the necessary dist between large wind farms offshore

8/6/2019 The Necessary Dist Between Large Wind Farms Offshore

1/29

Ris-R-1518(EN)

The necessary distance between large

wind farms offshore - study

Sten Frandsen, Rebecca Barthelmie, Sara Pryor, OleRathmann, Sren Larsen, Jrgen Hjstrup

Wind Energy DepartmentRis National Laboratory

Per Nielsen, Morten Lybech Thgersen

EMD

Ris National LaboratoryRoskildeDenmark

August 2004


2/29

Author: Sten Frandsen, Rebecca Barthelmie, Sara Pryor, OleRathmann, Sren Larsen, Jrgen Hjstrup, Per Nielsen, MortenLybech ThgersenTitle: The necessary distance between large wind farms offshore -study

Report number

Ris-R-1518

August 2004

ISBN: 87-550-3447-0

Contract no.:

Danish Public Service Obligation(PSO) funds F&U 2108.

Group's own reg. no.:1120137-00

Sponsorship:PSO F&U 2108

Cover :

Pages: 29Tables: 2References: 17

Executive summary

A review of state of the art wake and boundary layer windfarms was conducted. The predictions made for windrecovery distances (that might be used to estimate optimalplacing of neighbouring wind farms) range between 2 and 14km. In order to model the link between wakes and theboundary layer the new Storpark Analytical Model has beendeveloped and evaluated. As it is often the need for offshorewind farms, the model handles a regular array-geometry withstraight rows of wind turbines and equidistant spacingbetween units in each row and equidistant spacing betweenrows. Firstly, the case with the flow direction being parallel torows in a rectangular geometry is considered by definingthree flow regimes. Secondly, when the flow is not in linewith the main rows, solutions are found for the patterns ofwind turbine units emerging corresponding to each winddirection. The model complex will be adjusted and calibratedwith measurements in the near future.

Ris National LaboratoryInformation Service DepartmentP.O.Box 49DK-4000 RoskildeDenmarkTelephone +45 [email protected]

Fax +45 46774013www.risoe.dk
mailto:[email protected]://www.risoe.dk/vea/storpark/storpark_model/www.risoe.dkhttp://www.risoe.dk/vea/storpark/storpark_model/www.risoe.dkmailto:[email protected]


3/29

Contents

OBJECTIVES AND STRUCTURE 5

1 SUMMARY OF MAIN RESULTS 6

1.1 Executive summary 6

1.2 Review of models 6

1.3 Paper submitted to EWEC conference 2004 7

1.4 Evaluation of the Storpark model 21

2. OVERVIEW OF SUPPORTING WORK 22

2.1. Review of wake and boundary layer models 222.1.1 WAsP8 wake effects model 222.1.2 Comparing WindPRO and Windfarmer wake loss calculation 222.1.3 Overview of models and preliminary analysis 222.1.4 Strmmingsmodeller 222.1.5 Overview of single and multiple wake models 23

2.2. Review of existing data 232.2.1 Vindeby analysis 23

2.2.2 Analyses on real versus calculated wind shadow 23

2.3. Development of new models 232.3.1 Wake model based on Navier stokes solution with eddy viscosity closure 232.3.2 Wind farm modelling using an added roughness approach in WindSim CFDmodel 242.3.3 Note re: energy budget model 242.3.4 Flow field around a turbine rotor 242.3.5 A new approach to multiple wake modelling 242.3.6 Verification of Storpark models 24

3. PRESENTATIONS FROM THE PROJECT 25

3.1 Analytical modelling of large wind farm clusters 25

3.2 Miscellaneous on roughness change models 25

3.3 WAsP 8 wake effect modelling 25

3.4 Preliminary results from the SAR-wake project 25

3.5 Roughness model, empirical analyses and wakes 25

3.6 Vindeby_wakes 25

Ris-R-1518(EN) 3


4/29

3.7 Design of offshore wind turbines 26

3.8 Spatially average of turbulence intensity inside large wind turbine arrays 26

3.9 Load measurements in wind farms 26

3.10 Background for the effective turbulence model 26

4 PAPERS AND POSTERS FROM THIS PROJECT 27

5 LIST OF SUPPORTING REFERENCES 28

6 ACKNOWLEDGEMENTS 28

4 Ris-R-1518(EN)


5/29

Objectives and structure

The main objective of the Storpark project was to develop methods to determine the

optimal distance between large wind farms in the offshore environment. The main results

are given in Section 1. An overview of the supporting work is given in Section 2 which

gives brief reviews of the notes produced for this report. Section 3 gives a list of

presentations, Section 4 papers and posters from the project and Section 5 a list of

additional references used in this work. All are given in full on the CD.

Ris-R-1518(EN) 5


6/29

1 Summary of main results

1.1 Executive summary

A review of state of the art wake and boundary layer wind farms was conducted. Thepredictions made for wind recovery distances (that might be used to estimate optimalplacing of neighbouring wind farms) range between 2 and 14 km. In order to modelthe link between wakes and the boundary layer the new Storpark Analytical Modelhas been developed and evaluated. As it is often the need for offshore wind farms,the model handles a regular array-geometry with straight rows of wind turbines and

equidistant spacing between units in each row and equidistant spacing between rows.Firstly, the case with the flow direction being parallel to rows in a rectangulargeometry is considered by defining three flow regimes. Secondly, when the flow isnot in line with the main rows, solutions are found for the patterns of wind turbineunits emerging corresponding to each wind direction. The model complex will beadjusted and calibrated with measurements in the near future.

1.2 Review of models

Reviews of boundary-layer and wake models ranging in from engineering models toCFD showed a wide range of predictions for recovery of wind speed after a large

offshore wind farm ranging from 2-3 km to 12-13 km. These are detailed in Section2.1. The table below gives a summary for recovery to 98% of the free stream windspeed/power density based on a westerly transect at a wind farm based on the HornsRev wind farm layout (72 turbines).

Model Wind speedrecovery

distance (km)

Power densityrecovery distance

(km)

WAsP z0(block) 0.1 m 6 12

WAsP z0(block) 0.5 m 7 12.5

WAsP z0(block) 1.0 m 8 13

WAsP wake decay 0.075 2 -WAsP wake decay 0.05 3 -

Added roughness: exponential z0 decay 14 (5%-7.5) -

Added roughness: constant z0 14 (5%-5.5) -

*EMD CFD model: z0 0.1-0.5 m 8 -

*EMD CFD model: z0 1 m 7 -

One of the main issues is that the wakes generated by the wind farm are notparameterised to interact with the boundary-layer. Hence a new model wasdeveloped which is described in the paper submitted to the EWEA. The paper isgiven in full in the next section and a comparison of the new model with other state

of the art wake models is given in section 1.3.

6 Ris-R-1518(EN)


7/29

1.3 Paper submitted to EWEC conference 2004

Analytical modelling of wind speed deficit in large offshore

wind farms

Sten Frandsen, Rebecca Barthelmie, Sara Pryor, Ole Rathmann, Sren Larsen, Jrgen Hjstrup, MortenThgersen1

Risoe National Laboratory,4000 Roskilde, Denmark

email: [email protected]

Abstract:The method is analytical and encompasses both small wind farms and wind farms extending over largeareas.As it is often the need for offshore wind farms, the model handles a regular array-geometry with straightrows of wind turbines and equidistant spacing between units in each row and equidistant spacing betweenrows. Firstly, the case with the flow direction being parallel to rows in a rectangular geometry isconsidered by defining three flow regimes. Secondly, when the flow is not in line with the main rows,solutions are found for the patterns of wind turbine units emerging corresponding to each wind direction.The presentation is an outline of a model complex that will be adjusted and calibrated with measurementsin the near future.

Keywords: wind farm, large, efficiency, analytical, model.

1 EMD, Aalborg Denmark

Ris-R-1518(EN) 7
mailto:[email protected]:[email protected]


8/29

1. Introduction

The engineering models presentlyapplied for calculating productionlosses due to wake effects fromneighbouring wind turbines are basedon local unit-by-unit momentum

equations, disregarding the two-wayinteraction with the atmosphere. Othermodels, which did not reachengineering relevance or maturity,predict the array efficiency ofinfinitely large wind farms by viewingthe wind turbines as roughnesselements. As a third option, attemptswere made to apply CFD schemes indetermining the flow field and thus thearray efficiency. The CFD schemespresently lack details and arecomputationally uneconomic.Here, as it is often the need foroffshore wind farms, the modelhandles a regular array-geometry withstraight rows of wind turbines andequidistant spacing between units ineach row and equidistant spacingbetween rows.Firstly, the case with the flow directionbeing parallel to rows in a rectangulargeometry is considered. Counting from

the upwind end of the wind farm, themodel encompasses 3 regimes asillustrated in Figure 1:

In the first regime, the windturbines are exposed to multiple-wake flow and an analytical linkbetween the expansion (decay) ofthe multiple-wake and theasymptotic flow speed deficit isderived.

The second regime materializes

when the (multiple) wakes fromneighbouring rows merge and thewakes can only expand verticallyupward. This regime corresponds(but is not identical) to the flowafter a simple roughness changeof terrain.

The third regime is when the windfarm is infinitely large and flowis in balance with the boundarylayer.

Wake merged

Separate singlerow

Somewheredownwind:Large wf

Wake merged

Separate singlerow

Somewheredownwind:Large wf

Figure 1 Illustration of the regimes of the

proposed model. The wind comes from the

South, parallel to the direction of the rows.

Secondly, when the flow direction isnot in line with the main rows,solutions are found for the patterns ofwind turbine units emergingcorresponding to each wind direction.The solutions are in principle the sameas for the base case, but with differentspacing in the along wind directionand different distance to theneighbouring rows.The regimes outlined above arediscussed in detail in the following,

and component models described.

2. Single wake

Initially, the flow through and aroundthe wind turbine rotor is considered.Lanchester (1915) and Betz (1920)derived expressions that link thrust andpower coefficients of the wind turbineto the flow speed deficit of its wake.The main device of these derivationswere a control volume with no flow

across the cylinder surface.Alternatively and this is practical inthe present context a cylindricalcontrol volume with constant cross-sectional area equal to the wake areaand with horizontal axis parallel to themean wind vector is defined, Figure 2.From Engelund (1968), the momentumequation in vector form for the flowvolumeXwith the surface areaATis

8 Ris-R-1518(EN)


9/29

+++

=+

TT

T

AXA

AX

dATdXgApd

AdUUdXt

U

r

r

r

r

rrr

r

)((1)

where the acceleration term (first onthe left side), the pressure term (first

on the right hand side) and the gravityterm (second on the right hand side)often, as is done in the following, areneglected in basic considerations.Further, the cylinder extends upwindand downwind far enough2 for thecontrol volume pressure to be equal to

the free-stream pressure. Tr

is the sumof forces from obstacles acting on theinterior of the control volume and thelast term on the right hand side is theturbulent shear forces acting on thecontrol volume surface.

Should it be acceptable to neglectshear forces in the cylinder surface andassume that pressure downwind hasregained the free-stream level, the

momentum equation convenientlyreduces to

==TT AA

dQUAdUUTrrrrr

)( , (2)

where dQ is the volume flow out of thesurface area dA. Assuming the wake tobe non-turbulent, the expression can bedeveloped further. The momentumflux out of the cylinder surface is

2Upstream of the order to 1 rotor diameter and

downwind 2-3 rotor diameters.

found the following way: the volumeflow (per sec.) out of the controlvolumes cylinder surface is equal tominus the volume flow Qe out of theends of the cylinder (with area A =

R2),

== AAecyl UdAdAUQQ 0 , (3)

where U0 is the free-flow speed and Uis the flow speed in the wake.Assuming that the radius of thecylinder is sufficiently large for theflow speed in the cylinder surface tobe approximated as U0, then themomentum flux out of the cylindersurface becomes

cylcyl QUM = 0 . (4)

The rotor thrust becomesU0

U=U0(1-b)

D0 D

x

X, AT

T A=(/4)D

2

Figure 2.Control volume around a wind turbine

rotor. The cylindrical control volume has the

surface area AT and volume X. The Betz control

volume (full line) follows the streamlines.

=+= Acyle dAUUUTMMT )( 0

(5)

This expression is the classical startingpoint for development of wake models,e.g. Engelund (1968), Schlichting(1968) and Tennekes and Lumley(1972). Next step in evaluation of the

wake characteristics is to assume self-similarity of the wake flow speedprofiles, i.e. the wake wind profile canbe written as

)/()( RrfxUU w = , (6)

where Uw is the minimum wake flowspeed, ris the distance from the centerof the wake and R is a characteristic ofthe wake width at the distance xdownwind of the rotor. Assuming thewake axis-symmetric, insertingequation (6) in (5) and introducingpolar coordinates and the substitution

Rry /= yield

( ) =

ww drRrfUURrfrUT2

0 00 )/()/(

( )

0

02 )()( dyyfUUyfyURT ww (7)

Ris-R-1518(EN) 9


10/29

The integral in (7) only depends on theminimum wake flow speed Uw.Therefore, equation (7) can be writtenas

)( '0'2

1 wwf UUURCT = , (8)

where is a characteristic

flow speed and C

wfw UCU = 2'

f1 and Cf2 areconstants depending only on the

integrals and i.e. the

shape of the wake profile.

0 )( dyyf

0

2

)( dyyf

The assumption of self-similaritythroughout the wake is not onlyquestionable in general terms for theregions of the wake, which is ofinterest in the present context. It isdefinitely wrong in the near-wakeregion. However, the self-similarityassumption maintained in here is

justified because the wake-affected

wind turbines rotor integrates thewake over a sizable fraction of its area,thus making the finer details lessimportant.Thus, any actual wake shape can berepresented by a rectangulardistribution of the flow speed withoutviolating the general principles of theabove derivations:

20

4),( D

AUUAUT == , (9)

whereD is the diameter of therectangular wake flow speed profileandA is the area of the wake . Thethrust may also be expressed as

200

2002

1

4, D

ACUAT T == , (10)

whereA0 is the swept area of the rotor,D0 is the rotor diameter and CTthethrust coefficient. As pointed outpreviously, the derived expression isonly valid some distance downwind ofhe rotor where the pressure has

regained its free-flow value.Denominating the induction factor

t

3

0/1 UUa a= , where Ua is the flow

speed in the wake after the initial wake

expansion, then the thrust coefficient isrelated to the induction factor by

1,11)2(


11/29

and 1 of the combined equations (9)and (10), see later.The following expression for the wakeflow speed is found:

TCA

A

U

U 0

0

212

1

2

1= . (14)

ForA(x=0) =Aa, equation (14) hassolutions for 10 a , where the +

applies for and - for .

Assuming monotonous expansion ofthe wake for increasingx, equation(14) only has solutions for ,

probably because one or more of theassumptions leading to the equationare violated. A frequently appliedapproximation to equation (9) forsmall wake flow speed deficits is

, which in turn

modifies equation (14):

5.0a 5.0>a

5.0a

)( 00 UUAUT

A

Aa

A

AC

U

UT

0021

0

11 . (15)

In principle this has solutions for alldistances downwind and for all

. The above considerations

allow only estimation of the initialwake flow speed deficit. In order toestimate the deficit any distance

downwind, a reliable model for thewake expansion must be identified.

10 a

Schlichting (1968), Engelund (1968)and others point to a solution

where . xxAxD for3/23/1

The result stems from severalassumptions (most prominent constanteddy viscosity in the wake and self-similarity of the wake deficit andturbulence profiles) and is only validin the far wake where the

approximation of equation (15) isvalid. Therefore and for reasonsgiven in the next section it is usefulto adopt a model for expansion of thewake cross-sectional area as functionof distance downwind that has theform:

( ) 00/12/ /,)( DxsDsxD

nn =+= ,

(16)

where the initial wake diameter is

0D . If the Schlichting solution is

chosen, then n=3. The constant must

be experimentally determined. Aninitial estimate could be obtained bycomparing Equation (15) with a modeldeveloped by Jensen (1983) and Katicet al (1986):

Un

U0

Un+1Dn+1Dn

D0

U0

xr

Figure 4Flow between two units in a long row of

wind turbines.

2)(

20

)(

0

0

0)()(

11

,21)(

nojnoj

nojnoj

D

Da

A

Aa

U

U

DsxD

==

+=

(17)

where 1.0)( noj . In this model, the

initial expansion of the wake has beenneglected and the linear wakeexpansion is presumably too large.However, being applied in the windresource computer code WasP, themodel has proven successful for windfarms of limited size. Matching theexpressions (15) and (17) for wakeflow speeds the distances downwindyields

( ) ( )( )[ ] 1)(2/

2)(

/22/

121

21

+=

+=+

ss

ss

nnoj

n

noj

nn

(18)

Ris-R-1518(EN) 11


12/29

Figure 3 shows the relative wake windspeed as function of downwinddistance from the wake generatingwind turbine for different wake shapesand with and without the linearizationof equation (14).Obviously, the decay factor depends of

the distance downwind chosen tomatch the flow speeds. For small CT

and larges, the decay factor is of

order 10(noj).The square root shape (n=2) is chosenfor reasons given hereafter.

3. Multiple wake, single row

(regime 1)

The case of multiple-wake is dealtwith as illustrated in Figure 4. Firstly,

the possible effects of boundaries suchas the ground and the neighboringwakes are included implicitly through

the area growth, . We

consider a single row of wind turbinesand in that row, the wake betweenwind turbine no. n and wake n+1 isdescribed, Figure 4. Outside (and in)the cylinder surface of control volumethe flow speed is U

nni AAdA = +1

0. The wake flow-speed is assumed constant. The flowspeed at the ends of the cylinder

surface is denominated as indicated inFigure 4. The areas corresponding tothe diametersD* are denominatedA*and is now referring to the wind speed

just in front of each unit. (note alsothat the cross section of the controlvolume need not be a circularcylinder).Without the approximation of equation(15), we get for momentumconservation:

( ) ( ) (( ) ++

= ++++TUUUA

UUUAAUUUA

nnn

nnnnn

0

00011011 )

( )

( ) +

= +++

TnRnnn

nnn

CUAUUUA

UUUA

2

21

0

1011

( ) ( )

0

11

0

2

121

111

,

,11

U

Uc

U

Uc

CcA

Acc

A

Acc

nn

nn

Tnn

Rnn

n

nnn

++

++++

==

+=

(19)where

0/),()( DxssnAsAA rrrnnn ===

is a function of the dimensionless

distances from the first wind turbine.With the approximation of the flowspeed deficit, equation (15), therecursive equation becomes

( )

+=

+++ nT

n

Rn

n

nn cC

A

Ac

A

Ac

111

2

111 .

(20)For both approaches, a model for thewake expansion is needed.

Asymptotically for n

For an infinite large number of windturbines, 0)(, 1 +nn ccn , it

must be assumed that there is anasymptotic, non-zero flow speed: if theflow speed becomes zero then theshear becomes zero and the flowwould accelerate etc. Denominatingthe asymptotic value of the ratio

1+== nnw ccc for large ns, an equation

for linking the asymptotic wake areaand wake flow speed is obtained:

( ) ( ) += ++Tw

n

Rww

n

nww CcA

A

ccA

A

cc2

121

111

Tw

wRnn C

c

cAAA

=+

121

1 .

(21)

12 Ris-R-1518(EN)


13/29

In Equation (21) the term

Tw

wR C

c

cA

121 is a constant, and thus

asymptotically wake cross-sectionalarea is expanding linearly withx.Equation (21) points to an interesting

result: With only conventionalassumptions, it is possible to derive thewake expansion for an infinite row oftwo-dimensional obstacles (wind

turbine rotors): 21

xD . That expansion

is the only shape that asymptoticallywill ensure a non-vanishing and non-increasing flow speed.By assuming the wake cross sectioncircular, it is now possible to link the

decay factor in equation (16) to theasymptotic flow speed ratio c1. With

the wake model of equation (16) withn=2 corresponding to the square rootexpansion of wake diameter, theincrease in wake cross section is

( ) ( ) rs Rrr

nn

AnsD

nsD

AA

=+++

=+

20

20

1

4)1(

4

(22)wheresris the dimensionless distancebetween the wind turbines in the row.

Inserting equation (22) into equation(21) yields

w

w

r

T

c

c

s

C

=12

1. (23)

Thus, if the asymptotic, relative flowspeed in the wake is known, then thedecay constant is given. Conversely,the relative wake flow speed is givenas

r

Tw

s

C

c

21+

= (24)

In Figure 5, the result of applying

equation (20) is compared with datafrom the wind farm Nrrekr Enge II.It is seen that the flow speed ratio (i.e.also cw is approximately constant) isonly marginally dependent on free-flow mean wind speed. With a CTmeasured on a wind turbine similar tothe units in question and with thatcurve approximated by

( ) 25.325.3 UUCT , it is foundthat the decay constant must beproportional to CTto satisfy equation(23). The full line in Figure 5 is theaverage of the model result for the 4different wind speeds.

0.75

0.80

0.85

0.90

0.95

1.00

1 2 3 4 5 6 7

Wind turbine No.

RelativeWS,c

U=6.9

U=8.9

U=10.9

U=11.9

Figure 5 Measurement of wind speed ratio, ci , at

Nrrekr Enge II. Average is taken over six rows

with each 7 units. sr7. The wind farm consists of

42 300kW units.

The consequence of a non-constantflow speed ratio cw is that the decay

constant is a function ofCT, i.e. theinitial wake deficit/turbulence.

4. Multiple wake, merged (regime 2)

When the wakes from different rows

meet, the lateral wake expansion isstopped and the wake area can onlyexpand upward. Since the area mustexpand linearly to satisfy equation(21), the height of the wake mustincrease linearly: this means that thegrowth of what is equivalent to theinternal boundary layer for roughnesschange models asymptotically has

xh .

Ris-R-1518(EN) 13


14/29

Also in regime 2, the wake areamust expand linearly for the flowspeed to approach a non-zero or everincreasing value. Since the wakecannot expand laterally, theincremental growth of the internalboundary layer, in regime 2, in the

limit for isn

0

1

0 Ds

AA

Ds

dAh

r

nn

r

== + , and (25)

=

=

+

00

202

1

021

0

1

11

41

11

1

1

DsDsCD

c

c

DsxC

c

cA

Dsx

AA

x

h

rfT

mw

mw

rT

mw

mwR

r

nn

0

1000

2000

3000

0 10000 20000 30000 40000 50000

x [m]

h

[m]

new model

elliott

elliott*.33

Figure 6Growth of internal boundary layer as

function of downwind distance to front end edge

of wind farm.

fr

Tt

t

mw

mwt

mw

mw

ss

Cc

hxxc

c

chc

c

c

x

h

8

,)(

1100

=

+

=

(26)

wheresf is the dimensionless distanceto the neighbouring rows, cmw is therelative flow speed in the wake andx0and h0 are integration constants to bedetermined. We want to make acomparison of this result with Elliott

(1958):

5

4

5

1

005

4xzh

. (27)

For the purpose we choose thefollowing values of the parameters:

mHDCss RTfr 100,5.0,7 ===== .

WhereHis hub height. This gives

019.0,m55.000 =

=

x

hz

Further, assuming that the wakeexpands similarly in lateral andvertical direction from hub height, weestimate the heights of the wakes whenthese merge to

mDDsHh RRf 500521

0 + .

The distance downwind from the edgeof the wind farm to where the wakesmerge is here estimated as:

mhx 500010 00 = .

In Figure 6 the growth of the internal

boundary layer is plotted for Elliottsmodel and for the model given byequations (26) and (27). As to thefunctional dependency on distancedownwind, the model compares wellwith Elliott (1958), who suggests the

approximation 54

xh . The Elliott

model estimates the internal boundaryapprox. 3 times higher than theproposed model. However, the basicElliot and Panofsky (1973) models are

based on ratios of surface stress at theupstream and downstream conditions.For velocity conditions, the proper IBLheight is one third of the basic height,see Sempreviva et al.(1990).The implementation of the model isunder way. Annex A describes theoperationalisation of the model basedon the theoretical framework describedin Sections 2-5.

5. Wind farm in balance with

boundary layer (regime 3)

A model for the effect of a very largewind farm on the planetary boundarylayer, Frandsen (1992) and Emeis andFrandsen (1993), is outlined in thefollowing. The first similar approachto the problem was given by Templin(1974) and Newman (1977) who together with a few others, Bossanyi(1980) pioneered the discipline. Atthe time, the approach was by mostpeople considered far-fetched, since

14 Ris-R-1518(EN)


15/29

wind farms extending many kilometresseemed totally unrealistic. The modelpresented below refines Newman(1977) by defining two flow layersdivided the wind turbine hub heightand by introducing the so-calledgeotropic drag law.

The geostrophic drag law is derived byassuming inertial and viscous forcessmall (low Rossby and Ekmannumber) relative to the Coriolis andfriction forces, respectively, andpressure force. The drag law forneutral atmospheric stratification canbe written as, Tennekes and Lumley(1972),

2

2

0

ln BAfz

uuG +

=

. (28)

Here, is the friction velocity,zu 0 is

the surface roughness, sin2=f is

the Coriolis parameter and G is the

geostrophic wind speed. is theangular speed of Earth and is thelatitude.A andB are constants, whichby Troen and Petersen (1989) areestimated to beA = 1.8 andB = 4.5.

Equation (27) is implicit in and for

practical purposes an approximation is

useful. Jensen (1978) proposed such anapproximation, and with an adjustmentto that approximation proposed byEmeis and Frandsen (1993), thegeostrophic drag law becomes

u

00

0

)(lnln

ln

* zef

G

G

Afz

G

Gu

Afz

G

uG

A

=

, (29)

where the constant by comparison with

equation (28) is estimated to at

latitude 55.

4A

Returning to the model for theinfluence of the wind farm on the localwind climate, the followingassumptions are made:

The wind farm is large enough forthe horizontally averaged, verticalwind profile to be horizontallyhomogeneous.

The thrust on the wind turbinerotors is assumed concentrated athub height.The horizontally averaged verticalwind profile is logarithmic overhub height and logarithmic underhub height. This assumption is

similar to the assumption for thedevelopment of the internalboundary layer after a change ofsurface roughness.The vertical wind profile iscontinuous at hub height.Horizontally averaged turbulentwind speed fluctuations arehorizontally homogeneous.The height of the PBL isconsiderably larger than windturbine hub height: H>>h. Here,we could comment that forced bytechnology, this assumption is nowonly partly satisfied, depending onwhich boundary layer height ischosen.

Uh

U

ln(z)

H

Geostrophic wind speed GHzzU => )(

Outerlayer

Innerlayer

Roughnessz00

Friction velocity 0u

0,zu i

Hub height shear 2htUct=

Figure 7The impact of an infinitely large wind

farm on the planetary boundary layer. The

di erence between GandU is exa erated.

Given that the last assumption isviolated, this will be addressed further

in later versions of the model.The model for an infinitely large windfarm has to some extent been reportedpreviously, Frandsen (1993) andFrandsen and Madsen (2003). Theapparent wind farm roughness maybe expressed as:

+=

20

00

))/ln(/(exp

zhchz

t

. (30)

Ris-R-1518(EN) 15


16/29

In particular for large wind speeddeficits, this result differs significantlyfrom Newman (1977) in that it predictsa lesser deficit. From the large-wind-farm solution the hub height windspeed and thus the flow speed ratio tothe free flow speed is found, cwf. The

way we have built the model, this mustbe the asymptotic value for regime 2.

6. Other wind directions

In the regular wind turbine array is tobe treated similarly: for each winddirection new rows (with larger windturbine spacing) will form, with new(smaller) distances between rows.Merging wakes from neighbouringrows becomes a little more elaborate.For typical situations, Annex Bproposes rules addition of the wakes.

7. Summary of proposed procedure

Summarizing, the model has thefollowing components:

1. From wake 2-3 to where thewake merge with neighbour-row wakes, use row of wts

wake shape expanding in 2directions:

( ) 2/1intint11

f

R

sD

D

+=

. The

asymptotic relative wakespeed deficit, , has

if the row is long enough anasymptotic value, c

0/UUc =

1. Thespecific value is found fromexperiments and this valuedetermines the decay constant

.2. From the point of neighbour-

wake merging and onward, themerged wake expands linearlyupward,

00 )(1

hxxcc

ch t

mw

mw +

= ,

wherex0 and h0 in principle isderived from the characteris-tics of the flow exiting regime1.

3. Determine the relative flowspeed deficit from the model

from the infinitely large windfarm, cwf. The firstapproximation is that cmw=cwf.

Apart from determining the efficiencyof the wind farm, the estimation of thegrowth of the internal boundary layer

is needed to determine what happensdownwind.

8. Conclusion

Present day and near-future offshorewind farms extend 5-10 km, which inrelation to the boundary layer islarge, but not infinitely large.Thus, there is a need for a model thathandles both single and multiple wakeandthe wind farms interaction withthe atmospheric boundary layer.It is believed that the suggested modelwill with appropriate experimentalcalibration encompass the flowcharacteristics of the very large windfarms in a realistic and consistentmanner.

9. Future work

The model will be verified/calibrated

by means of existing data and datafrom the large offshore demonstrationproject at Horns Rev and Nysted.To verify experimentally the flowspeed deficit in the infinitely largewind farm, cwf, will be difficult and ispresently viewed as a major challenge.Experimental data, Hjstrup et al(1993), show significant speedup ofthe flow in between the rows,indicating that the flow is constrainedalready before the wake from

neighbouring rows merge in the sensedescribed above. It is believed that theproposed model can handle this byappropriate adjustments.Presently, the model only allowssimple geometries and there is a needto extend it to irregular geometries.

10. Acknowledgement

The work has in part been financed byDanish Public Service Obligation

(PSO) funds.

16 Ris-R-1518(EN)


17/29

Annex A: Implementation

The model has been operationalisedensuring that momentum is conservedat each model step (currently 1 mdistance).

By utilising the equations given in theabove sections, the expansion of thewake is as a circular disk (= axis-symmetric). The primary variable isthe wake height. Once the wake radius(height) exceeds the hub-height, thewake is considered to have impactedthe ground surface. The totalmomentum deficit is conserved but thearea of the wake is computed byremoving the below-ground portion.This occurs at approximately 10 rotordiameters (D) distance downstream ofthe turbine.In the third regime when half the wakewidth equals the turbine spacing theneighbouring wakes merge. Thisoccurs at ~30 D.Again the total momentum deficit isconserved but nowwe remove thearea below groundas before and half

of the overlappingarea (sector) asshown above ifthe turbine is anedge turbine only one sector isremoved.The model has been implementedusing the Bonus 500 kW wind turbinethrust curve (see (Frandsen et al.1996).) with a hub-height of 38 m anda rotor diameter of 35 m. In the casestudy shown in Figure 8, the

freestream wind speed is 10 m and thewind farm contains 10 rows, each of 3turbines with between and along rowspacing of 300 m. Figure 8 shows thehub-height wind speed passing throughthe wind farm (1-3000 m) and then fora further 7000 m. In this case study thedownstream wakes merge immediatelywith the wind farm total wake.Figure 9 shows a close up of the first600 m of the wind farm with two rows.The wake height increases for the first

wake but then the two wakes merge

giving a rapid increase in the wakearea. As shown the expansion of thesingle wake follows the single wake

shape equation given in the Summaryof the proposed procedure. Thedouble wake expansion cannot becompared directly because the totalwake area for the wind farm is the areaexpanding in the model version.However, after the wind farm whilethe development of the wake heightafter the boundary layer follows theexpansion given in equation (25) (seeFigure 8).

Annex B: Merging wakes

In general

Thrust on the individual units:( ) ( 10111011

1

UUUAdAUUUTA

)= =

0 2000 4000 6000 8000 10000Distance (m)

0.0x100

2.0x104

4.0x104

6.0x104

8.0x104

1.0x105

Wakearea(m2)

50

100

150

200

250

300

Wakeheight(m)

6

7

8

9

10

Hubheightwindspeed(ms-1)

Wake area

Wake height

Wind speed

Eqn. 16

Figure 8 The model operationalised for afreestream wind speed of 10 ms-1 for a windfarm with 10 rows. The wake height, area andwind speed are shown for the turbine in thecentre of the row.

Ris-R-1518(EN) 17


18/29

( ) ( 20222022 2 UUUAdAUUUT A )=

=

Sum of thrust on the two machines:( ) ( )2022101121 UUUAUUUATTTT +=+=

I.e.:

( ) ( ) ( )2U02210110 UUAUUUAUUUA TTT +=Where asymptotically downwind, thesum of thrust on the two machines is:

( )TTTT UUUAT = 0

Assume that where the wakes meet:

21 AAAT +=

Then:

( ) ( )( ) ( ) +=

+

20221011

021

UUUAUUUA

UUUAA TT

( )

( ) ( ) =+

++

=

cUUUAA

AUUU

AA

A

UUU TT

20221

2101

21

1

0

cUUUT =200

4

1

2

1, where the +

prevails.UT is the integrated, initial flow speed.

A1 andA2 are the initial wake areas atthe instance when the wakes meet.One approach is

to assume that UT is the commonflow speed from the point wherethe wakes joint, and that it developsaccording to the (common) wakeexpansion.

-100 0 100 200 300 400 500 600Distance (m)

0.0x100

5.0x103

1.0x104

1.5x104

2.0x104

2.5x104

Wake

area(m2)

40

60

80

100

120

140

Wake

height(m)

6

7

8

9

10

Hubheightwindspeed(ms-1)

Wake area

Wake height

Wind speed

Eqn. 25

Figure 9 The model operationalised for a windfarm with 10 rows (for the first two rows). Thewake height, area and wind speed are shown forthe turbine in the centre of the row.

Another approach (and this ispreferred) is

to assume that from the pointwhere the wakes meet, the value ofUTdevelops from where the wakesmeet and outward and thus the twooriginal deficits (each decreasing aswere these alone) are graduallyeroded according to internalwake expansion from the meetingpoint of the wakes.

By argument of momentum

conservation we have( ) ( ) constant021 =+ TT UUUAA aftereach wind turbine.

Same thrust on two adjacent wind

turbines:

If furthermore the wakes have beengenerated by the same thrust,

TRCAUT202

1 = , then

( ) ( )20221011 UUUAUUUA =

Therefore in this case( ) ( )101

21

10 2 UUU

AA

AUUU TT

+=

and

( ) ( )20221

20 2 UUU

AA

AUUU TT

+=

thus, with

21

22

21

11 22and22

AA

Ar

AA

Ar

+=

+= ,

we get solutions

( )

( )2022200

1011

2

00

24

1

2

1

and24

1

2

1

UUUrUUU

UUUrUUU

T

T

+=

+=

( )TRT

TT

CAUA

UU

T

AUUU

202

1200

200

12

4

1

2

1

12

4

1

2

1

+

=+=

whereAR is the wt rotor area and

21 AAAT += is the area of the summed

wake.

18 Ris-R-1518(EN)


19/29

Same length of the two wakes

Compare the above result with theindividual wake:

( )TRCAUA

UUU 2021

1

2001

1

4

1

2

1+=

If , corresponding to the samelength of the two wakes, thenobviously

21 AA =

21 UUUT == . Thus, in this

case, the joint-wake has the samedeficit as the individual wakes. Thesame goes for many adjoining wakes,as illustrated in the figure. We get

( )

( )

( ) 120211

200

202

1

1

200

202

1200)(

1

4

1

2

1

4

1

2

1

4

1

2

1

UCAUA

UU

CAUnA

nUU

CAUA

nUUU

TR

TR

TRi

nT

=+=

+=

+=

( )

+= T

RnT C

A

AUU 211

2

1

10)(

References

Betz, A. (1920) Der Maximum der

theoretisch mlichen Ausntzung des

Windes durch Windmotoren, Zeitschriftfr das gesamte Turbinenwesen, Heft

26, Sept. 26, pp. 307-309.

Bossanyi, E.A, C. Maclean, G. E. Whittle,

P. D. Dunn, N. H. Lipman and P. J.

Musgrove (1980) The efficiency of wind

turbine clusters, Proc. Third

International Symposium on Wind

Energy Systems (BHRA) Copenhagen,

Denmark, pp. 401-416.

Emeis, S. and Frandsen, S. (1993)Reduction of horizontal wind speed in a

boundary layer with obstacles, Boundary

Layer Meteorol. 64, pp. 297-305.

Elliott, W.P. (1958) The growth of the

atmospheric internal boundary layer,

Transactions of the American

Geophysical Union 39, pp. 1048-1054.

Engelund, F.A. (1968) Hydraulik,

Newtonske vskers mekanik, Den

Private Ingenirfond, Danmarks Tekniske

Hjskole, in Danish (Hydraulic, the

Mechanics of Newtonian Fluids, thee

Private Engineering Fund, Technical

University of Denmark), 322 p.

Frandsen, S. (1991) On the wind speed

reduction in the center of large clusters of

wind turbines, Proc. of European Wind

Energy Conference 1991, October,Amsterdam, Netherlands, pp. 375-380.

Frandsen, S. (1992) On the wind speed

reduction in the center of large clusters

of wind turbines, Jour. of Wind

Engineering and Industrial

Aerodynamics, 39, pp. 251-265

Frandsen, S. and P.H. Madsen (2003)

Spatially average of turbulence intensity

inside large wind turbine arrays,

European Seminar on Offshore WindEnergy in the Mediterranean and Other

European Seas (OWEMES 2003),

Naples, Italy, April 10-12.

Frandsen, S., Chacon, L., Crespo, A.,

Enevoldsen, P., Gomez-Elvira, R.,

Hernandez, J., Hjstrup, J., Manuel, F.,

Thomsen, K., and Srensen, P. (1996).

"Measurements on and modelling of

offshore wind farms." Ris-R-903(EN),

Ris National Laboratory, Denmark.

Hjstrup, J., M. Courtney, C.J. Christensen

and P. Sanderhoff (1993) Full-scale

measurements in wind turbine arrays.

Nrrekr Enge II. CEC/Joule. Ris

report I684. March.

Jensen, N. O. (1983) A note on wind

turbine interaction, Ris National

Laboratory, DK-4000 Roskilde,

Denmark, Ris-M-2411, 16 p.

Jensen, N.O. (1978) Change of surface

roughness and the planetary boundary

layer, Quart. J. R. Met. Soc, No. 104, pp.

351-356.

Katic, I., J. Hjstrup and N.O. Jensen

(1986) A simple model for cluster

efficiency, Proc. European Wind Energy

Conference and Exibition, Rome, Italy,

pp. 407-410.

Lanchester, F. W. (1915) Contribution to

the Theory of Propulsion and the Screw

Propeller, Transaction of the Institution

Ris-R-1518(EN) 19


20/29

of Naval Architects, Vol. LVII, March

25, pp. 98-116.

Newman, B. G. (1977) The spacing of

wind turbines in large arrays, J. Energy

Conversion, vol. 16, pp. 169-171.

Panofsky, H. A. (1973); Tower

climatology, in D. A. Haugen (ed.)

Workshop on Micrometeorology, Amer.

Meteorol. Soc., Boston, USA) pp. 151-

176.

Schlichting, H. (1968) Boundary layer

Theory, McGraw-Hill Book Company,

Sixth edition.

Sempreviva, A.M., Larsen, S.E.,

Mortensen, N.G. and Troen, I. (1990)

Response of neutral boundary layers to

changes of roughness. Boundary-Layer

Meteorology, 50, 205-225.

Templin, R. J. (1974); An estimation of

the interaction of windmills in

widespread arrays, National

Aeronautical Establishment, Laboratory

Report LTR-LA-171. Otawa, Canada,

23 p.

Tennekes, H. and J. L. Lumley (1972) A

first course in turbulence, MIT press,

Cambridge, Massachusetts, and London,England, 300 p.

Troen, I. and E. L. Petersen (1989)

European Wind Atlas, Ris National

Laboratory, ISBN 87-550-1482-8, 656

p.

20 Ris-R-1518(EN)


21/29

1.4 Evaluation of the Storpark model

The new Storpark model has been compared against a number of state of the artwake models listed in the Table below.

Model owner Name Type

RGU 3D-NS CFDECN Wakefarm AinslieUOL FlaP AinslieGH WindFarmer AinslieRISOE Analytical Momentum deficitRISOE Engineering model EngineeringRISOE WAsP/PARK (Version 8) Engineering

The measured data were from an experiment using sodar at the Vindeby wind farmwhich gave a number of cases of single wakes at different distances from the windturbine between 1.7 and 7.1 D. In general terms it is very difficult to prove that anyof the models outperformed each other. There is also fairly high measurementuncertainty. The Storpark Analytical model typically gives results for the velocitydeficit at hub-height which is in the centre to the high end of the range of thepredictions by the different models. However, it is important to remember that theStorpark Analytical Model is not designed for single wake predictions. The mostimportant evaluation will be against data from large offshore wind farms. Animportant part of this evaluation will be the constants used in the model to describethe wake expansion in different regimes which requires observational input.

Experiment #

1

2

3

4

5

6

Velocitydeficit(ms-1)

sodar measured

measured corrected

WAsP

UO

RGU

ECN

Risoe Eng

GH

Risoe Anal

3 1 4 2 6 5

Comparison of measured and modelled velocity deficits at hub-height arranged inorder of increasing distance between the turbine and the measurement point from1.7 to 7.4D.

Ris-R-1518(EN) 21


22/29

2.Overview of supporting work

The objectives of Storpark were:

to review wake and boundary layer models

to review available data

to develop and evaluate new models

A series of notes, presentations and papers was produced for each objective

which are summarised below.

2.1. Review of wake and boundary layer models

2.1.1 WAsP8 wake effects model

Author: Ole Rathmann (Ris)Wake effects in WAsP8 use the WAsP approach to wake calculation calculating thevelocity deficit according to the thrust coefficient and the wake expansion angle.WAsP8 allows calculation of wakes from different turbines by considering theoverlap area of the new wake with the upwind wake as a ratio of the overlap areawith the new wake area. It does not account for terrain effects in the wake expansion.

2.1.2 Comparing WindPRO and Windfarmer wake loss calculation

Author: Per Nielsen (EMD)The performance of the two models was compared at the Klim Fjordholme windfarm with 35 600 kW Vestas V44 wind turbines. Windfarmer appears tounderestimate the wake losses in the array by about 2% relative to WindPRO. Thiscan be altered using different Wake Decay Coefficients (or different Ct curves).

2.1.3 Overview of models and preliminary analysis

Authors: Rebecca Barthelmie and Sara Pryor (Ris)This review includes boundary layer models WAsP and WAsP Engineering, the

Coastal Discontinuity Model, the KNMI model and mesoscale models (KAMM).The UPMPARK wind farm model is also described. The main issue is that wakemodels in general do not include a feedback loop describing the impact of theturbine induced changes to the boundary-layer structure. This paper also presentspreliminary analysis from the Vindeby wind farm and meteorological masts and themeteorological data from Om Stlgrunde. These data seem to indicate that the windfarm at Vindeby can be detected 2 km downwind and that the variability withdifferent stability conditions cannot be detected, possibly due to statistical noise.

2.1.4 Strmmingsmodeller

Author: Mads Srensen (EMD)

22 Ris-R-1518(EN)


23/29

This review describes available boundary-layer models from mesoscale tomicroscale and gives web site addresses where the models can be obtained.

2.1.5 Overview of single and multiple wake models

Author: Morten Lybech Thgersen (EMD)

This review describes the available wake models divided into i) analytical models ii)2-d numerical models and iii) 3-d numerical models and gives references to eachmodel. Different approaches to moving from single to multiple wakes are described.

2.2. Review of existing data

2.2.1 Vindeby analysis

Authors: Sara Pryor and Rebecca BarthelmieData from the Vindeby wind farm have been used to assess whether the velocity

deficit or width of the wake is different from single, multiple or quintuple wakes.The wake width increases slightly from 10 in a single wake (at 8.6D) to 13 in aquintuple wake but it is difficult to assess whether this is significant, due to noise orpossibly the definition of wake width used. Another explanation is that it is the wakedirectly upwind which influences the measurements. Data were also used tocalculate the equivalent to WAsPs wake decay coefficient which was calculated as0.12 this higher value may reflect the presence of multiple wakes. Finallycomparison of data collected at 1 minute and 30 minutes showed no significantdifferences which may imply that wake meandering is not detectable in wind speedobservations in wakes.

2.2.2 Analyses on real versus calculated wind shadow

Author: Per NielsenSelecting data for specific directions from the Nrrekr Enge wind farms givesfreestream wind directions to one mast and full wind farm shadow to the other. Thepower curves compare well. Significant pre processing of the data was undertaken toremove roughness, terrain and obstacle effects. After this data cleaning no clearevidence of the shadow of Nrrekr Enge 2 could be determined at a distance of 100D but this be due to the higher turbulence at these land sites.

2.3. Development of new models

2.3.1 Wake model based on Navier stokes solution with eddy viscosity closure

Author: Morten Lybech Thgersen (EMD)

The model is based on the Ainslie approach using eddy viscosity closure. Theboundary conditions are set for the near-wake (2D) with a Gaussian velocity deficitprofile and a wake width define according to the thrust coefficient Ct.

Ris-R-1518(EN) 23


24/29

2.3.2 Wind farm modelling using an added roughness approach in WindSim CFDmodel

Author: Morten Lybech Thgersen (EMD)Using an added roughness area to represent a wind farm (here the case is Horns Rev)simulations were run with WindSim. Assuming a wind speed of 10 m/s at hub-heightthe recovery distance behind the wind farm (to within 2% of the freestream) was

found to vary between 7.5 and 8.5 km from the last turbine in the wind farmaccording to the value assigned to the roughness (0.1 m to 1 m).

2.3.3 Note re: energy budget model

Author: Sten Frandsen (Ris)The preliminary assumptions for the new wake model focused on the energy balanceflowing into and out of a box around the rotor.

2.3.4 Flow field around a turbine rotor

Author: Sten Frandsen (Ris)

A more extensive discussion of the assumptions for the new wake model focused onthe momentum deficit assuming a balance between the momentum flowing into andout of a cylinder and consideration of multiple wakes.

2.3.5 A new approach to multiple wake modelling

Author: Sten Frandsen (Ris)The new approach to wake modelling is based on describing the wake expansion inthree different regimes. Initially the diameter of the wake expands to the power onethird, in the multiple wake situation this becomes the power one half and finally theexpansion becomes wither linear or to the power fourth fifths. This was the basis forthe development of the new Analytical model which is described in the EWEA

paper.

2.3.6 Verification of Storpark models

Author: Morten Lybech ThgersenThis note outlines the proposed procedure for verifying the Storpark models basedon existing data sets.

24 Ris-R-1518(EN)


25/29

3.Presentations from the project

3.1 Analytical modelling of large wind farm clusters

Authors: Rebecca Barthelmie, Sten Frandsen, Sara Pryor and Sren LarsenThis presentation was given at the international conference in Delft The Science ofmaking torque from wind and summarises the results of the project including thereview of recovery distances and modelling with the added roughness model.

3.2 Miscellaneous on roughness change models

Author: Sten FrandsenThis summary was given at the 3rd Storpark meeting illustrating some fundamentalsfrom roughness change models which could be applied within the new model.

3.3 WAsP 8 wake effect modelling

Author: Ole RathmannAt the 4th Storpark meeting a summary of how wake effects are modelled in WasP 8was given. The biggest change from previous versions of WAsP is the possibility toinclude turbines with different hub-heights in the same wind farm.

3.4 Preliminary results from the SAR-wake project

Author: Charlotte Bay HasagerThe SARwake project is using satellite images to investigate wake effects at HornsRev and a summary was given of the progress so far in Meeting 5. These illustratethat satellite derived wind speeds from Horns Rev can be used to examine the wakeof the wind farm.

3.5 Roughness model, empirical analyses and wakes

Authors: Rebecca Barthelmie and Sara Pryor

This presentation focuses on the comparison of data from Vindeby and OmStlgrunde which indicates that WAsP may under-predict wake losses from offshorewind farms. However, the results are highly uncertain because of coastal effects onthese data sets.

3.6 Vindeby_wakes

Author: Sara PryorData from Vindeby indicate that at 8.6 rotor diameter distance the width and depth ofwakes are not highly dependent on the number of wakes (single or multiple) present.One minute and 30 minute averaged data were compared and no differences were

Ris-R-1518(EN) 25
http://www.risoe.dk/vea/storpark/presentations/Barthelmiestorpark.pdfhttp://www.risoe.dk/vea/storpark/presentations/sf-meeting%202.ppthttp://www.risoe.dk/vea/storpark/presentations/WAsP8%20Wake-effect%20model.pdfhttp://www.risoe.dk/vea/storpark/presentations/STORPARK_meeting_sep2003_cbh.pdfhttp://www.risoe.dk/vea/storpark/presentations/storpark4_rb.pdfhttp://www.risoe.dk/vea/storpark/presentations/Vindeby_wakes.pdfhttp://www.risoe.dk/vea/storpark/presentations/Vindeby_wakes.pdfhttp://www.risoe.dk/vea/storpark/presentations/storpark4_rb.pdfhttp://www.risoe.dk/vea/storpark/presentations/STORPARK_meeting_sep2003_cbh.pdfhttp://www.risoe.dk/vea/storpark/presentations/WAsP8%20Wake-effect%20model.pdfhttp://www.risoe.dk/vea/storpark/presentations/sf-meeting%202.ppthttp://www.risoe.dk/vea/storpark/presentations/Barthelmiestorpark.pdf


26/29

found this is taken t suggest that wake meandering is not a large influence on themeasured wake.

3.7 Design of offshore wind turbines

Author: Sten Frandsen

This presentation given in Hamburg 2002 relates current design standards to state ofthe art modelling of the turbulence inside wind farms.

3.8 Spatially average of turbulence intensity inside large wind turbine arrays

Author: Sten FrandsenThis presentation which was the basis for the presentation at OWEMES 2003examines models for predicting the turbulence intensity inside large wind farms andcompares those with measurements e.g. from Nrrekr Enge.

3.9 Load measurements in wind farms

Author: Sten FrandsenThis presentation at NREL focuses on the need to relate modelling andmeasurements for load calculations inside wind farms which also incorporatesextreme loads.

3.10 Background for the effective turbulence model

Author: Sten FrandsenOn overview of the state-of-the-art in fatigue load modelling and measurements

using empirical models and measurements.

26 Ris-R-1518(EN)
http://www.risoe.dk/vea/storpark/presentations/Hamburg%202002.pdfhttp://www.risoe.dk/vea/storpark/presentations/Rumlig%20middelturbulens.ppthttp://www.risoe.dk/vea/storpark/presentations/NREL%20210102.pdfhttp://www.risoe.dk/vea/storpark/presentations/Turbulence%20model.pdfhttp://www.risoe.dk/vea/storpark/presentations/Turbulence%20model.pdfhttp://www.risoe.dk/vea/storpark/presentations/NREL%20210102.pdfhttp://www.risoe.dk/vea/storpark/presentations/Rumlig%20middelturbulens.ppthttp://www.risoe.dk/vea/storpark/presentations/Hamburg%202002.pdf


27/29

4Papers and posters from this project

Title Author Location

Paper- 2004 EWEC SF et al.EWEA, London, 2004

Paper - Analytical modelling of windspeed deficit in large offshore wind

farms (abstract)SF et al. EWEA, London, 2004

Paper - Challenges in predictingpower output from offshorewind farms

RB & SPJournal of Energy Engineering on

Sustainable Energy Systems(submitted).

Paper - Wind energy prognoses for theBaltic region

SP/RB & JSBaltex Meeting, Bornholm, May

2004.

Poster- Flow within and downwind oflarge wind farm clusters.

RB/SF/SP/SL

Nato Advanced Study Institute:Flow And Transport Processes InComplex Obstructed Geometries:

From Cities And VegetativeCanopies To Industrial Problems,

Kiev, May 2004.

Poster-Analytical modelling of largewind farm clusters

RB/SF/SP/SL/MT/JM

European Geophysical SocietyConference, Nice, April 2004

Paper- Historical and prognostic changesin 'a normal wind year': A case study

from the BalticSP/RB/JS

The science of making torque fromwind, Delft, April 2004

Paper - Review of wakes and large windfarms.pdf

RB/SF/SP/SLThe science of making torque from

wind, Delft, April 2004

Paper (Presentation in proceedings) -Uncertainties in power prediction

offshoreRB et al.

43rd Topical Expert Meeting,Skrbk, Denmark, March 2004

Paper - Spatial average of turbulenceintensity inside large wind turbine arrays

SF/PHOffshore Wind Energy in

Mediterranean and Other EuropeanSeas, Naples, April 2003.

Poster-Statistical and physical modellingof large wind farm clusters

RB/SF/SP/SLEuropean Geophysical SocietyConference, Nice, April 2003

Ris-R-1518(EN) 27
http://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20EWEC.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/BALTEX_abstract_Pryor.pdhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/BALTEX_abstract_Pryor.pdhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/kiev.ppthttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/kiev.ppthttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/storpark.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/storpark.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/delft_013.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/delft_013.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/SFOwemes.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/SFOwemes.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/theft1.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/theft1.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/theft1.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/theft1.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/SFOwemes.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/SFOwemes.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/IEA_Barthelmie.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/delft_013.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/delft_013.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/Delft04_Pryor_43.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/storpark.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/storpark.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/kiev.ppthttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/kiev.ppthttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/BALTEX_abstract_Pryor.pdhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/BALTEX_abstract_Pryor.pdhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/JEE_2004_RB.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20European%20Wind%20Energy%20-%20Conference%20&%20Exhibition%20-%2022-25%20November%202004.htmhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/2004%20EWEC.pdf


28/29

5List of supporting references

Other relevant presentations, reports and papers

Jrgensen, H.E.; Frandsen, S.; Vlund, P. 2003: Wake effects on Middelgrund Windfarm.Ris-R-1415(EN) 43 p.

Hjstrup et al. 1993: Full scale measurements in wind-turbine arrays. Nrrekr Enge II.Ris_I-684(EN) 30 pp. nrkrenge1.pdf+ nrkrenge2.pdf

Engelund H, 1968: Excerpts from Hydrodynamik 1968.pdf

Crespo and Frandsen,1999: Survey of modelling wakes and wind farms, Wind Energy, 2.

Hunt, J. 2002 The disappearance of laminar and turbulent wakes in complex flows, Fluid

Mech. 457 (2002)Gomez-Elvira, R. and Crespo, A. 2001: An explicit algebraic turbulent model to reproducethe aniostropy of the momentum turbulent flows in a wind turbine wake, European WindEnergy Conference

Bossanyi, E. et al. 1980: The efficiency of wind turbine clusters. Third Internationalsymposium on Wind energy Systems.

Hstrup, J. 1981: A simple model for the adjustment of velocity spectra in unstableconditions downstream of an abrupt change in roughness and heat flux, Boundary-LayerMeteorology 21.

Elliot, W.1958: The growth of the atmospheric internal boundary layer. Transactions of theAmerican Geophysical Union 39.

Presentation on Roughness of large wind farms, SF, 2001

Frandsen, S. 2001: Vindlaster p havmller. Presentation on Loads on offshore turbines.

Schepers, G. 2003: ENDOW : Validation and improvement of ECN's wake model.

Barthelmie et al. 2002: ENDOW workshop proceedings, Ris-R-1326(EN)

Djerf and Mattsson, 2000: Windfarm predictions & Alsvik data (FFA)

Kristensen et al. 2003: Power loss at the cutout wind speed.

Lange, B. et al. 2003: Modelling of offshore wind turbine wakes with the wind farmprogram FLaP, Wind Energy, 6.

Tarp-Johanssen, N.J. 2003. Extrapolation including wave loads (Presentation)

6Acknowledgements

The work has in part been financed by Danish Public Service Obligation (PSO)funds F&U 2108.

28 Ris-R-1518(EN)
http://iis-03.risoe.dk/netacgi/nph-brs.exe?d=PUBL&s1=Middelgrund&pg1=ALL&co1=and&s2=&pg2=ALL&co2=and&s3=0&co3=and&s4=@SAAR%3E=1991&co4=and&s5=0&l=20&p=1&Sect1=PUBNEKS&Sect2=TXT&u=/netahtml/risoe/publ_uk.htm&op1=ADJ&r=0&f=Shttp://iis-03.risoe.dk/netacgi/nph-brs.exe?d=PUBL&s1=Middelgrund&pg1=ALL&co1=and&s2=&pg2=ALL&co2=and&s3=0&co3=and&s4=@SAAR%3E=1991&co4=and&s5=0&l=20&p=1&Sect1=PUBNEKS&Sect2=TXT&u=/netahtml/risoe/publ_uk.htm&op1=ADJ&r=0&f=Shttp://iis-03.risoe.dk/netacgi/nph-brs.exe?d=PUBL&s1=Middelgrund&pg1=ALL&co1=and&s2=&pg2=ALL&co2=and&s3=0&co3=and&s4=@SAAR%3E=1991&co4=and&s5=0&l=20&p=1&Sect1=PUBNEKS&Sect2=TXT&u=/netahtml/risoe/publ_uk.htm&op1=ADJ&r=0&f=Shttp://www.risoe.dk/vea/storpark/links/n%E8%B2%AB%E6%B2%A5nge1.pdfhttp://www.risoe.dk/vea/storpark/links/n%E8%B2%AB%E6%B2%A5nge2.pdfhttp://www.risoe.dk/vea/storpark/links/Engelund%20Hydrodynamik%201968.pdfhttp://www.risoe.dk/vea/storpark/links/Crespo%20et%20al%20+sf%201999.pdfhttp://www.risoe.dk/vea/storpark/links/hunt.rtfhttp://www.risoe.dk/vea/storpark/links/hunt.rtfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/Bossanyi%201980.pdfhttp://www.risoe.dk/vea/storpark/links/Bossanyi%201980.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/Elliott%201958.pdfhttp://www.risoe.dk/vea/storpark/links/Elliott%201958.pdfhttp://www.risoe.dk/vea/storpark/presentations/ens2001.ppthttp://www.risoe.dk/vea/storpark/presentations/DVTS.pdfhttp://www.risoe.dk/vea/storpark/links/ENDOW_ECNmodel.pdfhttp://www.risoe.dk/vea/storpark/links/ris-r-1326.pdfhttp://www.risoe.dk/vea/storpark/links/TN2000_30_WindFarm.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/we-paper.pdfhttp://www.risoe.dk/vea/storpark/links/wind_energy_flap.pdfhttp://www.risoe.dk/vea/storpark/links/wind_energy_flap.pdfhttp://www.risoe.dk/vea/storpark/presentations/WindWaveExtrapolation%20til%20Sten.pdfhttp://www.risoe.dk/vea/storpark/presentations/WindWaveExtrapolation%20til%20Sten.pdfhttp://www.risoe.dk/vea/storpark/links/wind_energy_flap.pdfhttp://www.risoe.dk/vea/storpark/links/wind_energy_flap.pdfhttp://www.risoe.dk/vea/storpark/Papers%20and%20posters/we-paper.pdfhttp://www.risoe.dk/vea/storpark/links/TN2000_30_WindFarm.pdfhttp://www.risoe.dk/vea/storpark/links/ris-r-1326.pdfhttp://www.risoe.dk/vea/storpark/links/ENDOW_ECNmodel.pdfhttp://www.risoe.dk/vea/storpark/presentations/DVTS.pdfhttp://www.risoe.dk/vea/storpark/presentations/ens2001.ppthttp://www.risoe.dk/vea/storpark/links/Elliott%201958.pdfhttp://www.risoe.dk/vea/storpark/links/Elliott%201958.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/JH-spektra%20ruhed.pdfhttp://www.risoe.dk/vea/storpark/links/Bossanyi%201980.pdfhttp://www.risoe.dk/vea/storpark/links/Bossanyi%201980.pdfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/ew20031-anisotropy-paper.pdfhttp://www.risoe.dk/vea/storpark/links/hunt.rtfhttp://www.risoe.dk/vea/storpark/links/hunt.rtfhttp://www.risoe.dk/vea/storpark/links/Crespo%20et%20al%20+sf%201999.pdfhttp://www.risoe.dk/vea/storpark/links/Engelund%20Hydrodynamik%201968.pdfhttp://www.risoe.dk/vea/storpark/links/n%E8%B2%AB%E6%B2%A5nge2.pdfhttp://www.risoe.dk/vea/storpark/links/n%E8%B2%AB%E6%B2%A5nge1.pdfhttp://iis-03.risoe.dk/netacgi/nph-brs.exe?d=PUBL&s1=Middelgrund&pg1=ALL&co1=and&s2=&pg2=ALL&co2=and&s3=0&co3=and&s4=@SAAR%3E=1991&co4=and&s5=0&l=20&p=1&Sect1=PUBNEKS&Sect2=TXT&u=/netahtml/risoe/publ_uk.htm&op1=ADJ&r=0&f=Shttp://iis-03.risoe.dk/netacgi/nph-brs.exe?d=PUBL&s1=Middelgrund&pg1=ALL&co1=and&s2=&pg2=ALL&co2=and&s3=0&co3=and&s4=@SAAR%3E=1991&co4=and&s5=0&l=20&p=1&Sect1=PUBNEKS&Sect2=TXT&u=/netahtml/risoe/publ_uk.htm&op1=ADJ&r=0&f=S


29/29

Mission

To promote an innovative and environmentally sustainable

technological development within the areas of energy, industrial

technology and bioproduction through research, innovation and

advisory services.

4. Vision

5. Riss research shall extend the boundaries for the

understanding of natures processes and interactions right

down to the molecular nanoscale.

6. The results obtained shall set new trends for the

development of sustainable technologies within the fields of

energy, industrial technology and biotechnology.

7. The efforts made shall benefit Danish society and lead to

the development of new multi-billion industries.

the necessary dist between large wind farms offshore

Documents