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

M. Damgaard*, L.V. AndersenƗ, L.B. IbsenƗ

* Technology and Engineering Solutions, Vestas Wind Systems A/S, Denmark

Ɨ Department of Civil Engineering, Aalborg University, Denmark

Danish Geotechnical Society ▪ Meeting 5 ▪ 2013

Outline of Presentation

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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

INTRODUCTION The importance of modal parameters for offshore

wind turbines

Introduction: Modal Decomposition of a Linear System

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𝐲 𝑡 = 𝚽 1 𝑞1 𝑡 + 𝚽 2 𝑞2 𝑡 + 𝚽 3 𝑞3 𝑡 + ⋯ + 𝚽 𝑛 𝑞𝑛 𝑡

Introduction: Modal Decomposition of a Linear System

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(fore-aft) 𝚽 1 (side-side) 𝚽 2

𝚽 5 𝚽 11

Introduction: Overall Design

System Stiffness

Larger turbines and increasing water

depths reduce the eigenfreqeuncy f1 of

the lowest damped eigenmode Φ(1).

￫ Eigenfrequency close to 1P and wave

excitations.

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System Damping

For wind-wave misalignment, the required damping must be found from:

Structural material damping

Hydrodynamic damping

Tower oscillation damper

Soil damping

Introduction: Free Vibration Tests

Fore-aft and side-side accelerations ay

and ax 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°.

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Free vibration tests of wind turbines are beneficial in order to achieve pure modal

vibrations from one single mode.

Introduction: Free Vibration Tests

Eigenfrequency Estimation

Least-squares fitting to the crossing

times determines the eigenfreqeuncy f1

of the lowest damped eigenmode Φ(1).

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Damping Estimation

Least-squares fitting to the natural logarithm of the rate of decay of the transient response determines the inherent modal damping δ1 of the lowest damped eigenmode Φ(1).

WIND TURBINES AND

SITE CONDITIONS Initial considerations

Wind Turbine Structure and Site Conditions

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More than 1.500 free vibration tests are investigated at four offshore wind parks.

Vestas V90-3.0 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

60

4.3

Dense

sand/Firm

clay

6/8

Wind

Park II

58

4.8

Dense

sand/Stiff

clay

13/18

Wind

Park III

54.1

4.7

Fine

sand/Stiff

clay

15/27

Wind

Park IV

53

5.0

Dense

sand/Stiff

clay

15/20

Wind Turbine Structure and Site Conditions

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Mean water level (MWL):

Dynamic Properties Based

on Experimental Testing Determination of eigenfrequencies and damping ratios

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.

Eigenfrequency and Damping Estimations – Wind Park I

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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.

Eigenfrequency and Damping Estimations

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Damping for Each Turbine

15

Only turbines with more than 10 measurements are included.

Oil Damper Performance

16

Selected Turbine Investigation

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Data collected with same acceleration level and slope of generator speed.

Beam on a Nonlinear

Winkler Foundation Model Evaluation of scour effects

Evaluation of Eigenfrequency and Soil Damping Based on a Winkler Model

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Elastic beam model with lateral soil-structure 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.

𝜁soil =𝚽 1 T𝐂𝚽(1)

2𝜔1M1

Evaluation of Eigenfrequency and Soil Damping Based on a Winkler Model

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Numerical analysis of scour development and strength of backfill material shows:

Soil damping in the range of 0.04-0.08 logarithmic decrement.

A variation of the 1st resonance frequency of 8%.

Linear Combination of Damping Contributors – An Example of Modal Soil Damping Estimation

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For low levels of damping and within the linear viscous region, it follows that the system damping can be expressed by

.

Based on a specific turbine at Wind Park I, the following damping contributors have been obtained:

𝛿1 = 𝛿steel+𝛿tower+𝛿aero+𝛿water+𝛿soil

Source

Logarithmic Decrement

[-]

Steel Hysteretic Damping δsteel 0.012

Oscillation Oil Damper δtower 0.000

Aerodynamic Damping δaero 0.008

Wave Making Radiation Damping δwater 0.008

Soil Damping δsoil 0.062

Conclusions

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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 0.15-0.16 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

δ5%

[-]

δ50%

[-]

Wind Park I

0.12

0.15

Wind Park II

0.10

0.16

Wind Park III

0.11

0.16

Wind Park IV

0.11

0.16

Conclusions

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Free vibration tests and operational modal analysis of a Vestas V90-3.0 MW and a Vestas V112-3.3 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.

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