Photovoltaic (PV) power systems are increasingly being used as renewable power generation sources. Quasi-Z-source inverters (qZSI) are a recent, high-potential technology that can be used to integrate PV power systems into AC networks. Simultaneously, concerns regarding the stability of PV power systems are increasing. Converters reduce the damping of grid-connected converter systems, leading to instability. Several studies have analyzed the stability and dynamics of qZSI, although the characterization of qZSI-PV system dynamics in order to study transient interactions and stability has not yet been properly completed. This paper contributes a small-signal, state-space-averaged model of qZSI-PV systems in order to study these issues. The model is also applied to investigate the stability of PV power systems by analyzing the influence of system parameters. Moreover, solutions to mitigate the instabilities are proposed and the stability is verified using PSCAD time domain simulations.