## 2 Properties and Characteristics of the Analyzed Wind Turbine  
This paper examines the operation of the wind turbine, \(WT\), which is equipped with a squirrel-cage induction generator, under substantial variations in wind speed [16; 22]. The technical characteristics of the turbines are rated power at 10 m/s--55 kW, wind speed--2.5 m/s to 25 m/s, survival wind speed--59.5 m/s, no of blades--3, diameter of rotor--20 m; swept area--314 m, and tower height--18 m [27]. We consider that the wind speed varies within the range of (0 to 120) km/h. It is known that at low wind speeds, specifically below 3 m/s, wind turbines remain stationary, with a rotational speed of zero [8; 26]. They become operational at speeds exceeding 3 m/s, and within the range of (3 to 10) km/h, they operate at maximum power points (_MPPs_) (Figure 3) [28]. In certain studies, an asynchronous generator equipped with a dual _AC-DC-AC_ power converter has been analyzed, which, through its control methodology, enables the maximization of power output across a wide range of wind speeds [29]. Figure 3: The power characteristics. The turbine's power, _WT_, depends on the wind speed, \(V\), and the _MAS_, \(\omega\), whereas the power of the electric generator, _EG_, is influenced by the stator voltage, _U_\({}_{S}\), along with the mechanical angular speed, \(\omega\). Additionally, it is essential to consider the altitude at which the turbines are installed, as a lower air density results in a decrease in the power output [30]. For the purpose of analysis, technical data pertaining to a 55 kW wind turbine was examined [31]. The power characteristics of the turbine at two wind speeds, _V_\({}_{1}\) = 3 m/s and _V_\({}_{2}\) = 10 m/s, are illustrated in Figure 3.  
The fluctuation in wind speed, represented within these parameters, is highlighted in green within the operational zone. The turbine's maximum power characteristic, _PWT-MAX_(\(\omega\)), intersects the maximum power points, _MPP_ 1, at a wind speed of _V_\({}_{1}\) = 3 m/s, and _MPP_ 2, at a wind speed of _V_\({}_{2}\) = 10 m/s. For the analyzed case, the power characteristic at _V_\({}_{1}\) = 3 m/s is defined by the relationship  
\[P_{WT-1}(\omega,3)=19182\left(\frac{3}{\omega}-1.3877\cdot 10^{-2}\right)\cdot e ^{-57.63\cdot\frac{3}{\omega}}\cdot 3^{3}\left[\text{W}\right] \tag{1}\]  
and for _V_\({}_{2}\) = 10 m/s by the relationship  
\[P_{WT-2}(\omega,10)=19182\left(\frac{10}{\omega}-1.3877\cdot 10^{-2}\right) \cdot e^{-57.63\cdot\frac{10}{\omega}}\cdot 10^{3}\left[\text{W}\right] \tag{2}\]  
The maximum power characteristic developed by the turbine is  
\[P_{WT-MAX}(\omega)=1.6744\cdot 10^{-3}\cdot\omega^{3}\left[\text{W}\right] \tag{3}\]  
Fixed-blade wind turbines are protected against strong winds (over 25 m/s) by several methods, because they do not have the ability to adjust the pitch of the blades to reduce speed. When wind speeds exceed 10 m/s, to prevent damage to the structural integrity of the wind system, it is necessary to engage the turbine rotor's braking mechanism using a furling system. This allows the turbine to automatically turn away from the direction of strong winds, thereby reducing the force exerted on the blades and limiting the generator's rotational speed. As the turbine blades are no longer perpendicular to the airflow, the rotational speed decreases and the load on the generator diminishes, thereby safeguarding the turbine from overloading. In the absence of a furling system, a mechanical brake will be employed at high wind speeds to keep the rotor's speed within the nominal operating limits [12; 13]. Consequently, the speed of the generator must be adjusted in accordance with the ratio 1/3.3. To achieve optimal energy performance within this speed range, adjustments are made to the voltage and frequency at the generator by utilizing power converters [32; 33] that are connected to the stator of induction generators with a short-circuited rotor or to the rotor of induction generators equipped with slip rings.