Modeling and Stability Analysis of Islanded AC Microgrids with Virtual Impedance and Line Impedance Compensation Control Loops

Small signal mathematical modeling and eigenvalue-based stability analysis of islanded AC microgrids with conventional droop control are well established in the literature. However, virtual impedance and line impedance compensation loops are not included in the controller to improve reactive power sharing when converters have different feeder impedances. This paper proposes small signal models with virtual impedances and line impedance compensation loops for an islanded AC microgrid. Each sub-module is modeled in a state-space representation and ultimately combined in a common reference frame. The formulated state space matrix includes all the controllers and system parameters. Further, an eigenvalue-based stability analysis is performed using the derived models. The effect of droop coefficients, virtual resistance, virtual reactance, and filter cutoff frequency of the line impedance compensation loop on the system stability is discussed in detail. The eigenvalue analysis reveals that with the addition of virtual resistance, the stability of the system is greatly improved. The accuracy of the proposed models are verified using the MATLAB/Simulink simulation platform.