**1. Introduction**

Wind turbines are mainly clustered as wind farms. Due to the limited space, the turbines are densely placed to obtain the full potential of the available space and to avoid unnecessary cabling costs especially at o ffshore sites. The turbine in the wake flow experiences lower wind speeds and increased turbulence intensity [1]. As a result maximizing the output of the individual turbine does not always lead to a global maximum wind farm output. Furthermore, the increased turbulence intensity leads to greater loads on the drive train and its structural components [1]. This results in accelerated damage accumulation and shortened maintenance intervals. However, there are two approaches to reduce these e ffects.

During power curtailment the power of an upstream turbine is reduced. This means that the wind speed in the wake is less reduced. Therefore, more power can be extracted by the downstream turbines. However, the turbine in the wake still experiences an increased turbulence intensity. This control scheme was the topic of a significant amount of research, see [2–5].

Wake-steering o ffers a promising approach. The upstream turbines are misaligned against the inflow direction, which directs the wake flow past the downstream turbine. Simulations showed that the average power capture could be increased by such a control scheme, see [6,7]. In [8] the simulation results were compared with real park measurements and the increase in energy capture matched the predicted values. Further, in [9] it was shown that a wind farm already optimized with respect to wake losses could increase its annual energy supply by up to 3.7% through the use of wake steering. In addition the non-torque loads of the downstream turbine are reduced because of the lower turbulence intensity as shown in [10,11]. In [12,13], the power output and blade root moments of the waked turbine were measured. It was found that the turbine power drops significantly when the yaw misalignment exceeds 10◦. Furthermore, a correlation between the yaw angle and flapwise bending moment was made. In [14] aerodynamic loads were compared between measurement and simulation. The results showed that aerodynamic loads could be calculated accurately, even for highly yawed inflows. With respect to these results, a significant influence of the yaw misalignment on bending and tilt moment at the main bearing is expected. Therefore, this study will address the torque and non-torque loads at the main bearing of the turbine in the front that is misaligned.

The main contribution of this work is the structure focussed approach. Many studies regarding wake-steering focus on the flow field and the ones that take the structure into account mostly observe the blade root moments. In this study, the transmission of the aerodynamic loads into the drive train and support structure of the turbine are studied as a function of the yaw misalignment. The work is limited in its consideration of the flow field since the Blade-Element-Momentum Theory is used to calculate the wind loads on the rotor blades instead of a complex CFD simulation which would be necessary to study the flow around the blade profiles. Because of that, the yaw angle is limited to a range of −10◦ to +10◦ due to the limitation of the utilised code. As an initial classification of the occurring load changes and the detection of further e ffects, load calculations are carried out on a generic wind turbine model with flexible structural components. For this purpose, a multi body simulation model of a 3 MW turbine with a rotor diameter of 126 m (C3 × 126 [15]) is simulated at Design Load Case 1.1 according to DIN EN 61400-1 (production operation) [16] with wind class 2B at multiple yaw misalignments. The loads at the main bearing are investigated, since this is where changes in the aerodynamic loads by an inclined flow will mainly be reflected and, for the most part, be introduced into the structure. The resulting understanding can be used both in the design process and in operation. On the one hand, the findings could be taken into account in the design of the bearings, and on the other hand, the park regulation could be adapted to prevent an uneconomical accumulation of damage in favour of energy production.

#### **2. Simulation Model and Setup**

Within the scope of this work the resulting turbine loads are determined by a co-simulation between SIMPACK, AERODYN [17] and MATLAB. The multi body simulation software SIMPACK Version 2019 is used to formulate the mechanical structure of the turbine including flexible tower and blades. The AERODYN-code delivers the aerodynamic loads acting in the blades and the controller of the turbine is formulated in MATLAB. For a wind speed below the rated wind speed the turbine is controlled by a generator torque and the above rated wind speed the turbine is pitch-controlled. The drive train of the turbine is modelled as a 2-mass-oscillator with equivalent sti ffness and inertia to a gearbox with a ratio of 92.28. Relevant turbine parameters can be found in Table 1. The turbine delivers power in a wind speed range from *vhub* = 3 m/s to *vhub* = 25 m/s (wind speed on hub height in front of the rotor). For this range, three-dimensional turbulent wind fields are generated in steps of 1 m/s with TurbSim [18]. According to the design load case (DLC) 1.1 of the industry standard DIN EN 61400-1 [16], wind fields of wind class 2B are generated with a normal turbulence model (*Ire f* = 0.14). The standard deviation of the longitudinal wind speed at the hub height results from Equation (1). The inflow data is arranged in a matrix representing a grid in front of the rotor. For each point on the grid the wind speed data for all three dimensions is stored as a time series. The frequency of the time series is 20 Hz.

$$
\sigma\_1 = I\_{ref}(0.75 \,\text{v}\_{hub} + b); b = 5.6 \,\text{m/s} \tag{1}
$$


**Table 1.** C3 × 126 turbine parameters [15].

The loads due to yaw misalignments of <sup>−</sup>10◦, <sup>−</sup>5◦, 0◦, +5◦ and +10◦ are investigated within the scope of this work. The potential weaknesses of the methodology are as follows. The Blade-Element-Momentum Theory doesn't take the interaction between the neighbouring blade elements into account. In addition, it neglects the wake expansion. Since a detailed examination of the flow field around the blades is not intended in this work, these assumptions will have a negligible influence on the results. The used AERODYN-Code utilizes the Blade-Element-Momentum Theory with Glauert Correction for yawed rotors [19], so the simulation is not valid beyond the chosen yaw angle values. However, the overall effects and trends resulting from the misalignment will be detectable within the chosen yaw angle range. In addition, there are the structural assumptions that were made to model the rotor blades which are built as shell elements. The natural frequencies of the flexible blades and tower are considered up to 11 Hz. This ensures that the most important deformations can be mapped but also allows for manageable computation times. For the blades, bending modes up to the first order and torsional modes up to the fourth order are considered. The tower model includes bending modes up to the fifth order and the torsional mode of the first order.

Figure 1 shows the nacelle position relative to the wind direction. The multi body simulation model of the entire turbine is also shown in Figure 1. A simulation of 10 min is performed at each wind speed. The calculated loads are then cumulated over a period of 20 years. The wind speeds are weighted with respect to the probability of their occurrence. The cumulative frequencies of the wind speeds result from the reference location described in the German renewable energies act (EEG 2017) [20]. The height profile of the wind is calculated according to the Hellmann power law with a Hellman exponent of α = 0.25 and the reference wind speed and reference hub height (Equation (2); *vre f* = 6.45 m/s, *hre f* = 100 m). This results in the mean wind speed at hub height with *vHub* = *v*(*h* = *hHub*). Using the mean wind speed at hub height *vHub*, the cumulative frequencies are to be determined by a Rayleigh distribution (Equation (3)). In order to determine the relative frequency of the respective wind speed, the difference of the sum frequencies of *vi* and *vi*−1 is calculated (Equation (3)). The distribution of the relative frequencies is shown in Figure 2. Identical wind fields are used for the load calculation of each yaw misalignment.

$$v = v\_{nf} \left(\frac{h}{h\_{ref}}\right)^d \tag{2}$$

$$F(v\_i) = 1 - \exp\left[-\frac{\pi}{4} \left(\frac{v\_i}{v\_{\text{hub}}}\right)^2\right] \tag{3}$$

$$H(\upsilon\_i) = F(\upsilon\_i) - F(\upsilon\_{i-1}) \tag{4}$$

**Figure 1.** (**a**) Nacelle positions relative to wind direction as seen from above; (**b**) multi body simulation model of the C3 × 126 with coordinate system [15].

**Figure2.**Relativefrequenciesofoccurrenceforvariouswindspeedsusedforloaddurationcalculation.
