2011-12-16

Advanced Energy Estimations

Project Assignment Hunflen

Paul Hines & Haseeb Ahmad

12/15/2011

Examiner: Stefan Ivanell

This report will use the software WindSim to estimate the annual energy production of 3

turbines at Hunflen in Sweden. Turbulence model RNG and Wake Model 1 will be employed

in the simulation in WindSim.

2

3

1. Introduction ..................................................................................................................................... 5

1.1. Background ............................................................................................................................. 5

1.2. Aim and question formulation ................................................................................................. 5

1.3. Delimitations ........................................................................................................................... 6

2. Theoretical framework .................................................................................................................... 6

2.1. Navier-Stokes equations .......................................................................................................... 6

2.2. Turbulent Flow Solutions ........................................................................................................ 6

2.2.1. Reynolds Averaged Navier-Stokes Equations ................................................................. 7

2.2.2. Direct Numerical Simulation (DNS) ............................................................................... 9

2.2.3. Large eddy simulation (LES) .......................................................................................... 9

2.2.4. Detached eddy simulation (DES) .................................................................................... 9

2.3. Weibull distribution ............................................................................................................... 10

3. Analysis ......................................................................................................................................... 10

3.1. Methodology ......................................................................................................................... 10

3.1.1. Wake effects .................................................................................................................. 13

3.1.2. Turbulence model .......................................................................................................... 14

4. Results ........................................................................................................................................... 15

4.1. Production according to vindstat.nu ...................................................................................... 15

4.2. WindSim Results ................................................................................................................... 16

4.2.1. Wake model 1 ................................................................................................................ 16

4.2.2. Wind Resources ............................................................................................................. 19

4.3. Comparison with other Turbulence models .......................................................................... 20

5. Discussion ..................................................................................................................................... 22

5.1. Vilhelm – Vestas V52 ........................................................................................................... 22

5.2. Ferdinand – Vestas V52 ........................................................................................................ 22

5.3. Freja NEG Micon 52 ............................................................................................................. 23

6. Conclusion ..................................................................................................................................... 23

Bibliography .......................................................................................................................................... 24

Appendices ............................................................................................................................................ 25

Table of Contents

4

Figure 1 Turbulence flow solution techniques ........................................................................................ 7

Figure 2 Sample output of energy module ............................................................................................ 10

Figure 3 Cell resolution at 5000 ............................................................................................................ 11

Figure 4 Cell resolution at 300000 ........................................................................................................ 11

Figure 5 Power curve Vestas V52 850 .................................................................................................. 12

Figure 6 Power curve NEG Micon 52 900 ............................................................................................ 12

Figure 7 Objects as placed in terrain module ........................................................................................ 13

Figure 8 Yearly output 2009-2010 Ferdinand from vindstat.nu ............................................................ 15

Figure 9 Yearly output Vilhelm 2009-2010 from vindstat.nu ............................................................... 15

Figure 10 Power output from WindSim frequency table ...................................................................... 16

Figure 11 Power output per turbine – Frequency .................................................................................. 16

Figure 12 Estimated production – actual production Frequency table .................................................. 17

Figure 13 Actual vs estimated production frequency table ................................................................... 17

Figure 14 Power output from WindSim frequency table ...................................................................... 17

Figure 15 Power output per turbine – Weibull distribution................................................................... 18

Figure 16 Estimated production – actual production Weibull distribution ........................................... 18

Figure 17 Actual vs estimated production frequency table ................................................................... 19

Figure 18 Wind Resource map and Wind Rose at 300000 cell resolution ............................................ 19

Figure 19 Turbulence model comparison – Ferdinand .......................................................................... 21

Figure 20 Turbulence model comparison - Freja .................................................................................. 21

Figure 21 Turbulence model comparison - Vilhelm ............................................................................. 22

List of Figures

5

1. Introduction

1.1. Background

In spite of early discussion questioning the profitability of wind power in forest

environments (Wizelius) interest in harvesting wind resource from complex/ and or hilly

terrain is growing in for example in Sweden with a number of projects in planning. Vindkraft

Norr is a joint venture between Statkraft, a large energy company and SCA a company

owning large amounts of forest land (vindkraftnorr.se) . The absence of a nearby residential

population can making planning easier but often the terrain can be more challenging.

The first software providing wind resource estimations was developed in the 1980s.

Windpro, a modular based Windows compatible software that can be used for design and

planning of individual wind turbines or wind farms was developed over 20 years ago in

Ålborg in Denmark. WAsP, the Wind Atlas Analysis and Application Program enables wind

simulation and estimation of power output from wind turbines through the use of linear

equations and has been in present in the industry for over 25 years (Facts about Risø DTU).

However, the limitations of this software in complex terrain have been recognized (Wallbank,

2008)

Software models such as Windpro using computational fluid dynamics (CFD) have been

seen to have considerable advantages when mapping complex terrain. The founder of

WindSim, Arne Grawdahl was working on the project to establish the Norwegian Wind Atlas.

The use of CFD was required to simulate the complex Norwegian coastline. The first

commercially available version of WindSim was launched in 2003.

CFD will be examined later in a discussion of the theoretical framework underlying this

study.

1.2. Aim and question formulation

This report will use the software WindSim to estimate the annual energy production of 3

turbines at Hunflen in Sweden. Hunflen lies in Dalarna in mid Sweden. The turbines are two

Vestas V52 and one NEG Micon 52.

Turbulence model RNG and Wake Model 1 will be employed in the simulation in WindSim.

6

1.3. Delimitations

This report is produced under limited time frame and by users who are not well skilled in

the use of CFD software. The users have the benefit of direction and assistance from members

of the department of wind power at Gotland University but even given WindSim’s user

friendly interface both of the above limitations much be acknowledged.

2. Theoretical framework

CFD uses a non-linear flow model based on Navier-Stokes equations. Navier-Stokes

equations describe fluid flow based on the laws of conservation of momentum, mass and

energy. (Karl Nilsson, Stefan Ivanell, 2010)

2.1. Navier-Stokes equations

Navier-Stokes equations are used to explain the motion of a fluid i.e. liquid or gas. These

equations are based on Newton’s Second Law which describes the relation between force,

mass and acceleration on a fluid. Navier Stock equations are quite useful in the modeling of

weather, understanding the flow behavior of fluids, designing of wind turbines blades,

aircraft, and in many other useful applications.

Navier-Stokes Equations are non-linear, partial differential equations which do not

explicitly describe the variables but these present how variables change with time. The

solution of Navier-Stokes Equations is velocity field which describe the velocity of fluid at a

point in time. (T. Wallbank, 2008). The assumption, on which Navier-Stokes equations are

based, is the continuous nature of fluid. The derivation of Navier-Stokes equations starts with

the conservation of mass, momentum and energy conservation for a finite arbitrary volume.

(T. Wallbank, 2008)

2.2. Turbulent Flow Solutions

The turbulence can be defined as the state of motion of a fluid which is characterized by

apparently random and chaotic three dimensional vorticity. (Introduction to turbulence/Nature

of turbulence, 2011) Vorticity can be defined as the measure of the rate of rotational spin in a

fluid. Turbulence dominates all other flow phenomena, and results in increased energy

dissipation, mixing, heat transfer, and drag.

Turbulent flows can be computed either by solving the Reynolds Average Navier-Stokes

(RANS) equations with suitable models or with direct computation.

7

2.2.1. Reynolds Averaged Navier-Stokes Equations

The Reynolds Averaged Navier-Stokes Equations are the simplification of Navier-Stokes

Equations by taking the time average of the velocity terms in the equations. RNS equations

are used to describe turbulent flows. The basic tool which is required to derive the RNS

equations from Instantaneous Navier-Stokes equations is the Reynold’s decomposition. The

Reynold decomposition means the separation of variable into the mean (time averaged)

component and fluctuating component. By this transformation, we get a set of unknowns

called Reynold Stresses which are the functions of velocity fluctuations and which require a

turbulence model to produce a closed system of solvable equations. The computational

requirements for RANS equations are far less than Navier-Stokes equations. (symscape, 2009)

Turbulence Models

Turbulence modeling is used to calculate the effects of turbulence in fluids. By taking

average, the solution of turbulence equations can be simplified but models are required to

represent scales of the flow that are not resolved. (Ching Jen Chen, 1998)

Figure 1 Turbulence flow solution techniques

RANS based

turbulence

models

Large eddy

simulation (LES)

Detached eddy

simulation (DES)

Direct Numerical Simulation DNS

Linear eddy viscosity Models

Non-Linear eddy viscosity Models

Reynolds stress Models

Algebric Models One equation Models

Two equation Models

k-epsilon Model k-omega Model Realisability Issues

Near Wall Treatment

RNG k-epsilon Model

Realisable k-epsilon Model

Standard k-epsilon Model

8

Following turbulence model is used in WindSim

K epsilon turbulence model

k-epsilon turbulence model is one of the most common turbulence models however it does not

work well in the cases where large pressure gradient occurs. (Wilcox, 1998, p. 174). This

model came from the main branch of turbulent solution techniques i.e. RANS based

turbulence models. The sub-branch of RANS based turbulence models is the linear eddy

viscosity models, it can be seen in figure below. It is a two equation turbulence model which

means it employs two extra transport equations to describe turbulent flow behavior.

The first transported variable is turbulent kinetic energy and second transported variable is

turbulent dissipation.

Turbulent kinetic energy

The turbulent kinetic energy is simply the energy in the turbulence. If the flow can be

partitioned into mean and turbulent parts, then the total kinetic energy of the flow will simply

be the sum of the kinetic energy of the mean and turbulent flows. (Turbulence Intensity and

Turbulent Kinetic Energy, 2011)

Turbulent dissipation

Turbulent dissipation describes the scale of the turbulence.

Some usual models of k-epsilon models are

Standard k-epsilon model

Realisable k-epsilon model

RNG k-espsilon model

WindSim uses k-epsilon as the turbulent model with standard form as well as modified

forms. The standard k-epsilon model is widely used turbulent model and has been verified

and validated for a wide variety of flows. It has less computational costs and is numerically

more stable than the more advanced and complex stress models, it is more successful in flow

where the normal Reynolds stresses are less important. In wind engineering, k-epsilon model

doesn’t perform well because its inability to cope with normal stresses which are more

dominant in wind flows. (Veersteeg, H.K., and Malalasekera, W., 1995)

9

WindSim uses some modified k-epsilon models like RNG k-epsilon model, k-epsilon

model with YAP correction. The RNG k-epsilon is based on the renormalization group

analysis of the Navier-Stoke equations. The transport equations for turbulence generation and

dissipation are the same as those for the standard model but the model differs because of one

additional constant which improves the performance for separating flow and recirculation

regions.

One of the main inadequacies of k-epsilon model is the over estimation of turbulent

kinetic energy however the slight improvement has been achieved after the development of

modified k-epsilon models.

2.2.2. Direct Numerical Simulation (DNS)

Direct Numerical Simulation is used in computational fluid dynamics to solve the Navier-

Stoke equations numerically without any turbulence model. This means that the whole range

of spatial and temporal scales of the turbulence must be resolved. The power required to

resolve such models with current computational capabilities, makes them inappropriate for

large CDF applications. (Direct numerical simulation (DNS), 2007)

2.2.3. Large eddy simulation (LES)

Large eddy simulation is a popular technique used for the simulation of turbulent flows.

This feature allows one to explicitly solve for the large eddies in a calculation and implicitly

account for the small eddies by using a subgrid-scale model (SGS model). (Large eddy

simulation (LES), 2007). The power requirement for LES is less than DNS but more than

RNS. The RANS methods give a time averaged result while LES methods are able to resolve

turbulent flow structures and predict instantaneous flow characteristics.

2.2.4. Detached eddy simulation (DES)

It is the hybrid technique which combines the best aspects of RANS and LES

methodologies in a single solution strategy. There are some difficulties associated with the

use of the standard LES models, particularly in near-wall regions. These issues lead to the

development of hybrid models like DES. This model attempts to treat near-wall regions in a

RANS-like manner, and treat the rest of the flow in an LES-like manner. (Detached eddy

simulation (DES), 2007)

10

2.3. Weibull distribution

WindSim uses Weibull distribution to create a wind frequency table from met mast

information (Wallbank, 2008)

Figure 2 Sample output of energy module

3. Analysis

3.1. Methodology

WindSim contains the following modules:

Terrain module

Establish the numerical model based on height and roughness data

• Wind Fields module

Calculation of the numerical wind fields

• Objects module

Place and process wind turbines and climatology data.

• Results module

Analyse the numerical wind fields

• Wind Resources module

Couple the numerical wind fields with climatology data by statistical means to provide the

wind resource map

• Energy module

Couple the numerical wind fields with climatology data by statistical means to provide the

Annual Energy Production (AEP); including wake losses. Determine the wind

characteristics used for turbine loading. (WindSim, 2011)

11

The terrain model generates a 3D model of the area under examination. Input includes

coordinates, height and roughness. A map is first converted using the terrain module. In

Refinement Type the Refinement area is detailed along with the number of cells to be used this

allows greater accuracy in computations for the chosen area. (WindSim, 2011) Resolutions in

the range 5000, 10000, 50000, 80000, 100000, 150000, 200000, 250000, 300000 will be

selected and the results recorded.

Cell resolution at 300000 and 5000 are shown below.

Figure 3 Cell resolution at 5000

Figure 4 Cell resolution at 300000

12

The Objects module is used to specify each of the proposed turbines. The turbine models are

as follows:

Vestas V52 Ferdinand, 850 KW, hub height 65m

Vestas V52 Vilhelm, 850 KW, hub height 65m

NEG Micon 52, Freja, 900 KW, hub height 49m

Figure 5 Power curve Vestas V52 850

Figure 6 Power curve NEG Micon 52 900

13

Figure 7 Objects as placed in terrain module

The Energy results for each increasing resolution will then be presented and discussed. A

wind resource map for the highest resolution will also be recorded.

3.1.1. Wake effects

The WindSim wind resource model provides for the calculation of wake effects based on

analytical models (WindSim, 2011). In this report Model 1 has been chosen. This model is

based on momentum deficit theory and gives a simple linear expansion of the wake on the

basis of the wake factor, k.

14

δV = (1 - SQRT(1 - CT))/(1 + (2kx/D))2

Where:

CT = thrust coefficient (-)

k = A/LOG(h/z0)

A = 0.5

h = hub height (m)

z0 = roughness height (m)

(Source: WindSim.com)

3.1.2. Turbulence model

The wind field’s module allows for the selection of a Turbulence model. The default

model is the standard k-ε model belonging to the family of eddy viscosity models. An eddy

viscosity is calculated by an analytical equation (WindSim, 2011). The standard form of the

k-ε model is summarized as follows, with, t denoting differentiation with respect to time and,

i denoting differentiation with respect to distance:

ρ k),t + (ρ Ui k - {ρ νt/PRT(k)} k,i ),i = ρ (Pk - ε)

(ρ ε),t + (ρ Ui ε - {ρ νt/PRT(ε)} ε,i ),i = {ρ ε/k} (C1 Pk - C2 ε)

νt = Cμ k2/ε

Here k is the turbulent kinetic energy; ε is the dissipation rate; ρ is the fluid density; νt is the

turbulent kinematic viscosity. Cμ,C1, C2, PRT(k), PRT(ε) are the model constants.

(WindSim, 2011)

15

4. Results

4.1. Production according to vindstat.nu

The production data for NEG Micon 52 Freja is not available on vindstat.nu

Vestas V52 850 KW Hunflen Ferdinand 800

2009 2010

January 104097

February 64299 112608

March 151877 158710

April 125396

May 165342

June 114888

July 132393

August 141227

September 235166

October 156036

November 191045

December 92123

Figure 8 Yearly output 2009-2010 Ferdinand from vindstat.nu

Average yearly output Feb 2009 – Jan 2010 is 1673, 8 MW

Vestas V52 850KW Hunflen Vilhelm 801

2009 2010

January 98847

February 50779 87414

March 132320 142738

April 109980

May 107988

June 92666

July 118927

August 125998

September 215377

October 141055

November 180530

December 87431

Figure 9 Yearly output Vilhelm 2009-2010 from vindstat.nu

16

Average yearly output Feb 2009 – Jan 2010 is 1461,8 MW

4.2. WindSim Results

4.2.1. Wake model 1

Frequency Table Power production in MWh/y for the differing cell resolutions based on

frequency table is presented below.

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Ferdinand 1867,1 2003,7 2110,4 2152,8 2214,8 2236,3 2088,7 2241,3 2259,6

Vilhelm 1946,5 1995,7 2086,9 2164,5 1972,3 2088,9 1847,1 2089,8 1960,4

Freja 1337,7 1508,0 2036,0 2221,4 2098,2 2200,6 2012,2 2224,3 2101,4

Total 5151,3 5507,4 6233,3 6538,7 6285,3 6525,8 5948,0 6555,4 6321,4

Figure 10 Power output from WindSim frequency table

The table below shows the variation in estimated energy output across differing cell

resolutions.

Figure 11 Power output per turbine – Frequency

The table below shows difference in actual production and forecast production for each of the

two turbines for which information is present on vindstat.nu.

Difference Ferdinand = Estimated production - Actual production 1673,8

Difference Vilhelm = Estimated production – Actual production 1461,8

1000.0

1200.0

1400.0

1600.0

1800.0

2000.0

2200.0

2400.0

P

o

w

e

r

o

u

t

p

u

t

Cell Resolution

Frequency

ferdinand

wilhelm

freja

17

Figure 12 Estimated production – actual production Frequency table

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Ferdinand 1867,1 2003,7 2110,4 2152,8 2214,8 2236,3 2088,7 2241,3 2259,6

Actual 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9

Difference 193,2 329,8 436,5 478,9 540,9 562,4 414,8 567,4 585,7

% 11,5426411 19,70328 26,07766 28,61068 32,31463 33,59906 24,78127 33,89777 34,99103

Figure 13 Actual vs estimated production frequency table

Weibull Distribution Power production in MWh/y for the differing cell resolutions based on

Wiebull distribution is presented below.

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Ferdinand 1908,6 2045,3 2146,3 2198,0 2252,0 2280,8 2125,0 2284,3 2305,5

Vilhelm 1986,7 2035,9 2125,2 2211,6 2010,3 2135,4 1885,7 2134,7 2006,6

Freja 1375,1 1548,4 2077,8 2266,2 2139,2 2246,0 2053,5 2268,2 2145,7

Total 5270,4 5629,6 6349,3 6675,8 6401,5 6662,2 6064,2 6687,2 6457,8

Figure 14 Power output from WindSim frequency table

0.0

100.0

200.0

300.0

400.0

500.0

600.0

700.0

800.0

p

o

w

e

r

o

u

t

p

u

t

Cell resolution

Difference between estimated and Actual production Frequency table

Ferdinand

Vilhelm

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Wilhelm 1946,5 1995,7 2086,9 2164,5 1972,3 2088,9 1847,1 2089,8 1960,4

Actual 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9

Difference 484,6 533,8 625,0 702,6 510,4 627,0 385,2 627,9 498,5

% 33,1488243 36,51431 42,75278 48,06095 34,91365 42,88959 26,34944 42,95115 34,09964

18

Figure 15 Power output per turbine – Weibull distribution

The table below shows the variation in estimated energy output across differing cell

resolutions. The table below shows difference in actual production and forecast production for

each of the two turbines for which information is present on vindstat.nu.

Difference Ferdinand = Estimated production - Actual production 1673,8

Difference Vilhelm = Estimated production – Actual production 1461,8

Figure 16 Estimated production – actual production Weibull distribution

1000.0

1200.0

1400.0

1600.0

1800.0

2000.0

2200.0

2400.0

P

o

w

e

r

o

u

t

p

u

t

Cell Resolution

Weibull distribution

Ferdinand

Wilhelm

Freja

0.0

200.0

400.0

600.0

800.0

1000.0

5000 10000 50000 80000 100000 150000 200000 250000 300000

P

o

w

e

r

o

u

t

p

u

t

Cell resolution

Difference estimated vs Actual production Weibull distribution

Ferdinand

Vilhelm

Freja

19

Figure 17 Actual vs estimated production frequency table

4.2.2. Wind Resources

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Ferdinand 1908,6 2045,3 2146,3 2198,0 2252,0 2280,8 2125,0 2284,3 2305,5

Actual 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9 1673,9

Difference 234,7 371,4 472,4 524,1 578,1 606,9 451,1 610,4 631,6

% 14,0218975 22,18851 28,22236 31,31098 34,537 36,25754 26,94988 36,46664 37,73315

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Wilhelm 1986,7 2035,9 2125,2 2211,6 2010,3 2135,4 1885,7 2134,7 2006,6

Actual 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9 1461,9

Difference 524,8 574,0 663,3 749,7 548,4 673,5 423,8 672,8 544,7

% 35,8986742 39,26416 45,37266 51,28278 37,51301 46,07038 28,98985 46,0225 37,25992

WTG 5000 10000 50000 80000 100000 150000 200000 250000 300000

Freja 1375,1 1548,4 2077,8 2266,2 2139,2 2246,0 2053,5 2268,2 2145,7

Actual 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1 1317,1

Difference 58,0 231,3 760,7 949,1 822,1 928,9 736,4 951,1 828,6

% 4,40 17,56 57,76 72,06 62,42 70,53 55,91 72,21 62,91

Figure 18 Wind Resource map and Wind Rose at 300000 cell resolution

20

Wind Resource maps can also be generated from WindSim. The map above gives some

idea of the effect of the topography on wind speed. The turbines placed on elevated ground

have the highest wind speeds. It is also possible to see the difference in wind speed between

the measurement station and the site. The prevailing wind direction is from the south west.

4.3. Comparison with other Turbulence models

As this study was undertaken in conjunction with other projects examining different

turbulence models it could be interesting to examine briefly results from another model. The

results below are taken from a parallel study of Modified Turbulence Model by Konstantina

Stamouli and Mahdi Lotfizadehdehkordi and a study of the Standard model by Åsa Abel and

Josefin Knudsen. The charts below show recorded results for the frequency table estimations.

The comparison with Standard and Modified turbulence models shows clearly that the

estimations fluctuate significantly between the models at different cell resolutions.

Ferdinand - the difference in estimated output is at times very large and there seems to

be no move toward convergence at higher resolutions.

Freja – the standard and RNG models start at similar positions for lower resolutions

before diverging. The models remain within a reasonably good range of each other

and appear to be converging at 300000 cell resolution.

Vilhelm - the standard and RNG models start at similar positions for lower resolutions

before diverging. At varying points up to 250000 each model assumes the position of

the highest estimate. The RNG and standard seem to give closer results and again

appear to be converging at higher resolution.

Each model in turn estimates the higher and lower output although it seems they could be

converging at higher resolutions. The comparison with Standard and Modified turbulence

models is not sufficient to demonstrate a trend although RNG and Standard are closer to each

other with the Modified Turbulence model

21

Figure 19 Turbulence model comparison – Ferdinand

Figure 20 Turbulence model comparison - Freja

1900.0

1950.0

2000.0

2050.0

2100.0

2150.0

2200.0

2250.0

2300.0

10000 100000 150000 200000 250000 300000

P

o

w

e

r

o

u

t

p

u

t

Resolution

Comparison RNG with Standard and Modified Turbulence models

Ferdinand RNG

Ferdinand Modifiied

Ferdinand Standard

1400.0

1500.0

1600.0

1700.0

1800.0

1900.0

2000.0

2100.0

2200.0

2300.0

10000 100000 150000 200000 250000 300000

P

o

w

e

r

o

u

t

p

u

t

Resolution

Comparison RNG with Standard and Modified Turbulence models

Freja RNG

Freja Mod

Freja Standard

22

Figure 21 Turbulence model comparison - Vilhelm

5. Discussion

The number of simulations within the limited time frame may affect the validity of the

results obtained. The processing power available did not allow for production of energy

estimations for cell resolution in excess of 300000.

As production data for the NEG Micon Freja is unavailable discussion against actual

production will be limited to the above results and is perhaps best examined per turbine.

5.1. Vilhelm – Vestas V52

As cited above yearly power output based on vindstat.nu was 1461,8 MW. The nearest

result to actual production comes at 200000 cell resolution at an estimated production of

1847, 1 MWh/y for frequency table and 1885, 7 MWh/y for Weibull distribution. The power

estimation is next closest at 5000 cell resolution at 1946, 5 MWh/y and 1986,7 MWh/y

respectively. The results in the range 10000- 150000 cell resolution show a fluctuation in

power output as can be seen in Fig 11 and 14 above. At cell resolution 300000 the power

output decreases again and it is possible with further resolution it would have decreased

further.

5.2. Ferdinand – Vestas V52

As cited above yearly power output based on vindstat.nu was 173,8 MW. The nearest

result to actual production comes at 5000 cell resolution at an estimated production of 1867,1

1700.0

1750.0

1800.0

1850.0

1900.0

1950.0

2000.0

2050.0

2100.0

2150.0

2200.0

10000 100000 150000 200000 250000 300000

P

o

w

e

r

o

u

t

p

u

t

Resolution

Comparison RNG with Standard and Modified Turbulence models

Vilhelm RNG

Vilhelm Mod

Vilhelm standard

23

MWh/y for frequency table and 1908,6 MWh/y for Weibull distribution. The power

estimation is next closest at 10000 cell resolution at 2003,7 MWh/y and 2045,3 MWh/y

respectively. The results in the range 50000- 250000 cell resolution show a fluctuation in

power output as can be seen in Fig 11 and 14 above. As opposed to the result for Vilhelm at

cell resolution 300000 the power output does not decrease again however it is possible with

further resolution it would have decreased.

5.3. Freja NEG Micon 52

The energy estimation results for Freja show a very similar pattern to Vilhelm. However,

there is quite a marked jump in estimation from 5000 and 10000 cell resolutions producing a

very low estimate when compared with 50000 and beyond. There is little stability that can be

observed in the estimations with both frequency table and Weibull distribution generating

energy estimates varying in size across the range of sampled resolutions.

6. Conclusion

The energy estimations from WindSim clearly overestimate the production from the

turbines as compared to actual production. As has been discussed in theoretical framework the

k-epsilon model has a tendency to over-estimate. The impact of availability may have a

significant impact on the difference in results along with the unavailability of simulations at

high resolution.

24

Bibliography

Detached eddy simulation (DES). (Feburary 2007). Hämtat från CFD-Online: http://www.cfd-

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25

Appendices

Table 1. Vindstat data, 850 Vestas Hunflen Ferdinand 800

2005 2006 2007 2008 2009 2010 2011

January 135509 198817 291270 277887 267069 104097 232270

February 151846 145239 107846 241300 64299 112608 164087

March 64267 126711 150467 215211 151877 158710 264617

April 147311 154722 205126 115484 125396 140118 170173

May 254261 100726 206088 93358 165342 108958 173498

June 192459 152794 82501 135849 114888 102062 109826

July 246063 132559 141528 87003 132393 187878 86645

August 128883 90937 147009 118517 141227 127678 103911

September 167647 249708 87951 235166 160690 187234

October 149726 217889 244696 156036 212775 257853

November 294222 225500 201147 191045 202575 200503

December 349604 233641 151972 92123 132287

Table 2. Vindstat data, 850 Vestas Hunflen Vilhelm 800

2005 2006 2007 2008 2009 2010 2011

January 103766 188613 259690 279079 244542 98847 200899

February 131170 48898 100040 215324 50779 87414 145993

March 57522 16772 153524 192645 132320 142738 190854

April 115597 137374 181073 109201 109980 116687 130356

May 236364 103011 186266 82239 107988 94455 147528

June 176052 134896 81121 119988 92666 88379 99229

July 224016 116525 126854 82524 118927 158707 74223

August 169196 81255 137331 100446 125998 112743 92149

September 146726 202549 84835 215377 124641 169207

October 135108 70606 179583 141055 193865 233937

November 239495 186387 190209 180530 183378 187747

December 306282 211737 118489 87431 119595