  An islanded microgrid supplied by multiple distributed energy resources
(DERs) often employs droop-control mechanisms for power sharing. Because
microgrids do not include inertial elements, and low pass filtering of noisy
measurements introduces lags in control, droop-like controllers may pose
significant stability concerns. This paper aims to understand the effects of
droop-control on the small-signal stability and transient response of the
microgrid. Towards this goal, we present a compendium of results on the
small-signal stability of droop-controlled inverter-based microgrids with
heterogeneous loads, which distinguishes: (1) lossless vs. lossy networks; (2)
droop mechanisms with and without filters, and (3) mesh vs. radial network
topologies. Small-signal and transient characteristics are also studied using
multiple simulation studies on IEEE test systems
