Badger, Jake

Hahmann, Andrea N.

Ott, Søren

Volker, Patrick

The project’s objective is to investigate and develop methods for prediction of mesoscale climate, wake effects and atmospheric feedbacks, for scenarios where large portions of the sea are covered with wind farms. The atmospheric flow is simulated with the WRF mesoscale model, since it has significantly lower computational costs compared to high 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, among others, the total energy extracted by the wind farm and its velocity deficit distribution. In the considered parametrization the individual turbines produce a thrust dependent on the background velocity. For the sub-grid scale velocity deficit, the entrainment from the free atmospheric flow into the wake region, which is responsible for the expansion, is taken into account. Furthermore, since the model horizontal distance is several times larger then the turbine diameter, it has been assumed that the generated turbulence and dissipation are balanced. From version 3.2.1 onwards, the WRF (Weather Research and Forecast) model includes a wind farm parametrization option (Fitch Scheme). In 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 wind turbines act as drag devices, where 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 (proportional to the extracted power) to the flow. The validity of both wind farm parametrizations has been verified against observational data. We use Synthetic Aperture Radar (SAR) satellite data, as well as mast measurements from meteorological masts and power measurements from wind turbines, at Horns Rev and Nysted. From the SAR satellite data the wake extension can be derived. The wind farm measurements have been used to compare the total thrust produced by both types of parametrization. In case studies the wake deficit has been estimated by the deflection of the wake due to the slowing down of the wind speed. The results of the wind farm parametrization will be used to investigate eventual climate impacts of large wind farms. Furthermore it will develop techniques for up-scaling the effects simulated by wind farm wake models into mesoscale atmospheric planetary boundary layer (PBL) parameterisations and perform simulations using these parameterisations to understand the feedbacks between the wind farms and the regional wind climate. The work will extend the current knowledge about wake effects from observations and small-scale models to potential feedbacks in the PBL atmosphere

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Downloaded from orbit.dtu.dk on: Dec 20, 2017Wind Farm parametrization in the mesoscale model WRFVolker, Patrick; Badger, Jake; Hahmann, Andrea  N.; Ott, SørenPublished in:ProceedingsPublication 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). Wind Farm parametrization in the mesoscale modelWRF. In Proceedings European Wind Energy Association (EWEA).Wind Farm parametrization in the mesoscalemodel WRFPatrick Volker(1), Jake Badger(1), Andrea Hahman(1), Søren Ott(1)(1) DTU Wind EnergyFrederiksborgvej 399DK-4000 RoskildeDenmarkSubmitted abstractThe project’s objective is to investigate and develop methods for predictionof mesoscale climate, wake effects and atmospheric feedbacks, for scenarioswhere large portions of the sea are covered with wind farms. The atmosphericflow is simulated with the WRF mesoscale model, since it has significantly lowercomputational costs compared to high resolution models. Due to the fact that itstypical horizontal grid spacing is on the order of 2km, the energy extracted by theturbine, 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 direc-tion, two properties are important, among others, the total energy extracted by thewind farm and its velocity deficit distribution. In the considered parametrizationthe individual turbines produce a thrust dependent on the background velocity.For the sub-grid scale velocity deficit, the entrainment from the free atmosphericflow into the wake region, which is responsible for the expansion, is taken intoaccount. Furthermore, since the model horizontal distance is several times largerthen the turbine diameter, it has been assumed that the generated turbulence anddissipation are balanced.From version 3.2.1 onwards, the WRF (Weather Research and Forecast) modelincludes a wind farm parametrization option (Fitch Scheme). In contrary to theabove described parametrization where the wind turbines are positioned explicitly,the wind farms in the default scheme are treated as a density distribution, whichlimits the description of the internal wind farm velocity deficit development andits related efficiency. In the Fitch Scheme the wind turbines act as drag devices,where the extracted force is proportional to the turbine area interfacing a gridcell. The sub-grid scale wake expansion is achieved by adding turbulence kineticenergy (proportional to the extracted power) to the flow. The validity of bothwind farm parametrizations has been verified against observational data. We use1Synthetic Aperture Radar (SAR) satellite data, as well as mast measurementsfrom meteorological masts and power measurements from wind turbines, at HornsRev and Nysted. From the SAR satellite data the wake extension can be derived.The wind farm measurements have been used to compare the total thrust pro-duced by both types of parametrization. In case studies the wake deficit has beenestimated by the deflection of the wake due to the slowing down of the wind speed.The results of the wind farm parametrization will be used to investigate even-tual climate impacts of large wind farms. Furthermore it will develop techniquesfor up-scaling the effects simulated by wind farm wake models into mesoscale at-mospheric planetary boundary layer (PBL) parameterisations and perform simula-tions using these parameterisations to understand the feedbacks between the windfarms and the regional wind climate. The work will extend the current knowledgeabout wake effects from observations and small-scale models to potential feed-backs in the PBL atmosphere.1 IntroductionFrom the mid-nineties onwards several off-shore wind farms have been installed. Inthe coming years at least two larger clusters, one in the German Bight and the otherin the Dogger bank (http://www.forewind.co.uk/) will arise. Therefore Clusteroptimization as function of e.g. wind farm design, grid structure, electricity supplyand/or wind-farm interaction (see e.g. the EERA-DTOC project1)) became a topic ofinterest. In the presented study we concentrate on the description of a single wind farmwake, which later-on can be used for the study of wind farm interaction. With the ac-tual tools and computer resources the most reasonable candidates to analyze the windfarm interaction and possible regional climate impacts are Mesoscale- and linearizedCFD-Models (see e.g. FUGA ren et al., 2011). Both methods have there disadvan-tages. The first option is not able to describe the individual turbine wakes explicitly,whereas the second option, generally, can not take into account the atmospheric condi-tions, which are important in the far wake regime. In this paper we will focus on thefirst alternative and present a new wind farm parametrization approach. In first placewe will aim to extract the right amount of energy and to take the sub-grid scale de-velopment of the velocity deficit into account. The typical horizontal grid spacing isof the order of kilometers and the vertical spacing in our simulations will be around10 meters in the near surface region. Due to the coarse horizontal grid spacing theenergy extracted by the turbine, as well as the wake development inside the turbine-containing grid-cells, cannot be described explicitly and is parametrized just as othersub-grid scale processes. In the following section we will motivate the physics behindthe new wind farm parametrization approach, then its implementation and the verifi-cation will be discussed. For our study we used the mesoscale model WRF (WeatherResearch and Forecast Model) (Skamarock et al., 2008). From WRFV3.2.1 onwardsit contains a wind farm parametrization option (Fitch), which will be used as refer-ence in the verification. This option is dependent on the MYNN Planetary Boundary1European Energy Research Alliance-Design Tools for Off-shore wind farm Clusters2Layer (PBL) scheme (Nakanishi and Niino, 2009), whereas the new parametriationis PBL-scheme independent. For consistency reasons the MYNN-scheme has beenused during our analysis. Before we introduce the new approach we will first describeshortly the WRF Wind Farm option and the motivation for a new approach. Thereafterboth parametrizations will be compared to in-situ and remote measurements.2 Fitch WRF Wind-Farm ParametrizationFrom version 3.2.1 onwards, the WRF model includes a wind farm parametrizationoption (Fitch Scheme) adapted from Blahak et al., 2010. In this parametrization thewind turbines are treated as a density function. All turbines will experience the sameup-stream velocity, equal to the grid-cell velocity. The implemented equation for thethrust readsTk =Ct Ni j Ak v2h,k2 (∆x)2∆zkNi, j is the number of turbines located in grid-cell (i,j), Ak the turbine blade segmentintersecting with the model level k, ∆x the horizontal grid-spacing and vh,k the hori-zontal velocity. It has been assumed that the turbulence kinetic energy inside a turbineeffected grid-cell will experience apart from the increased shear an additional sourceproportional to the cube of the wind speed. The influence on the turbulence lengthscale, the dissipation as well as the stability function has not been considered. In themodel we find for the qke = u′2i , i = 1,2,3, which is equal to twice the turbulencekinetic energyqke(model+wake) = qke(model)+αNi j Ak v3h,k∆t(∆x)2 ∆zkwhere α =Ct −Cp3 New approachThe new approach is following the classical far wake theory see e.g. Tennekes andLumley (1972), which assumes that the far velocity deficit region can be described byone characteristic length scale ` and one velocity scale Us (maximum velocity deficit).Since the horizontal distance in the model is several times larger then the turbine diam-eter, it has been assumed that the generated turbulence and dissipation are balanced. Inthis way it is possible to determine explicitly the influence of each turbine on any down-stream turbine, thereby addressing the efficiency issue. From the diffusion equation wecan obtain`2 =(2KmU0)x+ `20 (3.1)3Eq. (3.1) describes the down-stream evolution of the velocity deficit region due toentrainment processes. U0 is the hub-height velocity, Km turbulence coefficient for mo-mentum and `0 the initial length scale, which has to be determined from measurements.Following the literature (e.g. Tennekes and Lumley, 1972) we can write for small ve-locity deficits U = U0−Us f (z, `) From the definition of the thrust, we can obtain forthe velocity deficitUs =U0√21−(1− Ct A20√pi W `) 12 (3.2)(3.1) and (3.2) form the full set of equations that describe the velocity deficit com-pletely.For the mesoscale field we used ` from (3.1) and assume that the wake width is equalto the horizontal grid spacing. This gives us Us from (3.2) and we obtain for the totalthrustCT A0U202V=1VW∞∫−∞U s f(U0−U s f)dz =1Vkmax∑k=1Tk (3.3)The r.h.s. will be applied to all model levels k. The up-stream velocity U0 comes fromthe wind farm parametrization, which take into account turbine-turbine interaction us-ing (3.1) and (3.2) to transport local (unresolved for the mesoscale model) wakes.The constants `0 and α were obtained from a comparison between a ”standalone” ver-sion of the model and Vindeby fast measurement data. We obtained α = 1 and `0 = 0m.In the figure below the result for a single wake at Vindeby has been plotted.Figure 3.1: Left: Normalized velocity deficit Uwake(k)−U(k)/U0 for the measurements(black line) and the model (grey line). Right: Measured upstream velocity (dots) andthe logarithmic fit (dotted line), the downstream measurements (squares) and the mea-surement interpolation (black line) plus the model wake velocity (grey line).44 ValidationWe used for the validation 10-min averaged data from top mounted cup anemometersM2 (63m), M6 (70m) and M7 (70m), the wind vane at 60m on M2 and the powermeasurements from the turbines in row 4 and 5 at Hornsrev. We selected only datafrom the met. masts in the up-stream wind directions betweeen 255◦ ≤ θ ≤ 285◦.The up-stream wind speed interval was selected in the range of 8m/s ≤U63 ≤10m/s,so that the corresponding time average wind speed at 70m was 9.3m/s (equal to themodel hub-height wind speed).The model consists of 60×50 horizontal levels, had in total 60 vertical levels and∆x =1400m. The mesoscale model was initialized with a constant geostrophic windUg =11m/s and Vg = -2m/s such that it converged to a wind profile with a hub heightvelocity 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 schemes we used the Ct from the thrustcurve.4.1 Velocity deficit recoveryWe normalized the wake measurements of M6 (8300m) and M7 (12300m) with thecorrected (logarithmic extrapolation to 70m) wind speed from M2. From the powermeasurement we derived the corresponding hub-height wind speeds via the powercurve. To be data consistent the derived velocities were normalized by the wind speedof the first row.The abscissa in fig.(4.1) indicates the down-stream distance from the first turbineonwards. The dots up to 6300m represent the averaged normalized hub-heightvelocities from row 4 and 5 and the dots at 8300m and 12300m are the averagednormalized velocities at hub-height from M6 and M7 respectively. The solid line isa part of the parametrization of the new approach and represents the local hub-heightvelocities of the turbines. The dashed lines are the model outputs, whereas the symbolsmark the model output position. The Fitch-scheme produces a deeper wake thenthe new approach. Inside the wind farm it reaches the measured local turbine velocities.4.2 Total ThrustIn this section we will compare the total modeled thrust with the measured thrust. Thisgives us for the total thrust of grid-cell (i, j) in the Fitch-scheme simplyTi, j =kmax∑k=1Ct Ni j Ak v2h,k2 (∆x)2∆zk,5Distance [m]Norm. Hub Height Vel0.60.70.80.91.0 lll llll ll llllllM7M6+ Fitch−schemex New approach0 2000 4000 6000 8000 10000 12000ModelAverage outputParametrizationRowl 4l 5Figure 4.1: Velocity deficit recovery at the Hornsrev windfarm.since the turbines are not resolved explicilty. Whereas the total thrust applied to grid-cell (i, j) for the new approach isTi, j =WVnturb∑n=1kmax∑k=1((U0,n−U s,n fk)U s,n fk)∆zkFor the measurements, we use the power and thrust curve to achieve the thrust perturbine. We sum up groups of four turbines to measure the equivalent total thrust pergrid-cell:Ti, j =4∑n=10.5Ct,n A20 U2n /V where V = D0 (∆x)2Since the turbine hub-height velocity deviates from the met. mast up-stream velocity,we selected 8m/s ≤U0 ≤11m/s to achieve an average velocity of 9.2m/s at the firstturbine (compared to 9.3m/s of the model).The total thrust per grid-cell for the models and the corresponding measured thrust areplotted in fig.(4.2). The dots represent the down-stream grid-cell thrusts per volume.From this figure we can conclude that the Fitch scheme overestimates the energyextracted from the flow by almost an order of magnitude. The new-approach followsthe measured thrust.6Distance [m]Total Thrust  [ms2]0.0000.0050.0100.0150.0200.0250.0300.035l l l l lllll l0 1000 2000 3000 4000 5000MethodFitchMeasurednew−approachFigure 4.2: Total thrusts per grid volume versus the down-stream distance at HornsrevFinally we can see from fig.(4.2) that the velocity deficit of the Fitch-scheme pene-trates from the first grid-cell on deep into the PBL. We notice also that the maximumvelocity deficit probably due to the enhanced turbulence has been transported upwards.Furthermore large positive velocity deficits at the lower boundary are obtained due tothe high turbulence mixing.Norm. Vel. deficitHeight [m]50100150200−0.10 −0.05 0.00 0.05Vel. [m/s]Height [m]501001502007.5 8.0 8.5 9.0 9.5 10.0MODDiffusionFitchPROF123Figure 4.3: Left: normalized velocity deficit (Udown−Uup)/U0 inside the wind-farm,decreasing darkness when proceeding donwstream. Right: Horizontal velocity insidethe wind farm5 ConclusionIn this paper we present a new approach, which allows us to simulate the flow dis-tortion caused by the thrust of wind farms in a mesoscale model. We compare thenew approach and the wind farm parametrization implemented in the WRF mesoscale7model (Fitch-scheme) against 10-min averaged velocity data from the large wind farmHornsrev off the west coast of Denmark. The results show that in the Fitch-scheme thethrust applied to the flow is overestimated by almost one order of magnitude. Further-more we found that the modeled sub-grid turbulence kinetic energy in the Fitch-schemediffuses the velocity deficit deep into the boundary layer, and causes unnaturally highpositive (grid-cell averaged) velocity deficits at the lower boundary. Both deficiencieswould have consequences on the analysis of the impact of wind farms on the atmo-sphere as well as its ocean feedbacks.After correcting the Fitch-scheme (results are not shown here), its total thrust appliedto the flow agreed with the measurements at the first up-stream turbine. However, sincethe scheme does not account for efficiency (turbine-turbine interaction), the down-stream thrust applied to the flow was therefore overestimated. Furthermore we noticedthat the down-stream recovery of the velocity deficit in the corrected Fitch-scheme, dueto its intensive mixing, is this time too fast. Finally we observed that it produced noweven relatively higher positive velocity deficits (same order as the deficits) at the lowerboundary. The new approach is able to follow, thanks to the internal turbine interaction,the reduced thrust applied to the flow. The recovery of the velocity deficit matches the(at 6km down-stream located met. mast M7) measurements.ReferencesU. Blahak, B. Goretzki, and J. Meis. A simple parametrization of drag forces inducedby large wind farms for numerical weather prediction models. EWEC Conference,2010.M. Nakanishi and H. Niino. Development of an improved turbulence closure modelfor the atmospheric boundary layer. Journal of the meteorological Society of Japan,87:895–912, 2009.Ott Søren, Jacob Berg, and Morten Nielsen. Linearised cfd models for wakes. RisøNational Laboratory, Roskilde, Denmark, Risø-R-1772(EN):01–41, 2011.William C. Skamarock, Joseph B. Klemp, Jimy Dudhia, David O. Gill, Dale M. Barker,Michael G. Duda, Xiang-Yu Huang, Wei Wang, and Jordan G. Powers. A Descrip-tion of the Advanced Research WRF Version 3. NCAR Technical note, 2008.H. Tennekes and J.L. Lumley. A first Course in Turbulence. The MIT Pess, 1972.8

Wind Farm parametrization in the mesoscale model WRF

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Wind Farm parametrization in the mesoscale model WRF

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