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

摘要

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.