This paper presents the explicit electromagnetic transient model of a Doubly Fed Induction Generator (DFIG), that includes its coupling with the back-to-back converter, when the generator/converter set is connected to the wind farm's Thevenin equivalent, as seen from DFIG's terminals. Besides that, DFIG's grid side converter control system is defined in detail, so that expressions for the direct tuning of all compensators are provided. The overall electromechanical wind generator model includes 24 state variables: four mechanical, eleven electrical, and nine more - one for each controller - associated to the control system. The developed model is complemented with a state machine that implements the sequential control among the different stages that define its operational modes. Simulation and experimental results show that the developed model is able to predict the behaviour of the generator in short and long term scenarios. (C) 2015 Elsevier Ltd. All rights reserved.