Downloaded from orbit.dtu.dk on: Jul 22, 208 Wake decay constant for the infinite wind turbine array Application of asymptotic speed deficit concept to existing engineering wake model Rathmann, Ole Steen; Frandsen, Sten Tronæs; Nielsen, Morten Published in: EWEC 200 Proceedings online Publication date: 200 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Rathmann, O., Frandsen, S. T., & Nielsen, M. (200). Wake decay constant for the infinite wind turbine array: Application of asymptotic speed deficit concept to existing engineering wake model. In EWEC 200 Proceedings online European Wind Energy Association (EWEA). General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
WAKE DECAY FOR THE INFINITE WIND TURBINE ARRAY Application of asymptotic speed deficit concept to existing engineering wake model Ole Rathmann, Sten Frandsen and Morten Nielsen Risoe-DTU, National Laboratory for Sustainable Energy Acknowledments: Dong, Vattenfall for providing data EU Upwind, Danish Strategic Research Council, Energinet.dk (PSO) for sponsoring the work Technical topic Wakes ID265 Wake Decay for the Infinite Wind Turbine Array []
WAKE DECAY FOR THE INFINITE WIND TURBINE ARRAY Application of asymptotic speed deficit concept to existing engineering wake model Outline Background Asymptotic speed deficit from boundary layer considerations WAsP Park model details Asymptotic speed deficit of the WAsP Park model Adjustment of WAsP Park model Comparative wind farm predictions Conclusions Wake Decay for the Infinite Wind Turbine Array [2]
Background Very large wind farms: Standard wake models seems to underpredict wake effects. Recent investigations by Sten Frandsen [, 2]: The reason is the lack of accounting for the effect a large wind farm may have on the atmospheric boundary layer, e.g. by modifying the vertical wind profile. In some way the effect of an extended wind farm resembles that of a change in surface roughness: increased equivalent roughness length. Idea: While more detailed models are underway [3], modify the existing WAsP Park engineering wind farm wake model to take this boundary-layer effect into account. [] Frandsen, S.T., Barthelmie, R.J., Pryor, S.C., Rathmann, O., Larsen, S., Højstrup, J. and M. Thøgersen, Analytical modelling of wind speed deficit in large offshore wind farms. Wind Energ. 2006, 9: 39-54. [2] Frandsen, S: The wake-decay constant for the infinite row of wind turbine rotors. Draft paper (2009 ). [3] Rathmann O., Frandsen S, Barthelmie R., Wake Modelling for intermediate and large wind farms, Paper BL3.99, EWEC 2007 Wake Decay for the Infinite Wind Turbine Array [3]
Asymptotic speed deficit from boundary layer considerations () When should a wind farm be considered as large/infinite? (Hand drawing illustrating the initial idea) Wake Decay for the Infinite Wind Turbine Array [4]
Asymptotic speed deficit from boundary layer considerations (2) BL-Limited infinite wind farm Geostrophic wind speed U ( z z > H ) = G Roughness z 00 ln(z) H Outer layer Friction velocity u 0 Hub height shear t = ρc 2 t U h U h Jump in friction velocity at hub-height due to rotor thrust: ρ(u * eff ) 2 = ρ(u *i ) 2 + t Inner layer u i, z 0 c 2 t = π/8 C t /(s r s f ), t = ρc t U h s r and s f : dimensionless* WTG-distances (along- and across-wind) *by D rotor Z<h: profile according to ground surface friction velocity u *i / roughness z 0. U Approximation: homogeneously distributed thrust c t Z>h: profile according to increased friction velocity u eff * (= u *0 ) / roughness z eff 0 (=z 00 ). ( ) eff Equivalent, effective surface roughness: z = h exp κ / c + ( κ / ln( h / z )) 0 H t H 0 2 Wake Decay for the Infinite Wind Turbine Array [5]
Asymptotic speed deficit from boundary layer considerations (3) Approximate geostrophic drag-law G u ln κ G fz 0 A G General hub-height wind speed: Uh ( ) = ln G + A* i h f Free flow: i = /ln h 0 z 0 Flow over wind farm: i = i + i i = 2 2 Tot 0 add, add c κ t G + ln i ' h f Relative speed deficit ε: ε = G + ln i h f ' 0 Tot Wake Decay for the Infinite Wind Turbine Array [6]
Asymptotic speed deficit from boundary layer considerations (3) Comparison with wind farm (Horns Rev): 0.9 s r s f 7, h=80m, D R = 60 m 0.85 Wake deficit about 50% of the BLlimiting value. Horns Rev wind farm NOT infinite. Speed ratio 0.8 0.75 0.7 Ct=0.4, z0=0.0 0 0 Ct=0.4, Z0=0.0002 Ct=0.8, z0=0.0 Ct=0.8, z0=0.0002 Data 0.65 4 6 8 0 2 4 6 Free wind speed (m/s) Distance for severe wake interference (k wake =0.075) Horns Rev Power density (W/m 2 )[4] Actual extension Horns Rev 2MW turb s (observed) Entire North Sea 5 MW turb s (Frandsen BL-limited) 7.5 km 5 km 2.9.8 [4] Barthelmie,R.J., Frandsen,S.T.,., Pryor, S.C., Energy dynamics of an infinitely large offshore wind farm., Paper 24, European Offshore WInd 2009 Conference and Exhibition, Stockholm, Sweden (Sept. 2009). Wake Decay for the Infinite Wind Turbine Array [7]
WAsP Park Model Details Wake Evolution and speed deficit [5,6] Adir.overlap( =A (R) ) Aref.overlap Speed deficit from single wake: D ( yp ) ( t ) A ( type ) 0 type overlap 0 0 ( R) D0 + 2kX0 A δvδ V = U C, ( type) = " dir.", " ref." Resulting speed deficit at a downwind turbine: dir ref ((, ) (, ) ) δv = δv + δv 2 (.) 2 (.) 2 turb i turb i turb i upwturb. ' s 2 [5] N.O.Jensen, A Note on Wind Generator Interaction, Risø-M-24, Risø National Laboratory 983. [6] I.Katic, J.Højstrup, N.O.Jensen, A Simple Model for Cluster Effeciency, Paper C6, EWEC 2006, Rome, Italy, 986. Wake Decay for the Infinite Wind Turbine Array [8]
Asymptotic speed deficit of the WAsP Park model Speed deficit for a turbine in an infinite wind farm Speed deficit the same for all turbines, thus also the turbine thrusts. Infinite (convergent!!) sum: ( ) 2 δ 2 D ( ) ( ) 2 R V U ε upwind 0 N( s ) ε j w( xj ) ; ε = w( x) = ; ε 0 = Ct j= The infinite sum may be approximated by an infinite integral - a simple function G: δ V Park = G k; sr, s f, h/ DR, Ct U ε D R + 2kx x j : Distance to upwind turbine row j. N(x j ): number of turbines row j throwing wake on the rotor in focus. U upwind : Wind speed immediately upwind of a turbine upwind 0 ( ) 2.5 0.5 2 G park s r = s f = 7; h/d R = Since U upwind = U w = U free -δv: 0 0 0.02 0.04 0.06 0.08 0. 0.2 0.4 Wake expansion coefficient k δv U Free app ε w app park = εw = ; εw = ε0g ( layout; k) app + ε w Wake Decay for the Infinite Wind Turbine Array [9]
Adjustment of the WAsP Park model Adjustment to match the BL based asymptotic speed deficit For deep positions the wake expansion coefficient k of the Park Model is modified to approach the BL-based asymptotic speed deficit value k inf : δvinfin. park ( kinf ;[ sr, sf, h, Ct ]) = δvbl based ( sr, sf, h, Ct ) Wake expansion coefficient k Original Adjusted to match asymptotic speed deficit The k-change applies when a wake overlaps with a downwind rotor (to both wakes involved), using a relaxation factor F relax : A adj adj adj overlap k = k + ( k + k ) F A j j inf j relax w The change of the wake expansion cofficient is indicated. segment j segment j+ Model-paramters used in the following (based on Horns Rev data): k initial := 0.075 (recommended value for onshore!) F relax = 0.2 relax Wake Decay for the Infinite Wind Turbine Array [0]
Comparative wind farm predictions: Horns Rev () Turbines: 2MW, D R = 80m, H hub = 60m Layout: s r = s f = 7 Wake Decay for the Infinite Wind Turbine Array []
Comparative wind farm predictions: Horns Rev (2) ed el. reduced wind spee R e 0.9 0.8 Horns Rev - 8.5 m/s - 270 o Data Pred. BL-Adjusted Pred. Std. park Wind direction: 270 o +/- 3 o Wind speed: 8.5 m/s +/- 0.5 m/s 0.7 0 2000 4000 6000 Downwind distance [m] Horns Rev - 2.0 m/s - 270 o Data - int.line Data - ext.line Pred. BL-Adjusted d Re el. reduced wind speed 0.9 0.8 Pred. Std. park Wind direction: 270 o +/- 3 o Wind speed: 2.0 m/s +/- 0.5 m/s 0.7 0 2000 4000 6000 Downwind distance [m] Wake Decay for the Infinite Wind Turbine Array [2]
Comparative wind farm predictions: Horns Rev (3) Rel. R reduced wind speed 0.9 08 0.8 Horns Rev - 8.5 m/s - 222 o (int.line) Data - int.line Pred. BL-Adjusted Pred. Std. park Rel. reduced wind speed 0.9 08 0.8 Horns Rev - 8.5 m/s - 222 o (ext.line) Data - int.line Pred. BL-Adjusted Pred. Std. park Wind direction: 222 o +/- 3 o Wind speed: 8.5 m/s +/- 0.5 m/s 0.7 0 2000 4000 6000 Downwind distance [m] 0.7 0 2000 4000 6000 Downwind distance [m] Rel. reduced wind speed d 0.9 0.8 Horns Rev - 2.0 m/s - 222 o (int.line) Data - int.line Pred. BL-Adjusted Pred. Std. park Rel. reduced wind spee ed 0.9 0.8 Horns Rev - 2.0 m/s - 222 o (ext.line) Data - int.line Pred. BL-Adjusted Pred. Std. park Wind direction: 222 o +/- 3 o Wind speed: 2.0 m/s +/- 0.5 m/s 0.7 0 2000 4000 6000 Downwind distance [m] 0.7 0 2000 4000 6000 Downwind distance [m] Wake Decay for the Infinite Wind Turbine Array [3]
Comparative wind farm predictions: Nysted () Turbines: 2.33 MW, D R = 82m, H hub = 69m Layout: s r = 0.6, s f = 5.9 Wake Decay for the Infinite Wind Turbine Array [4]
Comparative wind farm predictions: Nysted(2) Rel. reduced turbine power 0.8 0.6 Nysted -0.0 m/s - 278 o Data Pred. BL-Adjusted Pred. Std. park Wind direction: 278 o +/- 2.5 o Wind speed: 0.0 m/s +/- 0.5 m/s 0.4 0 2000 4000 6000 Downwind distance [m].2 Rel. reduced turbine power 0.8 Nysted -0.2 m/s - 263 o Data Pred. BL-Adjusted Pred. Std. park Wind direction: 263 o +/- 2.5 o Wind speed: 0.2 m/s +/- 0.5 m/s 0.6 0 2000 4000 6000 Downwind distance [m] Wake Decay for the Infinite Wind Turbine Array [5]
Conclusions The adjustment of the wake expansion coefficient towards a value matching the BL-limited asymptotic speed deficit seems a valuable engineering approach A value for the wake expansion coefficient close to that normally used for onshore locations seems reasonable in this approach also for off-shore wind farms The model (relaxation factor) needs to be fine-tuned in order not to produce over estimations. The model needs to be tested t on situations ti with wake effects between neighboring wind farms. Wake Decay for the Infinite Wind Turbine Array [6]