IDEAS home Printed from https://ideas.repec.org/a/eee/appene/v230y2018icp1230-1241.html
   My bibliography  Save this article

Using stochastic programming and statistical extrapolation to mitigate long-term extreme loads in wind turbines

Author

Listed:
  • Cao, Yankai
  • Zavala, Victor M.
  • D’Amato, Fernando

Abstract

We propose stochastic programming formulations to enforce mechanical load requirements in wind turbine controller design procedures. The formulations use statistical extrapolation techniques to construct a probabilistic (chance) constraint that controls the long-term probability of exceeding an extreme load threshold (as described by the IEC-61400 standard). This approach is based on the observation that extreme loads follow a generalized extreme value distribution, which enables an explicit algebraic representation of the probabilistic constraint. We illustrate how to use the formulations to find design parameters for pitch angle and torque controllers that maximize power output while constraining long-term extreme loads. We also use the formulation to explore the ability of a hypothetical model predictive controller to mitigate extreme loads. The proposed formulations can be cast as large-scale (but structured) nonlinear programming problems that contain up to 7.5 million variables and constraints. We show that these problems can be solved in less than 1.3 h on a multi-core computer with existing optimization tools.

Suggested Citation

  • Cao, Yankai & Zavala, Victor M. & D’Amato, Fernando, 2018. "Using stochastic programming and statistical extrapolation to mitigate long-term extreme loads in wind turbines," Applied Energy, Elsevier, vol. 230(C), pages 1230-1241.
    • Handle: RePEc:eee:appene:v:230:y:2018:i:c:p:1230-1241
    DOI: 10.1016/j.apenergy.2018.09.062
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0306261918313667
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.apenergy.2018.09.062?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Park, Jinkyoo & Law, Kincho H., 2015. "Layout optimization for maximizing wind farm power production using sequential convex programming," Applied Energy, Elsevier, vol. 151(C), pages 320-334.
    2. Nai-Yuan Chiang & Victor M. Zavala, 2016. "An inertia-free filter line-search algorithm for large-scale nonlinear programming," Computational Optimization and Applications, Springer, vol. 64(2), pages 327-354, June.
    3. Song, Jingjing & Wang, Jianzhou & Lu, Haiyan, 2018. "A novel combined model based on advanced optimization algorithm for short-term wind speed forecasting," Applied Energy, Elsevier, vol. 215(C), pages 643-658.
    4. Eligius M. T. Hendrix & Boglárka G.-Tóth, 2010. "Nonlinear Programming algorithms," Springer Optimization and Its Applications, in: Introduction to Nonlinear and Global Optimization, chapter 5, pages 91-136, Springer.
    5. Song, Dongran & Fan, Xinyu & Yang, Jian & Liu, Anfeng & Chen, Sifan & Joo, Young Hoon, 2018. "Power extraction efficiency optimization of horizontal-axis wind turbines through optimizing control parameters of yaw control systems using an intelligent method," Applied Energy, Elsevier, vol. 224(C), pages 267-279.
    6. Yin, Minghui & Yang, Zhiqiang & Xu, Yan & Liu, Jiankun & Zhou, Lianjun & Zou, Yun, 2018. "Aerodynamic optimization for variable-speed wind turbines based on wind energy capture efficiency," Applied Energy, Elsevier, vol. 221(C), pages 508-521.
    7. Park, Jinkyoo & Law, Kincho H., 2016. "A data-driven, cooperative wind farm control to maximize the total power production," Applied Energy, Elsevier, vol. 165(C), pages 151-165.
    8. 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.
    9. Odgaard, Peter Fogh & Larsen, Lars F.S. & Wisniewski, Rafael & Hovgaard, Tobias Gybel, 2016. "On using Pareto optimality to tune a linear model predictive controller for wind turbines," Renewable Energy, Elsevier, vol. 87(P2), pages 884-891.
    10. Loukatou, Angeliki & Howell, Sydney & Johnson, Paul & Duck, Peter, 2018. "Stochastic wind speed modelling for estimation of expected wind power output," Applied Energy, Elsevier, vol. 228(C), pages 1328-1340.
    11. Miles Lubin & Iain Dunning, 2015. "Computing in Operations Research Using Julia," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 238-248, May.
    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. Xie, Shiwei & Hu, Zhijian & Wang, Jueying, 2020. "Two-stage robust optimization for expansion planning of active distribution systems coupled with urban transportation networks," Applied Energy, Elsevier, vol. 261(C).

    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. Lin, Zhongwei & Chen, Zhenyu & Liu, Jizhen & Wu, Qiuwei, 2019. "Coordinated mechanical loads and power optimization of wind energy conversion systems with variable-weight model predictive control strategy," Applied Energy, Elsevier, vol. 236(C), pages 307-317.
    2. Cheng, Yi & Azizipanah-Abarghooee, Rasoul & Azizi, Sadegh & Ding, Lei & Terzija, Vladimir, 2020. "Smart frequency control in low inertia energy systems based on frequency response techniques: A review," Applied Energy, Elsevier, vol. 279(C).
    3. Rafael V. Rodrigues & Corinne Lengsfeld, 2019. "Development of a Computational System to Improve Wind Farm Layout, Part I: Model Validation and Near Wake Analysis," Energies, MDPI, vol. 12(5), pages 1-24, March.
    4. Wang, Han & Han, Shuang & Liu, Yongqian & Yan, Jie & Li, Li, 2019. "Sequence transfer correction algorithm for numerical weather prediction wind speed and its application in a wind power forecasting system," Applied Energy, Elsevier, vol. 237(C), pages 1-10.
    5. Gionfra, Nicolò & Sandou, Guillaume & Siguerdidjane, Houria & Faille, Damien & Loevenbruck, Philippe, 2019. "Wind farm distributed PSO-based control for constrained power generation maximization," Renewable Energy, Elsevier, vol. 133(C), pages 103-117.
    6. Dou, Bingzheng & Guala, Michele & Lei, Liping & Zeng, Pan, 2019. "Wake model for horizontal-axis wind and hydrokinetic turbines in yawed conditions," Applied Energy, Elsevier, vol. 242(C), pages 1383-1395.
    7. Longfu Luo & Xiaofeng Zhang & Dongran Song & Weiyi Tang & Jian Yang & Li Li & Xiaoyu Tian & Wu Wen, 2018. "Optimal Design of Rated Wind Speed and Rotor Radius to Minimizing the Cost of Energy for Offshore Wind Turbines," Energies, MDPI, vol. 11(10), pages 1-17, October.
    8. Lo Brutto, Ottavio A. & Thiébot, Jérôme & Guillou, Sylvain S. & Gualous, Hamid, 2016. "A semi-analytic method to optimize tidal farm layouts – Application to the Alderney Race (Raz Blanchard), France," Applied Energy, Elsevier, vol. 183(C), pages 1168-1180.
    9. Wei Li & Shinai Xu & Baiyun Qian & Xiaoxia Gao & Xiaoxun Zhu & Zeqi Shi & Wei Liu & Qiaoliang Hu, 2022. "Large-Scale Wind Turbine’s Load Characteristics Excited by the Wind and Grid in Complex Terrain: A Review," Sustainability, MDPI, vol. 14(24), pages 1-29, December.
    10. Yang, Mao & Che, Runqi & Yu, Xinnan & Su, Xin, 2024. "Dual NWP wind speed correction based on trend fusion and fluctuation clustering and its application in short-term wind power prediction," Energy, Elsevier, vol. 302(C).
    11. Song, Dongran & Yang, Yinggang & Zheng, Songyue & Tang, Weiyi & Yang, Jian & Su, Mei & Yang, Xuebing & Joo, Young Hoon, 2019. "Capacity factor estimation of variable-speed wind turbines considering the coupled influence of the QN-curve and the air density," Energy, Elsevier, vol. 183(C), pages 1049-1060.
    12. Cao, Lichao & Ge, Mingwei & Gao, Xiaoxia & Du, Bowen & Li, Baoliang & Huang, Zhi & Liu, Yongqian, 2022. "Wind farm layout optimization to minimize the wake induced turbulence effect on wind turbines," Applied Energy, Elsevier, vol. 323(C).
    13. Li, Min & Yang, Yi & He, Zhaoshuang & Guo, Xinbo & Zhang, Ruisheng & Huang, Bingqing, 2023. "A wind speed forecasting model based on multi-objective algorithm and interpretability learning," Energy, Elsevier, vol. 269(C).
    14. Arenas-López, J. Pablo & Badaoui, Mohamed, 2020. "The Ornstein-Uhlenbeck process for estimating wind power under a memoryless transformation," Energy, Elsevier, vol. 213(C).
    15. Tanvir Ahmad & Abdul Basit & Muneeb Ahsan & Olivier Coupiac & Nicolas Girard & Behzad Kazemtabrizi & Peter C. Matthews, 2019. "Implementation and Analyses of Yaw Based Coordinated Control of Wind Farms," Energies, MDPI, vol. 12(7), pages 1-15, April.
    16. Liang, Tao & Zhao, Qing & Lv, Qingzhao & Sun, Hexu, 2021. "A novel wind speed prediction strategy based on Bi-LSTM, MOOFADA and transfer learning for centralized control centers," Energy, Elsevier, vol. 230(C).
    17. Liu, Xingdou & Zhang, Li & Wang, Jiangong & Zhou, Yue & Gan, Wei, 2023. "A unified multi-step wind speed forecasting framework based on numerical weather prediction grids and wind farm monitoring data," Renewable Energy, Elsevier, vol. 211(C), pages 948-963.
    18. Zhao, Lin-Chuan & Zou, Hong-Xiang & Yan, Ge & Liu, Feng-Rui & Tan, Ting & Zhang, Wen-Ming & Peng, Zhi-Ke & Meng, Guang, 2019. "A water-proof magnetically coupled piezoelectric-electromagnetic hybrid wind energy harvester," Applied Energy, Elsevier, vol. 239(C), pages 735-746.
    19. Mojtaba Qolipour & Ali Mostafaeipour & Mohammad Saidi-Mehrabad & Hamid R Arabnia, 2019. "Prediction of wind speed using a new Grey-extreme learning machine hybrid algorithm: A case study," Energy & Environment, , vol. 30(1), pages 44-62, February.
    20. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2010. "Combining predictive densities using Bayesian filtering with applications to US economics data," Working Paper 2010/29, Norges Bank.

    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:eee:appene:v:230:y:2018:i:c:p:1230-1241. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/405891/description#description .

    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.