Damping analysis of Floating Offshore Wind Turbine (FOWT): a new control strategy reducing the platform vibrations

Capaldo, Matteo; Mella, Paul

doi:https://doi.org/10.5194/wes-2022-109

Preprints

https://doi.org/10.5194/wes-2022-109

Preprints

21 Dec 2022

| 21 Dec 2022

Status: a revised version of this preprint is currently under review for the journal WES.

Damping analysis of Floating Offshore Wind Turbine (FOWT): a new control strategy reducing the platform vibrations

Matteo Capaldo and Paul Mella

Abstract. In this paper, the coupled dynamics of the floating platform and the wind turbine rotor is analysed. In particular, the damping is explicitly derived from the coupled equations of rotor and floating platform. The analysis of the damping leads to the study of the instability phenomena obtaining the explicit conditions that lead to the Non Minimum Phase Zero (NMPZ). Two NMPZs are analysed, one related to the rotor dynamics and the other one to the platform pitch dynamics. The latter is a novelty and an explicit condition is introduced in this work for its verification. In the second part of the paper, from the analysis of the damping of the floating platform, a new strategy for the control of Floating Offshore Wind Turbines (FOWTs) is proposed. This strategy allows one to impose to the controller an explicit level of damping in the platform pitch motion without changing the period of platform pitching. Finally the new strategy is compared to the one without compensation by performing aero-hydro-servo-elastic numerical simulations of a reference FOWT. Generated power, movements, blade pitch and tower base fatigue are compared showing that the new control strategy can reduce fatigue in the structure without affecting the power production.

Received: 27 Nov 2022 – Discussion started: 21 Dec 2022

Matteo Capaldo and Paul Mella

Status: final response (author comments only)

RC1:
'Comment on wes-2022-109', Anonymous Referee #1, 17 Jan 2023

The paper addresses feedback control of Floating Wind Turbines (FWTs). It investigates the appearances of zeros on the right hand-side (NMPZ) in the transfer dynamics from blade pitch angle to rotor speed and from blade pitch angle to the platform pitch angle. It proposes an analytical model to tune controller gains, which control rotor speed but also platform pitch motion. Load results by OpenFAST of a 15MW FWT are shown, fatigue damage of blade bearings and tower-base is calculated.

The illustration of the effect of the NMPZs is very nice. The analytical control design model model is well explained but not new. The tuning procedure uses assumptions, which significantly simplifiy the level of coupling in FWT dynamics. The results are still significant, although they should be compared to another approach including a platform pitch damping (i.e. the existing procedure of ROSCO including platform pitch damping), not to a controller without platform pitch damping. It would be beneficial to check if the NMPZ is really compensated by the control approach. Robustness of the controller against instability is not quantified.

A few characteristic features are not sufficiently explained, like the calculation of the generator torque compensation. Without this feature, the proposed controller is very comparable to ROSCO.

Variables should be explained thoroughly and text and captions written in a way for easier readability (use text rather than symbols, only).

References to other work are acceptable. Still, there is more relevant literature on tuning controllers at every wind speed, which is above the rated wind speed. These should be included in the introduction.

Citation: https://doi.org/10.5194/wes-2022-109-RC1
- AC1: 'Reply on RC1', Matteo Capaldo, 10 Feb 2023
  
  Dear anonymous ref. #1,
  first of all, we would thank you for your remarks, comments and suggestions.
  please find in attachement the document with our answers.
  Best regards,
  Matteo Capaldo
  
  Citation: https://doi.org/10.5194/wes-2022-109-AC1
RC2:
'Comment on wes-2022-109', Anonymous Referee #2, 28 Jan 2023
This paper analyzes the appearance of nonminimum phase zeros in a linearized FOWT model, which are known to lead to closed-loop instability. Care is taken in acknowledging that the zeros of the platform-pitch-output transfer function may cross into the RHP for certain model parameter values, which is often overshadowed in existing literature by the NMPZs of the generator-speed-output transfer function. Additional control loops found in the literature are described: feedback of platform pitch velocity to either generator torque or blade pitch. The blade-pitch feedback control loop is given a method of tuning the decoupled platform pitch damping to be constant over operating points and implemented in simulation with the IEA-15MW reference wind turbine. Performance output signals are compared to a reference controller without nacelle feedback.
The paper does not answer if the phi NMPZs are particularly relevant to the control problem, not often found in literature because they do not lead to closed-loop instability under a SISO PI controller, the primary impact of the better-known NMPZs. While a discussion of stability and "negative damping" is offered with time-series simulations of the linearized dynamics, it is lacking in basic systems-theory rigor such as pole locations, root locus, stability margins, etc. that would drastically aid the impact of the analysis.
A few notes on specific sections of the manuscript follow. Line numbers refer to numbers in the left margin of the draft preprint.
1 Introduction:
lines 25-26, and again line 29: What is meant by "oscillating stability"? In particular, what is meant to be the difference between "oscillating stability" and "instability" as used in the text? Khalil's "Nonlinear Systems" is a good source for more precise definitions of nonlinear system stability.

line 40: "In ... (Lenfest et al., 2020), the platform pitch velocity is used to adjust the rated speed set-point to reduce platform motions. However, the platform pitch damping analysis is not investigated and the link with the compensation parameter is not given" is misrepresenting the cited work. The cited work uses a similar nacelle feedback approach as (Jonkman, 2008) and (Abbas et al., 2022), and as that used in the present work. Additionally, the cited work does in fact investigate the (coupled) platform pitch damping and parameter tuning (Lenfest et al., 2020, Figure 6).

lines 52-54: See comments on 'References' below. The generator torque parallel compensation feedback loop for removing NMPZs was introduced before (Stockhouse et al., 2022), at least as early as (Fischer, 2013).

2 Floating Offshore Wind Turbine and its controller:
line 120: The way $\theta = \int \omega dt$ is defined as the integral of the speed error on line 113, the integral control equation $k_I (\theta - t \Omega_r)$ looks incorrect. In addition, this simplification would only apply if $\Omega_r$ is constant, which is not explicitly mentioned (and contradicts earlier statements about the approach of (Lackner, 2009)).

lines 165-175: Could add some citations to aid this interpretation of NMPZs.

line 180: It would be nice to see what effect the model parameters have on the poles as well as the zeros.

Table 1: Where do these parameters come from? Are they based on a real turbine design? Discussion of these zeros would be more compelling if a real turbine design was shown to satisfy Ineq. (25).

Figure 2: The flipped sign of the steady-state response is hard to explain using only the zeros.

While the plotted time series is somewhat helpful, it would be nice to see a pole-zero plot for both of these cases to see the full differences in the resulting linearized model.

Figure 2: What are the units on the multiple y-axes? And what is the size of the $\beta$ step input?

Eq. (28): Should cite (Fischer, 2013)

lines 207-225: There is no mention of $D_t$ although it appears in Eq. (28). What is the value used in the simulations of Fig. 3?

line 215: Why doesn't this comp control equation match Eq. (13)?

line 221: This statement could use clarification.

Table 2: Same comment as Table 1.

Sec. 2.3.3: The analysis in this section doesn't fully explain the observed result. The presence of NMPZs alone would not cause the system to become unstable. Stability or instability is the result of the open-loop poles (which are not shown, nor discussed). This further suggests that realistic parameter values for the partial derivatives of T_a and F_a should be chosen to match a real wind turbine design instead of "hypothetical" values.

line 232: "The NMPZ \beta -> \phi doesn't depend on above defined parameters" this is inconsistent with Table 1.

line 233: "condition eq. 25 forecasts which operating points it affects" but there is no discussion of operating points. Overall this section could use more explanation of how the gradient parameters vary over operating points and relation to gain scheduling. Gain scheduling is never mentioned in the manuscript.

line 238: Negative damping is the result of a high-gain controller, not a property of the open-loop FOWT system, so the instability observed here is not the same as "negative damping" commonly referred to in the literature.

3 Numerical tests with time domain simulations:
Since generator torque parallel compensation is discussed above, is it implemented in simulation?

Now that the control approach is being applied to a real wind turbine design, does the model of the IEA15 have the NMPZs discussed above?

line 352: This is where there should be some discussion of gain scheduling.

line 354: A natural frequency of 0.01 rad/s for the PI controller seems very low, less than 1/10th the platform natural frequency. Did you test with higher values, and at different wind speed operating points?

Sec. 3.3: What is the value of the left-hand side of the third inequality in (51)? I'm surprised that zeta=0.1 is larger than the natural dynamics.

Fig. 6: What is the explanation for the zeta=0.25 case having a different mean than the reference?

Figs. 8-9: It's hard to interpret this result. What is the benefit to structural loading performance with these different density profiles, versus computing DELs and extreme loads?

Sec. 3.4: There is some inconsistency in which wind speed is used to draw conclusions. Line 390 and Table 6 say you tested mean wind speeds ranging from 12 m/s to 24 m/s. Then Fig. 12 shows a case at 8 m/s. Then Table 7 shows results at 10 m/s. Then Fig. 13 shows 4 m/s to 24 m/s.

Fig. 12: Since you show below-rated usage of the platform damper feedback, how was the blade pitch saturation handled?

Fig. 13: It would be nice to see maximum rotor speed and gen pwr instead of just the average (at all wind speeds, not just at 10 m/s). The variation in average values near cut-out may be due to the very low natural frequency of the PI controller. Also, why does one case have an avg power of 0 at 4 m/s?

References:
Abbas et al., was published in 2022

Stockhouse et al., was published in proc. American Control Conference, 2022: https://doi.org/10.23919/ACC53348.2022.9867498

One of the early works studying NMPZs in the FOWT system with generator torque compensation feedback should be cited: Fischer, B., 2013, https://doi.org/10.1049/iet-rpg.2012.0263

The paper by Fischer also features a derivation of Eq. (28) used in the present work.

Another citation to investigate is Yu, W. et al., 2018, "Evaluation of control methods for floating offshore wind turbines", which demonstrates a controller with combined blade pitch and generator torque parallel compensation.

Technical corrections:
Overall, the work is readable, but it could be improved by additional review of the English used.

line 27: "variate" is not a verb and should be replaced by "vary". Also line 124.

line 37: "this solution do not"

line 107: Equation cross-references are usually in parentheses to match label definitions, i.e. "Equations (1) and (2)", and similar.

lines 117-120: Here and occasionally above, there is some inconsistency in the use of capital versus lowercase variable names to represent a "true" value versus a perturbation from equilibrium.

line 129: "It is analysed the performance of the control strategy" is grammatically incorrect.

line 133: "linear form for of the global equations"

line 142: Eq. (13), fix subscript $k_\beta$

line 177, "Gain equation" should be "The gain equation", and several other occurrences of missing grammatical articles.

line 185: Acronym "WTG" has not been defined in the text.

Table 1: Are these units correct? I would expect the units for $dTa/dB$ and $dFa/dB$ to include $rad^{-1}$.

Eq. (51): Since this equation has three parts that are referred to separately in the text, each line of the equation should have a separate identifier, such as (a), (b), (c).
Citation: https://doi.org/10.5194/wes-2022-109-RC2
- AC2: 'Reply on RC2', Matteo Capaldo, 10 Feb 2023
  
  Dear anonymous ref. #2,
  first of all we would thank you for your remarks, suggestions and comments to the article.
  Please find in attachement our answers.
  Best regards,
  Matteo Capaldo
  
  Citation: https://doi.org/10.5194/wes-2022-109-AC2
RC3:
'Comment on wes-2022-109', Anonymous Referee #3, 31 Jan 2023
Overall:
This is a detailed analytical account of floating wind turbine dynamics and a controller designed to provide a fixed amount of damping to the platform motion. Some analytical derivations are novel, but most are already presented in the literature. The controller is compared against a scheme known to not work well for floating systems, rather than a standard floating feedback controller, so its benefits are unclear. The article could be used to find, or eliminate, FOWT designs with controllability issues. This article could be improved by tailoring the presentation to a wind energy audience.

Major Comments:
The introduction is clear and focused. However, in L46, the authors give the impression that they will be varying the rated generator speed of the controller based on the platform pitch velocity. The controller described in Section 3 only changes the blade pitch angle, similar to other floating feedback controllers. Maybe the authors are talking about "this paper," and not the paper that I am currently reviewing. Either way, the article could be revised throughout for clarity, e.g., be clear about what "this" is. The introduction does not mention ROSCO or other platform/generator speed decoupling methods, though they appear later in the manuscript.

The choice and use of k_tau_g are not clear and based on reading this paper, it seems like that is one of the main contributions of the controller, along with switching the sign of k_\beta

The analysis and reasoning in Section 2.3.1 are not clear. Please elaborate on "Is rather influenced by" as this is not typical verbiage for a wind energy audience.

Overall, the references to sections, figures, and tables in this paper are broken. As there are a lot of equations and references to them, it hinders the readability of the paper.

In the NMPZ analysis, the tables and figures should probably be combined, since each table corresponds to a plot. Additionally, it's not clear where these partial derivatives come from. Are they the IEA-15MW VolturnUS turbine at a specific wind speed? It would be very helpful to put the sensitivities of that turbine (at a specific wind speed, probably 12 m/s where the NMPZ issues are greatest) for reference. Then, the readers would have a better understanding of the conditions that cause the NMPZs you describe.

A fixed k_\beta is a better reference than k_\beta = 0. Please include this case in the simulation study, as tuned by the ROSCO toolbox for reference. Most readers will want to compare this controller with one that has a simple floating feedback controller.

Please revise and edit this manuscript throughout for grammar and for in-text references. E.g.,

L254: It is complicated to explicit[ly determine] the damping

L374: [Section] 2.5. Copernicus journals typically use Fig. [X] and eq. (Y) for references.

Is it true that the signs are flipped from the standard ROSCO floating feedback controller? Please make this very clear in the article.

In the results section, please use specific language when comparing the performance of controllers. E.g., The X measure is 15% greater in A than in B. The term "gain" can have multiple meanings and is not explicitly clear.

It would be great to see a time series (600 seconds) of the control signals, generator speed, and platform pitch for the proposed controller and both references in a figure.

Minor Comments:
What is the characteristic time? The wave period? Please use wind energy verbiage for this journal. Why is the focus of this analysis outside of the likely wave periods? Please base the analysis on realistic wave conditions (6-10 seconds).

Figure 10 shows very large rotor speed excursions. Why is that?

L370: what is diagram 5?

Figures 10 and 11 could be combined. Please include case information in the caption. Other figures, like 6 and 7, could be combined, as well. In general, it's helpful to have the figures near where they are referenced in the manuscript.

Is Figure 8 necessary? The reader can see these results in Figs. 6 and 7, and the load "densities" are not typical wind energy measures. You could easily include the amplitude or standard deviations in Figs. 6 and 7.

What is the quality factor Q? Is it necessary for this audience? There are already a lot of equations and terms. Please consider what other terms can be eliminated to improve readability.
Citation: https://doi.org/10.5194/wes-2022-109-RC3
- AC3: 'Reply on RC3', Matteo Capaldo, 10 Feb 2023
  
  Dear anonymous ref. #3,
  we would like to thank you for your remarks, comments and suggestions that will improve the article.
  Please find in attachement our answers.
  Best Regards,
  Matteo Capaldo
  
  Citation: https://doi.org/10.5194/wes-2022-109-AC3

Matteo Capaldo and Paul Mella

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Short summary

The controller impact the movements, loads and yield of wind turbines. Standard controllers are not adapted for floating and they can lead to under-performances and over-loads. New control strategies, considering the coupling between the floating dynamics and the rotor dynamics, are necessary to reduce platform movements and improving performances. This work proposes a new control strategy adapted to floating wind, showing a reduction in loads without affecting the power production.


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