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Adjoint optimisation for wind farm flow control with a free-vortex wake model

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  • van den Broek, Maarten J.
  • De Tavernier, Delphine
  • Sanderse, Benjamin
  • van Wingerden, Jan-Willem

Abstract

Wind farm flow control aims to improve wind turbine performance by reducing aerodynamic wake interaction between turbines. Dynamic, physics-based models of wind farm flows have been essential for exploring control strategies such as wake redirection and dynamic induction control. Free-vortex methods can provide a computationally efficient way to model wind turbine wake dynamics for control optimisation. We present a control-oriented free-vortex wake model of a 2D and 3D actuator disc to represent wind turbine wakes. The novel derivation of the discrete adjoint equations allows efficient gradient evaluation for gradient-based optimisation in an economic model-predictive control algorithm. Initial results are presented for mean power maximisation in a two-turbine case study. An induction control signal is found using the 2D model that is roughly periodic and supports previous results on dynamic induction control to stimulate wake mixing. The 3D model formulation effectively models a curled wake under yaw misalignment. Under time-varying wind direction, the optimisation finds solutions demonstrating both wake steering and a smooth transition to greedy control. The free-vortex wake model with gradient information shows potential for efficient optimisation and provides a promising way to further explore dynamic wind farm flow control.

Suggested Citation

  • van den Broek, Maarten J. & De Tavernier, Delphine & Sanderse, Benjamin & van Wingerden, Jan-Willem, 2022. "Adjoint optimisation for wind farm flow control with a free-vortex wake model," Renewable Energy, Elsevier, vol. 201(P1), pages 752-765.
    • Handle: RePEc:eee:renene:v:201:y:2022:i:p1:p:752-765
    DOI: 10.1016/j.renene.2022.10.120
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    References listed on IDEAS

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    1. Doekemeijer, Bart M. & van der Hoek, Daan & van Wingerden, Jan-Willem, 2020. "Closed-loop model-based wind farm control using FLORIS under time-varying inflow conditions," Renewable Energy, Elsevier, vol. 156(C), pages 719-730.
    2. Jay P. Goit & Wim Munters & Johan Meyers, 2016. "Optimal Coordinated Control of Power Extraction in LES of a Wind Farm with Entrance Effects," Energies, MDPI, vol. 9(1), pages 1-20, January.
    3. van der Hoek, Daan & Kanev, Stoyan & Allin, Julian & Bieniek, David & Mittelmeier, Niko, 2019. "Effects of axial induction control on wind farm energy production - A field test," Renewable Energy, Elsevier, vol. 140(C), pages 994-1003.
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    5. Jing Dong & Axelle Viré & Carlos Simao Ferreira & Zhangrui Li & Gerard van Bussel, 2019. "A Modified Free Wake Vortex Ring Method for Horizontal-Axis Wind Turbines," Energies, MDPI, vol. 12(20), pages 1-24, October.
    6. Bastankhah, Majid & Porté-Agel, Fernando, 2014. "A new analytical model for wind-turbine wakes," Renewable Energy, Elsevier, vol. 70(C), pages 116-123.
    7. Ciri, Umberto & Rotea, Mario A. & Leonardi, Stefano, 2017. "Model-free control of wind farms: A comparative study between individual and coordinated extremum seeking," Renewable Energy, Elsevier, vol. 113(C), pages 1033-1045.
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