Modelling and measurements of power losses ... - Wiley Online Library

WIND ENERGY Wind Energ. 2007; 10:517–528 Published online 16 July 2007 in Wiley Interscience (www.interscience.wiley.com) DOI: 10.1002/we.238

Research Article

Modelling and Measurements of Power Losses and Turbulence Intensity in Wind Turbine Wakes at Middelgrunden Offshore Wind Farm R. J. Barthelmie*,†, S. T. Frandsen and M. N. Nielsen, Wind Energy Department, Risø National Laboratory, DK 4000 Roskilde, Denmark S. C. Pryor, Atmospheric Science Program, Department of Geography, Indiana University, Bloomington, IN, USA P.-E. Rethore and H. E. Jørgensen, Wind Energy Department, Risø National Laboratory, DK 4000 Roskilde, Denmark

Key words: wind turbine wakes; offshore wind farm; power loss; turbulence intensity

Understanding of power losses and turbulence increase due to wind turbine wake interactions in large offshore wind farms is crucial to optimizing wind farm design. Power losses and turbulence increase due to wakes are quantified based on observations from Middelgrunden and state-of-the-art models. Observed power losses due solely to wakes are approximately 10% on average. These are relatively high for a single line of wind turbines due in part to the close spacing of the wind farm. The wind farm model Wind Analysis and Application Program (WAsP) is shown to capture wake losses despite operating beyond its specifications for turbine spacing. The paper describes two methods of estimating turbulence intensity: one based on the mean and standard deviation (SD) of wind speed from the nacelle anemometer, the other from mean power output and its SD. Observations from the nacelle anemometer indicate turbulence intensity which is around 9% higher in absolute terms than those derived from the power measurements. For comparison, turbulence intensity is also derived from wind speed and SD from a meteorological mast at the same site prior to wind farm construction. Despite differences in the measurement height and period, overall agreement is better between the turbulence intensity derived from power measurements and the meteorological mast than with those derived from data from the nacelle anemometers.The turbulence in wind farm model indicates turbulence increase of the order 20% in absolute terms for flow directly along the row which is in good agreement with the observations. Copyright © 2007 John Wiley & Sons, Ltd. Received 12 July 2006; Revised 6 June 2007; Accepted 6 June 2007

Introduction Understanding of power losses and turbulence increase due to wind turbine wake interactions in large offshore wind farms is crucial to optimizing wind farm design. Power losses due to turbine wakes in large offshore wind farms are predicted by state-of-the-art models to be of the order 10–20% of the total potential power output and hence are a significant component of the overall economics of these wind farms. In addition to power losses, wake-generated turbulence is also a major source of fatigue loading1 and hence impacts turbine lifetimes. * Correspondence to: R. J. Barthelmie, Wind Energy Department, Risø National Laboratory, DK 4000 Roskilde, Denmark. E-mail: [email protected] † Also: Institute of Energy Systems, School of Engineering and Electronics, University of Edinburgh, Scotland

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Here we present observational data from the 40 MW Middelgrunden offshore wind farm to quantify wake effects offshore and use these data to evaluate the performance of state-of-the-art wind farm models in terms of predicted wake losses and wind turbine-induced turbulence intensity under a variety of wind speed conditions in this tightly spaced wind farm. Power losses due to wakes in the Middelgrunden offshore wind farm are quantified using wind farm Supervisory Control and Data Acquisition (SCADA) observations which are compared to a priori predictions of wake losses made using wind climate available from an onsite meteorological mast for 1997–1999 and the Wind Analysis and Application Program (WAsP).2 Prediction of wake-generated turbulence is based on the model presented in Frandsen and Madsen3 and the results are compared to results from two methods of calculating turbulence intensity using data from turbines in a wind farm. The overall objectives of this work are to assess the performance of simple but state-of-the-art models for prediction of power losses and turbulence increase in offshore wind farms.

Site and Data The Middelgrunden offshore wind farm is located in the Øresund strait between Denmark and Sweden approximately 2 km east of the Copenhagen harbour (Figure 1). The wind farm is owned by Middelgrunden Wind Turbine Cooperative and Energi E2, and provides more than 3% of Copenhagen’s electricity.4 It consists of 20 2 MW Bonus wind turbines (power curve and thrust coefficients are shown in Figure 2) arranged in a distinctive bow shape (Figure 1). The hub height is 64 m and the rotor diameter is 76 m with wind turbine spacing of 2.4 D (rotor diameters). 6180000

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Figure 1. Location and set-up of Middelgrunden wind farm. Coordinates shown are UTM Zone 32 (in m). On the map (left), the anemometer marks the location of the meteorological mast which was operated 1997–1999 and the turbines are marked with small turbine symbols. Turbine 1 is the northernmost turbine and the turbine number increases moving southward to turbine 20 as the southernmost turbine. The wind farm is approximately 2 km from the coastline. The shaded area indicates the land surface. On the figure (right), the layout of the wind farm is shown with wake directions 174 ± 15° and 354 ± 15° marked Copyright © 2007 John Wiley & Sons, Ltd.

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Figure 2. Bonus 2 MW turbine power curve (P) and thrust coefficients (Ct)

Observational data describing the wind turbine performance as presented here are 10 min averages from the SCADA system for each turbine for the period 2001–2004. Only data where all turbines are working and all variables are available were extracted (∼35% of the total data period). These variables include mean and standard deviation (SD) of power output, yaw angle, and mean and SD of the wind speed measured by the nacelle anemometer. The criteria applied to selected data mean the extracted data are not evenly distributed by month of the year or hour of the day. There are more than twice as many observations in autumn (47%) than in winter (17%), spring (18%) or summer (18%). There are also more observations during the night than in the day (44% between 07:00 and 18:00) with a minimum between 09:00 and 12:00. The majority of observations fall between 4 and 12 m s−1 (determined from the power output and the power curve) and are dominated by the prevailing west/south-westerly directions. Although there is a direct easterly component, there are very few observations from the north-east or south-east. For comparison with the operating data, we present analyses based on data collected prior to the wind farm construction. We use 30 min average mean and SD of wind speed from a cup anemometer at 50 m height and wind direction from 48 m taken on a 50 m meteorological mast installed and operated from October 1997 to December 1999 (location shown in Figure 1).5

Wind Speed Decrease and Power Loss in Wind Turbine Wakes Measurements The efficiency of the wind farm is defined here such that it would be 100% if there were no wake losses (i.e. the power output from each turbine is the same as the freestream turbine), under the assumption that no other losses occur. The actual observed efficiency of the Middelgrunden offshore wind farm, calculated by assuming that either the north turbine (directions from 270–90° over north) or the south turbine (directions from 90–270°) represents the freestream wind speed, is 90%. The presence of wind gradients at the site due to the proximity to the coast of Denmark to the south and west and Sweden to the east means that the end (north or south) turbine does not necessarily produce the highest power output and this gives wind farm efficiencies of over 100% for some directions. In accordance with expectations from the wind farm layout (Figure 1), wake losses are concentrated in two sectors around north and south which are about 50° wide. The lowest efficiencies/highest wake losses are at moderate wind speeds of 6–10 m s−1 associated with high thrust coefficients (Figure 2) with a gradual increase in efficiency with increasing wind speeds (Figure 3). The directional dependence of the efficiency of the wind farm calculated from the observed power output is summarized for all wind speeds (greater than 4 m s−1 and less than 25 m s−1) in Figure 4. The efficiency by wind direction depends on wake effects in the north/south sectors and also varies according to the wind speed frequency distribution, although the difference between the average wind speed in the north and south sectors is relatively small. Copyright © 2007 John Wiley & Sons, Ltd.

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Figure 4. A comparison of observed and modelled wind farm efficiencies by wind direction at Middelgrunden. Observed efficiencies are calculated using turbine operating (power output) data from 2001 to 2004 when all wind turbines were working. Power output from the north or the south turbine is used as the freestream, according to the wind direction. Error bars are one SD of the normalized power output. Modelled values are from WAsP based on the 1997–1999 wind climate and use the manufacturer’s power curve/thrust coefficients. The wake decay coefficient (k) in these simulations was set to 0.05

Wake losses at Middelgrunden are concentrated in two narrow sectors but it would be useful for comparison with other offshore wind farms if the direct wake losses at the wake centre could be determined. In a typical wind farm, the rows, and therefore the largest (direct) wake losses, are aligned with a particular wind direction but recall that at Middelgrunden the wind farm is configured in a bow shape. Figure 5 shows the relative observed power by the turbine position in the row for a sector around 174 ± 15° from south and 354 ± 15° around north for wind speeds between 8 and 9 m s−1. From both directions, the second turbine generates only approximately 20% of the power production at the first turbine in these narrow sectors and in this Copyright © 2007 John Wiley & Sons, Ltd.

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Figure 5. Relative power at each downstream turbine compared to the power output from the ‘freestream’ turbine (i.e. power from the first turbine which is impinged upon by the undisturbed flow) for the Middelgrunden wind farm. Wind directions are defined as 174 ± 15° for south and 354 ± 15° for north. Data are shown for freestream wind speeds of 8–9 m s−1. Also shown is the normalized wake wind speed at the centre of the wake at each turbine for southerly flow

wind speed band where wake losses are largest due to the high values of the thrust coefficient (see Figure 2). However, power production from the third and subsequent turbines then begins to increase. The most likely reason for this is that choosing a narrow sector means the wake centre shifts out of the chosen wind direction sector. This hypothesis is supported by analysis showing the measured mean wind speed in the wake as it moves down the row when the wind direction is not constrained and instead the wind speed at the wake centre is identified. As shown in Figure 5, after the initial drop to the second turbine, the wake wind speed remains relatively constant. Differences between the power increase with winds from the north and south are postulated to be due to wind speed gradients from the south where wind speed is increasing as it moves from land over the sea or differences in prevailing atmospheric stability under northerly and southerly winds.

Modelling For modelling purposes, the wind climate was computed based on data from the meteorological mast for 1997–1999. However, it is important to note that this period was characterized by more frequent southerly winds than is expected for this location in the long term. Given that wake losses occur only in the north-south directions, this is expected to lead to some over-prediction of wake losses for the wind farm. The turbines are relatively closely spaced (2·4 D). This is slightly outside the operating range of most stateof-the-art wake models which do not model the near-wake in detail. The lower limit for the model used (WAsP6) is 4 D.7 However, most models make a reasonable approximation of wake wind speeds at distances down to 1·7 D.8 WAsP was applied to model wake losses at Middelgrunden using a wake decay coefficient (k) of 0.05 which has been suggested for small offshore wind farms.7 WAsP contains a simple wake model based on linear expansion of the wake downstream based on that of Jensen9 and Katic et al.10 where the wake has a ‘top hat’ form and the spread of the wake (Dw) is assumed to be symmetric in the vertical and lateral directions according to the value of k, the wake decay coefficient. The wake wind speed is calculated using Copyright © 2007 John Wiley & Sons, Ltd.

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Dw = D + 2 kX

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where D is the rotor diameter of the turbine and X is the downstream distance from the turbine. Overall, using the 1997–1999 wind climate and WAsP, the efficiency of the Middelgrunden offshore wind farm is predicted to be 85.5%. There is limited sensitivity of the wind farm efficiency to the wake decay coefficient (k) for this single-row wind farm configuration. The wind farm efficiency is predicted as 85.4% if k is set to 0.04 and 85.7% if k is 0.06. The WAsP model results are presented in Figure 4 in terms of the average wake losses by direction, noting that this model does not account for local wind speed gradients. However, this prediction made using the available meteorological data is in reasonable agreement with the observations (also shown in Figure 4). Wake losses in the direct wake sectors are over-predicted by the model in part due to the different data periods. There was a higher frequency of southerly observations in 1997–1999 compared with those in the wind farm data set from 2001 to 2004.

Comparison of Measurements and Modelling The overall wind farm efficiency of 90% calculated from wind farm data is slightly lower than estimated prior to wind farm construction (93%) in Larsen et al.4 and 4% higher than predicted using WAsP with k = 0.05. However, use of the 1997–1999 wind climate may account for some of the WAsP discrepancy as mentioned above. This is considered to be in good agreement especially in light of a number of confounding influences: (1) Differences between the wind speed and direction climate from the period used for the modelling to the wind farm observation period. There were more southerly observations (14%) in the modelling period than during the wind farm observation period (7%). Also, the wind direction during the wind farm operation period is inferred from the yaw angle of the freestream wind turbine, which may be less accurate than the data from the meteorological mast or biased relative to the actual wind direction. (2) Mean wind speeds cannot be determined accurately for the wind farm observation period because no direct wind speed measurements are available. Wind speed during the wind farm operation period was determined from the wind turbine power output and manufacturer’s power curve. Since the turbines produced 5.7% more power than expected from the manufacturer’s power curve (see Larsen et al.4), this gives differences between predicted and observed power output in the modelling. (3) The wake decay coefficient used here of 0.05 is within the range suggested for small offshore wind farms of 0.04–0.05; however, the site has a relatively high turbulence intensity which may be atypical for offshore wind farms. (4) It is difficult to analyse wake effects unless all turbines are working and data from this site were not randomly distributed by season or time of day.

Turbulence Intensity in Wind Turbine Wakes Ambient turbulence levels offshore are lower than over land surfaces. Typical values at turbine hub height are 6–8% offshore5 and 10–12% over land. However, this may not result in reduced loads on offshore wind turbines due to high levels of wake-generated turbulence in large wind farms. Fatigue loading of wind turbines is assumed to be proportional to the SD sU of wind speed U even under full or partial wake conditions.1 Hence there is a need for both models and measurements to evaluate turbulence intensity (I) at offshore wind farms where I is defined as I=

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Frandsen1 presented a model for estimating both ambient wind farm turbulence, IT,wf , and direct wakegenerated turbulence and for generating a spatial average of the combined turbulence in wind farms in nearneutral conditions. In this research, the model is evaluated using data from the Middelgrunden offshore wind Copyright © 2007 John Wiley & Sons, Ltd.

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farm which is a bow-shaped single line with relatively close spacing of 2.4 D. The objective is to assess how to determine turbulence intensity from the wind farm data, to compare turbulence levels with those predicted by the model for both freestream and wake conditions, and to identify conditions under which the model works optimally.

Measurements Since independent meteorological measurements are not available for the period of wind farm operation, total turbulence intensity is calculated from the power output using the method of Jørgensen et al.11 based on Thomsen and Markilde Petersen12 where the relationship between the SD of power output and the SD of wind speed is given as dP  s p = Bs u   dU  u

(3)

where sp is the SD of power output, su is the SD of wind speed, B is a constant which is in the range of 0.8–0.9, depending on mean wind speed,13 P is power output and U is the wind speed. The choice of the constant B makes a difference of about 1% in the turbulence level, being higher if 0.8 is chosen. In this analysis, B was initially set to 0.9. Clearly, differences between the manufacturer’s power curve and the site power curve will also affect the result. Note that here calculations are made between 4 and 15 m s−1 because the power SD method cannot be applied outside these limits. The reason for this is that the change of power output over the change of wind speed must be calculated (equation (3)), so the turbine must be operating. At low wind speeds, the turbine can either be starting to produce power or shutting down depending on the wind speed transition causing a high SD. As wind speeds increase towards the rated wind speed, moderate changes of wind speed produce small changes in power output (see Figure 2). Likely the wind speed limits should be narrower to exclude the possibility of including start-up times and times when turbine power output is close to rated. For comparison, the wind speed (U) and SD (sU) from the nacelle anemometers on each turbine at Middelgrunden were also used to calculate the turbulence intensity using equation (2), although there are data issues with the nacelle anemometer recording only whole digits for the SD of wind speed prior to March 2002. Figure 6 shows the freestream ambient turbulence I0met at 50 m by wind direction at Middelgrunden measured at the meteorological mast prior to the construction of the wind farm. High turbulence intensity at around 90° is due to mast interference/mast shadow whereas the sectors from south-west to north-west are affected by the presence of land. Figure 6 also shows the variation of turbulence intensity with wind speed. Computed I0met at Middelgrunden is slightly different from that at other offshore sites around Denmark. Typically, the offshore minimum I0met is found between 8 and 12 m s−1 and, at higher wind speeds, turbulence intensity begins to increase due to higher roughness of the sea surface.5 Average I0met for all wind directions is 12% for wind speeds between 4 and 15 m s−1 and 13% for all wind speeds. This is higher than what would be expected for an offshore site and is due to the short distance to land (fetch) in the prevailing wind direction. The freestream (or ambient) turbulence was also computed from nacelle anemometer (I0na) and the turbine power data (I0pw) from the freestream wind turbine (either turbine 1 or turbine 20 selected by wind direction). As shown in Figure 6, I0pw in general is closer to I0met than to I0na as I0na is higher than both I0pw and I0met. Overall mean I0na is 22% while I0pw is 13%, while average I0met for 4–15 m s−1 is 12%. Although the meteorological and wind turbine measurements are not from the same time period, their overall behaviour with respect to wind speed and direction is consistent. However I0pw shows significantly more variability with wind speed than does I0met. Turbulence intensity shown in Figure 6 can be used to estimate B using equations (2) and (3), and assuming I0 pw = I0 met sp B= dP   U I  dU  u pow 0 met Copyright © 2007 John Wiley & Sons, Ltd.

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Figure 6. Ambient turbulence intensity at Middelgrunden presented by wind direction (above) and wind speed (below). I0met shows the results from measurements on a meteorological mast 1997–1999 at a height of 50 m. I0pw is derived from power measurements while I0na is from nacelle anemometer data both derived from measurements on the freestream wind turbine for the period 2001–2004. The top figure shows I0 averaged for all wind speeds by 10° direction bins. The bottom figure shows freestream I0 averaged for all wind directions by 1 m s−1 wind speed bins. Note turbine data were calculated using freestream measurements from turbine 1 or 20 so no wake data are included

Averaging results between 6 and 12 m s−1 gives B = 0.797 which has been used in the remainder of the analysis. It should be recalled that turbulence intensity is height dependent. Power measurements used to derive I are integrated over the rotor diameter from 26 to 102 m, whereas turbulence intensity calculated from the nacelle anemometer data is measured at one height slightly above the hub height of 70 m. Assuming turbulence intensity offshore decreases approximately linearly with height,14 the difference between the turbulence intensity at 26 and 102 m is about 3.8%, and the difference between 50 and 70 m about 1%. The differences of about 9% in the turbulence level derived from the nacelle anemometer and the power SD data cannot, therefore, be explained only by differences in the height of measurement. Assuming that I0pw is closer to the true ambient turbulence, over-prediction of turbulence by data from the nacelle anemometer is likely due to data issues such as the recording of sU with only one significant figure in the early part of the record or higher turbulence from flow around the nacelle. While the power SD method is unable to provide the detailed level of turbulence information (e.g. turbulence spectra) which may be required for some applications, this comparison suggests that it is a better option for the calculation of a general turbulence level within the wind farm than using data from the nacelle anemometer. However, it cannot be used at wind speeds below the cut-in or above rated.

Modelling Within or downwind of a wind farm, there are two components of the total ambient wind farm turbulence IT,wf , the free-flow ambient turbulence I0 and the added turbulence generated by wind farm wakes Iaddwf : 2 IT2,wf = I02 + Iaddwf


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The ‘added turbulence’ model applied in Appendix D of the IEC61400 standard15 has been adapted to utilize the information from the WasP6 and WAsP Engineering16 models, and to further account for irregular wind farm layouts in a Windfarm Assessment Tool (WAT).2 Freestream turbulence intensity is provided by a neutral formulation from WAsP Engineering.16 This likely under-predicts turbulence at low wind speeds where thermal turbulence plays a role. Turbulence in wake conditions is calculated by the following IEC 61400 formula: Iaddwf =

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Where u is wind speed c is a velocity scale (=1 m s−1) and dj is the distance to the turbine j which is normalized by the turbine rotor diameter.

Comparison of Measurements and Modelling The WAT model predicts ambient turbulence for Middelgrunden which is too low (∼5% at hub height, relative to observed values of approximately 12–13%) because it is predicted based on neutral conditions only, whereas the turbulence at the site is influenced by both non-neutral stability and the proximity to land. Figure 7 shows the wake-generated turbulence intensity at Middelgrunden derived from the individual turbine power measurements (Ipw) and the WAT model by wind direction for all wind speeds between 4 and 15 m s−1. As expected, there are large increases in the level of turbulence under wake conditions from north and south. From north, turbulence intensity increases from about 14% ambient to 34% under wake conditions, and from south from about 10 to 32%. The turbulence level at each turbine is more varied under wake conditions. Turbulence intensity predicted by the WAT model shows good agreement with the variation by direction. Note that averaging over 10° sectors reduces modelled turbulence intensity from its peak values. 40 Ipw

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As noted above, the wind speed range 4–15 m s−1 is likely too expansive, so here we focus on a narrower range of 7 to 13 m s−1 to avoid conditions when turbines are starting or stopping as the wind speed moves around the cut-in velocity, and the transition of operation as wind speeds increase to the rated level of 15 m s−1. Figure 8 shows the total turbulence intensity calculated for each wind speed (computed in 1 m s−1 bins between 7 to 13 m s−1) and each turbine at the Middelgrunden wind farm from the power data Ipw and the WAT model. As shown, while average total turbulence intensity at Middelgrunden is accurately simulated by the WAT model, the model does not fully replicate the wind speed dependence. In general, differences between the levels of turbulence at the individual turbines are small. As noted in Figure 6, Ipw varies significantly with wind speed whereas the modelled turbulence intensity from WAT shows only a slight decrease by wind speed class. The minor variation of the WAT results with wind speed is due to the configuration of the WAT model used for Middelgrunden. Here, the bow shape means that the wind farm essentially consists of double wakes with minor impact from a third turbine in some directions. Note the average turbulence intensity is not strongly impacted by higher turbulence intensity in wake conditions because these occur only in two fairly narrow sectors (north and south) while the prevailing wind direction is south-westerly. Since the north and south sectors comprise only a small fraction of the overall data set, the additional variability of turbulence in the wake is not discernible when turbulence is averaged only by wind speed.

Conclusions Understanding power losses and turbulence increase in wind farms is crucial to optimizing wind farm layouts. There is therefore considerable interest in evaluating wake data from the first offshore wind farms and examining the performance of state-of-the-art and new wind farm models in their ability to predict wake losses under a variety of wind speed conditions and for different wind farm layouts. Here we present such as an analysis based on Middelgrunden, an offshore wind farm comprising a single curved line of turbines 2 km east of the city of Copenhagen. Copyright © 2007 John Wiley & Sons, Ltd.

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Due to the configuration of the wind farm, wake losses at Middelgrunden are confined to two wind direction sectors and can be reasonably well predicted by the WAsP model despite the irregular layout of the turbines. Observed wake losses are highest at low wind speeds and decrease as wind speeds increase in accord with expectations. Overall wind farm efficiency was calculated as 90% using wind farm data from 2001 to 2004, and 86% from the WAsP model. However, some discrepancy between the results is to be expected given that the time period for the modelling is independent of the data from the wind farm production and the turbines generated 5.7% more power than predicted using the manufacturer’s power curve. The curved shape of the wind farm makes wake development moving down the row difficult to quantify. Using a narrow sector and comparing power output at each turbine suggest that power output initially decreases but then increases along the row. This appears to be the result of the wake losses moving out of the sector under study. Using a different approach (allowing the wake direction to vary and calculating the mean wind speed in the centre of the wake) gives an initial wind speed decrease which subsequently remains almost constant. Offshore turbulence intensity is strongly related to wind speed. At Middelgrunden, this relationship is less well defined, possibly due to the proximity of the site to the coast. Average ambient turbulent levels are around 13%. Using the power SD method to determine turbulence, this relationship between turbulence intensity and wind speed is very evident. Turbulence levels are at a minimum of ∼6.5% at around 11 m s−1 and then increase with wind speed. There is variability in the levels of turbulence experienced by different turbines at the same wind speed but this is typically within 5% of the average. Turbulence intensity is about 9% higher (absolute terms) when computed using data from the nacelle anemometer on wind turbines than those derived from the turbine power SD. These differences could not be explained by differences in the heights of the measurements and it is concluded that the power SD method gives a closer representation of ambient turbulence in non-wake conditions than does the nacelle anemometer method. The constant in the derivation of turbulence intensity using the SD method (equation (3)) was determined to be approximately 0.8. Turbulence generated from wind turbine wakes was examined using the turbine power data and also the predictions from the ‘added turbulence’ model. Turbulence intensity at the Middelgrunden wind farm is strongly dependent on wind direction. Comparing turbulence in two major wake sectors in the north-south directions with ambient turbulence in the east sector shows that in the wake sectors, the measured turbulence intensity increases by about ∼20% at the second turbine. The model gives a good prediction of the increase in turbulence intensity in wind turbine wakes but under-predicts ambient turbulence in comparison with turbulence from the power data. It is worth noting here that the turbine spacing is 2.4 D which is beyond the limits of most wake models. Nevertheless, there is good agreement between the model and measurements for the wake sectors at Middelgrunden for both power losses in wakes and the added wake turbulence. The models will next be evaluated for a large (multi-row) offshore wind farm.

Acknowledgements This work has in part been financed by EU project UPWIND (SES6 019945), Danish Public Service Obligation (PSO) funds (F&U 4103) and by the Danish Research Ministry of Science Research and Innovation (210404-0005). Data from Middelgrunden were provided by Københavns Miljø- og Energikontor. Thanks also to two anonymous reviewers for their helpful comments and suggestions.

References 1. Frandsen S. Turbulence and Turbulence-Generated Fatigue Loading in Wind Turbine Clusters. Risø National Laboratory: Roskilde, Denmark, 2005; 128. Risø-R-1188(EN). [Online]. Available: http://www.risoe.dk/rispubl/VEA/ris-r1188.htm. (Accessed 6 June 2007) Copyright © 2007 John Wiley & Sons, Ltd.

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Wind Energ 2007; 10:517–528 DOI: 10.1002/we