Identification of Stability Regions in Inverter-Based Microgrids

TL;DR

This paper introduces a computationally efficient method to identify stability regions in inverter-based microgrids using eigenvalues of a generalized Laplacian matrix, enabling better gain optimization without exhaustive searches.

Contribution

The paper presents a novel eigenvalue-based approach to certify stability regions in microgrids, independent of topology and scalable to large systems.

Findings

Eigenvalue thresholds depend only on R/X ratio, not topology.

The method's complexity is nearly independent of inverter count.

Validated on IEEE 123-node system with 10 inverters.

Abstract

A new method for the stability assessment of inverter-based microgrids is presented in this paper. Directly determining stability boundaries by searching the multidimensional space of inverters' droop gains is a computationally prohibitive task. Instead, we build a certified stability region by utilizing a generalized Laplacian matrix eigenvalues, which are a measure of proximity to stability boundary. We establish an upper threshold for the eigenvalues that determines the stability boundary of the entire system and demonstrate that this value depends only on the network's R/X ratio but does not depend on the grid topology. We also provide a conservative upper threshold of the eigenvalues that are universal for any systems within a reasonable range of R/X ratios. We then construct approximate certified stability regions representing convex sets in the multidimensional space of droop gains that could be utilized for gains optimization. We show how the certified stability region can be maximized by properly choosing droop gains, and we provide closed-form analytic expressions for the certified stability regions. The computational complexity of our method is almost independent of the number of inverters. The proposed methodology has been tested using IEEE 123 node test system with 10 inverters.