SAWEP Workshop. and. Hans E. Jørgensen Head of programme Meteorology Wind Energy Division Risø DTU. Cape Town, 4 th March 2010

Transcription

1 SAWEP Workshop Wind Atlas for South Africa (WASA) Cape Town, 4 th March 2010 WAsP Engineering Introduction and Extreme winds and design conditions for turbine By Hans E. Jørgensen Head of programme Meteorology Wind Energy Division Risø DTU

2 The models behind WAsP Engineering LINCOM, a linearized flow model Fetch- and wind-speed-dependent water roughness Spatial structure of turbulence over flat terrain Modification of turbulence due to orography and roughness changes Turbulence simulation Extreme wind statistics

3 Examples of problems Middelgrunden wind Farm to the east of Copenhagen: How much is turbulence and the 50-year wind affected by Copenhagen?

4 Complex terrain How much is the 50 year wind enhanced? How is the local turbulence? Are local shear and flow inclination angles too high? How steep is the terrain?

5 Check of different wind directions in complex terrain? Winds from 330º flow inclination OK at turbine positions negative velocity gradient at some positions

6 Windfarm Assessment Tool Check IEC site assessment rules, including effective turbulence by Frandsen model

7 Lexicon Orography Measured wind Obstacles Surface roughness Wind profile Friction velocity Fetch Displacement height ht Atmospheric stability Velocity shear Flow inclination angle Flow speed up factor Flow separation Geostrophic wind Reduced geostrophic wind Geostrophic drag law Power spectrum Taylor s hypothesis Micro-/Meso-/Macroscale /Macroscale Weibull distribution Gumbel plot mkel1

8 Slide 7 mkel1 added Weibull and Gumbel, is that ok? Mark Kelly, 08/01/2009

9 Wind direction, flow angle, shear Wind direction is the compass direction from where the wind is coming N θ Flow inclination is the tilt angle (φ) of the velocity vector with respect to horizontal Wind shear is the vertical gradient of the horizontal variation of the wind speed u z u z variation of the wind speed Δu ( 2) ( 1) Wind shear exponent (α) is defined by a power-law fit to the wind profile, ( ) = ( ) u z u z z hub hub α = Δz z z 2 1 z u(z) d u z z u z z z dz α ( ) = α ( ) hub hub hub hub hub z du α 1 1 ( g for a log-profile) l( ln( ) hub α fit = (e.g. α fit = uhub dz hub zhub z0

10 Three types of winds in WAsP Engineering Geostrophic wind: {u, Dir} above atmospheric boundary layer Measured wind: u and Dir observed at h in real terrain Reduced geostrophic wind: u and Dir at reference h over idealized flat terrain with uniform z 0 Geostrophic drag law 2 u u B G = A + B = κ fz 0 * * 2 ln, tanα fz u 0 * ln A

11 Turbulence Reynolds decomposition Standard variation and turbulence intensity u = u + u' σ = u' 2 I = u u σ u u Distribution among velocity components for neutral conditions and flat terrain σ u = Au* σv σu σw σu A

12 Schematic spectrum

13 Extreme winds and Definitions 1. The 50 year wind is the wind speed which on average is exceeded d once in 50 years by the 10 minute averaged wind speed 2. The 50 years is called the return period 3. The 10 minutes is called the averaging time Distribution of one-year maxima & extrapolation to 50 years ( ) 1 ( ) ( ) = 1 T T P u u = F u = T T F u

14 The Gumbel extreme distribution tion Cumulated probability 1 Linear plot using return periods F(U1yr) 0.5 U1yr) f(u (U 1yr -β)/α Probability bilit density function (U 1yr -β)/α F( UT ) = 1 0 ( U) = ( ( U β α) ) UT β α ( ) = exp ( exp ( ( β ) α ) ) exp ( ( β ) α ) α U α ln ( T T ) F exp exp ( ) f U U U T T ( ( T0 T) ) ( ) = ln ln 1 T 0 + β

15 WEng extreme winds by observation

16 WEng extreme winds by reanalysis data (form NCEP/NCAR) Pressure at model surface P s P 0 = P exp Pressure at the sea level l P o s gh RT m WP5 will create an atlas based on Meso-scale simulations u g 1 ΔP 1 ΔP =, vg = f ρ 2 a Δφ f ρ 2 a Δλ cos φ Geostrophic wind by pressure gradient u * u * G = ug + vg = ln A + B κ fz Surface wind at 10 m with z 0 =5cm u 10 u* 10m = ln κ z Regional extreme wind climate (REWC) 0 2

17 WEng and IEC site assessment Technical consultant Land owner Finance Measurement Project developer Wind farm owner Turbine manufacturer Authorities Power utility

18 Engineering standards National standards Dansk Standard (DS) British Standard (BS) Deutsche Institut für Normung (DIN) + many others International standards Intl. Organization for Standardization (ISO) Intl. Electrotechnical Commission (IEC) + many others WA sp

19 IEC (Ed. 3) turbine classification scheme Wind conditions in design load cases modelled by V ref I ref hub-height fifty-year extreme wind reference turbulence intensity in a 10-min period z hub hub-height Differences in IEC (Ed. 2) extra wind turbine class IV with V ref = 30 m/s no turbulence category C turbulence parameterized by I 15 (μ+σ) instead of I ref (μ) (see CTI ) WA sp

20 IEC Design Load cases Turbine operation normal power production start up and shut down control failure or network failure parked or idling state yaw error Wind conditions Extreme wind Wind distribution Turbulence Wind shear Dynamic events Load type Fatigue loads Ultimate load

21 IEC wind profile Power law Fitting power law to data z ( ) ( ) α u z = u z z ( ) = ( ) hub u(z) hub α e.g. d α u z z u z z dz hub hub hub hub zhub α = fit hub 0 z u 1 α fit = ln ( z z ) hub hub du dz hub α 1 for logarithmic profile Shear parameter (α) normal shear α = 0.11 enhanced shear α = 0.2

22 IEC Extreme-wind model V hub Yaw error Turbulence Shear V 50yr =1.4 V ref no no moderate 1 V 1yr = V ref ±15º no moderate V 50yr =1.0 V ref no σ 1 =0.11V hub moderate V 1yr =0.8 V ref ±15º σ 1 =0.11V hub moderate 1 the moderate ( normal ) shear exponent is α=0.11

23 Observed ed 10-min turbulence intensities Reasons for scatter Variable stability Trend WA sp

24 IEC normal-turbulence rb lence model pdf Weibull distribution with k=2 π u π u = exp 2uave 4u ( ) 2 p u 2 ave V ave =0.2 V ref Edition 2 Edition 3 Classification scheme I 15 I ref reference TI Design rules I char characteristic TI I rep representative TI ( ) ( ) ( V ) σ = I 15m/s + av 1 + a Edition hub σ = I m/s Edition 3 1 ref hub WA sp

25 Turbulence simulation Multivariate Fourier simulation Veers method (1988) 3D Fourier simulation WASP Engineering WA sp

26 From wind to loads on turbines Rotor aerodynamics Loads on blade element Structural dynamics Nacelle Node Blade y b Tower x b z b ( 1 ) 1 ( ) U = a U = C U U induction aa, 0 T 0 0 inflow angle α ( ) ( α ) lift and drag C α, C axial and tangential forces ( φ) ( φ) ( φ) ( φ) C = cos C + sin C L N L D C = sin C cos C T L D D Mx &&() t + Cx& () t + Kx() t = F() t WA sp

27 Aeroelastic load simulations Fatigue load criteria safe after 20 years with standard Weibull distribution (k=2, V ave =0.2V ref ) and enhanced wind shear α=0.2 and flow inclination angles of ±8º and a representative number of start/stop situations WA sp

28 Dynamic wind events ents for IEC load cases Amplitudes depend on turbine class and wind speed WA sp

29 IEC site assessment rules Class I V ref 50 m/s Checklist Extreme winds Shear of vertical wind profile Flow inclination Background turbulence II 42.5 m/s Wake turbulence III 37.5 m/s Wind-speed distribution IV* S 30 m/s Designer specifies averaged over all directions for any direction

30 Modeling by WASP Engineering Extreme winds Shear of vertical profiles Inclination of terrain and flow lines Turbulence intensity Wind-speed probability distribution calling WASP from a script Effective turbulence intensity IEC wake model with Windfarm Assessment Tool (WAT)

31 IEC turbulence model Characteristic TI (IEC ed.2) ( 15 m/s ) ( 1 ) σ = I + av + a 1 15 hub Representative TI (IEC ed.3) ( ) ( ) σ 1 = Iref 15 m/s + avhub 1 + a m/s IEC edition 2 IEC edition 3 Class I 15 a Class I ref a A A B B S Designer specifies C S Designer specifies I ref 1 + a = IWEng a 1.44m s I 15 = I ref 1+ 15m s

32 IEC complex terrain indicator 1. fit big circle 2. check slope 3. fit small circles 4. check displacement σ σ + σ σ enhanced TI in complex terrain! ( 2 1) ( 3 1 ) C = complex 1.375

33 Wake turbulence in the IEC standard Risø-R-1188(EN)

34 IEC effective e turbulence Small m ductile material e.g. steel Large m brittle material e.g. glass fiber Traditional fatigue-load calculus m neqivalent Sref = ni S m i Effective turbulence is a weighted average depending on Wöhler coefficient m Ieff ( u) I u p u d 2π m = actual ( θ ) ( θ ) θ 0 Optional whether to apply a uniform or actual wind distribution m 1

35 IEC effective e turbulence (2) IEC model for wake turbulence with I = I + I 2 2 wake added ambient I = added d 2 ( d u) Basic Frandsen formula I = 2 1 added = 2 ( d CT )

36 IEC effective e turbulence (3) exposure angle is fixed to 21.6 deg ignore distant turbines Δx>10 d rotor no wake superposition enhance background turbulence in large dense wind farms, i.e. farms with more than five rows of turbines in the predominant wind direction and column separation less than three rotor diameters ( ) 2 2 I = I + I + I I w 1 2 w dd 1 2 C T Approximation for irregular layout 0.36 Iw = Δθ d N C = + ( ) sec 2 max sec T

37 Verification of wake model I I_w_mod add d Quarton Crespo I_ad I add Andros Taff Ely Alsvik Vindeby Separations, s s=x/d 0

38 Conditional wind-direction direction distributiontion 2π m Ieff ( u) = Iactual ( θ u) p( θ u) dθ 0 p ( θ u) ( θ) p( θ) p u = = N ( ) = (, ) p ua k j j j (, ) 1 p u p ua i 0 i ki fi f m 1 using WASP sector-wise wind climates 1. Frequency, f 2. Weibull scale parameter, A 3. Weibull shape parameter, k 1 j j u ( j, j) = exp ( uaj) pua k k k k j A j A j

39 Site assessment with WEng + WAT wind WAT 2.0 Excel (requires WAsP) sites height

40 Script output be patient export results to ASCII file

41 Windfarm Assessment Tool (WAT) input, export & help site list results plots & options speed material plot options windfarm plot

42 Windfarm layout Extreme wind Streamline inclination

43 Turbulence plot Effective turbulence NB: Effects of wind and material constant affects turbulence! Background turbulence Added wake turbulence

44 Effective e turbulence (2)

45 Comparison of actual al and design PDFs IEC rules: design PDF is Rayleigh distribution with V ave =0.2V ref actual al PDF must be less than design PDF in speed range [0.2V ref..0.4v 04V ref ]

46 Summary Modern site assessment for a wind farm involves both estimates of resources and external design conditions, they even sometimes go hand in hand e.g. high resources in complex terrain => large loads Proper estimates of external conditions optimizes the material use in wind turbines => increase the competitiveness of wind energy compared to conventional energy types