Analysis of an Impedance Modeling Approach for Droop-Controlled Inverters in System DQ Frame

Small-signal stability of droop-controlled inverters in islanded ac microgrids can be assessed by using impedance-based criterion. In order to have an accurate output impedance model for these systems, the effect of fundamental frequency must be taken into account. The existing works suggest to characterize each inverter by two transfer matrices: first, the transfer matrix between output current and output voltage (i.e., the dq-domain impedance matrix), and second, the transfer matrix between output current and fundamental angular frequency. Addressing the frequency contribution in a separate term, leads to a stability criterion, that requires an additional step, compared to the conventional impedance-based criterion in dq frame, that only needs the dq impedance matrix. This paper proposes to include the frequency contribution in the dq output impedance of droop-controlled inverters. This gives the possibility to use the dq- domain impedance-based stability criterion, even in off-grid systems. A laboratory prototype of droop-controlled inverter is implemented, and its output impedance is measured. The good matching between analytical models and experimentally-measured impedances, confirms the validity of the performed small-signal analysis.