Abstract: Wind turbine systems are complex, nonlinear, unstable systems with inherent uncertainties, making model establishment difficult. Adaptive control studies such uncertain systems and can reduce the impact of uncertainties by adjusting controller parameters. A model reference adaptive method is used to control a variable-speed wind turbine at rated wind speed, maximizing wind energy output. Simulation results show that this method is effective in controlling variable-speed wind turbines at rated wind speed. Keywords : Wind turbine; Model reference adaptive control; Lyapunov equations Introduction In the past five years, the newly installed capacity of wind farms in China has doubled, thanks to increased emphasis on environmental protection and advancements in wind turbine technology. Although fixed-speed wind turbines remain dominant in China, variable-speed wind turbines are gradually maturing and being put into operation. By adjusting the speed, the tip speed ratio of the wind turbine is maintained at an optimal position. Variable-speed wind turbines offer up to 20% higher wind energy utilization, reduce blade load, and increase single-unit capacity, but also increase the complexity of the control and power systems. Therefore, research on control systems is essential. The rotor of a wind turbine converts part of the wind's kinetic energy into mechanical energy, and its efficiency varies with the blade pitch angle and tip speed ratio. For variable-pitch wind turbines, the output power is adjusted by regulating the pitch angle when the wind speed is above the rated speed. Below the rated wind speed, the pitch angle of a variable-speed wind turbine is typically zero degrees, and the conversion efficiency reaches its maximum at a certain tip speed ratio, theoretically not exceeding the Betz limit (0.593). Considering the nonlinearity of the wind turbine and the operating characteristics of the system, the literature uses linearization near the operating point to establish a linear model and designs the controller using linear system methods. Using nonlinear theory to establish a more accurate nonlinear model, establishing error equations, and making the error asymptotically stable requires a high degree of fit between the model and the system. In addition, intelligent control methods have been reported in recent years. In fact, the nonlinearity of wind turbines originates from aerodynamic relationships, therefore its accuracy is not high, and due to the influence of climate, temperature, and humidity, the system usually exhibits slow time-varying characteristics. This paper uses the Model Reference Adaptive Control (MRAC) method to analyze the variable-speed wind turbine system. The linearized model of the wind turbine system near the operating point is introduced in Part 2. Since wind speed is uncontrollable, it can only be used as a disturbance input. The model reference adaptive method is described in detail in Part 3. Considering the difference between the disturbance input and the natural frequency of the wind turbine system, an inertial element is used as the reference model, and the control input is designed to meet the requirements of MRAC to obtain the adaptive rate of the control quantity. Finally, a simulation of a certain turbine model is performed to verify the effectiveness of the method. [b]For more details, please click to download the variable speed wind turbine model reference adaptive control[/b]