A model of the back-to-back converter is set up and implemented in the simulation tool PSS/E as a user-developed model. This model is applied with that of the doubly-fed induction generator (DFIG), described in previous parts of this work [parts II and I]. The latter models variable-speed wind turbines in power stability investigations. Subjected to a short circuit fault, there will be a risk of converter blocking, followed by tripping of the wind turbine [1, 3]. The main reasons of blocking are over-current in the rotor converter and over-voltage in the dc-link. The DFIG model, with representation of the back-to-back converter, results in (a) more accurate replication of the current in the rotor converter and (b) improved computation of the dc-link voltage. These improvements are compared with the model with representation of the rotor converter only. Hence, the DFIG model with representation of the back-to-back converters might be preferred, in practical investigations of power system stability, to models with representation of the rotor converter only.