# Analysis of the aerodynamic damping in the modal parameter estimation of wind turbines

Javier Ibarrola Chamizo<sup>1,2</sup>, Iñigo Vilella<sup>3</sup>, Gorka Gainza<sup>3</sup>, Miroslav Zivanovic<sup>1,2</sup>, Aitor Plaza<sup>1</sup>, Xabier Iriarte<sup>1,2</sup> and Alfonso Carlosena<sup>1,2</sup>

## ABSTRACT

In this paper we propose a procedure to estimate the modal parameters of a Wind Turbine working at rated power, but for different wind speeds. The effects of harmonic excitations are first removed by a novel method already proposed by the authors and then Randomdec signatures are calculated on signal frames sharing similar conditions in terms of mean value and deviation of wind. In this way we can track the influence of aeroelastic effects to the estimation of damping. The analysis has been tested on the well known NREL model of a 5MW Wind Turbine.

Keywords: Conference, Operational, Modal, Analysis

## 1. INTRODUCTION

As the number of installed wind parks grows, and the oldest ones are approaching their predicted life-time, it is becoming more and more necessary to assess their true operation conditions in order have precise information of their accumulated fatigue and therefore their remaining life-time prediction. Structural Health Monitoring (SHM) techniques, which are already applied to other civil structures, are also being introduced to Wind Turbines to this end. It has to be recognized, however, that SHM has not been widely accepted by operators and owners of structures, or adopted by companies, since its implementation requires huge investments, whose economic revenues are not yet clear [1]. The need to deploy a network of sensors, which have to be operated and maintained, and also the need to analyse the huge amount of data generated by expert engineers are discouraging factors. Above all, the relation between the measured variables and estimated parameters (typically modal parameters), and the health condition

<footnote n="1"><sup>1</sup> Public University of Navarre (UPNA), 31006 Pamplona, Spain.
{javier.ibarrola, miro, aitor.plaza, xabier.iriarte, alfonso.carlosena}@unavarra.es</footnote>

<footnote n="2"><sup>2</sup> Institute of Smart Cities (ISC), 31006 Pamplona, Spain.</footnote>

<footnote n="3"><sup>3</sup> IED Electronics, Pol. Ind Plazaola, 31195 Aizoaín, Spain. {ggainza, ivilella}@iedcompany.com</footnote>
of the structure is not always clear and need to be deeply investigated. Given the cost of a civil struc-
ture, experimental tests are not easy, and thus it is rare the situation where the effect of an intentionally
introduced damage can be observed in the estimated parameters [2, 3]. Moreover, and common to most
civil structures, the application of conventional modal analysis is limited by the impossibility to excite
the structure in a controlled way, leaving the solution in the hands Operational Modal Analysis (OMA).
The application of SHM/OMA techniques to WT is particularly difficult for a number of reasons.

* A WT is a very complex structure with very diverse structural elements, i.e. foundations, tower, nacelle and blades, whose individual behaviour is difficult to isolate and characterize.

* A WT is, obviously, a rotating structure, and under operation conditions periodic excitations as-
sociated with such rotation make the application of OMA techniques more involved, when not
impossible.

* Moreover, operating environmental conditions vary widely depending mainly on wind (and wave in off-shore WT), which introduces aeroelastic effects resulting in a change of the effective modal parameters measured. Even in situations of apparently stable conditions, e.g., nominal regime, the WT is subjected to control strategies which adjust the blade pitch angle, and somehow modify the structure.

The modal parameter which is more widely accepted as an indicator of the condition of a structure, like a WT, is damping [4]. To the variability in its estimation introduced by the factors described above, we have to add the uncertainty introduced by the estimation (OMA) method used [5]. Moreover, and once a method has been chosen, a number of decisions have to be taken in terms of the number of sensors used, length of registers, model order, etc. In [6] it is shown for instance how even reducing the variability of the environmental conditions of a Wind Tower to the idle state, and selecting a particular identification method (Multi-reference Ibrahim Time Domain), there is still ample room for deviations in the estimation of modal dampings, and to a lesser extent, frequencies. It is not surprising that most published works limit the analysis to idle or standstill conditions [7].

In another paper by the same authors [8] the variability of the environmental (wind and waves) and op-
erational conditions of the same Off-Shore WT introduced into the analysis, trying to extrapolate from
such analysis ideal modal parameters as if they were obtained under zero wind and wave excitation.
Both interesting papers analyse data from a campaign on a single Wind Turbine, which has been pro-
fusely sensorized. Data from the sensors have been processed off-line, incorporating other environmental
parameters obtained from other sources. The research projects described in his kind of papers are fun-
damental to gain insight into the problem at hand, and to develop a solid theoretical ground. However,
we think that in order to make SHM techniques truly practical and accepted by the industry, it is manda-
tory to drastically simplify the measurement systems, and the data processing. Actually, the wisdom of
park operators is to get usable and practical information of the WT condition, from the already installed
monitoring systems (e.g. SCADA), which were not initially intended for SHM [9].

This is the approach we follow, as for instance in [10], where we estimated the modal parameters for
four modes (1FA, 1SS, 2 FA, 2 SS) for a set of 7 WT of a wind park. The method for the estimation is
intended to be computationally efficient, with the objective to be implemented on a low-cost sensor. In
the case of the paper, signals are obtained from an accelerometer initially intended to detect failures in
the main rotor bearing. In spite of the limitations of both the raw data, and processing capabilities, we
manage to show differences between towers, which can be associated to differences to their foundation.
Data used corresponded to the nominal regime of rated power, though wind speed differences were
noticeable between 10 and 20 m/s. The processing method incorporated an algorithm to remove the
influence of harmonics, mainly 1P and 3P. In this paper we make use of similar techniques but on a
different dimension, analysing how modal parameters change depending on the wind speed, but with the
WT operating at nominal regime. The results presented here correspond to synthetic signals generated
with a NREL model. The model is simulated for 23 different 1-hour simulations, setting category C wind series and targeting the wind speeds from 3 to 25 m/s in 1 m/s steps. The resulting simulation data have been used since it is the only way we can compare the estimations with design values. We have also results from data from a real turbine, but there is no way to assess how good they are.

In Section 2 we recall the method we use to isolate modes from harmonics in a WT under operation conditions, and then estimate both modal frequencies and damping. Also, the RandomDec Technique (RDT) is briefly revisited as it is pertinent to this paper. In Section 3 we propose a procedure to classify the acceleration signals under different wind conditions, always under the rated power regime of the WT. Since we are using synthetic signals, we also explain how the different wind conditions are generated. Sections 4 and 5 address the results and conclusions, respectively.

## 2. COMMON APPLICATION OF THE RANDOM DECREMENT TECHNIQUE (RDT)

In [11] we proposed a method to estimate modal parameters, amenable to operate in real time, and then potentially implementable on the sensor (edge computing). The method is based on the use of the so called RandomDec Technique (RDT), as a computationally efficient method to calculate autocorrelation functions. Since the method only works ideally on Single Degree of Freedom Systems (SDOF), the acceleration measured in a wind turbine must be decomposed to isolate each one of the modes (and also eliminate the influence of interfering harmonics). To this end, we extended in the paper mentioned above [11] the method described originally in [12] to extract the main modes, and at the same time remove the influence of harmonics produced by rotation. This was obtained by simultaneously modelling modes and harmonics. We will not dig here into the details of the method, and on limit ourselves to describe the basics of the RandomDEC method necessary to understand the remaining of the paper. Note that the results provided by the RDT strongly depend on the decisions taken on its selectable parameters (trigger level, number of averages,) [13].

The RandomDec is an algorithm that can be used as a prior step to estimate the natural frequency and damping of a SDOF system from its output. As the harmonics and modes extraction algorithm will be applied to the output of a MDOF system, the individual time-varying amplitudes of the individual modes will be available and the RDT will be applied only to the SDOF signals, which is a necessary condition for the RDT to work. Let us now introduce the most basic steps of this algorithm.

The RDT monitors a signal to detect every single value that is greater than a certain threshold (i.e. trigger condition). When such a value is obtained, this point and the previous and following $N$ data points are saved in a vector of length $2N + 1$ which in this paper will be called *frame*. The signal, threshold and data frame are depicted in Fig. 1.

By doing so for every single data point over the threshold, the mean of all the frames is calculated. The outcome of this averaging is demonstrated to converge to the autocorrelation function and therefore the so-called RD signature resembles the free decay of a second order system when forced to initial conditions equal to the imposed trigger level. As can be seen in Fig. 2, the output is symmetric, as the algorithm takes the values before and after the trigger condition. Mirroring the left-hand part and averaging with the right-hand part, it is straightforward to identify the frequency and damping of the system by classical methods such as the Ibrahim Time Domain method (ITD) [14].

The *Harmonic and Mode Extraction* algorithm has already been used by the authors, together with the *Random Decrement Technique*, for the estimation of the natural frequencies and dampings of wind turbines in operation [10]. However, a great amount of dispersion is present in the damping calculation. The reasons for this have been outlined in the introduction, but the most important in this case can be attributed to aeroelastic effects, which result in additional aerodynamic damping. Actually, the analysis carried out in [10] focused on the rated power regime of the WT where most environmental conditions are controlled (i.e rotation speed) whereas wind speed varies widely (10-20 m/s). Therefore, the most straightforward manner of dealing with this issue is to discriminate the signal frames by wind speed
<figure><img src="image_1.png" /><figcaption>**Figure 1:** Example of the signal frame selection for a point over the threshold</figcaption></figure>

<figure><img src="image_2.png" /><figcaption>**Figure 2:** Example of the output signature of the RDT algorithm</figcaption></figure>

to obtain estimates of different damping values for different wind speeds. In fact, the most important objective of this paper is to determine a means to modify the standard RDT algorithm in order to select the signal frames that are used to calculate the damping coefficient of different modes and for different wind speeds.

### 3. DAMPING CALCULATION WITH DISCRIMINATION BY WIND SPEED

Let us classify the different steps of the algorithm that will have to be modified in order to calculate different frequency and damping values for every wind speed.

**Data availability:** The first step is to have data in wind speed ranges that cover the desired range of analysis. Acceleration (or other measurement) and wind speed must be available synchronously.

**Amplitude calculation for the individual modes:** Each signal (with its multiple channels if applicable) is processed using the harmonic and mode extraction algorithm including all vibration modes of interest. In addition, the different harmonics present in the signal must be taken into consideration. Thus, the instantaneous amplitude of each mode is obtained, and as a residual, the amplitude of the harmonics.

From this point on, it will be necessary to take into account some factors that will influence the way in which we will discriminate the signals based on wind speed.

**Wind speeds gathered in bins:** The first consideration to be made is that it will not be possible to obtain
continuous functions of natural frequency and damping in terms of the wind speed. On the contrary, our objective will be to determine values of damping (and frequency) for finite intervals of wind speed which will denote as *bins*. For example, we aim to calculate a different damping value for each of the intervals 3-5 m/s, 5-7 m/s and so on.

**Width of the wind speed bins:** It is a known fact that, for wind conditions with a given turbulence category, the variance of the observed wind speed grows the larger its mean value is [15]. Thus, the intervals of wind values in which to group the signal will be designed with a greater amplitude the larger their value. In this article, the following wind speed bins used are: 3-5, 5-7, 7-10, 10-13, 13-17, 17-21 and 21-25 m/s.

**RDT threshold for the mean wind speeds:** Likewise, the amplitude of the measured accelerations will tend to be higher the higher the incident wind speed. Thus, for each wind speed, a different acceleration threshold will be selected for the RDT algorithm. In order to determine these threshold values, very long signals have been taken whose mean wind speeds range from 3 to 25 m/s at intervals of 1 m/s. Moreover, the standard deviation of the acceleration signals has been calculated for each case, choosing these values as the thresholds for the wind speed.

**Criterion to assign an acceleration data frame to a specific wind speed bin:** Each time the acceleration signal exceeds a threshold value, $2N + 1$ samples will be obtained and must be weighted with those acquired in previous instants. However, since we want to discriminate the signals by wind speed, we must make sure that the signal frame will have the appropriate properties to be considered as belonging to a given bin. Thus the next criteria will be adopted in order to assign a data frame to a specific wind speed bin:

* The average wind speed for the data frame must belong to the wind speed bin.

* The standard deviation of the wind speed must be less than 1/4 times the bin width. In this way, assuming that the wind speed is normally distributed, it can be guaranteed that 95% of the samples are been acquired for a wind speed values belonging to the bin.

If the data frame meets these characteristics, then it becomes part of the data from which the signature for that bin of wind speeds is calculated. If it does not, the acquired data frame is discarded.

**Data samples number N for different modes:** When setting the number of samples *N* to be used to obtain the frames of the RDT algorithm, it will be necessary to take into account, approximately, the expected values of the frequency and damping ratio to be measured. Thus we will have to take a value of *N* that meets the following criteria:

* The value of *N* should be large enough to have several signal cycles.

* The value of *N* must have a value such that in the frame during, the decay of the signal is clearly observed but the amplitude does not completely drop to zero.

Therefore, it will be advisable to perform a preliminary analysis of frequencies and damping ratios (without wind speed dependence) in order to estimate, approximately, which values of *N* will be optimal for estimating the frequency and damping of each mode, for each wind speed.

The algorithm to perform a natural frequency and damping calculation for different values of the wind speed can be written in pseudo-code as shown in Algorithm 1.
<figure><img src="image_3.png" /><figcaption>**Algorithm 1:** Pseudo-code to calculate frequencies and damping ratios of multiple natural modes for different wind speed binned values.</figcaption></figure>

## 4. RESULTS

The presented algorithm has been applied to synthetic data (without any additional noise) in order to compare the obtained results to the ground truth. The 5-MW wind turbine model proposed in [16] has been used together with the OpenFAST software. Using category C wind series, 23 different 1 hour simulations have been performed, targeting the wind speeds from 3 to 25 m/s, every 1 m/s. The measured quantities have been the accelerations of the tower top in the two horizontal directions. Moreover, the instantaneous wind speeds have also been recorded, in order to assign each signal frame to its corresponding wind speed bin.

The first step of the algorithm has been to extract the first 4 tower modes, i.e.: 1FA, 1SS, 2FA, 2SS, where FA stands for fore-aft and SS stands for side-to-side. Therefore, in the extraction of the mode amplitudes, these 4 modes have been included in the model, together with the 1P, 3P, 6P and 9P harmonics.

Applying the algorithm presented above, the natural frequencies and damping ratios are obtained, for the 4 natural modes and for the prescribed wind speed bins. The results, compared with those presented in [17] for the same wind turbine, are shown in Fig. 3.

However, it is important to note that those results are not directly comparable, as both methods are different. In [17] the results are obtained by the linearization of the non-linear system equations around an equilibrium point (operating point) for a given wind speed. Then, by applying the Multi-Blade Coordinate (MBC) transformation, the system state is expressed in a fixed frame and frequencies and damping coefficients are obtained. In this case, neither wind nor control actions are involved in the process and those two have a direct impact on the estimated damping. On the other hand, the method presented here, being a method that is used while the machine is in operating conditions, does take into account those effects in the estimated damping. It can be concluded, however, that in both cases the variation in damping
with respect to wind speed is broadly similar. Regarding frequencies, 1FA frequency follows a similar pattern to damping but with much smaller percentual deviations. 2 FA remains much more stable, while SS frequencies exhibit a raising trend with wind.

<figure><img src="image_4.png" /><figcaption>**Figure 3:** Frequency and damping estimates of the presented method (*) compared to the frequency and damping values given by Bir in [17] (-).</figcaption></figure>

## 5. CONCLUSIONS

We have analysed in this paper how modal frequencies, and particularly modal damping, depend on wind speed under almost constant rotation speed conditions (rated power). The analysis has been carried out on an OpenFast model of a WT. A sharp increase in the 1FA mode is noticeable in the transition region (around 10 m/s), followed by a decrease and then a final increase at the highest speeds. It is difficult to know the precise reason for this outcome, but it could be related to the pitch control algorithm. The control law is obviously different below and above the rated wind speed and it is designed to semi-actively damp the 1FA mode but not the 2FA. On the other hand, for the 2FA, 1SS and 2SS modes, a growing trend in damping is observed. The trend in the parameters is similar to the results presented in [17] though the results are not straightforwardly comparable, since those in the mentioned paper correspond to linearizations of the model which do not take into account effects present under operation (e.g. the pitch control).

## ACKNOWLEDGMENTS

The research described in the paper has been supported Spanish Research Agency and the EU NextGeneration funds under grants TED2021-131052B-C2, PID2022-138510OB-181-C21 and PDC2023-145876-C22.

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