IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v13y2020i22p6125-d449285.html
   My bibliography  Save this article

Probability Density Forecasting of Wind Speed Based on Quantile Regression and Kernel Density Estimation

Author

Listed:
  • Lei Zhang

    (School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China)

  • Lun Xie

    (School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China)

  • Qinkai Han

    (The State Key Laboratory of Tribology, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China)

  • Zhiliang Wang

    (School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing 100083, China)

  • Chen Huang

    (TAIJI Computer Corporations Limited, Beijing 100083, China)

Abstract

Based on quantile regression (QR) and kernel density estimation (KDE), a framework for probability density forecasting of short-term wind speed is proposed in this study. The empirical mode decomposition (EMD) technique is implemented to reduce the noise of raw wind speed series. Both linear QR (LQR) and nonlinear QR (NQR, including quantile regression neural network (QRNN), quantile regression random forest (QRRF), and quantile regression support vector machine (QRSVM)) models are, respectively, utilized to study the de-noised wind speed series. An ensemble of conditional quantiles is obtained and then used for point and interval predictions of wind speed accordingly. After various experiments and comparisons on the real wind speed data at four wind observation stations of China, it is found that the EMD-LQR-KDE and EMD-QRNN-KDE generally have the best performance and robustness in both point and interval predictions. By taking conditional quantiles obtained by the EMD-QRNN-KDE model as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method, whose bandwidth is optimally determined according to the normal reference criterion. It is found that most actual wind speeds lie near the peak of predicted PDF curves, indicating that the probabilistic density prediction by EMD-QRNN-KDE is believable. Compared with the PDF curves of the 90% confidence level, the PDF curves of the 80% confidence level usually have narrower wind speed ranges and higher peak values. The PDF curves also vary with time. At some times, they might be biased, bimodal, or even multi-modal distributions. Based on the EMD-QRNN-KDE model, one can not only obtain the specific PDF curves of future wind speeds, but also understand the dynamic variation of density distributions with time. Compared with the traditional point and interval prediction models, the proposed QR-KDE models could acquire more information about the randomness and uncertainty of the actual wind speed, and thus provide more powerful support for the decision-making work.

Suggested Citation

  • Lei Zhang & Lun Xie & Qinkai Han & Zhiliang Wang & Chen Huang, 2020. "Probability Density Forecasting of Wind Speed Based on Quantile Regression and Kernel Density Estimation," Energies, MDPI, vol. 13(22), pages 1-24, November.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:22:p:6125-:d:449285
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/13/22/6125/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/13/22/6125/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, H.Z. & Wang, G.B. & Li, G.Q. & Peng, J.C. & Liu, Y.T., 2016. "Deep belief network based deterministic and probabilistic wind speed forecasting approach," Applied Energy, Elsevier, vol. 182(C), pages 80-93.
    2. Tascikaraoglu, A. & Uzunoglu, M., 2014. "A review of combined approaches for prediction of short-term wind speed and power," Renewable and Sustainable Energy Reviews, Elsevier, vol. 34(C), pages 243-254.
    3. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    4. Shrivastava, Nitin Anand & Lohia, Kunal & Panigrahi, Bijaya Ketan, 2016. "A multiobjective framework for wind speed prediction interval forecasts," Renewable Energy, Elsevier, vol. 87(P2), pages 903-910.
    5. Hu, Jianming & Wang, Jianzhou, 2015. "Short-term wind speed prediction using empirical wavelet transform and Gaussian process regression," Energy, Elsevier, vol. 93(P2), pages 1456-1466.
    6. Song, Zhe & Jiang, Yu & Zhang, Zijun, 2014. "Short-term wind speed forecasting with Markov-switching model," Applied Energy, Elsevier, vol. 130(C), pages 103-112.
    7. Liu, Hui & Duan, Zhu & Li, Yanfei & Lu, Haibo, 2018. "A novel ensemble model of different mother wavelets for wind speed multi-step forecasting," Applied Energy, Elsevier, vol. 228(C), pages 1783-1800.
    8. Li, Ranran & Jin, Yu, 2018. "A wind speed interval prediction system based on multi-objective optimization for machine learning method," Applied Energy, Elsevier, vol. 228(C), pages 2207-2220.
    9. Sloughter, J. McLean & Gneiting, Tilmann & Raftery, Adrian E., 2010. "Probabilistic Wind Speed Forecasting Using Ensembles and Bayesian Model Averaging," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 25-35.
    10. He, Yaoyao & Xu, Qifa & Wan, Jinhong & Yang, Shanlin, 2016. "Short-term power load probability density forecasting based on quantile regression neural network and triangle kernel function," Energy, Elsevier, vol. 114(C), pages 498-512.
    11. Wang, Jianzhou & Niu, Tong & Lu, Haiyan & Guo, Zhenhai & Yang, Wendong & Du, Pei, 2018. "An analysis-forecast system for uncertainty modeling of wind speed: A case study of large-scale wind farms," Applied Energy, Elsevier, vol. 211(C), pages 492-512.
    12. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    13. Han, Qinkai & Ma, Sai & Wang, Tianyang & Chu, Fulei, 2019. "Kernel density estimation model for wind speed probability distribution with applicability to wind energy assessment in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 115(C).
    14. Tian, Chengshi & Hao, Yan & Hu, Jianming, 2018. "A novel wind speed forecasting system based on hybrid data preprocessing and multi-objective optimization," Applied Energy, Elsevier, vol. 231(C), pages 301-319.
    15. Thordis L. Thorarinsdottir & Tilmann Gneiting, 2010. "Probabilistic forecasts of wind speed: ensemble model output statistics by using heteroscedastic censored regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(2), pages 371-388, April.
    16. Han, Qinkai & Hao, Zhuolin & Hu, Tao & Chu, Fulei, 2018. "Non-parametric models for joint probabilistic distributions of wind speed and direction data," Renewable Energy, Elsevier, vol. 126(C), pages 1032-1042.
    17. Wang, Jianzhou & Hu, Jianming & Ma, Kailiang, 2016. "Wind speed probability distribution estimation and wind energy assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 60(C), pages 881-899.
    18. He, Qingqing & Wang, Jianzhou & Lu, Haiyan, 2018. "A hybrid system for short-term wind speed forecasting," Applied Energy, Elsevier, vol. 226(C), pages 756-771.
    19. He, Yaoyao & Liu, Rui & Li, Haiyan & Wang, Shuo & Lu, Xiaofen, 2017. "Short-term power load probability density forecasting method using kernel-based support vector quantile regression and Copula theory," Applied Energy, Elsevier, vol. 185(P1), pages 254-266.
    20. Iversen, Emil B. & Morales, Juan M. & Møller, Jan K. & Madsen, Henrik, 2016. "Short-term probabilistic forecasting of wind speed using stochastic differential equations," International Journal of Forecasting, Elsevier, vol. 32(3), pages 981-990.
    21. Baran, Sándor, 2014. "Probabilistic wind speed forecasting using Bayesian model averaging with truncated normal components," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 227-238.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mirosław Kornatka & Anna Gawlak, 2021. "An Analysis of the Operation of Distribution Networks Using Kernel Density Estimators," Energies, MDPI, vol. 14(21), pages 1-12, October.
    2. Xiong, Zhanhang & Yao, Jianjiang & Huang, Yongmin & Yu, Zhaoxu & Liu, Yalei, 2024. "A wind speed forecasting method based on EMD-MGM with switching QR loss function and novel subsequence superposition," Applied Energy, Elsevier, vol. 353(PB).
    3. Ma, Long & Huang, Ling & Shi, Huifeng, 2023. "A novel spatial–temporal generative autoencoder for wind speed uncertainty forecasting," Energy, Elsevier, vol. 282(C).
    4. He, Yaoyao & Wang, Yun & Wang, Shuo & Yao, Xin, 2022. "A cooperative ensemble method for multistep wind speed probabilistic forecasting," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. Huazhu Xue & Hui Wu & Guotao Dong & Jianjun Gao, 2023. "A Hybrid Forecasting Model to Simulate the Runoff of the Upper Heihe River," Sustainability, MDPI, vol. 15(10), pages 1-19, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lu, Peng & Ye, Lin & Zhao, Yongning & Dai, Binhua & Pei, Ming & Tang, Yong, 2021. "Review of meta-heuristic algorithms for wind power prediction: Methodologies, applications and challenges," Applied Energy, Elsevier, vol. 301(C).
    2. Qian, Zheng & Pei, Yan & Zareipour, Hamidreza & Chen, Niya, 2019. "A review and discussion of decomposition-based hybrid models for wind energy forecasting applications," Applied Energy, Elsevier, vol. 235(C), pages 939-953.
    3. Liu, Hui & Chen, Chao, 2019. "Data processing strategies in wind energy forecasting models and applications: A comprehensive review," Applied Energy, Elsevier, vol. 249(C), pages 392-408.
    4. Han, Qinkai & Chu, Fulei, 2021. "Directional wind energy assessment of China based on nonparametric copula models," Renewable Energy, Elsevier, vol. 164(C), pages 1334-1349.
    5. Jianzhou Wang & Chunying Wu & Tong Niu, 2019. "A Novel System for Wind Speed Forecasting Based on Multi-Objective Optimization and Echo State Network," Sustainability, MDPI, vol. 11(2), pages 1-34, January.
    6. Zhou, Qingguo & Wang, Chen & Zhang, Gaofeng, 2019. "Hybrid forecasting system based on an optimal model selection strategy for different wind speed forecasting problems," Applied Energy, Elsevier, vol. 250(C), pages 1559-1580.
    7. Lilin Cheng & Haixiang Zang & Tao Ding & Rong Sun & Miaomiao Wang & Zhinong Wei & Guoqiang Sun, 2018. "Ensemble Recurrent Neural Network Based Probabilistic Wind Speed Forecasting Approach," Energies, MDPI, vol. 11(8), pages 1-23, July.
    8. Liu, Hui & Chen, Chao, 2019. "Multi-objective data-ensemble wind speed forecasting model with stacked sparse autoencoder and adaptive decomposition-based error correction," Applied Energy, Elsevier, vol. 254(C).
    9. Chinmoy, Lakshmi & Iniyan, S. & Goic, Ranko, 2019. "Modeling wind power investments, policies and social benefits for deregulated electricity market – A review," Applied Energy, Elsevier, vol. 242(C), pages 364-377.
    10. Han, Qinkai & Wang, Tianyang & Chu, Fulei, 2022. "Nonparametric copula modeling of wind speed-wind shear for the assessment of height-dependent wind energy in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 161(C).
    11. Sebastian Lerch & Sándor Baran, 2017. "Similarity-based semilocal estimation of post-processing models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 29-51, January.
    12. Wang, Huaizhi & Xue, Wenli & Liu, Yitao & Peng, Jianchun & Jiang, Hui, 2020. "Probabilistic wind power forecasting based on spiking neural network," Energy, Elsevier, vol. 196(C).
    13. Hu, Jianming & Heng, Jiani & Wen, Jiemei & Zhao, Weigang, 2020. "Deterministic and probabilistic wind speed forecasting with de-noising-reconstruction strategy and quantile regression based algorithm," Renewable Energy, Elsevier, vol. 162(C), pages 1208-1226.
    14. Gensler, André & Sick, Bernhard & Vogt, Stephan, 2018. "A review of uncertainty representations and metaverification of uncertainty assessment techniques for renewable energies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 96(C), pages 352-379.
    15. Fuqiang Li & Shiying Zhang & Wenxuan Li & Wei Zhao & Bingkang Li & Huiru Zhao, 2019. "Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques," Sustainability, MDPI, vol. 11(24), pages 1-17, December.
    16. Jin, Huaiping & Shi, Lixian & Chen, Xiangguang & Qian, Bin & Yang, Biao & Jin, Huaikang, 2021. "Probabilistic wind power forecasting using selective ensemble of finite mixture Gaussian process regression models," Renewable Energy, Elsevier, vol. 174(C), pages 1-18.
    17. Li, Chaoshun & Xiao, Zhengguang & Xia, Xin & Zou, Wen & Zhang, Chu, 2018. "A hybrid model based on synchronous optimisation for multi-step short-term wind speed forecasting," Applied Energy, Elsevier, vol. 215(C), pages 131-144.
    18. Hu, Weicheng & Yang, Qingshan & Chen, Hua-Peng & Yuan, Ziting & Li, Chen & Shao, Shuai & Zhang, Jian, 2021. "New hybrid approach for short-term wind speed predictions based on preprocessing algorithm and optimization theory," Renewable Energy, Elsevier, vol. 179(C), pages 2174-2186.
    19. Han, Qinkai & Ma, Sai & Wang, Tianyang & Chu, Fulei, 2019. "Kernel density estimation model for wind speed probability distribution with applicability to wind energy assessment in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 115(C).
    20. Li, Ranran & Jin, Yu, 2018. "A wind speed interval prediction system based on multi-objective optimization for machine learning method," Applied Energy, Elsevier, vol. 228(C), pages 2207-2220.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:13:y:2020:i:22:p:6125-:d:449285. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.