Turbulence Intensity in Complex Environments and Its Influence on Small Wind Turbines

Examensarbete vid Institutionen för geovetenskaper ISSN 1650-6553 Nr 219

Turbulence Intensity in Complex Environments and its Influence on Small Wind Turbines

Nicole Carpman

ABSTRACT The market of wind power as a sustainable energy source is growing, both on large and small scale. Conventional large scale wind turbines normally operate in uniform areas where expected wind speeds and turbulence characteristics are well investigated and the constructional design of the wind turbines is regulated by standard classes for different external conditions. Small scale wind turbines (SWT), on the other hand, are sometimes placed in more complex environments where the turbulence conditions are rougher. A larger amount of turbulence will generate a larger amount of fatigue loadings on the construction, increasing the risk of breakdown. It is therefore of major concern to perform more measurements and further investigate the turbulence characteristics in complex environments and the effect that these will have on small wind turbine construction. Thus, turbulence is measured with sonic anemometers at two sites with complex environments; at an urban site above a rooftop in a medium sized city (Uppsala, Sweden) and above a forest in Norunda (outside Uppsala) at two heights, near the treetops (33 ) defined as complex and further up (97 ) defined as more uniform. The turbulence data is analyzed and the results are compared to the normal turbulence model (NTM) as it is defined for the standard SWT classes by the International Electrotechnical Commission in the International standard 61400‐2: Design requirements for small wind turbines (IEC, 2006). Measurements of 10 minute standard deviations of longitudinal wind speed () and turbulence intensity () are reported, as well as the distributions of and of 10 minute mean wind speeds () for the different sites and stabilities. The results show that the NTM represents the turbulence at 97 height above the forest only for light wind speeds, smaller than 10 /, but underestimates the turbulence for higher wind speeds. It should also be noted that the data is scattered and contain a number of occasions with extreme values of and . For wind speeds higher than 10 / the number of observations is limited but the majority of the observations are more extreme than the NTM. At the complex sites (near the treetops and the rooftop) the NTM clearly underestimates both the magnitude and rate of change of with increasing wind speed, although the observed wind speeds close to these rough surfaces are low so the conclusions are limited.

Average at 97 height is 19 %, compared to 41 % close above forest and 43 % above rooftop. Mean values of above forest are generally 10 % lower during stable conditions (⁄ 0.05 while above rooftop, the wind material is sparse and 95 % of the observations had stable stratification so no dependence on stability can be seen. From these results it can be concluded that the turbulence characteristics close above treetops is similar to those above rooftop, but that the NTM, as it is defined for the standard SWT classes, is not valid in these complex and urban terrains and need to be modified to correctly estimate the turbulence intensities, and consequently also the loadings, affecting small wind turbines located at these kinds of sites.

Key words: turbulence intensity, complex, uniform, urban, small wind turbines, IEC standard classes, normal turbulence model

III

REFERAT Marknaden för vindkraft som en förnyelsebar energikälla växer snabbt, både stor‐ och småskaligt. Traditionella storskaliga vindkraftverk placeras normalt på homogena platser där vindklimatet och turbulensens karaktär är ganska väl kartlagda och konstruktionsstandarden regleras av standardklasser utifrån olika externa förhållanden. Små vindkraftverk (SWT) å andra sidan placeras ofta i mer komplex eller urban miljö där turbulensen är mer intensiv. En större andel turbulens genererar större utmattningslaster på konstruktionen vilket ökar risken att vindturbinen går sönder. Det är därför av stor vikt att utföra fler mätningar och ytterligare undersöka turbulensen i komplexa miljöer och vilken effekt den kommer ha på de små vindkraftverkens konstruktion. Med anledning av detta så har turbulensdata analyserats från mätningar med sonicanemometrar. Dels på en urban plats, ovanför ett hustak i en medelstor stad (Uppsala, Sverige). Dels vanför en skog i Norunda (utanför Uppsala) på två höjder, nära trädtopparna (33 m) som anses komplex och högre upp (97 m) som anes mer homogen. Resultaten är jämförda med den normala turbulensmodellen (NTM) så som den definieras för standard SWT klasserna av International Electrotechnical Commission i International standard 61400‐2: Design requirements for small wind turbines (IEC, 2006). Mätningar av 10 minuters standardavvikelse av den longitudinella vindhastigheten () och turbulensintensiteten () redovisas, liksom fördelningen av och 10 minuters medelvinden () för olika stabilitet för de olika mätplatserna. Resultaten visar att NTM är representativ på 97 höjd endast för låga vindhastigheter, under 10 m/s, medan modellen underskattar turbulensen för högre vindhastigheter. Det bör också noteras att spridningen är stor i data och att extrema värden av

och uppmätts vid flertalet tillfällen. För vindhastigheter över 10 m/s så är antalet mätvärden begränsade, men majoriteten av mätvärdena är högre än NTM. På de komplexa mätplatserna (nära trädtopparna och ovan hustaket) så underskattar NTM avsevärt både storleken av och dess förändring med ökad vindhastighet på de komplexa platserna (nära trädtopparna och ovan hustaket). Dock är de observerade vindhastigheterna låga såhär nära de skrovliga ytorna så slutsatserna är begränsade. På 97 höjd är medelvärdet av 19 %, jämfört med 41 % nära trädtopparna och 43 % ovan hustak. De är generellt 10 % lägre under stabila förhållanden (⁄ 0.05 över skog, medan ovan hustak där vindmaterialet är begränsat och 95 % av observationerna var stabilt skiktade så ses inte något stabilitetsberoende. Från dessa resultat kan slutsatserna dras att turbulensens karaktär nära trädtoppar liknar den ovan hustak, men att NTM, så som den definieras för standard SWT klasserna, inte gäller vid dessa komplexa och urbana platser och behöver modifieras för att korrekt uppskatta turbulensintensiteterna och därmed också de laster som påverkar små vindkraftverk placerade på den här typen av platser.

Nyckelord: turbulensintensitet, komplex, homogen, urban, små vindkraftverk, IEC standard klasser, normal turbulensmodell

TABLE OF CONTENTS

ABSTRACT ...... III REFERAT ...... IV 1 INTRODUCTION...... 1

1.1 BACKGROUND ...... 1 1.2 OBJECTIVES ...... 2 2 THEORY ...... 3

2.1 METEOROLOGY ...... 3 2.1.1 The Planetary Boundary Layer ...... 3 2.1.2 Turbulence Characteristics ...... 5 2.1.3 Dynamic and Thermal Instability ...... 6 2.1.4 TKE – Turbulent Kinetic Energy ...... 7 2.1.5 Turbulence Characteristics in Uniform and Complex Environments ...... 7 2.2 STATISTICAL TOOLS AND PARAMETERS ...... 11 2.2.1 Vertical Fluxes and Stress ...... 13 2.2.2 Stability Parameter ...... 13 2.3 SMALL WIND TURBINES ...... 14 2.3.1 Wind Turbines in General ...... 14 2.3.2 Construction ...... 14 2.3.3 Aerodynamics ...... 16 2.3.4 Wind energy ...... 17 2.4 IEC SMALL WIND TURBINE CLASSES ...... 17 2.4.1 Normal Wind Conditions ...... 18 2.4.2 Extreme Wind Conditions ...... 19 3 MEASUREMENTS ...... 20

3.1 SITES ...... 20 3.1.1 Norunda ...... 20 3.1.2 Earth Sciences Center, Uppsala University ...... 20 3.2 INSTRUMENTATION ...... 21 3.3 DATA ...... 21 4 METHOD ...... 22

4.1 CALCULATIONS AND MODIFICATIONS OF DATA ...... 22 4.1.1 Wind Direction ...... 22 4.1.2 Rotation of Coordinate Axes ...... 22 4.1.3 Mean Values ...... 22 4.1.4 Standard Deviations and Covariance Terms ...... 23 4.1.5 Detection of Errors in the Data ...... 23 4.1.6 Turbulence Intensity ...... 24 4.1.7 Stability Parameter ...... 24 5 RESULTS ...... 25

5.1 STANDARD DEVIATION OF WIND SPEED ...... 25 5.2 OBSERVATIONS OF TURBULENCE INTENSITY ...... 28 5.4 DISTRIBUTION OF TURBULENCE INTENSITY ...... 30

5.5 DISTRIBUTION OF WIND SPEEDS ...... 30 5.7 AVERAGE TURBULENCE INTENSITY ...... 32 5.8 STABILITY DISTRIBUTION ...... 32 5.10 CUMULATIVE DISTRIBUTION OF TURBULENCE INTENSITY AND STABILITY ...... 34 6 DISCUSSION AND CONCLUSIONS ...... 37

6.1 VALIDATION OF THE NTM ...... 37 6.1.1 Uniform Site ...... 37 6.1.2 Complex Sites ...... 37 6.2 STABILITY DEPENDENCE ...... 38 6.3 CONCLUSIONS ...... 39 7 ACKNOWLEDGEMENTS ...... 40 8 REFERENCES ...... 41 APPENDIX A SYMBOLS AND DESCRIPTIONS ...... I APPENDIX B ...... III APPENDIX C PERCENTILE VALUES FROM A NORMAL DISTRIBUTION ...... IV

1 INTRODUCTION

The demand for a more sustainable energy supply is constantly growing. Hydro power, wave power and wind power are only a few examples of natural sources of energy. This growing use of new energy sources leads to a demand for new technical solutions. The market for wind turbines is growing fast. In Sweden, almost 2 % of the total electricity production nowadays comes from wind power. Most wind turbines are of large scale, designed to yield as much energy as possible in a cost‐efficient way. These large wind turbines are preferably placed at sites where the wind speed capacity is high. Normally, this means sites with a uniform environment with a flat terrain and a long undisturbed upwind fetch. At these kinds of sites, the knowledge about the characteristics of the lower part of the atmosphere, i.e. the boundary layer, are extensive when it comes to parameters like annual and seasonal average wind speed and turbulence characteristics. But as the demand for environmentally friendly energy production grows, there is also an increased interest in small scale wind turbines located in more complex environment and at lower height with high turbulence levels but lower wind speeds. This includes areas where mountains affect the wind pattern, or above forests as well as in urban areas close to buildings. Small wind turbines (SWT) have a rotor sweep area smaller than 200 , which yields a rotor diameter of less than 16 . They are designed to be placed e.g. near farms or on the roofs of buildings in a city. But in these urban, or in other ways complex, environments the boundary layer flow acts rather differently compared to the flow in uniform environments. For example, wind speeds are normally lower in irregular terrain, but in return the turbulence rate is much larger due to the larger production of turbulent kinetic energy near the rougher surface and in the presence of varying obstacles. This changes the constructional design requirements of the wind turbines. For example, the wind turbines have to withstand a larger amount of fatigue loadings. If the SWTs are not designed for these new, rougher conditions they might break down and falling pieces may act as projectiles and cause severe accidents and material damage due to their nearness to buildings and people.

1.1 BACKGROUND The International Electrotechnical Commission (IEC) is a worldwide organization that works with questions concerning standardization in the electrical and electronic fields (IEC, 2006). The organization discusses and formulates new standards for a variety of products, one example being small wind turbines. It is a collaboration between all interested national electrotechnical committees where every committee can have a representative in the discussions preceding the formulation and publishing of new standards. The IEC publications are thus in agreement with the overall international opinion and are meant to be used as recommendations for international use. The IEC International standard number 61400‐2: Design requirements for small wind turbines (2006), contains four standard SWT classes defined by a few basic parameters. These classes are formulated to describe the characteristic external conditions of many different sites. The basic parameters are defined in terms of wind speed and turbulence parameters and are used in the wind and turbulence models described in the standard, such as the Normal 1

Turbulence Model (NTM). This description of external conditions was originally developed for a uniform environment, typical for larger wind turbines, and may therefore need to be modified in the case of small wind turbines located in complex environment. Since 2009, Maintenance Team 2 of IEC’s Technical Committee 88 is working to revise this standard, and in liaison with IEA Wind1 Task 27, to introduce consumer labeling for small wind turbines. The intention of the labeling initiative is to define a globally standardized product label for small wind turbines and minimum requirements for a testing process which are said to benefit the entire wind sector (IEA Wind, 2011). One problem when investigating the currently used standards is that urban terrain observations are hard to find since it is such a new field of interest. Meteorological investigations of the planetary boundary layer often try to avoid urban sites and the wind power researchers usually find the economic benefits from placing wind turbines in urban terrain too small to invest in such measurements. It is therefore of interest to investigate whether the characteristics of wind measurements from other complex environments, for example above forests, where much more data is available, can be used as a frame of reference also for urban environments.

1.2 OBJECTIVES To support the above described investigations concerning SWTs in IEC and IEA, this report aims to analyze high frequency turbulence measurements from sites in complex environments and compare the results to the Normal Turbulence Model (NTM), as it is defined for the standard SWT classes by the IEC (2006). Therefore, measurements performed on top of the roof of a building in an urban environment are compared to existing data from above a forest at two heights. The environment close to the treetops is considered to be complex and very rough, while further up, the environment can be considered to be more uniform. The results are then compared to the NTM to see whether this model provide a correct representation of the turbulence characteristics of complex environments. The model is also compared to the more uniform environment. Because of the lack of measurements in urban terrain, it is of interest to investigate whether turbulence characteristics at other complex sites can be used in a model, with some kind of modification, to describe turbulence characteristics at urban sites. The results of the study are planned to be used as an informative annex of the coming IEC International Standard 61400‐2 Ed. 3. As a background, boundary layer flow characteristics are presented as well as a description of flow over plant or tree canopies and flow over cubical obstacles. Also, the constructional and aerodynamic properties of wind turbines are presented. Methods used to analyze high frequency turbulence data are described. A table of symbol descriptions and abbreviations is presented in Appendix A.

1 The IEA Wind agreement is also known as the Implementing Agreement for Co‐Operation in The Research, Developement and Deployment of Wind Energy Systems functions within a framework created by the International Energy Agency, IEA (IEA Wind, 2011). IEA is an organization which works to ensure reliable, affordable and clean energy for its 28 member countries and beyond (IEA, 2011). 2

2 THEORY

2.1 METEOROLOGY To be able to describe the external conditions that a wind turbine is exposed to, knowledge about how the wind field behaves in different environments and during varying meteorological conditions is important. The initiator to all atmospheric motions is the irregular surface heating from the absorption of solar radiation. The absorbed energy is transferred into the atmosphere mainly by thermal or turbulent exchange processes near the surface. These give rise to air temperature differences which in turn yield pressure differences. Therefore, due to the constant strive for balance in the atmosphere, air movements are initiated. These winds transport kinetic energy which can be extracted by the wind turbines. Unfortunately, the winds are not constant, they are often gusty and hit the wind turbine from different directions. This behavior is due to turbulence and is a large contributor to fatigue loads on the turbines. Air that flows over any surface is decelerated near the surface due to viscous and frictional forces. A vertical wind velocity gradient is thus created which generates turbulence. A turbulent air flow consists of totally stochastic air motions, characterized by rapid variations in wind speed and direction. These motions consist of whirls of varying sizes and they effectively transport both energy and matter throughout the boundary layer. The planetary boundary layer (PBL) is always turbulent (Högström & Smedman, 1989) even though the degree of turbulence varies with time and is affected by the structure of the surface elements as well as the vertical temperature and humidity distribution, i.e. the thermal stability. Above the PBL is the Ekman‐layer where the wind field turns and adapts to the free atmosphere above where the turbulence can be ignored and the wind is governed by the pressure gradients. The following sections will give a description of the characteristics of the lower parts of the atmosphere, mainly the planetary boundary layer. A comparison of turbulence characteristics is made between uniform and complex environments and statistical tools needed to analyze turbulence data are presented.

2.1.1 THE PLANETARY BOUNDARY LAYER The atmosphere contains a number of layers that behave different when it comes to wind conditions and turbulence characteristics. They interact in different ways with the surface and have varying depth depending on meteorological conditions that are changing with time. The planetary boundary layer (PBL) is the part of the atmosphere closest to the surface, except for a very thin laminar layer, in which the flow field is strongly influenced by the interaction with the surface. A significant part of the energy exchange between the atmosphere and the surface of the earth occurs in this layer through the turbulent transports of momentum, heat and humidity, which are due to shear forces and thermal instabilities (discussed in Chapter 2.1.3). Shear forces arise in the presence of wind gradients. The wind velocity profile in the PBL has a logarithmic form due the friction at the, more or less, rough underlying surface. All surfaces have some degree of aerodynamic roughness exerting a frictional force on the air above it. In the first few millimeters, closest to the surface, this interaction is called molecular viscosity. Every fluid has a viscosity, , which is a measure of the internal friction between the

fluid elements. Viscosity acts to resist the tendency to flow and forces the fluid particles to move with the same speed as the surface that they are in contact with (Holton, 2004). This force is called shearing stress, , and is defined as viscous force per unit area. It is ultimately responsible for the deceleration near the surface so that the mean wind speed reaches zero near the ground, which gives rise to a large wind velocity gradient. The roughness of a surface depends on the sizes and distribution of the so called roughness elements. The roughness elements can have the size of gravel to the size of trees or houses and be distributed far away from each other or very dense. The disturbed air volume in between the roughness elements is called a canopy layer. It may refer to both crop fields, forests and urban areas. In this layer, the vertical wind profile takes an exponential form but it is completely dependent on the geometry of the roughness elements and cannot be generally described. The top of the roughness elements are at height . If there is a mix of different roughness elements this height is the mean value . The height where the roughness elements appear as a uniform rough surface, instead of a number of individual roughness elements, is denoted

. Above , a relation for the increase of mean wind speed as a function of height can be obtained by integrating the wind speed gradient (Equation 2.1). This general relation, called the logarithmic wind law, is valid above the roughness elements during neutral stratification (Equation 2.2). 2.1

ln 2.2 where is the frictional velocity, 0.4 is the von Kármán constant, is the displacement height and is the roughness length. The frictional velocity is a characteristic velocity that relates shear between layers of flow (defined in Chapter 2.2.1). The roughness length is a measure of the surface roughness. It is defined as the height at which the extrapolated logarithmic wind law reaches zero, typically in the order of 10 % of (Högström & Smedman, 1989). This so called zeroplane is displaced vertically at the presence of roughness elements, so that the flow behaves as if there were a physical boundary at height (as described by Rotach (1991)) so that, theoretically,

0. Above a canopy, the zeroplane will rather denote an inflection point, which will cause turbulence production, as will be described in Chapter 2.1.5.1. The planetary boundary layer can have a depth of a couple of tens of meters up to a couple of kilometers depending on the stability (described in Chapter 2.1.2). This layer can be divided into a number of sublayers depending on the structure of the surface, i.e. the roughness elements (Figure 1). In an urban environment the layer interacting with the surface is called the urban boundary layer (UBL) (Oke, 1988). It consists of a mixed layer (ML), an inertial sublayer (IS) and a surface layer (SL) as seen in Figure 1. The surface layer, which is the lower part, is divided into a roughness sublayer (RS) and an urban canopy layer (UCL). The urban canopy layer has a vertical extent of 0 and encloses the air in between the roughness elements (Rotach, 1991). The roughness sublayer starts at the top of the UCL and extends to ( ).

Figure 1. Schematic illustration of the different layers of the planetary boundary layer above an urban area. The urban boundary layer (UBL) is divided into a mixed layer (ML), inertial sublayer (IS) and surface layer (SL), which in turn is divided into a roughness sublayer (RS) and an urban canopy layer (UCL). Also illustrated are the vertical wind speed profiles, , and its difference between rural and urban areas (Fernando, 2010).

2.1.2 TURBULENCE CHARACTERISTICS The planetary boundary layer is always characterized with some degree of turbulence. Turbulence is defined as a continuous, three dimensional flow that is non linear and contains whirls of different sizes. A fully developed turbulent flow is completely irregular and random and the turbulent eddies effectively transport both energy and matter (momentum, heat and humidity etc.) over time and length scales of varying sizes (Högström & Smedman, 1989). The whirls are not static, they are constantly breaking down through the cascade process which describes how larger turbulent eddies are scaling down by transferring their kinetic energy to smaller and smaller eddies until viscosity dissipate the eddies into heat. The dissipation is proportional to the radius of the eddy by 1r⁄ , which means that the smaller turbulent eddies are breaking down turbulent energy much more effectively than larger ones (Högström & Smedman, 1989). A flow converts from being laminar to being turbulent when the ratio between inertial forces and viscous forces reaches a certain value (Högström & Smedman, 1989). This ratio is called Reynolds number given by Equation 2.3. Turbulence occurs at high enough Reynolds numbers, that is, when the inertial forces of the flow are large while the viscous forces are small so that turbulent eddies cannot be prevented from occurring.

2.3

is defined with the air density , scale representative wind speed and length (defined in Chapter 2.2.2), and the viscosity of the fluid .

2.1.3 DYNAMIC AND THERMAL INSTABILITY Turbulence arises because of dynamic and thermal instabilities. Dynamical instability is primarily due to wind shear. Turbulence through wind shear arises in the boundary between air volumes with different velocity, so that ⁄ 0. It can be either between the surface of the earth and the air flow above it, as described earlier, between flows at different heights with different wind speeds, or in the wakes behind obstacles where the wind speed is locally reduced. All obstacles cause deflection of the flow of the air. An obstacle can have different density, it can be solid, like a building, or less dense, like a forest but it will always affect the flow. In the wake of an obstacle, the wind speed is locally reduced, compared to the mean flow, generating a wind gradient. This wind gradient creates shear stress that will produce turbulence. Especially in complex environments this is an important source to turbulence. The flow around buildings has fairly complex characteristics and the amount of turbulence in an urban environment is higher than in more uniform sites like a crop field. A more detailed description of flow characteristics for uniform and urban sites will be found in Chapter 2.1.5. Thermal instability is a result of the solar heating of the surface or by cooling of the surface due to emitted long‐wave radiation. When a surface is heated the air above it is also heated. When the air parcel is warmer than the air surrounding it, the air parcel starts to lift due to buoyancy forces. These thermal bubbles, also referred to as convection, create turbulence as they rise through the atmosphere (Stull, 1988). The stability, i.e. the stratification, of the atmosphere depends on the potential temperature gradient ⁄ , where denotes the potential temperature. If the atmosphere is stably stratified, the temperature increases with height so that the temperature gradient is positive (⁄ 0). Since the density of cold air is higher than that of warmer air, the buoyancy forces are negative and therefore oppose vertical motion so that no spontaneous convection occurs. This is normal conditions during nighttime or during winter when the solar radiation is small so that there is a net loss of energy at the surface which then becomes cooler than the air above it. Warm air that is advected over a cold surface will also generate a stable stratification. In stable stratification all thermally induced turbulence is dampened. Only shear production of turbulence is present. For an unstably stratified atmosphere the temperature gradient is negative (⁄ 0) so that the air closest to the ground is warmer, and thus have a lower density than the surrounding air, resulting in positive buoyancy forces that will make the air parcel start lifting. In an unstable atmosphere, even a small vertical displacement of an air parcel would make the air keep on rising until the air surrounding it is warmer. This convection might be due to irregular heating of the surface by the solar radiation. If some obstacle forces the air to be lifted it is called forced convection. Both results in thermal production of turbulent eddies in addition to the shear production. The turbulent eddies in an unstable boundary layer can reach a significant vertical extent. In a neutral, or near neutral, atmosphere the air is well mixed so that the vertical potential temperature gradient is close to zero, hence the buoyancy force will be close to zero. This can be due to high wind speeds and a cloudy sky that prevent any significant temperature gradient to occur. High wind speeds also mean high wind shear at the surface resulting in a significant production of turbulence.

2.1.4 TKE – TURBULENT KINETIC ENERGY Since the planetary boundary layer is always turbulent there must be a continuous production of turbulent kinetic energy (TKE) to oppose the cascade process. The budget equation for turbulent kinetic energy describes how TKE is produced, redistributed and destructed. As described by Rotach (1991) and Högström & Smedman (1989), it states

i) Shear production ‐ the rate of production of TKE by the mean wind shear ii) Buoyancy production ‐ the rate of production of TKE in unstable stratification due to convective processes (or vice versa destruction of TKE in stable stratification due to buoyancy when kinetic energy is transferred into potential energy) iii) Pressure transport ‐ the redistribution of TKE performed by pressure perturbations (turbulent energy from convection is transferred from the vertical component to the horizontal components) iv) Turbulent transport ‐ the vertical turbulent transport of TKE v) Dissipation ‐ how TKE is dissipated into heat through the viscosity in the end of the cascade process.

Depending on the structure of the wind and temperature profiles, i.e. the stratification of the atmosphere, the importance of shear induced versus convective TKE production varies significantly. This dependence is given by the flux Richardson number which is the ratio of the buoyancy term (ii) divided by the shear generated turbulence term (i) in the TKE budget equation (AMS Glossary, 2000). A comparison of the two processes shows that shear induced turbulence is most important in a neutral stratification while in stable stratification the shear induced turbulence is dampened by buoyancy forces so that the turbulence starts to decay (Rotach, 1991). In an unstable atmosphere the convection is strong and the shear induced turbulence becomes more and more unimportant. When a flow becomes turbulent the wind shear ⁄ is automatically reduced.

2.1.5 TURBULENCE CHARACTERISTICS IN UNIFORM AND COMPLEX ENVIRONMENTS Meteorological studies of air flow and turbulence characteristics in the planetary boundary layer are commonly performed at sites with flat and homogenous environments. A lot of information is therefore available from the numerous measurements carried out at uniform tree or plant canopies. But the flow and turbulence characteristics at uniform sites deviate essentially from those at complex and urban sites, as will be described in the following sections.

2.1.5.1 Uniform Tree or Plant Canopies Flow and turbulence characteristics in and above uniform tree or plant canopies are widely investigated for meteorological purposes. The studies have been performed in varying kinds of plant canopies such as crop fields, e.g. wheat, corn or other cereals, as well as forests of various height and density complemented with numerous wind tunnel experiments. A plant canopy has a more or less complex structure of roughness elements such as stems, branches, leaves, needles and seeds referred to as canopy elements, contributing to the roughness of the surface. In a plant canopy the roughness density may be defined as the total frontal area of canopy elements per unit ground area affecting a air volume (Finnigan, 2000).

Earlier, canopy turbulence was thought of as a superposition of general boundary layer turbulence and energetic small‐scale eddies produced in the wakes of the canopy elements. But this is true only in very sparse canopies where the turbulence is a result of wake effects from individual plants. Now, decades of surveys show that canopy turbulence is dominated by organized structures of large scale eddies. These dominating energy‐containing turbulent structures have horizontal length scales in the order of the canopy height and vertically about /3. They are found to transfer a vast majority of the momentum and other scalars both within the roughness sublayer and above (Finnigan, 2000). It is found that gusts of higher wind speed, that rapidly move downward from the inertial sublayer, are affecting the entire roughness sublayer. In the case of uniformly distributed, non rigid roughness elements, as in crop fields or forests, these downward moving so called sweeps are able to penetrate the canopy. This results in a displacement of the zeroplane so that it lay well within the canopy, commonly at 3/4 of the mean canopy height (Rotach, 1991). In and above plant and tree canopies, the vertical profile of wind speed is shown to increase exponentially within the canopy. At the zeroplane there is an inflection point above which the velocity profile takes the standard boundary layer logarithmic form (as given by Equation 2.2). The inflection point is characteristic for such canopy roughness layers (Finnigan, 2000). Here the shear stress has its maximum, affecting the characteristics of the turbulent flow and the turbulent kinetic energy production. Below the canopy top there is a peak in the wake production implemented by the canopy elements.

Coherent structures Roughness sublayer turbulence is better described from the patterns typically seen in a so called plane mixing layer than in the inertial sublayer, as discussed by Finnigan (2000). A mixing layer is obtained by initially letting two airstreams of different velocity be separated by a splitter plate at 0. At the trailing edge of the plate (0), the two airstreams mix and become turbulent. The velocity field is found to have an inflection point at 0, which is the level of maximum shear between the two initial air streams resulting in a peak in the shear production of TKE at this level. It is also the level where the velocity variances and shear stress reaches its maximum value (discussed in more detail in Chapter 2.2). In this kind of mixing layer the organized structures arise from instabilities supposedly created when high‐wind speed gusts sweep down and increase the shear at the inflection point. The initiated small perturbations evolve into waves that are growing rapidly until they eventually break down into small‐scale turbulence (known as Kelvin‐Helmholtz waves). First, they form complex but organized patterns of transverse rollers connected by twinned regions of intense plane strain. The initial vorticity is amplified and the rollers merge together, forming irregularly spaced energy‐containing rollers in the streamwise direction. After a while, these rollers break down forming fully developed turbulence. This is what is seen in field studies as well.

TKE transfer A turbulent wind field in the roughness sublayer always undergoes a conversion of energy through the cascade process from large to small eddies, as discussed earlier. But in canopy layers there are processes that let the energy take shortcuts through the eddy cascade. Generally, energy of the mean flow (MKE) is transferred into organized structures and viscous dissipation transfer turbulent kinetic energy (TKE) of the high frequency eddies into

heat. Additionally, the turbulent wind field flow is exposed to aerodynamic drag forces absorbing momentum from all eddies of scales larger than the canopy elements, i.e. the scales of seeds, leaves or branches and so on. The aerodynamic drag is the sum of the dominating pressure drag force and the smaller, but still considerable, viscous drag force. Work against pressure drag converts MKE into fine‐scale TKE called wake kinetic energy (WKE). Work against the viscous component converts MKE directly into heat bypassing a large part of the eddy cascade (Finnigan, 2000). The waving of the canopy elements also contribute to the production of turbulent eddies by temporarily storing MKE as potential energy and thereafter release it as TKE (Raupach, 1981). Production, transport and dissipation of turbulent kinetic energy above canopies are given by modifying the TKE budget equation (presented in Chapter 2.1.4). To fully describe the area‐ averaged wind field in and above a canopy it must include a shear production term, a wake production term, a dispersive transport term, the correlation of plant motion to pressure drag and the correlation of plant motion to viscous drag.

Turbulence intensity The intensity of turbulence, , (defined in Chapter 2.2) in and above canopies is studied in various field and wind tunnel experiments. Measurements of standard deviations of horizontal and vertical velocity fluctuations, , (defined in Chapter 2.2) show that these variables are very scattered within canopies (Finnigan, 2000). The scatter is due to effects from the structure of the canopy as well as pressure gradients and turbulence characteristics above the canopy (Seginer et al., 1976). Other factors that play a crucial role to the amount turbulence are changes in mean wind speed, which affect the magnitude of the turbulence intensity, and thermal stability, which has a dampening effect on the turbulent eddies. Generally, velocity standard deviations are found to increase with height within and above the canopy, with maximum increasing rate in the upper part of the foliage. Due to the normalization with mean wind speed, turbulence intensity is found to slowly increase with height within the canopy with a maximum in the upper part of the canopy. If the canopy density is vertically constant, then so is the turbulence intensity. This confirms the dependence on canopy density and that the fluctuations are larger in the presence of wakes behind the canopy elements. Above the canopy top, decreases with height and is always lower than within the canopy. Maximum values range between 50 80 % in forest while for plant canopies like corn and wheat maximum is smaller, about 20 80 % (Baldocchi & Meyers, 1987).

2.1.5.2 Urban and Complex Environments The turbulence characteristics of a flow in an urban canopy layer (UCL) are dependent on the high roughness lengths and the inhomogeneous surface. Also thermal effects are different compared to plant or tree canopies, changing the stability distribution. The stratifications in cities are mostly near neutral due to extensive mixing and do not play a very important role either to enhance or dampen the turbulence (Yersel & Goble, 1986). A built area consists of randomly distributed roughness elements which all together form what is called an urban canopy. A typical medium sized city contains an inhomogeneous mix of houses and residential buildings, gardens and trees, separated by roads and possibly rivers positioned with inconsistent geometry. These elements of varying heights, shapes and densities therefore affect the atmospheric flow in complex ways.

Flow around a single obstacle The randomness of the roughness elements makes it almost impossible to give a general description of how the flow will behave at a specific site within the canopy. Not even strong computers and well developed numeric computational models can fully describe the three‐ dimensional flow characteristics of such complex environments. For less complex installations, on the other hand, large eddy simulation (LES) models are shown to be able to simulate the average flow in quite good alignment with field study results (Shah & Ferziger, 1997). The streamlines of a shear flow around a single three dimensional cubic obstacle is described in detail by Shah & Ferziger (1997). According to their LES simulations, and in agreement with other field studies, the oncoming flow is separated ahead of the obstacle, forming a commonly seen horizontal horse‐shoe shaped vortex (i.e. three‐dimensional pattern of whirls). The separation point is at a distance of one obstacle height ahead of the obstacle and the vortex is advected by the mean flow, converging again at 1.6 obstacle heights behind the obstacle. The vortex is wrapped around the cube and widens downstream of the obstacle simultaneously as its center is lifting from the surface. At the boundaries of the horse‐shoe vortex, regions with significant mixing are found, caused by strong vertical motions; upwash (on the inner boundary) and downwash (on the outer boundary). The breaking up of the horse‐shoe vortex, far behind the obstacle, contributes to the background TKE in the roughness sublayer. On the sides of the obstacle, enclosed by the horse‐shoe vortex, are regions of flow that oppose the mean flow. Here the viscous drag is small and negative. Fluid enters this region from the sides instead of from the direction of the mean flow. This kind of reversed circulation is also found, momentarily, directly behind the obstacle where a vertical vortex is formed, shaped like an arch, with two separated “feet” of strong circulation on the ground. The locations of these ground‐based circulations are dependent on the angle of attack of the mean flow. In the vertical, the arch vortex has its center in alignment with the top surface of the obstacle (as sketched up by Becker, Lienhart & Durst (2002)). The frontal top border of the obstacle is affecting the flow significantly. Here, the streamlines of the mean flow are curved above the top surface and a region of reversed circulation is formed, which separates the mean flow from the obstacle. It should be noted that the flow streamline characteristics described, are only the averaged representation of this kind of flow. Although coherent structures of these types are found in the flow pattern, they are not periodic nor have the same sizes or strengths so that instantaneous pictures are highly intermittent (Shah & Ferziger, 1997).

Complex terrain The LES simulations, mentioned above, show an example on how complex air flows across single obstacles can be. Expanding this to cases with numerous obstacles of varying character, like an urban area, the flow patterns are highly complex and vary significantly depending on the direction of the oncoming flow, as discussed by for example (Heath, Walsche, & Watson, 2007). At any site, within a complex area, the surface area that influences a measurement, called the source area, varies significantly with mean flow direction and measuring height. This variability also makes it difficult to define a general zeroplane displacement height or a roughness length for a certain measuring point.

The mean roughness length of a city can vary between 0.5 to 4.5 although it is somewhat misleading to give a single value of in such an inhomogeneous area (Yersel & Goble, 1986).

Turbulence intensity Turbulence intensity is found to decrease with height above an urban area as a consequence of the increase of mean wind speed with height while the standard deviation of wind speed is found to be nearly constant with height above rough surfaces (for example by Mulhearn & Finnigan (1978)). A minimum in wind speed is found at the top of the roughness elements which, by definition, result in a maximum in turbulence intensity. Turbulence intensity is also observed to increase with increasing roughness length, due to the large mechanical production of TKE. Also, horizontal velocity variances are found in a larger span in complex environments. They are both considerably larger in complex environments resulting in larger turbulence intensity (Rotach, 1991)

2.2 STATISTICAL TOOLS AND PARAMETERS Turbulence can be detected in a time series of high frequency measurements as rapid deviations from a larger scale mean value in the signal (an example of this can be seen in Chapter 4.1.2). These fluctuations can be seen in parameters like temperature and both horizontal and vertical wind speeds. To be able to describe such irregularly behaving phenomena some statistical analyzing tools are needed. Standard procedure when analyzing turbulence data is to transform the horizontal wind vector in the geographical coordinate system , into a rotated coordinate system that aligns with the mean wind direction during every averaging period. The mean wind direction is given by tan as shown in Figure 2. The new components are given by

cos 2.4

Now the new rotated components and will describe the longitudinal and lateral wind velocities ,. In a wind turbine system the longitudinal component is directed along the hub and the lateral component is perpendicular to the hub. From here on and will refer to these rotated variables. A first step to analyze measured turbulent variables is to use Reynolds averaging where the variables are separated into a slowly varying mean part and a rapidly varying turbulent part , so that the total field variable is describes as

2.5

From this definition follows that 0. The arithmetic mean value is calculated using Equation 2.6 where is number of elements in each averaging period. 1 2.6 1

From the turbulent part of the flow one can form variance and covariance terms describing turbulent fluxes and stress (see Chapter 2.2.1). The variance describes the dispersion of the measurements around a mean value, which also can be expressed as the standard deviation from the mean, defined as the square root of the variance (Equation 2.7). This quantity can therefore be used as a measure of the intensity of turbulence (Stull, 1988).

1 2.7

The covariance is calculated according to Equation 2.8 and can be interpreted as a measure of how much two variables vary together.

1 1 2.8

Turbulence intensity, , is often defined as the standard deviation of longitudinal wind speed,

, normalized with the mean wind speed, (Equation 2.9).

2.9

Figure 2. Principal of an axes rotation (From Sahlée, 2009)

2.2.1 VERTICAL FLUXES AND STRESS As mentioned earlier, turbulent eddies transport quantities like momentum and heat through the atmosphere. This transport is called flux and is physically described with covariance terms. Heat flux can be described as the rate that air of different temperature is transported vertically. Similarly, momentum flux can be described as the rate that air of different speed is transported vertically (Stull, 1988).

where is the longitudinal wind speed deviation, is the vertical wind speed deviation and is the air temperature deviation. Turbulent momentum flux has the same effect as a shearing stress. Stress can be described as a force that, when applied to a body, will cause deformation (Stull, 1988). In the turbulent boundary layer two types of stresses are of interest, the turbulent shearing stress and the viscous shear stress. The turbulent shearing stress is that given by the turbulent momentum flux and can be described as . The turbulent momentum flux is also used to define the friction velocity since it describes the frictional force between the surface and the air. 2.10

2.2.2 STABILITY PARAMETER The stratification of the boundary layer can be determined with the parameter (Monin Obukhovs length) which can be read as the height where the turbulent forcing from thermal and shear processes are in balance. is constant with height but vary with stability in the surface layer and can therefore be used as a stability parameter (Högström & Smedman, 1989) is defined as

2.11

where is the friction velocity, is the mean air temperature in Kelvin, 9.82 ⁄ the gravitational acceleration and 0.4 von Karmáns constant and is the kinematic heat flux. Normalizing the measuring height above ground, , with gives the dimensionless stability parameter ⁄ where

0 0 0

In reality, neutral conditions are extremely rare. Instead, near neutral conditions are defined with a small span so that ⁄ 0 for near neutral conditions.

2.3 SMALL WIND TURBINES

2.3.1 WIND TURBINES IN GENERAL Conventional large scale wind turbines are normally placed in wind farms at sites with high wind energy potential, either on land or offshore, but often some distance away from where the energy supply is needed. The harvested energy is therefore often transported long distances which is quite inefficient. Small wind turbines on the other hand, can be placed directly near a farm, alongside of manufactory buildings or on rooftops and therefore yield energy where it is needed. But some of these locations provide different external conditions and therefore demand new design requirements of the turbines. The principle of a wind turbine is to convert the energy in the wind into electrical energy by retarding the wind using rotors that are driving a generator which in turn generates electrical energy. The most common large scale wind turbine construction is the three bladed horizontal axis wind turbine with a rotor diameter of about 100 and a hub height in the same scale. This constructional principle is also found for small wind turbines. Small wind turbines have a rotor sweep area of less than 200 (IEC, 2006) which corresponds to a rotor diameter of maximum 16 . The hub height for these small wind turbines often spans between 10 – 40 depending on where they will be mounted. Wind energy production is constantly expanding with the installation of new and more efficient wind turbines. During the year 2009, wind energy accounted for 2.49 TWh in Sweden which amount to 1.9 % of the total electricity production (Energimyndigheten, 2010). The total number of wind turbines was 1359 by the end of 2009. Of these are 1288 95 % land‐ based while 71 wind turbines are located offshore2. In Sweden, the largest land‐based wind park consists of 48 wind turbines. According to an estimation done within IEA Wind Task 27, small wind turbines in Sweden 2009 produced about 2 GWh

2.3.2 CONSTRUCTION A small wind turbine that is built to operate in urban environment has some requirements. It has to be technically reliable during long turn operation in turbulent conditions, the noise emissions have to be minimized so that it does not disturb the neighborhood and vibrations has to be as small as possible to minimize the structure‐borne sound and the strain on the construction. Additionally, the esthetic appearance has to be taken into consideration (van Bussel & Mertens, 2005). Wind turbines can be designed in various ways which will affect their performance, aerodynamics and efficiency. One way to categorize them is according to the orientation of the axis of rotation.

 Horizontal axis wind turbine (HAWT)  Vertical axis wind turbine (VAWT)

Horizontal axis wind turbines (HAWTs) consist of a tower with a nacelle on top which is the housing of mechanical and electrical components. On the nacelle, propeller type rotor blades are attached with a hub in the center of rotation. The basic components contained in the

2 New publications show that the number of wind turbines in Sweden now exceeds 1500 and the wind energy production during 2010 will be more than 3 TWh (Energimyndigheten, 2010), but the potential is still much larger and Sweden should be able to reach 30 TWh wind power by the year 2020. 14

nacelle are a rotor shaft and bearings, a generator and often, but not always, a gear system and a rotor brake mechanism. A yaw system used to turn the axis of rotation into the mean wind connects the nacelle to the tower. Power cables running through the tower transports the electricity which may pass through power electronics and/or a transformer before entering the power distribution grid. HAWTs have a high efficiency and demand a small amount of material. They are normally located at homogenous sites with high wind speeds and operate with a tip speed that is several times faster than the prevailing wind speed. The HAWT is designed to operate with the axis of rotation turned into the mean wind direction, otherwise it loses much of its efficiency. This design is therefore not very convenient in complex environments with gusty winds and rapid wind direction changes. Vertical axis wind turbines (VAWTs) consist of curved or straight rotor blades which rotate around a central column that is mounted to the ground. The rotor diameter is measured as the horizontal distance between the blades. All mechanical and electrical components are placed on the ground, which makes maintenance more convenient. No tower is needed, which has economic benefits but with the disadvantage that it is therefore operating closer to the ground where wind speeds are lower and the shear in the vertical wind profile is larger. The VAWT have a lower efficiency compared to the HAWT in smooth wind conditions (van Bussel & Mertens, 2005). On the other hand, it is insensitive to wind direction because of its symmetry and is therefore preferable in complex environments where turbulence is high and wind direction changes are rapid. The drawbacks of the VAWT include operation with lower tip speed so that the loading on the rotor blades is larger generating a higher torque that put strain on the construction. There is also a high cyclic aerodynamic loading on the blades due to the 360 degree rotation with respect to the wind direction (Scheurich, 2009). Still, VAWTs are found to be more convenient in complex terrain. A control system controlling the rotor brake mechanism can be built into the wind turbines. It is coupled to a wind speed measuring instrument (anemometer) and controls for which wind speeds the turbine will be operating. When the wind speed is high enough to overcome the internal friction in the drive train, the brake is loosened and the blades start rotating. This so‐called cut‐in wind speed is normally about 2 – 4 / for small wind turbines. The generator is dimensioned for a certain maximum wind speed, which is the wind speed when maximum energy is produced. Above this wind speed, the wind turbine will still operate but the power production will be constant. At really high wind speeds the brake system kicks in and the turbine is turned off to prevent it from breaking down. This cut‐out wind speed is approximately 25 /. The blades of the wind turbines are preferably made of a light but strong material with a low rotational inertia and thus a quick acceleration so that the tip speed ratio3 can be maintained nearly constant, even in gusty conditions. The larger the blades, the more important it is to keep the blade weight under control. All wind turbines are a source of noise emissions of different character and intensity and at different frequencies that is spread in the nearby area. The rotation of the blades through the air gives rise to a sweeping sound and in some constructions the cogwheels in the gearbox emits a humming noise that is amplified through the tower of the wind turbine. The noise level decreases with distance due to geometrical spreading, weather effects and dampening effects

3 ratio between tip speed and wind speed 15

by vegetation or buildings as well as the atmosphere itself. The effect of the latter on sound propagation is dependent on atmospheric stability and wind direction. But the noises can also be minimized by installing damping systems that produce counter vibrations. One problem is that modern wind turbines change their rotational speed depending on the wind speed, producing noise at varying frequencies. Older versions of the damping systems only produce certain counter frequencies but modifications of these damping systems are under development. The new versions detect the varying frequencies of the sound and produces negative, dampening vibrations at those frequencies (Fraunhofer‐Gesellschaft, 2008).

2.3.3 AERODYNAMICS The rotor blades of wind turbines are typically airfoil shaped, using the same airfoil design as in airplane wings or helicopter rotors. Airfoils are streamline‐shaped with a thicker leading edge that gets thinner towards the sharp trailing edge. The curvature of the airfoil can either be symmetric or asymmetric. The airfoil design will create an aerodynamic force that can be divided into two components.

1) A drag force in the direction of the flow 2) A lift force perpendicular to the flow

Wind turbines can either be drag driven or lift driven. Drag driven rotors are pushed around by the wind. The drag force opposes the motion of an object through a fluid and can be seen as the friction exerted by the fluid. The drag force is perpendicular to the area facing the wind so that a larger frontal area will generate a larger drag force. A larger angle of attack will also generate a larger drag force. Since the rotor blades are moving in the same direction as the wind they are bound to rotate with maximum tip speed given by the prevailing wind speed. Drag driven rotors also demand a larger amount of material. They therefore become less economic and less efficient compared to the lift driven rotors (Mertens, 2002). Lift driven rotors consist of air‐foiled shaped blades. When the rotor is exposed to the wind the air flow will be divided into two air streams at the leading edge, one that is flowing above the upper surface and one that is flowing beneath the lower surface. Both streams will be deflected, the upper stream tube will be compressed while the lower stream tube area will be increased. Flow speed will increase above the airfoil, due to the law of conservation of mass, and therefore decrease underneath the airfoil. Thus a pressure difference will arise between the two stream tubes according to Bernoulli's principle, which states that a faster flow speed will generate a lower pressure and a slower wind speed will generate a higher pressure. The pressure difference results in an aerodynamic lift force, perpendicular to the direction of the flow, which will make the rotor blade turn in the direction of rotation. Lift driven rotors operate at tip speeds higher than the wind speed and are therefore much more efficient than drag driven rotors. If the blades are not helically twisted they will suffer from oscillations in the aerodynamic loading which results in vibrations and material fatigue (Scheurich, 2009). One of the most appropriate design choices for application on rooftops is the lift driven VAWT, for example the Darrieus turbine. Even though this kind of wind turbine has a lower efficiency in undisturbed air flows with low turbulence it has the advantage of running smoothly in turbulent flows with rapid wind direction changes (van Bussel & Mertens, 2005).

2.3.4 WIND ENERGY Wind is a continually renewable energy source driven by the temperature and pressure differences in the atmosphere due to solar heating of the earth. Air in motion contains kinetic energy that is converted into electrical energy by the wind turbine. The energy given by the wind is a function of the third power of wind speed as seen in Equation 2.12 (Boeker & van Grondelle, 1999), thus wind turbines are best placed in areas with a high wind speed climate. The total amount of energy given by the wind, which passes a unit area per second, , is given by Equation 2.12. 1 cos 2.12 2 where is the air density, normally about 1.2 ⁄ 10 % (Holton, 2004) and is the wind speed perpendicular to the given area. The last term is a modification that is required if the wind is not perpendicular to the area of consideration. The angle denotes the incline of the wind. The total energy content in the wind at a specific site is not easily determined. Knowledge about for example the annual or monthly mean wind speed is not enough. The frequency of occurrence of the different wind speeds need to be taken into account. This frequency distribution is widely shown to coincide with the Weibull probability distribution. This relationship is investigated for a wide range of sites showing a higher frequency of low and modest winds and a lower frequency of the more extreme high wind speeds.

2.4 IEC SMALL WIND TURBINE CLASSES When designing a wind turbine, careful consideration needs to be taken on safety and quality in order to reach operational reliability and durability. For that task, the IEC standards provide valuable guidance to the wind turbine designer of how these requirements are fulfilled. One critical requirement for small wind turbines is to be able to withstand a variety of external wind conditions, including turbulence, which will add both transient and fatigue loading on the construction. In the IEC International standard 61400‐2 (from 2006), four different standard SWT classes (I‐IV) are defined to describe the external conditions of various types of sites. The standard SWT classes include information about reference wind speed, annual average wind speed and turbulence intensity, as given by Table 1. These classes are in many ways similar to the classes defined for large wind turbines in IEC 61400‐1 (IEC, 2005). Note that for special conditions, such as urban environments, it is possible for the wind turbine designer to define a class S with relevant parameters and models for that environment. External conditions primary refers to wind conditions, which can be divided into normal or extreme wind conditions, and will be presented below. Apart from these basic parameters, several other important parameters need to be specified, for example environmental conditions like temperature, lightning, icing and electrical load conditions like voltage and frequency deviations (not discussed).

Table 1. Basic parameters for the standard SWT classes I‐IV. The class S is to be described by the manufacturer (from IEC, 2006).

SWT Class I II III IV S Basic parameters (m/s) 50 42.5 37.5 30 Values

(m/s) 10 8.5 7.5 6 specified

(‐) 0.18 0.18 0.18 0.18 by the a (‐) 2 2 2 2 designer

Definitions: Reference wind speed averaged over 10 min. Maximum extreme wind speed with a recurrence period of 50 years that the SWT is designed to

withstand /.

Annual average wind speed at hub height /. Characteristic value of hub‐height turbulence intensity (ratio of the wind speed standard deviation to the mean wind speed) at a 10 min average wind speed of 15 /. a Slope parameter for turbulence standard deviation model.

2.4.1 NORMAL WIND CONDITIONS Normal wind conditions are those that will occur frequently during normal operation of a SWT. In the standard classes, the wind is assumed to be Rayleigh distributed, which is identical to a Weibull distribution with shape parameter 2.0. The wind speed distribution at the intended site is important for the calculation of specific loadings since it determines the frequency of occurrence of certain load conditions. The cumulative probability distribution is given by Equation 2.13, which describes the probability that the wind speed at the site is lower than a certain wind speed (given by ).

V 1 2.13 where is the mean wind speed at hub height averaged over 10 min and is the annual mean wind speed at the site. Vertically, the variation of wind speed with height z is given by the Normal Wind Profile (NWP) for the standard classes according to Equation 2.14.

. 2.14

Additionally, turbulence and turbulence intensity is described using a Normal Turbulence Model (NTM) that include the effects of varying wind speed and varying direction. Turbulence is defined as “stochastic variations in wind velocity” in three dimensions; longitudinally, laterally and vertically, from 10 minute mean values. NTM states that the expected standard deviation of longitudinal wind, , should be given by Equation 2.15.

15 ∆ 2.15 1 18

where is the assumed turbulence intensity at a mean wind speed of 15 / and is a slope parameter. As seen in Table 1, these parameters have a constant value of 18 % and 2 for all standard classes. The term ∆ (Equation 2.16) is a modification which let the model correspond to different percentile values.

∆ 21 2.16 where is determined from the normal probability distribution function which corresponds to 0 for the 50th percentile, and 1.28 for the 90th percentile (see Appendix C).

The expected 10 minute mean turbulence intensity, , is given by normalizing with mean wind speed at hub height (Equation 2.17).

2.17

2.4.2 EXTREME WIND CONDITIONS Extreme wind conditions are taken into account to determine potential extreme loadings on the wind turbines. They are determined as extreme 10 minute mean values with recurrence period of 1 or 50 years and include peaks in wind speeds, due to storms, and rapid changes in wind speed or wind direction, due to strong gusts and turbulence (IEC, 2006). A wind turbine needs to withstand the extreme loadings that follow from all of these extreme situations. The 50 year extreme wind speed is calculated with an extreme wind speed model as

. 1.4 and is assumed to be 75 % of . Additionally, both temporary extreme gusts, i.e. rapid changes in wind speed, and permanent rapid wind speed changes are modeled for as well as extreme direction changes and situations when these occur simultaneously. Further details of the relations used in the models are found in IEC 61400‐2 (IEC, 2006).

3 MEASUREMENTS

Measurements of turbulent wind variations require a high sampling rate to be able to detect the entire spectral range of turbulent cells of varying sizes. To be able to fully analyze turbulence characteristics e.g. fluxes of momentum and heat, stability, wind directions and wind variations, the measurements also require high frequency temperature fluctuations in addition to the wind velocity in three dimensions.

3.1 SITES The analyzed data has been collected at two different sites at two different time periods with a sampling rate of 10 Hz or 20 Hz respectively.

3.1.1 NORUNDA The site is located in Norunda north of Uppsala, Sweden (60°05’14”N 17°29’00”E). The area is covered with forest containing full‐grown trees, mostly spruce mixed with pine and broad‐ leaved trees. The topography is flat with no hills or valleys in a wide range surrounding the site. The measurements have been carried out in a 100 high mast located in the forest with an approximate mean tree top height, , of 28 . The instrumentation was placed at two heights. The lower one was close to the top of the canopy at 33 height, only 5 above the treetops. The other one was further away, at 97 height, 69 above the treetops. Following the discussion in Chapter 2.1.5, the lower setting corresponds to turbulence characteristics very close to a tree canopy acting as a very rough surface made out of branches, leaves and needles in the tree crows. The friction and aerodynamic drag exerted by these canopy elements, as well as the effect of waving canopy elements, can be expected to significantly influence the measurements at lower height. The top setting corresponds to the more common hub height of conventional large scale wind turbines where the influence from the rough surface will be less profound. Here, wind speeds will be higher and thermal stability will have a higher impact on the measurements. Measurements have been performed at the site for a longer period of time. In this study, 1 year of measurements performed with a sampling rate of 10 Hz have been used from the period 1 January – 31 December 2009.

3.1.2 EARTH SCIENCES CENTER, UPPSALA UNIVERSITY The site is located at Earth Sciences Centre, Uppsala University at Villavägen 16 in Uppsala, Sweden (59°50’57”N 17°38’01”E). The site is located in the outskirts of Uppsala city centre, where the surroundings are a mix of urban and rural areas containing buildings of varying sizes, some grass covered areas and also areas with trees. The surrounding buildings are maximum five‐story residential buildings and mostly lower houses with gardens. Close to the measuring point are a small wood in southwest and a botanic garden in northeast. The measurements have been carried out on the roof of a complex building structure divided by courtyards in two or three stories, see Figure 3. The instrument is placed in a 4 high mast mounted on the roof of the highest wing of the three‐story building, approximately 11 high (see Figure 12 and 13 in Appendix B). This building extends to a two‐story building in the south‐southeast direction. The measurements used in this study were carried out during September – November 2010 and the sampling rate was 20 Hz.

Figure 3. Map showing the measuring site at Earth Sciences Centre. The measuring point is marked with a red star. (From Google, 2011).

3.2 INSTRUMENTATION Three dimensional turbulence data was measured with sonic anemometers that use three pairs of transmitters/receivers. The transmitter sends out high frequency pulses of sound and the time it takes to reach the receiver is measured. Since the travelled distance and the speed of sound are known, the three dimensional wind velocity vector can be calculated by combining the sound velocities of different propagation directions. The sonic anemometer is a solid instrument with no moving parts so it performs well in all weather conditions and measure all wind speeds with good accuracy. Possible sources of errors can be icing covering the sensors or technical problems in sending and storing the data. At the site of Earth Sciences Centre a Gill Solent 1012R2 Ultrasonic Anemometer is used. It has a wind direction resolution of 1°, a wind speed resolution of and it can measure in the range (Gill Instruments, 2010). At the site of Norunda a METEK Ultrasonic Anemometer USA is used. It measures in the range (METEK, 2010).

3.3 DATA The data used in this analyze consist of high frequency measurements of wind velocity in three components together with temperature and the time of measurement. The data was saved in files containing hours of measurements. Some of the measurements contained errors or gaps in the time series. The detected gaps were only a couple of hours, or days at most, and do not affect the results of this study. The errors were deleted either automatically or manually. A description of notations and sign conventions used in this study is seen in Table 2. Wind speed is given in meters per second and temperature in degree Celsius .

Table 2. Measured components and their notifications together with sign conventions.

Wind speed running West‐East. From West (+). From East (‐) Wind speed running South‐North. From South (+). From North (‐) Wind speed running vertically. Up (+). Down (‐) Temperature in degrees Celsius.

4 METHOD

4.1 CALCULATIONS AND MODIFICATIONS OF DATA

4.1.1 WIND DIRECTION

Mean wind direction () is calculated from the averaged horizontal wind vector ,. The mathematical vector angle is transformed into the meteorological system (where 0° , 90°, 180° and 270° ) with the formula

270 tan 4.1

The results are then modified to fit in the interval 0° 360° so that

0 360 360 360

4.1.2 ROTATION OF COORDINATE AXES

The measured wind components and (Table 2) are rotated from the geographical coordinate system into a rotated coordinate system that aligns with the mean wind direction according to Equation 2.4, with the use of . The rotated variables are then referred to as and . No rotation is needed of the vertical wind speed or the temperature. For consistency, these are from now on referred to as and .

4.1.3 MEAN VALUES The next step is to calculate the mean values of the temperature and velocity components in every averaging period. Different averaging periods can be chosen depending on which kind of turbulence that is to be analyzed. Turbulent fluxes of heat and momentum require an averaging period of at least 10 minutes (Högström & Smedman, 1989). This is also the period used when calculating mean values in the application of small wind turbines in the IEC standard (IEC, 2006). Therefore, the averaging period was chosen to 10 minutes so that the number of elements in every averaging period is 60 .

Measured mean wind speed, , is presented as a 10 minute arithmetic mean value (Equation 4.2). 1 4.2

Mean values can be calculated either as arithmetic means or as running means. The most appropriate technique used when distinguishing the fluctuating part from the mean part is to use a running mean. This will give a smooth curve of mean values where the risk that false turbulence appears, due to abrupt changes between the arithmetic mean values, is minimized. An example of a time series with high frequency wind measurements where arithmetic and running mean values are shown for comparison is seen in Figure 4. To reduce the time required to perform the calculations, a method with cumulative sums, , was used when creating the running mean values. Arrays of the cumulative sums were computed for the different variables. For each element of the array, the difference was 22

taken between two values with a distance of one averaging period and divided by the number of data points in each period, , as seen in Equation 4.3. Thus, one arithmetic average is found for each element of the array, slightly modified compared to the adjacent mean values. Together they form a smooth curve of centered mean values. In the boundaries of each 12 hour data file half an average period (5 min) of data is lost when mean values are calculated.

4.3 /

Now, the following deviation parameters are calculated (from Equation 2.5).

These prime‐values are then used to compute variance and covariance terms using the method described in Chapter2.2.

4.1.4 STANDARD DEVIATIONS AND COVARIANCE TERMS With the use of the prime‐values, the following variance and covariance terms were calculated using arithmetic mean values according to Equation 2.7 and Equation 2.8 respectively, with 60 .

1 4.4

1 4.5

1 4.6

Equation 4.4 describes the standard variation of longitudinal wind speed. The covariance terms in Equation 4.5 and Equation 4.6 corresponds to the flux of momentum and heat respectively as described in Chapter 2.2.1.

4.1.5 DETECTION OF ERRORS IN THE DATA Errors and gaps in the data were automatically detected and rejected based on different criteria. If any observations were missing due to some technical complication in the measurement or saving process, the last measurements in each 12 hour file were duplicated to get the correct number of elements in each file. This corresponded to an insignificant amount of the observations and did not affect the results. The errors appeared simultaneously in different parameters, e.g. time intervals with constant wind direction corresponded to situations with constant wind speed or 0, and could therefore easily be detected. Additionally, a manual verification was performed where uncharacteristic behavior like peaks, jumps or gaps, were detected. 23

Except for this, elements where (Equation 2.10) became imaginary due to positive momentum flux were deleted in the calculations of the stabilities from (Equation 2.11).

4.1.6 TURBULENCE INTENSITY

Measured 10 minute turbulence intensity, , is given by the standard deviation of longitudinal wind speed normalized with the mean wind speed and is expressed as a percentage (Equation 4.7).

4.7

Due to this definition can become infinitely large when the wind speed reaches zero.

4.1.6.1 Percentile Values of Turbulence Intensity th To be able to compare observed with the NTM, 90 percentile values of the observations has to be created. This is done by assuming a normal distribution and use the conventional definition of percentile values (see Appendix C) which states that 1.28 will th represent 90 % of the observations so that the 90 percentile of is given by 1.28.

4.1.7 STABILITY PARAMETER The stability condition during each 10 minute averaging period is given by

0.05 |0.05| 4.8 0.05 where is calculated according to Equation 2.11, with 273.15 where is the measured 10 minute mean temperature in degree Celsius.

Figure 4. Example of time series of observations of wind speed (grey line) averaged with arithmetic mean (black line) and running mean (red line). The deviations from the mean are used as a measure of the turbulence.

5 RESULTS

The results from this study are presented from the three different measuring points (described in Chapter 3.1) in the following order

a) Above a forest at 97 height, 69 above the treetops. Jan‐Dec 2009. b) Above a forest at 33 height, 5 above the treetops. Jan‐Dec 2009. c) Above a rooftop at approximately 15 height, 4 above the roof. Sep‐Nov 2010.

The amount of analyzed 10 minute mean values differs from the three measuring points due to the difference in measuring period length and due to gaps in the time series caused by problems with the instruments as well as the rejection of elements with detected errors (described in Chapter 3.3). The amount of rejected elements is approximately in a) 2.4 %, in b) 2.6 %, and in c) 7.5 % with the result that the total amount of analyzed data elements was a) 46 643 elements, b) 50 672 elements and c) 8 361 elements. The measurements at the two complex sites (b and c) are performed very close to rough surfaces, so the mean wind speeds barely exceeds 8 / and 4 / respectively during the measuring periods. As a consequence of this, the wind material is a bit sparse in a wind energy perspective. Still, these measurements give information about the wind climate of complex sites and they also give a hint of what turbulence characteristics would have been found if also higher wind speeds had been experienced.

5.1 STANDARD DEVIATION OF WIND SPEED

The standard deviation of wind speed, as given by Equation 4.4, is plotted as a function of 10 minute mean wind speed, , in Figure 5 a‐c. The dots represent each observation. A linear regression is calculated, with the use of the least square method, and drawn as a thin line through all of the data points. The observations are compared to the Normal Turbulence th Model, NTM, given by Equation 2.15 where the thick line represents the 90 percentile of and the dotted line is the 50th percentile. A comparison between the linear regression and the NTM lines can be used as an indicator of the representativeness of the standard model in the sense that the rate of change of with increasing mean wind speed is directly comparable but the magnitudes are a bit misleading due to their different definitions. The NTM has a slope of 0.12 which denotes the ratio between the standard deviation of wind speed to mean wind speed. The 90th percentile of the NTM has an initial magnitude of

1.0 / for 0 / which is a physical impossibility and should only be seen as a theoretic value. This model parameter is justified in the application of wind turbines since wind speeds below the cut‐in wind speed (defined in Chapter 2.3.2) are irrelevant for the loading calculations. A summary of the parameterizations used in the comparison is found in Table 3. Figure 5 a) shows the results from above forest at 97 height during January – December 2009. The measurements show an annual mean wind speed of 5.4 / with a maximum value of 18 / during the period, but observations higher than 13 / are sparse.

There is a large scatter in the observations of at this height and take both small and large values. For wind speeds lower than 10 / there is a large amount of small scale standard deviations. This indicates that the flow at this height, during about 30 % of the time,

is characterized with small scale turbulent eddies corresponding to situations with no, or only light, turbulence ( 10 %). This is what could be expected at such a long distance from the canopy. For wind speeds above an apparent threshold of 10 /, the scatter is reduced due to a significant decrease in small scale standard deviations, and the observations cluster around the NTM. The majority of the observations lie underneath the estimated NTM 90th percentile as expected. 9.4 % lie above it, among these are a number of occasions when take extreme values, much larger than what is expected in the model. The most extreme value of

14.6 / is measured at 11.2 /. The linear regression of the observations in Figure 5 a) has a slope of 0.11. A comparison with the NTM thus shows that, apart from a difference in magnitude in the order of 0.7 /, the standard model correctly describes the observed increase of with increasing wind speed at this altitude above the tree canopy. Figure 5 b) shows the results from closely above forest, at 33 height, during January – December 2009. Here, the aerodynamic forces from the roughness of the canopy have a significant impact on wind speeds, reducing the annual mean wind speed to 2.2 / with a maximum of 10.3 / during the year. Also, the scatter in is relatively small and the maximum standard deviation is 3.7 /, measured during a 10 minute period. This close to the treetops, the standard deviations differ significantly, both in magnitude and rate of change with wind speed, compared to further away from the canopy. The linear regression has a slope of 0.47 and thus clearly deviates from the NTM which is seen to poorly represent the observed turbulence characteristics. For wind speeds higher than 2 /, the magnitude of the standard deviation can be observed to constantly increase with increasing wind speed. This indicates that the flow close to treetops is always characterized with some degree of turbulence for high enough wind speeds. The same pattern is seen above rooftop in Figure 5 c) from the period September – November 2010. The slope of the linear regression is 0.33 and is thus smaller than close above tree tops but much larger than in the NTM.

The scatter in data in Figure 5 c) is relatively small and maximum 1.7 /. Average wind speed is only 1.4 / with a maximum of 4.1 /. The measurements were performed during a relatively short period, thus no annual mean wind speed can be given for this site.

Table 3. Parameterizations of as a linear function of , as used in the NTM (Equation 2.15), and corresponding linear regressions seen in Figure 5 a‐c.

Summary

NTM 50th percentile 0.12 0.54

NTM 90th percentile 0.12 1.00

Linear regression 97 0.108 0.31

Linear regression 33 0.47 0.12

Linear regression 15 0.33 0.09

a) Figure 5 a‐c Observations of standard deviations of wind speed as a function of mean wind speed (dots). The linear regression (thin red line) compared to the Normal Turbulence Model used by IEC (Equation 2.15). 90th percentile (thick line) and 50th percentile (dotted line) respectively with incline 0.12.

a) b) Above forest (Norunda) at height z 97 m during January – December 2009. Linear regression has incline 0.108.

b) Above forest (Norunda) at height z 33 m during January – December 2009. Linear regression has incline 0.47.

c) Above rooftop (Earth c) Sciences Centre) at height 15 during September – November 2010. Linear regression has incline 0.33.

Since the wind speeds this close to the roof are very low, it is difficult to draw any real conclusion about how the pattern will look like for higher wind speeds in such complex environment but the overall agreement with Figure 5 b) can be said to give a hint of what kind of turbulence characteristics might be found also above buildings. Unlike close above forest, the scale of the standard deviations of wind speed above rooftop is growing already from 0.5 /, illustrating the constant presence of larger scale turbulent eddies in the vicinity of obstacles like buildings.

5.2 OBSERVATIONS OF TURBULENCE INTENSITY

Figure 6 a‐c show the observations of 10 minute mean turbulence intensity, as given by Equation 4.7, plotted as a function of 10 minute mean wind speed, (dots). Also shown is the Normal Turbulence Model, NTM, given by Equation 2.17, for the 90th percentile (thick line) th and the 50 percentile (dotted line). The ‐axes of the graphs are cut at 120 % for convenience, values greater than this are only found for very low wind speeds which corresponds to minimal loadings on the wind turbines and are thus irrelevant for the results. Figure 6 a) shows the results from above forest at 97 height during January – December 2009. It is seen that the scatter of the observations is significant for wind speeds below 10 /. There are numerous occasions when the flow at this height is not turbulent at all, or only slightly turbulent, as indicated by the large amount of observations with turbulence intensities close to zero. For higher wind speeds, the small scale turbulence intensity is reduced and most of the measured cluster around the NTM. But it should be noted that about half of the measurements contain larger values than estimated by the NTM and among these a number of very large . At 15 / average 24 %, compared the the modeled value of 18 %, although confirming observations at these high wind speeds are extremely sparse. The observations in Figure 6 a) show that the pattern of the turbulence intensity at this site differ from the NTM and is found to be both lower and higher than the standard model. For the highly turbulent cases, it seems like the observed values generally are in the order of 10 20 % higher than the model for all relevant wind speeds. Except for this deviation, there are a number of extreme cases when the turbulence intensity is much more severe than the modeled values, as indicated by the scattered dots with high . Extreme values like these need to be taken into consideration if a wind turbine is to be installed at a site with corresponding conditions. Figure 6 b) shows the results from closely above forest, at 33 height, during January – December 2009. Here, the scatter in the observations is smaller compared to that of higher altitude, as indicated already in Figure 5 a) and b). For all measured wind speeds above 2 / the flow is always characterized with deviations from the mean wind speed and thus some amount of turbulence. The observed is constantly higher than the NTM for wind speeds higher than 4 /. The deviation from the model is generally in the order of 30 40 % for the relevant wind speeds. Unlike at 97 height, no cases of extremely high turbulence intensities are observed this close to the treetops. Figure 6 b) shows undoubtedly that the turbulence characteristics of a complex site are fundamentally different from those of uniform sites.

a) Figure 6 a‐c Observations of turbulence intensity as a function of mean wind speed (dots) compared to the Normal Turbulence Model (Equation 2.17) used by IEC. 90th percentile (thick line) and 50th percentile (dotted line) respectively.

a) Above forest (Norunda) at height 97 during January – December 2009. b) b) Above forest (Norunda) at height 33 during January – December 2009.

c) Above rooftop (Earth Sciences Centre) at height 15 during September – November 2010.

The results from above rooftop, illustrated in Figure 6 c), show indications of the same pattern although the measured wind speeds were very low during this period (September – November 2010) so it is again difficult to draw any unambiguous conclusions (as discussed earlier). As indicated by Figure 5 c), an interesting deviation from the results above is the absence of low turbulence intensity levels for the lowest wind speeds ( 2 /).

5.4 DISTRIBUTION OF TURBULENCE INTENSITY In the following figures (Figure 7 a‐c), the distribution of 10 minute mean turbulence intensity,

, is shown as bars divided into intervals with bin size 5 %. The ‐axis denotes the relative frequency of occurrence of within the specified intervals (%). Also presented in the figures is average turbulence intensity for the entire measuring period. The ‐axes are cut at

120 % for convenience. Above forest in Norunda, analyzes of the seasonal differences implies that the turbulence levels are higher during spring and summer than during autumn and winter (not shown).

Above forest at 97 height, the annual average value of was 19 %. The seasonal variability showed 21 % average during spring and a reduction to 16 % during winter. The highest frequency of events had between 15 20 % turbulence intensity as seen in Figure 7 a). The distribution at higher altitude is skewed compared to the distributions seen in Figure 7 b‐c. Further away from the rough underlying surface, less turbulence is expected and there is thus a larger amount of low turbulence intensity levels

Closer to the tree tops, at 33 height, the annual average is significantly larger with 41 % as seen in Figure 7 b). Mean value during summer was 42 % compared to 39 % during winter. Here, the observations have the shape of a normal distribution around the mean value. The majority of the measurements are between 35 50 % turbulence intensity with a peak at 40 45 %. Figure 7 c) shows the corresponding results from above rooftop, at 15 , with mean turbulence intensity during the measuring period (September – November 2010) of 43 % with a peak in the distribution at 35 45 %. The distribution is close to normal also at this site. The dependence of turbulence intensity on wind direction has been investigated but the results have not been consistent, i.e. there is no significant variation of with wind direction for neither of the sites (not shown).

5.5 DISTRIBUTION OF WIND SPEEDS The distributions of mean wind speed can be seen in Figure 8 a‐c as bars binned with intervals of 1 /. The frequency of occurrence is given on the right axis as a percentage of total number of elements. At all investigated sites in this study, the mean wind speed distribution is found to be Weibull distributed with Weibull shape parameters in a) 2.46, b) 2.37 and c) 2.23 compared to the Rayleigh distribution (with Weibull shape parameter 2.0) that is assumed, for all sites, by IEC (Equation 2.13). Figure 8 a‐c show that the distribution of lower mean wind speeds is overrepresented at the complex sites and that wind speeds higher than 6 / at 33 over forest and wind speeds higher than 4 / above rooftop are extremely rare.

a) Figure 7 a‐c Distribution of turbulence intensity (bars) binned with bin size 5 % denoted by frequency of occurrence (%). Annual and total average turbulence intensity, respectively, is written in the graphs.

a) Above forest (Norunda) at height z 97 m during January – December 2009. The distribution is skewed with a larger distribution b) of low . Annual average 19 %.

b) Above forest (Norunda) at height z 33 m during January – December 2009. Annual average 41 %.

c) Above rooftop (Earth Sciences Centre) at height 15 during September – November 2010. Total average c) 43 %.

5.7 AVERAGE TURBULENCE INTENSITY Figure 8 a‐c show a summary of the results illustrated by observations in Figure 6 a‐c. The turbulence intensities are averaged according to mean wind speed. For every mean wind speed interval of 1 /, average turbulence intensity, , is given together with corresponding standard deviation, , from this average value (thin line with errorbars). The thin dotted line represents the 90th percentile of the observed turbulence intensity in each mean wind speed interval, given by 1.28 (as discussed in Chapter 4.1.6). These average values can then be compared to the 90th and 50th percentiles (solid line and dashed line) respectively of the NTM (Equation 2.17). Above forest (97 in Figure 8 a), the average turbulence intensity has a minimum for wind speeds around 89 / and then increases for increasing wind speed (although the observations of high wind speeds are sparse). The NTM represents the 90th percentile of the observations up to wind speeds of 10 /. For higher wind speeds, the observed average turbulence intensity is almost twice as high as the modeled value. The standard deviations of

for each wind speed interval, illustrated by the errorbars, is quite large for all observed wind speeds (as expected when studying Figure 6 a).

Closer to the tree tops, at 33 (Figure 8 b), average for each wind speed interval lies well above the NTM. The difference between the 90th percentile of the observations and the model is generally 22 % for wind speeds relevant to the wind turbines (above 3 /). No minima can be seen for these wind speeds, either because it is nonexistent or because the wind material is too sparse. Above rooftop, at 15 (Figure 8 c), the 90th percentile of the observations lie close to or underneath the NTM. But not enough occasions with mean wind speeds higher than 4 / is observed to be able to draw any further conclusions.

5.8 STABILITY DISTRIBUTION Figure 9 illustrates the differences in stability distribution for the three measuring points a‐c. Above forest, stable stratification is most frequently occurring whereas above the rooftop, more than 90 % of the observations were unstable. This graph stresses the fact that the atmosphere cannot be considered to generally have a neutral stratification. It is seen that near neutral conditions close to the forest are found for less than 30 % of the observations, far above the forest this number is less than 10 % and above rooftop it is even smaller. Figure 10 a‐c show the observed average turbulence intensity for each mean wind speed interval with bin size 1 / for the three different stability classes, stable (blue circles), near neutral (green stars) and unstable (red squares). The observations are compared to the NTM (90th and 50th percentiles) given by Equation 2.17. Above the forest, Figure 10 a) and b), a characteristic difference can be seen between turbulence intensity levels during stable or near neutral/unstable conditions. is generally 10 % lower during stable stratification. This relation seems to be changing for wind speeds higher than 11 / at 97 although not too much weight should be put into this conclusion due to the small amount of observations. Above rooftop, Figure 10 c), no difference is seen between the different stabilities. But this is probably due to the extreme dominance of unstable conditions (95 % of the observations) as seen in Figure 9 as well as the low wind speeds.

a) Figure 8 a‐c On the left axis, average turbulence intensity together with corresponding standard deviation (thin line with errorbars) for each mean wind speed interval, binned with 1 /. Also the 90th percentile of the average observed is shown, given by 1.28 (thin dotted line) for each wind speed interval. These should be compared to

the IEC Normal b) Turbulence Model (Equation 2. 17) of 90th (thick line) and 50th percentiles (dotted line). On the right axis, mean wind speed distribution for each bin (bars) given by frequency of occurrence (%).

a) Above forest (Norunda) at height 97 during January – December 2009.

b) Above forest (Norunda) at height 33 during c) January – December 2009.

c) Above rooftop (Earth Sciences Centre) at height 15 during September – November 2010.

Figure 9. Distribution of stabilities defined using ⁄ (Equation 4.8), stable, near neutral or unstable, of the three different measuring points respectively. From above forest at a) and b) , and above rooftop at c) .

5.10 CUMULATIVE DISTRIBUTION OF TURBULENCE INTENSITY AND STABILITY Another way to illustrate the turbulence intensity distribution for different stabilities is through the cumulative distributions shown in Figure 11 a‐c. The total cumulative distribution is shown with a black line. The stable (blue dashed line), near neutral (green dash‐dotted line) and unstable (red dotted line) cumulative distributions are normalized with total number of observations so that addition of the maximum values of the three lines will correspond to the total cumulative distribution. The relative amount of observations for each stability class is given and denoted by arrows in the figures. It is seen that the atmosphere above forest is more often stable at higher altitude (62 % of the observations at 97 ) compared to closer to the treetops (49 % of the observations at 33 ) and that near neutral stratification is more common close to the treetops (26 % of the observations at 33 compared to 7.5 % at 97 ). Whereas above rooftop 95 % is unstable and 4.9 % is near neutral.

a) Figure 10 a‐c Average turbulence intensity for each mean wind speed interval of 1/ for different stabilities. Stable (blue circles), near neutral (green stars) and unstable (red squares) respectively. Compared to the NTM (Equation 2. 17) 90th percentile (thick line) and 50th percentile (dotted line).

a) Above forest (Norunda) at height 97 during January – December 2009. b)

b) Above forest (Norunda) at height 33 during January – December 2009.

c) Above rooftop (Earth Sciences Centre) at height 15 during September – November 2010.

a) Figure 11 a‐c Cumulative distribution of turbulence intensity for all observations (black solid line) and the different stabilities, stable (blue dashed line), near neutral (green dash‐dotted line) and unstable (red dotted line).

a) Above forest (Norunda) at height 97 during January – December 2009.

b) Above forest (Norunda) at height 33 during January – December 2009. b) c) Above rooftop (Earth Sciences Centre) at height 15 during September – November 2010.

6 DISCUSSION AND CONCLUSIONS

6.1 VALIDATION OF THE NTM

6.1.1 UNIFORM SITE Above forest at 97 , corresponding to 69 above the treetops, the NTM coincides quite well with the rate of change of (Equation 4.4) with increasing wind speed (Figure 5 a). th Also the magnitude of is correctly modeled; 9.4 % of the observations lie above the 90 percentile. However, the scatter is significant and there are a number of observations with extreme values of which corresponds to occasions with large variations in wind speed and thus should be associated with increased loading on the wind turbine.

Noticeable is also the large amount of very low values for wind speeds below 10 /, corresponding to the presence of no, or only small amounts of, turbulent eddies and thus a significant amount of light, or no, turbulence at this height. This could be due to the fact that this far from the treetops, much of the mechanically produced turbulence near the underlying surface has vanished and the shear production of turbulent eddies is limited. The frequent occurrence of low turbulence levels and thus low (Equation 4.7) is seen in Figure 6 a) also reflects in the distribution of shown in Figure 7 a), giving it a skewed shape. For wind speeds higher than 10 /, on the other hand, the atmosphere at 97 is always turbulent. For these wind speeds, observed average is about 20 %. At mean wind speeds of about 15 / the mean observed 25 % compared to the standard model value (given in Table 1) of 18 % at wind speeds of 15 / (illustrated in Figure 8 a) which is therefore a clear indicator that the NTM, as it is defined for the standard SWT classes, underestimates the turbulence intensity levels even at a long distance from such a rough surface as a forest.

The overall pattern of average , seen in Figure 8 a), with very high values for very low wind speeds, a minimum at 89 / and then an increase again for higher wind speeds is commonly seen also at other sites in observations above forest (Bergström, 2011). The analysis of wind speed distribution in Figure 7 a) show that the Norunda site is not very windy. Observations of high wind speeds are sparse even at 97 height and 8 / for 90 % of the observations.

6.1.2 COMPLEX SITES The observations from the more complex sites, 5 above treetops ( 33 ) and 4 above rooftop ( 15 ), show that the flow and turbulence characteristics of complex terrain deviate essentially from what is estimated by the NTM, as it is defined for the standard SWT classes. This is indicated by the lower wind speeds, on average 2.2 / above forest and

1.7 / above rooftop, and the very rapid growth of with increasing wind speed (Figure 5 b‐c), resulting in high turbulence intensities (Figure 6 b‐c). is on average 41 % above forest and 43 % above rooftop. These measuring points are located very close to rough surfaces that significantly affect both flow and turbulence characteristics. The top of the forest consist of canopy elements which have irregular height, shape and densities and can be expected to wave in the wind. These canopy elements exert frictional and aerodynamic forces on the air flow that retard the

flow velocity and therefore lower the wind speeds, as illustrated by the mean wind speed distributions in Figure 8 b) where 90 % of the observations correspond to 3 /. This strong retardation of the mean wind speed results in large vertical wind gradients and thus a large wind shear. These shear stress forces are responsible for a large shear production of turbulent kinetic energy and thus a larger amount of turbulent eddies. Above forest this results in a larger amount of small eddies, symbolized by small at low wind speeds. The same processes are dominating in the urban area. Here the air flow is affected by a long, very rough upwind fetch with roughness elements that consists of a mix of obstacles, mostly buildings but also trees and hedges of varying sizes and heights. This results in very low wind speeds above rooftop and a less amount of small (cf. Figure 5 b‐c). At both sites, it is seen that all the eddies grow rapidly with increasing wind speed with the consequence that increases much more rapidly with increasing wind speed than estimated by the NTM. As seen in Figure 5 b‐c), the linear regressions fitted to the observations has a much steeper slope than the NTM; 0.47 above treetops and 0.33 above rooftop compared to 0.12 in the NTM. This rapid growth rate of causes to significantly deviate from the NTM, this is seen most easily above forest where the wind speeds are higher and the number of observations is higher. As seen in Figure 6 b) and Figure 8 b), the deviation between measured and modeled is on average 22 %. But since almost identical patterns can be seen at the two complex sites, the same conclusion could be drawn also above rooftop. Although some caution should be taken to put too much weight into this conclusion due to the short measuring period (3 months) and the low wind speeds. These rougher conditions, with a more frequent occurrence of higher values, reflect in the distribution plots (Figure 7 b‐c).

6.2 STABILITY DEPENDENCE The stability of the atmosphere will either enhance the turbulence production or suppress it. The suppression is effective during stable stratification, as illustrated by the stability dependence of the observations above forest at 97 in Figure 10 a) where most of the eddies are dampened, so that only some of the turbulent eddies will reach this far up. However, in the context of wind turbine construction and siting, it is common to only consider neutral conditions corresponding to high wind speeds (as discussed in Chapter 2.1.3). But the wind turbines have to withstand all kinds of stratifications experienced at the site. The distribution of different stabilities will give a measure on the recurrence frequency. A site with a high recurrence of turbulent unstable conditions is rougher on the wind turbine than a less turbulent site with mostly stable stratification. The stability is dependent on the temperature gradient (as discussed in Chapter 2.1.3) which is dependent on the energy balance at the surface. The energy balance at a site during a specific time period is dependent on mainly two variables. First, the overall synoptic weather situations determine the amount of clouds/sunshine and thus the amount of insolation and heat emission. These effects are varying with the time of day and the seasons. Second, the structure of the surface determines the capability to absorb and emit energy. The energy balance will thus be different in urban areas, where the surface is differently heated by the presence of buildings, compared to rural areas, where the vegetation absorbs and emits humidity which is a source of latent heat.

As seen in Figure 9 a), the atmosphere at 97 height above forest was stably stratified during 62 % of the measuring period when the different stabilities were classified from the stability parameter ⁄ in accordance with Equation 4.8.

Also the measurements close to the treetops can be seen to have a stability dependence (Figure 10 b) where is found to be generally 10 % lower during stable conditions which is the most frequently occurring stability class (49 % of the measuring period). Above rooftop, on the other hand, 94 % of the measurements were unstable (classified in accordance with Equation 4.8) even though near neutral conditions are expected to dominate. This could be due to several factors affecting the heat balance. For example, some amount of heat could be expected to leak out through windows, walls and ventilation shafts, warming the air close to the building. Also, tunneling effects on the flow by the building itself could affect the air flow and therefore the fluxes of heat and momentum.

6.3 CONCLUSIONS The results from the analysis of high frequency measurements performed in this study show that the Normal Turbulence Model, NTM, (Equation 2.15) as it is defined for the standard SWT classes in IEC 61400‐2 (IEC, 2006), underestimates the turbulence intensity in complex environments and only represents the turbulence at the more uniform site for light winds ( 10 /) while for higher wind speeds the model again underestimates the turbulence. The NTM poorly estimates the turbulence characteristics in complex and urban environments. It provides a very bad representation of the growth rate and magnitude of , and consequently also of the turbulence intensities as illustrated by the observations from the complex sites, 5 above treetops ( 33 ) and 4 above rooftop ( 15 ). These environments show completely different turbulence characteristics than at the more uniform site, 69 above forest ( 97 ), where the NTM better represent the growth rate and magnitude of but for higher wind speeds the observed is almost twice as high as expected by the model. In these rougher conditions, the wind turbines will suffer from larger amount of strain and loadings due to the gustiness and the frequent occurrence of rapid wind direction changes that is to be expected in turbulent environments, but the extreme loadings on the construction will be smaller due to the lower mean and extreme wind speeds. Therefore it can be concluded that the NTM, as defined for the standard SWT classes, needs to be modified to correctly describe the turbulence in the application of small wind turbines in complex environments, such as urban application; the S class can be used for this. It can be concluded from the measurements included in this study that the turbulence characteristics above rooftop in an urban area are similar to those close above the treetops of a tall forest. Since almost identical patterns can be seen at the two complex sites, these measurements give information about the wind climate of both complex and urban sites. Even though the wind material is a bit sparse in a wind energy perspective, they still give a hint of what turbulence characteristics would have been found above rooftop if also higher wind speeds had been experienced. So in the absence of on‐site rooftop measurements, turbulence data from another complex site, e.g. above treetops, as described in this study, therefore can be used as background material that give guidance when quantifying turbulence above rooftops. But more information is needed from analyses of longer periods of measurements at other similar sites to verify this conclusion. 39

7 ACKNOWLEDGEMENTS I want to thank my supervisors Hans Bergström and Cecilia Johansson at Uppsala University for your help and support throughout the process of realizing this thesis. I would like to give a special thank to Sven Ruin at TEROC for giving me the idea to this project and for your input and knowledge about the work of IEC and the requirements of wind turbines. Thanks also to Meelis Mölder at Lund University, Dept. of Physical Geography and Ecosystems Analysis, for providing me with turbulence data from the site of Norunda and Jonathan Whale, Lecturer in Energy Studies and Renewable Energy Engineering, at Murdoch University, for giving me valuable guidance and new ideas in the data analysis process.

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Stull, R. B. (1988). An Introduction to Boundary Layer Meteorology. Vancouver, Canada: Kluwer Academic Publishers. van Bussel, G., & Mertens, S. (2005). Small Wind Turbines for the Built Environment. The Fourth European & African Conference on Wind Engineering. Prague.

Yersel, M., & Goble, R. (1986). Roughness Effects on Urban Turbulence Parameters. D. Reidel Publishing Company.

APPENDIX A SYMBOLS AND DESCRIPTIONS UNITS a Slope parameter for turbulence standard deviation model [‐] d Displacement height [m] g Gravitational constant (=9.82 m/s2) [m/s2] h Height of roughness element [m] Mean height of roughness elements [m] I 10 minute mean turbulence intensity (IEC) [%] i Index [‐]

Turbulence intensity at 15 / wind speed [%] int Averaging period (interval of 10 minutes) [minutes] k von Kármáns constant (= 0.4) [‐] L Scale representative length (Monin Obukhovs length) [m] n Number of elements [‐] P Total amount of energy given by the wind, which passes a unit area [J/sm2] per second p Percentile value defined from the normal probability function [‐]

PRayleigh Probability [‐] r Radius [m] Re Reynnolds number [‐]

Rf Richardson number [‐] T Air temperature [°C] T' Air temperature deviation [°C]

Mean air temperature in Kelvin ( 273.15) [K]

Turbulence intensity in longitudinal componenet [%] Mean wind speed [m/s] U Scale representative wind speed [m/s] u Longitudinal wind velocity [m/s] u' Longitudinal wind speed deviation [m/s]

u* Friction velocity [m/s]

u1 Horizontal wind component in geographical coordinate system [m/s]

Measured mean wind speed [m/s] Kinematic shear stress [m2/s2] v Lateral wind velocity [m/s]

v1 Vertical wind component in geographical coordinate system [m/s]

Vave Annual average wind speed at hub height [m/s] Vdesign Wind speed that the wind turbine is designed for (used in the design [m/s] equations)

Vhub 10 minute mean wind speed at hub height [m/s] Vref Maximum 10 minute mean wind speed at hub height with a [m/s] recurrence period of 50 years that the wind turbine is designed to withstand

w Vertical wind velocity [m/s] w' Vertical wind speed deviation [m/s] Kinematic heat flux [mK/s] Horizontal direction [‐] Mean value [‐] Rapidly varying turbulent part [‐] y Lateral direction [‐] z Height (vertical direction) [m] z/L Stability parameter [‐]

z0 Characteristic roughness lenght [m]

zRS Height of roughness sublayer [m] β Incline of the wind onto a wind turbine [°] θ Potential temperature [°C] μ Viscosity (of a fluid) [Pa/sm] ρ (Air) density [kg/m3] σ Standard deviation [‐]

σ1 Standard deviation of longitudinal wind speed (IEC, 2006) [m/s] σ2 Variance [‐]

σu Standard deviation of longitudinal wind speed [m/s]

σxy Covariance [‐] τ Shearing stress [kgm/s2] 2 τturb Turbulent shearing stress () [kgm/s ] ABBREVATIONS HAWT Horizontal axis wind turbine IEC International Electrotechnical Comission IS Inertial sublayer MKE Mean flow energy ML Mixed layer NTM Normal turbulence model as it is described for the standard SWT classes in IEC 61400‐2 NWP Normal wind profile PBL Planetary boundary layer RS Roughness sublayer SL Surface layer SWT Small wind turbine TKE Turbulent kinetic energy UBL Urban boundary layer UCL Urban canopy layer VAWT Vertical axis wind turbine WD Wind direction WKE Wake kinetik energy ii

APPENDIX B

Figure 12. Overview of the rural site at Earth Sciences Centre in Uppsala. Above the rooftop the mast and the mounted instrumentation is seen. Photo Nicole Carpman (2011).

Figure 13. Close up of the mast with the sonic anemometer mounted (to the right). To the left, a wind vane not used in this study. Photo Nicole Carpman (2011).

iii

APPENDIX C

PERCENTILE VALUES FROM A NORMAL DISTRIBUTION Figure 14 illustrates a bell shaped normal distribution where the 0‐line represents the mean value. The distribution curve is divided into sections with the size of one standard deviation, . Underneath, the cumulative percentage for each section is given on the horizontal axis together with the percentile values. The red line corresponds to 90 % of the observation and thus the 90th percentile and is given by the mean value 1.28. The exact value can be given from tables of normal distribution functions (for example Alexandersson & Bergström (2008)).

Figure 14. Normal distribution curve with mean value on the ‐line, divided into sections of standard deviations, . Values of cumulative percentages and percentiles are given on the bottom axis. The red line represents the 90th percentile given by the mean value .

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