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the Creative Commons Attribution 4.0 License.
| 21 Nov 2024
A multi-objective Economic Nonlinear Model Predictive Controller for Power and Platform Motion on Floating Offshore Wind Turbines
Abstract. A main target of the wind energy industry is the reduction of the Levelized Cost of Energy, especially for the emerging sector of floating turbines. An Economic Nonlinear Model Predictive Controller is developed to maximise power and reduce longitudinal motion, increasing revenues, and reducing capital and operating expenses. A novel comprehensive nonlinear Reduced Order Model of floating turbines is developed to predict platform motion, rotor thrust, aerodynamic power, and generator temperature. A grey-box approach and a black-box approach to platform modelling have been successfully vali dated and compared, identifying pros and cons. Then, the model is used in a constrained optimisation problem that computes the control action. The objectives are maximising aerodynamic power and reducing longitudinal nacelle velocity under realistic constraints (including bounds on rotor thrust, generator temperature, and platform velocities). The controller performance and robustness are assessed using a wide set of realistic wind and sea state load cases. Significant higher power production and a lower longitudinal platform motion concerning the standard NREL reference controller are achieved by adopting the multi-objective ENMPC. Finally, considering the difficulty in predicting the sea diffraction forces and the incoming wind, the performances are positively verified in the absence of that information.
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RC1: 'Comment on wes-2024-144', Anonymous Referee #1, 27 Nov 2024
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A multi-objective Economic Nonlinear Model Predictive Controller for Power and Platform Motion on Floating Offshore Wind Turbines
This paper presents a multi-objective ENMPC controller for the control of power and platform motion for FOWTs. A reduced order model is developed, and a gray box and black box approaches are evaluated and used for the ENMPC controller. The controller is compared to the NREL baseline 2009 controller for floating turbines.
The paper is unclear about the scientific gap it fills: why do we need an ENMPC controller, and is it practically implementable? This should be directly clear from the abstract and introduction; now, the abstract only talks about the current work without putting it into perspective of the current state-of-the-art. The introduction discusses irrelevant details, and says little about the contributions of the current work. Some figures in the paper are from other papers (why not make your own?), or are not referred to in the running text (fig 1+2). The formulation and motivation of the ENMPC problem is unclear, and assumptions on wind speed info in the prediction horizon are not discussed (in Section 4.6 you do, should be part of methodology). The structure and clarity (storyline) of the paper should be greatly improved. Because of the above, I think the paper needs a very major revision and is not of high enough quality for consideration in WES. Therefore I recommend rejecting the paper.
MAJOR
- ABSTRACT: Lacks a discussion on previous work and identifying the scientific gap and motivation of the current work
- ABSTRACT: "the objectives are maximising aerodynamic power" - would be good to elaborate your approach for this in abstract briefly.
- ABSTRACT: "the standard NREL reference controller" - ROSCO?
- ABSTRACT: It is unclear what you mean by multi-objective. Is it a single objective that consists of a weighted summation of objectives? Or truly multi-objective?
- INTRO: No need for the table in INTRO, you didn't produce it yourself and way too complicated/detailed.
- INTRO: Describing Region 1/2/3 is really unnessacary. Remove
- INTRO: "A completely different type of control for wind turbines is Model Predictive Control (MPC). " -- You haven't discussed any other specific controller contribution before.
- INTRO: You don't cite the main contributions in E(N)MPC for (floating) wind turbine control
- INTRO: You contribution(s) are unclear. You discuss briefly what you do but it is in the middle of discussing other's works. Explicitly define your contributions.
- INTRO: "OpenFast 1 and the the standard control strategy", why 1, what is the standard control strategy (ROSCO?).
- INTRO: Why did you choose the NREL5MW turbine? That's quite outdated, or is it still relevant for floating?
- INTRO: Fig 1 and Fig 2 not discussed in text.
- 1.1: Merge in INTRO, and too many contributions for 1 paper.
- 2: "Since KT does not depend on wind speed, "-- Mention this is the standard KW2 controller strategy and cite relevant works.
- 2: "This is because, when the relative wind speed increases due ..." -- This is the negative damping effect, right? Why not mention and cite relevant works?
- 2: Why a whole literature survey here about different control strategies? Move to INTRO
- 2: The content is very minimal of this section and not worth a dedicated section
- 3: Fig 3, why not make a nice figure yourself?
- 3.2.1/2: Not very clear what the purpose is of these sections, and what is being derived. Just show and motivate what you used in the end.
- 3.3: Unclear what the purpose is of this section
- 3.4: Is (13) an alternative form of (12)? Explain better, don't understand it now
- 3.4: What do you assume for the wind speed in the (future) prediction horizon? Constant value equal to WS at current time? Assume to be fully known? --> I see you do consider in Section 4.6, but this is an integral part of your controller implementation and assumptions, so should be discussed before results.
- 4: Aborted review from this pointCitation: https://doi.org/10.5194/wes-2024-144-RC1 -
AC1: 'Reply on RC1', Jacopo Serafini, 06 Jan 2025
reply
ABSTRACT: Lacks a discussion on previous work and identifying the scientific gap and motivation of the current work
ABSTRACT: "the objectives are maximising aerodynamic power" would be good to elaborate your approach for this in abstract briefly.
All these aspects will be clarified in the revised version
ABSTRACT: "the standard NREL reference controller" ROSCO?
The abstract refers to the standard controller described in "Definition of a 5-MW Reference Wind Turbine for Offshore System Development" by Jonkman et al. This controller was widely adopted as the benchmark for floating offshore wind turbines. While we acknowledge that the ROSCO controller has since been developed with support for floating applications (e.g., by incorporating nacelle velocity feedback, as described in NREL/TP-5000-82134), to the best of our knowledge, a tuned test case for the 5-MW floating turbine is not yet publicly available, likely due to inherent challenges in parameter tuning for floating systems.
ABSTRACT: It is unclear what you mean by multi-objective. Is it a single objective that consists of a weighted summation of objectives? Or truly multi-objective?
Linear Scalarization is a way to approach multi-objective optimization. In this case, it is an almost obliged solution, since the solution of the control problem requires the numerical solution of a complex nonlinear system's future time evolution to obtain the optimal set of design variables. Indeed we formulated the multiobjective problem as a convex weighted sum of two objectives L = sum_i=1^N w_i*l_i where w_i in [0,1] and sum_i=1^N w_i = 1. In our case, we have N = 2 with two goals (i.e. power maximisation and platform motion minimisation). For every value of the weight w_i (from 0 to 1) we obtain an optimal value on the Pareto front. This is what we did. This approach is suitable for both exploring the solutions on the Pareto front and also solving an optimisation problem when the weight is predefined that scales the importance of one goal with respect to the other. See “Algorithms for Optimization” by Mykel J. Kochenderfer and Tim A. Wheeler, 2019, The MIT Press, Chapter 12
INTRO: No need for the table in INTRO, you didn't produce it yourself and way too complicated/detailed.
INTRO: Describing Region 1/2/3 is really unnessacary. Remove
ok
INTRO: "A completely different type of control for wind turbines is Model Predictive Control (MPC). " -You haven't discussed any other specific controller contribution before.It was referred to the standard controller
INTRO: You don't cite the main contributions in E(N)MPC for (floating) wind turbine controlThe review and discussions of applications of MPC on FOWT have been done in the introduction. When we wrote the article, we did not find any application of ENMPC to FOWT. However, since the paper has been under review for several months, we will search again to look for new applications.
INTRO: You contribution(s) are unclear. You discuss briefly what you do but it is in the middle of discussing other's works. Explicitly define your contributions.
Actually, we have written an entire section about our original contributions. Please see 1.1.
INTRO: "OpenFast 1 and the the standard control strategy", why 1, what is the standard control strategy (ROSCO?).
Sorry, it was a formatting issue, the correct sentence is: In Section 4 the ROMs models are validated with OpenFast (fig. 1) and the standard control strategy and the novel controller are compared (fig. 2)
INTRO: Why did you choose the NREL5MW turbine? That's quite outdated, or is it still relevant for floating?
The power output of NREL 5MW is surely low compared to current ones (also for floating applications). However, all the issues of interest (power output optimization, platform motion reduction) are perfectly valid and are still present in the larger turbines. Thus, proving the effectiveness and flexibility of the ENMPC control proposed on a turbine of a smaller size does not jeopardise the results and the discussions of the findings. On the other hand, we had the turbine part of the ROM already available and tested and, broadly speaking, the NREL 5MW has been widely used in the past. Thus, many researchers may be more confident in trying to implement similar or different controllers on NREL 5MW. Note that our controller is available on request for comparisons.
INTRO: Fig 1 and Fig 2 not discussed in text.
see above
2: "Since KT does not depend on wind speed, "-Mention this is the standard KW2 controller strategy and cite relevant works.
ok
2: "This is because, when the relative wind speed increases due ..." -This is the negative damping effect, right? Why not mention and cite relevant works?
We can explicitly refer to "negative damping". Some references are present in the text (Jonkman 2009, Yang 2023, Jonkman 2010). We can search for newer ones.
2: Why a whole literature survey here about different control strategies? Move to INTRO
2: The content is very minimal of this section and not worth a dedicated section
3: Fig 3, why not make a nice figure yourself?
ok
3.2.1/2: Not very clear what the purpose is of these sections, and what is being derived. Just show and motivate what you used in the end.
We need to describe the two approaches to compare them in the results section. In our opinion, the optimal way to derive a ROM for WT is not a trivial choice.
3.3: Unclear what the purpose is of this section
The generator thermal model is part of the turbine ROM for ENMPC control purposes since the limit is imposed on generator temperature instead of power output. We will explain that in the text.
3.4: Is (13) an alternative form of (12)? Explain better, don't understand it now
Yes, 13 is an objective function collecting power and platform motion. We will explain it better.
3.4: What do you assume for the wind speed in the (future) prediction horizon? Constant value equal to WS at current time? Assume to be fully known? -I see you do consider in Section 4.6, but this is an integral part of your controller implementation and assumptions, so should be discussed before results.
This problem has been introduced in the introduction and, as you noted, it will be assessed in the numerical results section. However, we can explain here the problemCitation: https://doi.org/10.5194/wes-2024-144-AC1
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AC1: 'Reply on RC1', Jacopo Serafini, 06 Jan 2025
reply
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RC2: 'Comment on wes-2024-144', Anonymous Referee #2, 28 Nov 2024
reply
The submitted paper introduces a multi-objective Economic Nonlinear Model Predictive Controller (ENMPC) for Floating Offshore Wind Turbines (FOWTs), designed to maximize power production while minimizing platform motion. By integrating a reduced-order model (ROM) of the turbine and platform dynamics, the controller accounts for surge and pitch motions, rotor thrust, and generator temperature under realistic constraints.
I agree with the main points raised by Reviewer 1. It is not entirely clear what the novelty of this work is and which research gap it fills. The presented methodology is difficult to follow due to incoherent structuring, too much focus on irrelevant details and too little focus on the core controller and ROM description. The same applies to the discussion of results, which lack a coherent storyline and it is difficult to keep track of which cases are compared to each other and why. Therefore, I recommend major revisions to the manuscript.
General
- The selection of the NREL 5MW turbine on the OC3 spar platform as the use case scenario is questionable. Firstly, the NREL 5MW turbine is significantly smaller than the turbines currently being deployed in the offshore industry, which feature capacities of up to 15 MW. A more appropriate choice would be the DTU 10 MW, IEA 15 MW turbine, or a comparable design. Secondly, the spar platform is an outdated concept that is less favorable compared to TLP and semi-submersible platforms due to its low stiffness and susceptibility to high pitch motions. Consequently, the reported advantages of the MPC in reducing platform motions may be overstated.
Introduction
- Please clarify the changes that were made to the control algorithm compared to previous works (Pustina et al. 2022a) to highlight the novelty of this work. A tabular summary of the amendments and changes could be helpful.
- Elaborate on the motivation to use MPC that minimize platform motions. What are the benefits in terms structural health and reliability? What are the potential drawbacks, for example in terms of the power quality? Are there limitations in applying this controller in practice? Would a wind farm operator have the required knowledge on platform specifications to build such a ROM? Is LIDAR needed for this approach? Cite relevant publications.
- Clearly define the scope of this work. Highlight that the nature of this work is numerical rather than experimental and briefly describe the parameters of the numerical case study.
- Remove Tab 1.
Methodology
- Condense or remove unnecessary sections:
- Section 2: Explaining the operational regions and the standard torque controller is not necessary
- Section 3.1 and 3.2: Remove the derivation of platform and rotor dynamics. Briefly state the mathematical description of each ROM
- Section 3.4.1 to 3.4.3: Remove entirely and refer to relevant publications, unless this a novel method that was developed
- Eq 12 and 13 are duplicates to Eq 16
- Improve structure
- Move Eq 16 to the front and begin to build up from there. Define the objective function, define the state and control variables, define the model and define the constraints.
- Clarification
- Please be more specific how the constraint parameters (Tab. 3) were selected, in particular the limits on platform surge and pitch motion. Are these specific to the use case of the NREL 5 MW turbine? How can they be modified for other applications?
- What are the measurement inputs for the controller? Is LIDAR used? What is the wind speed prediction horizon?
- Fig 1 contains no information. It would be helpful to add more details to better understand the difference between each ROM. For example, the input/output variables, number of DOFs and mathematical model description.
- It is not clear how the generator thermal model relates to the ROMs.
- Define the reference NREL controller. Is this ROSCO?
Discussion of results
- Sec 4.1 should be part of the methodology.
- Sec 4.2: The validation of the ROMs by RMSE is insufficient and does not show if the pitch and surge dynamics are captured accurately. An eigenmode analysis or dynamic response analysis in the time domain would greatly strengthen the model validation.
- Sec 4.3: Condense this section and move to the methodology.
- “The constraint violation relaxation strategy (see section 3.4.3) is not necessary and thus not adopted in this work”. Then why do you dedicate an entire section to this?
- Sec 4.4 and 4.5: It would be helpful to describe each case study in the beginning including onshore, offshore, single-objective and multi-objective MPC and why they are compared to each other. Think about if Sec 4.4 is really necessary, as this does not provide much value and only adds to the confusion. Focus on the novelty of your work, which from my understanding lies in the multi-objective MPC and the reduction of platform motions.
- “At about the rated wind speed, the onshore and offshore ENMPCs have a blade pitch standard deviation similar to the reference one,…” Which LC is at rated wind speed? Mark in the figure or mention in the text.
- “Note that, as in Pustina et al. (2022a), the thrust constraint (700kN) is also slightly violated by the offshore ENMPC because it lacks high-frequency aerodynamic effects.” The thrust constraint is violated in 6 out of the 13 LCs by a significant margin. What are the implications of this violation and how can this be improved? What is meant by “high-frequency aerodynamic effects”. This should be clear to the reader without having to read Pustina et al. (2022a)
- “The increase in nacelle velocity observed in the single-objective ENMPC for LC7 and LC8 is obviously absent.” This is not so obvious to me.
- Fig 12 (left): Provide more context. The power increase for LC1 is high, but the probability of occurrence and the actual power production is very low. Since the impact on the LCOE is more relevant, it would be more informative to provide the relative power increase over the turbine life cycle.
- Sec 4.6: It is not very clear how each case is calculated. Specify how the EKF considers the platform motions and which measurement signals are used.
Conclusions
- These are not concluding remarks, but rather a repetition of previous statements. It would be of higher value to the reader to state the implications and the context of your findings. Is it a worthwhile trade-off to reduce platform motions, while decreasing the power quality and increasing thrust loads? Is it technologically feasible for wind farm operators to implement this type of MPC? Are the findings representative given the limited scope of this numerical study focused on spar platforms.
Minor comments
- Enclose references with brackets in the text
- Fore-aft and side-side nacelle velocity are more precise terms and more commonly used in this field compared to longitudinal and lateral
Citation: https://doi.org/10.5194/wes-2024-144-RC2 -
AC2: 'Reply on RC2', Jacopo Serafini, 06 Jan 2025
reply
General
The selection of the NREL 5MW turbine on the OC3 spar platform as the use case scenario is questionable. Firstly, the NREL 5MW turbine is significantly smaller than the turbines currently being deployed in the offshore industry, which feature capacities of up to 15 MW. A more appropriate choice would be the DTU 10 MW, IEA 15 MW turbine, or a comparable design. Secondly, the spar platform is an outdated concept that is less favorable compared to TLP and semi-submersible platforms due to its low stiffness and susceptibility to high pitch motions. Consequently, the reported advantages of the MPC in reducing platform motions may be overstated.
As we answered to REV1, the choice of using the NREL 5MW turbine is determined by 3 facts: the prior knowledge that we have on this turbine (including a validated ROM), the wide use of it in the literature (so many researchers may be more confident in using it to compare other control strategy), and the fact that although smaller in size than current WT, all the problems related to optimization of power production and platform motion remains. Indeed, although bigger wind turbines tend to rotate less, the motion is amplified by the size in terms of aerodynamic and inertial loads.
Introduction
Please clarify the changes that were made to the control algorithm compared to previous works (Pustina et al. 2022a) to highlight the novelty of this work. A tabular summary of the amendments and changes could be helpful.
This is already explained in sec. 1.1. If necessary, we can further expand but we think is already clear.
Elaborate on the motivation to use MPC that minimize platform motions. What are the benefits in terms structural health and reliability? What are the potential drawbacks, for example in terms of the power quality? Are there limitations in applying this controller in practice? Would a wind farm operator have the required knowledge on platform specifications to build such a ROM?
We think we already explained the benefits in terms of structural health and reliability. Nevertheless, we will address these topics and also the other mentioned by the reviewer to better clarify the advantages and disadvantages of the proposed solution.Is LIDAR needed for this approach? Cite relevant publications.
This is present in the introduction in lines 90-96. We can expand the discussion, maybe in the control section, as requested also by REV1.
Clearly define the scope of this work. Highlight that the nature of this work is numerical rather than experimental and briefly describe the parameters of the numerical case study.
Remove Tab 1.
Ok
Methodology
Condense or remove unnecessary sections:
Section 2: Explaining the operational regions and the standard torque controller is not necessary
Ok we can shorten the description
Section 3.1 and 3.2: Remove the derivation of platform and rotor dynamics. Briefly state the mathematical description of each ROM
Also here, we can shorten the description and refer to previous works.Section 3.4.1 to 3.4.3: Remove entirely and refer to relevant publications, unless this a novel method that was developed
We believe this section provides a practical guide to how the numerical solution can be made more robust especially when inaccuracies is present on state estimation. Nevertheless, we understand that it may distract the reader and thus we decided to move it to an Appendix.
Eq 12 and 13 are duplicates to Eq 16
Improve structure
Move Eq 16 to the front and begin to build up from there. Define the objective function, define the state and control variables, define the model and define the constraints.
OkClarification
Please be more specific how the constraint parameters (Tab. 3) were selected, in particular the limits on platform surge and pitch motion. Are these specific to the use case of the NREL 5 MW turbine? How can they be modified for other applications?
They are partly selected from NREL 5MW data, partly by engineering considerations and partly from analysis of the turbine with the standard controller.
What are the measurement inputs for the controller? Is LIDAR used? What is the wind speed rediction horizon?
We imagine 2 extreme cases: 1) Knowledge of the wind (and waves) for the entire controller horizon (60s). 2) Knowledge of the wind (and waves) only at the starting point of each controller window (i.e. the current time instant in real applications). The results are compared in sec 4.6.
Fig 1 contains no information. It would be helpful to add more details to better understand the difference between each ROM. For example, the input/output variables, number of DOFs and mathematical model description.
Ok
It is not clear how the generator thermal model relates to the ROMs.
It is forced by generator power and the temperature sensor output is given to the controller since the rated condition is expressed in terms of temperature instead of power output.
Define the reference NREL controller. Is this ROSCO?
No, it is the standard controller KW2-PID controller.
Discussion of results
Sec 4.1 should be part of the methodology.
Ok
Sec 4.2: The validation of the ROMs by RMSE is insufficient and does not show if the pitch and surge dynamics are captured accurately. An eigenmode analysis or dynamic response analysis in the time domain would greatly strengthen the model validation.
Ok, we can add different analyses to better represent the quality of the simulation
Sec 4.3: Condense this section and move to the methodology.
Ok
“The constraint violation relaxation strategy (see section 3.4.3) is not necessary and thus not adopted in this work”. Then why do you dedicate an entire section to this?
Here we decided not to use it only because we preferred to have faster simulations. In actual implementation, it is a required feature to make the optimal controller converge in the presence of noise and other disturbances. Here, the robustness was not a critical issue, since in case of convergence issues we can restart the simulation and introduce the violation relaxation strategy.Sec 4.4 and 4.5: It would be helpful to describe each case study in the beginning including onshore, offshore, single-objective and multi-objective MPC and why they are compared to each other.
Ok
Think about if Sec 4.4 is really necessary, as this does not provide much value and only adds to the confusion. Focus on the novelty of your work, which from my understanding lies in the multi-objective MPC and the reduction of platform motions.
Our objective here was to report the fact that, for energy purposes alone, the onshore controller is still valid. In principle, one can expect to have a larger power increment
“At about the rated wind speed, the onshore and offshore ENMPCs have a blade pitch standard deviation similar to the reference one,…” Which LC is at rated wind speed? Mark in the figure or mention in the text.
Ok
“Note that, as in Pustina et al. (2022a), the thrust constraint (700kN) is also slightly violated by the offshore ENMPC because it lacks high-frequency aerodynamic effects.” The thrust constraint is violated in 6 out of the 13 LCs by a significant margin. What are the implications of this violation and how can this be improved? What is meant by “high-frequency aerodynamic effects”. This should be clear to the reader without having to read Pustina et al. (2022a)
As you can see, we put the limit way lower than the Reference case. This is because we can't assure the perfect correspondence between ROM and actual data (simulated or, worse, real). Then we considered a safety threshold. In this way, the ENMPC thrust is below the reference controller one when the 700 kN limit is violated.
“The increase in nacelle velocity observed in the single-objective ENMPC for LC7 and LC8 is obviously absent.” This is not so obvious to me.
ok, we will better explain it
Fig 12 (left): Provide more context. The power increase for LC1 is high, but the probability of occurrence and the actual power production is very low. Since the impact on the LCOE is more relevant, it would be more informative to provide the relative power increase over the turbine life cycle.
We agree we can add an AEP simulation
Sec 4.6: It is not very clear how each case is calculated. Specify how the EKF considers the platform motions and which measurement signals are used.
Thank you for your feedback. We have revised the paper to clarify the measurement signals considered in the controller and how each case is analyzed. In our study, we hypothesize that the following signals are perfectly measured: rotor speed, platform pitch and surge displacements, platform pitch rotational speed, surge velocity, and generator temperature. At each iteration of the Model Predictive Controller (MPC), these measurements are used to correct and update the system state. For the mean wake inflow state, which is not directly measurable, the MPC itself acts as an observer. Specifically, the state of the previous time window is used to initialize the Optimal Control Problem (OCP).
While we reference the challenges of using an Extended Kalman Filter (EKF) for floating offshore wind turbines (FOWTs), we did not explicitly implement an EKF in our analysis. Instead, the numerical results are based on two distinct cases:
1) Ideal Case:
- The hydrodynamic diffraction forces are assumed to be perfectly known for the entire prediction horizon (60 seconds).
- The mean disc wind speed is assumed to be perfectly measured for the entire prediction horizon (60 seconds).
In practice, this would require the adoption of a LIDAR and a Wave Radar, which would have a non-perfect prediction, in any case
2) Realistic Case:
- We assume no direct measurement of the hydrodynamic diffraction forces; the MPC is provided with zero values for these forces.
- An EKF is assumed to estimate the mean disc wind speed at the current time, with a random noise error of ±0.2 m/s. This estimate is considered constant over the entire 60-second prediction horizon.
In a realistic scenario that considers both LIDAR and wave radar measurements, with errors in the prediction of both wind speed and hydrodynamic diffraction forces, we would expect the controller performance to fall between the two cases analyzed. We hope this clarifies the methodology and assumptions in our analysis.
Conclusions
These are not concluding remarks, but rather a repetition of previous statements. It would be of higher value to the reader to state the implications and the context of your findings. Is it a worthwhile trade-off to reduce platform motions, while decreasing the power quality and increasing thrust loads? Is it technologically feasible for wind farm operators to implement this type of MPC? Are the findings representative given the limited scope of this numerical study focused on spar platforms.
We agree we will change this section according to the suggestions
Minor comments
Enclose references with brackets in the text
Fore-aft and side-side nacelle velocity are more precise terms and more commonly used in this field compared to longitudinal and lateraleplyOk
Citation: https://doi.org/10.5194/wes-2024-144-AC2
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