# Wind Turbines Around Cut-In Speed: Startup Optimization and Behavior Analysis Reported to MPP
## 1 Introduction  
The fulfillment of the Sustainable Development Goals also envisages the development of renewable energy production systems, so that it is accessible to all socio-economic sectors, and the price is convenient for consumers [1]. Wind energy is one of several renewable energy sources used in the production of electricity due to rising electricity consumption and environmental pollution. In choosing the type of wind turbine, the control system must consider the characteristics of the area, wind speed, climatic conditions, local and regional regulations as well as the length of the investment, which for a wind farm is about 10 years [2, 3]. Currently, wind systems are also used together with other electricity production and/or storage systems. One of the most widely used storage systems is the pumped storage plant, which has a large storage capacity and contributes to the stability of the power supply system [4, 5]. The overall efficiency of the wind energy system is significantly affected by the aerodynamic characteristics of the turbine, which can be enhanced through advanced aerodynamic modeling and refined design techniques. In the realm of design, certain researchers advocate for the integration of Industry 5.0 principles alongside optimization methods utilizing genetic algorithms. This innovative strategy has resulted in production improvements of as much as 10% [6]. Most wind turbines are designed to provide power output depending on wind speed, not being able to quickly change their power to sudden changes in load [7]. In order to ensure maximum capture of wind energy, it is necessary to identify the dependence of the optimal mechanical angular speed (_MAS_) on wind speed. This dependence can be determined by calculating the maximum power provided by the wind turbine, _WT_, at different wind speeds, also considering the energy efficiency of the wind system [8; 9]. In the case of offshore wind systems, it has been found that the tracking of the maximum power point (_MPP_) and the control of the total output power of the wind system can be performed by controlling the current of the d-axis of the active rectifier related to the system [10]. Recent studies examine and outline various control strategies, including maximum power point tracking, control of turbine blade pitch angles, and stationary wind turbine control [11]. A challenge for variable renewable energy sources (_RES_) in isolated grids is to ensure control of the frequency of supply voltage and system stability [12]. Thus, in the situation where the share of _RES_ is 100%, and the production system is hybrid, consisting of a hydroelectric unit, a pumping plant and a wind farm, it is also necessary to introduce energy storage system [13; 14]. This will significantly improve frequency control and ensure continuity in supply, even if the wind speed is not constant. Power oscillations affect the structural system of turbines. To dampen these oscillations, power oscillation damping (_POD_) regulators are used, whose effect on the wind tur-bines is comparable to that determined by variations in wind speed and much lower than that determined by transient effects in the case of three-phase short circuit [15]. In cases of the use of a double-powered induction generator (_DFIG_) with an adequate controller in wind power systems, following determinations based on numerical simulations, it was found that it works properly in dynamic regimes determined by fluctuations in wind speed and changes in grid energy values [16; 17]. In order to analyze the operation of the wind system, it is necessary to know the wind speed [18]. This is usually measured with the sensor located on the nacelle, but there are situations in which the measured value is different from the actual wind value. In [19], to determine the effective wind speed it is proposed to reverse the aerodynamic model of the turbine after estimating the related torque and the speed of the turbine rotor.