks,” Water Resources Management, vol. 33, pp. 1571-1590, Mar. 2019. [Baidu Scholar]
Y. Wu, “Research on fault diagnosis of wind turbine transmission system based on variational modal decomposition,” Ph.D. dissertation, School of Control and Computer Engineering, North China Electric Power University, Beijing, China, 2016. [Baidu Scholar]
H. Peng, F. Long, and C. Ding, “Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 8, pp. 1226-1238, Aug. 2005. [Baidu Scholar]
Y. Zhang, Y. Wang, H. Deng et al., “IAFSA-BPNN for wind power probabilistic forecasting,” Power System Protection and Control, vol. 45, no. 7, pp. 58-63, Apr. 2017. [Baidu Scholar]
D. Zhang, Y. Yue, X. Zhang et al., “Review and prospect of research on wind power ramp events,” Power System Technology, vol. 42, no. 6, pp. 1783-1792, Mar. 2018. [Baidu Scholar]
M. F. Tahir, Tehzeeb-ul-Hassan, and M. A. Saqib. “Optimal scheduling of electrical power in energy-deficient scenarios using artificial neural network and Bootstrap aggregating,” International Journal of Electrical Power and Energy Systems, vol. 83, pp. 49-57, Dec. 2016. [Baidu Scholar]
A. Kusiak and H. Zheng. “Data mining for prediction of wind farm power ramp rates,” in Proceedings of 2008 IEEE International Conference on Sustainable Energy Technologies, Singapore, Singapore, Nov. 2008, pp. 1099-1103. [Baidu Scholar]