Due to the increasing popularity of renewable energies, a significant share of the power generation in future microgrids is expected to originate from converter-interfaced Distributed Energy Resources (DERs). Traditionally, idealized device models are used to conduct grid stability studies. For instance, a DER interfaced via a Voltage-Source Converter (VSC) would be modeled as an ideal current or power source (depending on the control schemes), ignoring non-ideal behavior like the response of the converter synchronization. However, such a simplification may lead to misjudging the stability, in particular for weak microgrids. To address this issue, ZIP models of grid-interfaced VSCs, which take into account both the control scheme and the synchronization, are developed in this paper. The influence of the synchronization response on the stability of a weak microgrid system is demonstrated using a benchmark system simulated in MATLAB/Simulink. It is shown that the idealized models normally used for static stability analysis do underestimate the voltage stability issue in the investigated microgrid system.