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Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
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https://doi.org/10.5194/wes-2020-74
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-2020-74
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 08 May 2020

Submitted as: research article | 08 May 2020

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This preprint is currently under review for the journal WES.

Set-point optimization in wind farms to mitigate effects of flow blockage induced by gravity waves

Luca Lanzilao and Johan Meyers Luca Lanzilao and Johan Meyers
  • Department of Mechanical Engineering, KU Leuven, Celestijnenlaan 300 A, 3001 Leuven, Belgium

Abstract. Recently, it has been shown that flow blockage in large wind farms may lift up the top of the boundary layer, thereby triggering atmospheric gravity waves in the inversion layer and in the free atmosphere. These waves impose significant pressure gradients in the boundary layer causing detrimental consequences in terms of farm's efficiency. In the current study, we investigate the idea of controlling the wind farm in order to mitigate the efficiency drop due to wind-farm induced gravity waves and blockage. The analysis is performed using a fast boundary layer model which divides the vertical structure of the atmosphere into three layers. The wind-farm drag force is applied over the whole wind-farm area in the lowest layer and is directly proportional to the wind-farm thrust set-point distribution. We implement an optimization model in order to derive the thrust-coefficient distribution which maximizes the wind-farm energy extraction. We use a continuous adjoint method to efficiently compute gradients for the optimization algorithm, which is based on a quasi-Newton method. Energy gains are evaluated with respect to a reference thrust-coefficient distribution based on the Betz–Joukowsky set point. We consider thrust coefficients that can change in space, as well as in time, i.e. considering time-periodic signals. However, in all our optimization results, we find that optimal thrust-coefficient distributions are steady; any time-periodic distribution is less optimal. The (steady) optimal thrust-coefficient distribution is inversely related to the vertical displacement of the boundary layer. Hence, it assumes a sinusoidal behaviour in the streamwise direction in subcritical flow conditions, whereas it becomes a U-shaped curve when the flow is supercritical. The sensitivity of the energy gain to the atmospheric state is studied using the developed optimization tool for almost two thousand different atmospheric states. Energy gains of up to 14 % are found for weakly stratified atmospheres in critical flow regimes.

Luca Lanzilao and Johan Meyers

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Luca Lanzilao and Johan Meyers

Luca Lanzilao and Johan Meyers

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Latest update: 29 May 2020
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Short summary
This research paper investigates for the first time the potential of thrust set-point optimization in large wind farms for mitigating gravity-wave induced blockage effects, with the aim of increasing the wind-farm energy extraction. The optimization tool is applied to almost two thousand different atmospheric states. Overall, energy gains above 4 % are observed for 77 % of the cases.
This research paper investigates for the first time the potential of thrust set-point...
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