Preprints
https://doi.org/10.5194/wes-2023-133
https://doi.org/10.5194/wes-2023-133
06 Nov 2023
 | 06 Nov 2023
Status: a revised version of this preprint was accepted for the journal WES and is expected to appear here in due course.

On the power and control of a misaligned rotor – Beyond the cosine law

Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso

Abstract. We present a new model to estimate the performance of a wind turbine operating in misaligned conditions. The model is based on the classic momentum and lifting-line theories, considering a misaligned rotor as a lifting wing of finite span, and accounts for the combined effects of both yaw and uptilt angles.

Improving on the classical empirical cosine law in widespread use, the new model reveals the dependency of power not only on the misalignment angle, but also on some rotor design parameters and – crucially – on the way a rotor is governed when it is yawed out of the wind. Additionally, the model also shows that a sheared inflow is responsible for the observed lack of symmetry for positive and negative misalignment angles. Notwithstanding its simplicity and insignificant computational cost, the new proposed approach is in excellent agreement with large eddy simulations (LES) and wind tunnel experiments.

Building on the new model, we derive the optimal control strategy for maximizing power on a misaligned rotor. Additionally, we maximize the total power of a cluster of two turbines by wake steering, improving on the solution based on the cosine law.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2023-133', Majid Bastankhah, 01 Dec 2023
  • RC2: 'Comment on wes-2023-133', Anonymous Referee #2, 07 Dec 2023

Status: closed

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on wes-2023-133', Majid Bastankhah, 01 Dec 2023
  • RC2: 'Comment on wes-2023-133', Anonymous Referee #2, 07 Dec 2023
Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso

Data sets

On the power and control of a misaligned rotor – Beyond the cosine law S. Tamaro, F. Campagnolo, C. L. Bottasso https://zenodo.org/record/8388901

Model code and software

On the power and control of a misaligned rotor – Beyond the cosine law S. Tamaro, F. Campagnolo, C. L. Bottasso https://zenodo.org/record/8388901

Interactive computing environment

On the power and control of a misaligned rotor – Beyond the cosine law S. Tamaro, F. Campagnolo, C. L. Bottasso https://mybinder.org/v2/gh/sTamaroTum/Beyond_the_cosine_law/main

Simone Tamaro, Filippo Campagnolo, and Carlo L. Bottasso

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Short summary
We develop a new simple model to predict power losses incurred by a wind turbine when it yaws out of the wind. The model reveals the effects of a number of rotor design parameters and, even more importantly, of how the turbine is governed when it yaws. The model exhibits an excellent agreement with LES simulations and wind tunnel measurements. We showcase the capabilities of the model by deriving the power-optimal yaw strategy for a single turbine, and for a cluster of wake-interacting turbines.
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