## 1 Introduction  
To achieve sustainable development goals, it is essential that green energy constitute an increasing share of gross energy consumption. Consequently, in accordance with the latest European directives, it has been established that by 2023, the proportion of renewable sources in gross energy consumption should be at least 42.5%, with a target of reaching 45% [1]. Figure 1 illustrates the variation in the primary sources contributing to electricity production [2]. The analysis reveals that in the year 2000, the energy generated from solid fuels was 800,340 GWh, whereas in 2023 it decreased to 321,498 GWh, representing 40.17% of the initial value. Concurrently, the share of renewable sources has increased significantly, from 406,997 GWh in 2000 to 1,213,388 GWh in 2023, indicating an approximate growth of 33 times compared to the value in 2000 [2]. Regarding the development of installed capacity in wind power plants across Europe, the period from 2013 to 2022 shows a doubling of the installed power (Figure 2) [3]. Regarding the utilization of renewable energy, several challenges have been identified that are relevant to this study, as noted in [4]:  
* The high cost of the initial investment, particularly in cases where there are no government subsidies for the large-scale implementation of these solutions;
* The shortage of qualified human resources capable of installing, operating, and maintaining electricity generation systems;
* The inadequate communication among the parties involved regarding the benefits associated with the implementation of renewable energy generation systems;
* The low reliability of transport networks, which prevents multiple individuals or legal entities from injecting any power into the grid. Recently, an increasing trend has been identified regarding the integration of wind systems in the production of electricity [5]. This fact is also determined by the consideration that the amortization period of the investment is an acceptable one. Thus, following new studies, it was established that for a wind farm with a power of 105 MW, investment is amortized in 9.1 years, so this sector is in continuous development due to the benefits brought in the long term [6]. Regarding the integration of wind turbines into electricity production systems, it is essential that this process also ensures the stability of the electricity transport/distribution  
Figure 1: The variation in electricity production based on the energy source. Figure 2: The variation in installed capacity of wind power plants across Europe. system. To verify the fulfillment of this requirement, prior simulations are necessary, utilizing dedicated programs to determine the impact of renewable sources on the stationery and dynamic stability of the system [7]. It is well known that wind turbines are designed and selected to operate under specific weather conditions and mechanical stress requirements. During operation, these parameters may vary, leading to the conclusion that a continuous correlation between wind speed and optimal angular mechanical speed is essential for delivering maximum power [8; 9; 10]. To measure or calculate wind speed, various methods are employed, such as  
* The use of a small power turbine operating at maximum power in free air [11];
* Reversing the aerodynamic model of the turbine based on the estimated values of the turbine's torque and rotor speed [12];
* Estimating the rotor speed of the turbine and its torque, utilizing the inverse aerodynamic model and nonlinear control theory [13]. The operation of wind turbines encounters the issue of unpredictable variability in wind speed, impacting both the output power and the structural stability of the turbine system [14].