The equilibrium points and stability of grid-connected synchronverters

TL;DR

This paper analyzes the equilibrium points and stability of grid-connected synchronverters, revealing geometric properties of their stable operating points and providing a way to predict their stable range based on system parameters.

Contribution

It formulates a fifth order model for synchronverters, derives conditions for equilibrium existence, and characterizes the stable operating range using geometric and singular perturbation analysis.

Findings

Equilibrium points form a two-dimensional manifold parametrized by (P,Q).

Stable equilibria lie within a specific angular sector in the (P,Q) plane.

The stable operating range can be predicted from system parameters and grid conditions.

Abstract

Virtual synchronous machines are inverters with a control algorithm that causes them to behave towards the power grid like synchronous generators. A popular way to realize such inverters are synchronverters. Their control algorithm has evolved over time, but all the different formulations in the literature share the same "basic control algorithm". We investigate the equilibrium points and the stability of a synchronverter described by this basic algorithm, when connected to an infinite bus. We formulate a fifth order model for a grid-connected synchronverter and derive a necessary and sufficient condition for the existence of equilibrium points. We show that the set of equilibrium points with positive field current is a two-dimensional manifold that can be parametrized by the corresponding pair $(P,Q)$, where $P$ is the active power and $Q$ is the reactive power. This parametrization has several surprizing geometric properties, for instance, the prime mover torque, the power angle and the field current can be seen directly as distances or angles in the $(P,Q)$ plane. In addition, the stable equilibrium points correspond to a subset of a certain angular sector in the $(P,Q)$ plane. Thus, we can predict the stable operating range of a synchronverter from its parameters and from the grid voltage and frequency. Our stability result is based on the intrinsic two time scales property of the system, using tools from singular perturbation theory. We illustrate our theoretical results with two numerical examples.