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.

In practical microgrid implementations, feeder impedance mismatches necessitate additional control mechanisms to achieve equal and proportional reactive power sharing among parallel converters. In addition, the literature review reveals the need for detailed model formulation and stability assessment of parallel grid-forming converters under practical deployment scenarios. To address this, droop control is employed for active and reactive power sharing, while virtual impedance and line impedance compensation loops are integrated to improve reactive power distribution. In this paper, a comprehensive small-signal state-space modeling for assessment of grid-forming converters in islanded AC microgrids is proposed. The proposed model includes droop control dynamics, virtual resistance and reactance loops, and line impedance compensation dynamics. Using the developed small-signal model, the influence of control and system parameters including active (m_p) and reactive power droop coefficients (n_q), virtual resistance (r_v) and reactance (x_v), line compensation filter cutoff frequencies (ω_v), active and reactive proportional power-sharing coefficients, and filter inductances (L_f) on system stability is thoroughly analyzed. Based on Eigen-value analysis, the stability boundaries of critical control and system parameters are identified, providing valuable insights for the design of robust and stable control strategies, while simultaneously ensuring accurate equal and proportional sharing of both active and reactive power among parallel grid forming converters under practical impedance mismatch conditions. The proposed models and stability analysis are validated through the Typhoon hardware-in-the-loop (HIL) testbed.