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This paper deals with modeling of the doubly-fed induction generator (DFIG) and the corresponding converter for stability studies. To enable efficient computation a reduced order DFIG model is developed that restricts the calculation to the fundamental frequency component. However, the model enhancement introduced in the paper allows the consideration of the alternating components of the rotor current as well which is necessary for triggering the crowbar operation. Suitable models are presented for the rotor and grid side converters as well as the DC-link taking into account all four possible operating modes. The proposed model for speed and pitch angle control can be used when wind and rotor speed variations are significant. Simulation results are presented for model verification purposes and also for demonstrating the dynamic behavior of offshore wind farm connected through a long submarine cable to the high voltage grid.