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Typically, permanent magnet synchronous generator (PMSG)-driven wind turbines (WTs) present a two-stage power converter topology based on a DC/DC boost converter and voltage source inverter. In this study, this configuration is substituted by a quasi-Z-source inverter (qZSI), which is an attractive solution for boosting and converting the voltage from DC to AC in a single stage. A 2 MW PMSG WT with qZSI was studied herein. A switched dynamic model (SDM) of the qZSI (including the modeling 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 firing pulses, which is not necessary in the averaged models. The two proposed models were 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 in the simulation time and computational efforts., This work was supported in part by the Spain's Ministerio de Ciencia, Innovacion y Universidades (MCIU), Agencia Estatal de Investigacion (AEI), and Fondo Europeo de Desarrollo Regional (FEDER) Union Europea (UE) under Grant RTI2018-095720-B-C32, in part by the National Council of Technological and Scientific Development (CNPq), Brazil, in part by the Federal Center for Technological Education of Minas Gerais, Brazil, under Process 23062-010087/2017-51, and in part by the Regional Ministry of Economic Transformation, Industry, Knowledge and Universities of Junta de Andalucia under Grant PY20_00317.