## 5 Results and Analysis  
The first experiment consists of tracking the power reference for a stepwise changing effective wind speed over 12 m/s, i.e., in Region III. Both the output power and pitch angle satisfy the operating conditions, as shown in Figure 11.  
As satisfied operational conditions, it is meant here that the power output follows the reference signal despite changes in wind speed, disturbances are compensated, and the output of the pitch controller never saturates. The settling time for a tolerance band of 5% is normally calculated as three times the second order time constant \(T_{s}\) (see, e.g., [35; 36]). Since \(T_{s}\) = 117.39 s for the rotor, the open-loop settling time is about 352.18 s. According to the simulation results, the settling time varies from 45 to 65 s, depending on the operating time, which corresponds to a reduction of about five times regarding the open-loop value. Thus, they can be considered good numbers for a machine with a very high inertia. The abrupt changes in wind speed are constant disturbances to the control system, which eliminates them in a short time of about 27 s. It should be mentioned that such abrupt changes are not realistic, and they are used to test the behaviour of the control system in the worst conditions. The gain scheduling adaption as well as the correction for \(P_{ref}>P_{max}\) are not necessary in this case. It is important to note that the power reference after 9.2 min is over the rated value, i.e., under up-regulation conditions. Thus, the control system responds correctly to both down-regulated and up-regulated operations. In the second experiment, the wind profile is changed such that between 6.7 and 10.85 min, the operation takes place in Region II. Moreover, between 9.15 and 10.85 min, \(P_{ref}>P_{max}\). The corresponding curves can be observed in Figure 12. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Parameters**} & **Torque** & **Pitch** & **Power** \\  & **Controller** & **Controller** & **Controller** * \\ \hline Proportional gain \(K_{P3}\) & 0 & 0 & 5.0 \\ Integral gain \(K_{i1}\) & 0.012 & \(-\)0.01565 & 1825.18 \\ Integral gain \(K_{i2}\) & 0 & 0 & 786.39 \\ Integral gain \(K_{i3}\) & 0 & 0 & 0.0005 \\ \hline \hline \end{tabular}  
* These parameters correspond only to the operating point at the rated power. All controller parameters are given in Table 3.  
\end{table} 
Table 2: _Cont._  
Figure 11: Power tracking control in Region III. It is possible to observe that the control performance deteriorates notoriously when the wind speed falls below 10 m/s. This is because the operating point is far away from the rated value, and the controller with fixed parameters is no longer optimal. In addition, the integrator of the PI controller integrates a constant control error, and the consequence becomes evident at the end of time 10.85 when the controller loses its tracking property and the power output becomes unacceptable. This situation should be prevented by the supervisor, but if that is not the case, the local controller has to be able to manage the situation to avoid the tracking operation or, sometimes, the system stability. Thus, the third experiment consists of testing mechanisms to avoid output saturation affecting the tracking control system. To this end, two mechanisms have been implemented and evaluated. The first one consists of switching off the integrator and resetting its internal states. The procedure can be formulated by  
\[K_{i}=(P_{ref}\leq P_{\max}(v_{w}))\cdot K_{i}+(P_{ref}>P_{\max}(v_{w}))\cdot 0,\ x_{i}(0)=0, \tag{6}\]  
where \(x_{i}\) is the internal state of the integrator. The second mechanism is to switch the reference signal to the maximum available power, i.e.,  
\[P_{ref}=(P_{ref}\leq P_{\max}(v_{w}))\cdot P_{ref}+(P_{ref}>P_{\max}(v_{w})) \cdot P_{\max}(v_{w}) \tag{7}\]  
All simulation conditions are the same as for the previous experiment. Both mechanisms lead to different dynamic behaviours. Therefore, controller parameters needed to be tuned separately for each case.