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

TL;DR

This work develops a network-level, structure-preserving small-signal framework for lossy, islanded microgrids employing generalized droop controls. By integrating resistive losses, droop filtering, and a shared set of bus types, the authors derive a nonlinear DAE model and its linearized small-signal form, then propose a decoupled design achieved by choosing $\alpha_i=\pi-\phi_0$ under near-uniform line impedance angles and small angle differences. They prove (via Theorems 1 and 2) that the angle dynamics are asymptotically stable for any positive droop gain and filter time constants, and the voltage dynamics are stable if the loopy active-power graph Laplacian is positive definite, independent of $D$ and $T$. Simulations on a modified IEEE $9$-bus microgrid validate that generalized droop controls can independently shape the settling times of angle and voltage in response to small disturbances, supporting the practical utility of the proposed approach.

Abstract

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.

Figures (4)

• Figure 1: Block diagram of generalized droop control with filtering.
• Figure 2: Small-disturbance angle and voltage response of modified IEEE 9-bus lossy system with radial topology for generalized droop with $T_{1i} =0.01, 0.5$ and $2$ sec in the droop controls.
• Figure 3: Small-disturbance angle and voltage response of modified IEEE 9-bus lossy system with radial topology for generalized droop with $T_{2i} =0.1, 2$ and $10$ sec in the droop controls.
• Figure 4: Diagram of the modified IEEE 9-bus lossy test system.