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Typically, permanent magnet synchronous generator (PMSG)-driven wind turbines (WTs) present a two-stage power converter topology based on DC/DC boost converter and voltage source inverter. In this paper, this configuration is substituted by a quasi-Z-source inverter (qZSI), which is an attractive solution to boost and convert voltage from DC to AC in a single stage. A 2 MW PMSG WT with qZSI is studied herein. A switched dynamic model (SDM) of the qZSI (including the modelling of all switches and firing pulses) is not recommended for steady-state stability studies, long-term simulations, or large electric power systems. For such studies, two averaged dynamic models are proposed in this work. Both models present the same control system as the SDM, except for the generation of the firing pulses, which is not necessary in the averaged models. The two proposed models are evaluated and compared with the SDM in the large-scale WT under different operating conditions, such as wind speed fluctuations, variable power references, and grid disturbances (voltage sag and 3 rd and 5 th order harmonics injection), in order to demonstrate their adequacy to represent the system response with a high reduction of the simulation time and computational efforts. INDEX TERMSControl system, modelling, quasi-Z-source inverter, wind turbine.