## 3 Results and Discussion
In the present case, the difference between the design operating conditions in the wind speed range between 8 m/s and 10 m/s was actually relatively small between the stall- and pitch-regulated turbines, since the pitch designs used in this work shared a \"soft stall\" with the stall turbine in that wind speed range, so the difference in fatigue life observed in Figure 11 was larger than one would expect. A plausible explanation for this is the use of the stall model used in the aeroelastic simulations; as mentioned above, reliable simulations without instabilities require the use of the Leishman-Beddoes dynamic stall model in the FAST program, whereas the pitch-regulated wind turbines were always simulated assuming steady flow conditions, even in the regime between 8 m/s and 10 m/s, where \"soft stall\" conditions could arise. The difference in fatigue life between the stall- and the pitch-regulated turbines became gradually smaller with wind speed and even inverted its sign at very high wind speeds. This cross-over occurred at 17 m/s for the low turbulence intensity cases and at 16 m/s for high TI. Similarly, the fatigue life curve for the pitch-regulated turbine with variable rotor speeds started to separate from the fixed-rpm curve, after being almost indistinguishable for all lower wind speeds. This joint behavior of both the stall and the variable-rpm pitch turbine clearly pointed to a common rotor speed-related root cause. The fact that this departure from the general trend of the fatigue life curves occurred for smaller wind speed classes in the case of high turbulence is readily attributed to the fact that the filter mask for the moving-average calculation used to get to Figure 11 had a larger spread to neighboring wind speed classes in this case, leading to an effectively larger averaging window. Therefore, the effect of the rpm reduction occurring in the stall- and variable-rpm pitch turbines manifested itself at lower wind  
Figure 10: Results of the rainflow analysis for 18 m/s. Upper row (**a**–**c**): results of the rainflow analysis for the three regulation schemes. Lower row (**d**–**f**): corresponding time series with inflection points marked. speeds. Other than that, the underlying effect appears to be the same. The most likely candidate for an explanation was the axial force or rotor thrust. At high wind speeds, the average thrust diminishes again in the case of the stall and variable-rpm pitch regulation, below the average thrust value of the fixed-rpm pitch-regulated wind turbine (not shown for brevity). This mechanism is likely to explain the observed behavior at very high wind speeds. Now, after the differences in fatigue life between the three regulation schemes and their underlying root causes have been discussed with some detail, it is convenient to close the discussion with some considerations regarding the practical implications of the regulation schemes introduced in this work. A simple way of doing this is by convoluting the damage function \(D(v,\text{TI},\text{reg})\) with a Weibull distribution function characteristic of a given wind regime, as described above, and then applying Equation (4) in order to obtain the corresponding (average) fatigue life. As mentioned before, the primary damage function was assumed to be zero for wind speed averages lower than 7 m/s, meaning \((D(v<7\text{ m/s},\text{TI},\text{reg})=0\); additionally, only wind speed classes up to 20 m/s were considered; for higher values, the turbines were assumed to be parked, and fatigue damage accumulated during parked conditions was assumed to be negligible; therefore, \((D(v>20\text{ m/s},\text{TI},\text{reg})=0\). Damage resulting from extreme events cannot, of course, be ruled out, but this is outside the scope of the current study. In Figure 12, the results for the average fatigue life are shown for the cases of low TI levels.