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Medium‐speed wind generators in the MW‐range with high‐temperature superconducting excitation winding are analyzed by means of non‐linear 2D and 3D FEM models. Besides an inverter‐based sinusoidal stator current feeding, a grid connection via a diode rectifier is analyzed by using coupled FEM and circuit simulations. The newly proposed modeling techniques are used to determine the excitation requirement for speed‐variable, unity power factor operation at constant stator voltage, as required for a diode rectifier feeding of the stator winding. 2D FEM models in the H‐A‐formulation are developed and used for the calculation of the hysteresis loss in the superconducting field winding at stationary operation as well as for an investigation of field current variations in the HTS field winding. The major modeling challenges consist in very long settling times of voltage‐fed models, several strong model non‐linearities and high requirements on the spatial discretization. Approaches for overcoming these difficulties with reasonable computational efficiency are proposed.