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Amplitude-optimized Koopman-linear flow estimator for wind turbine wake dynamics: Approximation, prediction and reconstruction

Author

Listed:
  • Chen, Zhenyu
  • Lin, Zhongwei
  • Ren, Xin
  • Chen, Kaixuan
  • Zhang, Guangming
  • Xie, Zhen
  • Wang, Chuanxi
  • She, Chao

Abstract

The low-order modeling of wind turbine dynamic wake is a challenging problem, which requires approximating high-dimensional, nonlinear dynamic systems with a limited number of states and linear structures. The Koopman-linear flow estimator is regarded as a promoting method in this area to approximate the dynamic wake field from a few physical-measured states. This paper presents optimization methods for the Koopman-linear flow estimator to improve its generalization applicability and modeling accuracy in specific applications. Firstly, the flow estimator’s wake field prediction process is organized using Koopman modes and amplitudes; both are identified initially. Then, a optimization method is proposed to optimize the Koopman amplitudes for a given application scenario, which maintains a consistent form for uncontrolled and controlled systems based on the error-source analysis. After this, a sequential particle swarm optimization algorithm is adopted, which improves the computationally-intensive problem during sensor configuration optimization. The proposed algorithm quickly solves a feasible and optimized sensor configuration plan instead of the unavailable global-optimal one. The verification results show two conclusions: On the one hand, the nonlinearity during the yaw-induced wake deflection process is evident, which poses a significant challenge to the linear low-order approximation of the dynamic wake field. On the other hand, the proposed optimization methods highly improve the dynamic wake modeling accuracy under free-wake and yaw-controlled scenarios. Sparse sampling is necessary for dynamic wake behavior study in industrial. This paper solves the incomplete measurements and wake deflection nonlinearity problem caused by sparse sampling and promotes the generalization applicability for specific applications.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:energy:v:263:y:2023:i:pe:s0360544222027803
    DOI: 10.1016/j.energy.2022.125894
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    References listed on IDEAS

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    1. Ishan Bajaj & Akhil Arora & M. M. Faruque Hasan, 2021. "Black-Box Optimization: Methods and Applications," Springer Optimization and Its Applications, in: Panos M. Pardalos & Varvara Rasskazova & Michael N. Vrahatis (ed.), Black Box Optimization, Machine Learning, and No-Free Lunch Theorems, pages 35-65, Springer.
    2. Lin, Zhongwei & Chen, Zhenyu & Wu, Qiuwei & Yang, Shuo & Meng, Hongmin, 2018. "Coordinated pitch & torque control of large-scale wind turbine based on Pareto efficiency analysis," Energy, Elsevier, vol. 147(C), pages 812-825.
    3. Chen, Zhenyu & Lin, Zhongwei & Zhai, Xiaoya & Liu, Jizhen, 2022. "Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator," Energy, Elsevier, vol. 238(PB).
    4. 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.
    5. Zhang, Jincheng & Zhao, Xiaowei, 2022. "Wind farm wake modeling based on deep convolutional conditional generative adversarial network," Energy, Elsevier, vol. 238(PB).
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