On the importance of wind predictions in wake steering optimization

Kadoche, Elie; Bianchi, Pascal; Carton, Florence; Ciblat, Philippe; Ernst, Damien

doi:https://doi.org/10.5194/wes-9-1577-2024

Articles | Volume 9, issue 7

https://doi.org/10.5194/wes-9-1577-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/wes-9-1577-2024

© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 9, issue 7

Research article

|

24 Jul 2024

Research article |

| 24 Jul 2024

On the importance of wind predictions in wake steering optimization

Elie Kadoche, Pascal Bianchi, Florence Carton, Philippe Ciblat, and Damien Ernst

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Final revised paper (published on 24 Jul 2024)
Preprint (discussion started on 04 Jan 2024)

Interactive discussion

Status: closed

RC1: 'Comment on wes-2023-172', Anonymous Referee #1, 19 Jan 2024

This paper describes the application of different controllers that maximize the power output of a wind farm by optimizing the turbines yaw angles under time-varying wind directions. Different control strategies are tested and the results are compared.
I have the following remarks/comments:
- The authors realize that a wind farm is a dynamical system (mainly due to wake delays). However, the authors try to push a steady state model in a dynamical control framework. Isaac Newton went through great lengths to introduce differential equations, why not use these in this application? Why not model the windfarm using differential equations? In fact, in algorithm 1, at each time step, the state s_t is evaluated and new control signals are computed accordingly. However, the wind farm will never reach the computed state s_t since this is a steady state of the farm and control signals are set at each time step and the wind velocity is changed at each time step. So what is actually optimized here?
- In the abstract, at the end, the authors write "it does not increase complexity". This seems to be a relative notion. What does complexity mean here and does it become more complex for everyone?
- it seems that the wind speed in front of turbine i is defined as v_t^i which is later defined as Kt. I would recommend to take out unnecessary variables to make the document easier to follow.
- In Figure 2, is it possible to also indicate u_t^i ?
- In (4), what does the one at the end of the equation mean?
- In (5), the notation is not clear. There is no function defined, but only {..}. Please detail this.
- The term MPC is used in the paper. However, the controller is clearly not an MPC. I would suggest taking out the term to avoid confusion.
- what is the relation between f_control, f_yaw and \pi(s_t). Is it possible to simplify notation? It seems overcomplicated, but maybe it is really necessary like this?
- In (12), what does clip() mean?
- Around 235 the authors write "At each iteration, it solves the optimization problem for the current turbine, considering the yaw angles of all others fixed. To do so, it uses a grid-search method..." What is now done in the end? A grid search or is an optimization problem solved?
- The prediction based controller is according to the authors a too difficult optimization problem and simplifications are proposed (top page 12). What is the effect of these simplifications on the original problem statement? Is it possible to quantify these? It feels now like, the original problem is simplified and we will solve the simplified problem. However, we have no idea how far the simplified problem is from the original problem.
- In Figure 4, please indicate better the meaning of all symbols/lines and the wind direction.
- In line 337 I read that some option are enabled. What does this mean?
- Overall, please provide tables with settings that are used throughout the simulations. These are now everywhere placed in the text which makes it for me impossible to follow.
- In line 350, L=11 is defined. What does this mean in the context of steady state models?
- In figure 9, how is the upper bound computed? how are the shaded areas computed?
- In line 411, the authors write "capture the dynamics of the system". I don't think that this is correct since a steady state model is used.
- Figure 3 seems to be not necessary? This is a well known figure, but what does it contribute to the story?

The major question that I have is regarding the use of a steady state model in a dynamical control framework. It raises many questions and the meaning of the results is not clear to me. In other words, how can anybody judge the scientific relevance of the work? I would also suggest the authors to also rewrite the paper so that it becomes more readable/understandable. Define all variables clearly, figures,
I hope that the above remarks can help and I am looking forward to a revised version.

Citation: https://doi.org/10.5194/wes-2023-172-RC1
RC2: 'Comment on wes-2023-172', Anonymous Referee #2, 06 Feb 2024

General comments
Overall, the paper is nicely formulated and presented. The problem statement is well defined, and the proposed solution is motivated, described, and validated well. I appreciate the pace of developing the wind farm flow control domain, the problem at hand (costly MPC-based optimization) and the proposed improvement (heuristic-based optimization). In general, I am convinced by the scientific method used, and I am interested to continue to understand the proposed control algorithm.

The paper would generally benefit from an effort to improve the flow and readability. Some statements are made without reference to their background or context. Also, there is possibly an excess of mathematical notation in the narrative content.

The most critical suggestion is to motivate and/or justify the simplifications proposed in section 3.2.2. Is it reasonable to ignore locally varying wind speeds and can you quantify the impact? Does assuming a naive controller for the forward-in-time yaw angles have an impact on the current time optimization result (if not, explain)? What is the impact of a cosine vs
linear yaw loss model?

With that clarification and a few notes below, I think this paper will be a strong study of an improved controls optimization algorithm.

Specific comments
See above for the questions on the motivation and justification for the simplifications to the MPC-based method.

Section 3.2.2 presenting a common MPC method - is the formulation a common or typical formulation? Suggest to reference.

Figure 4 is difficult to understand. What are the symbols and how do I know which (a or b) is better?

Line 392: These are important statements, but they seem to come suddenly and the values aren't traceable. It would help to derive these results or relate to Figure 9. Also, consider mentioning section 4.1 or making the "tau x delta-k" statement into an equation that you can reference back to here.

Technical corrections
Apologies if it is intentional, but it's unclear if you intended "sensibility analysis" or "sensitivity analysis".
Line 42: Suggest to replace "wind direction" with "wind direction variation" to note that it's the change in wind direction that you're studying.
Line 43: Suggest to motivate the use of steady-state models. You did this in the conclusions, but it would be helpful in the intro.

Citation: https://doi.org/10.5194/wes-2023-172-RC2
AC1: 'Comment on wes-2023-172', Elie Kadoche, 12 Mar 2024

We are grateful to the reviewers for dedicating their time to reading the document and providing their insightful remarks. It helped us improve the paper. The attached file contains the response to the comments from both reviewers and the differences between the first document and the revised document.

Citation: https://doi.org/10.5194/wes-2023-172-AC1

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Elie Kadoche on behalf of the Authors (13 Mar 2024) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (13 Mar 2024) by Johan Meyers

RR by Anonymous Referee #1 (21 Mar 2024)

Suggestions for revision or reasons for rejection

I think that there is a misunderstanding about what dynamics are. If a signal (like the wind or yaw angles) is changing over time, it does not mean that dynamics are taken into account. Dynamics are taken into account when there is a model that takes as an input the time-varying signals and outputs another signal (like turbine power). This output signal is then changing due to the input signal, and its exact change depends on the model dynamics. Delays and inertia are typical phenomena that you model with a dynamical model and clearly present in the application at hand and not taken into account.

The authors write:
“Steady-state models are necessary for optimization. Higher fidelity models, taking into account the dynamics of the wind and the variations of the wake effects between time steps, exist. But these models are too computationally expensive to be used for optimization.”

The statement that steady state model are necessary is questionable. It is a (over?) simplification of the reality and consequently, certain optimization problems can be solved. However, dynamical models can also be used in optimization problems, like high fidelity models with CPU time as a challenge. These things are known/researched, but where is the middle ground? A computational efficient enough dynamical model that can be used in an optimization. This seems to me the important and open question. Using a steady state model in some dynamical control framework remains questionable for me and the authors did not really convince me with their answers.

At last, the authors state that the original optimization problem is not solvable. Why not perform a grid search? You can let the CPU do the work. If the search space is too large (which I doubt when taking a relatively small farm and relatively small prediction horizon), you can limit it around the optimal solution found by the simplified optimization problem.

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RR by Anonymous Referee #2 (30 Apr 2024)

ED: Publish subject to minor revisions (review by editor) (01 May 2024) by Johan Meyers

AR by Elie Kadoche on behalf of the Authors (10 May 2024) Author's response Author's tracked changes Manuscript

ED: Publish as is (20 May 2024) by Johan Meyers

ED: Publish as is (23 May 2024) by Paul Fleming (Chief editor)

AR by Elie Kadoche on behalf of the Authors (29 May 2024)

Short summary

This work proposes a new wind farm controller based on wind predictions and conducts a synthetic sensitivity analysis of wake steering and the variations of the wind direction. For wind turbines that can rotate from −15 to 15° every 10 min, if the wind direction changes by more than 7.34° every 10 min, it is important to consider future wind data in a steady-state yaw control optimization.