## 4 Case Studies to Validate the Self-Tuning Algorithm  
For the considered process, an induction generator integrated into a wind energy conversion system, high variations of the wind speed (produced by wind gusts), over a certain limit, may require the disengagement of the energy conversion system to protect it (for example, by furling the wind turbine). Also, a strong disturbance produced by a high electrical load/unload can activate the protections that disengage the system. Any solution that can increase the allowed value range of disturbances extends the functionality domain of the controlled process. Therefore, maintaining the functional capabilities of the control system (energy production, energy supply to consumers), even under harsher conditions caused by highly disturbances, is the main goal of the proposed strategy. Any disturbance that acts on the system causes a process output error (this being the main indicator that signals a disturbance). For this reason, the next tests will target both the load/unload regime (when the disturbance is not directly measurable) and the case of a mechanical torque variation (although this could be also directly measured, but an output error occurs anyway). The mechanical torque variation is an effect of wind speed variation, considering the generator integrated into a wind energy conversion system. The load/unload regime means a variation of the electrical admittance at generator terminal, as effect of consumers connecting/disconnecting. The mechanical torque \(T_{m}\) (its variation being seen as a disturbance) is a parameter referred in the equation describing the mechanical motion within the induction generator mathematical model. Also, the connection between the induction generator and the power system includes a local electrical consumer connected at generator terminals, so the equations describing the terminal voltage projections of the stator load winding \(d\)-\(q\) axis integrates the consumer electrical admittance, also considered as an internal parameter whose variation disturbs the system. The complete model of the dual fed induction generator (DFIG) connected to a power system (PS) through a long transmission line is presented in the Appendix A[10]. For different values of the control penalty factor (\(\rho\)), the control system performance and the stability will be analyzed in order to find the maximum allowed perturbation for which the process can still operate. The first study case takes into consideration a mechanical torque variation as an external perturbation produced by wind gusts. (a) Mechanical torque variation (\(\Delta T_{m}\))  
For several tuning values of \(\rho\), Table 1 concisely shows the results of performed tests, highlighting the control performance. For a set of smaller values of the control penalty factor (\(\rho=0.0001\), \(\rho=0.001\), \(\rho=0.01\)), the controlled output is depicted in Figure 3a-c. For all these three values of the control penalty factor, the maximum disturbance for which the control system remains stable is \(\Delta T_{m}=16\%\). A higher variation of the mechanical torque, over this threshold (\(\Delta T_{m}>16\%\)), leads to an unstable system due to the huge values of a weakly penalized control. Also, a degradation of the control performance can be noticed with the increase of the control penalty. Thus, the settling time successively increases and the transient regime is longer (see Table 1). The best performance is obtained for \(\rho=0.0001\) (settling time = 0.2 s, overshoot approx. 4 V), while for \(\rho=0.001\), the settling time is over 0.5 s, respectively, and for \(\rho=0.01\), it is over 1 sec.