Experiences on representative and effective turbulence calculation: WindSim approach and possible refinements

Transcription

1 WindSim 202 Experiences on representative and effective turbulence calculation: WindSim approach and possible refinements Beatrice Pistoni, Matteo Giannì

2 Objective Analyzing WindSim approach on computation of turbulence intensity parameters I rep and I eff (IEC rd ed.) Discussing possible approaches on I rep computation Comparing and discussing about different approaches Analyzing a test case on I eff computation Discussing about statistical significance issues on I eff computation and possible refinements

3 Turbulence in wind data Turbulence expresses the stochastic fluctuations of wind speed u (m/s) u ( t) = u + u'( t) wind speed mean value turbulent fluctuation In a boundary layer, turbulence is related to fluid viscosity, i.e. friction, and its interaction with the boundary (ground surface) Turbulence depends on wind shear, hence on surface topography, vegetation and presence of obstacles (i.e. friction velocity) Turbulence intensity: I σ u = u = N N i= u ' ( u ) i 2

4 Turbulence in IEC (2 nd -3 rd ed.) I ref Expected value of hub-height turbulence intensity at a 0 min average wind speed I = char I ref + σ I ref I 84 th quantile: characteristic value of hub-height turbulence intensitiy at a 0 min average wind speed I = rep I ref +.28σ I ref I 90 th quantile: representative value of hub-height turbulence intensitiy at a 0 min average wind speed

5 Effective Turbulence in IEC (3 rd ed.) Effective turbulence Intensity I eff Structural stress of turbine component s material (Wöhler exponent: m) m=0, valid to verify glass fiber of the blades, the most fragile component. Wake effects from neighbouring wind turbines (Frandsen)

6 I rep calculation:windsim approach.tws at mast position is transferred to each hub position computation of I ref and σ Iref of transferred.tws computation of I rep =I ref +.28 σ Iref mast For each bin (3 25 m/s), I rep is an average value over the all.tws so it s independent from wind direction

7 I rep calculation:alternative approach wind sector bin I rep = I ref +.28σ Ιref I ref σ Ιref f N I = f rep i= i I rep i For each bin (3 25 m/s), sector-wise I rep_i are weighted by the wind rose.

8 Differences between the two approaches on I rep computation : a sample case Hp. Wind directions equally distributed between E and W bin=5 m/s WindSim approach I ref =3.5 % σ Iref =0.05 m/s I rep =5.4 % alternative approach I refe =2.0 % σ IrefE = m/s I repe =2.0 % I refw =5.0 % σ IrefW = m/s I repw =5.0 % I rep_weighted =3.5 %

9 I rep computation: a real case bin=5 m/s 7 months of data WindSim approach I rep =9.6 % alternative approach I rep =8.6 %

10 Observations on I rep computation IEC rd ed. doesn t explain how to calculate I rep, either as an average value independent from wind sectors (WindSim approach), or as a weighted average of I rep values, in different wind sectors (alternative approach). I rep values obtained with the two different approaches show a difference of % WindSim approach can lead to conservative values due to less sector-wise wind turbulence variability than in the whole time series. Since turbines work in a sector-wise mode, would it be sensible to assess I rep by a sector-wise approach?

11 I eff computation: WindSim approach WindSim follows IEC approach (Frandsen, 2007) Conceived a simple model for flow conditions, { } 2π applicable for structural m I m design against fatigue eff ( vhub) = p( θ, vhub) I ( θ, vhub) dθ 0 failure, in wind turbine clusters. p: probability density function I: turbulence intensity of the combined ambient and wake flows from wind direction θ m: is the Whöler exponent of the considered material (m=0, glass fiber of the blades) I eff is discretized as: I eff _ s ( vhub) = s w_ s r _ s hub w_ s σ T _ s hub) vhub [ ] m m ( N p ) σ ( v ) + p ( v m representative value of ambient standard deviation probability to be under wake for a given sector representative value of standard deviation in wake condition

12 Typical output of I eff calculation Wind turbine classification offers a range of robustness, clearly defined in terms of turbulence parameter (besides wind speed). The aim is to compare I eff trend with the three classes turbulence intensity in Normal Turbulence Model (IEC 6400 ) S A Special Class Design values for the wind turbine class S shall be chosen by the designer 0.2 v ref 0.4 v ref 0.6 v rate v cut-out B C

13 I eff trend in a real case I eff output in several cases shows anomalous peaks deviating from the trend anomalous peak 2 m/s

14 bin 2m/s: what happens? I eff f i (I eff ) m m=0 I eff N samples 2 = i= f i I m eff i m Weighted sum will be strictly influenced by effective turbulence intensity in sector 7, due to the elevation to m=0 Can a sample size of 7 be representative of turbulence site conditions?

15 Setting a threshold of significant sample size in I eff computation Introducing a threshold of significant sample size removes anomalous peaks For high thresholds, there could be missing I eff results for high wind speeds

16 Conlusions Computing I eff according to IEC rd ed. leads to anomalous peaks on I eff trends Anomalous peaks are caused by high turbulence from low frequency wind sectors Introducing a threshold of significant sample size removes anomalous peaks Analyzing the I eff trend at hub height, for each site, it may be useful to define and apply a threshold of significant sample size in order to obtain more consistent results

17 Contacts Via G.L. Lagrange, Roma Tel Fax web: Ing. Beatrice Pistoni b.pistoni@studiorinnovabili.it Ing. Luigi Imperato l.imperato@studiorinnovabili.it Matteo Giannì, PhD m.gianni@studiorinnovabili.it

18 Appendix Computing Sample size D = 2σt d n, α * 2

19 Appendix (.9 IEC ed.) Normal Turbulence Model σ σ rep = I ( 0. 75V b) σ ref hub + I = A A I ref B B C C b V hub 0.2 v ref 0.4 v ref 0.6 v rate v cut-out

20 Appendix (Annex D - IEC ed.) I eff _ s ( vhub) = s w_ s r _ s hub w_ s σ T _ s hub) vhub σ r _ s + = σ. 28 σ σ [ ] m m ( N p ) σ ( v ) + p ( v m 2 hub V σ T _ s = +σ 2 0.8d i.5 + C T 2 r _ s C T = thrust coefficient for V hub d i = distance normalized by rotor diameters to neighbouring wind turbines i