## 1 Introduction
To manage the output power and, by extension, the wind turbines at varying wind speeds, different control algorithms and methods are employed, such as  
* The implementation of an advanced torque controller, which relies on an efficient estimation of wind speed, has been shown to enhance the accuracy of wind speed estimation by 2-7% compared to alternative methods [15];
* The application of a _PID_ controller, with results assessed through performance index parameters in the time domain [16];
* The use of a controller that, based on the power curve corresponding to various wind speeds, aims to track the optimal power curve identified by the control system [17];
* The application of modified virtual inertial controllers, which also serve to enhance the damping capacity of power oscillations within the energy system [18];
* The application of vector control oriented by stator flux, achieving a reduction in the generator's impact on system stability [19]. In certain instances, various dispatch commands for the wind generator are utilized, enabling control of the generator across different wind speed profiles [20], particularly in systems that also allow energy storage [21]. In the case of isolated networks, relying solely on green energy creates challenges regarding stability and frequency control. Following a simulation analysis of a hybrid installation composed of hydropower units, a pumping station, and a wind farm, it was determined that the implementation of a battery storage system would enhance frequency control and ensure the operational security of the electricity generation system [22; 23]. Another challenge that must be considered in the operation of wind turbines involves controlling the speed during sudden discharges, which can lead to the rotor accelerating beyond the established limits [24]. There are situations in which wind farms are utilized for secondary frequency regulation [25]. In such cases, it has been observed that the use of energy for frequency regulation generates significantly higher revenue compared to merely supplying electrical energy [26]. This study addresses several significant issues in wind energy, especially concerning variable wind speeds over time: determining the mathematical model for the turbine and generator based on the technical data of the wind system; computing the values of stator frequency, current, and power factor based on wind speed; based on numerical simulations, the analysis highlights notable differences in wind energy capture, particularly at constant and variable generator power under conditions of significant temporal variations in wind speed. In contrast to the existing research, this paper places particular emphasis on cases where wind speed fluctuates significantly over time, a topic that has been inadequately addressed in the literature, which predominantly focuses on constant wind speeds. The simulations conducted highlight the effects of temporal variations in wind speed. The primary objectives pursued in this work are  
* Presentation of the current state of research concerning the behavior of wind turbines under significant variations in wind speed;
* Determining the potential power output based on the characteristics of the wind turbine and the power curve as a function of angular velocity;
* Determining the power output of the induction generator and constructing the power characteristic as a function of angular velocity, based on its rated values;
* Establishing the optimal angular mechanical speed by utilizing the mathematical model of the turbine based on its technical parameters, specifically the wind speed;
* Determining the maximum value of the power supplied by the wind turbine. The primary objective is to visualize the essential elements--power, energy, and currents--as they relate to the variable speed of the wind.