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The dynamics of the doubly fed induction generator (DFIG) with a closed-loop control is analysed. The analysis provides explanations of the impact of the closed-loop control on the DFIG dynamics and relevant modelling requirements for power system stability studies. The discussion considers generic PI controllers for the regulation of rotor speed, reactive power and pitch angle. It is shown that for the closed-loop-controlled DFIG, a simplified model, whereby both stator and rotor dynamics are neglected, is adequate. In such model, stator and rotor variables are algebraic, that is, they change instantaneously and the modelled dynamics are those of the controllers and mechanical parts. The observations and conclusions are obtained from eigenvalue, participation factor and time-domain analysis.