Uncertainty in wind climate parameters and the consequence for fatigue load assessment

Transcription

1 Uncertainty in wind climate parameters and the consequence for fatigue load assessment Henrik Stensgaard Toft (1,2) Lasse Svenningsen (2), Morten Lybech Thøgersen (2), John Dalsgaard Sørensen (1) (1) Aalborg University, Denmark (2) EMD International A/S, Denmark 1

2 Presentation outline Research project and general perspectives Types of uncertainty and structural reliability theory Uncertainty modelling for wind climate parameters and structural resistance Example: Deterministic and probabilistic design Conclusion and future work 2

3 Optimized integration of load calculations in development and design of wind farms Load Response Simple and accurate load assessment method for fatigue loads which can be used early in the design phase. Presentation Assessment of reliability for fatigue limit states taking the influence of uncertain wind climate parameters into account. Wind & Site Power Production Structural Design Ultimate/Fatigue Loads 3

4 Workflow in assessment of wind turbine loads Wind Climate Measurements at Site Short-term Reference Wind Climate Measurements Long-term Terrain and Roughness Data Measure-Correlate-Predict (MCP) Micro-scale Flow Model (WEng, WAsP, CFD) Wind Turbine Structure & Controller Equivalent Wind Climate (Design Load Cases) Turbulence Simulation Aero-elastic Simulation Model (FLEX5, HAWC2, Bladed, FAST) Characteristic Load Assessment (Structural Integrity) 4

5 Types of uncertainty and structural reliability theory Types of uncertainty: R ~ Resistance S ~ Load Physical uncertainty (aleatory) f R, f S Model uncertainty (epistemic) Measurement uncertainty (epistemic) Statistical uncertainty (epistemic) S c R c R, S Deterministic/Codified design: Design equation: Probabilistic design: G Rc fsc 0 m Limit state equation: g R S Probability of failure: PF PR S 1 Reliability index: P F Blade root flap bending moment 5

6 Modelling of uncertainty in wind climate parameter Uncertainty in the wind climate parameters are modelled based on: A systematic method for quantifying wind flow modelling uncertainty in wind resource assessment (A. Clerc et al. 2012). Uncertainty in the speed-up factor S() depend on: The absolute value of the speed-up factor The distance between mast and wind turbine Coefficient of variation [-] Distance uncertainty Based on engineering judgement models for the distance related uncertainty are proposed for: Wind speed standard deviation (turbulence) Wind shear Correlation [-] Distance D [m] Correlation function Difference betw een w ind directions [deg] 6

7 Average wind speed and Ambient turbulence The average sectorwise wind speed U WTG is estimated from: U Mast () ~ Average sectorwise wind speed at mast position X U X MCP S() U S X X U WTG MCP U Mast ~ Uncertainty wind speed measurements ~ Uncertainty Measure-Correlate-Predict correction ~ Speed-up factor between mast and wind turbine (incl. uncertainty) The ambient turbulence is modelled by a Lognormal distribution: U Amb, Mast U Amb, Mast f, ~, Amb, WTG Amb U LN X X Amb X X Amb S S X ~ Uncertainty ambient turbulence measurements X Amb () ~ Uncertainty ambient turbulence dependent on distance from mast 7

8 Wind shear, Inflow angle, Air density and Wake effects The wind shear is modelled by a Normal distribution: X ~ Uncertainty wind shear measurements, ~, f U N X X U U Profile X profile () ~ Uncertainty wind profile dependent on distance from mast The inflow angle and air density are modelled by the mean values but applied a measurement uncertainty X and X, respectively. Wake-effects are determined by the Frandsen model and applied a general physical and model uncertainty X wake (). The damage equivalent load are determined by numerical integration for the four integrals (wind sector, wind speed, turbulence, shear) using a response surface methodology. 8

9 Modelling of uncertainty in structural resistance The limit state equation for fatigue during normal power production (DLC 1.2) is modelled by: m neqtl Feq,limit g X load X SCF K z ~ Uncertainty in Miner s rule K ~ Uncertainty linear SN-curve n eq ~ Equivalent number of load cycles (10 7 ) T L X load X SCF F eq,limit z m ~ Wind turbine life time (20 years) ~ Uncertainty in load assessment (aero-elastic model) ~ Uncertainty Stress Concentration Factor ~ Damage equivalent fatigue load ~ Design parameter (wind turbine designed to the limit) ~ Wöhler exponent 9

10 Example: Wind farm in flat terrain Wind farm with 40 wind turbines located in flat terrain (onshore) in northern part of Europe Two metrological masts (1 year measurement) with three cup anemometer (24-49m) Two wind turbines in the layout approximately at the mast positions are considered. Mast 1 & WTG 1 Mast 2 & WTG m 10

11 Example: Deterministic design The two wind turbines are designed based on the traditional deterministic design approach (IEC ) using each measurement mast. Using the distant measurement mast to estimate the local wind climate leads to a nonconservative / conservative assessment of the fatigue loads in the range of 0-4%. Relative fatigue damage equivalent loads. Component Wohler WTG 1 Mast 1 WTG 1 Mast 2 WTG 2 Mast 2 WTG 2 Mast 1 Blade root in-plane Blade root out-of-plane Tower bottom for-aft Shaft torque

12 Example: Probabilistic design Uncertainty modelling Variable Description Distribution Mean Std. X U Wind speed measurement Lognormal X MCP MCP model Lognormal S() Speed-up (distance + absolute) Normal (COV) X Turbulence measurement Lognormal X Amb () Ambient turbulence (distance) Normal X Wind shear measurement Lognormal X Profile () Wind shear (distance) Normal X Inflow angle measurement Lognormal X Air density measurement Lognormal X wake () Wake effects Normal Miners rule (welded, cast, composite) Lognormal /0.40/0.50 logk SN-curve (welded, cast, composite) Normal /0.15/0.25 X load Uncertainty load assessment Lognormal X SCF Uncertainty local stress analysis Lognormal

13 Example: Probabilistic design Reliability level The probability of failure / reliability level is assessed for the four combinations of metrological mast and wind turbine using the First Order Reliability Method (FORM). The reliability level is in general decreased with increasing distance between mast and turbine, but bias in the assessment of the wind climate parameters influence the results. The target accumulated reliability index for wind turbines are t = (P F = ) Accumulated reliability index and probability of failure P F. Component WTG 1 Design: Mast 1 Limit: Mast 1 WTG 1 Design: Mast 2 Limit: Mast 1 WTG 2 Design: Mast 2 Limit: Mast 2 WTG 2 Design: Mast 1 Limit: Mast 2 Blade root in-plane =2.8, P F =310-3 =2.8, P F =310-3 =2.8, P F =310-3 =2.8, P F =310-3 Blade root out-of-plane =3.1, P F =110-3 =2.7, P F =310-3 =3.1, P F =110-3 =3.2, P F =710-4 Tower bottom for-aft =2.9, P F =210-3 =2.7, P F =410-3 =2.9, P F =210-3 =3.0, P F =110-3 Shaft torque =2.7, P F =310-3 =2.5, P F =710-3 =2.7, P F =310-3 =2.9, P F =

14 Example: Probabilistic design Sensitivity analysis The influence of the different types of uncertainty on the reliability level are quantified by the -vector. The general uncertainties (load assessment, stress concentration factor) has the largest influence on the reliability level followed by the uncertainties related to the material properties (fatigue resistance). The wind climate parameters has a moderate influence on the reliability level. Influence of different uncertainties on the reliability level (-vector). Component WTG 1, Design: Mast 2, Limit: Mast 1 2 wind 2 material 2 general Blade root in-plane 0% 27% 73% Blade root out-of-plane 20% 21% 59% Tower bottom for-aft 13% 47% 40% Shaft torque 15% 27% 58% 14

15 Conclusion A framework for assessment of the uncertainty in the site specific wind climate parameters using probabilistic design are proposed. The reliability level shows some variation with the uncertainty in the wind climate parameters modelled by the distance between the mast and wind turbine. The uncertainty in the wind climate parameters influence on the structural reliability level is moderate compared to other uncertainties in fatigue limit state. Future Work Assess the uncertainty and spatial variation for the wind speed standard deviation which for some components has a large influence on the fatigue loads. Investigate the influence of uncertain wind climate parameters for complex sites. Propose a similar framework for the ultimate limit state. Larger influence of the wind climate parameters are expected. 15

16 Acknowledgement The work presented in this presentation is part of the project Optimized Integration of Load Calculations in Development and Design of Wind Farms supported by Innovation Fund Denmark (Højteknologifonden), grant no The financial support is greatly appreciated. EMD International A/S 16

17 Uncertainty in wind climate parameters and the consequence for fatigue load assessment Henrik Stensgaard Toft (1,2) Lasse Svenningsen (2), Morten Lybech Thøgersen (2), John Dalsgaard Sørensen (1) (1) Aalborg University, Denmark (2) EMD International A/S, Denmark 17