Ultimate boundedness of droop controlled Microgrids with secondary loops

TL;DR

This paper demonstrates that inverter-based microgrids can achieve frequency regulation and bounded stability without relying on time-scale separation, using a novel approach based on nonlinear mappings.

Contribution

It introduces a new theoretical framework for ensuring stability and boundedness in microgrids without the traditional time-scale separation assumption.

Findings

Frequency regulation without time-scale separation.

Guaranteed ultimate boundedness of trajectories.

A simple iterative method to compute stability bounds.

Abstract

In this paper we study theoretical properties of inverter-based microgrids controlled via primary and secondary loops. Stability of these microgrids has been the subject of a number of recent studies. Conventional approaches based on standard hierarchical control rely on time-scale separation between primary and secondary control loops to show local stability of equilibria. In this paper we show that (i) frequency regulation can be ensured without assuming time-scale separation and, (ii) ultimate boundedness of the trajectories starting inside a region of the state space can be guaranteed under a condition on the inverters power injection errors. The trajectory ultimate bound can be computed by simple iterations of a nonlinear mapping and provides a certificate of the overall performance of the controlled microgrid.