Compared with a conventional two-stage inverter, the quasi-Z-source inverter (qZSI) has several advantages for renewable applications because of its buck-boost capability and continuous input current. This paper addresses modeling and control issues resulted from the impedance-source network resonance. Considering shoot-through states, null states, and active states, the modulation ratio is included in the modeling process. Unlike prior-art modeling methods to separate the DC and AC parts, the proposed modeling method considers the impedance source network as an open-loop impedance at the input of the AC side. The resonant characteristic of the converter is investigated and the AC controller is designed in detail. Simulations are presented to validate the modeling and control methods.