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In this paper, a full (expanded) model of basic components of a 2.5 MW doubly fed induction generator (DFIG) based wind turbine will be described. This model includes mechanical components like wind turbines rotor, shaft and gear box; and electrical components such as DFIG and active and reactive power controller systems. After that, a new fast model of DFIG based wind turbine will be developed based on algebraic equations. And at the end, comparison between two described models proves the effectiveness of suggested fast algebraic model. All models have been developed by MATLAB/Simulink in d-q synchronous reference frame.