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1

Stochastic Dynamic Analysis of Offshore Wind Turbines

in a Reliability Perspective

Torgeir Moan Centre of Ships and Ocean Structures (CeSOS)

Department of Marine TechnologyNorwegian Research Centre for Offshore Wind Technology

(NOWITECH)tormo@ntnu.no

http://www.cesos.ntnu.no/http://www.marin.ntnu.no/~tormo

e

London-Croydon, UK 2-4 July 2012

2 Outline• Background

- Wind energy offshore- Wind energy conversion- System development trends

• Integrated stochastic dynamic analysis- reliability perspective- loads- load effect analysis- extreme load effects for ULS analysis- FLS analysis

• Concluding remarks

3 Background

Motivation: “The threat of climate change calls for an energy revolution”,

- investment in renewable energy(IEA Energy Technology Perspectives 2010; IPCC SRREN,2011))

year

Offshore wind

Europe : 40 GW by 2020150 GW by 2030

USA : 10 GW by 202054 GW by 2030

China : 2 GW by 2020Korea : 13.5 GW by 2025

installing 40 GW requiresabout 10-15 000 windmills. This will imply a multi-billion-euro/dollar-industryin the years to come.

4

Wind energy conversion throughmechanical torque to electrical power

• Kinetic energy in wind:• Power in the wind:• Electrical power: P = CP Pmax

• Power generation depends on:– Air density– Wind velocity (cubed)– Swept area

Average annual produced power (kWh/h)- electrical to absorbed or aerodynamicpower (”efficiency”= 95%)

Rated power (instantaneous peak power) for design of the drive train system

Background

5

Control systemControl system objectives:• Ensure efficient and safe

operation- control torque at below rated speed and the power above rated, and limitthe structural loads.

Supervisory systems to control:• Yaw control• Rotor speed control (blade-pitch)• Power control (generator torque)

Schematic illustration of power productionby a 5 MW bottom fixed wind turbine

Rotor condition

Maximizepower

Constantpower

Background6

To avoid negative damping implied by a conventional controller, the controller frequency should be less than the natural frequency of the floating wind turbine

Servo-induced negative damping

Power production

0

100

200

300

400

500

600

700

800

0 5 10 15 20 25

Relative wind speed (m/s)

Thru

st(k

N) Maximum

powerConstantpower

Operating wind turbine, active control

Relative wind speed (m/s)

Control system, continued

at 10 mat the nacelle(90 m aboveMWL)

pdf

Pow

er (M

W)

Wind speed (m/s)

Maximizepower

Constantpower

Background

7

System Development trends

- deeper waterfrom fixed to floating

- increased size:California 1980 : 55 kWto 3.6 MW and upwards

5 MW

Integratingknowledge

Background 8

Floating support structures - no commercial wind farms based on floating turbines yet

Floating turbinesespecially fordeep water areas inthe North Sea, USA, Medeterainean sea, Japan, Korea

- Design for mass production and easy installation; i.e..cost reduction

- At which water depthwould floating windturbines be competitive ?

(Bachynski and Moan, ISOPE Conf., 2012)

Spar with tension leg / catenary mooring

Tension-leg support structure

Semi-submersible with catenary mooring

Background

Tension-leg support structure

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Floating wind turbines for more shallow water- by comparison of responses

Spar for 320 m vs 150 m water depth

(Karimirad and Moan, OMAE Conf., 2012)

Combined spar WT and Torus WEC

(Muliawan et al., OMAE, 2012)

Background10Reliability perspective • Hazards

- external loads (extreme, repetitive), internal faults(control system)

• Different limit states –failure modes

• Different components indifferent concepts

Classical reliability- Data bases (operational/failure)Structural reliability- Methods (predicting degradadtion)

Measure of degradation’

Monitoring degradationIndividual vs farm

Gearbox (visual, oil, condition monitoring)Blades, structure

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Courtesy: NREL/Wind power today, 2010.

Integrated stochastic dynamic analysisOverview

Load effect analysisAerodynamic, hydrodynamics,….Integrated (aero-, hydro-, elastic-, servo-) analysis

- loads: irregular waves, turbulent wind, rotor rotation in a gravitationalfield and a nonuniform wind field,

- conditions: operating, parked –intact or with faults

- time versus frequencydomain simulation

- refined versus simplified methodsLaboratory or field tests

Load effects- extremes and histories - st.dev. etc (for fatigue, wear..)

Stochasticdynamicfeatures

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Load effects analysis of wind turbinesScope: Determination of load effects for the SLS, ULS, FLS design of

the support structure, tower, rotor, drive train

The system modeling includes: ■modeling of excitation mechanisms (turbulent wind, irreg. waves and current) –

aerodynamics and hydrodynamics

■ rotor; mechanical or hydraulic drive train; 

generator – electrical grid.

■ structural dynamic model

■ automatic control theory

Wind-industry based• Bladed (Garrad Hassan)• Flex5  (S.Øye, DTU)• HAWC2  (Risø DTU), • FAST (NREL)

Offshore industry based• Simo/Riflex (Marintek)• Orcaflex• Others (e.g. FEDEM,  USFOS/VpOne )

Tools

Drive train:Rotor-generator

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• Jacket structure– Water depth: 70m– Soil data (Ekofisk)

• Wind turbine– 5MW NREL three-blade upwind wind turbine– Nacelle mass: 240 ton– Rotor diameter: 126m; mass: 110ton– Tower height: 70m; mass: 225ton– Wind speed:

Rated=12m/s, Cut_in=5m/s, Cut_out=25m/s– Controller:

Variable speed/ variable pitch from Risø Nat. Lab.(DTU Wind)

• Model- aerodynamics: steady and turbulent wind

BEM, CFD for special issues- hydrodynamics: Kinematics Airy with Wheeler stretching,

Morison formula

Offshore jacket wind turbine14

Joint environmental data used in case studies- long-term distribution of the mean wind speed- distribution of wave height and – periodconditional upon mean wind speed

(Johannesen et al, 2001)

pdf of themean wind speedat a northernNorth Sea site

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• Methods to account for the long term variability:- Full long-term analysis- Contour-surface method (by assuming that the extreme response can be

determined by the largest response in an extreme environmental condition).

• Methods for short-term extreme value analysis in a 3-h periodbased on up to 396 10 min samples (3960 min) - for a given short term condition- ref.value: max in 3-h by max in 18 10 min samples

Gumbel fit to the 22 data points- global max: obs max in each 10 min period (n points),

fit Gumbel and determine 3-h max- upcrossing rate – with extrapolation- Weibull tail

Long-term extreme value analysis16

Ensemble averages of statistical properties ofglobal response for a parked rotor (v = 50 m/s, Hs = 14 m, Tp = 16.0 s)

(Saha, Gao, Moan, Næss, J. Wind Energy, submitted 2012)

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The reference value is obtained by grouping the 4 × 99 samples of 10-minsimulations into 22 time-series of 3–h simulations.

Three hour extreme shear force at the sea bed usingvarious extrapolation methods for the parked condition.

Combined wind and waveWind only

(Saha, Gao, Moan, Næss, J.Wind Energy, submitted 2012)

Max (X) = μx+κσx

18Fatigue analysis of an offshore wind turbinewith a jacket support structure

Largest contributionto fatigue due to wind loads only: v=20 m/sandwave only: Hs = 5 m

Contribution to cumulative fatigue damage ofwind loads and wave loads

Normal power production- Turbulence in wind (wake operation)- Misalignment of wind and waves- Windrose

Fault, survival, start-up and shut down, standstill conditions

(Source: WB Dong et al, 2010, 2011,..)

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• Fatigue formulation based on fracture mechanics method

• Failure probability: Pf = P(M<0)

• Uncertainty analysis– Fatigue strength– Load effects (dominating)

• Statistical uncertainty– Wind/wave simulation– Long-term analysis– Weibull distribution

• Model uncertainty

Fatigue reliability analysis (1)

( )( )

( )0

0 0 (1 )c

mm

a Y

a da mM t C t T ABY a

νγ π

= − − Γ +∫

( )mda C KdN

= Δ

Normal plot of stress range distribution parameter lnA and 1/B, based on twenty long-term time-domain simulations

Corr. Coef. = -0.862

K S aYπΔ =

(Weibull distribution of stress ranges)

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• Effect of inspection and repair• Inspection event with

crack detection (or no crack detection)

Fatigue reliability analysis (2)

Probability events with inspections Time-varying reliability index with / without inspection

( )( )

0

0 1 0 1 0νγ π

⎛ ⎞= − − Γ + ≤⎜ ⎟⎝ ⎠∫

Dm

a

ma Y

da mH C T T ABY a

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Reliability-based WT Gear Design

• Decoupled analysisto determineTooth contact and Bearingforces and Gear deflections.

- Global aero-hydro-servo-elasticsimulation

- Drive train multi-bodysimulation based on main shaftloading and nacelle motions

GRC Drive train configuration

Surface Failure (pitting)

Failure Modes:

Root Failure (bending fatigue)

Limit state formulations:analogous those for traditionalfatigue: initiation and growthNREL 750kw land-based

wind turbine model

22Time histories of tooth contact force based ontime domain simulation of the torque in SIMPACK

WB Dong et al, ”Some remarks on time domain based gear contact fatigue analysisunder dynamic conditions for wind turbines”, submitted in 2012.

Long term pdf ofthe wind speed

Long-term distributionof the contactforce range

Contact forceconditionalupon windspeed

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ReliabilityFailure function (based on 2-parameter Weibull model of long term contact pressure)

Planet gear results

(Sun gir is more critical)

Time

Planet gear tooth

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NREL 5-MW Wind Turbine mounted on a 120-m spar platform

CatenaryMooredSpar (CMS) (similar to HYWIND)

Tension Leg Spar (TLS) (similar to SWAY)

Integrated dynamic analysis of floating turbinesExample: Spar type wind turbines

(M. Karimirad, T.Moan, various papers)

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Natural periods

Constrained5Yaw31.328Pitch/Roll1.731.4Heave

125.677Sway125.682Surge

Tension-legmooring

Catenarymooring

Natural periodsMotions

Excitation- Wind- Waves-1 P corresponds to 1.26 rad/s

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Dynamic performance: Spar type turbine of size 5 MW

If resonancecan not be avoideddamping becomescrucial

water depth:300 m

Natural frequenciesfor wind turbinewith a 5 MW capacity and aspar type supportstructure

Cautious selection of eigenperiodsin heave, pitch and roll and flexiblemodes to avoid coincidencewith wave and wind load excitation

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Different seed numbersDifferent time steps

Surge spectra at the MWL, smoothed spectra based on one-hour time domain simulations for TLS (Hs=15 m and Tp =16 sec) using Hawc2.

Time domain simulation-Charcteristic features of motions-Sampling accuracy

Karimirad et al, J. Marine Structures, 2012

Sample of 5 hours for estimating the 3 hours extremes

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Tension spectrum, smoothed spectrum based on aone-hour time domain simulation Hs =15 m and Tp =16 s,identical wave elevation)Hydrodynamic code-to-code comparison for HAWC2 and USFOS/VpOne

K - line stiffness, A - crosssectional area of the line, T - line force vector, ΔL- line length,

- the unit vector of the line x, y,z – coordinates of the bottom

of the spar.

Characteristic features of tension in tension-leg mooring

29 Ameliorating the Negative Damping in the Dynamic Responses of a TLS with Downwind turbine

Nacelle surge spectra for responses induced by the wave-only and wind and waves for theoperating and parked rotors in the over-ratedconstant wind condition(V =17 m/sec, Hs =4.2 m and Tp =10.5).

Ratio of standard deviation for a not tuned and tuned controller

8.0Power1.6Tension5.0Shaft speed

4.4BM at tower-spar

2.7BM at blade root

14.5Nacelle surge

Not Tuned/Tuned Responses

Very important for: •Fatigue limit state (FLS)•Power production•Drive train loads

(Karimirad and Moan, EWEC, 2011)

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Aerodynamic and hydrodynamic damping

Power take-off introduces, aerodynamic damping

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Mean tension Standard deviation

Tension in the mooring line

Mean of the responses are wind-induced and the standard deviations of the responses are primarily wave-induced- response in the tower, blades and mooring line

32 Normalized extreme responses for the Tension-leg Spar

Normalised maximum of the bending moment (BBM) at the blade root, bending moment (BM) at the towerspar interface, shear force (SF) at the tower-sparinterface, nacelle surge (NS) and tension (TE). The wind speed (V) refers to the loadcases in Table 5. The statistics are based on five 1-hour samples. The maximumresponses correspond to an up-crossing rate of 0.0001 and are obtained by extrapolation.

33Response analysis under faults during operation of a Spar wind turbine with catenary mooring

• IEC code requires checking of nearly 40 cases with environmental loads for a system which is intact or fault.

• One case is:

(Jiang et al, to appear)

Time history of tower bottom bending moment of a spar-typewind turbine under different fault conditions. Mean wind speed: 25m/s, Turbulence Intensity: 0.15, Hs=5.9m, Tp=11.3s

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The resulting wind forces on the rotor consist of 3 force and 3 moment components. A simplified model is achieved by only considering the thrust force.

2 212 a T RELT R C Uπρ=

Simplified aerodynamic response analysis

Further simplification is achieved by simulatingthe effect of control in the over rated responseup to cut-out wind speed by a filter.

Tower bending moment

Load cases for operational conditions

The simulation time for 1 hour real time:-15 min for SRT -24 hours for

the ”full” method

(Karimirad and Moan, J. Marine Structures, 2012)

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• Decoupled analysis to determineTooth contact forces, Bearing forces, Gear deflections.

- Global aero-hydro-servo-elastic simulation- Drivetrain multi-body simulation

based on main shaft loading andnacelle motions

Comparison of drivetrain responses in FWT and WT

GRC Drive train config.

Both mean and st.dev. ofthe low speed shaft BM(and hence bearing, tooth contactforces) increases significantly Comparison of the standard deviation

(Xing et al., 2012)

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Concluding remarksA huge untapped potential for offshore wind power exists.

Technology is still at an early stage, especially for floating wind turbines

Rules and standards for design of floating wind turbine is urgently needed – for floating wind turbines.

Significant efforts are required to - increase robustness/reliability, - reduce costs (utilise mass production potential)

Efforts are required to develop accurate and simplified methods forintegrated dynamic analysis

Concerted efforts in R & D are required by the industry, research institutesand universities

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AcknowledgementThanks to researchers Z Gao and M Karimirad, and PhD candidates E E Bachynski, Z Jiang, M I Kvittem, M. Muliawan, Y Xing, in CeSOS and Nowitech for excellent cooperation

Thank you!

Courtesy: EWEA. B.Faulkner

38References

Moan T., Gao Z., Ayala-Uraga E., 2005. Uncertainty of wave-induced response of marine structures due to long-term variation of extratropical wave conditions. Journal of Marine Structures 18(4), 359-382.

Karimirad, M., Gao, Z. and Moan, T. (2009) Dynamic Motion Analysis of Catenary Moored Spar Wind Turbine In Extreme Environmental Condition. Offshore Wind Conference 2009, Sweden.

Karimirad, M. and Moan, T. (2010) Effect of Aerodynamic and Hydrodynamic Damping on DynamicResponse of a Spar Type Floating Wind Turbine. European Wind Energy Conference EWEC 2010, Warsaw, Poland.

Gao, Z.; Moan, T. Long-term fatigue analysis of offshore fixed wind turbines based on time-domainsimulations. In: Proceedings of PRADS. Rio de Janeiro (Brazil): 2010.

Dong, W.B.; Gao, Z.; Moan, T. Fatigue reliability analysis of jacket-type offshore wind turbine consideringinspection and repair. In: Proc. European Wind Energy Conference .Warsaw (Poland): 2010. 259-263

Gao Z.,Saha N.L.J., Moan T., Amdahl J., 2010. Dynamic analysis of offshore fixed wind turbines under wind and wave loads using alternative computer codes. In: Proc. the TORQUE 2010 conference. FORTH, Heraklion, Crete, Greece.

Karimirad, M., Meissonier, Q., Gao, Z. and Moan, T., ‘Hydroelastic Code-to-Code Comparison for a Tension Leg Spar-Type Floating Wind Turbine’, J. Marine Structures, 24: 412–435, 2011.

Dong W.B., Moan T. and Gao Z., 2011. Statistical Uncertainty Analysis In The Long-term Distribution ofWind&Wave Induced Hot-spot Stress for Fatigue Design of Jacket Wind Turbine Based on Time DomainSimulations. In: Proc. 30th Int. OMAE Conference . Rotterdam, The Netherlands.

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Gao, Z. et al., ‘Comparative Study of Wind- and Wave-Induced Dynamic Responses of Three Floating Wind Turbines Supported by Spar, Semi-Submersible and Tension-Leg Floaters’, Proc.ICOWEOEConference, Beijing, 2011.

Karimirad, M. and Moan, T. (2011) Ameliorating the Negative Damping in the Dynamic Responses ofa Tension Leg Spar-Type Support Structure with a Downwind Turbine, Proc. European Wind Energy Conference, March 2011, Brussels, Belgium

Xing, Y.H.; Moan, T. Wind turbine gearbox planet carrier modeling and analysis in a multibody setting, accepted for Wind Energy Journal (2012).

Dong, W.B.; Xing, Y.H.; Moan, T.; Gao, Z. (2012) Time domain based gear contact fatigue analysis of a wind turbine drivetrain under dynamic conditions. Submitted for publication.

Xing,Y.H.; Karimirad, M.; Moan, T. (2012) Modeling and analysis of floating wind turbine drivetrain, submitted to Wind Energy Journal.

Karimirad, M. and Moan, T.(2012), ‘Comparative Study of Spar-Type Wind Turbines in Deep and Moderate Water Depths’, Proc. 31st OMAE Conf., Rio de Janeiro, Brazil, 2012.

Muliawan, M.J., Karimirad, M., Moan, T. and Gao, Z., ‘STC (Spar-Torus Combination): A Combined Spar-Type Floating Wind Turbine and Large Point Absorber Floating Wave Energy Converter – Promising and Challenging’, Proc. 31st OMAE Conf., Rio de Janeiro, Brazil, 2012.

Bachynski, E.E. and Moan, T. ‘Linear and Nonlinear Analysis of Tension Leg Platform Wind Turbines’,Proc. ISOPE Conf., Rhodes, June 2012.

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Karimirad, M. and Moan, T., ‘A Simplified Method for Coupled Analysis of Floating Offshore Wind Turbines’, on-line, J. Marine Structures, 2012.

Kvittem, M.I, Bachynski, E.E. and Moan, T., ‘Effects of Hydrodynamic Modelling in Fully CoupledSimulations of a Semi-Submersible Wind Turbine’, to appear in Energy Procedia, 2012.

Karimirad, M. and Moan, T., Stochastic Dynamic Response Analysis of a Tension Leg Spar-Type Offshore Wind Turbine, submitted for publication

Jiang, Z., Karimirad, M. and Moan, T., ‘Effect of Fault Conditions on the Dynamic Response of Spar-Type Floating Wind Turbines’, to appear.

Saha, N., Gao,Z., Moan, T. and Næss, A. , Short term extreme response analysis of a jacket supportingan offshore wind turbine, submitted to J. Wind Energy.