the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Apr 2025
Economic lifetime-aware wind farm control
Abstract. We present the economic lifetime-aware formulation of wind farm control (WFC), a novel approach that incorporates the current state of damage of turbines – either provided by a digital twin or estimated from operational data – to compute control policies that optimize the long-term life management of a wind farm. The optimization is guided by an economic value function that balances power capture (taking into account variable spot market prices) with operation and maintenance (O&M) costs, including potential revenue losses due to turbine downtime. The optimization process is subject to constraints ensuring that the target lifetime of selected turbine components is met, considering varying inflow conditions. This results in optimal control setpoints for each turbine as functions of ambient conditions.
After introducing the economic lifetime-aware WFC approach, the paper analyzes two case studies. The first is a synthetic scenario with a simplified set of environmental conditions, designed to demonstrate the behavior of the new control strategy and its impact on fatigue loads. The second case features the more realistic setup of a small wind farm, with wind climate data derived from a real meteorological mast. The benefits of the proposed methodology are highlighted by comparing it to a range of reference control strategies, which either ignore component damage or address fatigue loads in alternative simplified ways. When compared to greedy and power-maximizing WFC strategies, results show that only the lifetime-aware formulation ensures the achievement of the desired lifetime targets. Additionally, it also results in the best economic performance.
Competing interests: CLB is the editor in chief of WES
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.- Preprint
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RC1: 'Comment on wes-2025-67', Anonymous Referee #1, 22 May 2025
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General Comments:
The paper “Economic lifetime-aware wind farm control” from Anand et al. presents an approach to optimizing wind farm control setpoints for profit optimization, considering component fatigue and related maintenance costs. The Approach is demonstrated in simplified case studies, showcasing the optimization using only yaw steering as a control mode.
While the paper is well written overall, it could benefit from some restructuring to improve understandability. I suggest a more rigorous differentiation between methodology, case study definition, and results. At times, these aspects are mixed.
It would be helpful to differentiate between the general discussion of control approaches (induction, derating, boosting) and the ones used in this work. I was confused about which ones are actually implemented in this work.
The introduction could benefit from a more in-depth discussion of previous work on the topic and the relation to / contribution of the present work. Relevant references include:
https://wes.copernicus.org/articles/8/1727/2023/
http://dx.doi.org/10.18419/opus-13959
Specific Comments:
Line 50: Control modes could also include de-rating, boosting etc.
Line 61: Isn't economic optimization equivalent to production maximization if damage is not a major concern (except in negative price scenarios)?
Section 2: It is not entirely clear to me if lifetime is subject to optimization or a prescribed value.
Line 120: How is lost lifetime cost defined? What does chosen lifetime mean here? Isn’t that an optimization parameter?
Section 3: Does the optimization take place over a (conditional) pdf of wind conditions with global profit objectives, or over a time series of input conditions sampled from a distribution.
Line 183: What does sufficiently accurate mean here?
Line 184: Are the parameters tuned based on the experimental measurements in the wind tunnel?
Line 200: Please elaborate on this. How are control effects captured “inherently”? Also, consider removing the mention of down-regulation, as you are not using this control mode.
Section 3.2.1/ 3.3 I think understandability can be improved by explaining the path from DEL àComponent damage à Lifetime à Farm lifetime in one section. This information is distributed over several sections, so it is hard to understand the approach in detail. Consider restructuring.
Equation 10: I understand that the electricity price model details are given in the reference, but I think it would improve understandability if you could include a plot showing the relationship between wind and price signal. Are there negative prices?
Equation 10: U is not defined, I guess it is the wind speed?
Figure 5: The caption is confusing to me. What are the DELs on the x-axis? Also it is a prediction of the load surrogate not of FLORIS?
Section 4.1: Some content here is not really "Result and Discussion". I suggest integrating this in the methodology sections.
Line 426: This strategy is not clear to me. What is the lifetime constraint here? In Figure 11 it is shown that this strategy ends up having a lifetime greater than the nominal lifetime. Wouldn’t a lifetime constraint of 20 years just maximize the production, while ensuring that the 20 years lifetime constraint is met?
Section 4.2.3: You mention how lifetime is calculated for one component, but I can’t find how you define lifetime for the farm (which you use as a metric later on).
Figure 12: What are the extended columns without outline? The extended lifetime?
Section 4.2.5: A table (or a more detailed description) of the parameters you vary would be helpful.
Line 623: Why did you choose 8% as a variation of input parameters? I would expect some input parameters to have uncertainty higher than 8% easily?
Citation: https://doi.org/10.5194/wes-2025-67-RC1 -
RC2: 'Comment on wes-2025-67', Anonymous Referee #2, 23 May 2025
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This work considers wind farm controls (in particular, wake steering via yaw misalignment) using a cost function that accounts for operation and maintenance costs arising from turbine damage alongside revenues generated by the wind farm from energy sales. Overall, I found the core ideas to be interesting, the work to be well-motivated, and the description of the load and cost model to be well done. I also appreciated the sensitivity study carried out on the cost model parameters and the general approach to tuning and initial comparisons using FAST.Farm.
I have three main concerns that I feel the authors need to address.
1. The first is, I believe, not a concern about the core approach but simply how it is presented. In the initial portions of the paper, the authors describe optimizing the control actions over the turbines' lifetime T. For instance, the net revenue sum in Eq. (1a) is given over "T", which is subsequently described as the "lifetime". This, as well as the surrounding text, gave me the impression that the control set points u were being optimized for each "time step" in the turbine's lifetime. After some further reading, and considerably further on in the manuscript, I realized (I think!) that this is not true---rather, the sum should be over the binned wind conditions {W_a} that the turbine will experience in its lifetime, presumably weighted by the frequency occurrence of that wind condition based on the wind rose. If I'm correct that that is what is happening, please consider revising the formulation of problem (1) to be clearer. Consider including: the actual variable that is being summed over in the main sum; where that variable appears in the cost function; whether (bold) u represents the control actions at all turbines _for a single wind condition_ or whether u represents the control actions at all turbines _for all wind conditions (time steps?)_; whether u_max and u_min are simply N-vectors (N x T vectors?) of the same values repeated, or if u_max and u_min may be different for different turbines; how weights corresponding to the frequency of occurrence of a given wind condition appear in the cost function (currently, it seems that all time steps appear in the cost function, but this seems unlikely, or that all wind conditions are given equal weighting of 1 in the cost function regardless of their probability of occurrence). I would also recommend updating the text of Section2 and possibly other sections to clarify whether the optimization happens over wind conditions or time steps.
2. I am also concerned about whether there is any time-discounting taking place in the optimization. I don't see any mention of using a discount rate when deciding on what control actions to take, but discounting is a major consideration in any years-long cost/revenue analysis and may have a major effect on your results. For instance, discounting will likely make lifetime extensions considerably less valuable than it appears if a dollar in 10 years' time is considered to have the same value as a dollar today; but if a discount rate of 8% is used (which I understand to be fairly typical in economics, but I am no economist so please feel free to disagree on that front), a dollar in 10 years time is worth less than 50 cents today. Do your results in Section 4 consider discounting? If so, please make this clear. If not, I think this should be included. Possibly more difficult: can your optimization problem take time value of money into account? When I at first thought that you were optimizing for each time step in the lifetime, it seemed straightforward to put a discount rate into the cost function; but now that I believe you are optimizing over each condition without considering "time" in the cost function, it's not totally clear to me how this would be done. Finally, the only mention of how value changes in time that I saw in the paper was in Section 4.3.1, "An annual inflation rate of 8% is applied for the economic evaluation.". This needs to be explained further. Are you saying that costs and revenue _increase_ at a rate of 8% per year (extremely high inflation if applied year over year for ten years) so that power generated in year 10 is actually worth more than power generated in year 1? I would strongly disagree with this approach, since it seems to be the inverse of discounting. Again, not being an economist I'm not sure how inflation should be handled, but my understanding with a quick search is that inflation is usually left out of discounting calculation under the expectation that while revenue will be higher due to inflation, so will all costs (salaries, normal operating costs, etc) so there is a net zero effect. I may be misunderstanding what you mean in the inflation sentence, so please explain this better so that readers understand the approach taken.
3. The authors argue that the 100-hour optimization time is acceptable since the optimization does not need to take place online. Still, looking at the curve given in Figure 17, I would argue that some (future) improvements will be needed to make this feasible. Very roughly extrapolating, it looks like a 100-turbine farm, which is pretty typical, would take around 1000 hours to optimize, and that's using a limited wind rose with only 3 wind speed bins. 1000 hours is over a month, which I feel is likely not acceptable. Although the authors suggest the optimization may not need to be repeated, it seems to me likely that a wind farm operator may want to rerun the optimization say, once per year, to update the turbine damage information and replan based on actual observed damage. It is clearly out of scope to design a new optimization approach, but do the authors have any thoughts about how the optimization might be sped up in future work? Could the problem be parallelized in any way? FLORIS itself has some inbuilt parallelization that may be useful for this. In fact, I didn't understand what approach/algorithm is taken for optimization---the authors mention a "one-shot" approach, but I'm not familiar with this term so it would be good to explain at least briefly in words how this works.
I also have the following minor points that I feel should be addressed to improve the manuscript:
- Line 65: What does "(future better)" mean? I'm unfamiliar with this phrase. Consider revising.
- Section 3.2.2: Horizontal shear is included in the load model, but not vertical shear, if I'm understanding correctly. I would have thought that vertical shear would also be an important driver of fatigue loads (especially blade loads), even if it is not controllable using wake steering. Do the authors have any comments on this?
- Line 318: Although I agree that the trend between wind power output and electricity price should be cited, having 6 citations for this seems excessive. Perhaps one or two citations would be enough here? Just a suggestion, feel free to ignore.
- Line 360: It might be interesting to help readers with intuition to demonstrate in a figure how the cost model (11) changes with respect to (non-optimized) control inputs. I personally would find this helpful. Again, just a suggestion, not critical.
- Eq. (12): Do the reference optimization problems (12)--(15) still consider the input constraint u_min <= u <= u_max (1c)? If not, I would suggest adding this to make it more consistent with the max profit optimization approach (or justify not including this constraint). If so, please make this clear.
- On several occasions the authors mention that the "max power" approach takes more "aggressive" offsets than the proposed "max profit" approach. Can the authors explain what they mean by this? Looking at Figure 7, it's not at all clear to me that the "max power" approach takes aggressive offsets (on the contrary, they seem to be smaller than the offsets selected by the "max profit" approach).
- Line 511: "Since FLORIS does not account for vertical shear...". I'm not sure what the authors mean by this---FLORIS does account for vertical shear across the rotor points when computing a rotor-average inflow, although not in the evolution of the wake. Perhaps this is what the authors are referring to? This sentence should be updated.
- Line 654: "It is assumed that these wind conditions remain constant over the course of the year". What do the authors mean by this?
- Line 657: Inflation of 8% year over year seems to be very high. I would recommend something much lower than this if inflation is still included after addressing my main comment 2. above.Citation: https://doi.org/10.5194/wes-2025-67-RC2
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Economic lifetime-aware wind farm control A. Anand et al. https://doi.org/10.5281/zenodo.15118524
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