The Photovoltaic Output Prediction Based on Variational Mode Decomposition and Maximum Relevance Minimum Redundancy
Abstract
:1. Introduction
2. Methodology
- (1)
- The VMD proposed by Dragomiretskiy K in 2014 is the new kind of non-stationary signal adaptive decomposition estimation method [31], which aims to decompose the original complex non-stationary photovoltaic sequence into sub-sequences with different characteristics. Compared with wavelet decomposition, EMD decomposition and EEMD decomposition, VMD decomposition can suppress modal aliasing more effectively.
- (2)
- The mRMR was proposed by Peng, HC. et al. in 2005, and is a feature selection method that uses mutual information and correlation distance to calculate correlation [32]. It has the feature of maximizing the correlation between features and categorical variables, and minimizing the correlation between features and features, mainly used to solve the redundancy of feature variables.
- (3)
- DBN is a deep network efficient learning algorithm proposed by Hinton et al., with adaptive and self-learning capabilities, mainly used to deal with high-dimensional, large-scale data problems [33]. A DBN network consists of several layers of unsupervised restricted Boltzmann machine (RBM) and a supervised back-propagation (BP). RBM is a probability graph model consisting of visible layers and hidden layers, two layers of neurons are connected by weights. In general, visible layer units are used to describe the characteristics of data, while hidden layer units can be regarded as feature extraction layers. The structure of the RBM is shown in Figure 1.
3. Case Study
3.1. Analysis and Decomposing the Photovoltaic Output
3.2. Establish Feature Sets of Each Component
- Use an incremental search method to establish a candidate feature set of the component;
- Calculate the mRMR values of each feature in and arrange them in descending order according to the magnitude of the mRMR value, and then input them into error function one by one to obtain the error;
- Take the number of features corresponding to the minimum error to establish a component feature set.
3.3. The Components and Photovoltaic Output Prediction
3.4. The Comparison
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Region | Yunnan | Gansu | ||||||
---|---|---|---|---|---|---|---|---|
Month | Index (MW) | |||||||
Max | Min | Average | Standard Deviation | Max | Min | Average | Standard Deviation | |
1 | 51.0880 | 0 | 8.5451 | 12.9116 | 74.3600 | 0 | 15.3126 | 23.8975 |
2 | 52.1515 | 0 | 10.1411 | 14.0405 | 74.0806 | 0 | 15.4304 | 22.9636 |
3 | 53.8360 | 0 | 10.5843 | 12.7793 | 78.0693 | 0 | 17.0654 | 23.7851 |
4 | 50.6495 | 0 | 14.4332 | 12.2235 | 76.0156 | 0 | 18.5160 | 23.8937 |
5 | 52.0025 | 0 | 14.4195 | 10.9419 | 70.4691 | 0 | 18.6636 | 22.8334 |
6 | 48.1051 | 0 | 13.8450 | 10.3952 | 79.0193 | 0 | 17.9615 | 23.4606 |
7 | 47.1511 | 0 | 8.5261 | 9.9922 | 81.0183 | 0 | 17.6143 | 22.8236 |
8 | 54.0445 | 0 | 9.9151 | 12.4363 | 83.4411 | 0 | 18.7014 | 24.9872 |
9 | 53.8485 | 0 | 8.9923 | 12.0795 | 79.5083 | 0 | 20.0493 | 26.4243 |
10 | 57.7775 | 0 | 10.0323 | 13.2926 | 77.3358 | 0 | 18.9459 | 26.1223 |
11 | 45.7834 | 0 | 9.5029 | 13.0666 | 71.6986 | 0 | 14.1018 | 21.9549 |
12 | 48.2302 | 0 | 9.0874 | 12.7911 | 73.2493 | 0 | 13.0200 | 21.3749 |
IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 |
---|---|---|---|---|---|---|---|---|---|
0.0887 | 0.0927 | 0.0842 | 0.0877 | 0.0806 | 0.1612 | 0.0561 | 0.1239 | 0.3889 | 0.0522 |
0.0531 | 0.0452 | 0.0903 | 0.0863 | 0.1178 | 0.1229 | 0.1697 | 0.1537 | 0.2397 | 0.0307 |
0.0254 | 0.0717 | 0.0773 | 0.1167 | 0.1080 | 0.1532 | 0.1387 | 0.1092 | 0.2474 | 0.0540 |
0.0714 | 0.0949 | 0.0862 | 0.0902 | 0.0783 | 0.1336 | 0.1766 | 0.2308 | 0.1507 | 0.0685 |
0.0908 | 0.0753 | 0.1006 | 0.0833 | 0.1090 | 0.1462 | 0.0629 | 0.1287 | 0.3041 | 0.0387 |
0.0752 | 0.0738 | 0.0834 | 0.1198 | 0.0876 | 0.0493 | 0.1163 | 0.1662 | 0.2194 | 0.0751 |
0.0701 | 0.0557 | 0.0754 | 0.0725 | 0.0921 | 0.0537 | 0.1427 | 0.0750 | 0.3341 | 0.0574 |
0.0404 | 0.0602 | 0.0787 | 0.1037 | 0.0904 | 0.0687 | 0.1066 | 0.0992 | 0.3742 | 0.0892 |
0.0635 | 0.0598 | 0.1097 | 0.1044 | 0.1165 | 0.1120 | 0.1312 | 0.1469 | 0.2239 | 0.0211 |
0.0493 | 0.0855 | 0.0797 | 0.1063 | 0.0993 | 0.0494 | 0.1310 | 0.2960 | 0.2478 | 0.0619 |
0.0623 | 0.0720 | 0.1324 | 0.0753 | 0.0930 | 0.1404 | 0.1218 | 0.2115 | 0.1322 | 0.0726 |
0.0868 | 0.0827 | 0.1219 | 0.1567 | 0.0893 | 0.0794 | 0.1466 | 0.2605 | 0.3907 | 0.0314 |
Component | Feature |
---|---|
IMF1 | |
IMF2 | |
IMF3 | |
IMF4 | |
IMF5 | |
IMF6 | |
IMF7 | |
IMF8 | |
IMF9 | |
IMF10 |
Component | Structure |
---|---|
IMF1 | 3-24-12-1 |
IMF2 | 3-16-6-4-1 |
IMF3 | 3-20-6-1 |
IMF4 | 3-20-8-1 |
IMF5 | 3-16-8-1 |
IMF6 | 3-24-6-1 |
IMF7 | 3-16-4-1 |
IMF8 | 3-12-6-1 |
IMF9 | 3-12-8-1 |
IMF10 | 3-8-1 |
Index | Model | |||||
---|---|---|---|---|---|---|
ARMA | DBN | EMD + DBN | EEMD + DBN | VMD + DBN | This Paper | |
MAE(MW) | 4.6721 | 3.9642 | 2.3263 | 1.7331 | 1.0147 | 0.4063 |
RMSE(MW) | 6.1381 | 5.3763 | 2.5324 | 2.0972 | 1.1364 | 0.7345 |
0.1359 | 0.1268 | 0.0572 | 0.0361 | 0.0092 | 0.0053 |
Index | Model | |||||
---|---|---|---|---|---|---|
ARMA | DBN | EMD + DBN | EEMD + DBN | VMD + DBN | This Paper | |
MAE(MW) | 5.2794 | 4.4682 | 2.1984 | 1.7069 | 1.0510 | 0.4414 |
RMSE(MW) | 6.8934 | 5.9792 | 2.4728 | 2.1421 | 1.2316 | 0.7816 |
0.1894 | 0.1659 | 0.0643 | 0.0579 | 0.0096 | 0.0061 |
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Du, P.; Zhang, G.; Li, P.; Li, M.; Liu, H.; Hou, J. The Photovoltaic Output Prediction Based on Variational Mode Decomposition and Maximum Relevance Minimum Redundancy. Appl. Sci. 2019, 9, 3593. https://doi.org/10.3390/app9173593
Du P, Zhang G, Li P, Li M, Liu H, Hou J. The Photovoltaic Output Prediction Based on Variational Mode Decomposition and Maximum Relevance Minimum Redundancy. Applied Sciences. 2019; 9(17):3593. https://doi.org/10.3390/app9173593
Chicago/Turabian StyleDu, Peidong, Gang Zhang, Pingli Li, Meng Li, Hongchi Liu, and Jinwang Hou. 2019. "The Photovoltaic Output Prediction Based on Variational Mode Decomposition and Maximum Relevance Minimum Redundancy" Applied Sciences 9, no. 17: 3593. https://doi.org/10.3390/app9173593
APA StyleDu, P., Zhang, G., Li, P., Li, M., Liu, H., & Hou, J. (2019). The Photovoltaic Output Prediction Based on Variational Mode Decomposition and Maximum Relevance Minimum Redundancy. Applied Sciences, 9(17), 3593. https://doi.org/10.3390/app9173593