Real-time estimation of optimal tip-speed ratio for controlling wind turbines with degraded blades

This paper considers the optimization of wind turbine torque controllers that track an optimal TSR value for below-rated load operation. Due to wear/tear/fouling the properties of the turbine rotor change over time, possibly leading to a shifted location of the optimal TSR, leading to suboptimal operation when this parameter remains nominal and uncalibrated. A novel LP-PIESC scheme is proposed to calibrate the TSR setpoint value.

The motivation of the paper is relevant, although numerous other works have been done in this field, which should be included and acknowledged in the introduction. Furthermore, I think that the major contribution of this paper is the LP-PIESC scheme, which supposedly can provide faster (instantaneous?) convergence. First, the new ESC scheme is not well described, leaving many questions about its working principles. Second, the tuning procedure of the scheme is not explained (only Appendix A elaborates on the excitation frequency). Third, the instantaneous convergence results are questionable: there is no excitation before the convergence, so how is the gradient obtained? Also, please explain how it is possible that there is instantaneous convergence; to me, this seems impossible without prior knowledge of the optimal setpoint value. Overall, I think this work needs significant improvements before it can be considered for publication in WES.

Abstract

- Announce in the abstract what type of wind turbine controller you are assuming.

- State the significance of using LP-PIESC as compared to regular ESC, as this is the main contribution of the paper.

Introduction:

- You write: "The LP-PIESC has been shown to be a faster variant of the traditional perturbation-based ESC (Kumar and Rotea, 2022)." --> This might be interpreted that you do not need perturbation using LP-PIESC. You would still need a perturbation to estimate the gradient, right?

- A more elaborate literature study and acknowledgment of the works in the field of setpoint/model/controller calibration should be included.

Background:

- Is it a valid assumption to have a precise measurement of the rotor effective wind speed?

- Fig 1: In the figure you indicate that \hat{v} comes from a wind speed estimator, while in the text you say something different.

- Fig 3: There seem to be few data points for Cd-curves. Can you increase the resolution?

Section 2

- You state that \theta_1 is proportional to the gradient. It could be better explained that in (2), you can observe that this quantity is subject to a proportional action with kp and an integral action with saturation capabilities.

- What estimation problem are the parameters in \theta a result of? What do they represent, and in which context?

- The paper does not describe the rationale behind the gradient estimation scheme. As this is the major contribution of the paper, you should have a proper description of its working principles.

Section 3

- Consider using a more state-of-the-art reference turbine model, like the IEA 15 MW turbine.

- Fig 5: The complete algorithm of finding \theta is given in this figure in the large block, without any explanation. It is too complex to understand from a list of relations without explanation and justification!

- All Figures in the paper are given without a proper elaborate caption that allows for interpretation of the figure. Improve on this.

- Table 2: How did you arrive at these ESC parameters? Through trial and error or a systematic tuning procedure?

--- In Appendix A, you provide justification for the dither frequency but not for the other values.

- You write: "The LP-PIESC converges to the new optimal tip-speed ratio almost instantaneously for all the cases." --> How is this possible? As far as I understand, you only estimate the gradient in the form of theta_1. Instantaneous convergence is only possible if you know how far you are from the optimum value, e.g., tuning the proportional gain to precisely the correct value. But this is just guessing, and maybe I am missing something. However, the paper does not clarify this aspect.

- Figure 8: How can the gradient be estimated without perturbation before 500 s? How is it possible to arrive at the optimal value instantaneously?

- It is unclear which variable you excite by dithering, is this lambda_sp?

This paper presents an extremum seeking controller for optimizing a wind turbine controller's tip speed ratio set point.  It's nice that the control scheme fits with an existing wind turbine architecture.  However, the benefit of using the log of the power is unclear, and the algorithm seems to converge to the optimal solution too quickly without adequate explanation.

Major questions:

• How does the algorithm converge to the optimal solution before a single dither signal cycle can compute the gradient?  I think that justification, in wind energy terms, should be provided in this article.
• How exactly is the gradient estimated over time?  What signals from the turbine are needed?  The variables in Fig. 5 are not defined in the text.  Can you show the gradient estimate over time?
• It appears that the TSR set point reaches the "optimal" before the power coefficient or actual tip speed ratio changes in any measurable way.  How is this possible?  The bandwidth of the torque controller limits the actual TSR; how can this algorithm converge faster than the torque controller?
• From cited work within this article, the authors claim that the log of the power allows the Cp to be maximized directly without requiring the wind speed.  \frac{\del J}{\del u} = 1/Cp \frac{\del Cp}{\del u}.  Doesn't the Cp in the denominator depend on the wind speed?
• In Fig. 8, there is a step change as soon as the algorithm is enabled, and then it seems to converge slowly to another point.  How do you account for this behavior?  Was an initial guess provided to the algorithm?

Without answers to these questions, the results cannot be adequately reviewed.  While some of my questions may have already been addressed by previous articles, more information in wind energy terms is required for this article's audience.