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On the Potential of Reduced Order Models for Wind Farm Control: A Koopman Dynamic Mode Decomposition Approach

Author

Listed:
  • Nassir Cassamo

    (Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal)

  • Jan-Willem van Wingerden

    (Delft Center for Systems and Control, Mekelweg 5, 2628 CD Delft, The Netherlands)

Abstract

The high dimensions and governing non-linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non-linearities. The work presented here applies the ideas motivated by non-linear dynamical systems theory—the Koopman Operator—to an innovative algorithm in the context of wind farm systems—Input Output Dynamic Mode Decomposition (IODMD)—to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:24:p:6513-:d:459644
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    References listed on IDEAS

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    1. David Bastine & Lukas Vollmer & Matthias Wächter & Joachim Peinke, 2018. "Stochastic Wake Modelling Based on POD Analysis," Energies, MDPI, vol. 11(3), pages 1-29, March.
    2. Steven L Brunton & Bingni W Brunton & Joshua L Proctor & J Nathan Kutz, 2016. "Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-19, February.
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    Cited by:

    1. Yuko Hirase & Yuki Ohara & Naoya Matsuura & Takeaki Yamazaki, 2021. "Dynamics Analysis Using Koopman Mode Decomposition of a Microgrid Including Virtual Synchronous Generator-Based Inverters," Energies, MDPI, vol. 14(15), pages 1-20, July.
    2. Dai, Xuan & Xu, Da & Zhang, Mengqi & Stevens, Richard J.A.M., 2022. "A three-dimensional dynamic mode decomposition analysis of wind farm flow aerodynamics," Renewable Energy, Elsevier, vol. 191(C), pages 608-624.
    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. Chen, Zhenyu & Lin, Zhongwei & Zhai, Xiaoya & Liu, Jizhen, 2022. "Dynamic wind turbine wake reconstruction: A Koopman-linear flow estimator," Energy, Elsevier, vol. 238(PB).
    5. González-Hernández, José Genaro & Salas-Cabrera, Rubén & Vázquez-Bautista, Roberto & Ong-de-la-Cruz, Luis Manuel & Rodríguez-Guillén, Joel, 2021. "A novel MPPT PI discrete reverse-acting controller for a wind energy conversion system," Renewable Energy, Elsevier, vol. 178(C), pages 904-915.

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