Reformulating dq Impedance Matrices via Pauli Decomposition for Root-Cause Analysis of Instabilities in Grid-Connected Converters
For power system engineers analyzing stability of converter-interfaced generators, this provides a more interpretable algebraic tool for root-cause analysis of instabilities, though it is an incremental improvement over existing impedance-based methods.
The paper proposes using Pauli decomposition to reformulate dq impedance matrices into a quaternion-like form, enabling explicit algebraic relationships with eigenvalues and characteristic equations for root-cause analysis of instabilities in grid-connected converters. The method is validated on a converter-interfaced generator connected to a weak grid, demonstrating improved interpretability over existing impedance-based criteria.
The increasing penetration of converter-interfaced generators in power systems has led to the adoption of impedance-based criteria as an alternative framework for assessing and ensuring stable integration. However, when the impedance criterion is used, identifying the root cause of instabilities is generally more challenging compared to other approaches, such as modal analysis. Moreover, the eigenvalues and characteristic equation used in the impedance criterion are non-linear functions, making it difficult to establish a clear relationship between impedance components and closed-loop stability. To address this issue, this paper proposes the application of the Pauli decomposition to analyse dq impedance matrices and minor-loop equations. By using this decomposition technique, the dq representation can be reformulated into a quaternion-like form, which has explicit algebraic relationships with the determinant, trace, eigenvalues, and characteristic equation. Moreover, this decomposition enables systematic assessment of the influence of each impedance term in the system stability, thus facilitating finding the root-cause of instabilities. The primary objective of this work is to develop the mathematical foundation of the Pauli decomposition and demonstrate its implications for root-cause analysis. The theoretical contributions are validated using a case study consisting of a converter-interfaced generator connected to a weak grid that has been previously analysed in the literature using existing techniques. The proposed Pauli decomposition provides an algebraic tool that enhances interpretability of impedance-based stability analysis and establishes a basis for further investigation of complex converter interactions.