the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
On the importance of wind predictions in wake steering optimization
Abstract. Wake steering is a technique that optimises the energy production of a wind farm by employing yaw control to misalign upstream turbines with the incoming wind direction. This work highlights the important dependence between wind direction variations and wake steering optimization. The problem is formalized over time as the succession of independent and steadystate yaw control problems. Then, this work proposes a reformulation of each steadystate problem by augmenting the objective function by a new heuristic based on a wind prediction. The heuristic acts as a penalization for the optimization, encouraging solutions that will guarantee future energy production. Finally, a synthetic sensibility analysis of the wind direction variations and wake steering optimization is conducted. Because of the rotational constraints of the turbines, as the magnitude of the wind direction fluctuations increases, the importance of considering wind prediction in a steadystate optimization is empirically demonstrated. The heuristic proposed in this work greatly improves the performance of controllers and compared to a model predictive control (MPC) approach, it does not increase complexity.
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Status: closed

RC1: 'Comment on wes2023172', 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 timevarying 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 gridsearch 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/wes2023172RC1 
RC2: 'Comment on wes2023172', Anonymous Referee #2, 06 Feb 2024
General commentsOverall, 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 MPCbased optimization) and the proposed improvement (heuristicbased 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 forwardintime yaw angles have an impact on the current time optimization result (if not, explain)? What is the impact of a cosine vslinear 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 commentsSee above for the questions on the motivation and justification for the simplifications to the MPCbased 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 deltak" statement into an equation that you can reference back to here.Technical correctionsApologies 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 steadystate models. You did this in the conclusions, but it would be helpful in the intro.Citation: https://doi.org/
10.5194/wes2023172RC2 
AC1: 'Comment on wes2023172', 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.
Interactive discussion
Status: closed

RC1: 'Comment on wes2023172', 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 timevarying 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 gridsearch 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/wes2023172RC1 
RC2: 'Comment on wes2023172', Anonymous Referee #2, 06 Feb 2024
General commentsOverall, 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 MPCbased optimization) and the proposed improvement (heuristicbased 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 forwardintime yaw angles have an impact on the current time optimization result (if not, explain)? What is the impact of a cosine vslinear 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 commentsSee above for the questions on the motivation and justification for the simplifications to the MPCbased 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 deltak" statement into an equation that you can reference back to here.Technical correctionsApologies 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 steadystate models. You did this in the conclusions, but it would be helpful in the intro.Citation: https://doi.org/
10.5194/wes2023172RC2 
AC1: 'Comment on wes2023172', 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.
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