the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 08 Oct 2024
Integer programming for optimal yaw control of wind farms
Abstract. It is well-known that wakes caused by the wind turbines within a wind farm negatively impact the power generation and mechanical load of downstream turbines. This is already partially considered in the farm layout. Nevertheless, the strong interactions between individual turbines provide further opportunities to mitigate adverse effects during operation, e.g., by repeatedly adjusting axial induction or yaw angles to current wind conditions. We propose a mathematical approach in form of integer programming for globally optimal yaw control (under some mild assumptions). While we prove the wind farm yaw problem to be strongly 𝒩𝒫-hard in general, we demonstrate through numerical experiments that our method is efficient in practice and enables optimal yaw control under real-world requirements on control update periods. In particular, the approach remains efficient if turbines are deactivated and scales reasonably well with increasing farm width.
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RC1: 'Comment on wes-2024-120', Anonymous Referee #1, 17 Oct 2024
The paper proposes an innovative method for yaw optimization that relies on integer programming. The authors have presented an exhaustive description of the state-of-the-art concerning this topic. This includes a detailed description of the wake models used to simulate the farm performance as well as the different constraints adopted by previous authors. These information are then properly used to motivate the assumptions considered by the authors of this work, such as the discretization of the possible yaw angles. Then, the complexity of the optimization problem is extensively described both through practical examples and detailed mathematical proofs. The methodology of the proposed structure of the optimization problem is also well explained (also using helpful visualizations), introducing the so called “covering approach” to tackle the curse of dimensionality. The test cases have been chosen appropriately and the results are shown highlighting the benefits in terms of computational time and power gains.
Nevertheless, I would like to make some minor suggestions to further improve the quality of this paper.
In Sec. 2.3.3 it is mentioned that this new formulation of the yaw optimization problem based on this “covering approach” is equivalent the direct (complete) problem. Within the optimization context, the term equivalent usually entails that two different formulations of the same problem have the exact same solution. However, in the paper (Sec. 4.1) it is mentioned that the calculation of the power using the covering approach slightly deviates from the global approach. It is also well motivated that such marginal deviation will most likely have no impact on the optimal solution. However, the exact optimal solution cannot be in principle guaranteed (especially is we decrease the number of yaw values allowed) . Therefore, I would suggest to rephrase the sentence in Sec. 2.3.3 where it is mentioned that these two formulations are equivalent, anticipating that there could be a minimal difference in the optimal solution.
Moreover, it would be nice to highlight qualitatively or quantitatively the advantages of the proposed method (e.g. in terms of accuracy and/or computational time) in comparison with other popular approaches for yaw optimization, such as the serial-refine method available in FLORIS.
Other minor comments:
- In most of the figures depicting a wind farm, a vector indicating the wind direction can be helpful to facilitate the reading in case of a quick scan.
- A table summarizing the results presented in Sec. 4.4 would facilitate the reading as well. If already present, it would be better to add the “cross-reference” in the text.
- The presence of some mild assumption is mentioned both in the Abstract and the Conclusion. For a better understanding in case of a quick reading, I would suggest to briefly mention them (e.g. in one line and focusing on the yaw discretization) in both cases.
Overall, very nice work!
Citation: https://doi.org/10.5194/wes-2024-120-RC1 -
RC2: 'Comment on wes-2024-120', Anonymous Referee #2, 30 Oct 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-120/wes-2024-120-RC2-supplement.pdf
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