Time-Varying Dynamic Properties of Offshore Wind Turbines Evaluated by Modal Testing

Transcription

1 Time-Varying Dynamic Properties of Offshore Wind Turbines Evaluated by Modal Testing M. Damgaard *, L.V. Andersen Ɨ, L.B. Ibsen Ɨ * Technology and Engineering Solutions, Vestas Wind Systems A/S, Denmark Ɨ Department of Civil Engineering, Aalborg University, Denmark Danish Geotechnical Society Meeting

2 Outline of Presentation Introduction and motivation Wind turbine structures and site conditions Eigenfrequency and damping estimations based on free vibration tests Eigenfrequency and soil damping estimations based on a beam on a nonlinear Winkler foundation model Conclusions 2

3 INTRODUCTION The importance of modal parameters for offshore wind turbines

4 Introduction: Modal Decomposition of a Linear System y t = Φ 1 q 1 t + Φ 2 q 2 t + Φ 3 q 3 t + + Φ n q n t 4

5 Introduction: Modal Decomposition of a Linear System Φ 1 (fore-aft) Φ 2 (side-side) Φ 5 Φ 11 5

6 Introduction: Overall Design System Stiffness System Damping Larger turbines and increasing water depths reduce the eigenfreqeuncy f 1 of the lowest damped eigenmode Φ (1). Eigenfrequency close to 1P and wave excitations. For wind-wave misalignment, the required damping must be found from: Structural material damping Hydrodynamic damping Tower oscillation damper Soil damping 6

7 Introduction: Free Vibration Tests Fore-aft and side-side accelerations a y and a x are measured by use of two accelerometers in the nacelle. To reduce aerodynamic effects, the modal parameters are derived from pitch angles higher than 85. Free vibration tests of wind turbines are beneficial in order to achieve pure modal vibrations from one single mode. 7

8 Introduction: Free Vibration Tests Eigenfrequency Estimation Damping Estimation Least-squares fitting to the crossing times determines the eigenfreqeuncy f 1 of the lowest damped eigenmode Φ (1). Least-squares fitting to the natural logarithm of the rate of decay of the transient response determines the inherent modal damping δ 1 of the lowest damped eigenmode Φ (1). 8

9 WIND TURBINES AND SITE CONDITIONS Initial considerations

10 Wind Turbine Structure and Site Conditions More than free vibration tests are investigated at four offshore wind parks. Vestas V MW turbines installed on the well-proven monopile concept. Soil profiles consist primarily of cohesionless soil in the top layers. Tower height [m] Mnopile diameter [m] Soil conditions [-] Average Water depth [m] Wind Park I Dense sand/firm clay 6/8 Wind Park II Dense sand/stiff clay 13/18 Wind Park III Fine sand/stiff clay 15/27 Wind Park IV Dense sand/stiff clay 15/20 10

11 Wind Turbine Structure and Site Conditions Mean water level (MWL): 11

12 Dynamic Properties Based on Experimental Testing Determination of eigenfrequencies and damping ratios

13 Eigenfrequency and Damping Estimations Wind Park I 29 turbines have been investigated for Wind Park 1. Eigenfrequency and damping depend on the acceleration level. R-square value of at least 0.99, meaning that the fit explains 99% of the total variation in the data about the average, reduces the scatter. 13

14 Eigenfrequency and Damping Estimations 27 turbines have been investigated for Wind Park II. 78 turbines have been investigated for Wind Park III. 34 turbines have been investigated for Wind Park IV. Local weighted linear regression to smooth out the modal damping for the four wind parks. 14

15 Damping for Each Turbine Only turbines with more than 10 measurements are included. 15

16 Oil Damper Performance 16

17 Selected Turbine Investigation Data collected with same acceleration level and slope of generator speed. 17

18 Beam on a Nonlinear Winkler Foundation Model Evaluation of scour effects

19 Evaluation of Eigenfrequency and Soil Damping Based on a Winkler Model Elastic beam model with lateral soilstructure interaction represented by linear/non-linear springs has been used to evaluate the eigenfrequency and soil damping. Reduction of effective soil stresses due to the presence of scour. Irreversible deformations in the soil are a measure of the energy dissipation in the first cycle after the free vibrations take place. 19 ζ soil = Φ 1 T CΦ (1) 2ω 1 M 1

20 Evaluation of Eigenfrequency and Soil Damping Based on a Winkler Model Numerical analysis of scour development and strength of backfill material shows: Soil damping in the range of logarithmic decrement. A variation of the 1 st resonance frequency of 8%. 20

21 Linear Combination of Damping Contributors An Example of Modal Soil Damping Estimation For low levels of damping and within the linear viscous region, it follows that the system damping can be expressed by δ 1 = δ steel +δ tower +δ aero +δ water +δ soil. Based on a specific turbine at Wind Park I, the following damping contributors have been obtained: Source Logarithmic Decrement [-] Steel Hysteretic Damping δ steel Oscillation Oil Damper δ tower Aerodynamic Damping δ aero Wave Making Radiation Damping δ water Soil Damping δ soil

22 Conclusions Analyses show distinctly time-dependent cross-wind dynamic properties. Based on numerical analysis, the variation is believed to be caused by sediment transportation at seabed level and varying performance of tower oscillation dampers. Reliable and similar mean values of the first modal damping in terms of the logarithmic decrement are observed to be in the range of for the four wind parks. The range corresponds very well with the mean damping value for each turbine. Assuming lognormal distributed modal damping, the following quantiles are obtained for each wind park: 5% and 50% Quantiles Logarithmic Decrement δ 5% [-] δ 50% [-] Wind Park I Wind Park II Wind Park III Wind Park IV

23 Conclusions Free vibration tests and operational modal analysis of a Vestas V MW and a Vestas V MW turbine indicate: Soil damping activation is small during normal turbine operation in the side-side direction. High aerodynamic damping during normal turbine operation in the side-side direction. Full integrated aeroelastic models indicate: For surface and bucket foundations, the geometrical soil damping has a small contribution. The side-side response is highly influenced by the soil-structure interaction. 23

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