Global phase and magnitude synchronization of coupled oscillators with application to the control of grid-forming power inverters

TL;DR

This paper introduces a novel synchronization method for coupled oscillators that does not rely on fixed-magnitude assumptions, enabling almost global stability and practical control of grid-forming power inverters using local information.

Contribution

It proposes a new synchronization approach that combines relative state feedback with magnitude control, addressing an open problem in inverter-based power system stability.

Findings

Achieves almost global asymptotic stability of oscillators.

Ensures grid-forming behavior in inverter networks.

Controller exhibits droop-like characteristics for compatibility.

Abstract

In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback based on relative state information and local measurements that induces consensus-like dynamics. We show that, under a mild stability condition, the combination of the synchronizing feedback with a decentralized magnitude control law renders the oscillators' almost globally asymptotically stable with respect to set-points for the phase shift, frequency, and magnitude. We apply these result to rigorously solve an open problem in control of inverter-based AC power systems. In this context, the proposed control strategy can be implemented using purely local information, induces a grid-forming behavior, and ensures that a network of AC power inverters is almost globally asymptotically stable with respect to a pre-specified solution of the AC power-flow equations. Moreover, we show that the controller exhibits a droop-like behavior around the standard operating point thus making it backward-compatible with the existing power system operation.