EWEA OFFSHORE 2011, 29 November – 1 December 2011, Amsterdam, The Netherlands

PO. 167

Seismic Load Evaluation of Wind Turbine Support Structures with Consideration of Uncertainty in Response Spectrum and Higher Modes

T. Ishihara, K. Takamoto, M. W. Sarwar

Department of Civil Engineering, The University of Tokyo

0

1000

2000

3000

4000

0.1 1

ζ=0.5%

Proposed Eq

γ=0.2

γ=0.5

γ=0.8

Fig. Model participation function

( , )n n

ij kj j kj a j kk i k i

Q F X S T mγ ζ= =

= =∑ ∑

( )n

ij kj k ik i

M F z z=

= −∑

2 2

1 1

, n n

i ij i ijj j

Q Q M M= =

= =∑ ∑

Seismic load for each mode:

SRSS mode superposition:

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

0

0.2

0.4

0.6

0.8

1

1st Mode

2nd Mode

3rd ModeEquation

Shear Force (KN)

-1500 -1000 -500 0 500 1000 15000

0.2

0.4

0.6

0.8

1

2MW

1st Mode

2nd Mode

3rd Mode

Hei

ght R

atio

∑=

+

=

3

1

1

k

ki

jkijj HzcXγ

1 2 3 1 1.1 0 0 1 2 5.87 -6.00 0 0.127 3 14.26 -38.20 24.00 0.043

jkcj k 1/ TTj

1 2 3 1 1.1 0 0 1 2 5.87 -6.00 0 0.127 3 14.26 -38.20 24.00 0.043

jkc jkcj k 1/ TTj 1/ TTj

Significant contribution to the design load by 2nd and 3rd

modes is observed for 2MW turbine as shown below.SRSS method is used for superposition of these modes.

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Previous ModelProposed ModelTime History Analysis

Shear Force Ratio Moment Ratio

Hei

ght R

atio

Hei

ght R

atio

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Previous ModelProposed ModelTime History Analysis

400kW & 2MW

Distribution of calculated load has successfully capturednon-linearity of the load profiles obtained by timehistory analysis.

Coefficients and time period ratio

To determine suitable quantile (γ) for defining reliabledesign spectrum, code calibration method[6] is adopted.In this study, seismic waves for obtaining the structuraldesign certification in Japan are used.

A γ-value of 0.7, i.e., 70% quantile, is identified to obtainreliability level similar to that of the current design code.

1. T. Ishihara, M. W. Sarwar, “Numerical and Theoretical Study on Seismic Response of Wind Turbines”, Proc. of EWEC 2008, 2008.

2. Eurocode 8: Design of structure for earthquake resistance;Part1:Genersl rules, seismic actions and rules for buildings,1998-1:2004.

3. BSL (2004), “The Building standard law of Japan”, The building centre of Japan. (in Japanese)4. IEC61400-1: Wind turbines, Part 1,Third edition.5. JSCE (2007), “Guidelines for design of wind turbine support structures and foundations”, Japan

society of civil engineers. (in Japanese)6. M. Hoshiya, K. Ishii:, “Reliability based design for structures”, Kajima Press, 1986.

References

Conclusions

This study proposes a model for the damping correctionfactor that accounts for uncertainty in the responsespectrum and natural period of wind turbine. In addition,formula for analytical estimation of complex profile ofseismic design loads are presented. Finally accuracy ofproposed formula is verified against time historyanalysis and reliability level similar to that of currentdesign code is demonstrated.

Determination of γ by Code Calibration Method

0 2 104 4 104 6 104 8 104 1 1050

0.2

0.4

0.6

0.8

1

HachinoheTaftElcentroKobeγ=0.7

2MW

400KW

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1

HachinoheTaftElcentroKobe

2MW400KW

Shear Force (KN) Moment (KNm)

Hei

ght R

atio

Hei

ght R

atio

( ) ( )7, , , ,2 10 ..0 .F T f Tα

ζ ζ γ α γζ

= =+

that are significantly low damped, this model fails toestimate large fluctuations of the spectral accelerationin order to establish reliable design spectrum.

Model for Damping Correction Factor

To account for excessive fluctuations in the responsespectrum of low damped systems, damping correctionfactor is proposed as a function of spectral uncertainty (γ),natural period (T) and damping ratio(ζ) so that,

A set of 35 seismic waves, with observed and randomphases, is used to evaluate uncertainty in accelerationresponse spectrum for damping ratios ranging from 0.5to 5%.

Fig. CRF of acc. for each sectionFig. Segments for Statistical analysis

0

0.2

0.4

0.6

0.8

1

1000 104

Section IA

Section IB

Log Normal Dist

Section IC

Cum

ulat

ive

Rel

ativ

e Fr

eque

ncy

Acc

[gal

]

Time Period T[s]

0

1000

2000

3000

4000

5000

Hachinohe

Taft

ElcentroKobe

0.1 1

ζ=0.5%

IB

IA

IC

The log normal distribution is found to have well defineduncertainty in all sections of the acceleration responsespectrum as shown in above figure. Investigations toidentify exponent α has shown linear relationship withquantile (γ) and natural period (T) that lead to following:

Proposed damping correction factor shows goodagreement with analytical one for all quantiles. Alsoproposed model performs well for both low and highlydamped structures whereas EuroCode underestimatesspectral acceleration for low damped systems.

Fig. Comparison of current and proposed model

0

1000

2000

3000

0.1 1

Eurocode EqProposed EqAnalysis

Wind Turbines = 0.5%

Acc

[gal

]

Time Period T[s]

Acc

[gal

]

Time Period T[s]

Eurocode EqProposed EqAnalysis

0

1000

2000

3000

0.1 1

Buildings = 4%

Formula for Vertical Profile of Seismic Loads

Estimation of design loads require natural periods andmodal participation function (γjXij) of the dominant modes.Since first three modes accounted for modal mass of85%[4], expression for calculating the respective modelparticipation function and coefficients are listed below:

Time Period T[s]

Acc

[gal

]

Fig. Variation of response spectrum with γ-values

( ) ,7, , 2 100F Tα

ζ ζ γζ

=+ 0.07 0.7 0.5Tα γ= − + +

Fig. Response spectrum for Level II earthquake

0.5.%EuroCodeζ =

Acce

lera

tion

[gal

]

Time Period T[s]

5%EuroCodeζ =

0

1000

2000

3000

4000

5000

0.1 1

ElCentroTaftHachinoheKobe

0.05 5.0

Objectives

Rapid development of wind energy in seismically activeregions like Japan requires evaluation of design seismicload of wind turbine support structures to ensurestructural integrity. Analytical estimation of the designloads is usually carried out by the response spectrummethod that encounters two problems when used forload analysis of wind turbine support structures[1].These support structures are extremely low dampedthat experience a wide range of frequencies whensubjected to seismic activities. Response spectrum forsuch low damped structures show excessive fluctuationand such uncertainty in response spectrum can not becaptured by existing models of the damping correctionfactors defined in Eurocode[2] and BSL[3]. In addition,use of the simplified SDOF model suggested by IEC[4]

results in linear vertical load profiles. However, verticaldistribution of the seismic loads is found to be largelyaffected by the higher modes[1] of wind turbines.Therefore simplified but accurate analysis method toestimate design load profiles is desired.

In this research, model for damping correction factorthat accounts for uncertainty in response spectrum, andmodal participation functions encompassing complexvertical distribution of seismic loads are proposed. Theaccuracy and reliability of the proposed method forevaluation of seismic design loads is examined againsttime history analysis and current design codes.

Parameters for a return period of 500 years[5]

Response Spectrum Method

However, in case of the wind turbine support structures

Eqation of motion for jth mode of a MDOF system is,

Here，ωj，ζj and γj are natural frequency, damping ratioand mode participation factor of jth mode. Force foreach mode of vibration is calculated as follows:

Seismic force depends upon:a. acceleration of response spectrum (Sa) of SDOF b. modal participation function (γjXij)

Design acceleration response spectrum[2] is defined as:

where ao is design ground acceleration, S is soil amplification factor and Fζ is damping correction factor.

Eurocode[2] defines the damping correction factor as afunction of damping ratio so that,

3.2 1.5 2.5 0.16 0.576

22j j j j j j j gq q q xζ ω ω γ+ + = −

( , )ij j ij a j iF X S T mγ ζ=

( )

)(

)(

)(0 )}1(1{

,

00

00

00

≤

⋅⋅⋅⋅

≤≤⋅⋅⋅

≤≤−⋅⋅+⋅⋅

=

TTTTFSa

TTTFSa

TTFTTSa

TS

CC

CB

BB

a

β

β

β

ζ

ζ

ζ

ζ

( ) ,72 100F

α

ζ ζζ

=+

0.5α =