  A network-level small-signal model is developed for lossy microgrids, which
considers coupled angle and voltage dynamics of inverter-based microgrids and
uses a more general framework of droop controls in the inverter. It is shown
that when relative resistances of the lines in the microgrid are reasonably
consistent and differences of voltage angles across the lines are small at the
operating point, the generalized droop controls can be designed to enforce
decoupling between angle dynamics and voltage dynamics. Next, structural
results for the asymptotic stability of small-signal angle and voltage dynamics
are given for the case when generalized droop control achieves decoupling.
Simulated transient responses of a modified IEEE 9-bus system are presented to
validate the theoretical findings which show the effectiveness of generalized
droop controls in independently shaping the settling times of the angle and
voltage responses of the lossy microgrid system.
