Small-Signal Dynamics of Lossy Inverter-Based Microgrids for Generalized Droop Controls

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 resistance to inductance ratios of the lines in the microgrid are consistent and differences of voltage angles across the lines are sufficiently 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.