mesoscale modeling of offshore wind turbine wakes at the

WIND ENERGY

Wind Energ. 2015; 18:559–566

Published online 12 February 2014 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/we.1708

SHORT COMMUNICATION

Mesoscale modeling of offshore wind turbine wakesat the wind farm resolving scale: a composite-basedanalysis with the Weather Research and Forecastingmodel over Horns RevPedro A. Jiménez1, 2, Jorge Navarro1, Ana M. Palomares1 and Jimy Dudhia1

1 División de Energías Renovables, CIEMAT, 28040 Madrid, Spain2 Mesoscale and Microscale Meteorology Division, NCAR, Boulder, 80301 Colorado, USA

ABSTRACT

The use of mesoscale modeling to reproduce the power deficits associated with wind turbine wakes in an offshore environ-ment is analyzed. The study is based on multiyear (3 years) observational and modeling results at the Horns Rev wind farm.The simulations are performed with the Weather Research and Forecasting mesoscale model configured at a high horizon-tal resolution of 333 m over Horns Rev. The wind turbines are represented as an elevated momentum sink and a sourceof turbulent kinetic energy. Composites with different atmospheric conditions are extracted from both the observed andsimulated datasets in order to inspect the ability of the model to reproduce the power deficit in a wide range of atmosphericconditions. Results indicate that mesoscale models such as Weather Research and Forecasting are able to qualitativelyreproduce the power deficit at the wind farm scale. Some specific differences are identified. Mesoscale modeling is there-fore a suitable framework to analyze potential downstream effects associated with offshore wind farms. Copyright © 2014John Wiley & Sons, Ltd.

KEYWORDS

wind turbine wakes; mesoscale modeling; wind farm scale; power deficit; WRF; SCADA dataset

Correspondence

Pedro A. Jiménez, Mesoscale and Microscale Meteorology Division, National Center for Atmospheric Research, 3450 Mitchell Ln.,Boulder, 80301 Colorado, USA.E-mail: [email protected]

Received 24 April 2013; Revised 4 December 2013; Accepted 11 December 2013

1. INTRODUCTION

Offshore wind energy has experienced a large increase in recent years being a promising technology to generate largeamounts of electricity.1 The majority of the existing wind farms have been installed in northern European countries andChina, with more offshore projects under construction.2 In view of the large development experienced, considerable effortshave been directed to quantify the power deficit generated by the wake of the wind turbines on downstream ones.3 Forthese purposes, different microscale modeling approaches have been used.3–6 Usually, the wind farm layout is analyzed inan idealized environment by prescribing the characteristics of the inflow.7

The increase in computational power reached during the last decades allows for the use of mesoscale models8 to reachhorizontal resolutions of the turbine separation (a few hundred meters). Hence, mesoscale models emerge as an alternativemodeling framework to characterize the influence that the individual wind turbines exert on the atmospheric flow. Theadvantage of using mesoscale models is that the simulation of the wind farm conditions can be accomplished in a realenvironment using initial and boundary conditions from reanalysis projects, for example. In addition, the large size of thearea over which the atmospheric evolution is simulated allows for the inspection of the characteristics of the wind farmwakes. Indeed, different parameterizations have been proposed to investigate the impact that the wind turbines producein weather and climate.9,10 In spite of the potential of mesoscale models to analyze the effects of wind turbine wakes,

Copyright © 2014 John Wiley & Sons, Ltd. 559

Mesoscale modeling at the wind farm resolving scale P. A. Jiménez et al.

a comprehensive comparison of model results with observations is still missing. Mesoscale model results should thereforebe interpreted with care.

This work presents the first comprehensive evaluation of a mesoscale model’s ability to reproduce the effects of windturbine wakes at the wind farm scale. The Weather Research and Forecasting (WRF) model version 3.411 is used to sim-ulate the atmospheric evolution over the Horns Rev offshore wind farm located off western Denmark. The effects of thewind farm in the atmosphere are simulated assuming that the turbines constitute an elevated momentum sink and a sourceof turbulent kinetic energy.12,13 A total of 3 years (2005–2007) are simulated at a high horizontal resolution of 333 min order to resolve the individual wind turbines within the wind farm and thus provide an exhaustive comparison with anobservational dataset created from a supervisory control and data acquisition system (SCADA dataset hereafter) that spansthe same temporal period.14 To our knowledge, the combination of the SCADA dataset and the WRF simulations hereinpresented provides the most comprehensive evaluation up to date.

2. EXPERIMENTAL DESIGN

The Horns Rev wind farm is located at 18 km from the western coast of Denmark (Figure 1). It consists of 80 Vestas V80wind turbines of 2 MW nominal power with the hub height at 70 m and 80 m of diameter. The shape of the wind farmis near rectangular with eight rows and 10 columns of turbines (see zoomed in area in Figure 1). The wind turbines areseparated between 560 m (seven diameters, east-west direction) and 832 m (10.4 diameters, NW-SE direction, the longdiagonal of the wind farm). Different samples of the SCADA dataset are used to analyze the wind power deficit underdifferent atmospheric conditions. Each sample presents different directions of the flow, turbulence intensity or atmosphericstability given the wind speed at the hub height of 8 m s�1. The power deficit (Pdef icit ) at a given turbine is definedwith respect to a free stream reference turbine (Pref ) according to Pdef icit D 1 � Pturbine=Pref . For instance, therecords at the wind turbine marked with a white circumference in the zoomed area in Figure 1 are used as a reference forthe samples with western winds. The atmospheric stability is calculated using observations at a nearby meteorological mastwith a method based on the bulk Richardson number that follows Grachev and Fairall.15 Data from the tower is also usedto quantify the turbulence intensity defined as the ratio of the wind speed standard deviation to the mean. The interestedreader is referred to Hansen et al.14 for specific details on the creation of the samples as well as to information regarding

Figure 1. The five domains used in the WRF simulation with 27,000, 9000, 3000, 1000 and 333 m of horizontal resolution. The num-ber of points of each domain (west-east by north-south) is also shown. The shaded gray areas represent the elevation of the coarserdomain, whereas the zoomed in area represents the wind (arrows) and the wind speed (shaded) in the innermost domain at a givenhour. The power production of each turbine (circles) is also shown. The wind turbine used as a reference to calculate the wind power

deficit for western flows is highlighted with a white circumference.

560Wind Energ. 2015; 18:559–566 © 2014 John Wiley & Sons, Ltd.

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P. A. Jiménez et al. Mesoscale modeling at the wind farm resolving scale

the quality control process imposed on the data. By categorizing the atmosphere into these groups, we are able to inspectthe ability of WRF to reproduce the wind power deficit under quite different atmospheric situations.

The WRF model has been configured using a total of five two-way domains interacting with a three to one spatial refine-ment in order to reach a horizontal resolution of 333 m in the innermost domain that comprises the Horns Rev wind farm(Figure 1). We prescribed a total of 36 vertical levels, five of them within the first 200 m of the atmosphere. A couple ofWRF simulations have been performed. The first one uses the WRF wind farm parameterization (WRF-default hereafter).However, the parameterization uses empirical approximations to the thrust and the power coefficients that are a potentialsource of errors in the simulation. To inspect the effects of this potential misrepresentation, a second WRF simulation isperformed using the data from the manufacturer to calculate these coefficients (WRF-manufac). Both sets of simulations,WRF-default and WRF-manufac, span the 3 years covered by the SCADA dataset (2005 to 2007). Each simulation consistsof a sequence of short runs of the model. In each set of runs, the model is initialized at 0 UTC every day of the 3 years andrun for 48 h storing the output every hour. The first day is discarded as a spin up of the model, whereas the output for thesecond day is retained as the simulation for that day. The initial and boundary conditions necessary to run the mesoscalemodel come from the ERA-Interim reanalysis project.16 A similar strategy has been used before to analyze the surfacewind variability over complex terrain at the synoptic scale,17,18 the mesoscale19,20 or to develop parameterizations.21,22

A number of subgrid scale processes are parameterized by WRF. The shortwave and longwave radiation schemes followthe works by Dudhia23 and Mlawer et al.24, respectively. Microphysical processes are represented with the WRF single-moment six class scheme,25 whereas the cumulus effects are parameterized only in the outermost three domains.26,27 Theair–sea momentum flux is parameterized following the work by Charnock.28 The effects of the turbulent vertical mixingwithin the planetary boundary layer are parameterized using a 1.5 order scheme that predicts the turbulent kinetic energy29

and advects it with the wind. The scheme is based on the work by Mellor and Yamada30 but includes a better formulationof buoyancy effects and a master length scale that depends on atmospheric stability. The effects of the wind turbines overthe atmospheric flow are parameterized following the work by Fitch et al.12 The wind turbines are represented as an ele-vated sink of momentum and a source of turbulent kinetic energy that responds to the wind speed according to a specifiedfunction approximating the effects of the turning rotors on the flow. The scheme is comprehensively documented in thework by Fitch et al.12 This method has been shown to produce a realistic representation of wind farm wakes,12,31 but acomprehensive evaluation of its performance has not yet been performed.

The realistic behavior of the WRF simulations is shown in the zoomed in area in Figure 1, which shows the wind at thehub height as well as the location of the wind turbines (circles) and its power production. The power production has beencalculated using the wind speed from the nearest grid point to the location of the wind turbines and the wind-power curveprovided by the manufacturer. The wind flow is from the NE, and a realistic attenuation of the wind speed is evidenced overthe wind farm in the downstream direction. The wind speed attenuation translates into a decrease in the power production.The power production from the turbine in the northeast to the turbine in the southwest of the wind farm ranges from 515to 405 kW. The power deficit is 0.21. Similar values have been observed in the wind farm.3 Although the mesoscale sim-ulation produces a realistic interaction with the atmosphere, it needs to be compared with observations in order to confirmthat it is able to reproduce the atmospheric behavior.

The evaluation herein presented consists of replicating the atmospheric conditions of the different samples calculatedwith the SCADA dataset14 with equivalent composites from the two WRF simulations. Hence, we are not imposing thecharacteristics of the incoming flow in the simulations but selecting those instances with the desired characteristics of theincoming flow from 3 years of simulated time. By comparing results from the observed and simulated composites, weare able to isolate the effects of the wind farm parameterization since both samples present the same atmospheric condi-tions. Comparison between WRF-default and WRF-manufac will allow us to inspect sensitivities with the wind turbinecharacteristics.

3. RESULTS

The wind speed attenuation as well as the power deficit as a result of the wind turbines interactions with the westerly flow(270˙ 2:5o) are shown in Figure 2 (red color). The values are averages for the different columns of wind turbines locatedin the inner rows (2–7). The composite contains observations and WRF outputs with a wind speed of 8 m s�1 at the hubheight and neutral atmosphere (jLj > 200 m, with L being the Obukhov length). In addition, only the simulated hourswith a turbulence intensity of 7% are selected since this is the mean value registered at a meteorological tower before theinstallation of the wind farm14 and the one used in a model intercomparison experiment.7,32 The observations show a clearreduction of the wind speed from the first to the second column of wind turbines and a more moderate decrease for subse-quent columns (red thick line in Figure 2(a)). WRF-default is able to reproduce these characteristics but the decrease fromthe first to the second column of turbines is not as pronounced as observed (thin red line). This is in part responsible for theunderestimation of the wind speed attenuation within the wind farm. In addition, there is a somewhat smoother reductionfor the last columns of turbines. WRF-manufac is in better agreement with observations (Figure 2(b)). The simulation

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Figure 2. Wind speed attenuation (a,b) and wind power deficit (c,d) as a result of averaging the values at rows 2 to 7. The inflow windspeed is 8 m s�1, and the atmospheric stratification is neutral. The colors indicate different wind directions (see legend), whereasthe thick (thin) lines correspond to observations (WRF). Error bars spanning the standard error of the mean33 are also shown. The left

(right) panels show results for WRF-default (WRF-manufac).

still underestimates the reduction of wind speed at the second column of turbines, but there is a much better agreementat the last one. The power deficit reflects similar characteristics (Figure 2(c),(d)). The deficit is about 0.25 (0.1) for theobservations (WRF-default) at the second column of turbines and about 0.45 (0.25) for the last column. WRF-manufacagrees better with observations especially at the last column, where the deficit is about 0.35. The higher power deficit simu-lated by WRF-manufac arises from the underestimation of the thrust coefficient, by 0.13 for a wind speed of 8 m s�1,by the generic formula used by WRF-default (an increase of 19 %). This result stresses the importance of an accu-rate representation of the wind turbine characteristics for an adequate simulation of the atmospheric interaction with thewind turbines.

The influence of small departures from the western direction is also shown in Figure 2 (green and blue colors). Thewind speed attenuation and the power deficit are higher when the wind is more westerly oriented (red) due to the directinfluence of the wakes on the downstream turbines. When the wind direction starts to deviate from the west, the wind speedattenuation and the power deficit decrease (green and blue lines). WRF is able to reproduce the direction of the changesbut shows a smaller reduction than the SCADA dataset.

The relationship of the power production with the direction of the flow is better appreciated in the composite shownin Figure 3. The power production of the wind farm is normalized by the expected production of 80 times a single windturbine to calculate the park efficiency. Again, the wind speed at the hub height is 8 m s�1, and the turbulence intensityis 7%. The observations reveal a clear reduction of the power production for wind directions of 90ı, 175ı, 270ı and 355ı

(red line). The higher power deficit at these directions is a consequence of the geometry of the wind farm (Figure 1) sincefor these directions, the inner turbines are directly affected by the wakes generated by the upstream turbines. WRF-defaultreproduces the power production for most of the wind directions (green line) but is not able to reproduce the large reductionof power generation at the previous four directions. Only for easterly/westerly winds, the model reproduces a reduction ofthe power production. WRF-manufac tends to overestimate the power deficit except for the four directions with the highestdeficits. This suggests that although the horizontal resolution is high enough to resolve individual turbines, it is not enoughto accurately represent directional effects of the wakes, which lead to an overestimation of downstream effects. WRF-default results are in better agreement with observations because of a compensation of errors resulting from the smallerdrag generated by the turbines associated with the underestimation of the thrust coefficient and this directional influence.


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Figure 3. Park efficiency versus the direction of the flow for wind speeds of 8 m s�1. The WRF simulations have a turbulenceintensity of 7%. The error bars span the standard error of the mean.

Figure 4. Wind power deficit as a result of averaging the values at rows 2 to 7 for westerly flow, 8 m s�1, and different atmosphericstabilities (see legend). The error bars span the standard error of the mean. Results for both WRF-default (a) and WRF-manufac (b) are

shown.

Complementary information of the simulation performance is shown in Figure 4, which represents the power deficit asa function of the atmospheric stability. Similarly to the previous comparison (Figure 2), the wind flow is from the west, thewind speed at the hub height is 8 m s�1 and the turbulence intensity is 7%. For stable situations, it was necessary to relaxthe conditions for the western flow (and turbulence intensity) from 270˙ 5ı to 270˙ 15ı (7˙ 1% to 7˙ 2%) in order tohave WRF outputs in the sample. This is associated with the reduction of the turbulence intensity during stable situations.14

The SCADA dataset (thick lines) reveals that after a strong deficit at the second column of wind turbines, the power deficitat subsequent columns is less pronounced. Stable situations (red) produce larger deficits than neutral (green) and unsta-ble (blue) conditions. Although both WRF simulations (thin lines) reproduce a smaller power deficit than observed at thesecond column of turbines, they are able to reproduce the different response to the atmospheric stability, with a certainunderestimation for unstable conditions. The simulated power deficit for stable situations could be overemphasized withrespect to the neutral and unstable cases since the stable sample contains WRF outputs with weaker turbulence intensity,and this may have an influence on the results. Indeed, Figure 5 indicates that the power deficit decreases for higher tur-bulence intensities for unperturbed easterly flow of 8 m s�1. Both the composite calculated with the observations and thesimulations present this characteristic. However, a systematic underestimation becomes evident in the power deficit simu-lated by WRF. This indicates that WRF is able to realistically respond to changes in turbulence states but underestimatesthe deficit consistent with previous results (Figures 2, 4).


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Figure 5. Wind power deficit versus turbulence intensity for eastern winds of 8 m s�1. The error bars span the standard error ofthe mean.

Figure 6. Average wind speed (shaded) at 70 m calculated with data from domain 4 (1 km of horizontal resolution, Figure 1) for thosehours with wind flow from the west, neutral stratification, wind speed of 8 m s�1 and turbulence intensity of 7%. The location of thewind turbines (white circles) and the grid points of the innermost domain 5 (black dots) are also shown. Results for WRF-default are

shown in panel a) and for WRF-manufac in panel b).

4. CONCLUSIONS

A composite-based evaluation of the ability of a mesoscale model, WRF, configured at a horizontal resolution high enough(333 m) to provide details of the flow at the wind farm scale has been presented. The model (WRF-default) is able to qual-itatively reproduce the interactions of the wind farm with the flow under different atmospheric conditions (e.g., directionof the flow, stability and turbulence intensity). However, the model tends to underestimate the power deficit, especially forthose wind directions that locate the wind turbines directly downstream of preceding ones. An improved representation ofthe turbine characteristics (WRF-manufac) improves the simulation for directions with the highest power deficit but over-estimates the deficit for the rest of the directions. This is probably a consequence of the horizontal resolution used, 333 m,which although it can be considered high, it is not enough to accurately represent directional effects of the wakes.

Although some progress needs to be made to improve the ability of mesoscale models to reproduce the interactionsbetween the atmosphere and offshore wind farms, important information regarding potential impacts in downstream loca-tions can be reasonably pursued. This kind of analysis stems from the possibility of modeling the wind farm in a realenvironment as with the present simulation. For instance, Figure 6 shows the wind speed at 1 km of horizontal resolu-tion (from domain 4, see Figure 1) for the composite with western winds, neutral conditions, turbulence intensity of 7%


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and wind speed of 8 m s�1. The effects of the wind farm can be noticed at about 15 km downstream for WRF-default(Figure 6(a)) and at even further distances for WRF-manufac (Figure 6(b)). The impact is likely higher given the underesti-mation of the wind speed attenuation for this particular wind direction (Figure 2). Mesoscale modeling is therefore a usefulmodeling framework to minimize potential power deficits generated by clusters of wind farms, an issue that is demandingmore attention given the increasing development of offshore wind energy.

ACKNOWLEDGEMENTS

Funding from the EERA DTOC contract FP7-ENERGY-2011/no 282797 is acknowledged. Funding from projectENE2012-38772-C02-01 is also acknowledged. We also would like to thank DONG Energy and Vattenfall as well asECMWF for facilitating the access to their datasets. Special thanks to K. Hansen for providing us with the compositesof the observations. The study was undertaken within the collaboration agreement 09/490 between CIEMAT and NCAR.We also thank the reviewers and the editor for their helpful comments and Mindi E. McDonald for her careful revision ofthe manuscript.

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mesoscale modeling of offshore wind turbine wakes at the

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