Fully decentralized conditions for local convergence of DC/AC converter network based on matching control

TL;DR

This paper presents decentralized conditions ensuring local convergence of a network of identical DC/AC converters to a synchronous equilibrium, using a Lyapunov-based approach and symmetry properties.

Contribution

It introduces a novel Lyapunov-based framework leveraging symmetry for analyzing local convergence in DC/AC converter networks, with fully decentralized conditions.

Findings

Derived sufficient decentralized convergence conditions.

Provided estimates of the contraction region.

Validated results through numerical simulations.

Abstract

We investigate local convergence of identical DC/AC converters interconnected via identical resistive and inductive lines towards a synchronous equilibrium manifold. We exploit the symmetry of the resulting vector field and develop a Lyapunov-based framework, in which we measure the distance of the solutions of the nonlinear power system model to the equilibrium manifold by analyzing the evolution of their tangent vectors. We derive sufficient and fully decentralized conditions to characterize the equilibria of interest, and provide an estimate of their region of contraction. We provide ways to satisfy these conditions and illustrate our results based on numerical simulations of a two-converter benchmark.