wind energy and weather conditions in the icelandic highlands

Wind Energy and Weather Conditions inthe Icelandic Highlands

Jón Ágúst Sigurðsson

Thesis of 30 ETCS creditsMaster of Science in Mechanical Engineering

June 2015

Wind Energy and Weather Conditions in the IcelandicHighlands


Thesis of 30 ECTS credits submitted to the School of Science and Engineeringat Reykjavík University in partial fulfillment of

the requirements for the degree ofMaster of Science in Mechanical Engineering

June 2015

Supervisor:

Ármann Gylfason Ph.D, SupervisorAssociate Professor, Reykjavík University

Examiner:

Hálfdán Ágústsson Ph.D, ExaminerMeteorologist, Icelandic Meteorological Office

CopyrightJón Ágúst Sigurðsson

June 2015

Student:


Supervisor:

Ármann Gylfason Ph.D

Examiner:

Hálfdán Ágústsson Ph.D

Wind Energy and Weather Conditions in the IcelandicHighlands


30 ECTS thesis submitted to the School of Science and Engineeringat Reykjavík University in partial fulfillment

of the requirements for the degree ofMaster of Science in Mechanical Engineering.

June 2015

Date

Jón Ágúst SigurðssonMaster of Science

The undersigned hereby grants permission to the Reykjavík University Li-brary to reproduce single copies of this project report entitled Wind Energyand Weather Conditions in the Icelandic Highlands and to lend or sellsuch copies for private, scholarly or scientific research purposes only.

The author reserves all other publication and other rights in association withthe copyright in the project report, and except as herein before provided, nei-ther the project report nor any substantial portion thereof may be printed orotherwise reproduced in any material form whatsoever without the author’sprior written permission.

Wind Energy and Weather Conditions in the Icelandic Highlands


June 2015

Abstract

In this study, the Monin-Obukhov similarity models were applied to meteo-rological data. The objective was to indicate the stability conditions in thesurface layer in the Búrfellshraun area where Landsvirkjun plans to installup to 80 wind turbines, for a production of up to 200MW.

The stability conditions in the surface layer are determined by the momen-tum and heat flux occurring at each time and classified as stable, unstable orneutral. Wind speed varies with height and increases logarithmically. Thestability conditions in the surface layer along with the surface roughness in-fluences the change in the wind speed at given time. Wind power is functionof the cube of the wind speed so the importance of strong wind is clear, fur-thermore it is important that the wind speed over the wind turbine rotor is asuniform as possible. The knowledge of the wind speed and changes causedby stability changes is very important from the wind energy farming point ofview.

Wind speed and temperature data from an 80m height mast and wind speeddata from Lidar (light detection and ranging) during the months May, Julyand October in 2014 were examined. The surface roughness length in thearea was estimated for each month as well s the non-dimensional wind shearand temperature gradients and compared to respective models. The leastsquare method was used to fit the models which were used to the data. TheR2 parameter (coefficient of determination) was calculated and used to assessthe quality of each fit.

Wind speed profiles fitted respective models quite well in all the monthswhich were examined. Wind speed profiles occurring at stable and neutralstate were dominant in all the months examined. Wind coming from thenortheast sector was dominant in October and the average wind speed washighest in that month. High rate of missing data from the Lidar caused thatlarge amount of data could not be analyzed. Wind speed measurement dif-ference between the Lidar and the cup anemometers on the 80m mast caused

4

that stability state of the corresponding wind speed profiles could not be de-termined. This difference reflects mainly the poor average caused by fluctu-ation in the wind.

Vindorka og Veðuraðstæður á Hálendi Íslands


Júní 2015

Útdráttur

Í þessu verkefni var sjálfsvipgerðar líkönum Monin-Obukhov beitt á veður-farsleg gögn með það að markmiði að ákvarða aðstæður í yfirborðslaginu íBúrfellshrauni þar sem Landsvirkjun áformar að að reisa allt að 80 vinhverflaí fyrirhuguðum Búrfellslundi til að framleiða allt að 200MW.

Aðstæður í yfirborðslagi ákvarðast af því skriðþunga og framaflæði sem ásér stað hverju sinni. Aðstæður er ýmist sagðar stöðugar, óstöðugar eða hlut-lausar. Vindraði er breytilegur með hæð og vex eftir lógaritmískum ferli.Aðstæður í yfirborðslagi hverju sinni og yfirborðshrýfi hafa mikil áhrif áþað hversu mikil vindhraðabreyting á sér stað. Vindafl vindhverfils er háðvindhraðanum í þriðja veldi og því er mikilvægt að vindhraði sé mikill eneinnig er ákjósanlegt að hann sé sem jafnastur yfir vænghaf vindmillun-nar. Vitneskja um þann vindhraða og þær vindhraðabreytingar sem eiga sérstað við mismunandi aðstæður eru því mjög mikilvægar frá sjónarhóli vin-dorkubúskapar.

Vindhraða og hitastigsmælingar frá 80m háu mælimastri og vindhraða mælin-gar frá Lidar sem framkvæmdar voru í maí, júlí og október árið 2014 voruskoðaðar. Yfirborðhrýfi svæðisins var ákvarðað fyrir hvern mánuð. Eininga-lausu vind og hitaskurðirnir voru ákvarðaðir og bornir saman við þau líkönsem notuð voru. Notast var við aðferð minnstu ferninga (e. least squaremethod) til að forma þau líkön sem notuð voru að gögnunum. KennistærðinR2 (e. coefficient of determination) var reiknuð og notuð við mat á hversuvel viðkomandi líkan formaðist að gögnunum.

Vindhraðaferlarnir eru góðir og formast ágætlega við tilsvarandi líkön í þeimmánuðum sem skoðaðir voru. Vindhraðaferlar sem áttu sér stað við stöðugarog hlutlausar aðstæður voru ráðandi í öllum mánuðunum sem voru skoðaðir.Vindáttir frá norðaustri voru ráðandi í Október og var meðalvindhraði mesturí þeim þeim mánuði. Hátt hlutfall vindhraðamælinga sem ekki skiluðu sérfrá Lidar varð til þess að ekki var hægt að greina stóran hluta gagnanna.Mismunur milli vindhraða mælinga frá Lidar og þeirra bolla vindhraða mæla

vi

sem notaðir voru á 80m mastrinu orsakaði einnig að ekki var hægt að segjatil um aðstæður viðkomandi vindhraðaferla. Þessi mismunur endurspeglarfyrst og fremst vond meðaltöl vegna flökts í vindi.

vii

Acknowledgements

My thanks go to: Margrét Arnardóttir and Andri Gunnarsson at Landsvirkjun for theirinformative help and Landsvirkjun for providing me with data, without their contributionthis study would not have been conducted. Orkurannsóknarsjóður Landsvirkjunar forfunding the research.. Special thanks go to my supervisor Ármann Gylfason for his men-toring and support during the work of this study. Erlingur Ívar Jóhannsson and HéðinnHauksson, students in the course T-629-URO1, for the collaboration during the prepro-cessing of the data used in this study. My best friend, Sigurður Óli Guðmundsson for hisadvise and review of this thesis. Last but not least, I want to thank my fiancé SigríðurElín Þórðardóttir for her support, motivation and endless support during this study andmy daughter Jana Kristín for entertaining me in times I needed the most.

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Contents

List of Figures xi

List of Tables xv

List of Abbreviations xvii

1 Introduction 1

2 Literature review 52.1 Wind energy fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Atmospheric boundary layer and its characteristics . . . . . . . . . . . . 112.3 The Monin-Obukhov similarity . . . . . . . . . . . . . . . . . . . . . . . 17

3 Methodology 233.1 Site description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Measurement instruments . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3 Surface roughness estimation . . . . . . . . . . . . . . . . . . . . . . . . 283.4 The universal functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4 Results 334.1 May 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1.1 Surface roughness length . . . . . . . . . . . . . . . . . . . . . . 354.1.2 The non dimensional wind shear and temperature gradient . . . . 374.1.3 Summary of results from May . . . . . . . . . . . . . . . . . . . 39

4.2 July 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2.1 Surface roughness length . . . . . . . . . . . . . . . . . . . . . . 414.2.2 The non dimensional wind shear and temperature gradient . . . . 434.2.3 Summary of results from July . . . . . . . . . . . . . . . . . . . 46

4.3 October 2014 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

x

4.3.1 Surface roughness length . . . . . . . . . . . . . . . . . . . . . . 484.3.2 The non dimensional wind shear and temperature gradient . . . . 504.3.3 Summary of results from October . . . . . . . . . . . . . . . . . 52

4.4 Wind speed measurements . . . . . . . . . . . . . . . . . . . . . . . . . 534.5 Summary of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5 Discussion and limitations 75

6 Conclusions 85

xi

List of Figures

1.1 The wind turbines which Landsvirkjun installed in December 2012. . . . 2

2.1 A schematic picture demonstrating the main components of a HAWT. . . 62.2 A wind turbine located in an stream tube shaped air flow. . . . . . . . . . 72.3 A plot showing CT and Cp curves with respect to change in the axial

induction factor a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.4 The behavior of the temperature profile in the surface layer. . . . . . . . . 132.5 Observations of φm in (a) and φh in (b) versus the Monin-Obukhov sta-

bility parameter (ξ = z/L) from the 1968 Kansas experiment. . . . . . . 19

3.1 The inset shows a satellite picture of Iceland with an indication of Búr-fellslundur location. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Wind rose digram demonstrating the prevailing wind directions in theBúrfellslundur area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3 A map showing the locations of the 80m mast and Lidar in the Búrfell-slundur area during a given period. . . . . . . . . . . . . . . . . . . . . . 25

3.4 The 80m meteorological mast. . . . . . . . . . . . . . . . . . . . . . . . 263.5 Windcube V2 Lidar device. . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1 A histogram demonstrating the wind speed distribution in May. . . . . . . 344.2 A wind rose diagram showing the prevailing wind directions in May. . . . 354.3 A scatter plot of the surface roughness length parameter obtained from

the 10 min average wind profiles occurring at neutral state in May. . . . . 364.4 A wind rose diagram showing the prevailing wind directions of the 10

min average wind speed profiles that were used to estimate the surfaceroughness data in May. . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.5 A graph showing the non dimensional wind shear, φm, in May as a func-tion of the dimensionless height, ξ(z/L), where z = 55m. . . . . . . . . . 37

4.6 A graph showing the non dimensional wind shear, φh, in May as a func-tion of the dimensionless height, ξ(z/L), where z = 55m. . . . . . . . . . 38

xii

4.7 A histogram demonstrating the wind speed distribution in July. . . . . . . 404.8 A wind rose diagram showing the prevailing wind directions in July. . . . 414.9 A scatter plot of the surface roughness length parameter obtained from

the 10 min average wind profiles occurring at neutral state in July. . . . . 424.10 A wind rose diagram which shows the prevailing wind directions of the 10

min average wind speed profiles which were used to estimate the surfaceroughness data in July. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.11 A graph showing the non dimensional wind shear, φm, in July as a func-tion of the dimensionless height, ξ(z/L), where z = 55m. . . . . . . . . . 44

4.12 A graph showing the non dimensional wind shear, φh, in July as a functionof the dimensionless height, ξ(z/L), where z = 55m. . . . . . . . . . . . 45

4.13 A histogram demonstrating the wind speed distribution in October. . . . . 474.14 A wind rose diagram showing the prevailing wind directions in October. . 484.15 A scatter plot of the surface roughness length parameter obtained from

the 10 min average wind profiles occurring at neutral state in October. . . 494.16 A wind rose diagram demonstrating the prevailing wind directions of the

10 min average wind speed profiles which were used to estimate the sur-face roughness data in October. . . . . . . . . . . . . . . . . . . . . . . . 49

4.17 A graph showing the non dimensional wind shear, φm, in October as afunction of the dimensionless height, ξ(z/L), where z = 55m. . . . . . . 50

4.18 A graph showing the non dimensional wind shear, φh, in October as afunction of the dimensionless height, ξ(z/L), where z = 55m. . . . . . . 51

4.19 Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in May. . . . . . . . . . . . . . . . . 54




4.23 Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in May. . . . . . 58

4.24 Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast in May. 59

4.25 Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in July. . . . . . . . . . . . . . . . . 60

xiii




4.29 Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in July. . . . . . . 64

4.30 Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast in July. 65

4.31 Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in October. . . . . . . . . . . . . . . 66




4.35 Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in October. . . . . 70

4.36 Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast inOctober. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.1 A graph demonstrating the shape and behavior of the wind speed profileat different stability state. . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.2 A graph demonstrating the power distribution over wind turbine rotor hav-ing the diameter D = 44m at each stability state. . . . . . . . . . . . . . 76

5.3 The average wind speed of the usable wind speed profiles occurring inOctober at each stability state. . . . . . . . . . . . . . . . . . . . . . . . 77

5.4 The graph shows the average TI in May for stable and unstable wind speedprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.5 The upper graph demonstrates wind speed profile having low averagewind speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.6 A graph demonstrating a wind speed profile having irregular behavior andat the same time does the wind directions vary with height. . . . . . . . . 81

5.7 A graph demonstrating a wind speed profile which behaves fairly regularly. 82

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5.8 The upper graph shows a wind speed profile data and a red line represent-ing the best fit line of the data. . . . . . . . . . . . . . . . . . . . . . . . 83

xv

List of Tables

2.1 Typical values of surface roughness length for several types of terrain. . . 21

3.1 List of measurement devises used on the mast and their respective instal-lation heights. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1 Obukhov length, L, interval and corresponding stability class which wasused to classify each wind speed profile. . . . . . . . . . . . . . . . . . . 33

4.2 The computed and estimated average values for the wind profiles in eachstability class. The total number of wind profiles which fulfilled the R2 >

0.9 criteria and its respective rate of the total number of wind profilesoccurring in May. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


0.9 criteria and its respective rate of the total number of wind profilesoccurring in July. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46


0.9 criteria and its respective rate of the total number of wind profilesoccurring in October. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5 The summary of results from May, July and October where the total rateof wind speed profiles categorized in each stability class in each month isdemonstrated. The average wind speed in each month, measured at 60mheight on the 80m mast is also demonstrated. . . . . . . . . . . . . . . . 72

5.1 The rate of wind speed data received from the Lidar at certain height inrespective month. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

xvii

List of Abbreviations

UN United Nations

IEA International Energy Agency

GHG Greenhouse gases

EPA Environmental Protection Agency

U.S United States

EU European Union

IMO Icelandic Meteorological Office

CF Capacity factor

MO Monin and Obukhov

HAWT Horizontal axis wind turbine

VAWT Vertical axis wind turbine

ABL Atmospheric boundary layer

TI Turbulence intensity

NS Navier Stokes

TKE Turbulent kinetic energy

1

Chapter 1

Introduction

Iceland, among other countries around the world is realizing that increasing world pop-ulation will make a huge impact on the future energy demand worldwide. The UnitedNations (UN) [1] estimate that the world population will become 7.8 billion in 2025 and8.9 billion in 2050. The International Energy Agency (IEA) predict that global energy de-mand will grow by 40% between the years 2007 and 2030. At the same time the amountof greenhouse gases (GHG) in the atmosphere are constantly increasing [2].

Climate change due to increase of GHGs is one of the most difficult environmental chal-lenges facing the world today. Electricity generation plays a huge role in this develop-ment. According to the United States Environmental Protection Agency (EPA) the rela-tive emission of greenhouse gases in the United States (U.S) in 2012, due to electricitygeneration, was 32% of the total emission. Majority of all electricity in the USA, or over70%, is generated by burning fossil fuels, mostly coal and natural gas. Due to these facts,increasing use of renewable energy for electricity generation will become more vital in thefuture, and could be one of the key factors helping turning this development around.

Wind energy is an inexhaustible natural resource which has been used for practical appli-cations e.g. to transport ships around the globe, grinding grain and to generate electricitywith wind turbines. The development of wind turbines has been rapid over the last decadewhich has reduced cost and along with government incentives to renewable energy tech-nologies has led to an increase in installed capacity of wind power both in Europe andthe U.S. According to the U.S Department of Energy [3], 13.1 GW of wind energy wasadded in 2012 which was an 90% increase from 2011. Similar development has beenobserved in the Europe, or roughly 10% annual growth rate of wind power installation inthe last 10 years in the European Union (EU) [4] according to the European Wind EnergyAssociation.

2 Wind energy and weather conditions in the Icelandic highlands

Wind energy in Iceland

Iceland is rich of renewable energy sources and is known for its electricity generationusing both hydro and geothermal energy. Around 71% of the electricity produced in 2013was generated from hydro energy and 28.95% was produced from geothermal energy [5].The relative generation of electricity by wind energy was only 0.02% and 0.02% by fossilfuel. However, studies done by the The Icelandic Meteorological Office (IMO) showsthat some places in Iceland are suitable for wind development. The IMO published areport [6] in 2013 along with an article [7] in 2014 which stated that wind potential inIceland is within the highest class as defined in the European Wind Atlas. This amongother factors have led to wind energy now being considered to be a feasible energy optionin Iceland.

Landsvirkjun’s wind power project

The National Power Company Landsvirkjun, supplies 73% of all electricity in the countryusing hydro and geothermal energy. In the last few years the company has been exploringthe possibility of utilizing wind energy. Wind power and hydro power can indeed interplayvery well, wind is strongest during the winter when the water level in the reservoirs are atthe lowest and vice versa. In December 2012, two 900 kW wind turbines were installedfor research purpose by Landsvirkjun. The turbines are located in the south side of Icelandin an area called Hafið near Búrfell and Sultartangi hydroelectric power stations. Theturbines can be seen in Fig. 1.1.

Figure 1.1: The wind turbines which Landsvirkjun installed in December 2012. The windturbines are located in an area above Búrfell Hydroelectric power Station called Hafið [8].

Jón Ágúst Sigurðsson 3

Landsvirkjun has also conducted measurements to profile the wind speed and temperaturein the area. The aim of this research project was to explore the feasibility of using windpower to generate electricity in Iceland. Results from 2014 are very promising, as thewind turbines capacity factor (CF) was 44% compared to the global average being around28% in the same year [9, 10].

Based on this results Landsvirkjun has decided to assess the possibility of installing awind farm on roughly 40 km2 area named Búrfellslundur. Installed capacity is estimatedto be up to 200 MW with 80 windmills producing around 705 GWh annually [11]. Envi-ronmental impact assessment for the project is being conducted the assessment report isestimated to be finished in October 2015.

Outline and focus of the thesis

As one would expect, the amount of power extracted from a given wind turbine dependson the wind velocity at given site. More specifically, the power output depends on thewind velocity in the power of three, so the importance of knowledge of the wind potentialat given site is vital. Wind speed is zero at the surface (no slip conditions) and increasesgenerally logarithmically with height. The atmospheric stability along with conditionsof the surface, known as the surface roughness, affects the wind speed variation withheight. This variation of the wind speed profile is interesting to examine in context withthe anticipated power output from the wind turbine at each time and also the dynamicwind load on wind turbine structure caused by cyclic load variation.

The work of this thesis will be focused on using the meteorological data which Landsvirkjunhas collected. The wind speed and temperature measurements will be used to estimate im-portant parameters which describe and influence the atmospheric conditions in the lowestregion of the boundary layer, called the surface layer. In that region, combination ofthe heat- and wind shear fluxes occurs at a given time influencing and determining theatmospheric conditions which are said to be stable, neutral or unstable. The parame-ters describing the atmospheric conditions will be evaluated by using the method namedMonin and Obukhov (MO) similarity theorem. The MO method is used to parameter-ize fluxes in the surface layer as function of the Obukhov length L, which is a stabilityparameter.

The wind energy sector is new in Iceland. Research on the atmospheric conditions in thelowest region of the boundary layer are rather limited with respect to effects of different


atmospheric stability states and anticipated energy output from the wind turbines, makingthis research topic highly relevant.

5

Chapter 2

Literature review

This chapter establishes the theoretical background of the study. In the first part windturbines and their main components will be discussed along with the wind energy theory.The atmospheric boundary layer and its structure will be introduced as well as the use ofthe MO similarity theorem.

2.1 Wind energy fundamentals

Wind turbine is a mechanism which converts the kinetic energy of the wind to mechani-cal energy which is then used to generate electricity with generators. Wind turbines arecategorized in two main groups; horizontal axis wind turbines (HAWT) and vertical axiswind turbines (VAWT). The main difference between HAWT and VAWT is the axis ofrotation, which is parallel and perpendicular to the ground respectively. Due to the factthat HAWT are more common option than VAWT in the wind energy industry and usedon Hafið, only HAWT turbines will be examined in the study. Main parts of an onshorewind turbine is the base, tower, nacelle, rotor and the blades attached to it. Schematic fig-ure of HAWT can be seen in Fig. 2.1. The base, which is most often reinforced concrete,supports the whole structure. The most common tower design is cylindrical steel tube ortruss but in some cases are towers also made of concrete. The nacelle which holds therotor, gearbox, generator and other control devices and is is on the top of the tower. Therotor consists of a hub and blades, commonly three as Fig. 2.1 illustrates. HAWT rotorsare usually classified according to the rotor orientation (upwind/downwind), hub design,rotor control (pitch/stall), number of blades and how they are aligned with the wind (freeyaw/active yaw) [12].


Figure 2.1: A schematic picture demonstrating the main components of a HAWT.

The power output of a wind turbine depends on the interaction between the rotor and thewind. The rotor is therefore considered to be the most important part of the turbine fromthe performance point of view. The wind’s kinetic energy can be calculated using

E =1

2mU∞

2 (J) (2.1)

where m is the air mass moving at a velocity U∞. The corresponding rate of powerflowing across the cross sectional area of the wind turbine is

P =1

2ρAdU∞

3 (W ) (2.2)

where ρ is the density of the air andAd is the cross sectional area of the wind turbine rotor.By examining Eq. 2.2 it can be seen how important the wind speed is compared to otherparameters. Wind power is a function of the cube of the wind speed while it increaseslinearly with the rotor area and density of the air.


One-dimensional momentum theory

An analytical approach can be used to calculate the power from an ideal HAWT rotorusing momentum theory. Albert Betz (1926), a German physicist, was one of the firstdevelopers of the classical analysis of wind turbines, presented a model which is basedon linear momentum theory and can be used to determine the power from a ideal windturbine rotor [13]. To be able use this model, the following assumptions have to be made[12]:

• a homogeneous, incompressible, steady fluid flow

• no friction drag is presented

• an infinite number of blades

• the thrust occurring over the rotor area is uniform

• the wake is non–rotating

• the static pressure occurring far upstream and far downstream is equal to the undis-turbed ambient static pressure.

When this model is used a control volume is assumed around a wind turbine rotor whichis bounded by a surface and cross-sections of a stream tube. Wind turbine located in astream tube control volume is demonstrated in Fig 2.2.

Figure 2.2: A wind turbine located in an stream tube shaped air flow [14].

The air flow in this control volume is one dimensional steady state flow following astreamline pattern so the flow can only cross the ends of the stream tube. The rotoris represented by an actuator disc located in middle of control volume. Airflow havingfree stream velocity, U∞, and pressure, p∞, enters the upstream cross-sectional area of the


stream tube and decelerates across the actuator disk to the wake velocity, Uw, downstreambefore exiting the control volume. By applying Bernoulli’s equation on both sides of thedisk and assuming that the far upstream and far downstream pressures are equal and thatthe velocity across the rotor is the same, the wind velocity at the rotor, Ud, is found to bethe average of the free stream velocity and wake velocity. The change in axial velocityacross the actuator disk can be represented as an induced velocity variation,−aU∞, whichmust be superimposed on the free stream velocity. The parameter a is defined as the axialinduction factor, or the inflow factor [14]. This factor indicates the fractional decrease inthe wind velocity from the free stream to the rotor plane as in

Ud = U∞(1− a) (2.3)

and from free stream to wake velocity in

Uw = U∞(1− 2a). (2.4)

To fulfill the above assumptions a mass flow rate, m entering the stream tube has tobe constant everywhere inside the control volume. By examine Eq. 2.5 and assumeconstant air density it is clear that expansion of the stream tube has to occur as Fig. 2.2indicates.

m = ρA∞U∞ = ρAdUd = ρAwUw (kg/s). (2.5)

When air flows across the actuator disk it creates a discontinuity in the pressure wherepd

+ occurs just before the air passes the rotor and pd− behind it. The pressure difference,(pd

+−pd−), multiplied by the disk area,Ad, gives the rate of change of momentum acrossthe actuator disk. This is equal to the change in the momentum flow rate, (U∞ − Uw)m,as showed in

(pd+ − pd−)Ad = (U∞ − Uw)ρAdUd. (2.6)

The force on the air can be found by substituting Eq. 2.3 and 2.4 into Eq. 2.6 resultingin

F = (pd+ − pd−)Ad = 2ρU∞

2a(1− a). (2.7)


The rate of work done by the force from Eq. 2.7 is equal to the power extracted from theair and becomes

P = FUd = 2ρAdU∞3a(1− a)2. (2.8)

Eq. 2.9 defines a power coefficient (Cp) which is obtained by dividing Eq. 2.8 by Eq. 2.2.Cp is a parameter which indicates the ratio between obtained power from the wind turbinethe maximum available power in the wind.

Cp =P

12ρAdU∞

3 =Rotor power

Maximum available power= 4a(1− a)2. (2.9)

A non dimensional thrust coefficient (CT ) can be expressed in similar manner as the Cp

by

CT =F

12ρAdU∞

2 =Thrust force

Dynamical force= 4a(1− a). (2.10)

Examine Eq. 2.9 and 2.10 and their curves on Fig. 2.3 it can be seen that CT peaks whena = 0.5 resulting in zero wake velocity (Eq. 2.4). Value of a ≥ 0.5 are not valid for thissimple model. Maximum Cp value occurs when a = 1/3 resulting in CT = 8/9.

Figure 2.3: A plot showing CT and Cp curves with respect to change in the axial inductionfactor a. The model validity range is also indicated by vertical line segment [12].


Betz limit

Theoretically, wind turbines can only extract a limited part of the wind’s kinetic energyand convert into mechanical energy. This limit is known as the Betz limit and is namedafter Albert Betz who concluded in 1919 that wind turbine could at most convert 16/27(59.3%) of the wind’s energy [13, 12]. Betz limit is the maximum theoretical powercoefficient of any wind turbine design and occurs when the following is fulfilled

dCp

da= 4(1− a)(1− 3a) = 0. (2.11)

Solving Eq. 2.11, the maximum Cp value is obtained when the axial induction factor isa = 1/3 resulting in Cp,max = 0.593. Every wind turbine has its unique Cp value which isinfluenced by rotation of the wake behind the rotor, finite number of blades and associatedtip losses, as well as aerodynamic drag [12]. Based on Eq. 2.2 available power from awind turbine can be calculated using

P =1

2ρACpηU

3 (W ) (2.12)

where η is an efficiency parameter which indicates the ratio of power which is lost in thedrive train due to friction, i.e., in bearings. Other parameters have been defined previ-ously.

Capacity factor

Capacity factor, CF, is an important measure, which indicates how efficient a given windturbine is at a specific site. It is defined as the ratio of total actual power produced over agiven time period, normally one year, divided by rated power which is the total maximumpower that the specific turbine can produce over same period. The capacity factor isevaluated according to

CF =Pw · tPR · t

(2.13)

where Pw is the average wind turbine power, PR is the rated power and t is a given timeperiod.


2.2 Atmospheric boundary layer and its characteristics

In wind energy engineering is important to know the conditions in the atmosphere andspecially in the wind turbines region. The lowest 1-2 km of the atmosphere is called theatmospheric boundary layer (ABL) and its characteristics are directly influenced by theexchange of momentum, heat and water vapor at the earth’s surface [15]. The ABL canbe divided into sub-layers where the lowest part is known as the surface layer, followedby several layers which will not be discussed further here. In the surface layer, windspeed, temperature and humidity does change rapidly with height. The variation of windspeed with height is known as the vertical wind speed profile or vertical wind shear [12].The wind speed is zero at the earth’s surface (no-slip condition) and increases with height[16, 17].

Determination of the wind speed profile is important since the production capacity of awind turbine is directly subjected to it. In addition the rotor blade lifetime is influenced bythe wind profile since the wind variation in vertical direction will result in a cyclic load. Itis known that the atmospheric stability and surface roughness are factors which affect theshape of the wind profile. To determine the atmospheric stability is the Monin-Obukhov(MO) similarity theorem well known method and will be introduced and explained inmore detail in a later section.

Lapse rate and stability of the atmosphere

The definition of lapse rate is the rate of temperature change with increasing height. Whenthe temperature decreases with height is the lapse rate considered positive, negative whentemperature increases with height and zero when the temperature is constant with height.The lapse rate is variable and is effected by solar radiations, convection and condensationoccurring at each time. The adiabatic lapse rate assumes no heat transfer in the processand is defined as

(dT

dz

)adiabatic

= −g 1

cp= −0.0098◦C

m(2.14)

where g = 9.81m/s2 and cp = 1.005kJ/kgK(the constant pressure specific heat) areassumed to be constant with height.


By examine Eq. 2.14 it can be seen that the temperature decrease is about 1◦C per 100m increase in height. This process is known as the dry adiabatic lapse (Γ) and is definedas

Γ = −(dT

dz

)adiabatic

(2.15)

having the negative sign of the temperature gradient. It is useful to introduce the potentialtemperature, Θ. It is defined as the temperature that a dry air parcel would have if itwould be brought adiabatically and reversibly from its initial state to standard pressureand is defined as

Θ = T

(p0

p

) Rcp

(2.16)

where T is the absolute temperature, p0 is the standard reference pressure, p is the currentpressure, R is the gas constant of air and cp is the specific heat capacity at constant pres-sure. The relationship between the temperature gradient, potential temperature gradientand the dry adiabatic lapse rate is

(dΘ

dz

)=

(dT

dz

)+ Γ. (2.17)

The temperature gradient is an important parameter which is used to determine the atmo-spheric stability [12, 18]. The stability of the atmosphere is usually classified as stable,neutral or unstable by the following

(dT

dz

)= Γ Neutral atmosphere (2.18)

(dT

dz

)> Γ Stable atmosphere (2.19)

(dT

dz

)< Γ Unstable atmosphere. (2.20)

with regard to dry air. Figure 2.4 illustrates the change in the typical temperature profilebefore and after sunrise and respective stability states which affect the vertical transportof heat in the atmosphere at given time. To simplify, one can imagine a parcel of airat temperature T located in the surface layer. During the period from sunset to sunrise


(stable state) the air temperature below the parcel is lower than the air temperature aboveit. This conditions causes the air parcel to remain at its level, resulting in minor verticalheat flux and the surface layer is characterized by wind shear. From sunrise to sunset(unstable state) is the air temperature below the parcel higher than the air temperatureabove. This condition allows the air parcel to move vertically in the surface layer causinga strong air mixing between layers at different altitude which leads to reduction in thewind shear [19].

Figure 2.4: The behavior of the temperature profile in the surface layer, before (solid line)and after (dashed line) sunrise. The vertical transport of a air parcel (blue circle) havingthe temperature T demonstrated for stable and unstable atmospheric conditions.

Turbulent flow

Turbulence in the wind in the ABL may be imagined as swirling motion of eddies. Theseeddies vary in size and are generated and maintained by surface friction along with buoy-ancy effects which cause vertical transportation of air parcels due to temperature differ-ence. The kinetic energy in the eddies is consistently transfered to smaller eddies througha process called energy cascade. Turbulent flow is chaotic and therefore difficult to pre-dict. For example can small changes in initial or boundary conditions over a short time


period lead to large difference in the flow pattern. Therefore, it is common to use statisti-cal methods to develop descriptions of turbulence and its behavior.

Turbulent flow can be described as wind speed fluctuation having a relatively constantmean over a long time period, for example an hour, but can vary in shorter periods. Tur-bulence is three dimensional having longitudinal, lateral and vertical components denotedby u(z, t), v(z, t) and w(z, t) respectively, where z is the height above ground in metersand t is the time in seconds. By applying Reynolds decomposition can each componentbe expressed in terms of mean wind seed, u, and the fluctuation of the wind speed, u′,as

u = u+ u′ (2.21)

for the longitudinal velocity component (x direction). Other atmospheric variables liketemperature, pressure, etc. can be expressed in the same manner into mean and fluctuatingpart. The over-bar representation of a variable (x) indicates that average value has beentaken of the variable over a given period of time as in

u =1

T

∫ t0+T

t0

u dt. (2.22)

The average value of the fluctuating part of the wind speed is always equal to zero asshown in

u′ =1

T

∫ t0+T

t0

(u− u) dt = u− u = 0. (2.23)

The data variance about the mean is also a common measure of the fluctuating part of theflow and is defined as

V ar(u) = σ2u = u′2 =

1

T

∫ t0+T

t0

u′2dt 6= 0. (2.24)

Turbulence intensity (TI) is the most basic measurement of turbulence and is the ratio ofstandard deviation of the wind speed and the mean wind speed and is frequently in therange of 0.1 and 0.4 [12, 20]. Turbulence intensity depends on the height above ground,earth’s surface roughness (z0), the thermal behavior in the atmosphere and the averageperiod of the data. Turbulence intensity is defined as


TI =σuu. (2.25)

The equation describing the mean flow velocity is the Reynolds equation which is ob-tained by taking an average of the Navier Stokes (NS) equation [17]. The x-componentof the NS equation is defined as

∂u

∂t+ u

∂u

∂x+ v

∂u

∂y+ w

∂u

∂z= −1

ρ

∂p

∂x+ ν

(∂2u

∂x2+∂2u

∂y2+∂2u

∂z2

)+ gx. (2.26)

The x-component of the Reynolds equation is defined as

∂u

∂t+ u

∂u

∂x+ v

∂u

∂y+ w

∂u

∂z=− 1

ρ

∂p

∂x

+1

ρ

∂

∂x

[µ∂u

∂x− ρu′2

]+

1

ρ

∂

∂y

[µ∂u

∂y− ρu′v′

]+

1

ρ

∂

∂z

[µ∂u

∂z− ρu′w′

](2.27)

where −ρu′2, −ρu′v′, −ρu′w′ are the Reynolds stresses and µ∂u∂x

, µ∂u∂y

, µ∂u∂z

are the vis-cous stresses. In the surface layer region, the Reynolds stresses dominate the viscusstresses.


The turbulence kinetic energy

Based on the Reynolds equation in Eq. 2.27 the turbulent kinetic energy (TKE) is definedas

k =1

2(u′2 + v′2 + w′2). (2.28)

The TKE is on of the most important parameters in fluid dynamics and meteorology. TheTKE is mean kinetic energy per unit mass which is directly related to the transport of heat,momentum and moisture in the ABL [18]. There for the TKE, obtained from Eq. 2.26 and2.27 can be expressed in Eq. 2.29 which demonstrates the change in TKE with time andis known as the TKE budget equation [17, 16]. It should be noted that Eq. 2.29 has beensimplified from the general TKE budget equation by assuming horizontal homogeneityand aligning the coordinate system parallel with the mean horizontal wind.

∂k

∂t=g

Θw′Θ′ − u′w′∂u

∂z− ∂

∂zw′k − 1

ρ

∂

∂zw′p′ − ε (2.29)

The 1st term from left in Eq. 2.29 is the rate of change in TKE with time. The 2ndterm describes the buoyancy flux production or consumption depending on the sign of theheat flux (w′Θ′) where Θ is the potential temperature and g is the Earth’s gravity. Theinteraction between turbulent momentum flux and vertical wind shear of the mean windis described in the 3rd term. The 4th term is the vertical transport of TKE by turbulenteddies. The 5th term describes the pressure perturbation and the last term is the dissipationrate [21].


2.3 The Monin-Obukhov similarity

The Monin-Obukhov, MO, similarity theorem was first presented by Obukhov (1946)paper and later by Monin and Obukhov (1954). The MO theorem is considered to bethe centerpiece of surface layer meteorology and has provided much of the foundationfor our understanding and determination of the profiles of wind and temperature in theatmospheric boundary layer. However, the use of the MO theorem limited to the surfacelayer (constant flux layer) and over homogeneous terrain. A historical summary of theMO theorem was published by Foken in [22] where he gives a brief historical overview ofexperiments and findings which has been used to formulate the MO universal functions.According to Foken’s paper, experimental results conducted under ideal conditions didshow that the accuracy of the MO method was about 10-20% [22]

The Obukhov length

The MO similarity hypothesis rests on the dimensional analysis and the Buckingham PiTheorem which is used to form dimensional groups of dependent parameters in a phys-ical problem. The MO hypothesis states that the parameters, z (height above ground),u∗ (velocity scale of the turbulence), Q0 (mean temperature flux at surface), C0 (meansurface flux) and g/Θ0 (buoyancy parameter) govern the turbulent structure above a ho-mogeneous surface [21]. From these parameters two dependent dimensionless quantitiescan be formed with, z, u∗, T∗ = −Q0/u∗, c∗ = −C0/u∗ and z/L , where L, is knownas the Obukhov length. The Obukhov length is a stability parameter which is used as ascaling parameter in the surface layer and is non-dimensionlized with z [23]. The lengthL is defined as

L = − u3∗ Θ0

κ g Q0

(m) (2.30)

where u∗ is the friction velocity, Θ0 is the surface potential temperature, κ is the vonKármán constant and is considered to be κ = 0.4 [21], g is the gravity of earth and Q0

is the mean potential temperature flux at the surface. The friction velocity is definedas

u∗ =

√τ0

ρo(m/s) (2.31)


where τ0 is surface shear stress and ρ0 is density of air in the surface layer. The surfaceheat flux is defined as

Q0 = cp ρ0 w′Θ′0 = −cp ρ0 u∗ T∗ (W/m2) (2.32)

where cp is specific heat for constant pressure and T∗ is the scaling temperature definedas

T∗ = −w′Θ′

u∗. (2.33)

As previously discussed L is a stability parameter having negative value during unstableconditions (Q0 > 0), positive value in stable conditions (Q0 < 0) and neutral (Q0 = 0)when L tends to infinity. Near neutral conditions are considered to occur when |z/L| <<1 which happens near the surface when |L| >> z [21, 24]. The M-O similarity theorythen implies that universal functions of momentum φm(z/L) and heat φh(z/L) existssuch that the surface layer gradients of mean wind speed and mean potential temperaturewill behave as

φm(ξ) =κ z

u∗

∂U

∂z(2.34)

and

φh(ξ) =κ z

T∗

∂Θ

∂z(2.35)

respectively where ξ = z/L.

Different values of κ have been proposed in the literature for example by Businger etall [25], Yaglom [26] and Högström [27]. The von Kármán constant is a dimensionlessscaling parameter for the friction velocity in the fully turbulent region near a wall [21]and is used to describe the logarithmic velocity profile (Law of the wall) of a turbulentfluid flow. The mean Log-law profile is defined as

U =u∗κ

ln

(z

z0

)(2.36)

where z0 is the surface roughness length parameter. From Eq. 2.36, the von Kármánconstant is defined as


κ =u∗

z ∂U∂z

. (2.37)

The function of momentum in Eq.2.34 is defined with κ so the value of φm(0) = 1. Nocomplete theory exists which predicts the form of φm(ξ) and φh(ξ) over the whole stableand unstable range and many forms of the universal function have been proposed in theliterature. The Kansas experiment [25] were among the first to measure the mean windand temperature profiles along with their turbulent fluxes in the surface [21]. A figureshowing the results of the experiment can be seen in Fig. 2.5.

(a) (b)

Figure 2.5: Observations of φm in (a) and φh in (b) with respect to the stability parameter(ξ = z/L) from the 1968 Kansas experiment [25].

One form of the universal function was suggested from the results of the Kansas experi-ment. Since then, several suggestions have been proposed. Högström in [28] suggestedthat the form of the universal functions for stable conditions would have the followingform

φm = 1 + 4.8z

Lφh = 1 + 7.8

z

L. (2.38)


Determination of the unstable form of the universal functions has been more complexand different forms have been proposed. Based on Högström experiment in [28] Wilsonproposed the following form for the unstable condition

φm =(

1− γm|z/L|2/3)−1/2

φh =(

1− γh|z/L|2/3)−1/2

(2.39)

where γm = 3.6 and γh = 7.9 [29].

The MO wind and temperature profiles

Integrating Eq. 2.34 and 2.35 with respect to height and by using the forms of the universalfunctions in Eq. 2.38, it is possible to formulate equation for the mean wind and meantemperature profiles for the stable state using

U(z) =u∗κ

[ln

(z

z0

)+ 4.8

z

L

](2.40)

Θ(z) = Θ(zr) +T∗κ

[ln

(z

zr

)+ 7.8

z

L

](2.41)

where Θ(zr) is the surface potential temperature and zr is the respective reference height.The neutral state wind profile can be derived from Eq. 2.40, by using the knowledge ofL >> z, resulting in already mentioned mean Log-law profile in Eq. 2.36.

For the unstable state, following mean wind and mean potential temperature profiles canbe determined with

U(z) =u∗κ

[ln

(z

z0

)− 3 ln

(1 +

√1 + γm|z/L|2/3

1 +√

1 + γm|z0/L|2/3

)](2.42)

Θ(z) = Θ(zr) +PtT∗κ

[ln

(z

zr

)− 3 ln

(1 +

√1 + γh|z/L|2/3

1 +√

1 + γh|zr/L|2/3

)](2.43)

from Wilson’s proposed functions in Eq. 2.39 where he suggested the constant Pt = 0.95

[21].

As previously discussed, z0 is a length parameter which characterizes the roughness of theground surface and is defined as the height where the wind according to the Log-law is


equal to zero. Examples of some types of terrains along with respective roughness lengthare listed in Table 2.1 below.

Type of terrain Roughness length [mm]

Very smooth, ice or mud 0.01

Calm open sea 0.2

Snow surface 3

Lawn grass 8

Rough pasture 10

Open flat terrain, few isolated obstacles 30

Crops 50

Few trees 100

Many trees, hedges, few buildings 250

Forest and woodlands 500

Center of cities with tall buildings 3000

Table 2.1: Typical values of surface roughness length for several types of terrain [12]

23

Chapter 3

Methodology

In this chapter, the methodology of the study is discussed. A description of the mea-surement site, measurements instruments and respective data is presented and the methodused to estimate the surface roughness is explained. Lastly, the approach to determine theMO universal functions from the data is explained.

3.1 Site description

The site where the measurement devices, discussed below in section 3.2, are located isa rural area called Búrfellslundur, demonstrated in Fig. 3.1 below. The site is located inBúrfellshraun which is above the Búrfell mountain, in the south side of Iceland, about200-300 m above sea level. The landscape is relatively flat, homogeneous and is char-acterized as lava and sand terrains. The Icelandic Meteorological Office has performedmeteorological measurements in the area since 1993. From 1993 to the present day theaverage temperature has been about 3◦C and the average wind speed 7 m/s, measured at10 m height. The measurements have also shown prevailing wind direction from northeast which can been seen on the wind rose diagram in Fig. 3.2. It seems that this pre-vailing wind flows down from the highlands and intensifies when flowing between theNæfurholts mountains and Búrfell mountain [9].


Figure 3.1: The inset shows a satellite picture of Iceland with an indication Búrfellslundurlocation. The area is on the south side of Iceland, above Búrfell mountain. [30].

Figure 3.2: Picture showing wind rose digram demonstrating the prevailing wind direc-tions in the Búrfellslundur area. The data colored in blue is result from Landsvirkjun’swind measurements and data colored in green is results from Icelandic MeteorologicalOffice [9].


3.2 Measurement instruments

The meteorological data used in the study was obtained from a wind Lidar and an 80mhigh tilt up mast equipped with measurement devices. The devices will be discussed inmore detail in the next two sections. Location of the Lidar and the mast can be seen inFig. 3.3. The 80m mast was installed on the 1. April 2014 and data from it was availablefrom 5. Apr 2014. The Lidar started to log data the 17. Feb 2014 and data was collecteduntil the 16. Apr 2014, its location is marked with green circle in Fig. 3.3. The distancefrom the mast to the Lidar was about 100m [31]. The Lidar was then moved to anotherlocation marked with blue circle in Fig. 3.3 and was located there until the 27. Oct 2014.The distance from the mast to the Lidar’s new location was about 24m [32].

Figure 3.3: A map showing the locations of the 80m mast and Lidar in the Búrfellslundurarea during a given period. The location of Landsvirkjun’s experimental wind turbinescan also be seen marked with a green stars [9].


The meteorological mast

The mast is a 81.3m high tower rigidly supported by steel wires which are fastened tothe ground by anchors. The mast can be seen in Fig 3.4. The mast is produced by thecompany Renewable NRG systems which specializes in providing measurement devicesand technical service for the global renewable energy industry.

Figure 3.4: The meteorological mast in (a) demonstrates the measuring heights of cor-responding instruments. (b) shows the mast at its location with Búrfell mountain in thebackground [33].

The mast was instrumented with cup anemometers at 40.65m, 60m, 69.53m, 69.87mand two at 82.05m height, two sonic anemometers at 78.06m height and one propelleranemometer at 10.47m height. Wind vanes were located at 10.47, 68.24 and 71.34mheight respectively. Temperature was measured at 2.27m, 10.27m, 10.3m, 40.47m, 80.53m,80.56m height. Barometric pressure was also measured at 2m height with Vaisala(PTB110500-1100) having±0.1hPa in resolution. The cup anemometers types was Thies(4.3351.10)and Vaisala(WAA252) with resolution of±0.05m/s and±0.17m/s respectively. The maindifference between them, the Vaisala meter is a heated cup anemometer. The type of the


propeller anemometer was Young(05106) with±0.3m/s resolution. Gill WindObserver(1390-75-B-322) and Thies Ultrasonic Anemometer 2D(4.382.01.310) were used both having±0.01m/s and ±1◦ in resolution. Logan(4159) temperature sensors with ±0.8% resolu-tion at 23◦C were used. List of the measurement devices and respective heights can beseen in Table 3.1. Data was sampled at 1 Hz and stored as 10 min averages.

Parameter Unit Inst. height (m)Barometer hPa 2.0

Temperature ◦C 2.27, 10.27, 10.3, 40.47, 80.53, 80.56

Humidity % 2.3, 10.3, 80.53

Wind direction ◦deg 10.47, 68.24, 71.34

Wind speed (Propeller) m/s 10.47

Wind speed (Cup) m/s 40.65, 60.0, 69.53, 2×82.05

Wind speed (Cup-heated) m/s 69.87

Wind speed & direction (2D ultrasonic) m/s,◦deg 2×78.06

Table 3.1: List of measurement devises used on the mast and their respective installationheights [33].

The Lidar

Lidar (Light detection and ranging) was used to measure and log wind speed at the site.Lidar is a remote sensing device which can measure three-dimensional wind field from40m up to 200m height. WindCube v2 Lidar from Leosphere is used by Landsvirkjunat Hafið. This type of Lidar has 0.1m/s wind speed accuracy and ±2◦ wind directionaccuracy. It measures and logs vertical and horizontal wind speed and directions up to12 different heights above ground. The Lidar was programmed to perform measurementsat 41m, 50m, 60m, 70m, 82m, 90m, 100m, 110m, 120m, 130m, 160m and 200m. Thedata was sampled at rate of 1 Hz and stored as 10 min averages. Lidar measurements ofa horizontal mean wind speed compared with anemometer observations from a meteoro-logical mast have been studied in [34] showing good correlation between the Lidar andthe anemometers instruments at all heights.

To be able to measure the wind speed and direction, Lidar emits a beam of light up inthe atmosphere. When the light interacts with aerosols which move relative to the beamdirection, the frequency of the light, f0, experiences a Doppler shift, ∆f . The movingparticle scatters some of the light back having frequency

f = f0 + ∆f ≈ f0(1 + 2U/c) (3.1)


where U is the wind speed and c is the speed of light. The returned light is analyzed todetermine the speed and distance to the particles from which it was scattered [12, 35, 36].Schematic figure of a Lidar in action is illustrated in Fig. 3.5.

(a) (b)

Figure 3.5: Windcube V2 Lidar device. The measurements heights from 40m up to 200mheight are shown in (a). (b) demonstrates how the Lidar transmits four infrared laserpulses, which are tilted 28◦ from vertical up in the atmosphere. Aerosol particles in theair backscatters the laser pulses back to the Lidar. The backscattered signal is then usedto calculate wind speed and direction from 10 different heights [37].

3.3 Surface roughness estimation

The surface roughness length parameter was estimated from the 10 min wind profilesoccurring at neutral or near neutral state from the time period of interest. Wind profilesoccurring when

Γ− ε <(dT

dz

)< Γ + ε (3.2)

were used where threshold parameter ε = 0.001 and Γ defined in Eq.2.14 were used.The value of ε was chosen with respect that at least 50 data points would be obtained toestimate the roughness parameter. Wind profiles having the average wind speeds above


2m/s were used and prevailing wind sectors was found from the wind vanes data whichwas used to check if the value of z0 could be assumed to be homogeneous. All windprofiles fulfilling the above requirements were used to determine the roughness lengthparameter. At neutral state the wind speed profile is defined as

U(z) =u∗κ

[ln

(z

z0

)]=u∗κ

ln(10) log10(z)− u∗κ

ln(z0).

(3.3)

Applying log linear fit to the wind speed profile data it was possible to determine thefriction velocity using

u∗ =α κ

ln(10)(3.4)

where α is the slope of the log linear fit

U(z) = α log10(z) + β. (3.5)

The value of z0 for each wind speed profile was then found in similar manner using

z0 = e−β κu∗ (3.6)

where β is the intersection of Eq. 3.5 which represents the height where the wind profilehas zero speed. An overall value of z0 was then estimated by taking the average valueof all z0 data, obtained from Eq. 3.6, except values of z0 > 0.1m and z0 < 0.0002m. Ifthese values are examined and compared with the typical values of z0 in Table 2.1 theymatch with terrain with few trees and calm open sea respectively, so they were consideredoutliers and filtered.


3.4 The universal functions

The universal functions φm(ξ) and φh(ξ) for stable and unstable range were determinedusing the estimated values of the parameters L, u∗, T∗, mean wind and mean temperaturegradients. Similar to the estimation method of the surface roughness above, all the meanwind and mean temperatures profiles were categorized first as stable or unstable accordingto

(dT

dz

)> −Γ + ε Stable (3.7)

(dT

dz

)< −Γ− ε Unstable. (3.8)

For the stable case the parameters L and u∗ were estimated by fitting Eq. 2.40 to each 10min wind profile data using the method of least squares. The T∗ parameter was similarlyfound by fitting Eq. 2.41 to each 10 min temperature profile data and by using estimatedvalues of L which was found earlier. The parameters occurring at unstable case weredetermined by same methodology by fitting Eq. 2.42 and 2.43 to the unstable mean windand mean temperature profiles. The parameters determined from fits having R2 > 0.9

were considered to be valid and were used for further calculations. The R2 parameteris known as the coefficient of determination and is used to indicate how well given datafits to a certain model. When R < 0.9, indicating poor fit, there are number of reasonsexplaining that, e.g. missing data in the profile, low wind speed and wind profiles notbehaving log linearly. To be able to use Eq. 2.41 and 2.43, all the mean temperatureprofiles were converted from absolute to mean potential temperature using

Θ(z) = T (z)

(p0

p(z)

) Rcp

(3.9)

where T is a measurement of absolute temperature from the mast, p0 is the standardreference pressure, p is the current pressure at given height and the value of the ratioR/cp was assumed to be 0.286 [18]. To determine the value of p at each z of interest thefollowing approximation was used

p(z) = p0 − 0.011837 z + (4.793× 10−7) z2 (3.10)


where p0 was measured with the barometric pressure sensor on the mast [12]. By follow-ing the same methodology as used in Yague et al. [24] and Johansson et al. in [38], themean wind and mean temperature gradients were determined by fitting

U = A z +B ln(z) + C (3.11)

Θ = A′ z +B′ ln(z) + C ′ (3.12)

to the stable data profiles, and

U = A ln(z) +B (ln(z))2 + C (3.13)

Θ = A′ ln(z) +B′ (ln(z))2 + C ′ (3.14)

to the unstable ones, where the coefficients A,B,C and A′, B′, C ′ where evaluated by theleast squares method. The same evaluation criteria as above was used to determine thequality of the fit. From these fits, the gradients of wind speed and potential temperaturewere directly obtained using

∂U

∂z= A+

B

z(3.15)

∂Θ

∂z= A′ +

B′

z(3.16)

for the stable case, and

∂U

∂z=A

z+ 2B

ln(z)

z(3.17)

∂Θ

∂z=A′

z+ 2B′

ln(z)

z(3.18)

for the unstable case. The height, z = 55m was chosen as the height of interest sincethe hub height of the experimental wind turbines is at that height. The dimensionlessfunctions φm(ξ) and φh(ξ) were then evaluated using


φm(ξ) =κz

u∗

∂u

∂z(3.19)

and

φh(ξ) =κz

T∗

∂Θ

∂z(3.20)

using the estimated values of u∗, T∗, ∂U∂z

, ∂Θ∂z

and κ = 0.4.

3.5 Data processing

All data handling in this study were carried out using the numerical computing envi-ronment MATLAB (Matrix laboratory). Two pre-programed MATLAB functions wereobtained from the MathWorks web page and used in this study to plot the prevailingwind directions and the wind distribution over a given time period. The developers ofthese programs are Marta Almeida [39] and Jiro Doke [40] respectively. Other MATLABcodes used in this study were programmed by author except for the scripts which wereused to import the measurements data into MATLAB and handling the time period se-lection of data of interest. Those were written in part by Erlingur Ívar Jóhannsson andHéðinn Hauksson, students in the course T-629-URO1 at Reykjavik University, and theauthor.

33

Chapter 4

Results

The results chapter is divided into four main sections where the first three sections con-tains the results obtained from a period within a given month of the year 2014, May, Julyand October respectively. Each section starts off by introducing the wind velocity distri-bution and the prevailing wind direction occurring in the respective month. The surfaceroughness data is presented along with the estimated z0 parameter. The results of the nondimensional wind shear and temperature gradient, calculated at z = 55m height, will thenbe demonstrated. A list of the average value of L and u∗ and total number of wind profilesoccurring in each stability class are also presented.

The wind profiles were categorized into stability classes according to the value of L asshown in Table 4.1, but this approach was used in Peña et al in [41].

Obukhov length interval [m] Atmospheric stability class10 ≤ L ≤ 50 Very stable (vs)

50 < L ≤ 200 Stable (s)

200 < L ≤ 500 Near stable (ns)

|L| > 500 Neutral (n)

−500 ≤ L < −200 Near unstable (nu)

−200 ≤ L < −100 Unstable (u)

−100 ≤ L ≤ −50 Very unstable (vu)

Table 4.1: Obukhov length, L, interval and corresponding stability class which was usedto classify each wind speed profile.

The wind speed measurements from Lidar and the anemometers on the 80m mast wereexamined and compared for May, July and October.


4.1 May 2014

Data from the period of May 7th to May 31st was examined, data from the 1st of Maywas excluded as it was not available. The wind speed distribution in May can be seen inFig. 4.1. The data used in this plot was the 10 min average wind speed at 60m heightobtained from the anemometers on the 80m mast. The average wind speed at 60m heightduring this time period was 6.6m/s.

Figure 4.1: A histogram demonstrating the wind speed distribution in May. A 10 minaverage wind speed measurements at 60m height from the 80m mast was used. Theabscissa is the wind velocity in m/s and the number of times when the wind occurred atcertain wind speed is on the ordinate.


The prevailing wind directions occurring in May can be seen on the wind rose diagramin Fig. 4.2. The diagram shows that wind coming from northeast occurs most often, butwind coming from the southeast and southwest sector also occurs.

Figure 4.2: A wind rose diagram showing the prevailing wind directions in May. A10 min average wind direction measurements from the 80m mast, conducted at 68.24mheight were used in this diagram. The color-bar in represents the wind speed range in m/s.Wind coming from the northeast sector is the prevalent one in May.

4.1.1 Surface roughness length

All 10 min wind speed profiles occurring at neutral or near neutral state were analyzed andrespective z0 data was obtained. The surface roughness length parameter was estimatedby taking the average value of the data points shown in Fig. 4.3. The total number of datapoints were 69 and the average value of z0 was 0.021m having the standard deviation of0.024m. The prevailing wind direction of the z0 data in Fig.4.3 is demonstrated in Fig.4.4 showing that the prevailing wind is southwest at neutral and near neutral state. Theaverage value of z0 was treated as a constant within the period, based on the assumptionthat changes in surface condition are minor. The change in the surface that could occur issnowing resulting in lower surface roughness value.


Figure 4.3: A scatter plot of the surface roughness length parameter obtained from the 10min average wind profiles occurring at neutral state in May. The average value of z0 isdemonstrated as red solid line on the graph. The abscissa is the number of data points andthe ordinate is the surface roughness value in meters.

Figure 4.4: A wind rose diagram showing the prevailing wind directions of the 10 minaverage wind speed profiles that were used to estimate the surface roughness data in May.The color-bar represents the wind speed range in m/s. Wind coming from the southwestis dominant at neutral and near neutral state in May.


4.1.2 The non dimensional wind shear and temperature gradient

The obtained values of the non dimensional wind shear and non temperature gradient,calculated at height z = 55m, can be seen in Fig. 4.5 and Fig. 4.6 respectively. Forcomparison is the universal functions of φm and φh plotted as a red line for the stablerange and green line for the unstable one. For both φm and φh the majority of the datapoints is in the range of 0 < φm,h < 5 when −1 < ξ < 1. Fig. 4.5 and Fig. 4.6 showthat values of φm and φh do follow their respective universal functions over the unstablerange. The values of φm over the stable range scatter more than the unstable data havingcorrelation of R2 = 0.978. The scatter increases as the value of ξ increases which occurswhen L → 0. The blue line on Fig. 4.5 shows the fitted line of the stable data. Theslope of the fitted line is 4.6 which is a little lower than the slope of the universal functionwhich is 4.8. The point of intersection of the fitted line is at φm(0) = 1.2 compared toφm(0) = 1 for the stable universal function.

Figure 4.5: A graph showing the non dimensional wind shear, φm, in May as a functionof the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shown in red andgreen, represents the proposed φm models for both stable and unstable state respectivelyfor comparison.


The φh data over the stable range in Fig. 4.6 shows high correlation having R2 = 0.982.A dashed blue line represents the fitted line of the stable φh data. The fitted line has theslope 5.4 which is lower than the slope of the respective universal function which is 7.8.The fitted line intersect at φh(0) = 1.2 but the intersection of the universal function is atφm(0) = 1.

Figure 4.6: A graph showing the non dimensional wind shear, φh, in May as a functionof the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shown in red andgreen, represents the proposed φh models for stable and unstable state respectively forcomparison.


4.1.3 Summary of results from May

A summary of the results from May can be seen in Table 4.2. The total number of meanwind profiles which had R2 > 0.9 were 288 or only 8% of all mean wind profiles inMay. The total number of mean wind profiles classified as neutral were 114 (39.6%), 139

(48.3%) where on the stable range and 35 (12.2%) were on the unstable range.

Stability class Lave [m] u∗,ave [m/s] No. of profiles

Very stable (vs) 23 0.04 14

Stable (s) 125 0.18 71

Near stable (ns) 324 0.27 54

Neutral (n) 2.2 · 108 0.38 114

Near unstable (nu) −302 0.50 11

Unstable (u) −144 0.55 15

Very unstable (vu) −78 0.60 9

Total: 288

% of data 8.0

Table 4.2: The computed and estimated average values for the wind profiles in each sta-bility class. The total number of wind profiles which fulfilled the R2 > 0.9 criteria andits respective rate of the total number of wind profiles occurring in May.

As Table 4.2 demonstrates, 87.9% of all usable mean wind speed profiles in the monthwere considered neutral or stable. A stable surface layer is characterized by wind shearand wind turbulence is induced. Furthermore, it can be seen that the average value of u∗for each stability class increases from the very stable state to very unstable state.


4.2 July 2014

Data from the period of July 1st to July 31st were examined in this section. The windspeed distribution in July can be seen in Fig. 4.7. The data used in this plot was the 10min average wind speed measured with cup anemometer at 60m height on the 80m mast.The average wind speed at 60m height during this time period in July was 6.5m/s.

Figure 4.7: A histogram demonstrating the wind speed distribution in July. A 10 minaverage wind speed measurements at 60m height from the 80m mast was used. Theabscissa is the wind velocity in m/s and the number of times when the wind occurred atcertain wind speed is on the ordinate.


The prevailing wind directions in July are demonstrated on a wind rose diagram in Fig.4.8. The diagram shows that the prevailing wind directions in July are northeast andsouthwest. Wind coming from the southeast sector occurs also but is much less fre-quently.

Figure 4.8: A wind rose diagram showing the prevailing wind directions in July. The10 min average wind direction measurements from the 80m mast, conducted at 68.24mheight were used in this diagram. The color-bar represents the wind speed range in m/s.Wind coming from the northeast and southwest sector are the prevalent one in July.


All 10 min wind speed profiles occurring at neutral or near neutral state were analyzed andrespective z0 data was obtained. The surface roughness length parameter was estimatedby taking the average value of the data points shown in Fig. 4.9. The total number ofdata points were 95 and the average value of z0 was 0.032m with the standard deviationof 0.029m. The prevailing wind directions of the z0 data in Fig.4.9 are demonstrated inFig. 4.10 showing that the prevailing wind is southwest at neutral and near neutral state.The difference in the average z0 value in May and July was minor but the value was littlehigher in July. The reason for this difference could be due to an increase in vegetationand that the snow that could have been in the area in May was gone. The average value of


z0 was treated as a constant value in July, based on the assumption that major conditionchanges of the surface cannot occur with respect to snow during summer.

Figure 4.9: A scatter plot of the surface roughness length parameter obtained from the 10min average wind profiles occurring at neutral state in July. The average value of z0 isdemonstrated as red solid line on the graph. On the abscissa is the number of data pointsand on the ordinate is the surface roughness value in meters.


Figure 4.10: A wind rose diagram which shows the prevailing wind directions of the 10min average wind speed profiles which were used to estimate the surface roughness datain July. The color-bar in inset represents the wind speed range in m/s. Wind coming fromthe southwest is dominant at neutral and near neutral state in July.


Graphs showing the results of the non dimensional wind shear and non temperature gra-dient can be seen in Fig. 4.11 and Fig. 4.12 respectively. The universal functions of φm

and φh are also plotted as a red line for the stable range and green line for the unstableone. The unstable values of φm on Fig. 4.11 seems to follow the universal function andshow a minor scatter around it. The values of φm over the stable range scatter more thanthe unstable data having correlation of R2 = 0.983. The dashed blue line on Fig. 4.11 isthe fitted line of the stable data. The slope of the fitted line is 4.7 which is nearly the sameslope of the universal function which is 4.8. The point of intersection of the fitted line isat φm(0) = 1 which is the same as for the stable universal function.


Figure 4.11: A graph showing the non dimensional wind shear, φm, in July as a functionof the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shown in red andgreen, represents the proposed φm models for both stable and unstable state respectivelyfor comparison.


The stable φh data in Fig. 4.12 shows a correlation of R2 = 0.973. A dashed blue linerepresents the fitted line of the stable φh data. The fitted line has the slope 5.9 but theslope of the respective universal function is 7.8. The fitted line intersection point is atφh(0) = 1.4 which is a little higher value than the intersection point φm(0) = 1 of theuniversal function. The unstable φh data shows a minor scatter and has a positive offsetfrom its respective universal function.

Figure 4.12: A graph showing the non dimensional wind shear, φh, in July as a functionof the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shown in red andgreen, represents the proposed φh models for both stable and unstable state respectivelyfor comparison.


4.2.3 Summary of results from July

A summary of the results from the time period in July can be seen in Table 4.3. Thetotal number of wind profiles which were usable (R2 > 0.9) were 389 which is 8.71%

of all wind profiles occurring in July. The total number of wind profiles classified asneutral were 204 (52.4%), 155 (39.8%) were on the stable range and 30 (7.7%) were onthe unstable range. The average friction velocity increases as the stability change fromvery stable to very unstable state.



Stable (s) 118 0.18 69


Neutral (n) 4.5 · 108 0.51 204


Unstable (u) −152 0.60 8

Very unstable (vu) −79 0.54 7

Total: 389

% of data 8.71

Table 4.3: The computed and estimated average values for the wind profiles in each sta-bility class. The total number of wind profiles which fulfilled the R2 > 0.9 criteria andits respective rate of the total number of wind profiles occurring in July.

Similar to the result from May, neutral and stable mean wind speed profiles are dominantin July as 92.2% of all usable mean wind speed profiles in the month were consideredneutral or stable.


4.3 October 2014

Data from the period of October 4th to October 26th was examined in this section. Datafrom October 1st to 3rd was missing and the Lidar was moved to another location afterOctober 27th. The wind speed distribution in October is demonstrated in Fig. 4.13. Thedata used in this plot was the 10 min average wind speed at 60m height obtained from theanemometers on the 80m mast. The average wind speed at 60m height during this periodin October was 8.6 m/s.

Figure 4.13: A histogram demonstrating the wind speed distribution in October. A 10min average wind speed measurements at 60m height from the 80m mast was used. Theabscissa is the wind velocity in m/s and the number of times when the wind occurred atcertain wind speed is on the ordinate.


The prevailing wind directions in October are demonstrated on a wind rose diagram in Fig.4.14. The prevailing wind direction was northeast. Unlike the prevailing wind directionsin May and July minor wind was occurring from the southwest and southeast sector.

Figure 4.14: A wind rose diagram showing the prevailing wind directions in October. The10 min average wind direction measurements from the 80m mast, conducted at 68.24mheight were used in this diagram. The color-bar represents the wind speed range in m/s.Wind coming from the northeast sector is the prevalent one in October.


In the same way as was done in May and July, all 10 min wind speed profiles occurring atneutral or near neutral state were analyzed and respective z0 data was obtained, shown inFig. 4.15. The surface roughness length parameter was estimated by taking the averagevalue of the data points shown in Fig. 4.15. The total number of z0 data points were 53

and the average value was 0.041m with the standard deviation of 0.026m. The prevailingwind directions of the z0 data in Fig.4.15 are demonstrated in Fig. 4.16 showing that theprevailing wind is northeast at neutral and near neutral state. If the average z0 value andthe prevailing wind direction during neutral state for October is examined and comparedto the results from May and July. It can be seen that the estimated z0 value is little higherin October than in the other months. Also, the prevailing wind during neutral state inOctober came from the northeast sector while the dominant neutral wind in May and Julycame from the southwest sector. Although the difference in the estimated z0 value is notgreat between the months, the result indicate that the surface type of the terrain northeastof the measurement site is different than the terrain southwest of the site. Similarly as


was done in May and July, the average value of z0 was treated as a constant in Octoberbased on the same assumption as before despite the fact that snow could occur in the area,resulting in a lower z0 value.

Figure 4.15: A scatter plot of the surface roughness length parameter obtained from the10 min average wind profiles occurring at neutral state in October. The average valueof z0 is demonstrated as red solid line on the graph. The abscissa is the number of datapoints and the ordinate is the surface roughness value in meters.

Figure 4.16: A wind rose diagram demonstrating the prevailing wind directions of the 10min average wind speed profiles which were used to estimate the surface roughness datain October. The color-bar in inset represents the wind speed range in m/s. Wind comingfrom the northeast is dominant at neutral and near neutral state in October.



The results of the non dimensional wind shear and non temperature gradient can be seenin Fig. 4.17 and Fig. 4.18 respectively. The universal functions of φm and φh are alsoplotted as a red line for the stable range and green line for the unstable one. The unstablevalues of φm on Fig. 4.17 followed the universal function and showed a minor scatteraround it. The values of the stable φm scattered more than the unstable φm data and hadcorrelation of R2 = 0.956. The dashed blue line on Fig. 4.17 represents the fitted lineof the stable data. The slope of the fitted line was 4.5 which is little lower than the slopeof the universal function which is 4.8. The point of intersection of the fitted line was atφm(0) = 1.1 which is 0.1 higher value than for the intersection point value of the stableuniversal function.

Figure 4.17: A graph showing the non dimensional wind shear, φm, in October as afunction of the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shownin red and green, represents the proposed φm models for both stable and unstable staterespectively for comparison.


The stable data of φh in Fig. 4.18 had the correlation R2 = 0.911. The dashed blue linerepresents the fitted line of the stable φh data. The fitted line had the slope of 6.4 but theslope of the respective universal function is 7.8. The fitted line intersection point was atφh(0) = 0.9 which is a 0.1 lower than the intersection point of the universal function.As Fig. 4.18 demonstrates was a lack of unstable φh data. Therefor, it is rather difficultto say about and estimate the behavior of the data with respect to the unstable universalfunction.

Figure 4.18: A graph showing the non dimensional wind shear, φh, in October as a func-tion of the dimensionless height, ξ(z/L), where z = 55m. The solid lines, shown in redand green, represents the proposed φh models for both stable and unstable state respec-tively for comparison.


4.3.3 Summary of results from October

A summary of the results from the data in October can be seen in Table 4.4. The totalnumber of wind profiles which were usable (R2 > 0.9) were 1148 which is 35% of allwind profiles occurring in selected time period in October. The total number of windprofiles classified as neutral were 603 (52.5%), 535 (46.6%) where on the stable rangeand only 10 (0.9%) were on the unstable range. The results also reveal that the stabilityhas a great influence on the friction velocity of each wind profile where the average valueof u∗ increases from 0.06 m/s at very stable state to 0.98 m/s at unstable state. No windprofiles which fulfilled the quality criteria were classified as very unstable during thisperiod.



Stable (s) 133 0.27 116


Neutral (n) 3.4 · 108 0.61 603


Unstable (u) −156 0.98 2

Very unstable (vu) − − 0

Total: 1148

% of data 35

Table 4.4: The computed and estimated average values for the wind profiles in each sta-bility class. The total number of wind profiles which fulfilled the R2 > 0.9 criteria andits respective rate of the total number of wind profiles occurring in October.

This results from October indicate similar atmospheric condition in the surface layer re-gion as occurred in May and July. 99.1% of the usable mean wind profiles in October wereeither considered to be neutral or stable indicating surface layer which is characterized bywind shear.


4.4 Wind speed measurements

The horizontal mean wind speed measurements, during May, July and October, from theLidar at 41m, 60m, 70m and 82m height were examined and compared to the cup windspeed measurements conducted at the same height on the 80m mast. Furthermore, themeasurements of the horizontal mean wind speed were examined at 78m height, were theultrasonic anemometers were located on the 80m mast, and at 69m height, were the heatedcup (Vaisala) and the normal cup (Thies) anemometer were located. A best fit line (green)of the data along with a reference line (red) having the slope 1 and intersection point at0 were also plotted to each graph to see the correlation between respective measurementsdevices.


Measurements from May

Fig. 4.19 demonstrates the agreement of the horizontal mean wind speed measurementsat 41m height from the Lidar and the cup anemometer on the 80m mast in May. Theslope of the best fit line of the data was 1.084 and the intersection point of the line wasat −0.107. By comparing the slope of the fitted line to the red line the Lidar has thetendency to measure higher wind speed than the cup anemometer with increasing windspeed. The correlation factor of the data was 0.972. By examine Fig. 4.19 it can be seenthat the scatter of the data points around the fitted line increases with increasing windspeed.

Figure 4.19: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in May. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. On the abscissa are the cup wind speed measurements and the Lidar wind speedmeasurements are on the ordinate.


The agreement of the horizontal mean wind speed measurements from the cup anemome-ter and the Lidar at 60m and 70m height can be seen in Fig. 4.20 and 4.21 respectively.The slope of the best fit line of the data at 60m was 1.08, the intersection point of the bestfit line was at −0.121 and the correlation factor was 0.975. The slope of the best fit lineof the data at 70m was 1.082, the intersection point of the best fit line was at −0.119 andthe correlation factor was 0.979. Similar pattern can be seen in Fig. 4.20 and 4.21 as wasdemonstrated in Fig. 4.19 where the agreement between the measurement devices bothat 60m and 70m decreases with increasing wind speed and more scatter of the data pointsaround the fitted line occurs also.

Figure 4.20: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 60m height in May. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. On the abscissa are the cup wind speed measurements and the Lidar wind speedmeasurements are on the ordinate.


Figure 4.21: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 70m height in May. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. The correlation coefficientR2 is also given. On the abscissa are the cup wind speedmeasurements and the Lidar wind speed measurements are on the ordinate.


Fig. 4.22 demonstrates the agreement of the horizontal mean wind speed measurementsat 82m height. The slope of the best fit line was 1.033 and the intersection point of thebest fit line was at 0.075. The slope of the fitted line indicates that Lidar was measuringhigher wind speed than the cup meter with increasing wind speed. The correlation factorof the data was 0.998 and by examine Fig. 4.22 very few data points lies outside the fittedline region, different from the results demonstrated in Fig. 4.19, 4.20 and 4.21.

Figure 4.22: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 82m height in May. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. The correlation coefficientR2 is also given. On the abscissa are the cup wind speedmeasurements and the Lidar wind speed measurements are on the ordinate.


Fig. 4.23 demonstrates the agreement of the horizontal mean wind speed measurementsat 78m height from the ultrasonic anemometers on the 80m mast in May. The slope ofthe best fit line of the data was 0.96 and the intersection point of the line was at 0.331.The correlation factor of the data was 0.986. By examine these values in the context ofFig. 4.23, interesting things can be seen and is worth taking closer look at. Accordingto the slope of the fitted line does the Gill anemometer have the tendency to measurehigher wind speed than the Thies anemometer with increasing wind speed. However, bytaking closer look at Fig. 4.23 seems the majority of the data points lie above the fittedline in the wind speed range from 6 − 8m/s which could explain the rather high value ofthe intersection point. According to these results seems to be going on some discrepancybetween the meters. As can be seen from Fig. 4.23 outliers exists and lie below the fittedline of the data and the distance from these data points to the fitted line increases withincreasing wind speed.

Figure 4.23: Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in May. A best fit line of the datais shown as green and the line y = x, shown in red, for comparison. The correlationcoefficient R2 is also given. On the abscissa are the wind speed measurements from theGill anemometer and the wind speed measurements from the Thies anemometer are onthe ordinate.


Fig. 4.24 demonstrates the agreement of the horizontal mean wind speed measurementsat 69m height from the Thies cup anemometer and the Vaisala (heated) cup anemometeron the 80m mast in May. The slope of the best fit line of the data was 0.993 and theintersection point of the line was at −0.102. The correlation factor of the data was 0.988.According to the slope of the fitted line and by examine Fig. 4.24 the Thies meter ismeasuring higher wind speeds then the Vaisala meter. Furthermore, it can be seen in Fig.4.24 that some data points lie above the fitted line of the data and the distance from thesedata points to the fitted line increases with increasing wind speed.

Figure 4.24: Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast in May. A best fitline of the data is shown as green and the line y = x, shown in red, for comparison. Thecorrelation coefficient R2 is also given. On the abscissa are the wind speed measurementsfrom the Thies cup anemometer and the wind speed measurements from the Vaisala cupanemometer are on the ordinate.


Measurements from July

Fig. 4.25 demonstrates the agreement of the horizontal mean wind speed measurementsat 41m height from the Lidar and the cup anemometer on the 80m mast in July. The slopeof the best fit line of the data was 1.042, the intersection point of the line was at 0.086

and the correlation factor of the data was 0.988. The slope of the fitted line indicatesthat the Lidar has the tendency to measure higher wind speed than the cup anemometer.By examine the scatter plot in Fig. 4.25, similar behavior seems to be occurring as wasdemonstrated in Fig. 4.19, where several data points are located either above or belovethe line.

Figure 4.25: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in July. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. On the abscissa are the cup wind speed measurements and the Lidar wind speedmeasurements are on the ordinate.


The agreement of the horizontal mean wind speed measurements from the cup anemome-ter and the Lidar at 60m and 70m height can be seen in Fig. 4.26 and 4.27 respectively.The slope of the best fit line of the data at 60m was 1.033, the intersection point of thebest fit line was at 0.106 and the correlation factor was 0.990. The slope of the best fitline of the data at 70m was 1.035, the intersection point of the best fit line was at 0.107

and the correlation factor was 0.992. Similar pattern can be seen in Fig. 4.26 and 4.27as was demonstrated in Fig. 4.25 where several data points lie either above or belovecorresponding fitted line. Furthermore, according to the slopes of the best fit lines of thedata at 60m and 70m height, the Lidar is measuring higher wind speed than respectivecup anemometer meter.

Figure 4.26: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 60m height in July. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. On the abscissa are the cup wind speed measurements and the Lidar wind speedmeasurements are on the ordinate.


Figure 4.27: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 70m height in July. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. The correlation coefficientR2 is also given. On the abscissa are the cup wind speedmeasurements and the Lidar wind speed measurements are on the ordinate.


The agreement of the horizontal mean wind speed measurements at 82m height is demon-strated in Fig. 4.28. The slope of the best fit line of the data was 1.033, the intersectionpoint of the line was 0.082 and the correlation factor of the data was 0.997. The slopeof the fitted line indicates that Lidar was measuring little higher wind speed than the cupmeter with increasing wind speed. The correlation factor of the data was 0.998 and byexamine Fig. 4.22 very few data points lies outside the fitted line region, different fromthe results demonstrated in Fig. 4.25, 4.26 and 4.27.

Figure 4.28: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 82m height in July. A best fit line of the data is shown as greenand the line y = x, shown in red, for comparison. The correlation coefficient R2 is alsogiven. The correlation coefficientR2 is also given. On the abscissa are the cup wind speedmeasurements and the Lidar wind speed measurements are on the ordinate.


Fig. 4.29 demonstrates the agreement of the horizontal mean wind speed measurementsat 78m height from the ultrasonic anemometers on the 80m mast in July. The slope of thebest fit line of the data was 0.996 and the intersection point of the line was at 0.085. Thecorrelation factor of the data was 0.997. According to the slope and intersection point ofthe fitted line does the meters agree well over the measured wind speed range. However,as can be seen in Fig. 4.29 some data points lie below the fitted line of the data and thedistance from these data points to the fitted line increases with increasing wind speed.This behavior occurred also in the measurements results from these meters in May andwas demonstrated in Fig. 4.23.

Figure 4.29: Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in July. A best fit line of the datais shown as green and the line y = x, shown in red, for comparison. The correlationcoefficient R2 is also given. On the abscissa are the wind speed measurements from theGill anemometer and the wind speed measurements from the Thies anemometer are onthe ordinate.


The agreement of the horizontal mean wind speed measurements at 69m height fromthe Thies cup anemometer and the Vaisala (heated) cup anemometer on the 80m mastin July are demonstrated Fig. 4.30. The slope of the best fit line of the data was 0.953,the intersection point of the line was at 0.061 and the correlation factor of the data was0.996. According to the slope of the fitted line and by examine Fig. 4.30 does the Thiescup meter measure higher wind speed than the Vaisala meter with increasing wind speed.This behavior was also occurring in May and was demonstrated in Fig. 4.24. As can beseen in Fig. 4.30 does some data points lie above the fitted line of the data resulting in aminor decreasing effect on the correlation factor.

Figure 4.30: Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast in July. A best fitline of the data is shown as green and the line y = x, shown in red, for comparison. Thecorrelation coefficient R2 is also given. On the abscissa are the wind speed measurementsfrom the Thies cup anemometer and the wind speed measurements from the Vaisala cupanemometer is on the ordinate.


Measurements from October

Fig. 4.31 demonstrates the agreement of the horizontal mean wind speed measurementsat 41m height from the Lidar and cup anemometer on the 80m mast in October. The slopeof the best fit line of the data was 0.991, the intersection point of the line was at 0.146

and the correlation factor of the measurements was 0.992. According to the slope and theintersection point of the fitted line does the wind speed measurement from Lidar and cupmeter agree well. However, as can be seen from Fig. 4.31 a sudden increase in scatterstarts to occur in the cup wind speed range around 8−10m/s but fades out with increasingwind speed. The reason for this behavior is not fully known but one explanation couldbe due to over speeding of the cup anemometer caused by the nonlinear response to thefluctuation in the wind (turbulence). This behavior was not noticed in the respective windspeed measurements from May and July.

Figure 4.31: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 41m height in October. A best fit line of the data is shown asgreen and the line y = x, shown in red, for comparison. The correlation coefficient R2

is also given. On the abscissa are the cup wind speed measurements and the Lidar windspeed measurements are on the ordinate.


Fig. 4.32 demonstrates the agreement of the horizontal mean wind speed measurementsat 60m height. The slope of the best fit line of the data was 0.984 and the intersectionpoint of the line was at 0.168. The value og the slope and the intersection point indicatesthat the wind speed measurements from the Lidar and the cup meter agree well. Thecorrelation factor of the data was the same as for the data at 41m height or 0.992. Similarbehavior can be seen in Fig. 4.32 as demonstrated in Fig. 4.31 where minor increasein scatter starts to occur in the cup wind speed range from 8 − 10m/s but fades out withincreasing wind speed.

Figure 4.32: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 60m height in October. A best fit line of the data is shown asgreen and the line y = x, shown in red, for comparison. The correlation coefficient R2

is also given. On the abscissa are the cup wind speed measurements and the Lidar windspeed measurements are on the ordinate.


Fig. 4.33 and 4.34 demonstrates the agreement of the horizontal mean wind speed mea-surements at 70m and 82m height respectively in October. The slope of the best fit line ofthe data at 70m height was 1.008, the intersection point of the best fit line was at 0.136 andthe correlation factor was 0.997. The slope of the best fit line of the data at 82m heightwas 1.011 and the intersection point of the best fit line was at 0.172. The correlation fac-tor of the data high or 0.998. The wind speed measurements from the Lidar and the cupanemometers at 70m and 82m agree well according to the slope and intersection point oftheir fitted line. No sign of sudden increase in scatter in Fig. 4.33 and 4.34 can be seen,unlike the wind speed measurements demonstrated in Fig. 4.31 and 4.32.

Figure 4.33: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 70m height in October. A best fit line of the data is shown asgreen and the line y = x, shown in red, for comparison. The correlation coefficient R2 isalso given. The correlation coefficient R2 is also given. On the abscissa are the cup windspeed measurements and the Lidar wind speed measurements are on the ordinate.


Figure 4.34: Comparison of the horizontal mean wind speed measurements from Lidarand cup anemometer at 82m height in October. A best fit line of the data is shown asgreen and the line y = x, shown in red, for comparison. The correlation coefficient R2 isalso given. The correlation coefficient R2 is also given. On the abscissa are the cup windspeed measurements and the Lidar wind speed measurements are on the ordinate.


Fig. 4.35 demonstrates the agreement of the horizontal mean wind speed measurementsat 78m height from the ultrasonic anemometers on the 80m mast in October. The slopeof the best fit line of the data was 1.022, the intersection point of the line was at 0.128

and the correlation factor of the data was 0.998. These values indicate that the ultrasonicmeasurement devices do agree well however, according to the slope of the fitted line theThies ultrasonic meter was measuring little higher wind speed than the Gill meter.

Figure 4.35: Comparison of the horizontal mean wind speed measurements from theultrasonic anemometers at 78m height on the 80m mast in October. A best fit line of thedata is shown as green and the line y = x, shown in red, for comparison. The correlationcoefficient R2 is also given. On the abscissa are the wind speed measurements from theGill anemometer and the wind speed measurements from the Thies anemometer are onthe ordinate.


Fig. 4.36 demonstrates the agreement of the horizontal mean wind speed measurementsat 69m height from the Thies cup anemometer and the Vaisala cup (heated) anemometeron the 80m mast in October. The slope of the best fit line of the data was 0.947, theintersection point of the line was at 0.104 and the correlation factor of the data was highor 0.998. By examine Fig. 4.36 and according to the slope of the fitted line the Thies cupmeter was measuring higher wind speed than the Vaisala meter.

Figure 4.36: Comparison of the horizontal mean wind speed measurements from theThies ans Vaisala cup anemometers at 69m height on the 80m mast in October. A best fitline of the data is shown as green and the line y = x, shown in red, for comparison. Thecorrelation coefficient R2 is also given. On the abscissa is the wind speed measurementsfrom the Thies cup anemometer and the wind speed measurements from the Vaisala cupanemometer are on the ordinate.


4.5 Summary of the results

The estimated values of the non dimensional wind shear followed corresponding universalfunction quite well in all three months. However, the values of the temperature gradientwere always lower than corresponding universal function over the stable range in all threemonths. The reason for this underestimation could be because there were only six temper-ature measurements, conducted at 2m, 10m, 40m and 80m height, available to evaluatethe non dimensional temperature gradient.

Table 4.5 demonstrates the total rate of wind speed profiles categorized in each stabilityclass in the months examined. The rate of wind profiles categorized as neutral was similarfor both July and October or about 52% and 53% respectively while being around 40% inMay. The total rate of wind profiles categorized as stable was lowest in July, 40%, andhighest in May or 48%. Wind profiles categorized as unstable in October were only 1%

but the ratio was 8% and 12% in July and May respectively.

Stable Neutral Unstable uave [m/s]

May 48% 40% 12% 6.6

July 40% 52% 8% 6.5

October 46% 53% 1% 8.6

Table 4.5: The summary of results from May, July and October where the total rate ofwind speed profiles categorized in each stability class in each month is demonstrated.The average wind speed in each month, measured at 60m height on the 80m mast is alsodemonstrated.

Stability variation of the wind speed profiles takes place more often in May and July thanin October. A pattern can be seen if these stability variations between the months arecompared with the prevailing wind directions occurring in respective month. During Mayand July the prevailing wind direction were northeast and southwest but the prevailingwind direction was northeast in October. During the summer months the sun is shiningmore per day than during the winter months. The solar radiation causes more heat flux tooccur in the surface layer resulting in unstable conditions to occur more often during thesummer than in the winter. The average wind speed was highest in October or 8.6m/s but6.6m/s and 6.5m/s in May and July. The estimated surface roughness value was higher inOctober than in May and July which gives certain indications that the landscape could berougher in the northeast area.

The horizontal mean wind speed measurements from the Lidar and the cup anemometerson the 82m mast were examined for all three months at common measurement heights.


The Lidar had the tendency to measure higher wind speed than corresponding cup meterin May and July. The correlation factor of the measurements from the Lidar and the cupmeters at 41m, 60m and 70m height was lower in May and July than in October.

Similar comparison was done for the horizontal wind speed measurements from the sonicanemometers at 78m height and the Thies cup meter and the Vaisala heated cup meterat 69m height on the 80m mast. The correlation factor of the wind speed measurementsfrom the sonic meters was lowest in May. The wind speed measurements from the sonicmeters agreed well in July but the Thies sonic meter was measuring higher wind speedthan the Gill meter in October. The comparison of the wind speed measurements from theThies cup meter and the heated Vaisala cup meter showed that the Thies cup meter wasmeasuring higher wind speed than the Vaisala cup meter in all the three months.

A clear inconsistency between the measurements devices can be seen, which may becaused by rapid changes (fluctuation) in the wind speed over the 10 min average periodof the data.

75

Chapter 5

Discussion and limitations

The atmospheric stability varies between months as the results indicate. This variationand furthermore the value of the stability parameter influences the behavior and shapeof the logarithmic wind speed profile at a given time as Fig. 5.1 illustrates. Fig. 5.1demonstrates a wind speed profiles at different stability state. The black vertical linedemonstrates the position of the wind turbine rotor.

Figure 5.1: A graph demonstrating the shape and behavior of the wind speed profile atdifferent stability state. The wind speed in all wind profiles is 15m/s at 55m height. Thewind speed inm/s is on the abscissa and height above ground in meters is on the ordinate.


The size of the rotor is 44m and the hub height is 55m, which is the same height as forthe wind turbines located at Hafið. All the wind profiles have the same wind speed at hubheight or 15m/s. The stability parameter of the stable and unstable wind profile is 100mand −100m respectively and the surface roughness height is defined as 0.02m. It can beseen from Fig. 5.1 that the wind speed varies over the wind turbine rotor with increasingheight. The variation is greatest for the stable wind speed profile, much less for the neutralprofile and the least one for the unstable one. From the wind power point of view it isinteresting to examine and compare the shape of the wind speed profile to the estimatedpower from a wind turbine. To do such estimation Eq. 5.1 can be used, defined as

P (z) =1

2· ρ ·Cp,betz ·A(z) ·U(z)3 (W ) (5.1)

where ρ = 1.228 kg/m3, Cp,betz = 16/27, A is the area of the rotor and U is the windspeed and both A and U are function of z (height above ground). Fig 5.2 demonstrates thepower distribution over the wind turbine rotor at each stability state. More importantly itshows the power contribution, dP, from each dA (small area) on the rotor as function ofthe z placement on the rotor.

Figure 5.2: A graph demonstrating the power distribution over wind turbine rotor havingthe diameter D = 44m at each stability state. The power contribution from each dA(small area) on the rotor is on the abscissa and height above ground in meters is on theordinate.


The total power which a wind turbine delivers at each stability state can then be calculatedby summarize all the dP over the rotor diameter. Based on this estimations and the definedwind speed profiles demonstrated in Fig. 5.1, a wind turbine located in the stable windspeed profile delivers 1883kW, 1857kW in the unstable one and 1856kW in the neutralwind speed profile. The power output from the wind turbine is 1.4% higher when locatedin the stable wind speed profile than in the unstable and the neutral one.

This analysis was done by assuming the same wind speed at hub height for all windprofiles resulting in the difference in power output only being minor for the differentstability classes. However, the average wind speed of wind profiles occurring at unstablestate is higher than at stable conditions as can be seen in Fig. 5.3. Fig. 5.3 shows theaverage wind speed of the wind profiles which were considered usable in October at eachstability state. Similar pattern in the mean wind speed between stable, neutral and unstablewind speed profiles occurred in May and July.

Figure 5.3: The average wind speed of the usable wind speed profiles occurring in Octoberat each stability state. The wind speed is on the abscissa and the height above ground ison the ordinate.


The analysis above only demonstrates the power in the mean wind but the turbulencein the wind is also important factor on the expected power output. Fig. 5.4 shows theaverage TI in May for stable and unstable wind speed profiles. By examining Fig. 5.4 itcan be seen that the average TI is higher at stable state than unstable in the region fromsurface up to 130m height above the ground. High TI can have increasing affect on thepower output at a given time, but is however unfavorable from the wind load perspective.Similar pattern in the TI occurred in July and October.

Figure 5.4: The graph shows the average TI in May for stable and unstable wind speedprofiles. The value of the TI is on the abscissa and the height above ground is on theordinate.

Fig. 5.4 demonstrates a clear measurement difference where the measurements from thedevices on the 80m mast indicate lower TI values than the Lidar. The circles filled withred and blue in Fig. 5.4 demonstrates the average TI from the the anemometers from the80m mast. The other circles in Fig. 5.4 demonstrates the average TI values from theLidar.


As stated in the results chapter, the rate of the wind profiles considered usable in eachmonth were only 8.0% and 8.71% in May and July respectively, but higher in Octoberor 34.7%. By comparing these ratios with the rate of wind speed data received from theLidar, shown in Table 5.1, it can be seen that the weighted average ratio is lowest in Mayand July, 75.9% and 76.6% respectively but 97.3% in October.

Height [m]: 41 50 60 70 82 90 100 110 120 130 160 200

May: 72% 75% 77% 80% 83% 84% 83% 81% 79% 76% 66% 53%

July: 72% 75% 78% 81% 83% 83% 83% 81% 79% 76% 65% 51%

Oct: 97% 97% 98% 99% 99% 99% 99% 99% 98% 98% 95% 88%

Table 5.1: The rate of wind speed data received from the Lidar at certain height in respec-tive month.

This lack of available data from the Lidar with increasing height is a known drawback.The quantity of aerosols in the atmosphere vary with height and since the Lidar techniquerelies on aerosols to backscatter the transmitted beam back to the device the aerosolsquantity at given time will influence the data availability at that time.

The ratio of received data from the 80m mast was 99.8% on average in these three months.Each 10 min average wind profile combined from both the Lidar and 80m mast was con-sidered damaged and not usable for further calculations if it had one or more missing datain it. Based on that criteria and by examining the ratios at 200m height in each month inTable 5.1, it can be seen that only half of the data was received from the Lidar in May andJuly respectively. In other words, only 53% and 54% of the data was usable for furtheranalysis.

Although this poor data availability from the Lidar explains the major part of the problem.Other factors seems to be affecting the mean wind speed profile and the shape of it at eachtime and these affects will be discussed further next.


Most often when the average wind speed was low (uave < 3 m/s), the wind speed profilehad the tendency to be irregular as seen in Fig. 5.5. This irregular behavior of the windspeed profile resulted in a poor fit of corresponding wind profile model and low R2 value.At the same time, it is interesting to see the variation of the wind direction. However,from the wind power point of view, these low wind speed profiles are not that importantsince most types of wind turbines don’t generate electricity while the wind speed is lowerthan 3 m/s.

Figure 5.5: The upper graph demonstrates wind speed profile having low average windspeed. The red line on the upper graph represents the best fit line of the wind speed data.The quality of the fit is demonstrated by the R2 value. The lower graph shows the winddirections with respect to height at the same time. The abscissa on the upper graph isthe wind speed and the abscissa on the lower graph is wind direction. The height aboveground is on the ordinate on both graphs.


To be able to use the wind profile data occurring at each time for further analysis theprofile must be semi regular and behave logarithmically with respect to height. Figure5.6 demonstrates one example of a wind speed profile behaving non-logarithmically withrespect to height were the wind direction also varies significantly. As a result of thisirregular behavior it is impossible to fit the data to a corresponding logarithmic windspeed model (red), well enough to fulfill the data quality criteria. The quality of the fit isR2 = −0.694 indicates a very poor model fit.

In these cases, the wind pattern is most likely katabatic wind or fall winds, which oc-curs when cold air (heavy) flows down from higher elevation under the force of gravityresulting in a strong wind near the surface independently of wind pattern at higher el-evation. The rate of wind speed profiles behaving in this manner was not calculatedaccurately.

Figure 5.6: A graph demonstrating a wind speed profile having irregular behavior and atthe same time does the wind directions vary with height. The red line on the upper graphrepresents the best fit line of the wind speed data. The quality of the fit is demonstrated bythe R2 value. The abscissa on the upper graph is the wind speed and the abscissa on thelower graph is wind direction. The height above ground is on the ordinate on both graphs.


Fig 5.7 demonstrates a wind speed profile data and a corresponding best fit line. It canbe seen from the figure that the line fits the data quite well. However, there is a clearwind speed measuring difference between the devices measuring at common measuringheights. This measuring difference between the Lidar and the anemometers on the 80mmast was demonstrated and examined in the results chapter. This difference seems to becausing the quality parameter,R2, to have value lower than 0.9 resulting in that majority ofthe wind profiles not usable for further analysis. The reason for this measuring differenceis not fully known. It is possible that the 10 min average period of the wind speed data isnot sufficiently descriptive and could be better to extend the average period to 20 min orlonger. Also, could the fluctuation of the wind speed be that much so the average of thewind speed is not good enough.

Figure 5.7: A graph demonstrating a wind speed profile which behaves fairly regularly.There is clear difference between wind speed measurements devices at common measure-ment heights. This difference in the measurements results in value lower than 0.9 for thequality parameter. The lower graph shows the wind directions with respect to height atthe same time. The abscissa on the upper graph is the wind speed and the abscissa on thelower graph is wind direction. The height above ground is on the ordinate on both graphs.


For comparison with Fig. 5.7, Fig. 5.8 demonstrates a wind speed profile and corre-sponding fitted line which fulfilled the quality criteria. By examining Fig. 5.8, little orno sign of a measurement difference can be seen and the profile behaves regularly andlogarithmically with increasing height.

Figure 5.8: The upper graph shows a wind speed profile data and a red line representingthe best fit line of the data. The quality of the fit is demonstrated by the R2 value. Thelower graph shows the wind directions with respect to height at the same time. Theabscissa on the upper graph is the wind speed and the abscissa on the lower graph is winddirection. The height above ground is on the ordinate on both graphs.

85

Chapter 6

Conclusions

This study was set out to assess and determine the factors that influence and indicate thestability in the surface layer in an area named Búrfellshraun. The stability in a surfacelayer varies and is either classified as stable, unstable or neutral. The stability in thesurface layer is characterized by the vertical turbulent transport of momentum, heat ateach time. The stability parameter, L, and the surface roughness parameter, z0, affectthe shape of the logarithmic wind speed profile in the surface layer. A MO similaritymodels were applied to the mean wind speed and mean temperature data, obtained froma 80m mast and Lidar. The parameters z0, L, u∗ and T∗ were estimated from the windspeed and temperature data by using the least square fit method. The estimated values ofthe parameters were then used to determine the universal functions of the dimensionlesswind shear and temperature gradient.

According to the results of this study the majority of the mean wind speed profiles whichwere considered usable in each month were either neutral or stable. A clear wind direc-tion pattern occurs in the area according to the results of the wind direction measurements.Wind coming from the north east and south west sector was dominant in May and July.However, the prevailing wind direction in October was north east. Furthermore, the high-est average wind speed at 60m height in these three months occurred in October, 8.6m/s,but the average wind speed was 6.6m/s and 6.5m/s in May and July respectively. Accord-ing to the results, the electric production should be more stable during the winter wherethe wind direction is more consistent and conditions are either stable or neutral. Duringthe summer, variability in conditions and wind directions occurs more often resulting inmore uncertainty.

The wind speed profiles did fit respective models quite well in the months examined.However, the lack of available data from the Lidar, specially May and July, caused that


large rate of wind speed profiles could not be analyzed. A fluctuations in wind, winddirection changes, low average wind speed and katabatic wind are one of the reasons whylarge rate of the wind speed profiles behaved non logarithmically and were not fitting wellenough to respective models. A measuring difference of the mean wind speed betweendevices at common measurement heights also caused a lot of wind speed profiles notfulfilling the R2 criteria. The measurement difference between the Lidar and the cupmeters was clearly greater in May and July, but the measurements agreed much better inOctober. This difference between devices mainly reflects poor average of the data causedby wind speed changes. The TI demonstrates that the devices measure differently thevalues that fluctuate with time.

The importance of knowing the variation of the average horizontal wind speed at certainarea from the wind energy point of view is clear. Furthermore, the importance of knowl-edge about the stability conditions at the same time should be considered as importantsince the behavior and shape of the wind speed profile depends on the vertical transportof momentum and heat in the boundary layer.

87

Bibliography

[1] U. Nations, “World Population Policies Report 2013.” Accessed Februar 9, 2015from http://www.un.org/en/development/desa/population/

publications/pdf/policy/WPP2013/wpp2013.pdfS, 2013.

[2] W. M. Organization, “The State of Greenhouse Gases in the Atmosphere Based onGlobal Observations through 2013,” September 2014.

[3] R. Wiser and M. Bolinger, “2012 wind technologies market report,” August 2013.Accessed Februar 9, 2015.

[4] EWEA, “Wind in power 2013 european statistics,” February 2014. AccessedFebruar 9, 2015.

[5] Orkustofnun, “Raforkuspá 2014-2050.” Accessed Februar 9, 2015, 2014.

[6] N. Nawri, G. N. Petersen, H. Bjornsson, and K. Jonasson, “The wind energy poten-tial of iceland,” tech. rep., 2013.

[7] N. Nawri, G. N. Petersen, H. Bjornsson, A. N. Hahmann, K. Jonasson, C. B.Hasager, and N.-E. Clausen, “The wind energy potential of iceland,” Renewable

Energy, vol. 69, no. 0, pp. 290 – 299, 2014.

[8] Landsvirkjun, “Environmental report 2013-Wind Turbines.” Landsvirkjun. AccessedMay 5. 2015 from http://environmentalreport2013.landsvirkjun.com/Significant-Events-in-2013/Wind-Turbines, May 2014.

[9] Landsvirkjun, “Búrfellslundur: Tilhögun virkjunarkosts r3301.” AccessedApril 5. 2015 from http://www.landsvirkjun.is/Media/burfellslundur-tilhogun-virkjunarkosts.pdf, 2015.

[10] Landsvirkjun, “Umhverfisskýrsla landsvikjunar 2014 - Mat á umhver-

fisáhrifum.” Landsvirkjun, LV-015-051. Accessed May 5. 2015 fromhttp://umhverfisskyrsla2014.landsvirkjun.is/markvert-a-arinu/mat-a-umhverfisahrifum, May 2015.

http://www.un.org/en/development/desa/population/publications/pdf/policy/WPP2013/wpp2013.pdfS

http://www.un.org/en/development/desa/population/publications/pdf/policy/WPP2013/wpp2013.pdfS


[11] Landsvirkjun, “Verðmæti úr vindorku,” July 2014.

[12] J. Manwell, J. McGowan, and A. Rogers, Wind Energy Explained: Theory, Design

and Application. Wiley, 2010.

[13] M. Hansen, Aerodynamics of Wind Turbines. Earthscan, 2nd ed., 2008.

[14] T. Burton, D. Sharpe, N. Jenkins, and E. Bossanyi, Wind Energy Handbook. JohnWiley & Sons, 2001.

[15] J. Kaimal and J. Finnigan, Atmospheric Boundary Layer Flows: Their Structure and

Measurement. Oxford University Press, 1994.

[16] F. M. White, Viscous Fluid Flow. McGraw Hill, 3rd ed., 2006.

[17] S. Pope, Turbulent Flows. Cambridge University Press, 1st ed., 2000.

[18] R. B. Stull, An Introduction to Boundary Layer Meteorology. The Netherlands:Kluwer Academic Publishers, 1988.

[19] J. Rohatgi and G. Barbezier, “Wind turbulence and atmospheric stability - their effecton wind turbine output,” Renewable Energy, vol. 16, pp. 908–911, Jan. 1999.

[20] F. White, Fluid Mechanics. McGraw-Hill, 7th ed., 2011.

[21] J. Wyngaard, Turbulence in the Atmosphere. Cambridge University Press, 2010.

[22] T. Foken, “50 years of the monin–obukhov similarity theory,” Boundary-Layer Me-

teorology, vol. 119, no. 3, pp. 431–447, 2006.

[23] A. Obukhov, “Turbulence in an atmosphere with a non-uniform temperature,”Boundary-Layer Meteorology, vol. 2, no. 1, pp. 7–29, 1971.

[24] C. Yagüe, S. Viana, G. Maqueda, and J. M. Redondo, “Influence of stability on theflux-profile relationships for wind speed, φm, and temperature, φh, for the stableatmospheric boundary layer,” Nonlinear Processes in Geophysics, vol. 13, no. 2,pp. 185–203, 2006.

[25] J. A. Businger, J. C. Wyngaard, Y. Izumi, and E. F. Bradley, “Flux-Profile relation-ships in the atmospheric surface layer,” J. Atmos. Sci., vol. 28, pp. 181–189, 1971.

[26] A. Yaglom, “Comments on wind and temperature flux-profile relationships,”Boundary-Layer Meteorology, vol. 11, no. 1, pp. 89–102, 1977.

[27] U. Högström, “Von Kármán Constant in Atmospheric Boundary Flow: Reevalu-ated,” J. Atmos. Sci., vol. 42, pp. 263–270, 1985.


[28] U. Högström, “Non-dimensional wind and temperature profiles in the atmosphericsurface layer: A re-evaluation,” Boundary-Layer Meteorology, vol. 42, no. 1-2,pp. 55–78, 1988.

[29] D. Wilson, “An alternative function for the wind and temperature gradients in un-stable surface layers,” Boundary-Layer Meteorology, vol. 99, no. 1, pp. 151–158,2001.

[30] Google maps, “Map of Burfell location in iceland.” Accessed May 2, 2015from https://www.google.com/maps/@64.11893,-19.6514,21430m/data=!3m1!1e3,2015.

[31] Rannsóknardeild Landsvirkjun, “Lidar deployment and maintainance: Bur-haf60-búrfellshraun i.” February 2014.

[32] Rannsóknardeild Landsvirkjun, “Lidar deployment and maintainance: Bur-haf60-búrfellshraun ii.” May 2014.

[33] Landsvirkjun, “Búrfellshraun 80 m mast: Mast documentation - instrument and sitelayout.” May 2014.

[34] A. Peña, S.-E. Gryning, J. Mann, and C. B. Hasager, “Length scales of the neutralwind profile over homogeneous terrain.,” Journal of Applied Meteorology & Clima-

tology, vol. 49, no. 4, pp. 792 – 806, 2010.

[35] A. Pena Diaz, Sensing the wind profile. PhD thesis, 2009. Risø-PhD-45(EN).

[36] A. Hannesdottir, A. Peña, S.-E. Gryning, and A. Hansen, “Boundary-layer heightdetection with a ceilometer at a coastal site in western denmark,” Master’s thesis,2013. Master Thesis.

[37] Leosphere, WINDCUBEv2: LIDAR remote sensor - user manual, 6 ed.

[38] C. Johansson, A.-S. Smedman, U. Hogstrom, J. G. Brasseur, and S. Khanna, “Crit-ical test of the validity of monin-obukhov similarity during convective conditions.,”Journal of the Atmospheric Sciences, vol. 58, no. 12, p. 1549, 2001.

[39] M. Almeida, “Wind rose of direction and intensity.” Retrived fromhttp://www.mathworks.com/matlabcentral/fileexchange/17748-wind-rose, Nov2007.

[40] J. Doke, “Distribution of wind speeds at hub height.” Retrived fromhttps://www.mathworks.com/examples/matlab/3412-wind-turbine-data-analysis,Oct 2013.


[41] A. Peña, S.-E. Gryning, and C. Hasager, “Comparing mixing-length models of thediabatic wind profile over homogeneous terrain,” Theoretical and Applied Climatol-

ogy, vol. 100, no. 3-4, pp. 325–335, 2010.

School of Science and EngineeringReykjavík UniversityMenntavegi 1101 Reykjavík, IcelandTel. +354 599 6200Fax +354 599 6201www.reykjavikuniversity.isISSN 1670-8539

wind energy and weather conditions in the icelandic highlands

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