Badger, Jake

Hahmann, Andrea N.

Ott, Søren

Volker, Patrick

We present a new approach, which allows us to simulate the flow distortion caused by the thrust of wind farms in a mesoscale model. The atmospheric flow is simulated with the WRF mesoscale model, since it has significantly lower computational costs compared to higher resolution models. Due to the fact that its typical horizontal grid spacing is on the order of 2km, the energy extracted by the turbine, as well as the wake development inside the turbine-containing grid-cells, are not described explicitly, but are parametrized as another sub-grid scale process.In order to appropriately capture the wind farm wake recovery and its direction, two properties are important, the total energy extracted by the wind farm and its velocity deficit distribution. In theconsidered parametrization the individual turbines apply a thrust dependent on a local sub grid scale velocity, which is influenced by the up-stream turbines. For the sub-grid scale velocity deficit, theentrainment from the free atmospheric flow into the wake region, is taken into account. Furthermore, since the model horizontal distance is several times larger then the turbine diameter, it has beenassumed that the generated turbulence and dissipation are balanced. From version 3.2.1 onwards, the WRF model includes a wind farm parametrization option (Fitch-Scheme). Contrary to the above described parametrization where the wind turbines are positioned explicitly, the wind farms in the default scheme are treated as a density distribution, which limits the description of the internal wind farm velocity deficit development and its related efficiency. In the Fitch-scheme the extracted force is proportional to the turbine area interfacing a grid-cell. The subgrid scale wake expansion is achieved by adding turbulence kinetic energy to the flow. The validity of both wind farm parametrizations has been verified against observational data. We use met. mast measurements and power measurements from wind turbines, at HornsRev. The wind farm measurements have been used to compare the total thrust produced by both types of parametrization, as well as the down-stream velocity recovery in the first 6km after the wind farm

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Wake effects of large offshore wind farms on the mesoscale atmosphereVolker, Patrick; Badger, Jake; Hahmann, Andrea  N.; Ott, SørenPublication date:2012Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Volker, P., Badger, J., Hahmann, A. N., & Ott, S. (2012). Wake effects of large offshore wind farms on themesoscale atmosphere. Poster session presented at EWEA 2012 - European Wind Energy Conference &Exhibition, Copenhagen, Denmark.Wake effects of large offshore wind farms on the mesoscaleatmospherePatrick J.H. Volker, Jake Badger, Andrea Hahman and Søren OttDTU Wind Energy, Risø Campus, Roskilde, DenmarkAbstractWe present a new approach, which allows us to simulate the flow distortion caused by the thrustof wind farms in a mesoscale model. The atmospheric flow is simulated with the WRF mesoscalemodel, since it has significantly lower computational costs compared to higher resolution models.Due to the fact that its typical horizontal grid spacing is on the order of 2km, the energy extractedby the turbine, as well as the wake development inside the turbine-containing grid-cells, are notdescribed explicitly, but are parametrized as another sub-grid scale process.In order to appropriately capture the wind farm wake recovery and its direction, two propertiesare important, the total energy extracted by the wind farm and its velocity deficit distribution. In theconsidered parametrization the individual turbines apply a thrust dependent on a local sub grid scalevelocity, which is influenced by the up-stream turbines. For the sub-grid scale velocity deficit, theentrainment from the free atmospheric flow into the wake region, is taken into account. Furthermore,since the model horizontal distance is several times larger then the turbine diameter, it has beenassumed that the generated turbulence and dissipation are balanced.From version 3.2.1 onwards, the WRF model includes a wind farm parametrization option (Fitch-Scheme). Contrary to the above described parametrization where the wind turbines are positionedexplicitly, the wind farms in the default scheme are treated as a density distribution, which limits thedescription of the internal wind farm velocity deficit development and its related efficiency. In theFitch-scheme the extracted force is proportional to the turbine area interfacing a grid-cell. The sub-grid scale wake expansion is achieved by adding turbulence kinetic energy to the flow. The validityof both wind farm parametrizations has been verified against observational data. We use met. mastmeasurements and power measurements from wind turbines, at HornsRev. The wind farm mea-surements have been used to compare the total thrust produced by both types of parametrization,as well as the down-stream velocity recovery in the first 6km after the wind farm.Fitch-schemeFrom version 3.2.1 onwards, the WRF model includes a wind farm parametrization option (FitchScheme) adapted from (blahak et al 2010). In this parametrization the wind turbines are treated asa density function. All turbines will experience the same up-stream velocity, equal to the grid-cellvelocity. The implemented equation for the thrust readsTk =Ct Nij Ak v2h,k2 (∆x)2∆zkNi,j is the number of turbines located in grid-cell (i,j), Ak the turbine blade segment intersectingwith the model level k, ∆x the horizontal grid-spacing and vh,k the horizontal velocity. It has beenassumed that the turbulence kinetic energy inside a turbine effected grid-cell will experience apartfrom the increased shear an additional source proportional to the cube of the wind speed. Theinfluence on the turbulence length scale, the dissipation as well as the stability function has notbeen considered. In the model we find for the qke = u′2i , i = 1,2,3, which is equal to twice theturbulence kinetic energyqke(model+wake) = qke(model) + αNij Ak v3h,k ∆t(∆x)2 ∆zkwhere α = Ct − CpNew AppoachThe new approach is following the classical far wake theory (see e.g. Tennekes and Lumley, 1972),which assumes that the far velocity deficit region can be described by one characteristic length scaleℓ and one velocity scale Us (maximum velocity deficit). Since the horizontal distance in the model isseveral times larger then the turbine diameter, it has been assumed that the generated turbulenceand dissipation are balanced. In this way it is possible to determine explicitly the influence of eachturbine on any down-stream turbine, thereby addressing the efficiency issue. From the diffusionequation we can obtainℓ2 =(2 KmU0)x + ℓ20 (1)Eq. (1) describes the down-stream evolution of the velocity deficit region due to entrainment pro-cesses. U0 is the hub-height velocity, Km turbulence coefficient for momentum and ℓ0 the initiallength scale, which has to be determined from measurements.Following the literature (e.g. Tennekes and Lumley, 1972) we can write for small velocity deficitsU = U0 − Usf (z,ℓ) From the definition of the thrust, we can obtain for the velocity deficitUs =U0√21−(1− Ct A20√π W ℓ)12 (2)(1) and (2) form the full set of equations that describe the velocity deficit completely.For the mesoscale field we used ℓ from (1) and assume that the wake width is equal to the horizontalgrid spacing. This gives us Us from (2) and we obtain for the total thrustCT A0U202 V=1VW∞∫−∞Usf(U0 − Usf)dz =1Vkmax∑k=1Tk (3)The r.h.s. will be applied to all model levels k . The up-stream velocity U0 comes from the wind farmparametrization, which take into account turbine-turbine interaction using (1) and (2) to transportlocal (unresolved for the mesoscale model) wakes.The constants ℓ0 and α were obtained from a comparison between a ”standalone” version of themodel and Vindeby fast measurement data. We obtained α = 1 and ℓ0 = 0m. In the figure belowthe result for a single wake at Vindeby has been plotted.Left: Normalized velocity deficit Uwake(k) −U(k)/U0 for the measurements (black line)and the model (grey line). Right: Measuredupstream velocity (dots) and the logarithmic fit(dotted line), the downstream measurements(squares) and the measurement interpolation(black line) plus the model wake velocity (greyline).Validation at HornsrevWe used for the validation 10-min averaged data from top mounted cup anemometers M2 (63m), M6(70m) and M7 (70m), the wind vane at 60m on M2 and the power measurements from the turbinesin row 4 and 5 at Hornsrev. We selected only data from the met. masts in the up-stream winddirections betweeen 255◦ ≤ θ ≤ 285◦. The up-stream wind speed interval was selected in therange of 8m/s ≤ U63 ≤10m/s, so that the corresponding time average wind speed at 70m was9.3m/s (equal to the model hub-height wind speed).The model consists of 60×50 horizontal levels, had in total 60 vertical levels and ∆x =1400m. Themesoscale model was initialized with a constant geostrophic wind Ug =11m/s and Vg = -2m/ssuch that it converged to a wind profile with a hub height velocity of 9.3m/s with an angle of 270◦.The wind farm was placed in 5×4 grid-cells, each of them containing 4 turbines. For both schemeswe used the Ct from the thrust curve.Velocity deficit recoveryWe normalized the wake measurements of M6 (8300m) and M7 (12300m) with the corrected (log-arithmic extrapolation to 70m) wind speed from M2. From the power measurement we derivedthe corresponding hub-height wind speeds via the power curve. To be data consistent the derivedvelocities were normalized by the wind speed of the first row.The abscissa indicates the down-stream dis-tance from the first turbine onwards. The dotsup to 6300m represent the averaged normal-ized hub-height velocities from row 4 and 5 andthe dots at 8300m and 12300m are the aver-aged normalized velocities at hub-height fromM6 and M7 respectively. The solid line is a partof the parametrization of the new approach andrepresents the local hub-height velocities of theturbines. The dashed lines are the model out-puts, whereas the symbols mark the model out-put position.The Fitch-scheme produces a deeper wake then the new approach. Inside the wind farm it reachesthe measured local turbine velocities.Total ThrustComparison of the total modeled thrust with the measured thrust.For the Fitch-scheme:Ti,j =kmax∑k=1Ct Nij Ak v2h,k2 (∆x)2∆zk.For the new approach we have:Ti,j =WV∑nturbkmax∑k=1((U0,i−Us,i fk)Us,ifk)∆zkFor the measurements, we use the power and thrust curve to achieve the thrust per turbine. Wesum up groups of four turbines to measure the equivalent total thrust per grid-cell:Ti,j =4∑n=10.5 Ct,n A20 U2n /V where V = D0 (∆x)2Since the turbine hub-height velocity deviates from the met. mast up-stream velocity, we selected8m/s ≤ U0 ≤11m/s to achieve an average velocity of 9.2m/s at the first turbine (compared to9.3m/s of the model).The total thrust per grid-cell for the modelsand the corresponding measured thrustare plotted. The dots represent thedown-stream grid-cell thrusts per volume.From this figure we can conclude that theFitch scheme overestimates the energyextracted from the flow by almost an orderof magnitude. The new-approach followsthe measured thrust.For instance, we see that in the graph onthe left side, where the normalized veloc-ity deficit (Udown − Uup)/U0 has beenplotted, the velocity deficit of the Fitchscheme penetrates from the first grid-cellon deep in the PBL. We notice also thatthe maximum velocity deficit due to the en-hanced turbulence has been transportedupwards. Furthermore large positive ve-locity deficits at the lower boundary areobtained due to the high turbulence mix-ing.ConclusionsIn this paper we present a new approach which allows to simulate the flow distortions caused by windfarms in a mesoscale model. We compared the new approach and the wind farm parametrizationimplemented in the WRF mesoscale model (Fitch-scheme) against 10-min averaged velocity datafrom the large wind farm Hornsrev at the west coast of Denmark. The results showed that thethrust applied to the flow is overestimated by almost one order of magnitude in the Fitch-scheme.Furthermore we found that the created turbulence kinetic energy diffuses the velocity deficit deepinto the boundary layer and causes unnaturally high positive velocity deficits at the lower boundary.Both deficiencies would have consequences on the analysis of the impact of wind farms on theatmosphere as well as its ocean feedbacks. With the new approach we applied the same thrust tothe flow as has been measured. Since the recovery of the velocity deficit matched with the at 6kmdown-stream located met. mast M7 measurements, we can conclude the vertical distribution of thevelocity deficit is well described by the new approach.FundingWAUDIT-Project (Marie Curie ESR)EWEA 2012, Copenhagen, Denmark: Europe’s Premier Wind Energy Event

Wake effects of large offshore wind farms on the mesoscale atmosphere

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Wake effects of large offshore wind farms on the mesoscale atmosphere

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