IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v238y2022ipbs036054422101971x.html
   My bibliography  Save this article

Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator

Author

Listed:
  • Chen, Zhenyu
  • Lin, Zhongwei
  • Zhai, Xiaoya
  • Liu, Jizhen

Abstract

A challenging topic arising in dynamic wind turbine wake is modeling, especially the low-order approximation. The central problem is the fact that it has high-dimensional and nonlinear wake characteristics. In this paper, a Koopman-linear flow estimator is designed according to the Koopman operator theory. Different from the conventional flow reconstruction with the linear stochastic estimation method, a dynamic state-space model with physical states is constructed. The wake dynamics are approximated using a limited number of measurable physical parameters by the dynamic part; then, the full wake flow is reconstructed from the low-order states by the estimation part. The flow estimator is designed into three different forms following Extended Dynamic Mode Decomposition (EDMD) method. Each form has its unique advantages. Precisely, probe sensors are placed in the studied space and provide direct information of the wake, and a few in-directly physical parameters are also included. Nonlinear integer programming is further adopted using a heuristic optimization algorithm, by which the sensor configurations are optimized. Comparisons with the standard Dynamic Mode Decomposition (DMD)-based wake model are adopted in time domain and frequency domain to verify the effectiveness of the proposed flow estimators. The results show acceptable accuracy in typical modeling cases and maintain good estimation accuracy when the measurement noises are involved. Finally, the proposed Koopman-linear flow estimator is compared with related stochastic estimation methods, in which the connections of the proposed estimator with stochastic ones are also discussed.

Suggested Citation

  • Chen, Zhenyu & Lin, Zhongwei & Zhai, Xiaoya & Liu, Jizhen, 2022. "Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator," Energy, Elsevier, vol. 238(PB).
    • Handle: RePEc:eee:energy:v:238:y:2022:i:pb:s036054422101971x
    DOI: 10.1016/j.energy.2021.121723
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S036054422101971X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2021.121723?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. Ti, Zilong & Deng, Xiao Wei & Yang, Hongxing, 2020. "Wake modeling of wind turbines using machine learning," Applied Energy, Elsevier, vol. 257(C).
    2. Sun, Haiying & Gao, Xiaoxia & Yang, Hongxing, 2019. "Validations of three-dimensional wake models with the wind field measurements in complex terrain," Energy, Elsevier, vol. 189(C).
    3. Nassir Cassamo & Jan-Willem van Wingerden, 2020. "On the Potential of Reduced Order Models for Wind Farm Control: A Koopman Dynamic Mode Decomposition Approach," Energies, MDPI, vol. 13(24), pages 1-21, December.
    4. Dou, Bingzheng & Qu, Timing & Lei, Liping & Zeng, Pan, 2020. "Optimization of wind turbine yaw angles in a wind farm using a three-dimensional yawed wake model," Energy, Elsevier, vol. 209(C).
    5. Wim Munters & Johan Meyers, 2018. "Dynamic Strategies for Yaw and Induction Control of Wind Farms Based on Large-Eddy Simulation and Optimization," Energies, MDPI, vol. 11(1), pages 1-32, January.
    6. Qian, Guo-Wei & Ishihara, Takeshi, 2021. "Wind farm power maximization through wake steering with a new multiple wake model for prediction of turbulence intensity," Energy, Elsevier, vol. 220(C).
    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. Chen, Zhenyu & Lin, Zhongwei & Ren, Xin & Chen, Kaixuan & Zhang, Guangming & Xie, Zhen & Wang, Chuanxi & She, Chao, 2023. "Amplitude-optimized Koopman-linear flow estimator for wind turbine wake dynamics: Approximation, prediction and reconstruction," Energy, Elsevier, vol. 263(PE).
    2. Luo, Zhaohui & Wang, Longyan & Xu, Jian & Wang, Zilu & Yuan, Jianping & Tan, Andy C.C., 2024. "A reduced order modeling-based machine learning approach for wind turbine wake flow estimation from sparse sensor measurements," Energy, Elsevier, vol. 294(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. Amiri, Mojtaba Maali & Shadman, Milad & Estefen, Segen F., 2024. "A review of physical and numerical modeling techniques for horizontal-axis wind turbine wakes," Renewable and Sustainable Energy Reviews, Elsevier, vol. 193(C).
    2. He, Ruiyang & Sun, Haiying & Gao, Xiaoxia & Yang, Hongxing, 2022. "Wind tunnel tests for wind turbines: A state-of-the-art review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 166(C).
    3. Zhiwen Deng & Chang Xu & Zhihong Huo & Xingxing Han & Feifei Xue, 2023. "Yaw Optimisation for Wind Farm Production Maximisation Based on a Dynamic Wake Model," Energies, MDPI, vol. 16(9), pages 1-20, May.
    4. Sun, Haiying & Yang, Hongxing, 2023. "Wind farm layout and hub height optimization with a novel wake model," Applied Energy, Elsevier, vol. 348(C).
    5. He, Ruiyang & Yang, Hongxing & Sun, Haiying & Gao, Xiaoxia, 2021. "A novel three-dimensional wake model based on anisotropic Gaussian distribution for wind turbine wakes," Applied Energy, Elsevier, vol. 296(C).
    6. Anagnostopoulos, Sokratis J. & Bauer, Jens & Clare, Mariana C.A. & Piggott, Matthew D., 2023. "Accelerated wind farm yaw and layout optimisation with multi-fidelity deep transfer learning wake models," Renewable Energy, Elsevier, vol. 218(C).
    7. Xu, Zongyuan & Gao, Xiaoxia & Zhang, Huanqiang & Lv, Tao & Han, Zhonghe & Zhu, Xiaoxun & Wang, Yu, 2023. "Analysis of the anisotropy aerodynamic characteristics of downstream wind turbine considering the 3D wake expansion based on coupling method," Energy, Elsevier, vol. 263(PD).
    8. Shu, Tong & Song, Dongran & Joo, Young Hoon, 2022. "Non-centralised coordinated optimisation for maximising offshore wind farm power via a sparse communication architecture," Applied Energy, Elsevier, vol. 324(C).
    9. Yang, Shanghui & Deng, Xiaowei & Ti, Zilong & Yan, Bowen & Yang, Qingshan, 2022. "Cooperative yaw control of wind farm using a double-layer machine learning framework," Renewable Energy, Elsevier, vol. 193(C), pages 519-537.
    10. Yang, Shanghui & Deng, Xiaowei & Yang, Kun, 2024. "Machine-learning-based wind farm optimization through layout design and yaw control," Renewable Energy, Elsevier, vol. 224(C).
    11. Song, Dongran & Shen, Xutao & Gao, Yang & Wang, Lei & Du, Xin & Xu, Zhiliang & Zhang, Zhihong & Huang, Chaoneng & Yang, Jian & Dong, Mi & Joo, Young Hoo, 2023. "Application of surrogate-assisted global optimization algorithm with dimension-reduction in power optimization of floating offshore wind farm," Applied Energy, Elsevier, vol. 351(C).
    12. Barasa, Maulidi & Li, Xuemin & Zhang, Yi & Xu, Weiming, 2022. "The balance effects of momentum deficit and thrust in cumulative wake models," Energy, Elsevier, vol. 246(C).
    13. He, Ruiyang & Yang, Hongxing & Lu, Lin & Gao, Xiaoxia, 2024. "Site-specific wake steering strategy for combined power enhancement and fatigue mitigation within wind farms," Renewable Energy, Elsevier, vol. 225(C).
    14. Reddy, Sohail R., 2021. "A machine learning approach for modeling irregular regions with multiple owners in wind farm layout design," Energy, Elsevier, vol. 220(C).
    15. Cheng, Biyi & Du, Jianjun & Yao, Yingxue, 2022. "Machine learning methods to assist structure design and optimization of Dual Darrieus Wind Turbines," Energy, Elsevier, vol. 244(PA).
    16. 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.
    17. Zhang, Shaohai & Duan, Huanfeng & Lu, Lin & He, Ruiyang & Gao, Xiaoxia & Zhu, Songye, 2024. "Quantification of three-dimensional added turbulence intensity for the horizontal-axis wind turbine considering the wake anisotropy," Energy, Elsevier, vol. 294(C).
    18. Fei Zhao & Yihan Gao & Tengyuan Wang & Jinsha Yuan & Xiaoxia Gao, 2020. "Experimental Study on Wake Evolution of a 1.5 MW Wind Turbine in a Complex Terrain Wind Farm Based on LiDAR Measurements," Sustainability, MDPI, vol. 12(6), pages 1-14, March.
    19. Li, Siyi & Zhang, Mingrui & Piggott, Matthew D., 2023. "End-to-end wind turbine wake modelling with deep graph representation learning," Applied Energy, Elsevier, vol. 339(C).
    20. Shen, Wen Zhong & Lin, Jian Wei & Jiang, Yu Hang & Feng, Ju & Cheng, Li & Zhu, Wei Jun, 2023. "A novel yaw wake model for wind farm control applications," Renewable Energy, Elsevier, vol. 218(C).

    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:energy:v:238:y:2022:i:pb:s036054422101971x. 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.journals.elsevier.com/energy .

    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.