# Distributed Barrier Certificates for Safe Operation of Inverter-Based Microgrids

## TL;DR

This paper introduces a distributed control method using barrier functions and sum-of-squares optimization to ensure voltage safety during transients in inverter-based microgrids, addressing their unique dynamic challenges.

## Contribution

It presents a novel approach for designing distributed control laws that guarantee voltage limits during transients in inverter-based microgrids, leveraging barrier functions and sum-of-squares optimization.

## Key findings

- Control laws certify voltage safety during transients
- Method demonstrated through numerical simulations
- Addresses stability without inertia in microgrids

## Abstract

Inverter-interfaced microgrids differ from the traditional power systems due to their lack of inertia. Vanishing timescale separation between voltage and frequency dynamics makes it critical that faster-timescale stabilizing control laws also guarantee by-construction the satisfaction of voltage limits during transients. In this article, we apply a barrier functions method to compute distributed active and reactive power setpoint control laws that certify satisfaction of voltage limits during transients. Using sum-of-squares optimization tools, we propose an algorithmic construction of these control laws. Numerical simulations are provided to illustrate the proposed method.