Effects on Support Structure Design Due to Wake-Generated Turbulence

Effects on support structure design due to wake-generated turbulence

M.Sc. Thesis by Russell A. Guzmán Tejada 2014 Delft, The Netherlands.

Effects on support structure design due to wake-generated turbulence

Russell A. Guzmán Tejada Ing. Mecatrónica por la UNAM, México.

in partial fulfilment of the requirements for the degree of

Master of Science in Sustainable Energy Technology

at the Delft University of Technology,

to be defended publicly on Tuesday October 24, 2014 at 9:30 AM.

Supervisor: Dr. ir. M.B. Zaaijer, TU Delft Thesis committee: Prof. dr. G.J.W. van Bussel, TU Delft Dr. Eliz-Mari Lourens TU Delft

This thesis is confidential and cannot be made public until October 23, 2014.

An electronic version of this thesis is available at http://repository.tudelft.nl/.

Abstract

As the world demands cleaner, sustainable and economical energy sources, the wind energy academia and industry battles to increase performance and reduce costs. One of the promising fields of study is wind turbine wakes in wind farms. The position of the turbines within the layout affects the intensity of their wake effects, such as reduced wind speed or turbulence, therefore the choice of its position has an impact on wake losses and fatigue damage induced by wake-generated turbulence on the components. In this work, the possibility of wind turbine’s support structure cost reduction is explored by studying the effect on its design (and cost) caused by wake-generated turbulence. Furthermore, layout optimization considering wake losses and the wake-affected support structure cost was studied. To obtain insights about these effects, the turbulence intensity calculation and a simple support structure design were implemented into the wind farm design tool TeamPlay (by M. Zaaijer in the Wind Energy Research Group at TU Delft) and used to perform a series of case studies. The turbulence calculation was implemented following the IEC guidelines for any layout and wind direction distribution. The simple support structure design approach used in this work is based on two key aspects: (1) a base design obtained from Teamplay which does not account for fatigue and (2) the assumption of proportionality between fatigue equivalent load and turbulence. By using these tools, a location-specific support structure design within the wind farm was performed. Further, the weight and cost of the support structures was compared with the case in which all support structures have the same design obtained from the worst turbulence regime.

It was found that wake-induced fatigue and its effect on the support structure design is not relevant for layout-spacing optimization because wake losses dominate the cost changes due to layout changes. Moreover, it was found that location-specific support structure design, according to their specific turbulence regime, would result in cost reductions that could account, as an upper limit, between 0.3 % and 0.7 % of the total capital costs in the studied cases. Finally, the cost reduction share of the total capital cost increases with increasing support structure size.

Acknowledgments

First and foremost, I thank Mexico’s Science and Technology National Council (Consejo Nacional de Ciencia y Tecnología, CONACYT) for sponsoring my master’s studies and livelihood in The Netherlands. Without which, this endeavor may have not be possible.

I appreciate the help and mentoring of Michiel Zaaijer as my supervisor throughout this thesis work. The thesis topic presented in this report came to be thanks to the help of Michiel; who formulated the topic based on my personal interests and his expertise.

Thanks to my parents, Martín and Gaby, who have encourage and support my studies abroad. Finally, special thanks to my girlfriend Mariana for her loving support and patience throughout these challenging two years.

October 10, 2014. Delft, The Netherlands.

Russell A. Guzman Tejada

Contents

Abstract ...... i Acknowledgments ...... ii 1. Introduction ...... 1 1.1. Energy sustainability and wind energy ...... 1 1.2. Wind farms ...... 1 1.3. Identification of the problem ...... 3 1.4. Objective ...... 3 1.5. Available resources ...... 4 1.6. Approach ...... 4 1.7. Outline of the thesis ...... 5 2. Wind turbine wakes ...... 6 2.1. Wake concepts ...... 6 2.2. Formation and characteristics ...... 7 2.3. Wake effects ...... 9 3. Wake models selection ...... 12 3.1. Types and requirements ...... 12 3.2. Wind speed deficit models ...... 13 3.2.1. Overview ...... 13 3.2.2. Single wake models ...... 13 3.3. Turbulence models ...... 14 3.3.1. Turbulence summation rule ...... 14 3.3.2. Atmospheric turbulence ...... 15 3.3.3. Wind turbine added turbulence ...... 15 3.3.4. Turbulence profile shape ...... 16 3.3.5. Increased ambient turbulence in wind farms ...... 16 3.3.6. Test example ...... 17 3.3.7. Selection ...... 18 4. Turbulence and Fatigue ...... 19 4.1. Basic fatigue concepts ...... 19 4.2. Turbulence generated fatigue loading in wind turbines ...... 20 4.2.1. Literature relevant conclusions ...... 20 4.2.2. The proportionality between equivalent load and turbulence ...... 20

iii

4.2.3. Contribution from wakes ...... 24 4.2.4. Remarks ...... 25 5. Qualitative support structure design ...... 26 5.1. Support structure scope ...... 26 5.2. General overview of the design process ...... 27 5.3. Design drivers ...... 27 5.4. Design approach for this work ...... 27 5.5. Base design general dimensions ...... 28 5.5.1. Tower...... 28 5.5.2. Transition piece ...... 28 5.5.3. Monopile ...... 29 5.6. Support structure design adjustment for fatigue ...... 29 5.7. Cost model ...... 30 6. The coupled methods ...... 31 6.1. Overview...... 31 6.2. Implementation ...... 31 6.2.1. Effective turbulence ...... 31 6.2.2. Fatigue life ...... 32 6.2.3. Equivalent load ...... 32 6.2.4. Support structure design adjustment for fatigue ...... 33 6.3. Algorithm parameters ...... 33 6.3.1. Wind rose ...... 33 6.3.2. Wind direction bin size ...... 33 6.4. Verification ...... 35 7. Qualitative study ...... 40 7.1. Increased support structure cost: wind turbine spacing effect ...... 40 7.2. Increased support structure cost: variations in wind turbine position ...... 43 7.3. Support structure weight reduction: wind turbine spacing and wind farm size effect ...... 46 7.4. Support structure weight reduction: layout shape and wind direction distribution ...... 48 7.5. Additional case studies ...... 50 7.5.1. Rotor-nacelle assembly ...... 50 7.5.2. Water depth ...... 51 8. Final conclusions and recommendations ...... 52 8.1. Conclusions ...... 52

8.2. Recommendations ...... 53 8.3. Future work...... 54 References ...... 55 A. Appendix: Wind speed and direction distributions ...... 57

1. Introduction 1.1. Energy sustainability and wind energy Our civilization is under pressure by the ticking clocks of pollution, increased temperature and ocean rising levels. There is a growing desire for a cleaner and more sustainable world. Several battle fronts are of our attention: from agricultural practices, forestry, energy efficiency, waste chemicals to sustainable energy sources. Wind energy has become one of the fastest growing sustainable energy technologies; according to the International Energy Agency (IEA 2013) installed capacity has doubled from 2008 to 2012 and now represents 2.5% of the global electricity consumption. The technology has become more accepted and mature, but its biggest challenge is still to come. Energy scenarios, from the IEA, indicate that wind energy could provide from 15 to 18% of the world’s electricity consumption by 2050. Furthermore, if we take a closer target, under a moderate scenario, we will have to install around 60 GW of wind power every year from now to 2030; meaning we will need to build, install and maintain 10,000 of our current biggest wind turbines every year. Even though these plans would have the positive impact that we desperately need, for instance: CO2 reduction, energy democracy1 and green jobs, it is clear that several challenges surge from it. Wind energy would have to become economically competitive with fossil fuel sources and overcome barriers for the technology (e.g. permit/authorization delays and electrical grid issues).

1.2. Wind farms The most common framework in wind energy are wind farms with several horizontal axis wind turbines. Typical large onshore wind farm numbers are in the order of 0.7 GW of installed capacity (350 turbines with 2MW nominal power) and current large offshore wind farms are about 0.3 GW of installed capacity (100 turbines with 3.5MW nominal power). As for comparison, coal power plants reach up to 5 GW of electricity. It is certainly a long way to go but current numbers in wind farms are rising continuously. At the moment (early 2014) the biggest onshore project is the Gansu Wind Farm Project in China, which first phase was completed in 2010 and it holds 3,500 wind turbines with a total installed capacity of 5.2 GW, the next two phases are expected to add up to a total of 37 GW by 2020 (Chen 2009). Offshore wind farms are smaller, the biggest project being the London Array in the UK with 175 wind turbines and 0.6 GW of installed capacity (Anon 2013). Offshore wind farms are expected to become fairly big for such remote conditions. A company in Sweden has proposed a 2.5 GW project (Blekinge 2013), and the number of offshore projects will likely increase due to offshore wind resources and space availability compared to inland.

As wind farms grow bigger only the outer turbines in the layout experience free-stream or ambient wind conditions, meaning most turbines experience altered and complex wind conditions. As the wind flows through a wind turbine energy is extracted from it and disrupted from its free-stream characteristics. As a result, a well-recognized —but not entirely understood (Barthelmie et al. 2009)— volume of air forms downstream the turbine with reduced wind velocity and increased turbulence2, known as wind turbine wake (see Figure 1.2-1). Wakes degrade until reaching ambient conditions after some distance of about 15 times the rotor diameter. As wind inflow direction varies in time, wind turbines experience wake conditions of another upstream turbine. As a result of this effect, wind turbines within wind farms will experience a

1 Energy democracy is related to decentralization of energy generation. In a global scale, means that countries generate their own energy to supply their demand without having to rely on other suppliers. 2 Turbulence is a measure of the velocity fluctuation in the flow with respect to the mean velocity.

1 reduced wind velocity from that of ambient conditions and will yield less energy than if they were isolated rather than in arrays (see Figure 1.2-1), also known as wake losses. Furthermore, turbines will experience extra fatigue damage resulting from the increased turbulence in the upstream wake. These particular impacts on wind turbines caused by operating downstream others are known as wake effects. More details are presented in Chapter 2.

The turbulence field behind the Horns Rev 1 offshore wind turbines. Unique meteorological conditions resulted in condensation of the very humid air, thus making it possible to see the turbulence pattern behind the wind turbines (Aeolus 2008). A numerical simulation shows the normalized power output vs. wind direction (Porté-Agel et al. 2013). Showing power reduction as a function of wind direction, due to wind farm array and wake losses.

FIGURE 1.2-1 HORNS REV 1 OFFSHORE WIND FARM

Determining wake characteristic parameters is of importance for energy yield calculations for wind farms and fatigue loading in wind turbines within. Mathematical equations or wake models are used to estimate such parameters, mainly wind speed deficit and turbulence intensity, from: atmospheric conditions (e.g. free stream wind speed and ambient turbulence), layout parameters (turbine separation) and upstream turbine parameters (e.g. rotor diameter, thrust coefficient). The models range from simple empirical relations to complicated differential equations which can only be solved by numerical computing. Simple models are used in wind farm design tools where calculations are needed for every wind direction and probable speed to evaluate wind farm efficiency. Whereas complex models are used to study details about wakes over short periods of time (e.g. 10 minutes series). Wake models provide designers two important aspects:

 Wind speed deficit is used to evaluate the performance of a certain wind turbine design and layout combination for a specific site. It is also possible to make use of optimization algorithms to find an optimum layout for the given turbine design and site conditions, to improve wind farm efficiency. Layout optimization by means of wake losses is a very well developed topic that is included in most wind farm tools.  Increased turbulence intensity which is used to compare with the allowable value set by the industry standards for the given wind turbine design.

1.3. Identification of the problem As established in the previous section and depicted in Figure 1.2-1, wakes have a big influence on wind farms. It is obvious that energy output and wind turbine durability are very important for the economic viability of any wind energy project and both must receive thorough attention. An optimal wind farm design considering all possible wind farm aspects is desirable to achieve the most cost-effective solution. Potentially, one could calculate wake characteristics (e.g. wind speed and turbulence intensity) at every wind turbine position for every wind direction, for a given wind farm layout and use this information to design such wind turbines and their correspondent support structure.

Regarding wind turbine design, due to manufacturing, logistic and time limitations, it is not current practice to design a specific wind turbine for each position within the wind farm. Depending on the general site conditions, designers can also choose from off-the-shelf wind turbine designs (classified by certain standard wind classes) that meet the conditions. The potential cost reduction by designing position- specific wind turbines is overshadow by the relative low cost that single or fewer designs provide.

In contrast, support structures do need to be designed specifically for each site, due to wide design- parameters variation (e.g. sea depth and soil conditions); even within the wind farm some conditions might differ. Design loads are divided in ultimate and fatigue loads. Fatigue is of interest because it is strongly related to turbulence levels (Frandsen & Thomsen 1997; Larsen et al. 1998), thus it depends on wake exposure, and is often a design driver. In practice, the most onerous turbine load-set is generally considered to design all support structures in order to keep the number of individual designs relatively low for fabrication and installation reasons (Jacquemin et al. 2010). Nevertheless, this flexible procedure offers the opportunity to make optimal site-specific support structures within the wind farm and reduce the project cost, mainly by lowering steel usage. The potential cost reduction is important if we consider, for example, that the cost of wind turbine towers and foundations can account up to 27% of the capital cost in an offshore project (IRENA 2012). Furthermore, there is an unexplored interaction between layout optimization and support structure design. A layout optimization that considers the others wake effects (mainly turbulence intensity) would mean that the choice of the turbine positions within the wind farm affects the support structure cost. For instance, a layout optimization that includes both wake effects might yield larger wind turbine separation as a more cost effective alternative rather that only considering the wind speed deficit effect.

1.4. Objective In the previous sections the wind turbine wake phenomena have been presented and their consequences for economical and design considerations. Moreover, the current —and potential— use of wake models for wind farm optimization have been introduced. Considering the scope and the aim for improving wind farm optimization, the following objective has been set for this work:

Use existing wake models and relevant load cases in an integral method to gain insight about the impact of wind speed deficit, partial wakes and increased turbulence intensity into support structure design. Furthermore, assess the interaction between support structure design and layout as means for wind farm optimization.

Meeting such objective could potentially yield recommendations for improvements in support structure design and provide motivation to include other wake effects in layout optimization algorithms. As an early possible outcome, we expect to see for instance, the support structure weight distribution over all wind

3 turbine positions and how changes in wind farm layout could potentially lead to cheaper support structures.

1.5. Available resources The resources found during the literature review are mainly:

 Wake models from research projects and industry standards (Larsen et al. 1998; Frandsen 2007; IEC-61400-1 2005; Thøgersen 2005). The choice of wake models is subject to available validation studies against measurements and computational cost.  General guidelines for support structures design (DNV-OS-J101 2011).  Mathematical tools to model wind farms. Framework that allows the implementation of wake models and the simplified support structure design. In the PhD. thesis by Michiel Zaaijer (Zaaijer 2013), the Wind Energy Group at TU Delft develops a wind farm optimization tool that emulates the wind farm design process called TeamPlay.  PhD. thesis by Sten Frandsen (Frandsen 2007), Risø National Laboratory. This provides a detailed study relating turbulence with fatigue damage by means of the so called effective turbulence. Furthermore, it provides guidelines about the implementation of engineering wake models within large wind farms.  Technical reports from GL Garran Hassan (Jacquemin et al. 2010; Frohboese & Schmuck 2010) relating the use of simple wake models in IEC standards and their effect on support structure design.

1.6. Approach The work set up for this project could be simply described as a study of turbulence related wake effects in support structure design and its interaction with wind farm layout, as depicted in Figure 1.6-1. The main steps to gain insight about such issues are:

1. Wake models selection; survey of available and potentially useful wake models that would allow the estimation of wake generated turbulence and wind speed deficit by simple computational means. 2. From wake characteristics to fatigue; devise a method to estimate fatigue damage in support structures from turbulence. 3. From fatigue damage to support structure parameters; develop a simplified support structure design from equivalent fatigue load that relates wake characteristics to support structure design parameters. 4. Implementation; elaborate an algorithm to couple wind farm parameters with support structure design. This combines the models obtained in the previous three steps. 5. Wake verification; compare the wake characteristics results with known cases from other research studies or using other wind farm tools. 6. Support structure verification; compare equivalent fatigue loads to other research studies. If available, compare support structure designs. 7. Case studies and sensitivity analysis; using different layouts and wind turbine characteristics, analyze the impact on support structures. Analyze the sensitivity of wake characteristics and support structure design caused by changes in layout parameters. 8. Conclusions and recommendations; infer the interactions between wake effects, support structures and layout and yield recommendations for wind farm designers.

Wind Farm Wind Turbines (C ) T Support structure Layout Turbulence design and cost (shape, spacing) Environment

(U,Iamb)

FIGURE 1.6-1 THESIS WORK REPRESENTATION 1.7. Outline of the thesis The chapters of this work are arranged in a conventional way where the important concepts and tools are presented first, followed by the implementation and case studies and finally conclusions.

I. In Chapter 2, turbulence and the wake phenomena are explained in more detail; in Chapter 3, the description and selection of the relevant wake models used is presented; Chapter 4 deals with the relationship between turbulence and fatigue in wind turbines; and Chapter 5 provides a simplified manner to design qualitatively the support structure as a function of turbulence. II. The next step is presented in Chapter 6 where the proposed method is implemented and verified. In Chapter 7, a qualitative analysis through case studies is conducted. III. Finally, in Chapter 8 the insights from Chapter 7 are discussed, recommendations are given and opportunities for future work are recognized.

2. Wind turbine wakes “…— it is mind boggling to me to see how well, and in how much detail, we can measure the flow field of a rotor. Modeling the flow field of a rotor is a terribly difficult problem. The airplane people have it easy compared to us. Capturing the details of the rotor wake and of what happens in the vicinity of the blade is very difficult”.

Leone U. Dadone (1995)

The previous section introduced a wind turbine’s wakes —in general a rotor’s wake— and its complicated nature, noted in the quote above by L. U. Dadone when referring to helicopter rotor wakes. This section describes further wind turbine wakes. First, some basic concepts are presented in order to describe its characteristics, how it is formed and its distinct areas, its effects on other wind turbines. Finally, a description of wake models is presented. The reader familiarized with such concepts may skip this chapter and continue with chapter 3 where the wake models used for this work are selected.

2.1. Wake concepts As is readily known, wind speed can vary from one place to another and in time. Time variability can be from large time frames, such as yearly and seasonal, or during the day and even in a matter of minutes. In the wind energy field, turbulence is a concept to describe the randomness, irregularity, unpredictability and chaotic nature of wind flow within short periods of time. Turbulence in a wind flow can be visualized as air particles moving in vortices or “eddies” (swirls), enclosed in a parcel that behaves as a structure. The parcel moves with the surrounding flow and can also rotate, stretch and expand. The parcel’s size or length scale can range from millimeters to kilometers. This turbulent parcel of air is not on a low energy level, thus large eddies transform into smaller ones until their energy dissipates into heat by means of fluid viscosity and friction. Turbulence is mainly generated in the interface between a fluid flow and another fluid or surface with different velocity and is a function of such relative velocity and the fluid’s properties. In the natural occurring wind that concerns us: speed, surface roughness, atmospheric stability, gradients in pressure and temperature, obstacles in the flow —such as a wind turbine— are all causes of turbulence. Turbulence is a complex phenomenon, and one that cannot be represented simply in terms of deterministic equations (Burton et al. 2001) but it can be described broadly by estimating some statistical parameters, for instance, its speed fluctuation and size. It is useful to think that wind consist of two parts: a mean wind speed which varies on a time scale of one to several hours and a turbulent fluctuating part — such as noise on an electric signal.

Turbulence intensity (TI) is a measure of the overall level of turbulence. It is defined as the ratio of the standard deviation () of the wind speed variations by the mean wind speed (Ū), usually defined over ten minutes; turbulence intensity is frequently in the range of 0.1 to 0.4 (Manwell et al. 2009). This means, for instance, if the 10 minutes mean wind speed is 10 m/s and turbulence intensity of 0.4, it is likely that the actual instantaneous speed lay between 6 and 14 m/s.

Although at first glance turbulence may seem a complicated compilation of air motions, it may be idealized as consisting of a variety of different size swirls or eddies. These eddies behave in a well-ordered manner when displayed in the form of a spectrum (Roland B. Stull 1988). The turbulence spectrum describes the frequency content of wind speed variation. According to the Kolmogorov law, the spectrum

6 must approach an asymptotic limit proportional to f -5/3 at high frequency (f is the frequency in Hz.). This relation is based on the decay of turbulent eddies to higher and higher frequencies as turbulent energy is dissipated as heat (Burton et al. 2001) and in the assumption that the turbulence is statistically self-similar at different scales. Furthermore, the length scale of an eddy is correlated to its frequency and energy content; high frequency eddies are small and contain less energy.

Wind turbines, being big rotating structures, can experience one or more of these parcels or turbulent structures in their rotors at the same time. This will obviously have some influence on the loads sensed by structures of some spatial extent, subjected to the turbulent wind (Højstrup 1999). Therefore, the spatial variation of turbulence in the lateral and vertical directions is also of importance. In order to model these effects, the spectral description of turbulence must be extended to include information about the cross- section between turbulent fluctuations at points separated laterally and vertically (Burton et al. 2001). Coherence is defined as the absolute value of the normalized two-point spectrum. It represents the degree to which two wind speeds at points separated in space are alike in their time histories (Sanderse 2009). Coherence describes the correlation as a function of frequency and separation.

As stated in the beginning of this section, turbulence is generated by several factors in a flow. In free stream wind flow it is mainly generated by roughness of the terrain and temperature gradients. When this free stream flow encounters a wind turbine in its path it modifies its “turbulent characteristics”. Generally speaking, it reduces its speed and length scale but increases its turbulence intensity. For stand-alone wind turbines this effect is of no importance but if another wind turbine is downstream the first one, it would encounter reduced wind speed and harsh turbulent conditions. In the next section we shall explain further the phenomena and their implications.

2.2. Formation and characteristics The purpose of a wind turbine is to extract energy from the wind. To do so, it converts kinetic energy from the wind into rotational mechanical energy and finally electrical energy. Therefore, the first step is to reduce the wind velocity, and thus momentum, by exerting an opposite force to the fluid, called thrust. This in turn, results in a volume of air with decreased wind speed known as wake. The gradient between this volume and the free flow outside it results in shear-generated turbulence (“shear layer”), which assist in the transfer of momentum into the wake from the surrounding flow. Furthermore, a sheet of vortices is generated along each blade and especially strong vortices shed from the tips and roots, due to an abrupt pressure jump, in a helical-rotational manner (see Figure 2.2-1). Additionally, the turbine itself, being a solid body (blades, nacelle and tower) in the flow path, generates additional mechanical turbulence. Finally, turbulence and reduced flow speed causes the wake to expand outwards and to mix with the outer flow, leading to blur away. All these effects contribute to the main wake characteristics which are depicted in Figure 2.2-2: wind speed deficit, wake expansion and increased turbulence. To gain understanding of the physical process in wakes, wind tunnel studies have captured in photographs (e.g. Figure 2.2-1) some of these wake characteristics.

FIGURE 2.2-1 WAKE FLOW VISUALIZATION PHOTOGRAPHS (Left) Flow visualization experiment at TU Delft, showing two revolutions of tip vortices for a two-bladed rotor. (Right) Flow visualization with smoke grenade in tip, revealing smoke trails for the NREL turbine in the NASA-Ames wind tunnel. Both taken from (Vermeer et al. 2003).

Colder colors represent reduced wind speeds as compared with the free flow speed in red. Balloon-like structures represent turbulence structures; darker colors represent increased turbulence intensity and size turbulent length-scale. The helical path represent the trail of tip vortices shed by one blade, the other two trails are not depicted.

FIGURE 2.2-2 WAKE STRUCTURE DIAGRAM

In literature, wind turbine wakes are commonly separated into near wake and far wake, the distinction being how do the wake’s characteristics evolve with distance or travel time from the rotor. The distinction becomes clear in Figure 2.2-3. When the shear layer becomes so thick that it reaches the wake axis, the end of the near-wake has been reached (2-5 D) (Crespo et al. 1999). At this point the far wake begins and, in theory, continues till infinity but in practice the effects are considered “noticeable” up to 15 diameters (Højstrup 1999). The main characteristics for near and far wake are summarized from (Sanderse 2009) and (Petersen et al. 1998) in Table 2-1.

FIGURE 2.2-3 WAKE VELOCITY DEFICIT AND REGIONS Velocity profile in the wake of a wind turbine (Sanderse 2009).

TABLE 2-1 CHARACTERISTICS OF WAKE REGIONS

Undisturbed flow Near wake (2-5D) Far wake (up to 15D) Atmospheric boundary Abrupt speed deficit Gaussian speed deficit. layer (ABL). (max. in 1-2D). Tip vortices broken down Logarithmic shear wind Wake expansion (full after ~4D. speed profile due to expansion ~2.25D). terrain roughness. Tip and root vortices. Turbulence: Turbulence: Turbulence: . Much larger scale . High intensity . Uniform . Ambient, low intensity . Large-scale . Less intensity but still . Anisotropic . ~ isotropic increased vs ambient . Smaller scale . ~ isotropic

The near wake research is focused on performance and the physical process of power extraction, while the far wake research is more focused on the mutual influence when wind turbines are placed in clusters, like wind farms. Other topics which contribute to the complexity of the general subject, are: wind shear, rotor–tower interaction, yawed conditions, dynamic inflow, dynamic stall and aeroelastics (Vermeer et al. 2003).

2.3. Wake effects As seen in the previous section, an inevitable wake is generated by wind turbines as a result of extracting energy from the wind flow. If another wind turbine is placed in the downstream path of this wake it will experience the so called “wake effects”. In literature (González-Longatt et al. 2012; Adaramola & Krogstad 2011; Vermeer et al. 2003) the two main recognized effects of a wake are:

1. A reduction in the wind speed, which in turn reduces the energy production of the wind farm; reducing wind farm efficiency. A study in the Horns Rev wind farm showed that some turbines experienced a power drop of around 20% with respect to the free stream case (Méchali et al. 2006).

2. An increase in turbulence in the flow, potentially increasing the dynamic mechanical loading on downwind turbines. Measured results from Sexbierum indicate that the greatest increase in loading in the wind farm is approximately 30 % (in 1 Hz fatigue equivalent load3). This occurs for wind speeds in the range 10 to 12 m/s within 5 diameter distance from the rotor (Tindall 1994).

Unless wind farms are built lightly-dense with huge separations between wind turbines, wake effects are unavoidable. However, wind farm designers and operators can still take some actions to mitigate their effects. Wake effects are a function of some factors, explained below:

o Wind farm factors: . Wind farm layout (the geometric distribution of wind turbines inside the wind farm); as wind direction changes, turbines within the wind farm can experience different wake- lengths or separation between turbines. As a result, power production will be different, even if the wind speed is the same. Wind farm layout is the most sensible design parameter to adjust (González-Longatt et al. 2012) therefore it is of mayor optimization focus. It influences wind speed deficit and turbulence intensity seen by the downstream turbine. . Wind turbine setting (e.g. thrust coefficient, rotor diameter) affect the force that the turbine exerts on the flow, making the turbine more or less transparent to the flow. o Environmental factors: . Ambient turbulence; high ambient turbulence levels lead to turbulent mixing in the wake, allowing the velocity field to recover faster. This has a positive impact on energy production but negative impact in terms of fatigue damage. . Wind-frequency distribution (wind rose); the wind speed distribution over all directions translates into probability of occurrence of wake situation for a specific wind farm layout. . Terrain; terrain roughness creates complex flow near the surface which propagate reduced wind speed and increased turbulence upwards to wind turbines. Furthermore, complex sites can offer different wind conditions for different directions. For instance, costal sites will experience high wind speeds and low turbulence coming from the sea but lower wind speeds and higher turbulence levels coming from land.

Wind farm factors, mainly wind farm layout and wind turbines operational setting, are design or are operational choices. This gives the designers and operators room to optimize wind farms. But many others, for instance ambient turbulence and wind-frequency distribution, are related to weather and the site conditions; nevertheless operators can forecast in advance and take some actions to reduce negative effects.

Offshore sites are ideal for wind energy extraction in the sense that offshore sites are big flat open spaces with little to no terrain roughness. They offer consistent wind speeds, more stable atmosphere and low turbulence levels. With such wind conditions, and given that wind turbines have a structural “extension” to be installed on the seabed, wake effects can be very influential. Typical turbulence intensity values at

3 Turbines experience fatigue loads throughout their lifetime at different amplitudes and frequencies. An equivalent fatigue load is a measure to express damage in a simple way by calculating a fatigue load with constant amplitude and frequency that would cause the same damage as the actual fatigue loads.

10 hub height are 6–8% for offshore and 10–12% over land. However, this may not result in reduced loads on offshore wind turbines due to high levels of wake-generated turbulence in large wind farms (Barthelmie et al. 2007). Because ambient turbulence is low and the atmosphere more stable, ambient flow does not help on wake mixing, resulting in more resilient wakes. It is recognized (Jacquemin et al. 2010; Sanderse 2009) that wake effects play a major role in fatigue loading of turbines and their support structures.

3. Wake models selection 3.1. Types and requirements As it was introduced in Section 1.2, wake models range in complexity from solving the actual flow governing equations, to semi-analytical models and simple empirical relations. The complexity of such models translates to computational expense and, thus, their application. The most complicated model are used to study wake behavior and validate other —simpler— models but they are certainly not suited for optimization purposes since a ten minute simulation time can take up to several hours using parallel computing. The less complex models are suited to estimate some wake characteristics in wind farms and, thus, are common in wind farm tools. In general, the choice of a suitable model depends on three factors: the desired computational time, the necessary accuracy of prediction, and the available wind modeling parameters (González-Longatt et al. 2012). For a review of all wake models and their fundaments the reader is referred to (Crespo et al. 1999; Thøgersen 2005).

In the scope of this work, the wake model (or models) need to comply with the following requirements:

 Low computational cost; straightforward equations without convergence algorithms.  Models should preferably provide average quantities over the rotor area rather than azimuthal distributions.  Have the most possible number of parameters function of design variables, for instance: wind turbine separation, rotor diameter, thrust coefficient or tower height.  The model and the method to apply needs verification backup against measurements or by means of other more complex models.  Input parameters need to be simple and representative enough as the ones obtained from high level site assessments; such as wind speed profile and mean ambient turbulence.  Be able to account for multiple wakes and large wind farm effects.  The model outputs need to be able to relate to fatigue evaluation.

Wake models are commonly separated in wake wind speed deficit models —or just “wake models”— which account mainly for the wind speed reduction in wakes and in turbulence models which estimate the rest of the wake characteristic parameters, mainly turbulence intensity. Since turbulence depends on wind speed, it is necessary to use a wind speed deficit model in conjunction with turbulence models, as opposed to if one is only interested in calculating wind farm efficiency where only reduced wind speed is of importance.

Bearing the necessary requirements for this work there are not many models to choose from. This is possibly due to the huge endeavor that represents the analysis of real wind farm data and the scarcity of measurements; two simple wind characteristics, speed (from 5 to 25 m/s) and direction (360 degrees), explode the number of data points that need analysis. The most relevant models are chosen from to main sources:

i) Risø National Laboratory: “Turbulence and turbulence generated structural loading in wind turbine clusters” is a PhD. thesis by S. Frandsen published in 2007 (Frandsen 2007). A simplified turbulence model from this research is given as a recommendation to deal with wake effects in wind farms in the IEC latest standards (IEC-61400-1 2005). ii) European Wind Turbine Standards (EWTS II); the report is intended for consideration in the wind industry standards and results from the JOULE programme (project for R&D of the

European Commission) in their subproject “Load Spectra and Extreme Wind Conditions/Wind Farms-Wind Field and turbine loading” (Larsen et al. 1998). It includes models to estimate all main turbulence parameters. iii) The modified Jensen model in reference (Katic et al. 1986) is commonly used to calculate wind speed deficit in wind farm tools.

3.2. Wind speed deficit models 3.2.1. Overview Wind speed deficit models, also called just “wake models”, deal with the reduced speed phenomena behind wind turbines. The phenomena was explained in Section 2.2 as a result of the energy extraction process of the rotor. Most wind speed deficit models depend on flow characteristics (wind speed and ambient turbulence), upstream turbine operational settings (rotor diameter and thrust coefficient) and downstream distance of interest (wind turbine spacing).

3.2.2. Single wake models The Jensen wake model is a single wake model in which the dimensionless wind speed deficit (1- Uw/U0) is subject to the assumption of a linearly increasing wake diameter with expansion coefficient “k” (onshore 0.075 and offshore 0.050). The wind speed deficit in this model as:

푈푤 1 − √1 − 퐶푇 1 − = 푈 2푘푥 2 0 (1 + ) 퐷푅 EQ. 3-1 Where:

U0 is the free stream wind speed at hub height

Uw is the average wind speed in the wake at certain axial distance “x”

DR is the wind turbine rotor diameter s = x/DR is the spacing between upstream and downwind turbines, expressed in rotor diameters

CT is the turbine’s thrust coefficient k is the wake expansion coefficient

Additionally other wake parameters that derive from Jensen model are: 1 Wake radius at “x” position, Rw, is: 푅 = (퐷 + 2푘푥) 푤 2 푅 1 And the characteristic view angle, w, is: 휃 = 푎푡푎푛 ( ) + 푎푡푎푛(푘) 푤 푠

The Larsen wake model is a semi analytical model derived from Prandtl’s rotational symmetric turbulent boundary layer equations. The Larsen wake model presented in Eq. 3-2 has the following features:

 The model states that the minimum turbulence intensity is 5 % and essentially states that the wake expansion is dominated by ambient turbulence.  Includes a simple modification to include the blocking effect from the ground.

3 2 1 3 1 10 1 푈0 − 35 − ∆푈 = 푈 − 푈 = − (퐶 퐴 (푥 + 푥 )−2)3 [푟2(3푐 2퐶 퐴 (푥 + 푥 )) 2 − ( ) (3푐 2) 5] 푤 0 9 푇 푅 0 1 푇 푅 0 2휋 1

EQ. 3-2

In which: 1 35 5 1 1 Rw is the wake radius at “x” position 푅 = ( ) (3푐 2)5(퐶 퐴 (푥 + 푥 ))3 푤 2휋 1 푇 푅 0

1 + √1 − 퐶푇 Deff is the effective diameter 퐷푒푓푓 = 퐷√ 2√1 − 퐶푇 5 1 − 2 2 5 퐷푒푓푓 105 − c1 is a non-dimensional mixing length 푐 = ( ) ( ) (퐶 퐴 푥 ) 6 1 2 2휋 푇 푅 0 9.5퐷푅 푥0 = x is an approximation parameter 2푅 3 0 ( 9.5) − 1 퐷푒푓푓

Empirical boundary condition applied at 9.5 푅9.5 = 0.5(푅푛푏 + 푚𝑖푛⁡(ℎ, 푅푛푏)) rotor diameters where Rw = R9.5 푅푛푏 = 푚푎푥⁡(1.08퐷푅⁡,1.08퐷푅 + 21.7퐷푅(퐼푎 − 0.05)

Where h is the wind turbine hub height, AR is the rotor area and Ia is the ambient turbulence intensity at hub height.

The output wake velocity in the Larsen model yields a velocity field dependent on azimuthal position. To average this wind field over the rotor field a squared momentum deficit is used as in reference (Thøgersen 2005), as follows:

2 1 2 (푈0 − 푈푅) = ∫(푈0 − 푈푤) 푑퐴 퐴푅 EQ. 3-3

Where UR is the averaged wind speed at the rotor.

3.3. Turbulence models 3.3.1. Turbulence summation rule To quantify turbulence levels it is common practices to account ambient turbulence (free stream flow) and turbulence generated from wind turbines separately and then merge them by means of sum of squares. It is assumed that only the surface (ambient turbulence, Ia) and the wake shear (turbine) mechanisms contribute significantly to the turbulence production. Furthermore, it is assumed that these two sources are statistically independent such that the turbulence energies are additive in the energy sense. For practical purpose, turbulence intensity is normalized with respect to undisturbed mean wind velocity. As a result, to obtain the turbulence intensity in the wake, Iwake, the following expression is most used:

2 2 퐼푤푎푘푒 = √퐼푎 + 퐼푤푡_푎푑푑

EQ. 3-4

Where Iwt_add is the extra turbulence intensity generated by a wind turbine.

3.3.2. Atmospheric turbulence Atmospheric turbulence measurements are often carried out as part of site assessment studies in which turbulence can be represented by statistical means. When only average wind speeds are available, ambient turbulence can be estimated by means of the surface roughness; roughness values dependent on the surface type (e.g. land or offshore) are found in literature or, in case of offshore sites, sea roughness can be related to wind speed (Türk & Emeis 2010). Moreover, for design purposes, a more robust model is desired. The IEC model (IEC-61400-1 2005) is based on the site type and mean wind speed at hub height. The IEC normal turbulence model (presented below) gives the design turbulence as the 90% quantile for the hub height wind speed; statistically 90% of the actual occurring values will be lower than the design turbulence intensity.

1 퐼푎 = [퐼푟푒푓(0.75푈ℎ푢푏 + 5.6)] 푈ℎ푢푏 EQ. 3-5

Where Iref is the expected value of the turbulence intensity at 15 m/s for the wind site class. Wind classes are categorized by turbulence levels as A, B and C which correspond to a reference turbulence intensity of 0.16, 0.14 and 0.12 respectively.

Additionally, the IEC standards allow assuming a log-normal distribution if other quantiles are desired for additional optional load calculations. By using the following expected value of the standard deviation of wind speed and its variance:

퐸⟨𝜎푢|푈ℎ푢푏⟩ = 퐼푟푒푓(0.75푈ℎ푢푏 + 3.8) 2 푉푎푟⟨𝜎푢|푈ℎ푢푏⟩ = (퐼푟푒푓(1.4)) EQ. 3-6

3.3.3. Wind turbine added turbulence The Larsen turbulence model is a simple empirical equation to determine the turbulence intensity level within the wake. The model is based on the maximal change in a standard deviation profile (which is usually associated with the upper part of the rotor plane) implying a slight conservatism. The model has the following features:

 The expression is only valid for distances greater than 2DR.

 Asymptotic feature as turbulence intensity increase with increasing CT and decrease with increasing S.

The Larsen turbulence model provides the additional turbulence intensity, Iwt_add, caused by an upwind turbine with thrust coefficient CT, at distance equal to sDR. The equations is presented here:

1 − 퐼푤푡_푎푑푑 = 0.29푠 3√1 − √1 − 퐶푇

EQ. 3-7

The Frandsen turbulence model is also an empirical expression that fits large amounts of data and its shape is inspired by an analysis of closely spaced turbines. The expression shown here is actually an intermediate equation from the one used in the IEC standards. The expression presented here does not assume a general thrust coefficient curve function of wind speed, such that CT = 7/U. Mainly because, as

15 stated in the requirements, it is of interest to relate turbulence intensity with turbine parameters. Moreover, Frandsen provides in his work “Section 7: Verification” an alternative model that provides approximately the same turbulence intensity for low wind speeds and less turbulence for high wind speeds. Frandsen states that the alternative model would better fit the verification data and would be less conservative at high wind speeds. Being the two Frandsen turbulence models as follows:

1 1 퐼푤푡_푎푑푑 = 푠 ⁡; ⁡⁡⁡⁡⁡⁡⁡푎푙푡푒푟푛푎푡𝑖푣푒⁡푚표푑푒푙:⁡⁡⁡퐼푤푡_푎푑푑 = 푠 1.5 + 0.8 1.5 + 0.8 퐶 √퐶푇 푇 EQ. 3-8

3.3.4. Turbulence profile shape When a wind turbine is in partial wake operation it will experience an alternating load on the rotor blades. The turbulence models presented above provide an average turbulence intensity which is valid for full wake operation. For partial wake operation the description of the turbulence profile becomes important, for instance where is the maximum and minimum turbulence within the wake. In reference (Frandsen 2007), based on the study conducted in reference (Vermeer et al. 2003), Frandsen concludes that assuming a bell-shaped profile with the maximum turbulence in the center of the wake is appropriate.

2 휃 1 180 1 ∘ 퐼 = 퐼푎 [1 + 훼 ∙ 푒푥푝 (− ( ) )] 휃푤 ≅ ( tan ( ) + 10 ) 휃푤 2 휋 푆 EQ. 3-9 EQ. 3-10

Where Ia is the ambient turbulence,  is the angle between the connection line of the two wind turbines and the wind direction and w is the characteristic view angle of the wake-generating unit, seen from the affected turbine (this is deduced by means of the wake width). The constant  is obtained by using the 2 2 2 basic concept of squared summation for added and ambient turbulence, Iwake = Iwt_dd + Ia , to obtain the maximum and the bell-shaped turbulence profile, the maximum turbulence in the center of the wake is:

퐼 2 2 2 푤푡_푎푑푑 퐼푇 = 퐼푎(1 + 훼) = √퐼푤푡_푎푑푑 + 퐼푎 ⁡⁡⁡⁡⁡⁡⁡⁡⁡ ⟹ ⁡⁡⁡⁡⁡훼 = √( ) + 1 − 1 퐼푎 EQ. 3-11

Frandsen concludes that despite the lack of convincing theoretical background the approach fits data fairly well for a broad range of separations. The hypothesis is that for a given mean wind direction, , the turbulence intensity experienced in the center of the wake-affected rotor applied over the whole rotor yields approximately the same response as if applying the spatially distributed turbulence intensity. The conclusion is also shared in the study presented in reference (Larsen et al. 1998).

3.3.5. Increased ambient turbulence in wind farms An interesting feature of the Frandsen model is the ambient wind farm turbulence. Inside a large wind farm no wind direction offers a flow that is unaffected by wind turbine wakes but the previous models only account for single upstream turbines. To account for this effect in large wind farms, Frandsen introduces the concept of ambient wind farm turbulence. The problem is approached by considering wind turbines as roughness elements. By obtaining the wind vertical profile above the wind farm and another below the wind turbine rotors (which correspond to ambient flow), the ambient wind farm turbulence is obtained by means of an average between those two wind flows. To apply the correction, Frandsen provides the following guidelines:

 The derivation must be considered as an average of direct wakes and partial wakes.  It is suggested to use it for wind turbines embedded in more than 5 rows and if the distance

between turbines in rows perpendicular to the predominant wind direction is less than 3DR.

* The corrected ambient wind farm turbulence, Ia , and the added turbulence by the wind farm, Iwf_add, are:

1 0.36 ∗ 2 2 퐼 = (√퐼 + 퐼 + 퐼 ) 퐼푤푓_푎푑푑 = 푎 2 푤푓_푎푑푑 푎 푎 푠 푠 1 + 0.2√ 푓 푟 퐶푇 EQ. 3-12 EQ. 3-13

Where sr is the distance between wind turbines within the row and sf is the distance between rows. 3.3.6. Test example To gain understanding about the models and sense of magnitude about the values, see Figure 3.3-1 below. The left hand-side plot shows wind speed deficit for both models, only one line is presented for the Jensen model since only a constant wake expansion factor is considered. They both show the desired characteristics: a very high jump in speed close to the rotor and an asymptotic speed recovery. The Jensen model is more conservative for closer distances and both perform similar for very large distances. The Larsen model shows the right behavior for different ambient turbulence intensities. As it is expected, higher turbulence increases the mixing process in the wake with the undisturbed surrounding flow, thus accelerating wind speed recovery.

In the Figure 3.3-1, a calculation for wind speed deficit and increased turbulence for a certain condition is presented as a function of downstream distance from a wind turbine. If another turbine were placed, for instance, in 8D from this turbine, it would experience about 10% less wind speed and 20% more turbulence intensity than the original flow. Moreover, if the newly placed turbine were embedded deeply in a wind farm (e.g. more than 5 row from the edges) it would experience a “wind farm ambient turbulence” (in the figure, black dotted curve) and wake conditions from its surrounding wind turbines. This would result in even higher turbulence intensity levels (in figure, magenta line with markers) of about 0.18 for this case, causing an increase of 40% from the original flow during wake conditions.

1 0.35 Iwake Larsen 0.95 Iwake Frandsen Iwake(alt) Frandsen 0.9 0.3 Iwake + Ia*

0.85

/ U ) [-] ) U /

 0.8 0.25

0.75 0.2 0.7

0.65 Larsen model 0.15 Jensen model k=0.04 Ia*

Wind speed deficit ( Uw/Uo ) [-] Uw/Uo ) ( deficit speedWind 0.6 ( TurbulenceIntensity Larsen model Ia=0.08 0.55 Larsen model Ia=0.10 Ia Larsen model Ia=0.16 0.1 0.5 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16 Downstream distance ( x/D ) [-] Downstream distance ( x/D ) [-] FIGURE 3.3-1 WAKE MODELS COMPARISON AS A FUNCTION OF DOWNSTREAM POSITION: (LEFT) WIND SPEED DEFICIT, (RIGHT) TURBULENCE MODELS. TURBINE: D = 100 M., CT = 0.57. AMBIENT WIND FLOW: U0 = 10 M/S, IA = 0.13.

3.3.7. Selection Both of the wind speed deficit models, Jensen and Larsen, are function of desirable variables such as separation and thrust coefficient. Since the purpose of this work is not about wind farm efficiency, the difference in the results (e.g. see Figure 3.3-1) are considered not important. Moreover, the computational time needed for the Larsen model is higher due to the integration needed in Eq. 3-3. Therefore the Jensen model in Eq. 3-1 is used.

Regarding turbulence models, the difference between the Larsen and Frandsen model are considerable and important in the scope of this work. The Frandsen model is chosen for two reasons: (1) it is more conservative for separations below 10D which are considered more used in the industry. (2) Frandsen developed additional formulations desirable for this work, such as: a scheme to account for partial wakes, correction for large wind farms and the concept of effective turbulence (which is a core concept in this work and is treated in Chapter 4). Therefore, the turbulence model used is the turbulence Gaussian profile in Eq. 3-9, where the ambient turbulence is the one recommended by the IEC standards in Eq. 3-5 and the wake added turbulence is the standard model in Eq. 3-8. Furthermore, the correction for large wind farms in Eq. 3-12 and Eq. 3-13 is used.

4. Turbulence and Fatigue 4.1. Basic fatigue concepts Fatigue damage is caused when a material sample or structural component is exposed to repeated, cyclic loading. It starts with small micro cracks that continue growing into large cracks until failure occurs. Characterization of the fatigue damage depends on material properties, stress range, mean stress and the number of load cycles. By probing a certain material sample under a constant load range (amplitude) until failure, it is possible to derive a stress range Sfat versus number of cycles until failure nfat (S-N curve or Wöhler curve) that characterize fatigue damage for that particular material. On a double logarithmic axis graph the S-N curve is, in general, a straight line with a negative slope.

1 1 푝표푤푒푟⁡푙푎푤 −⁡ 푙표푔(푆 ) = − ⁡푙표푔(푛 ) + 푙표푔(푎)⁡⁡⁡⁡→ ⁡⁡⁡⁡푆 = a ∙ 푛 푚 푓푎푡 푚 푓푎푡 푓푎푡 푓푎푡 EQ. 4-1

In the fatigue power law, a and m are material constants. The inverse slope of the logarithmic line or the power exponent m in the power law is called the Wöhler exponent and it is for steel in the order of 3 - 5 and for fiber glass in the order of 10 - 12.

When a component is subjected to different stress ranges, the total fatigue damage (DT) can be estimated by means of the Miner’s rule. The simple rule states that the sum of all partial damage caused by each stress range is equivalent to the total fatigue damage experience by the component and if the total damage exceeds 1, failure will occur. The partial damage for a specific stress range is the ratio of the number of cycles experienced (ni) divided by the maximum number of cycles until failure (nfat), both, at the specific stress range (Si):

푁 푛푖(푆푖) 퐷푇 = ∑ < 1 푛푓푎푡(푆푖) 푖 EQ. 4-2

Moreover, it is very useful to summarize all the different load ranges and their number of cycles by using m the concept of an equivalent stress range. This is based on the fact that the product nx Sx is constant, therefor there must be an equivalent stress range Seq at a reference number of cycles nref (or vice-versa) m that caused the same damage as the sum of all individual ni Si products.

푁 푚 푚 푛푟푒푓푆푒푞 = ∑ 푛푖푆푖 푖 EQ. 4-3

The number of cycles experienced for every stress range level is usually obtained by means of “rainflow counting” method or field measurements. Alternatively, it can be estimated by probabilistic means by assuming that the stress ranges are Weibull distributed (Sørensen et al. 2008a) or, in case of turbulence generated fatigue, with the use of the effective turbulence concept (Frandsen 2007), as explained in the following sections.

4.2. Turbulence generated fatigue loading in wind turbines 4.2.1. Literature relevant conclusions Fatigue loads on a wind turbine are a combination of periodic deterministic loads (e.g. gravity and mean wind speed) and stochastic loads caused by turbulence. It is well accepted that turbulence generated fatigue loading is dominant, compared with deterministic loads (Larsen et al. 1998; Frandsen 2007) and the dynamic response of wind-exposed structures is strongly correlated to wind speed fluctuations. Other important findings about fatigue damage are:

 The modified wake turbulence field is generally characterized by an increase turbulence intensity, a decrease turbulence length scale and an increase in the coherence decay. Moreover, no significant qualitative modifications in the spectral shape is recognized.  All four parameters (wind speed deficit, turbulence intensity, length scale and coherence) are demonstrated to be in relation to fatigue life consumption and act additively. However, the effect originated from increased turbulence intensity dominates the other parameters by a factor of 2-3.  Partial wake operation does not represent a significantly more severe fatigue loading than full wake operation.  Double wake situations mainly differ from single wake situations by increasing further wind speed deficit but the turbulence field is only marginally modified.

4.2.2. The proportionality between equivalent load and turbulence The effect of turbulence on the wind turbine —or any wind exposed structure— can be simply demonstrated by considering the forces acting on the structure as a function of wind speed, in which the wind speed is decomposed in a mean wind speed term and a turbulent part. For instance the drag force on a body can be expressed as:

1 퐹 = 휌풖2퐴퐶 ,⁡⁡⁡⁡푤ℎ푒푟푒⁡풖(푡) = 푈 + 푢̅(푡) 2 퐷 1 퐹 = 휌(푈2 + 2푈푢̅ + 푢̅2)퐴퐶 2 퐷 EQ. 4-4

Where F is the drag force,  is the air density, A is the area exposed to the flow, CD the drag coefficient and u(t, z) is the instantaneous wind speed. The instantaneous wind speed is further expressed by a no-time dependent mean wind speed U and a turbulent part ū. To make the drag force linear with respect to ū and since ū is small (thus ū2 is smaller) then the force can be approximated as:

1 퐹(푡) ≈ 휌퐴퐶 푈2 + 휌퐴퐶 푈푢̅(푡) 2 퐷 퐷 EQ. 4-5

Assuming a constant fixed value  for the turbulent part of the flow ū(t), which is by definition the standard deviation of the wind speed, such as u(t) = U ± .

1 퐹 ≈ 휌퐴퐶 푈2 + 휌퐴퐶 푈𝜍 +𝜍 2 퐷 퐷 1 퐹 ≈ 휌퐴퐶 푈2 − 휌퐴퐶 푈𝜍 −𝜍 2 퐷 퐷 EQ. 4-6

Therefore, and in the interest of turbulence induced fatigue loading, the force range that the body will experience under this particular turbulent condition is ⁡퐹 ≈ 2휌퐴퐶퐷푈𝜍 . Hence the load range is proportional to turbulence. Based on this principle, reference (Veldkamp 2013) presents the results in Figure 4.2-1. In this result, the fatigue damage caused by the blade root flap moment is presented as equivalent load range versus turbulence (standard deviation of the wind speed); the results are for all wind speeds and then sorted by turbulence. In Figure 4.2-2 reference (Frandsen 2007) presents similar results, based on measurements, but differentiating among wind speeds. The results are presented as the ratio of equivalent flap-wise bending moment (m=5) and the standard deviation of the response fluctuations (which is associated with turbulence) versus wind speed. Furthermore the occurred turbulence intensity is between 0.07 and 0.11.

FIGURE 4.2-1 EQUIVALENT LOAD RANGE (BLADE ROOT FLAP-WISE BENDING MOMENT) AS A FUNCTION OF TURBULENCE (STD. WIND SPEED).

The approximated proportional relation between equivalent load and turbulence is clear in the results presented in Figure 4.2-1. Where the fitted lines yield correlation coefficients above 0.9. In these particular results, the effect of the material’s Wöhler exponent, as explained in Section 4.1, is appreciated.

FIGURE 4.2-2 RATIO OF EQUIVALENT LOAD RANGE (BLADE ROOT FLAP-WISE BENDING MOMENT, M=5) TO STANDARD DEVIATION OF THE SAME QUANTITY, AS A FUNCTION OF WIND SPEED.

In Figure 4.2-2 the results add the wind speed dimension. For a particular wind speed the ratio between the equivalent load and its standard deviation is fairly constant disregarding the different turbulent conditions; supporting the proportionality argument between equivalent load and turbulence. In this case, the picture changes for different wind speeds, although it seems to be valid for certain wind speed ranges and the ratio lays between only two levels (around 3 and 4). The author reasons that the increasing ratio with increasing wind speed indicates that the equivalent load is more sensitive to the frequency-scale of turbulence (which increases with wind speed) than the standard deviation of the load. Based on these results it is best to say that for a fixed mean wind speed: the standard deviation of the response is proportional to the standard deviation of the wind speed, given that the equivalent load is proportional to the standard deviation of the response, therefore the equivalent load is proportional to turbulence intensity.

As mentioned in the beginning of this section it is expected that the equivalent load is also function of other turbulence characteristics, such as length scale. Other sources of dynamic loading are vertical and horizontal shear of the mean flow. All these sources act approximately additively (Larsen et al. 1998). Therefore (Frandsen 2007) gives a function for the response in terms of equivalent load:

휕푒 푒(푈, 휃) = 훼 𝜎 + 훼 𝜏 + 훼 𝜏 + 훼 푓,⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡훼 = 𝜎푢 푢 𝜏 푤 푤 푓 ∗ 휕(∗) EQ. 4-7 푔 = 푔(𝜎푢, 𝜏, 𝜏푤, 푓|푈, 휃)) EQ. 4-8

Where e(U,) is the equivalent load, u is the standard deviation of the wind speed,  is the vertical mean shear, w is the wake induced mean wind speed deficit (horizontal shear), f is the frequency-scale of turbulence. All are a function of mean wind speed U and wind direction . The quantities * are the sensitivities coefficients of the respective variables. The function g is the conditional joint probability density function of the input variables. The author conducts an experimental approach to estimate the values and behavior of the sensitivity coefficients using data from Vindeby, Middelgrunder, Alsvik and other wind turbines exposed to wakes. The finding are that the ranges of variation are approximately the same and therefore the magnitudes of the sensitivity coefficients also indicate the relative load-wise

22 importance of the variables. In turn, Frandsen reports that the turbulent fluctuations weigh approximately 3 times more than vertical ambient flow shear and wake mean deficit. It is also noted a tight relationship between response and turbulence also under wake conditions. The study supports the notion of the equivalent load being fairly represented only by means of the standard deviation of the wind speed at a fixed mean wind speed. The equivalent load is then:

푒(푈, 휃) = 훼𝜎푢(푈) ∙ 𝜎푢,푒푓푓(푈, 휃) EQ. 4-9

Where u,eff is the “effective standard deviation”. To account for the material properties, under the concept of the Wöhler exponent, the standard deviation of the wind speed is first raised to the power of m, then is weighed by its PDF and integrated over all u; the result is finally raised back to the inverse power of m. In this sense, u,eff is the fixed standard deviation of wind speed that causes the same fatigue as the varying quantity.

1 ∞ 푚 푚 𝜎푢,푒푓푓(푈, 휃) = [∫(𝜎푢(푈, 휃)) ∙ 푔(𝜎푢|푈, 휃))⁡푑𝜎푢] 0 EQ. 4-10

Frandsen also provides another, more common representation, by means of the “effective turbulence intensity, Ieff” and the wind direction distribution fwd( U). In which the integrated equivalent load conditioned to wind speed U is:

푒(푈) = 훼𝜎푢 ∙ 푈 ∙ 퐼푒푓푓(푈) EQ. 4-11 Where the effective turbulence intensity is defined by Frandsen as:

1 180 푚 푚 𝜎푢,푒푓푓(푈, 휃) 퐼 (푈) = [ ∫ ( ) ∙ 푓 (휃|푈))⁡푑휃] 푒푓푓 푈 푤푑 −180 EQ. 4-12

Under this approach, the effective standard deviation of the wind speed, is more related to equivalent fatigue damage than to the physical turbulence property of the flow. This becomes clearer by using the concept of equivalent stress presented in Section 4.1, where the following derives:

푈표푢푡 푈표푢푡 푚 푚 푚 ∑ 푛푖 ∙ (훼𝜎푢(푈) ∙ 푈 ∙ 퐼푒푓푓(푈)) = ∑ 푛푖 ∙ 푒푖(푈) = 푛푟푒푓푒푒푞 푖=푈푖푛 푖=푈푖푛 EQ. 4-13

Where ni is the number of cycles experienced at a given wind speed and nref is an arbitrary number of cycles chosen as reference for the life time of the component.

For this work, the relation needed is that between the equivalent load in the support structure bending moment and turbulence. Unfortunately, the information is not readily available on published literature and obtaining such sensitivity coefficient from aeroelastic simulations is out of the scope of this thesis work. Instead, other approach to estimate the equivalent load from turbulence is to assume the response Weibull distributed (Sørensen et al. 2008a). In Sørensen et al. 2008a the mud-line bending moment data

23 for a typical pitch regulated wind turbine is available. The data is given as the ratio between the standard deviation of the stress range (U) and the standard deviation of wind speed u(U), presented in Figure 4.2-3. Therefore, according to Sørensen et al., the stress ranges can be assumed Weibull distributed with a shape coefficient between 0.8 and 1.0 given the standard deviation of the stress range.

FIGURE 4.2-3 RATIO BETWEEN THE STD. DEVIATION OF THE STRESS RANGE AND THE STD. DEVIATION OF WIND SPEED FOR MUD-LINE BENDING MOMENT; FOR A PITCH REGULATED WIND TURBINE (Sørensen et al. 2008a).

훼Δ𝜎(푈) 𝜎 (푈) = ∙ 𝜎 (푈) Δ𝜎 푧 푢 EQ. 4-14

Where (U) is the influence —or sensitivity— coefficient for stress ranges given the mean wind speed U and z is a design parameter proportional to the cross sectional area. Thus, the ratio (U) /u(U) is equivalent to the ratio (U)/z. Moreover, the equivalent load, e(U), is the product of  (U)z.

The ratio can be used to obtain the PDF of the stress range  given its standard deviation (obtained from

Figure 4.2-3 and turbulence), conditioned to wind speed, f. Further the expected value raised to the Wöhler can be obtained using the expected value definition, EQ. 4-15, to be used in EQ. 4-13.

∞ 푚 푚 퐸{Δ𝜎 } = ∫ 푠 푓Δ𝜎(푠|𝜎Δ𝜎(푈)) 푑푠 0 EQ. 4-15

Additionally, the effective turbulence has to account for wake effects according to the turbine position within the wind farm. This in order to represent its specific fatigue damage and to obtain a representative equivalent load for such turbine’s support structure.

4.2.3. Contribution from wakes To account for wake exposure in clusters, the Gaussian bell shape turbulence model for increased turbulence behind wind turbines IT, presented in Section 3.3, is applied to the effective turbulence conditioned on mean wind speed but not conditioned on wind direction. This provides the effective turbulence model used in this work. Furthermore, the wind speed to obtain IT for each wind turbine is the reduced wind speed caused by wakes obtained from Jensen wind speed deficit wake model.

1 360 푚 푚 퐼푒푓푓(푈) = [∑(퐼푇(휃푗|푈)) ∙ 푓푤푑(휃푗|푈) ∙ 푑휃] 푗=0 EQ. 4-16

Therefore, the total equivalent load caused by ambient turbulence and added turbulence from wakes can be obtained from the fatigue damage concept:

푈표푢푡 푚 푚 ∑ 푓푤(푈) ∙ (훼𝜎푢 ∙ 퐼푒푓푓(푈) ∙ 푈) ∙ 푑푈 = 푛푟푒푓푆푒푞 푈=푈푖푛 EQ. 4-17

푘−1 푘 푓푤(푈|퐴푗, 푘푗)푓푗 푘 푈 푈 푓푤푑(휃푗|푈) = 푁−1 푓푤(푈) = ( ) 푒푥푝 (− ( ) ) ∑푖=0 푓푤(푈|퐴푖, 푘푖)푓푖 퐴 퐴 퐴 EQ. 4-18 EQ. 4-19

Where Uin and Uout are the cut-in and cut-out wind speeds respectively and fw is the wind speed Weibull probability density function with global shape parameters A and k or wind direction dependent Ai and ki.

The wind direction joint probability formulation, conditioned to wind speed, fwd is obtain from reference

(Nielsen et al. 2009) where fi is the frequency of occurrence dependent on the wind rose distribution and N is the number of wind direction bins.

Finally, the integrated turbulence intensity over all wind speeds is a concept adopted by (Frandsen 2007) known as turbulence fatigue life and can be used as a measure of fatigue damage, as follows:

1 푈표푢푡 푚 푚 퐼푙푖푓푒 = ( ∫ 푓푤(푈) ∙ 퐼푒푓푓(푈)⁡푑푈) 푈푖푛 EQ. 4-20

4.2.4. Remarks Even though the models presented above for turbulence intensity and fatigue damage were conceived under many assumptions and uncertainties, Frandsen states that they fit measurements fair enough with deviations towards conservationism. Such models provide an analytical, fast and safe way to estimate fatigue loads on wind farms; qualities that are always desirable for design purposes. Furthermore, the model are chosen given that, in this work, it is not intended to calculate the different variables of interest with precision but rather provide a qualitative approach to compare different cases and yield insights about the relations between them.

5. Qualitative support structure design 5.1. Support structure scope There are a number of support structure configurations for offshore wind farms and the choice is in general driven by the site water depth and cost. Monopile structures are the most common solution at the moment because such a relatively simple construction has fabrication and installation benefits. In the limited scope of this work, monopiles have also the advantage of having limited design parameters and wider range of published studies. Therefor it is chosen herein as the support structure for this thesis work. Moreover, it is not intended to develop or use a complete method to design the structure rather to use a simplistic approach to gain insight in how support structure design and cost are affected by turbulence caused by wakes.

The general components of the considered support structure are the tower, transition piece and monopile (or foundation pile), see Figure 5.1-1 below.

FIGURE 5.1-1 OFFSHORE WIND TURBINE MAIN COMPONENTS, MODIFIED FROM (Van Der Tempel 2006).

5.2. General overview of the design process In general, the design should aim to sustain the loads that the structure will experience during all temporal, operating and adverse conditions. Furthermore, it should ensure an acceptable safety and have proper durability against deterioration during the design lifetime of the structure. Experience gained in the industry has identified that the sizing of the structure is governed by three key factors:

 Resistance to extreme loads.  Resistance to fatigue loads.  Tuning of support structure natural frequency to avoid excitation by cyclic loading.

The designer follows the industry standards to ensure the structure complies with the above key factors. Since fatigue and natural frequency depends on the dynamics of the structure and this, in turn, depends on the stiffness distribution, the process becomes iterative. Therefore, it is simpler to develop an initial design based on resistance to extreme loads which can then be used to obtain the structures dynamics and then evaluate fatigue loads. The designer also encounters other challenges such as structural buckling, foundation stability or manufacturing restrictions.

To account for all the possible loads that a wind turbine will be subject to during its lifetime, designers summarized the possible scenarios representing ultimate, fatigue and other special cases into load cases. The damage caused by each load case are accounted together by weighing them using its probability of occurrence (unique, rare or operational events). The collective damage is then estimated and is a key parameter to decide whether the design is acceptable or not. In Chapter 4 it is described a simple method to determine the fatigue damage caused by turbulence.

5.3. Design drivers In the general case, a range of factors, including the relative magnitude of extreme and fatigue loads, the critical fatigue detail category and the monopile wall slenderness (diameter and wall thickness ratio), will determine whether extreme or fatigue loads govern at different heights in the structure. For offshore support structures, in practice extreme load cases tend to govern the embedment depth and fatigue tends to govern other dimensions, such as wall thickness (Burton et al. 2001; Jacquemin et al. 2010). The other key design driver is the restriction on support structure natural frequency.

The main loads come from the gravitational, aerodynamic, hydrodynamic and sea ice loads. For support structures wave loading is very important in terms of ultimate and fatigue states but in wind farms, wave loading is fairly equal among all positions. Since this work is aimed at the load difference across the wind farm positions for comparison purposes, wave loading is assumed constant and therefore not directly taken into account.

5.4. Design approach for this work To assess the influence of turbulence on the support structure design, the support structure design proposed in this thesis is assumed to be mainly driven by fatigue. A base design, considering ambient turbulence, is obtained by general design rules and three main load cases in the same way as (Zaaijer 2013). Subsequently, the base design will be exposed to the increased turbulence and its components’ wall thicknesses adjusted to endure the increased fatigue loads while keeping its diameter unchanged.

The loads for the base design are obtained from three main load cases by using an analysis of the static response only. These load cases are:

 Operation, rated wind speed, maximum wave in 1 year extreme sea state  Parked, reduced gust in 50 year averaged wind speed, maximum wave in 50 year extreme sea state  Parked, maximum gust in 50 year averaged wind speed, reduced wave in 50 year extreme sea state

The load case to obtain the equivalent fatigue load is:

 Operation, wind speed between cut-in and cut-out according to PDF, turbulence according to ambient and wake exposure and normal sea state

5.5. Base design general dimensions The most important design parameters of monopile support structures are its components’ length, diameter and wall thickness and their relative position to water depth, mean sea level, highest wave height and blade tip clearance. The general dimensions and rules presented in this section are derived from (Zaaijer 2013) in which the author follows knowledge based engineering rules, design standards and constraints. Furthermore, Zaaijer is the author of the design work-frame used in this thesis, that is, the wind farm design tool “TeamPlay”.

5.5.1. Tower Given that in offshore climates, the wind shear profile is less pronounced due to low sea roughness, in practice tower length is set to the minimum allowed by constraints. The clearance between the blade tip and maximum sea level is set to 20 m with highest astronomical tide and the clearance between the blade tip and the platform, for safety reasons, is set to 4 m.

The tower top diameter has to cope with the yaw system in the RNA assembly, therefore the tower top diameter is set equal to the yaw bearing diameter and is an input from the RNA design. Moreover, the tower base diameter has to fit with the transition piece diameter (treated below).

The tower wall thickness per segment (maximum segment length of 2.4 m.) is determined by finding the thickness at which the maximum combined stress in the tower equals the critical stress for each of the three load cases. The largest of the three resulting wall thickness per segment is chosen. The combined stress and critical stress include the effects of axial loading, bending and buckling. The search for the wall thickness is formulated in TeamPlay as a root finding problem, by subtracting the combined stress from the critical stress.

5.5.2. Transition piece The platform height is set considering the maximum water elevation plus a margin for run-up of waves against the structure. The margin is set to 0.2 times the maximum wave height, with a minimum of 1 m. The bottom of the transition piece is set to either 6 m above seabed or below the lowest water elevation, whichever of the two is lowest. The overlap between the transition piece and the monopile has been related as 1.44 times the outer diameter of the monopile.

The transition piece diameter is set to be 300 mm larger than the outer monopile diameter. The wall thickness is determined in the same way as the tower wall thickness but differentiating for parts with only aerodynamic loading from parts with hydrodynamic loading. A stress concentration of 1.2 is applied to the bending moment in the overlap between the transition piece and the monopile.

5.5.3. Monopile The monopile length can be determined from the height of the transition piece base, the overlap length between the transition piece and the monopile and the monopile penetration depth.

The general consensus about foundation design is that lateral loading is much more important than vertical loading. The clamping depth is determined using a simple analytical ultimate strength model for laterally loaded foundation piles, the Blum model. Since Blum’s model assumes that clamping takes place at a singular point at the end of the pile, the penetration depth is taken to be 1.1 times the largest clamping depth that is found for the three load cases. Furthermore, the loads are divided by a safety factor on the bearing capacity of the pile of 0.8.

The monopile diameter is determined by finding the diameter at which the maximum stress in the pile is equal to the yield stress for each of the three load cases; choosing the resulting largest. It is assumed that the maximum stresses occur at mud-line level. The search for the diameter where the stress and yield stress equate is formulated in TeamPlay as a root finding problem, by subtracting the stresses.

The monopile wall thickness is made a function of its diameter according to the minimum allowed to avoid buckling during pile driving. The rule being, thickness = 0.0635 + 0.01*Diameter.

5.6. Support structure design adjustment for fatigue The base design, described in the previous section, is expected to endure ultimate load cases but the fatigue damage caused by wake effects is not considered. In this work, to account for such damage, the wall thickness in the support structure is increased accordingly to its wake exposure.

Firstly, it is assumed that the support structure wall thickness is driven by fatigue and that the base design is suited to handle the fatigue caused by ambient turbulence. Furthermore, it is assumed that there is a linear relation between equivalent load and turbulence dependent on mean wind speed; as explained in Chapter 4. Such relation can be obtain from a few aeroelastic simulations, from measurements or from publish data. In this study the data used is presented in Section 4.2.2 and comes from a published study in reference (Sørensen et al. 2008a).

The equivalent fatigue load, which in this case is the mud-line bending moment, for the site’s ambient turbulences is obtain. The load is then interpolated to all the tower sections. The equivalent bending moments are then applied to all the corresponding cross-sectional areas of the base design, to obtain the equivalent stresses caused by such turbulence level.

For the wind turbines of interest, inside the wind farm, their equivalent fatigue load is obtained in the same manner, according their specific wake regime. Then the equivalent stresses in each support structure of interest are compared with those obtain for the base design. The equivalent stresses in the support structures within the wind farm will be larger compared with the base design, which means that the wall- thickness on each support structure will have to increase to match the stress level of the base design, such that:

푆푁,푏푎푠푒 + 푆푇퐼,푏푎푠푒 + 푆표푡ℎ푒푟푠,푏푎푠푒 = 푆푁,푖 + 푆푇퐼,푖 + 푆표푡ℎ푒푟푠,푖 EQ. 5-1 Or in terms of equivalent loads: 푁푏푎푠푒 푀푇퐼_푏푎푠푒 푀표푡ℎ푒푟푠 푁푖 푀푇퐼_푖 푀표푡ℎ푒푟푠 + + = + + 퐴푏푎푠푒 푊푏푎푠푒 푊푏푎푠푒 퐴푖 푊푖 푊푖 EQ. 5-2

Where N is the gravitational force, MTI is the equivalent bending moment acting on the “base” design and on the “i” turbine, Mothers is the bending moment caused by other sources (e.g. thrust, waves), A is the cross-sectional area and W is the section modulus.

Based on the assumptions presented previously, the effect on the stresses caused by mass change is neglected and the other forces acting on the structure, than the response caused by turbulence, discarded (assuming the design is driven by fatigue). Then, the relation between the equivalent loads on a particular section in both structures is simply:

푊푖 푀푇퐼_푖 = 푀푇퐼_푏푎푠푒⁡ 푊푏푎푠푒 EQ. 5-3 휋 (푟4 − (푟 − 푡)4) 푊 = 4 푟 EQ. 5-4 1 4 4 4 4 푀푇퐼_푖 푡푖 = 푟 − [푟 − [푟 − (푟 − 푡푏푎푠푒) ] ] 푀푇퐼_푏푎푠푒 EQ. 5-5

The approximation below shows that, for an unchanged exterior geometry (r), an increase in equivalent load immediately signifies material consumption. For instance, if the equivalent load is up a factor of 2, then the wall thickness of the support structure in question must be doubled (Frandsen 2007).

3 푀푇퐼_푖 𝑖푓⁡푊 ≈ 휋푟 푡; ⁡푡ℎ푒푛⁡푡푖 ≈ 푡푏푎푠푒 푀푇퐼_푏푎푠푒

5.7. Cost model An appropriate choice for the support structure cost model in the framework of this thesis needs to capture the causal effects rather than be accurate in practice. The causal effect of study is the increased turbulence due to wakes which is expected to affect the support structure mass. Cost models based on mass for this kind of structures are considered useful in the industry (DNV-GL seminar, 2014) and is adopted by (Zaaijer 2013) in the wind farm tool TeamPlay . The tool considers most of the costs incurred by an offshore wind farm. It is not expected that other costs, such as installation or transportation, will vary considerably compared with cost variation in the support structure itself.

The support structure model used in TeamPlay considers: tower, transition piece, boat landing, grout, monopile and scour protection. The boat landing cost is fixed and the rest is a linear function of their mass. The relevant models per support structure are presented below:

TABLE 5-1 INVESTMENT COST MODELS PER UNIT (Zaaijer 2013) Tower [USD 2002] 2.04mass

Transition piece [Euro 2007] 3.75mass

Monopile [Euro 2007] 2.25mass

6. The coupled methods 6.1. Overview The previous chapters have explained that there is a link between both environmental flow characteristics and wind farm layout, and support structure design and cost. Furthermore, the link between them is the proportional relation between increased effective turbulence and equivalent fatigue load. The purpose of this chapter is to implement a method that estimates the effective turbulence intensity on each wind turbine within a given wind farm site and layout, to then obtain a tailored support structure design that withstands the increased fatigue loads.

As a tool to implement such method, this thesis work makes use of the wind farm design tool, TeamPlay by M. Zaaijer (Zaaijer 2013) from the Wind Energy Group at TU Delft. The tool calculates the wind speed distribution upon each wind turbine within the wind farm and also provides an initial support structure design. Furthermore, the tool also anticipates the Levelized Production Costs (LPC) of wind farms.

6.2. Implementation 6.2.1. Effective turbulence As explained in Chapter 4 the effective turbulence is a function of the atmospheric turbulence intensity, wind speed, separation and the view angle. In the framework of TeamPlay, wind speed and wind direction is categorized in discrete bins. Recalling the concept the effective turbulence equation and the rules for the calculations are presented below.

. Atmospheric turbulence is set by the model in the IEC standard . To account for partial wakes the turbulence behind a wind turbine has been set as a Gaussian profile, where the maximum is set by Frandsen wake model and the minimum is the atmospheric turbulence intensity . Only the immediate incident wake is considered . The wind speed deficit is calculated using Jensen wake model . The modified ambient turbulence intensity for large wind farms is used when required . The effective turbulence is calculated using the equation and corresponding probabilities presented in Section 4.2.3.

The algorithm to obtain the upcoming wind speed and turbulence intensity is performed for all the wind turbines in the array, as follows: for every wind direction-bin a list of all the upstream turbines upon the one in question is obtained and sorted in incoming order. Then, the wind speed deficit and wake turbulence intensity is calculated for all the list. For instance: starting from the first wind turbine the wind speed and turbulence that will encounter the next wind turbine on the list is obtain and so forth for all the turbines in the sorted list. This process is performed for every wind speed-bin. Therefore, every wind turbine has a list for every wind speed-bin and wind direction-bin with the actual incoming wind speed and turbulence intensity.

The next step is to account for every wind speed all the incoming turbulence for the wind turbine in question. This is done by the effective turbulence concept where the turbulence is weighted by the probability of occurrence and integrated over all wind directions. This is done by a simple numerical integration where the probability of occurrence is set as the probability of such wind direction-bin (e.g. 1 divided by the number of bins in case of a uniform distribution) and the wind direction differential is set as the bin width. The probability used in this work accounts for other wind direction distributions according

31 to any wind rose given as input. The result of these processes is the effective turbulence intensity on each wind turbine conditioned to wind speed but not conditioned to wind direction, Ieff(U).

The correction for ambient turbulence intensity inside the wind farm has two main rules where the correction should not be applied, according to Addendum 88/339/CDV 2008 (IEC-61400-1 2005). When the number of rows from the edge of the wind farm is less than or equal to 5 and when the spacing to the upwind turbine is less than 10 rotor diameters. When a selective approach to implement the correction is used, the view angle becomes important. The view angle determines the number of wind turbines that affect the turbine under consideration from the edge of the wind farm. Moreover, the view angle is also used to calculate the added turbulence in the Gaussian profile for partial wakes. Two common options for view angles are the Park wake-expansion model (section 3.2.2) and the one used by Frandsen (section 3.3.4) in his work to derive the effective turbulence concept. In Section 6.3 the results for the two options are compared in a verification-case study.

6.2.2. Fatigue life Effective turbulences is conditioned to wind speed. A relative measure of the lifetime fatigue loading is the wind speed weighted turbulence; integrating effective turbulence intensity over all wind speeds, weighted by the probability of occurrence of each wind speed fw (Weibull distribution) not conditioned on wind direction as expressed in Eq. 4-20.

Again, the numerical integration is done by adding up the product and the wind speed differential is the size of the wind speed bin. This results in a relative measure of fatigue summarized in just one number for every wind turbine in the wind farm.

6.2.3. Equivalent load Using the effective turbulence conditioned to wind speed, is used in Eq. 4-13 to obtain the standard deviation of the stress range of the response. Then, this standard deviation is used in Eq. 4-15 which yields the expected value of the stress range raised to the Wöhler exponent. The PDF used, is obtain by assuming that the response is Weibull distributed with shape parameter of 0.8 and standard deviation proportional to turbulence, according to Figure 4.2-3 (Sørensen et al. 2007), conditioned to wind speed. This procedure is only performed for every wind speed bin, since the effective turbulence contains the summarized effect of wind direction.

As a side note and mentioned in the description of Eq. 4-14, the stress range obtained needs to be multiplied by a parameter proportional to the cross sectional area (z) to obtain the response in terms of loads. Since, in this work, the equivalent load is compared with a base case (see Section 5.6) the z parameter drops out. Therefore, the parameter is obviated turning the transition from equivalent stress range to equivalent load straightforward for this load-comparative approach.

The equations yields a set of equivalent response for each wind speed bin. To obtain the total equivalent load raised to the power of the Wöhler exponent m, the load range e is weighted by the wind speed probability fwbinU and numerically integrated. Following the partial damage concept applied to the effective turbulence in Eq. 4-17, which in summation form translates to:

푈표푢푡 푚 푚 푛푒푞푢푒푒푞푢 = ∑ [푓푤(푈) ∙ 푏𝑖푛푈 ∙ 휈 ∙ 푒푈 (푈)]

푈=푈푖푛 EQ. 6-1

This results in an equivalent mud-line bending moment specific for the site and for the wind turbine position within the wind farm. The equivalent load is also obtained for the base case in which the ambient effective turbulence is used according to the IEC turbulence model for comparative purposes. The number of fatigue cycles per year  are typically in the order of 5x 107 (Sørensen et al. 2008b).

6.2.4. Support structure design adjustment for fatigue The equivalent load for the base case is applied to the base support structure design. This sets the reference stress level for all the wind turbines. Since the number of cycles and the outer diameter is the same in all cases, the relation Eq. 5-5 applies to obtain the wall thickness in the wake-exposed support structures. Such relation is used to obtain the wall thickness in the monopile, transition piece and on each segment of the tower. Once all dimensions are set, the mass is calculated for each of the components by calculating the geometric volume and using the steel density of 7850.0 [kg/m3].

The relation Eq. 5-5 derived in Section 5.6 assumes that the design is driven by fatigue in all the support structure which sets a maximum effect (wall thickness increase) that wake generated turbulence can have on the support structure design and its mass. Other fatigue driven proportions in the structure are investigated, for instance, the adjustment can be applied only to the tower and transition piece elements while the monopile is kept the same as the base design.

6.3. Algorithm parameters For the implementation of the algorithm proposed in this work some choices had to be made in order to meet the requirements set in Section 3.1; mainly being a tradeoff between accuracy and computational cost. The most relevant parameters regarding wake effects are presented here.

6.3.1. Wind rose The wind rose to obtain the speed distribution on each wind direction sector and the wind direction probability of occurrence has a resolution of 12 sectors or 30 degrees. Then if more wind direction sectors are being used for the calculations a linear interpolation is performed to obtain the needed data for wind speed and wind direction.

The actual distribution is an input parameter where a frequency and a reference wind speed fraction for each wind rose sector is needed. Additionally, a Weibull shape parameter for each sector is also required. The algorithm calculates the Weibull-scale parameter based the wanted mean wind speed for the site and on such input data.

6.3.2. Wind direction bin size As mentioned above, the algorithm allows a user specified number of wind direction sectors which sets the wind direction bin size. The bin size is very important to assess the wake influence correctly; a large bin size would ignore upwind turbines, thus, their influence would not be accounted. Moreover, very small bin sizes would assess the wakes in more detail but would increase the computational time significantly.

To assess the influence of ranging number of sectors a case study with 36 wind turbines under different spacing is used, with layout depicted in Figure 6.3-2. A wind turbine in the middle of the array is chosen, in this case turbine number 22, to count the number of bins in which there is an incident wake under different spacing and number of sectors. The number of sectors are 36, 40 and 60 with corresponding bin sizes of 10, 9 and 6 degrees. The results are presented in Figure 6.3-1 where the total effect due to spacing

33 and number of sectors is appreciated, further, in Figure 6.3-2 contains the wake incidence of each wind turbine upon turbine number 22 (depicted in the figure as visual aid) for 7D spacing.

100% 90% 80% 70% 60% 60 bins 50% 40 bins 40% 36 bins 30% 20%

10% Occurrence of wake condition wake of Occurrence 0% 3 4 5 6 7 8 9 10 11 12 15 18 Spacing [diameters] FIGURE 6.3-1 PERCENTAGE OF WAKE OCCURRENCE AS A FUNCTION OF WIND FARM SPACING, UNDER RANGING NUMBER OF WIND DIRECTION SECTORS.

7 7 [%]

7 7 7 7

9 9 7 6 6 7 7 6 6 7 Current WT 7 7 60 bins 2 2 2 2 2 2 2 2 6 6 6 6 40 bins 3 3 3 3 3 9 9 9 9 3 9 9 3 3 3 3

36 bins Occurrence of wake condition condition wake of Occurrence 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Wind turbine number

FIGURE 6.3-2 (UPPER CORNER) WIND FARM LAYOUT FOR WIND DIRECTION BIN SIZE ASSESSMENT. THE GRAPH SHOWS THE PERCENTAGE OF WAKE OCCURRENCE UPON TURBINE 22 WITH 7D SPACING UNDER RANGING NUMBER OF WIND DIRECTION SECTORS.

The first effect caused by spacing can be seen in Figure 6.3-1 in which increasing the distance causes the algorithm no to account more upwind turbines. This is because the swept length, even with small angles, increases with increasing distance. This effect is not of considerable importance because large separations also diminishes the increased wake-generated turbulence. In the same figure it is seen that for 40 and 60 sectors the difference is small for almost all separations; except for the very large 18D separation where the difference starts to show. Whereas, the 36 sectors case tends to over account incident wakes for separations below 9D; in some cases with critical differences, such as 6D, 7D and 8 D.

In Figure 6.3-2 the percentage of wake occurrence caused by each specific wind turbine in the array is shown. The wake occurrence calculation in this example case is for 7D separation. From Figure 6.3-1 it is

34 seen that the occurrence of wake conditions for separations between 9D and 15D is fairly similar for the three cases, whereas between 6D and 8D the occurrence of the 36-bins case has significant differences. Being such case, and considering that 7D is a common separation choice, this separation is presented as an example.

The most important turbines that the algorithm should consider are the ones closest to the turbine in consideration. In this example the 36-bins case over accounts the nearest 6 turbines (numbers: 16, 17, 21, 23, 27 and 28) as compared with the more detail case of 60-bins by a 2% difference. Further undercounts the next closest 4 turbines (numbers: 15, 18, 26 and 29) with an occurrence of only 3%. Whereas the 40- bin case follows better the 60-bin case in these 10 surrounding turbines.

From this findings it is concluded that the 60 sectors implementation does not add significant improvement compared to the 40 sectors case; considering the increased amount of computational time needed. Further, the 36 sector implementation over counts some critical turbines. Finally, the performance of the 40 sectors implementations is acceptable and will be used further.

6.4. Verification The models used in this work are already validated against measurements therefore, in this section, only the implementation is verified against a published case study. The chosen validation case study was performed by the company GL Garrad Hassan, presented in reference (Jacquemin et al. 2010), in which a set of conditions are set to expose some of the features and ambiguities about effective turbulence calculations. Furthermore, the study addresses the issue of how differences in effective turbulence caused by different interpretations of the standards affect support structure design in two extreme-interpretation cases. The wind farm characteristics of the study are reproduced in Table 6-1 and Figure 6.4-1 from the mentioned publication.

The publication presents an opportunity to compare the effective turbulence calculations at 15 m/s on each wind turbine. The calculations in the study were performed by an in-house wind farm tool. The results are available under 4 possible cases according to the interpretation of the standards; using two different view angles and applying selectively or globally the ambient turbulence correction. For the effective turbulence calculation a representative Wöhler exponent of 4 for steel components was used. In this verification study, the difference in interpretations or view angles are not of main interest. Nevertheless, the results for the two view angles under the selective correction approach were obtained for comparison in this section.

The original results are reproduced in Figure 6.4-2 in which the results using the algorithm developed in this work are superimposed for comparison. The correct implementation of the wake models can be appreciated in the figure. In some turbines the results from this work seem to deviate from the ones in the published study by small amounts but overall seem to follow the correct pattern following the particular layout.

TABLE 6-1 WIND FARM LAYOUT AND CHARACTERISTIC FROM CASE STUDY IN (Jacquemin et al. 2010) Wind Farm No. of wind turbines 130 Equilateral layout 6D Mean wind speed 9.2 m/s Ambient turbulence at 0.06 15 m/s (I15) Wind rose distribution Typical north European Water depth 30 m Wind turbines Rotor diameter 107 m Rated wind speed 12 m/s Cut-in wind speed 4 m/s Cut-out wind speed 25 m/s Tower top mass 220 tons Lifetime 20 years FIGURE 6.4-1 WIND FARM LAYOUT (Jacquemin et al. 2010). Rated power 3.5 MW

FIGURE 6.4-2 PERCENTAGE EFFECTIVE TURBULENCE AT 15 [M/S] ON EACH TURBINE FOR THE CASES ACCORDING TO:

Large wind farm correction Global Selective Selective (This work) Park X (right graph) View (k=0.04) angles Frandsen X (left graph)

Some uncertainties while replicating the case study in this work implementation were mainly the choice of wind rose and the thrust coefficient curve. The wind rose used in this verification case is described in Appendix 0 which corresponds to a site about 20 km from the coast of The Netherlands in the North Sea. The data has been adjusted to match the mean wind speed used in the GH case study. The scale Weibull parameter was obtained and scaled up to match the mean wind speed for the case study site using a constant shape parameter of 2 for all wind directions. It was found that using different shape parameters (for instance other typical values are 2.3 or 1.8) would have an impact on turbulence, especially to the most outer wind turbines where the ambient turbulence dominates the results.

Regarding the thrust coefficient, it was found that using the approximation CT = 7.0/U recommended in the standards (and accounting for cut-in, cut-out and maximum CT) yields similar results to the ones in the study, whereas using a specific thrust curve would yield a similar turbulence pattern but with lower values.

Additionally, the GH study provides a relative mass difference in a support structure due to a difference in effective turbulence intensity. In the GH case the difference in turbulence intensity is caused by the different interpretations of the standards. The authors chose a change of 1.8% in effective turbulence intensity at 15 m/s; from about 12.0% to 10.2%. By means of aeroelastic simulations and IEC load cases in GL Bladed they obtained the damage equivalent loads (using Miner’s rule) for the support structure under both turbulence levels. Wall thickness optimization was carried out using in-house fatigue analysis software, while ensuring that the predicted fatigue life at all positions matched or exceeded the baseline fatigue life. The wall thickness optimization was only achieve in the tower and transition piece but not in the monopile component. They concluded that such turbulence intensity difference would lead to a 4% difference of the total primary steel weight of the support structure. Furthermore fabrication costs would be expected to decrease by 3%. The study also analyzes the case of the most onerous turbine location between the two interpretations, yielding a turbulence intensity difference of only 0.5% and concluding that such small difference could impact support structure weights and costs by 1-2%. Moreover, the publication performs the same comparison for a 5MW and 128m in diameter wind turbine on a jacket support structure concept obtaining a 7% mass difference for the 1.8% turbulence intensity case.

To compare this implementation with the results for mass reduction published in the GH study a single interpretation is chosen, in this case Frandsen-Selective. Next, the simple fatigue adjustment, explained in Section 6.2.4, is applied to all the wind turbines in the verification case. The adjustment was applied only to the tower and transition piece elements since in the GH study only in these elements a thickness optimization was achieve. Finally, two wind turbines are chosen for the comparison: the worst turbulence affected wind turbine position at 15 m/s (Ieff, 15 ≈ 12%) and a position which has 1.8% less turbulence intensity (Ieff, 15 ≈ 10.2%); in this case wind turbine numbers 42 and 1 respectively. Comparing the support structure masses a 9.1% difference is estimated between turbine number 42 and 1. Further, using two onerous locations (Ieff, 15 ≈ 9.5% and 9.0%) with a 0.5% turbulence intensity difference a mass difference of 3.0% is estimated. Even though the approach to verify the results differs from the GL case study the mass reduction difference should be comparable.

In comparison, the weight reduction estimated in this work is about twice the one estimated in the GL study. The assumption that the support design is totally driven by fatigue in this work implementation over-estimates the loads and, thus, weight reduction. This sets an upper limit to the weight reduction that could be achieved by specific support structure design in reality.

Furthermore, the implementation in this work provides the possibility to compare all the support structures mass difference in the wind farm. By comparing the mass (and cost) of two support structure design approaches under two fatigue schemes in Table 6-2. Frist, if the worse turbulence affected design is used in for all positions. And the second design approach being a location-specific support structure design according to each location turbulence regime. The average support structure mass difference between the two design approaches is estimated to be 7.9-11.5% for the fatigue schemes in Table 6-1. In Figure 6.4-3 a graphical representation of the mass reduction with respect to the worse turbulence affected location is shown under fatigue scheme (1)-implementation in Table 6-2 to compare all the support structures.

The results in Figure 6.4-3 show expected behavior for the particular layout and a south-west main wind direction. Firstly, the outer wind turbines facing south-west exhibit less fatigue damage than the outer ones facing north-east because the first group faces most of the time free-stream flow as opposed to the latter group. Secondly, inside the wind farm, three groups of wind turbines can be distinguished in warm colors near the corners (e.g. around no. 59, around no. 31 and around no. 81) where this areas are more affected by the ambient turbulence correction; being the group opposite to the main wind direction the most affected one by both the correction and incident wakes. Finally the group in the middle of the wind farm seems contra intuitively unaffected but this is merely because the correction rarely applies in the area since wind turbines there rarely are behind more than 5 upwind turbines.

TABLE 6-2 MASS REDUCTION IN SUPPORT STRUCTURE DUE TO EFFECTIVE IEFF REDUCTION [%].

Difference in Ieff at 15 m/s [%] Average all support 1.8 0.5 structures (12.0-10.2) (9.5-9.0) Fatigue schemes used in this work: (1) Adjustment only to tower and TP 9.1 3.0 7.9 (2) Adjustment to tower, TP and monopile 13.3 4.5 11.5

FIGURE 6.4-3 PERCENTAGE OF MASS REDUCTION COMPARING WORSE TURBULENCE AFFECTED TURBINE (NO. 42) TO THE REST OF THE WIND FARM. USING IMPLEMENTATION CASE (1) IN TABLE 6-2. THE MAIN WIND DIRECTION IS SOUTH-WEST.

It is concluded that the implementation of the wake-turbulence models and recommendations proposed in the IEC standards into “Teamplay” provide similar effective turbulence estimations as compared with the GH case study under similar conditions. Furthermore, the estimation of fatigue and support design adjustment provides an upper level for possible weight reduction on the whole wind farm.

7. Qualitative study In this section a series of case studies are carried out on different wind farm setups using the implementation presented in Chapter 6. This is with the purpose to gain insight about the interaction between wake-generated fatigue on the support structures and the wind farm layout. Furthermore, assess the relative importance of the increased support structure cost to wake losses and estimate potential support structure cost reductions.

The wind turbines used for the case studies (unless specified) are 80 meters in diameter with a thrust and power coefficients corresponding to a V80 wind turbine (Zaaijer 2013). The flow conditions in this case are mean wind speed of 9.6 m/s and with a reference turbulence intensity of 0.12 at 15 m/s (offshore site, IEC standards). Two wind direction distributions are used: uniform for cases 7.1, 7.2, 7.3 and 7.4; and south- west main wind direction (similar to Horns Rev I site, see Appendix A.2) for cases 7.4 and 7.5. The site water depth is 13.5 m and other conditions are similar to the Horns Rev 1 site.

7.1. Increased support structure cost: wind turbine spacing effect It is readily anticipated that increasing wind turbine separation will decrease the effects of wake- generated turbulence, resulting in less fatigue damage and, thus, reduced support structure weight. Furthermore, energy yield would also increase due to reduced wake-losses under larger separations. The drawback upon increasing wind turbine separation is mainly area usage and increased in-field cable length connecting the turbines and its associated cable losses. To evaluate the overall effect of such phenomena a series of simulations under increasing wind turbine spacing is carried out using several wind farm sizes.

Four wind farm cases are used with equilateral spacing between turbines: (1) two turbines in a row, (2) 9 turbines in a 3 by 3 array; (3) 36 turbines in a 6 by 6 array; and (4) 100 turbines in a 10 by 10 array.

The comparison of the above mentioned issues is performed by monetizing the effects under different wind turbine separation. The support structure increased robustness to account for the fatigue regime is translated to cost by the mass-cost model presented in Section 5.7 and using as design reference case where all the support structures are design for ambient turbulence conditions. Cable cost is assessed by Teamplay considering several factors, for instance transmission energy, length and copper cost. The total energy yield is estimated by Teamplay considering the flow regime, turbine characteristics, wake and electrical efficiencies. In order to monetize the energy loss by the wake effect, an electricity price of 9 [euro cents/KWh] is chosen and production span of 20 years; energy production is referenced to the case where there are no wake losses.

Two support structure fatigue schemes are used: (1) “FS 1” assumes that the whole support structure is adjusted for increased fatigue and (2) “FS 2” assumes that the fatigue adjustment is not performed on the monopile component. Additionally, (3) “No SS cost” does not account for the increased support structure cost. Moreover, the symbol “d_” in the figures denote a change (e.g. “d_SS_cost” denotes a change in the support structure cost).

Firstly, the separated incurred costs, disregarding area usage, of the 2-turbine and 100-turbine cases are shown in Figure 7.1-1 and Figure 7.1-3. The summation of the costs for these cases is reported in Figure 7.1-2 and Figure 7.1-4. As seen in the figures, the energy lost due to wakes completely drives the total cost, making the increased support structure costs due to wakes irrelevant for optimal spacing considerations.

€ 450

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Costs € 200 d_SS_cost, FS 1 € 150 d_SS_cost, FS 2 € 100 Cable cost € 50 Lost enery cost € 0 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-1 TWO WIND TURBINES CASE: INCREASED COSTS PER WIND TURBINE AS A FUNCTION OF SEPARATION.

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No SS cost € 0 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-2 TWO WIND TURBINES CASE: SUMMATION OF INCREASED SUPPORT STRUCTURE COST, CABLE COST AND WAKE-LOSSES PER WIND TURBINE FOR DIFFERENT FATIGUE ADJUSTMENT SCHEMES AS A FUNCTION OF WIND TURBINE SEPARATION.

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Costs d_SS_cost, FS 1 € 1,500 d_SS_cost, FS 2 € 1,000 Cable cost € 500 lost energy cost € 0 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-3 WIND FARM 10 X 10 CASE: INCREASED COSTS PER WIND TURBINE AS A FUNCTION OF SEPARATION.

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€ 500 No SS cost € 0 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-4 WIND FARM 10 X 10 CASE: SUMMATION OF INCREASED SUPPORT STRUCTURE COST, CABLE COST AND WAKE-LOSSES PER WIND TURBINE FOR DIFFERENT FATIGUE ADJUSTMENT SCHEMES AS A FUNCTION OF WIND TURBINE SEPARATION.

In the past cases area use was not included in the analysis. In this case it is considered and monetized by means of bottom lease. Even though bottom lease might not exist in some countries, area usage is still an important restriction for other reasons. For instance, merely space availability or environmental impact. An example using the 9-turbines wind farm is presented in Figure 7.1-5 and Figure 7.1-6. In this case the increased operational and management costs are taken into account; of which the bottom lease drives the increased cost as separation increases. In this case, it is seen that such cost becomes as important as wake losses and drives the spacing optimization towards smaller separations.

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€ 1,500 Costs € 1,000 d_SS_cost, FS 1 d_SS_cost, FS 2 € 500 Cable cost lost energy cost € 0 O&M 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-5 WIND FARM 3 X 3 CASE: INCREASED COSTS PER WIND TURBINE AS A FUNCTION OF SEPARATION.

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€ 500 FS 2 No SS cost € 0 2 4 6 8 10 12 14 16 18 Separation [diameters] FIGURE 7.1-6 WIND FARM 3 X 3 CASE: SUMMATION OF INCREASED SUPPORT STRUCTURE COST, CABLE COST, WAKE-LOSSES AND O&M COST PER WIND TURBINE FOR DIFFERENT FATIGUE ADJUSTMENT SCHEMES AS A FUNCTION OF WIND TURBINE SEPARATION. 7.2. Increased support structure cost: variations in wind turbine position Another interesting case study is to observe the effect of moving a particular wind turbine around its place. The increased or decreased support structure cost is compared with its associated change in wake losses. For this case study a 49-turbine wind farm with square layout and 7D spacing is used. The wind turbine in the middle of the wind farm (number 25) is observed while displacing its position horizontally and vertically. The relative costs as a function of displacements are presented in Figure 7.2-1, where the base case is the origin or the original position in the lattice. In the figure colored circles mean a positive effect: support structure cost reduction and less wake losses. As opposed, empty circles depict a negative effect: increased support structure cost and more wake losses.

1.20

1.00

0.80

0.60

0.40

d_wake losses 0.20

d_SS_cost Vertical displacement [diameters] displacement Vertical 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

-0.20 Horizontal displacement [diameters]

FIGURE 7.2-1 WAKE LOSSES AND SUPPORT STRUCTURE COSTS CHANGE AS A FUNCTION OF VERTICAL AND HORIZONTAL DISPLACEMENT. WIND TURBINE NO. 25 IN A 7X7 WIND FARM (7D SPACING).

The first remarkable effect in this case is that no reduced wake loss was observed for any x-y displacement (in the figure, no filled red circles). Observing only the horizontal displacement, while moving the turbine to the right, wake losses increase to a maximum around 0.5D then find a local minimum around 1D. This first effect could be because as the turbine displaces gets closer to turbines on the right but does not get rid of the effects from the original position yet. Then, as the displacement continues, the effect of the now closer wind turbines from the right hand side, mainly turbine no. 26, increase their influence upon the observed turbine even though the effects of the original surrounding turbines from the left hand side start to dissipate.

For the support structure effect, it is noted that there are some favorable positions in this case (e.g. x=0.5D, y=0.5D). But the cost change is still dominated by wake losses.

Next, a case when all even rows of wind turbines are displaced to obtain a “zig-zag” layout is studied. In this case, the total support cost and wake losses of the whole wind farm are analyzed. The increased support structure cost and wake losses divided by the number of wind turbines are presented in Figure 7.2-2 where the base case is the rectangular case.

It is noted, that in this case, the 1D displacement does improve energy yield. As opposed in the last analysis where it was only a local minimum for the wake losses. The reason could be that in this case, the contiguous turbine is also displaced therefore its effect on the horizontal neighbors is constant.

The support structure cost shows again irrelevant influence when compare with wake losses. To show the effect of the support structure cost in this case study the same results are presented in Figure 7.2-3 but without including the wake losses.

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Thousands € 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 -€ 50

-€ 100 Cost reduction Cost

-€ 150 d_SS_cost d_wake losses -€ 200 Displacement [diameters]

FIGURE 7.2-2 CHANGE IN SUPPORT STRUCTURE AND WAKE LOSSES COST AS A FUNCTION OF ROW DISPLACEMENT WITH RESPECT OF THE SQUARED CASE IN A 7X7 WIND FARM (7D SPACING). POSITIVE VALUES IMPLY A POSITIVE IMPACT SUCH AS COST REDUCTION OR LESS WAKE LOSSES.

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€ 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 -€ 1

Cost reduction Cost -€ 2 d_SS_cost -€ 3 Displacement [diameters]

FIGURE 7.2-3 CHANGE IN SUPPORT STRUCTURE AND WAKE LOSSES COST AS A FUNCTION OF ROW DISPLACEMENT WITH RESPECT OF THE SQUARED CASE IN A 7X7 WIND FARM (7D SPACING). POSITIVE VALUES IMPLY A POSITIVE IMPACT SUCH AS COST REDUCTION.

In Figure 7.2-2 (with the aid of Figure 7.2-3) it is noticeable that the positive or negative effects of the support structure cost or wake losses, are not necessarily correlated. A fundamental reason for this effect has to do with how the wind speed deficit (related to wake efficiency) and how the incident turbulence are calculated. The speed deficit calculation includes the effect of all “hidden” turbines or all the turbines aligned with the flow, whereas the turbulence calculation only includes the effect of the closest turbine. Therefore, when a turbine is displaced out of the squared arrangement, the algorithm will now account turbines that were before hidden as incident in some cases in the turbulence calculation.

From cases 7.1 and 7.2 it is concluded that the support structure cost change caused by the separation change is not as relevant as other incurred costs. Being wake losses the biggest driver when optimizing the layout spacing. Other lower energy prices were considered (e.g. 5 euro cents per KWh) but wake losses still dominate the results therefore the conclusion is insensitive to the assumed energy price. This economic aspect makes it irrelevant to consider increased cost of support structures caused by wake generated turbulence in layout-spacing optimizations.

7.3. Support structure weight reduction: wind turbine spacing and wind farm size effect In the past case studies the specific support structure design for each wind turbine position within the wind farm is used. As expressed in Section 1.3: Identification of the problem, this tailored support structure design is not common practice in the wind industry. In this section several wind farm sizes and wind turbine spacings are analyzed to estimate the potential savings in capital cost of such approach. For this purpose, the worse turbulence affected wind turbine position is chosen to use its support structure design in all others positions. Then the cost difference with the fatigue adjusted designs is determined.

For this study, the wind farms 3 by 3, 6 by 6 and 10 by 10 are used under different spacings and under a uniform wind distribution. The same two fatigue schemes defined in case study 7.1 are used. The results under both fatigue schemes are reported in Figure 7.3-1, Figure 7.3-2 and Figure 7.3-3 for the three cases.

In all figures the dependency of turbine spacing can be appreciated. This shows that wake effects dilute with increasing separation. It is noticed that for big wind farms, even with large separations, effects of wake turbulence still play a role, and the mass (or cost) reduction is still noticeable. Moreover, the difference in fatigue schemes is more important for small to medium separations and is still persistent in big wind farms with large separations.

Another important effect regarding wind farm size is the amount of reduction. In this cases the 3 by 3 wind farm could reach values up to 3 times higher compared with the 10 by 10 wind farm. Further, the gradient with which the reduction drops as separation increases is higher in the small wind farm cases than in the big wind farm case. This effect is due to the fact that wake generated turbulence has an upper limit (empirical and included in the models) even for small separations. On the other hand, in the center of large wind farms wake incidence is still noticeable even for large separations. As a result, the power law behavior of the reduction is mitigated by increasing wind farm size; the reduction becomes less steep with increasing spacing in large wind farms.

These cases show an upper limit of mass and cost reduction in support structures when designing accordingly to their specific turbulence regime. For large wind farms this potential reduction becomes less sensitive to turbine spacing. The reduction in this case, 10 by 10 wind farm, could account for instance at 7D separation, for 1.3% mass and cost reduction.

The relatively low reduction values obtained in these cases with respect to the ones obtained in the verification Section 6.4 are mainly because of three fundamental differences: the layout shape, the wind direction distribution and the reference turbulence intensity. The regular arrangement and uniform wind distribution used in these case studies cause a more uniform wind turbulence regime on the bulk of the turbines. This in turn, makes the support structure designs more uniform and, thus, with less mass and cost difference between each support structure and the worse affected position. Finally, the GH study uses a reference turbulence intensity of 6% instead of the minimum 12% appointed by the IEC standards. Such low turbulence value causes a bigger turbulence jump between the outer turbines and the worse affected ones, which also exacerbates the support structure design difference. This latter issue is not further reported because the reference turbulence intensity is not considered a choice while following the IEC standards, as the implementation in this work intends to follow.

9% 8% 7% 6% 5% 4%

Reduction 3% 2% FS 1 1% FS 2 0% 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Spacing [diameters]

FIGURE 7.3-1 WIND FARM 3X3: TOTAL SUPPORT STRUCTURE MASS REDUCTION AS A FUNCTION OF WIND TURBINE SPACING.

9% 8% 7% 6% 5% 4%

Reduction 3% 2% FS 1 1% FS 2 0% 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Spacing [diameters]

FIGURE 7.3-2 WIND FARM 6X6: TOTAL SUPPORT STRUCTURE MASS REDUCTION AS A FUNCTION OF WIND TURBINE SPACING.

9% 8% 7% 6% 5% 4%

Reduction 3%

2% FS 1 1% FS 2 0% 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Spacing [diameters]

FIGURE 7.3-3 WIND FARM 10X10: TOTAL SUPPORT STRUCTURE MASS REDUCTION AS A FUNCTION OF WIND TURBINE SPACING.

7.4. Support structure weight reduction: layout shape and wind direction distribution As noted in the last case studies the layout shape with respect of the wind direction distribution appears to influence the support structure design to an important extent. In this case study several wind farm shapes are analyzed under both uniform distribution and south-west main wind direction (similar to Horns Rev I site) with the same mean wind speed of 9.6 m/s. In all cases, the same wind turbines of 80 meters in diameter are used. The layouts used are presented in Table 7-1 for reference. Firstly, three 80-turbines wind farms with 7D in-row and 7D in-column spacing are used, with shapes: vertical rectangle (8 by 10), horizontal rectangle (10 by 8) and trapezoidal (10 by 8, matching Horns Rev I layout). Additionally, the Horns Rev II layout is used which consists of 13 radial branches with 7 turbines per branch, the in-row spacing is about 6D and between branches the spacing is 9D. Further, the layout from the Garrad-Hassan study, used in the verification Section 6.4, is also used but with 7D by 7D spacing in this case.

The results of the mass (or cost) reduction in the support structure using the total fatigue adjustment are presented in Figure 7.4-1. The results represent the difference when using the worse turbulence position to design all support structures in the wind farm, compared with a specific design according to each position’s turbulence regime. Furthermore, the reduction can also be interpreted as a measure of how evenly the support structures are affected by wake induced fatigue. For instance, a small reduction value indicates that the layout and wind distribution combination in question does not exhibit high turbulence zones in some regions and low turbulence zones in other regions, but rather that the turbulence level is more evenly distributed across the wind farm.

5.0%

4.0%

3.0% Uniform

Reduction 2.0% South-West

1.0%

0.0% Rectangular Rectangular Horns Rev I Horns Rev II GH study Vertical Horizontal

FIGURE 7.4-1 MASS REDUCTION COMPARING WORSE TURBULENCE AFFECTED SUPPORT STRUCTURE DESIGN TO LOCATION SPECIFIC SUPPORT STRUCTURE DESIGN FOR DIFFERENT WIND FARMS, UNDER DIFFERENT WIND DIRECTION DISTRIBUTIONS.

TABLE 7-1 WIND FARM LAYOUTS. THE NORTH DIRECTION IS FACING UPWARDS THE FIGURES. Rectangular Rectangular Horns Rev I Horns Rev II GH study Vertical Horizontal

As expected, there is an important difference between the two wind direction distributions in some layouts, with the notable exception of Horns Rev I (which will be discuss later in this section). Firstly, the most noticeable differences between the two distributions are in the layouts that cause more wake incidence upon a subsection in the wind farm under the south-west distribution compared with the uniform one. This is readily seen from layout shapes in Table 7-1 and the wind direction deviations from purely south-west wind direction (see wind rose in Appendix A.2), where for instance, in the rectangular vertical layout, wind flowing mainly from the south-west direction will cause turbines in the upper right corner to be affected by wakes more frequently as compared with the rectangular horizontal case.

An interesting effect when comparing the rectangular vertical, horizontal and Horns Rev I under the uniform distribution is that in the first two the reduction is significantly lower. This is because the rectangular layouts create a symmetrical turbulence pattern (e.g. location of similar turbulence level zones) over two axis of symmetry, whereas the Horns Rev I layout creates its turbulence pattern only over one symmetry axis. This particularity creates more zones with different turbulence levels and, thus, higher mass differences on the support structures.

The Horns Rev I layout it is notable because fatigue-wise it is better utilized with the south-west wind direction distribution than with the uniform distribution. Furthermore, under this direction distribution, it is the one with less reduction than any of the other cases. This implies that such layout design is desirable for its benefits regarding wake induced fatigue. Nevertheless, still a 1.8% cost reduction could potentially be achieved by tailoring every support structure to its turbulence regime. By estimating the total capital cost of Horns Rev I using the TeamPlay tool, the reduction accounts for 0.3% of the total capital costs just over 1 million euros.

Another example of a real wind farm is in this case the potential saving in Horns Rev II. That could reach 3.9% of the support structures costs or, by estimating the wind farm capital cost using TeamPlay, 0.6% of the total capital costs or 2.6 million euros.

It is noted that no layout-shape optimizations were carried out with support structure feedback. It is possible that, for instance, different layout-shapes with the same turbine-spacing could yield similar wake efficiencies but different support structure fatigue utilization. Nevertheless, the cases used here give insight that layout-shapes which allow a more uniform turbulence distribution, given the wind direction distribution, would utilize the support structure material better.

It is concluded that the layout shape does contribute to propitiate high or low turbulence zones within the wind farm. Under the traditional worst-case support structure design practice, this results in underutilization of materials in support structures. Further, designing support structures specifically to their positions could result in important cost savings that are exacerbated by the specific combination of layout shape and the site wind direction distribution.

7.5. Additional case studies Even though the objective of this work only intends to tackle the interaction between support structure design and the wind farm layout, it is of interest to obtain an overview of some other wind farm parameters sensitivities.

7.5.1. Rotor-nacelle assembly It is readily seen that bigger wind turbine blades will cause wider wakes and cause higher wake-generated fatigue in other turbines when the absolute spacing is kept the same. In this study it is of interest to study the effects of increasing turbine diameter while keeping the relative spacing (s = x/D) constant. Furthermore, a larger blade set also implies larger top mass thus a more robust support structure.

For this case study the 80 meters in diameter turbine described in the beginning of this chapter is compared with the 107 meters turbine used in the verification chapter. The wind farms used were the ones described in Table 7-1 except for Horns Rev II due to time limitations during for this work. For this case, the south-west main wind direction condition is used.

It was found that the relative mass or cost reduction in the support structure, presented in Figure 7.5-1, is in fact very similar for both rotor-nacelle assembly sizes used. But the relative cost reduction compare to the total capital costs is slightly higher in the larger diameter turbine case, see Figure 7.5-2. The rotor- nacelle assembly purchase costs, in this case, increase but since the support structure cost change increases in a higher extent, the total capital cost reduction still reports an increase.

3% 80 m

Reduction 2% 107 m

0% Rectangular Rectangular Horns Rev I GH study Vertical Horizontal

FIGURE 7.5-1 MASS REDUCTION COMPARING WORSE TURBULENCE AFFECTED SUPPORT STRUCTURE DESIGN TO LOCATION SPECIFIC SUPPORT STRUCTURE DESIGN FOR DIFFERENT WIND FARMS, UNDER SOUTH-WEST WIND DIRECTION DISTRIBUTIONS, FOR TWO ROTOR-NACELLE ASSEMBLY SIZES.

0.90% 0.80% 0.70% 0.60% 0.50% 80 m 0.40% 107 m 0.30% 0.20%

0.10% Percentage Percentage of reduction CAPEX 0.00% Rectangular Rectangular Horns Rev I GH study Vertical Horizontal

FIGURE 7.5-2 PERCENTAGE OF THE POTENTIAL SUPPORT STRUCTURE COST REDUCTION RELATIVE TO TOTAL CAPITAL COST FOR TWO ROTOR-NACELLE ASSEMBLY SIZES.

7.5.2. Water depth The water depth in offshore wind farm design is one of the most important design drivers for the support structure. In this case study several water depths are studied using the Horns Rev I wind farm. This of course, is more relevant if the monopile component is in some degree fatigue driven.

It was found that the support structure reduction costs maintained the same level for all cases, of about 1.8%. But regarding the cost reduction with respect of the total capital costs and important increase was registered. The results are presented in Figure 7.5-3. The capital cost reduction for the deepest water depth of 28.5 meters doubles compared with the lowest level of 8.5 meters.

0.45% 0.40% 0.35% 0.30% 0.25% 0.20% 0.15% 0.10% 0.05% Percentage Percentage of reduction CAPEX 0.00% 5 10 15 20 25 30 Water depth [m]

FIGURE 7.5-3 PERCENTAGE OF THE POTENTIAL SUPPORT STRUCTURE COST REDUCTION RELATIVE TO TOTAL CAPITAL COST AS A FUNCTION OF WATER DEPTH.

In both of these additional case studies it was found that the support structure cost reduction was maintained but the share of the potential support structure cost reduction compared to the total capital costs increases with increasing support structure size.

8. Final conclusions and recommendations 8.1. Conclusions An algorithm to calculate turbulence intensity on each wind turbine position within a wind farm has been implemented in the TeamPlay wind farm design tool. The implementation makes use of simple wake models and recommendations from the IEC industry standards. Turbulence from wakes is calculated considering wind flow characteristics, such as the wind rose and reference turbulence intensity, and the wind farm layout. Turbulence intensity values were compared in a verification case study obtaining satisfactory results. The turbulence addition to Teamplay performs in a reasonable amount of time and can be used to assess the location-specific turbulence intensity with any wind rose - layout combination.

The above mention implementation was coupled with a simple support structure design adjustment for wake-generated fatigue. An initial design was obtained from the TeamPlay tool and used as a base case. Fatigue damage caused by turbulence is assessed through the equivalent load and effective turbulence concepts and assumption of their proportionality. The base case is assumed to be exposed to free flow turbulence and its components thicknesses are adjusted according to each location-specific turbulence regime. This simple approach assumes that the support structure design is fatigue driven and therefore provides an upper limit for the effect of turbulence on the support structure mass.

Using the Teamplay tool with the turbulence and support structure design additions, several case studies were carried out in order to gain insight and yield recommendations regarding the interaction between wake-generated turbulence, support structure design and the wind farm layout.

Regarding the turbine spacing, it was confirmed that the support structure mass increased with reducing spacing following a power law behavior to withstand the, also power law, increase of wake-generated turbulence. Moreover, wake losses exhibit a similar behavior whereas cable cost and area usage increase with increasing spacing. A comparison between such tradeoff was performed by monetizing the four effects under different spacings, layout displacements and wind farm sizes. It was observed that wake losses and area usage (monetize via bottom lease in this work) drive the spacing optimization. This effect persist even with low energy prices because the potential support structure costs changes are not as substantial as the changes in wake losses throughout the life time of the project. Therefore it is concluded, contrary to the original hypothesis, that the wake-induced fatigue and its effect on the support structure design is not relevant in layout-spacing optimization.

Two support structure design approaches are compared to study the potential cost saving under different circumstances. The base case, which is also the most common practice in the industry, is to design the support structures using the worst turbulence regime encounter in the particular layout. Such design approach is compared with a location-specific turbulence regime design approach. This analysis was carried out through several case studies to assess the influence of some wind farm aspects, such as: turbine spacing, wind farm size, layout-shape and wind direction combination, rotor-nacelle assembly size and water depth.

The interaction between the potential support structure mass or cost reduction increases while reducing the spacing, in a power law fashion. Further, small wind farms exhibit larger reductions for small to medium spacings than large wind farms but this effects reverses for larger spacing (e.g. larger than 9D). This means that the power law behavior of the reduction is flatten by increasing wind farm size but maintain even for extreme separations.

Other case studies with large wind farms revealed qualitative insight regarding the layout-shape relative to the wind direction distribution. It was found that layouts that exhibit zones with higher turbulence levels yield higher cost reduction. Even though this can be interpreted as a positive argument to perform a location-specific support structure design it also shows that the layout design does not exhibit an evenly distributed fatigue damage throughout the wind farm.

The variations in the rotor-nacelle assembly and water depth, causing increasing support structure size, showed that the potential support structure cost reduction was maintained but the corresponding total capital cost reduction increases with increasing support structure size. This is because as the support structure size increases, its share in the capital cost increases in a higher extent than the other incurred costs (e.g. larger rotor nacelle-assembly or longer transmission cables).

Finally, some numbers are mention here to give an idea of the potential, or upper level, cost reduction by employing a location-specific support structure design. The reduction obtain from the cases studied range from about 0.3 – 0.7 % is total capital cost is estimated. Figures that account between 1.0 and 5 million euros. It is again noted, that these potential savings assume that the whole support structure design is driven by wake-induced fatigue and that the true cost reductions would be a fraction of such numbers. For instance, the GH published study found that in such case only the tower and transition piece were optimized. Even though it was not found more data than that, during the literature review of this work, such information can be used as an example: considering that the monopile component accounts for about 50% of the support structure mass, in such conditions, this means that the potential cost reductions are halved. Moreover, in this work, the additional or reduced associated costs that imply to design location-specific support structure are not assessed. It is expected that engineering and installation logistics costs would increase but, according to (Jacquemin et al. 2010), fabrication costs are expected to decrease. Nevertheless, if the considered wind farm has different water depths and, therefore, the support structures need to be design specifically to its location then performing a location-specific fatigue adjustment would be a simple implementation and cost reductions assured.

8.2. Recommendations In this section some recommendations are given for wind farm and support structure designers. The recommendations are based on the insight gain and the results obtained during the realization of this work.

. It was found that for layout-spacing optimization the possible support structure cost reductions by spacing variations are overshadowed by wake losses. Therefore it is not fruitful to include support structure design feedback in such optimization efforts.

. Cost reductions in the support structure are possible by designing them accordingly to each location turbulence regime. Furthermore, the potential savings increase when the support structure needed is large and when the layout used propitiates high and low turbulence zones.

. In case the location-specific design approach is not pursued, it is still highly recommended to check the turbulence distribution in every position, in an effort to search for isolated high turbulence affected locations. This will cause an over-dimensioning of most support structures. For instance, to avoid that a small group of turbines lay behind 6 or more rows for a large share of the wind rose distribution compared to the majority of the turbines.

8.3. Future work A persistent uncertainty throughout the realization of this work was the lack of guidelines about the degree of which the support structure design is driven by fatigue. Certainly it would be useful to obtain more information of varying realizations about the determinant load cases.

Lack of data was also experienced regarding the relation between turbulence and equivalent over-turning moment for the support structure. It would be desirable to perform aeroelastic simulations under ranging turbulence levels to obtain turbine specific results.

The simple implementation used in this work could be used for other purposes other than support structure design. The algorithm, being computationally inexpensive and reflecting qualitative results, could be implemented to develop and analyze a control strategy for fatigue mitigation. Moreover, by keeping track of the accumulated equivalent fatigue during operation, it can be used as a non-sensing monitoring tool to perform schedule maintenance.

References Adaramola, M.S. & Krogstad, P.-Å., 2011. Experimental investigation of wake effects on wind turbine performance. Renewable Energy, 36(8), pp.2078–2086. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0960148111000462 [Accessed January 22, 2014]. Aeolus, 2008. Aeolus Project. Available at: http://www.ict-aeolus.eu/about.html [Accessed February 10, 2014]. Anon, 2006. Horns Rev I wind rose. TU Delft SET course slide. Available at: http://mstudioblackboard.tudelft.nl/duwind/Wind energy online reader/Video_frames_pages/wind_farm_optimization.htm [Accessed June 20, 2014]. Anon, 2013. London Array. Available at: http://www.londonarray.com/the-project/ [Accessed February 7, 2014]. Barthelmie, R.J. et al., 2007. Modelling and Measurements of Power Losses and Turbulence Intensity in Wind Turbine Wakes at Middelgrunden Offshore Wind Farm. Wind Energy, 10(July), pp.517–528. Available at: http://doi.wiley.com/10.1002/we.238 [Accessed January 21, 2014]. Barthelmie, R.J. et al., 2009. Modelling and measuring flow and wind turbine wakes in large wind farms offshore. Wind Energy, 12(5), pp.431–444. Available at: http://doi.wiley.com/10.1002/we.348 [Accessed January 22, 2014]. Blekinge, 2013. Blekinge Offshore. Available at: http://www.blekingeoffshore.se/ [Accessed February 7, 2014]. Burton, T. et al., 2001. Wind Energy Handbook, John Wiley & Sons, Ltd. Chen, E., 2009. China starts building first 10-GW mega wind farm. Available at: http://www.reuters.com/article/2009/08/08/us-china-wind-power-idUSTRE5771IP20090808. Crespo, A., Hernández, J. & Frandsen, S., 1999. Survey of Modelling Methods for Wind Turbine Wakes and Wind Farms. Wind Energy, 24, pp.1–24. DNV-OS-J101, 2011. Design of Offshore Wind Turbine Structures DNV-OS-J101, Frandsen, S., 2007. Turbulence and turbulence generated structural loading in wind turbine clusters, Frandsen, S. & Thomsen, K., 1997. Change in Fatigue and Extreme Loading when Moving Wind Farms Offshore. Wind Engineering, 21(3), pp.197–214. Frohboese, P. & Schmuck, C., 2010. Thrust coefficients used for estimation of wake effects for fatigue load calculation, González-Longatt, F., Wall, P. & Terzija, V., 2012. Wake effect in wind farm performance: Steady-state and dynamic behavior. Renewable Energy, 39(1), pp.329–338. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0960148111005155 [Accessed February 6, 2014]. Højstrup, J., 1999. Spectral coherence in wind turbine wakes. Journal of Wind Engineering and Industrial Aerodynamics, 80(1-2), pp.137–146. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0167610598001986. IEA, 2013. Wind Energy Technology Roadmap, IEC-61400-1, 2005. IEC 61400-1 Ed.3: Wind turbines - Part 1: Design requirements, IRENA, 2012. Cost analysis-Wind Power, Jacquemin, J. et al., 2010. Effective turbulence calculations using IEC 61400-1 Edition 3 : Reaching consensus through dialogue and action, Katic, I., Højstrup, J. & Jensen, N.O., 1986. A simple model for cluster efficiency. In European Wind Energy Association. pp. 407–410. Larsen, G.C., Carlén, I. & Schepers, G.J., 1998. Wind Farms - Wind Field and Turbine Loading. In European Wind Turbine Standards II. ECN Solar & Wind Energy. Manwell, J.F., McGowan, J.G. & Rogers, A.L., 2009. Wind Energy Explained Theory, Design and Application, John Wiley & Sons, Ltd.

Méchali, M. et al., 2006. Wake effects at Horns Rev and their influence on energy production, Nielsen, M., Jørgensen, H.E. & Frandsen, S.T., 2009. Wind and wake models for IEC 61400-1 site assessment. In EWEC 2009 Wind Energy Conference and Exhibition. Petersen, E.L. et al., 1998. Wind power meteorology. Part I: climate and turbulence. Wind Energy, 1(S1), pp.25–45. Available at: http://ftp.risoe.dk/pub/met/ahah/WASA/Petersenetal1998.pdf [Accessed March 4, 2014]. Porté-Agel, F., Wu, Y.-T. & Chen, C.-H., 2013. A Numerical Study of the Effects of Wind Direction on Turbine Wakes and Power Losses in a Large Wind Farm. Energies, 6(10), pp.5297–5313. Available at: http://www.mdpi.com/1996-1073/6/10/5297/ [Accessed February 10, 2014]. Roland B. Stull, 1988. An Introduction to Boundary Layer Meteorology, Springer New York. Sanderse, B., 2009. Aerodynamics of wind turbine wakes: Literature review, Sørensen, J.D., Frandsen, S. & Tarp-Johansen, N.J., 2008a. Effective turbulence models and fatigue reliability in wind farms. Probabilistic Engineering Mechanics, 23(4), pp.531–538. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0266892008000349 [Accessed January 22, 2014]. Sørensen, J.D., Frandsen, S. & Tarp-Johansen, N.J., 2008b. Effective turbulence models and fatigue reliability in wind farms. Probabilistic Engineering Mechanics, 23(4), pp.531–538. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0266892008000349 [Accessed June 5, 2014]. Sørensen, J.D., Frandsen, S. & Tarp-Johansen, N.J., 2007. Fatigue reliability and effective turbulence models in wind farms. Applications of Statistics and Probability in Civil Engineering, pp.1–8. Van Der Tempel, J., 2006. Design of Support Structures for Offshore Wind Turbines. TU Delft. Thøgersen, M.L., 2005. WindPRO / PARK: Introduction to Wind Turbine Wake Modelling and Wake Generated Turbulence, Tindall, A.J., 1994. Dynamic loads in Wind Farms, Türk, M. & Emeis, S., 2010. The dependence of offshore turbulence intensity on wind speed. Journal of Wind Engineering and Industrial Aerodynamics, 98(8-9), pp.466–471. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0167610510000279 [Accessed May 29, 2014]. Veldkamp, D., 2013. Load calculations and Standards (AE4-W10/W11 Handout), Vermeer, L.J., Sørensen, J.N. & Crespo, a., 2003. Wind turbine wake aerodynamics. Progress in Aerospace Sciences, 39(6-7), pp.467–510. Available at: http://linkinghub.elsevier.com/retrieve/pii/S0376042103000782 [Accessed February 20, 2014]. Zaaijer, M., 2013. Great expectations for offshore wind turbines: Emulation of wind farm design to anticipate their value to customers. TU Delft.

A. Appendix: Wind speed and direction distributions A.1. North-European wind direction distribution This wind rose corresponds to a site about 20 km from the coast of The Netherlands in the North Sea (Latitude 52.0, Longitude 3.75). The data is from the Argoss database in the period from 1992 to 2010 and adjusted to match a 9.2 m/s mean wind speed. The wind rose data is presented below:

Sector Occurrence U Shape Scale 10 min Graphical representation [deg.] [-] [m/s] [-] [m/s] 0 0.0600 8.03 2 9.06 30 0.0700 8.09 2 9.13 N 60 0.0550 7.85 2 8.86 150° 210° 90 0.0650 7.22 2 8.14 120° 240° 120 0.0600 7.79 2 8.79 150 0.0550 9.61 2 10.84 W E 180 0.1000 11.04 2 12.46 210 0.1500 10.77 2 12.15 60° 300° 240 0.1250 9.98 2 11.27

270 0.1000 9.18 2 10.36 30° 330° 300 0.0900 8.93 2 10.08 S

330 0.0700 8.07 2 9.11

A.2. Horns Rev I wind direction distribution The approximate wind direction occurrence was obtained from (Anon 2006). Furthermore, in reference (Zaaijer 2013) it is reported for this site an annual average wind speed of 9.6 m/s and shape parameter of 2.35. From this data the average wind speed per sector was obtained by adjusting wind speed per sector data from wind rose A.1 to match the site’s annual wind speed. The resulting wind rose data is:

Sector Occurrence U Shape Scale 10 min Graphical representation [deg.] [-] [m/s] [-] [m/s] 0 0.0510 8.40 2.35 9.48 30 0.0420 8.46 2.35 9.55 N 60 0.0330 8.21 2.35 9.26 150° 210° 90 0.0675 7.55 2.35 8.52 120° 240° 120 0.0900 8.15 2.35 9.20 150 0.0660 10.05 2.35 11.34 W E 180 0.1050 11.55 2.35 13.03 210 0.1200 11.26 2.35 12.71 60° 300° 240 0.1230 10.44 2.35 11.78

270 0.1050 9.60 2.35 10.84 30° 330° 300 0.1230 9.34 2.35 10.54 S

330 0.0750 8.44 2.35 9.53