the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
How to identify design optimization problems that can be improved with a control co-design approach ?
Carlo Luigi Bottasso
Michael Kenneth McWilliam
Abstract. Control co-design is a promising approach for wind turbine design due to the importance of the controller in power production, stability and load alleviation. However, the high computational effort required to solve optimization problems with added control design variables is a major obstacle to quantify the benefit of this approach. In this work, we propose a methodology to identify if a design problem can benefit from control co-design. The estimation method, based on post-optimum sensitivity analysis, quantifies how the optimal objective value varies with a change in control tuning.
The performance of the method is evaluated on a tower design optimization problem, where fatigue load constraints are a major driver, and using a Linear Quadratic Regulator targeting fatigue load alleviation. We use the gradient-based multi-disciplinary optimization framework Cp-max. Fatigue damage is evaluated with time-domain simulations corresponding to the certification standards. The estimation method applied to the optimal tower mass and optimal levelized cost of energy show good agreement with the results of the control-co design optimization, while using only a fraction of the computational effort.
Our results additionally show that there may be little benefit to use control co-design in the presence of an active frequency constraint. However, for a soft-soft tower configuration where the resonance can be avoided with active control, using control co-design results in a higher tower with reduced mass.
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Jenna Iori et al.
Status: open (until 05 Oct 2023)
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RC1: 'Comment on wes-2023-58', Anonymous Referee #1, 04 Jul 2023
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Overall Thoughts
Overall, this manuscript has a clear objective and application. The authors propose a method to estimate the impact of changes in control design variable on the objective function in an optimization study without directly solving a control co-design (CCD) optimization problem. The authors argue that this method would save the user time in identifying a scenario where the objective function is insensitive to the control design variable—making CCD somewhat trivial—without actually going through the effort of solving the more complex problem. This intention to reduce computational time in the design process is well-motivated, but I believe the discussion of this point could be more comprehensive.
A second thread of the manuscript is the application of the proposed method to the optimal design of a wind turbine tower with fatigue load constraints. I believe the details of this case study convolute and overshadow the main objective at times, and a more refined description is necessary.
After addressing these comments and some other minor revisions, I believe this manuscript will be suitable for publication in Wind Energy Science.
Major Comments
Line 171: What is the surrogate model for LCOE and how was it calibrated? The model form of the objective function and its dependence on the design variables is necessary information for the reader to understand the case study.
Line 189: “A gain schedule is created by varying the parameters r and q over the operational range.” I don’t think this phrase is intuitive for a reader unfamiliar with LQR control. Also, a few lines later: “The weight matrix entry associated to the tower top velocity was found to give a good fatigue damage reduction, without affecting the standard deviation of the power production in a significant manner.” This description is vague and not reproducible. Similar to the previous comment, the details of the case study (LQR control law, LCOE minimization, etc.) are extensive compared to the objective function sensitivity estimator. I think they require more explanation to be comprehensible by the reader or should be removed or moved to an appendix.
Line 261: I think the comparison of computational cost between the proposed estimator and the full CCD solution could be clearer. The authors state that “12 [shouldn’t this be 16?] evaluations of the full set of aeroelastic simulations for each configuration” were run for the estimator, while the CCD problem requires “running the full set of simulations 50 times for the soft-soft configuration and 20 times for the standard configuration.” I’m not sure why these specific numbers of simulations were chosen. Furthermore, how could this result generalize outside of the tower design case study?
Minor Comments
Title: I find the question format of the title to be a bit strange and not descriptive of the particular methods introduced by the paper. Perhaps something in the vein of: "Identifying design optimization problems for control co-design approach with objective function sensitivity estimator”?
Line 95: How valid is the simplification to only consider active constraints, and assuming that the active set of constraints does not change with control tuning? If your constraint is a function of control tuning, it seems plausible that a change in control could cause an inactive constraint to become active.
Line 114: There is repeated use of the phrase “diminishing returns” of controller tuning without any elaboration on what the authors mean. I understand that in Figure 5, a marginal increase in control tuning leads to a diminishing change in optimal tower mass. I think this point could be clearly defined earlier in the manuscript if this phrase is to be used.
Line 133: Is resonance avoidance not included in the soft-soft configuration in order to simplify the problem and focus on the objective function sensitivity? This is a valid approach, but I think the authors should state that point clearly. Otherwise, the problem definition for the soft-soft case seems impractical.
Line 147: “On the other hand, the AEP used to calculate the LCOE is only marginally impacted by the control tuning, since it is based on the average power production, which tends to be relatively insensitive to such changes.” Is there a source to justify this statement?
Line 149: I have trouble following the process for solving the optimization problems. For a given tower height, the loads on the tower are simulated and used to optimize the tower mass. When is the height of the tower changed and LCOE minimized? It seems like the solution of the outer optimization problem has not been described. Also, it is stated that “If the change in [tower mass] design is greater than a given threshold, the process is repeated iteratively (Bottasso et al., 2016).” What threshold is used in this paper?
Line 203: I think more details on the aeroelastic simulations could be given. What certification standards were used for fatigue analysis? How is turbulence synthetically generated and modeled? How long is the transient period?
Line 203: How is the fatigue damage resulting from different wind speeds combined into a single estimate of lifetime fatigue damage? Is there a probability distribution of wind speeds that inform taking a weighted average of the different fatigue values?
Figure 4: Panel ‘b’ contains the Lagrange multipliers for geometric constraints, and ‘c’ for the fatigue damage. The caption appears to have the wrong labels.
Table 1: The caption could be simpler and less confusing. The reference for the table is the optimization solution without CCD for a control input of zero. Then, LCOE is optimized with CCD and with the estimator method and compared relative to that reference value. There are a few points in the manuscript where the change of optimal LCOE is presented without a clear definition of what the reference value is.
Line 269: The authors state that the estimator accurately predicts the optimal objective value, but not the optimal design. I think it could be useful to clarify here that the goal of this method is to identify how much the objective function can be improved by control tuning, and in cases where the estimator signals much potential, a full CCD study would be performed. Otherwise, the reader could jump to the conclusion that the proposed method would not ultimately reach an optimal design.
Line 284: Would there be any advantage to quantifying uncertainty of the estimator? In other words, high uncertainty in the estimator could encourage a user to explore the CCD problem regardless of the compared sensitivity in the objective function.
Typographical Comments
Equation 10: Could be split up into two separately numbered equations, one for the “outer” optimization problem and one for the “inner” problem.
Citation: https://doi.org/10.5194/wes-2023-58-RC1
Jenna Iori et al.
Jenna Iori et al.
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