Pauli Decomposition of Impedance Matrices for Understanding the Root Cause of Instabilities in Grid-Connected Power Electronic Converters

TL;DR

This paper introduces Pauli decomposition of impedance matrices to clarify the physical origins of instabilities in grid-connected power electronic converters, enhancing stability analysis.

Contribution

It applies Pauli decomposition to impedance matrices, providing a clearer physical interpretation and root cause analysis of instabilities in power electronic converters.

Findings

Pauli decomposition links impedance matrix terms to stability properties

Transforming impedance matrices into quaternion-like form aids root cause analysis

Validated approach on a weak grid power converter case study

Abstract

The impedance criterion has emerged as an alternative way to stability assessment of grid-connected power electronic converters. However, the lack of physical meaning of impedance and admittance matrices hinders the ability to understand the root cause of instabilities. To address this issue, this paper proposes the application of Pauli decomposition to the impedance matrices and the minor loop of grid-connected power electronic converters. The application of this methodology simplifies establishing the link between impedance matrix terms and closed-loop stability properties. Moreover, Pauli decomposition transforms impedance matrices in a quaternion-like form that is helpful to assess the root cause of instabilities. The theoretical contributions are validated using a case study consisting of a power electronic converter connected to a weak grid that has been previously analysed in the literature using existing techniques.