## 4 Simulation Results
### Variable Environmental Conditions  
Two of the major drawbacks of renewables are the difficult predictability and the high variability of their primary resources, i.e., the wind and solar irradiance. In the field of primary frequency control, which takes place in the time window of a few seconds after a disturbance, this variability affects their response, especially for what concerns the wind energy. If the sun variations are fast but occur less frequently, the wind variations are huge and occur continuously. In this sense, the most critical situation is represented by windy days with some small clouds, in which both the wind and the irradiance are very variable. The aim of these tests is to understand how much the variability of the renewable source affects primary frequency control if the renewables are rigid and they do not participate in it and, on the other hand, in the case they are able to modulate their power output to smooth their power variations. Furthermore, as for the second group, a part of the reserve will be already occupied to balance the natural variability of the resource, so, in case of a perturbation of the load, the reserve level could be less than the nominal amount. The first analysis regards the most critical of the two resources: wind. In Simulation 6 and 7, the system is tested in the four scenarios with a real high variable wind profile. The wind profile has been downloaded from a DTU database of measurements in [38] and has the shape depicted in Figure 17.  
Figure 16: Simulation 5 frequency trend. Figure 17: Real wind profile used in the simulations. The profile has been used as an input for the wind turbine system, which is not anymore free to adapt its output only to balance the frequency: now it also has to face a variable availability of the wind resource. This means that a part of the reserve could be already involved in the balancing of the frequency consequent to a wind speed variation, reducing the capability to counter a step of load power. Simulation 6 studies the effect of the variable wind profile on the frequency. In particular, it is interesting to observe the response in the case of the wind turbine with virtual inertia control enabled compared with the base case without frequency response capabilities. The results are shown in Figure 18. In this simulation, the variability of the wind has been introduced after 64 s, so that its effects are more visible starting from a steady state condition. In the base case without frequency control enabled, the wind turbines modulate their power to always produce at their maximum. This means that they do not detect that their behavior is causing the system's frequency to oscillate. It is possible to observe, indeed, that the frequency has a number of peaks in correspondence with the peaks of the wind speed. This trend will stress the system, requiring an intense control action from the synchronous generators. On the other hand, if the wind turbines are able to exploit their kinetic energy using the Extended OPPT method, it is evident how they smooth their power variation, producing lower peaks and stressing the power system less. Looking at the largest nadir reached in the variable wind period, in the first scenario it is equal to 0.9975 pu (49.875 Hz), while in the updated scenario is 0.9977 pu (49.885 Hz). The reduction in the nadir is not so pronounced between the two, but the benefits consequent to the introduction of the Extended OPPT Method are evident considering the trend of frequency, since the amplitude of each oscillation is lowered. This fact is confirmed by the plot of the RoCoF, which highlights how the rate of variation of frequency is slower and smoother in the second scenario (Figure 19). For what concerns the irradiance variation, Simulation 8 has been inspired by the dynamic EN50530 test, which is recognized as one of the techniques to evaluate the MPP tracking effectiveness [19]. It consists of a sequence of ramping up, constancy, and ramping-down the solar irradiance hitting the module.