# Wind Turbines Around Cut-In Speed: Startup Optimization and Behavior Analysis Reported to MPP
## 1 Introduction
This method proved to be accurate under laboratory conditions and can be used in regulation and control structures related to wind power systems. Another method used to measure wind speed is to determine the speed with a low-power turbine, which operates without load at mechanical angular speed [20]. Previous research on wind speed forecasting, essential for modeling, employs artificial intelligence that utilizes statistical models grounded in machine learning [21]. In all cases, the control functions of the entire system play an essential role in achieving increased wind turbine efficiency [9; 22; 23; 24]. The use of applications for modeling and simulating the operation of wind systems is important both in the design and operation optimization phases, as they allow, through the mathematical models used, the realization of different configurations and different operating scenarios for the steady state and transient regime [25; 26; 27; 28]. Also based on simulations and experimental data regarding the value of the wind turbines provided power, it is possible to establish whether their operation is in the optimal zone in terms of captured energy [29; 30; 31; 32]. In this paper, the mathematical models of the wind turbine and the double powered asynchronous motor are determined by switching the electric generator into motor mode, so that the turbine reaches the optimal speed in the shortest possible time interval and operates in _MPP_[8; 9]. One of the main contributions consists of visualizing the commissioning process of high-power wind turbines equipped with dual-powered induction generators. In the specialized literature of the approached field, for the commissioning of high-power wind turbines to operate at the point of maximum power, simulations with the dual motor powered by the stator and rotor connected to the same frequency network have not been identified [2; 5; 20]. Wind turbines reach the _MPP_ at the optimal mechanical angular speed, in a time interval of tens of seconds. This article addresses precisely this problem: the optimal operation of high-power wind power plants by driving the wind turbine with the dual motor powered by the stator and rotor at the same frequency. At wind speeds that vary over time, the wind turbine operates permanently in dynamic mode at variable speeds [10; 13]. The process being dynamic, we use the equation of the kinetic momentum [7; 14; 16] of the form:  
\[J\cdot\frac{d\omega}{dt}\cdot\omega=P_{WT}+P_{ENGINE} \tag{1}\]  
where \(\omega\)--mechanical angular speed, _MAS_, at the shaft of the electric motor/generator, _J_--the equivalent moment of inertia, \(d\omega\)--the derivative with respect to time of _MAS_, \(P_{WT}\)--the useful power given by _WT_ relative to the shaft of the electric motor/generator, \(P_{ENGINE}\)--the electromagnetic power at the shaft of the induction motor. The double-powered induction motor, coming from the double-powered induction generator, having the same frequency in the stator and rotor, becomes the synchronous motor. The synchronous motor operates at variable frequency and controlled stator flow. This paper examines the challenges associated with the integration of wind turbines into the energy system, particularly as wind speed increases from zero to the cut-in speed. The power generated by the turbine is contingent upon the wind speed, \(\
u\), and the rotational speed, \(n\). The wind energy system operates at the maximum power point within the optimal range at the ideal rotational speed [29], as exemplified in Figure 1.  
The rotational speeds of wind turbines equipped with a gearbox are referenced to the shaft of the electric generator. At the turbine shaft, the rotational speed values are \(k_{\rm T}\) times lower, where \(k_{T}\) represents the gear ratio of the transmission. The wind speed is a fundamental parameter that determines the optimal rotational speed, \(n_{OPTIM}\), ensuring that the turbine operates at its maximum power point.