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With the integration of renewable energy sources into the power grid, a number of power electronic converters need to be connected together in parallel. Due to this interconnection among the power converters with a common DC bus, the equivalent impedance of the DC network, i.e., DC network impedance (DCNI) of these parallel converters, may vary and can cause oscillations in the DC link voltage (DCLV). In the literature, impedance models of grid-tied converters (GCs) based on the AC side are well reported without including these variations in DCNI. In addition, the dynamics of a phase-locked loop (PLL) play a significant role in GC system stability. To evaluate these stability issues, this paper proposes small signal impedance models viewing from the DC side of a three-phase GC operating under different control modes considering the PLL dynamics and the DCNI variations. Using the proposed DC impedance models (DCIM), DCLV stability analysis is evaluated for a GC. It is verified through bode plots that the interaction between the proposed DCIM and DCNI leads to unstable operation of the closed-loop converter near the PLL bandwidth when the phase difference between DCIM and DCNI is more than 180 degrees. Finally, the analytically developed models are validated using hardware in-the-loop (HIL) testing. [ABSTRACT FROM AUTHOR]