# A Maximum Power Point Tracking Control Method Based on Rotor Speed PDF Shape for Wind Turbines
## 1 Introduction  
As a green renewable clean energy, wind power has attracted much attention, and its conversion has been widely concerned in recent decades [1; 2]. The acquisition of more wind energy not only needs to improve the mechanical characteristics of wind turbines but also needs to continuously optimize the control method. The strategy to improve its power coefficient (\(C_{p}\)) or achieve power close to its maximum value is known as maximum power point tracking (MPPT). However, with the continuous large-scale development of wind turbines, the slow motion caused by the large inertia and the nonlinearity of wind turbine make it more and more difficult for the wind turbine to respond to the stochastic wind timely and accurately. Therefore, it is of great significance to study how to better improve the conversion efficiency of wind energy based on the dynamic tracking process and wind speed distribution characteristics. Most of the reported MPPT algorithms in general fall into three major categories, namely, tip speed ratio (TSR) algorithm, hill-climbing search (HCS)/perturb and observe (P&O) algorithm, and optimal torque (OT)/power signal feedback (PSF) algorithm [3]. The OT algorithm focused on this paper is often used in engineering practice because of its simplicity and practicality. To make full use of wind energy, many scholars have conducted in-depth studies on the application of OT control [4; 5; 6]. [PERSON] et al. [7] added a correction component of generator torque to accelerate the transient response of wind turbines considering the influence of acceleration torque term on tracking effect. [PERSON] et al. [8] estimated the turbine aerodynamic torque on the premise of centralized single mass transmission system. Based on the previous research, [PERSON] et al. [9] proposed two improved MPPT methods based on the double-mass flexible-shamost reported improvements focus on the tracking of precise operating points, ignoring the influence of wind speed distribution characteristics. For wind turbines, especially large inertia turbines, the current MPPT control methods cannot guarantee the effective tracking of any wind speed, i.e., these methods cannot guarantee the real-time and accurate tracking of the optimal tip speed ratio. Even in some cases, it may lead to an additional energy extraction from the power grid to achieve good tracking, which violates the fundamental purpose of wind turbine control. In wind power generation system, the random wind speed will increase the difficulty of the stochastic control. Since [PERSON] et al. [10] introduced the probability density function (PDF) into the field of stochastic control, PDF shape control has been widely used. PDF control method emphasizes that the controller is designed by tracking the desired PDF shape. The application of introducing PDF shape control theory into MPPT control can not only avoid the shortcomings of blind tracking, but also consider the wind speed distribution characteristics. At present, the Fokker-Planck-Kolmogorov (FPK) equation [11] is the most advantageous method to study the PDF shape control of nonlinear stochastic systems. Some related control designs in wind power generation system have been proposed. [PERSON] et al. [12] proposed that PDF controller should be designed by the error between output and optimal turbine rotor speed, that is, by controlling the PDF shape of tracking error to present a narrow distribution. This method can ensure that the system tracking error is gradually reduced and finally stabilized near zero, to achieve the output distribution control of maximum wind energy tracking. [PERSON] et al. [13] proposed a PDF adjustment algorithm to obtain the adjustment gain of the system controller by solving the FPK equation. Although several design methods [14; 15] to solve FPK equation have been provided, few scholars have paid attention to the PDF control applied to the application of PDF control in wind turbine control.