## 4 Results and Discussion
### Simulation Results in the Rotating Reference Frame  
The response of the previously designed IPC schemes is evaluated in this section. Three simulations were run with different wind profiles that included a stochastic turbulent component. The mean wind speed varied within the full load region. These different wind conditions were analyzed to study the performance of the proposed adaptive IPCs and their robustness. Wind profiles were created with the assistance of TurbSim in accordance with the IEC 61400-1 standard. The simulation time was 1200 s; however, the first 200 s were removed to discard transient effects in the data. In the first simulation (case 1), the average wind speed component ranged between 14 and 18 m/s. In case 2, the average wind speed varied between 16 and 20 m/s, and in case 3, between 18 and 22 m/s. The most significant variables in both the time and frequency domains were analyzed using the data obtained from each control strategy. Additionally, for each control strategy, various performance indicators related to blade moments, generated power, generator rotational speed, and pitch actuator effort were quantified. In the analysis, a reimplementation of the ROSCO CPC in Simulink without considering IPC was employed as the baseline control for comparison. Figure 7 shows the simulated time responses of some proposed IPC schemes compared with the baseline CPC for simulation case 2. For clarity, only three IPC schemes are shown: the IPC with two different proportional controllers plus the azimuth offset (IPC_P2\(\Downarrow\)), the IPC with two different integral controllers without the azimuth offset (IPC_I2), and the IPC with two identical integral controllers plus the azimuth offset (IPC_I1\(\Downarrow\)). Also for clarity, only 250 s of the simulations are shown. Tables 4 and 5 present several performance indicators of the different control schemes for quantitative analysis; they were calculated for each case from the 1000 s simulation data. Figure 7: Time responses in the rotating reference frame of wind speed (\(\
u\)), generator angular velocity (\(\omega_{\mathrm{g}}\)), generated power (\(\mathrm{P_{g}}\)), OoP moment of blade 1, and pitch signal of blade 1 for simulation case 2 from 250 s to 500 s.  
Figure 7 shows the following variables in the rotating reference frame: wind speed, generator angular velocity, generated power, OoP moment of blade 1, and pitch signal of blade 1. The corresponding performance indicators are presented in Table 4, showing the average DEL value of the OoP blade moments, the average normalized actuator travel (NAT) of the pitch signals, the standard deviation (STD) of the generated power, and the STD of the generator rotational speed. The average NAT of the pitch signals is a measure of the average total traveled pitch angle and is defined as follows:  
\[\overline{NAT}(\beta)=\frac{1}{3}\sum_{i=1}^{3}\left(\frac{1}{T}\int_{0}^{T} \left|\frac{\dot{\beta}_{i}(t)}{\dot{\beta}_{max}}\right|dt\right). \tag{10}\]  
There were no significant differences, neither qualitatively nor quantitatively, between the control schemes in either the power generated or the generator speed, which indicates that the IPCs do not affect the response of the CPC loop. The STDs of Pg and \(\omega_{\text{g}}\) of the different control schemes were practically the same in each case. The average Pg, not shown in Table 4, was also the same for the different schemes. The average generated power was 15.015 MW for case 1, 15.037 MW for case 2, and 15.021 for case 3. In contrast, there were significant differences in the variables mainly related to the IPC loop. The baseline CPC showed the greatest oscillations of the OoP blade moment, whereas the IPCs managed to considerably mitigate the amplitude of these oscillations, as shown in Figure 7. Similar responses were obtained from the other simulation cases. Quantitatively, the CPC had the highest \(\overline{\text{DEL}}\)(M) value for all cases, as shown in Table 4. All the proposed IPC schemes reduced these DEL values.