Identification of support structure damping of a full scale offshore wind turbine in normal operation
Introduction
The accurate estimation of the wind turbine damping has a pronounced effect on the design loads and lifetime prediction as well as on the dynamic response of the system. There are various ways of identifying the damping, mainly from output-only data, usually called Operational Modal Analysis (OMA), where no artificial excitation to the structure is required. The damping can be extracted either as a modal parameter or as a full damping matrix C. The modal damping identification can be divided into two groups: non-parametric methods applied in the frequency domain and parametric methods in the time domain [1]. In Ref. [2] a comparison of four different system identification methods (Peak-picking, Polyreference LSCE, Stochastic Subspace method and prediction error) emphasizing on the advantages of each technique is discussed. In Ref. [3] a survey of viscous damping identification methods is presented. Several studies have been conducted for the damping estimation of full scale wind turbines from measurements. In Ref. [4] measurements of all sources of damping in an offshore wind turbine at Horns Rev 1 and the Burbo offshore wind farms resulted in a logarithmic decrement δ of about 10% (excluding aerodynamic damping). It was concluded that the available system damping is more than what is used in the simulations. In Ref. [5] the logarithmic decrement considering only the additional damping is estimated as 14–15% (2.25% damping ratio).
In the frequency domain the most commonly applied methods are the Peak-Picking (PP) and the Frequency Domain Decomposition (FDD/Enhanced FDD) techniques. The former, thoroughly analyzed and implemented in Ref. [6] is based on the construction of averaged normalized power spectral density functions (ANPSD) by performing a Discrete Fourier Transformation to the data. The resonance peaks of the spectrum corresponding to the vibration modes are the identified natural frequencies of the system. The half-power bandwidth method is used for the estimation of the damping. The FDD and EFDD proposed in Refs. [7], [8], [9] apply a Singular Value Decomposition (SVD) to the power spectral density function matrix and the spectral response is decomposed into a set of single degree of freedom (SDOF) systems. The auto spectral density functions are transformed back to time domain using the inverse fast Fourier transformation resulting in auto correlation functions for each mode. The damping ratios are estimated from the logarithmic decrement of these functions using a simple linear regression curve fitting technique. The potential of the Frequency Domain Decomposition method is shown in Ref. [10], where the technique is applied to a wind turbine blade for modal parameters identification.
In the time domain the different methods can either be directly applied to the response time series or the correlation functions. Impulse response is widely used in wind turbines to accurately identify the damping ratios. An exponential curve is fitted to the relative maxima of the decay response and an estimation of the damping is obtained by the exponent of this function. In references [11], [12] the method of obtaining the damping ratios directly from vibrations of the tower under ambient excitation from waves and wind is analyzed and compared with the commonly used over-speed stop. In reference [5] the measured acceleration of the tower in the thrust-wise and the side-to-side direction is used to estimate the total system damping of the first bending mode. ”Rotor stops” and fitting of theoretical energy spectra to measured response were used in Ref. [13] for estimation of the first modal damping of offshore wind turbines on a monopile foundation. Accelerometers for the measurement of the vibration decay of twelve ’rotor-stop’ tests were also used in Ref. [14], where the damping is both identified in the frequency and the time domain and a model was developed to further analyze the results. A difference observed in the displacements of the first two modes, allowed the investigation of the influence that the soil-system interaction has on the vibrations of the wind turbine. Also reported in the literature [15], [16], [17], [18], a system identification method (SI) is applied to estimate damping from structures excited by stochastic loads. The (SI) method has been extensively tested and applied to various vibration problems, like offshore structures and bridges. In reference [15] a Stochastic Subspace Identification (SSI) method for estimation of the wind turbine damping is compared with excitation of the system by a harmonic force at its natural frequency.
The identification methods of output-only data provide accurate results under certain assumptions both for the system itself and the nature of the input excitation. The system is supposed to be linear time invariant and the excitation is white noise. The input forces are uncorrelated and distributed over the entire structure. However, the harmonics of the rotating parts, which can be considered as a forced vibration with very low damping, can coincide or be close with one of the natural frequencies of the system resulting in a high energy in the spectrum and causing the identification to fail. The time invariance assumption is also violated by the rotation of the rotor around its axis (azimuth position), the blade pitch angle depending on the operational conditions and the rotation of the nacelle around the tower axis (yaw angle). To deal with the last two problems, periods where these angles do not change significantly should be chosen for the identification procedure. A Coleman transformation is proposed in Ref. [19] to transform the system matrices to a time invariant frame of reference. The limits of Operational Modal Analysis in wind turbines are presented in Ref. [20]. For the separation of the harmonics from the real structural modes various methods are proposed in Ref. [21]. A technique based on the Kurtosis of the measured data to eliminate the harmonics using the EFDD method is proposed in reference [22].
Very often the selection of the method is a trade-off between simplicity and accuracy. The most appropriate technique depends on each application and usually methods are combined. The main assumption present in all techniques is that the considered modes to be identified are sufficiently excited, otherwise they cannot be observed.
Verification of component reliability of offshore wind turbines requires accurate design loads prediction and the validation of load simulations on large turbines. The understanding of the environment and the effect of wakes from the surrounding turbines would be equally important factors. Validation of models in general has been reported by Slootweg et al. [23], where a general model of a variable speed wind turbine was developed and a qualitative comparison with available measurements was performed to prove the accuracy of the derived model. In references [24] and [25] simulation methods for wind turbines in wake were validated with measurements from the Tjæreborg wind farm and with experimental data from the National Renewable Energy Laboratory. A comparison of the modeled loads with measurements for the offshore wind farm at Blyth, was performed by Ref. [26]. A comparison and verification of the aero-elastic codes for offshore wind turbines developed by universities and companies worldwide is presented in references [27], [28]. The aero-elastic model HAWC2 [29] developed in DTU Wind Energy and the dynamic wake meander model for loads and power production were validated in Ref. [30] by comparing simulation results from HAWC2 and full-scale measurements from the Dutch Egmond aan Zee wind farm.
In this paper the target is to identify the available damping of the first two modes of an offshore wind turbine in monopile foundation in real operational conditions. In Ref. [31] the first modal damping of an offshore wind turbine in standstill is identified both from measurements and simulations, considering over-speed stops and ambient excitation. In the present paper the support structure damping is also estimated in normal operation under wind and wave loading. The Enhanced Frequency Domain Decomposition (EFDD) method used for damping identification under ambient excitation is a general method applied to vibrating structures. Its fast and easy application and the indication of harmonics due to rotating parts make EFDD appropriate for damping identification of offshore wind turbines. In the current work the damping in standstill is identified through the parameters of an exponential curve fitted to the relative maxima of a decaying response. The damping estimation through the auto-correlation function technique is validated against the impulse response. The simulation loads from the in-house developed aero-elastic code HAWC2 have been validated with measurements, taken from a fully instrumented 3.6MW Siemens wind turbine in operation, installed in the Walney farm, in the West coast of England (Irish Sea) [32]. The importance of accurate damping in the model for load prediction is pointed out.
The outline of this paper is as follows: firstly the site and the measurements calibration is described. Secondly the wind and wave distributions fitted to the site conditions are analyzed and the soil model is presented. Thirdly the damping of the wind turbine is estimated both in standstill and in normal operation. Finally a model implemented in HAWC2 was validated against site measurements.
Section snippets
Site description
The measurements used for the model calibration are from the Walney Offshore Wind farm 1 (Fig. 1a), located at the west coast of England, 15 km from the shore, (Irish Sea). The annual average wind speed at 80 m height is 9 m/s. Although it is a sheltered area, wind and waves in the site appear to have a misalignment of 10°. A nacelle mounted cup-anemometer provides wind speed measurements as seen by the instrumented turbine and a buoy installed close to the foundation measures the wave
Measurements calibration
The data received from the strain gauges of the instrumented wind turbine require calibration. Imbalances in the bridge circuit introduce an offset in the output data from the acquisition device. The offset on the strain gauges mounted on the tower and the monopile is calculated by performing a yaw test with low mean wind speed, where the Rotor-Nacelle Assembly (RNA) is rotated 360° around its vertical axis. The weight of the rotor creates a moment, captured by the strain gauges
Wind-wave distribution
Mean wind speed measurements of one year from the site obtained from a nacelle mounted cup-anemometer are used to fit a Weibull distribution to the data of the free wind sector (130°–170°). The scale and shape parameters are α = 10.69 m/s and β = 1.98 respectively. The resulting Weibull probability distribution function is shown in Fig. 3a.
Fig. 3b presents the scattered wind turbulence intensity obtained from wind speed measurements from a nacelle-mounted cup-anemometer, along with the fitted
Soil model
The importance of an accurate soil model that accounts for the dynamic soil-structure interaction is often reported in the literature. Three different soil-pile interaction models (distributed springs model, apparent fixity model and uncoupled springs model) that are usually applied in the aero-elastic codes for the investigation of the wind turbine response are presented and validated in Refs. [35], [36]. A study by Zaaijer in Ref. [37] showed that the results implementing the effective fixity
Damping estimation
The total damping of an offshore wind turbine consists of the structural damping , the hydrodynamic damping , the soil damping due to inner soil friction and soil-pile interaction, the passive damper on the tower top , the active damping from the control system during operation and the aerodynamic damping (Equation (4)). In standstill conditions when the blades are pitched to their maximum pitch angle the aerodynamic damping can be neglected and the
Simulation model set-up
The aero-elastic software HAWC2 [29] is used for performing all load simulations. The code is based on a multi-body formulation, where each body is a Timoshenko beam. The 3 bladed 3.6 MW variable-speed variable-pitch wind turbine model is developed as multi-body finite element beam model and implemented in HAWC2. The modeling of the support structure (foundation and tower) is based on internal communication with DONG Energy. The blade is built using information provided by Siemens wind power
Model damping estimation
The Enhanced Frequency Decomposition method was applied to the simulation results for all mean wind speeds and the natural frequencies and logarithmic decrements as a function of the wind speed are presented in Fig. 13. Results both from measurements and simulations are presented and discrepancies are discussed. The environmental conditions used in the simulations are the same with the measured ones. Each simulation is half an hour of time series and was performed with the aero-elastic code
Conclusions
The modal damping of a full scale offshore wind turbine on a monopile foundation was estimated both in standstill and in normal operation. An exponential curve was fitted to the relative maxima of the decaying response after the application of an impulse, for the estimation of the additional offshore damping. The result was used to verify the corresponding estimation given by the auto-correlation function, which is further developed to predict damping under normal operation. A mean value of the
Acknowledgments
The work presented is a part of the Danish Energy Agency funded EUDP project titled, Offshore wind turbine reliability through complete loads measurements, project no. 64010-0123. The financial support is greatly appreciated.
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2022, Journal of Wind Engineering and Industrial AerodynamicsCitation Excerpt :For example, in the present case it was found that the standard error of mean thrust force from each analysis became ‘steady’ at 15 samples. The damping matrix can be estimated by some of the methods mentioned in Section 2.3 (Chen et al., 2017, 2020, 2021; Hansen et al., 2006; Damgaard et al., 2013; Koukoura et al., 2015; Valamanesh and Myers, 2014). As damping identification is out of the scope of the present study, only a brief discussion is covered in Section 5.1 about its influence in the statistical properties of the structural response.