Grid-forming lambda-omega virtual oscillator control in converter-based power systems

Inspired by the kinetics of wave phenomena in reaction-diffusion models of biological systems, we propose a novel grid-forming control strategy for control of three-phase DC/AC converters in power systems. The ($\lambda-\omega$) virtual oscillator control or (lambda-omega) VOC is a natural increment on ideas from virtual oscillator dynamics rotating at a fixed nominal frequency to adaptive, angle-based frequency function. We study a network of identical three-phase DC/AC converters interconnected via $\Pi$ transmission lines. For this, we prove almost global asymptotic stability for a reduced (time-scale separated) version of the model, associated to a well-defined set of controller gains and system parameters. Additionally, we link the (\lambda-\omega) VOC to well-studied controllers in the literature, e.g. droop control. Finally, we validate our results on an example three DC/AC converter network.