# Identifying Parameter Space for Robust Stability in Nonlinear Networks: A Microgrid Application

## TL;DR

This paper develops a sum-of-squares optimization method to identify parameter regions ensuring robust stability of modules in nonlinear networks, demonstrated on a microgrid example.

## Contribution

It introduces a novel SOS-based algorithm for determining stability-guaranteeing parameter regions in uncertain nonlinear systems.

## Key findings

- Identified parameter regions for robust stability in a microgrid.
- Showed how uncertainty levels affect stability regions.
- Validated the approach with a practical inverter-based microgrid.

## Abstract

As modern engineering systems grow in complexity, attitudes toward a modular design approach become increasingly more favorable. A key challenge to a modular design approach is the certification of robust stability under uncertainties in the rest of the network. In this paper, we consider the problem of identifying the parametric region, which guarantees stability of the connected module in the robust sense under uncertainties. We derive the conditions under which the robust stability of the connected module is guaranteed for some values of the design parameters, and present a sum-of-squares (SOS) optimization-based algorithm to identify such a parametric region for polynomial systems. Using the example of an inverter-based microgrid, we show how this parametric region changes with variations in the level of uncertainties in the network.