Flow and wakes in large wind farms in complex terrain and offshore

R.J. Barthelmie S.T. Frandsen, O. Rathmann, K. Hansen University of Edinburgh (UK) Risø National Laboratory/DTU (Denmark) [email protected]

E.S. Politis, J. Prospathopoulos D. Cabezón CRES (Greece) CENER National Renewable Energy Center (Spain)

K. Rados S.P. van der Pijl, J.G. Schepers NTUA (Greece) ECN (Netherlands),

W. Schlez, J. Phillips and A. Neubert Garrad Hassan and Partners (Germany/UK)

1 Abstract 2 Introduction Wind farms being developed are large and Power losses due to wind turbine wakes often in complex terrain, close to forests or are of the order of 10 and 20% of total offshore. There is a need for further power output in large wind farms. The focus research to examine the performance of of this research carried out within the EC wind farm and wake models in these more funded UPWIND project is wind speed and difficult environments. In ideal turbulence modelling for large wind circumstances, wind and turbulence would farms/wind turbines in complex terrain and be predicted on a fine mesh (horizontal and offshore in order to optimise wind farm vertical) for the whole wind farm over a layouts to reduce wake losses and loads. range of wind speeds and directions for a For complex terrain, a set of three long time period. There is a gap between evaluations is underway. The first is a engineering solutions and computational model comparison for a Gaussian Hill fluid dynamics (CFD) models and a bridge where CFD models and wind farm models is needed between these in order to provide are being compared for the case of one hill- more detailed information for modelling top wind turbine. The next case is for five power losses, for better wind farm and turbines in flat terrain. Finally a complex turbine design and for more sophisticated terrain wind farm will be modelled and control strategies and load calculations. compared with observations. This is the focus of our work within the UPWIND projects that aims to develop the For offshore wind farms, the focus is on next generation of large wind turbines. cases at the Horns Rev wind farm which indicate wind farm models require modification to reduce under-prediction of 3 Measurements wake losses while CFD models typically For evaluating wakes there are essentially over-predict wake losses. Further two types of measurements; meteorological investigation is underway to determine the and wind farm data. Meteorological data causes of these discrepancies. can be divided into two types – mast and The project therefore represents a set of sodar/lidar data. The advantage of unique evaluations of models with meteorological mast data is; it is available observations in different environments. for a long period, it is accurate and wind Progress towards improving wind farm speed, direction and turbulence profiles to models will be described. hub-height are available at a good time resolution and with high data capture. The most obvious disadvantage is that the location of the measurements is giving fixed wake distances. Measurements are rarely • Establishing the freestream flow made above hub-height. Both sodar and • Wind direction, nacelle direction doppler lidar are able to measure wind and yaw misalignment speed profiles both beyond and above hub- height and may be particularly useful • Wind speed gradients across the offshore due to the expense of erecting tall wind farm meteorological masts e.g. [1]. • Accuracy of the site specific power curve and thrust Obviously for wake studies in large wind • Time averaging between models farms, wind farm data are needed. and measurements Parameters include power output, nacelle direction and yaw misalignment and a • Natural fluctuations in the wind status signal. These data are routinely speed and direction in any period collected using Supervisory Control And • Wake transport time through the Data Acquisition (SCADA) systems wind farm although storage and retrieval of these data • Turbulence intensity and for research purposes may be a time atmospheric stability consuming process. A more significant issue is that all wind farm data are typically confidential and developers are reticent to 4 Models share raw data. This is a big issue in model The model comparison in Section 5 evaluation exercises where data are (Complex Terrain) and Section 6 (Offshore) necessary and also by the nature of the uses the full spectrum of models from exercise many different groups are whole wind farm codes which use involved. Nevertheless it is clear that moderately simple wake models to full CFD access to data is critical at this point while models. Models are listed below in the wind farm model evaluation for more approximate order of complexity from the challenging environments is conducted. In simplest (in terms of wake modelling) to the the POWWOW project, a virtual laboratory most complex. has been developed to allow other users of wake models access to data from offshore WAsP from RISOE wind farms which can be made public and The Wind Atlas Analysis and Application to results from wind farm models with which Program (WAsP) is based on a linearised they can compare their own modelling. To model used in the European Wind Atlas. date, access has been given to data from The WAsP program [2] uses meteorological Vindeby, Middelgrunden and Horns Rev data from a measurement station to and may be expanded to incorporate more generate a local wind climate from which data and model simulations. Users can the effects of obstacles, roughness and register and access the wiki at complex terrain have been removed. To www.see.ed.ac.uk/powwowwiki. produce a wind climate for a nearby wind Power loss modelling should encompass farm or wind turbine site these local effects the whole range of wind speeds and are reintroduced. In terms of wind farm directions. In general, computing modelling the wake model in the requirements for CFD models means we commercial version is based on [3]. A new are restricted to examining a number of wake model (‘Mosaic tile’) is being specific wind speed and direction cases developed for use within WAsP [4]. The and only a moderate number of turbines main advantage of the program is that it is rather than wind farms with ~100 turbines fast and robust. It does not model flow in which can easily be done by wind farm complex terrain if flow separation occurs models. On the other hand it can be difficult although there are methods for improving to extract reasonable simulations from its predictions in complex terrain [5]. For the some of the wind farm models for very simulations discussed below it is important specific cases when models are being used to note that the program is being used in a beyond their operational windows. In way which is not recommended. addition to this there are a number of WindFarmer from GH specific issues relating to wake measurements: In this project the ambient wind speed distribution and boundary layer profile is calculated by an external wind flow model, equations. The (axial) pressure gradients WAsP. The wind turbine wake model are prescribed as external forces and (based on Ainslie [6]) then makes use of enforce the flow to decelerate and the wake these data superimposing the effect of the to expand in the near wake. A free vortex offshore wind farm. The initial wake is a wake method is used to compute these function of the wind turbine dimensions, pressure gradient terms a priori. thrust coefficient and local ambient wind CENER speed and turbulence. The eddy viscosity wake model in GH WindFarmer is a CFD The model, based on the commercial CFD calculation representing the development of code Fluent, allows simulating the rotor the velocity deficit using a finite-difference effect over the flow as axial momentum solution of the Navier-Stokes equations in sources assigned to the cells corresponding axis-symmetric co-ordinates. The eddy to the rotor volume. The forces are viscosity model thus automatically observes calculated as a function of the thrust the conservation of mass and momentum in coefficient, the incident wind speed and the the wake. An eddy viscosity turbulence rotor area. As input, the model needs basic closure scheme is used to relate the shear wind farm data including, among others, the stress to gradients of velocity deficit. thrust coefficients of the wind turbines as Empirical expressions are used to model well as the surrounding topography. For a the wake turbulence [7] and the certain wind direction, the description of the superposition of several wakes that are wake is obtained through the calculation impacting on one single location. Multiple over the whole domain of the general fluid wakes are calculated by consecutive equations in its RANS form with a k-ε downstream modelling of individual wakes. turbulence closure scheme. Due to the empirical components in GH WindFarmer it is possible to model typically CRES–flowNS from CRES 7200 wind speed and directional scenarios The governing equations are numerically needed for a complete energy assessment integrated by means of an implicit pressure of a wind farm in reasonable time. The correction scheme, where wind turbines are model has performed well in all modelled as momentum absorbers by environments, including small offshore wind means of their thrust coefficient [10]. A farms [8]. For very large wind farms, the matrix-free algorithm for pressure updating boundary layer profile is modified by the is introduced, which maintains the presence of wind turbines. One approach to compatibility of the velocity and pressure account for this is to represent the wind field corrections, allowing for practical farm area by area of higher roughness [9]. unlimited large time steps within the time WAKEFARM from ECN integration process. Spatial discretization is performed on a computational domain, ECN's WAKEFARM model is based on the resulting from a body-fitted coordinate UPMWAKE code which originally was transformation, using finite difference/finite developed by the Universidad Polytecnica volume techniques. The convection terms de Madrid. It is based on parabolized in the momentum equations are handled by Navier-Stokes equations. Turbulence is a second order upwind scheme bounded modelled by means of the k-epsilon through a limiter. Centred second order turbulence model. Through the schemes are employed for the parabolization of the governing equations it discretization of the diffusion terms. The is assumed that there exists a predominant Cartesian velocity components are stored direction of flow and that the downstream at grid-nodes while pressure is computed at pressure field has little influence on the mid-cells. This staggering technique allows upstream flow conditions. These for pressure field computation without any assumptions no longer hold in the near explicit need of pressure boundary wake where additional modelling is conditions. A linear fourth order dissipation necessary. In the present project a hybrid term is added into the continuity equation to method is used which is still based on the prevent the velocity-pressure decoupling. WAKEFARM model but the near wake To accommodate the large computational expansion and flow-deceleration is grids needed in most applications for a fair accounted for directly. This is achieved by discretization of the topography at hand, a an analogy with the boundary-layer multi-block version of the implicit solver has been developed. Turbulence closure is turbine with a diameter (D) of 126 m and 90 achieved using the standard k–
model m hub height. The input wind velocity profile [11], suitably modified for atmospheric is assumed logarithmic with 500 m flows. boundary layer height and 10m/s velocity at hub height. Three different levels of NTUA turbulence intensity (5%, 13% and 15%) NTUA CFD model solves the 3D Reynolds and six different wind directions (0, ±15o, averaged incompressible Navier-Stokes ±30o) were examined. Although there are equations with second order spatial differences between the two CFD model accuracy. The model [12] (see also [13]) simulations (Figure 1) the following points assumes Cartesian grids, uses the k- can be summarised: turbulence closure model and • The wind speed deficit remains accommodates wind turbines embedded in significant even 20D downstream its grid as momentum sinks representing from the wind turbine the force applied on the rotor disk that is in turn evaluated from the local thrust • Wind speed deficit at hub height is coefficient. NTUA has performed not decreasing smoothly with preliminary offshore wake calculations for distance the Horns Rev Wind Farm. • Increasing TI results in a faster flow recovery at long distances 5 Complex terrain cases • The wind speed deficit decays much faster in flat terrain. Three model simulation types are planned to compare the performance of the CFD 3D axisymmetric hill, L=1750 models with wind farm models where 0.8 TI =5%, Ct=0.393, CRES appropriate. To date, the first set is in 0.7 TIin=5%, Ct=0.36, CENER complete and the second underway. The TIin=13%, Ct=0.325, CRES 0.6 TIin=13%, Ct=0.27, CENER third is not described further here. Hill surface )

t 0.5 C

• Simple terrain (Gaussian Hill). x f 0.4 e Simulations shown in [14] and r U

( 0.3 summarised below. / x

U 0.2 • Five turbines in flat terrain. D • The complex terrain wind farm. A 0.1 real wind farm located in a 0

moderately complex terrain is -0.1 -50 0 50 proposed for the comparison and Axial distance [ x / D ] validation of wake models. The study represents a first attempt of 3D axisymmetric hill, L=1750 comparing and validating the 0.8 TIin=5%, Ct=0.393, CRES existing wake models on a real 0.7 TIin=5%, Ct=0.36, CENER TI =13%, Ct=0.325, CRES moderately complex site and with in 0.6 TIin=13%, Ct=0.27, CENER wind farm measurements. Hill surface 0.5

0.4

5.1 Gaussian Hill I T 0.3 The idealized simulation of a single wake in the case of a Gaussian hill constitutes the 0.2 basis for the comparison of the wake 0.1 characteristics between flat and complex 0 terrain. The different configurations were -0.1 simulated with one wind turbine at hilltop -50 0 50 Axial distance [ x / D ] and without the wind turbine (to provide the value of wind speed at the wind turbine position for the calculation of the actuator Figure 1. Comparison of two CFD model disk force as well as the reference velocity simulations for the Gaussian Hill. Top: field for the evaluation of the wind speed velocity deficit. Bottom: Turbulence deficit). The turbine is a 5 MW theoretical intensity. 5.2 Five turbines in a row TI=13%, Distance=3D In flat terrain wind parks, wind turbines are 1.2 often aligned in parallel rows, which means Ct=0.3 1 that turbines are often partially or Ct=0.5 completely situated in the wake of a Ct=0.7 )

neighbouring wind turbine. In order to t 0.8 C estimate the effect of a neighbouring wake x f e on the wind turbine efficiency, multi-wake r 0.6 U (

simulations are needed. / x

U 0.4 Eventually simulations will be compared D with observations. Initially, however, simulations were made to evaluate the 0.2 impact of the thrust coefficient Ct and turbulence intensity TI. One multi-wake 0 0 10 20 30 case, probably the worst in terms of Axial distance [x/D] efficiency, is simulated: Five subsequent wind turbines positioned one behind the other. A parametric analysis is done for TI=13%, Distance=5D different values of the distance between the 1.2 wind turbines (3, 5 and 7D, with D being the Ct=0.3 Ct=0.5 wind turbine rotor diameter) and different 1 Ct=0.7 values of Ct (0.3, 0.5 and 0.7). The level of )

inlet TI at hub height is set equal to 13%. In t 0.8 C

this manner, the effects of the intermediate x f e distance and the C are assessed. r t 0.6 U ( It is noted that the velocity deficit at a (x,y,z) / x

U 0.4 point is expressed in dimensionless form D as:

DU Uref ( z ) −U x ( x,y,z ) 0.2 = , Uref ×Ct Uref ( z )×Ct 0 0 10 20 30 40 whereU x is the local axial velocity and Uref Axial distance [x/D] is the inlet velocity at height z.

In Figure 2, the axial variation of the TI=13%, Distance=7D velocity deficit at hub height is represented 1.2 for the case of five wind turbines with the Ct=0.3 distance between the machines varying 1 Ct=0.5 Ct=0.7 from 3D to 7D. For high values of Ct

(Ct=0.7) the increase of the velocity deficit ) nd th t 0.8 at the following (2 -5 ) wind turbines is not C x f e

significant even when the distance between r 0.6 U the machines is small (3D). However, for ( / lower values of Ct there is a significant x U 0.4 increase in the deficit of the second wind D turbine which is greater if the wind turbines are more closely spaced (3D). In general, 0.2 there is no significant increase in the velocity deficit after the third wind turbine. 0 0 10 20 30 40 High values of the turbulence intensity for Axial distance [x/D] the five wind turbines case are observed. In comparison to the one wind turbine case, Figure 2: CFD simulations of five wind the level of maximum turbulence intensity is turbines in flat terrain. Distance between almost doubled (Figure 3). wind turbines is from the top panel down 3D, 5D and 7D and inlet turbulence intensity at hub height is 13%. TI=13%, Distance=5D 6.1 Wake modelling 0.5 A number of flow cases have been defined Ct=0.3 Ct=0.5 for the Danish offshore wind farm Horns 0.4 Ct=0.7 Rev that is owned by DONG Energy A/S and Vattenfall AB, consisting of 80 Vestas V80 wind turbines located in a 8 by 10 grid, 0.3 with a basic spacing of 7D as shown in I T Figure 4 [19]. 0.2 Power deficit in Horns Rev wind farm, 8 m/s, 2 degree sector 1 0.1 spacing=7D 0.9 spacing=9.4D r

e spacing=10.5D w

o 0.8

0 P 0 10 20 30 40 d

Axial distance [x/D] e 0.7 s i l a

m 0.6 r

Figure 3: 5W/Ts in flat terrain – Effect of Ct o N on TI at hub height. Distance between W/Ts 0.5 is 5 D and inlet TI at hub height is 13%. 0.4 0 1 2 3 4 5 6 7 8 Turbine number 6 Wake modelling offshore The main issue for the current project is Figure 5: Observed power deficit inside that there appears to be a fundamental Horns Rev wind farm for V=8±0.5 m/s difference between the behaviour of wakes inflow for different spacing. in small offshore wind farms where Electrical power, nacelle position and wind standard models perform adequately [15] turbine status signals have been extracted and those in large multi-row wind farms from the SCADA system with a reference where current wind farm models appear to period of 10-minutes and merged with under-predict wake losses [16]. It can be meteorological measurements from three postulated that this is due to the interaction masts (M2, M6 and M7). The undisturbed of turbulence generated by wind turbines power values are used to define 3x3 flow wakes with the overlying atmosphere [17] cases, corresponding to wind speeds levels and that a new generation of models is of 6±0.5, 8±0.5 and 10±0.5 m/s, which are required to deal with this complex combined with three different spacings 7 D, interaction of wakes with each other and 9.4 D and 10.5 D (Figure 5). The offshore the boundary-layer [18]. wind farm at Horns Rev is characterized with low turbulence (<8%) and many Case 2 6154000 operational hours in near neutral stability. M2 The mean deficit along a row of turbines has been calculated and presented in 6152000 Figure 6 for different wake widths. The wind 1 11 21 31 41 51 61 71 81 91 2 12 22 32 42 52 62 72 82 92 speed calculated from the power output of ) m

( 3 13 23 33 43 53 63 73 83 93 the first turbine is 8±0.5 m/s. At these low to

M 6150000 T 4 14 24 34 44 54 64 74 84 94 Case 1 U M6 M7 5 15 25 35 45 55 65 75 85 95 moderate wind speeds, the thrust 6 16 26 36 46 56 66 76 86 96 coefficient is relatively high. Thus the wake 6148000 7 17 27 37 47 57 67 77 87 97 losses shown are likely to be the most 8 18 28 38 48 58 68 78 88 98 severe but wind directions in the relatively

6146000 narrow wind direction bins will also occur

424000 428000 432000 436000 relatively infrequently. The major finding is UTM (m) Case 3 an almost constant power loss to about Figure 4: Horns Rev layout including 60% of freestream values during the pure definition of Case 1 (7D), Case 2 (9.4D) wake situation for a very small sector of 2°. and Case 3 (10.5D) flow directions. Turbine If larger wake widths are considered the locations are given by numbers and the deficit decreases down wind. This is due in location of the meteorological masts are part to the wake shape as illustrated in marked with MX. Figure 7. 1 r

e ±1o w

o 0.8 p

d e

s 0.6 i l a m

r 0.4 o N 0.2 0 1 2 3 4 5 6 7 8

1 o r ±5 e w

o 0.8 p

d e

s 0.6 i l a m

r 0.4 o N 0.2 0 1 2 3 4 5 6 7 8 1 r e w

o 0.8 p

d e

s 0.6 i l a m

r 0.4 o o

N ±10 0.2 0 1 2 3 4 5 6 7 8 1 r e w

o 0.8 p

d

e Observed

s 0.6 i

l Model A a Model B m

r 0.4

o Model C o

N Model D ±15 0.2 0 1 2 3 4 5 6 7 8 Turbine number

Figure 6: Comparison of models and measurements for Horns Rev (direction 270°, case 1 in Figure 2) for 8±0.5 m/s for different widths of wake sectors.

1 e n i b r u

t 0.9

d n 2

t a

r

e 0.8 w o p

d e s i l

a 0.7 m r o N

0.6

-15 -12 -9 -6 -3 0 3 6 9 12 15 Distance from wake centre in deg Figure 7. Wake width illustrating the portion of the wake captured by the measurements for ±1°, ±5°,±10° and ±15° for comparison with Figure 6. Figure 8 shows two different flow directions models are lacking one or more for wind speeds in the 8 m/s bin. Results components which account for the are similar to those for Case 1 but modification of the overlying boundary-layer comparing the observed wake losses for by the reduced wind speed, high turbulence Case 2 and Case 3 in the ±1° case atmosphere generated by large wind farms. illustrates the uncertainty in the This effect is likely to be particularly measurements which is mainly due to the important offshore due to the low ambient small number of observations. It has turbulence. This is described further in become apparent that standard wind farm section 6.2.

1 r 1 r e e w w o 0.8 o

p 0.8

p

d d e e

s 0.6 i

s 0.6 l i l a a m r

0.4 m

r 0.4 o

o o N ±1 o N ±1 0.2 0.2 1 2 3 4 5 1 2 3 4 5 1 r 1 r e e w w o 0.8 o

p 0.8

p

d d e e

s 0.6 i

s 0.6 l i l a a m r 0.4 m

r 0.4 o

o o N ±5 o N ±5 0.2 0.2 1 2 3 4 5 1 2 3 4 5 1 r 1 r e e w w o 0.8 o

p 0.8

p

d d e e

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0.4 m

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o o N ±10 N ±10o 0.2 0.2 1 2 3 4 5 1 2 3 4 5 1 r 1 r e e w w o 0.8 o

p 0.8

Observed p

d

d Observed e Model A e

s 0.6 i

s 0.6 l Model A i

Model B l a

a Model B m

r Model C 0.4 m

r 0.4 o Model C Model D o o N ±15 o N Model D ±15 0.2 0.2 1 2 3 4 5 1 2 3 4 5 Turbine number Turbine number .

Figure 8: Preliminary comparison of models and measurements for two cases (Left: Case 2 and Right: Case 3 in Figure 4) and 8±0.5 m/s at Horns Rev. From the top down, the width of the wake sectors considered in the four panels are ±1°, ±5°, ±10° and ±15°.

approaches including the development of a 6.2 Large offshore wind farms new analytical model [18], modifications to It has become apparent that power losses the WAsP model [20], modification of added from wakes exceed those predicted using roughness models and development of a standard wind farm models. GH have made canopy type model [21]. In all, seven an additional feature available in their models were compared with data from the WindFarmer model to allow assessment of offshore wind farms at Horns Rev and these effects according to the current state Nysted in Denmark. As yet it has not been of knowledge. RISOE have taken several possible to undertake a full model comparison using a years data from the 8 Acknowledgements wind farm. This is more straightforward with the parameterised models than with the Research funded in part by EU project CFD models which are intensive in terms of UPWIND # SES6 019945 and POWWOW # their computing resource requirements. SES6 019898. RB acknowledges the Comparisons have therefore tended to Scottish Funding Council via the Edinburgh focus on a limited range of wind speeds Research Partnership. We would like to with high thrust coefficient for westerly acknowledge DONG Energy A/S and winds which are well-represented in the Vattenfall AB, owners of the Horns Rev database, have flow directly down rows of wind farm. wind turbines and have downstream masts at distances between 4 and 11 km for 9 References comparison with models. In general, models where some tuning of the 1. Antoniou, I., H. Jørgensen, T. turbulence intensity is undertaken (either Mikkelsen, S. Frandsen, R. directly or through increased roughness) Barthelmie, C. Perstrup and M. show good agreement with measurements. Hurtig. Offshore wind profile The wind speed determined from power measurements from remote output within the wind farm can drop to less sensing instruments. in European than 80% of its freestream value (according Wind Energy Association to the initial wind speed and direction Conference. 2006. Athens, Greece, angles considered). Recovery to February 2006: p. 10 pp. approximately 90% of the freestream value 2. Mortensen, N.G., D.N. Heathfield, appears to occur with the first 5 km L. Myllerup, L. Landberg and O. downwind of the last turbine in the wind Rathmann (2005) Wind Atlas farm. However, further recovery is more Analysis and Application Program: gradual and appears to extend for an WAsP 8 Help Facility. Risø additional 15-20 km downwind. National Laboratory, Roskilde, Considerable work remains to be done in Denmark. 335 topics. ISBN 87-550- terms of model evaluation and this also 3457-8. relies on additional data from large offshore http://www.risoe.dk/vea/projects/ni wind farms becoming available in order that mo/WAsPHelp/Wasp8.htm. the impact of a range of wind turbine types and wind farm configurations can be 3. Katic, I., J. Højstrup and N.O. determined. Jensen. A simple model for cluster efficiency. in European Wind 7 Conclusions Energy Association. 1986. Rome: p. 407-409. Within the Upwind project research in 4. Rathmann, O., S.T. Frandsen and support of upscaling of wind turbines to the R.J. Barthelmie. Wake modelling 12 MW size and beyond is underway. The for intermediate and large wind research presented in this paper focuses on farms. in European Wind Energy special issues relating to the development Conference and Exhibition. 2007. of large wind farms both in complex terrain Milan. and offshore. The results presented here are preliminary focusing on the comparison 5. Bowen, A.J. and N.G. Mortensen. of different complexities of wake model in a Exploring the limits of WASP: the number of scenarios. Significant work wind analysis and application remains to be done including developing a programme. in European Union physical understanding of the causes of Wind Energy Conference. 1996. over- or under-prediction of wake losses in Goteborg: H.S. Stephens and large offshore wind farms by the different Associates, Bedford, UK. types of models. A cross-cutting theme is 6. Ainslie, J.F., Calculating the flow the introduction of CFD models in both field in the wake of wind turbines. complex terrain and offshore and in their Journal of Wind Engineering and representation of multiple wind turbines. Industrial Aerodynamics, 1988. 27: p. 213-224. 7. Quarton, D. and J. Ainslie, 15. Barthelmie, R.J., S.T. Frandsen, Turbulence in wind turbine wakes. M.N. Nielsen, S.C. Pryor, P.-E. Wind Engineering, 1990. 14(1). Rethore and H.E. Jørgensen, Modelling and measurements of 8. Barthelmie, R.J., G.C. Larsen, S.C. power losses and turbulence Pryor, H.E. Jørgensen, H. intensity in wind turbine wakes at Bergström, M. Magnusson, W. Middelgrunden offshore wind farm. Schlez, K. Rados, B. Lange, P. Wind Energy 2007. 10, 517-528. Vølund, S. Neckelmann, S. Mogensen, G. Schepers, T. 16. Mechali, M., L. Jensen, R. Hegberg, and L. Folkerts (2003) Barthelmie, S. Frandsen and P.E. Efficient development of offshore Rethore. Wake effects at Horns windfarms (ENDOW): Final report Rev and their influence on energy to the European Commission., Risø production. in European Wind National Laboratory, Risø-R- Energy Conference and Exhibition. 1407(EN): 30 pp. 2006. Athens, Greece: p. 10. 9. Schlez, W., A. Neubert and G. 17. Frandsen, S. (2005) Turbulence Smith. New developments in and turbulence-generated fatigue precision wind farm modelling. in loading in wind turbine clusters. Deutsche Windenergie Konferenz. Risø-R-1188(EN). p. 128 2006. Bremen: 5 pp. http://www.risoe.dk/rispubl/VEA/ris- r-1188.htm. 10. Chaviaropoulos and Douvikas. Mean-flow-field simulations over 18. Frandsen, S., R. Barthelmie, S. complex terrain using a 3-D Pryor, O. Rathmann, S. Larsen, J. Reynolds average Navier Stokes Højstrup and M. Thøgersen, solver. in ECCOMASS ’98. 1998. Analytical modelling of wind speed Athens 1998. deficit in large offshore wind farms. Wind Energy 2006. 9(1-2): p. 39- 11. Wilcox, D.C. (1993) Turbulence 53. modelling for CFD. DCW Industries Inc., IBSN 0-9636051-0-0. 19. Jensen, L. Wake measurements from the Horns Rev wind farm. in 12. Magnusson, M., K.G. Rados and European Wind Energy S.G. Voutsinas, A study of the flow Conference. 2004: EWEA (on CD): down stream of a wind turbine p. 9 pp. using measurements and simulations. Wind Engineering, 20. Rathmann, O., R.J. Barthelmie and 1996. 20(2): p. 389-403. S.T. Frandsen. Wind turbine wake model for wind farm power 13. Rados, K., G. Larsen, R. production. in European Wind Barthelmie, W. Schelz, B. Lange, Energy Conference. 2006. Athens: G. Schepers, T. Hegberg and M. 10 pp. Magnusson, Comparison of wake models with data for offshore 21. Frandsen, S.T., R.J. Barthelmie, O. windfarms. Wind Engineering, Rathmann, H.E. Jørgensen, J. 2002. 25: p. 271-280. Badger, K. Hansen, S. Ott, P.E. Rethore, S.E. Larsen and L.E. 14. Barthelmie, R.J., G. Schepers, S. Jensen (2007) Summary report: van der Pijl, O. Rathmann, S.T. The shadow effect of large wind Frandsen, D. Cabezón, E. Politis, J. farms: measurements, data Prospathopoulos, K. Rados, K. analysis and modeling. Risø Hansen, W. Schlez, J. Phillips, and National Laboratory/DTU, Risø-R- A. Neubert. Flow and wakes in 1615(EN): p. 34. complex terrain and offshore: Model development and verification in UpWind. in European Wind

Energy Conference. 2007. Milan: p. 10.