The generator acts as the primary component in a wind turbine (WT) system since it transforms mechanical energy into electrical energy. Most wind turbine malfunctions are caused by an unreliable generator. As a result, it is now more important than ever to understand the specific characteristics of the generator in wind turbines in order to avoid errors. The objective of this paper is to create a mathematical model of a wind turbine generator that is simply changeable to apply any generator fault for the research of the dynamic WT system. This is because the majority of developed WT models are either too simplistic in generator modelling or have intellectual property protection. MATLAB/Simulink was used in this research to create the mathematical model of the induction generator based on a wind turbine. The wind turbine model that was built comprises of an induction generator model, an aerodynamic model, and a wind turbine drive train based on two mass models. Electrical equations in Park's reference frame served as the basis for the development of the induction generator. Electrical and mechanical subsystems make up the model. The proposed model of the wind turbine with an induction generator was then verified using a thorough MATLAB model of a wind farm with a doubly-fed induction generator (DFIG). Comparisons were made between the two models' simulated responses for mechanical torque, electrical torque, generator speed, and power. The outcome demonstrates that both WT models' simulated responses shared the same waveform shape