Javier Roldán‐Pérez

Pablo Rodriguez-Ortega, Dionysios Moutevelis, Javier Roldan-Perez et al.

Stability of power electronic converters connected to power grids is commonly assessed by using the impedance criterion while the stability of power grids is typically analysed by using the network state-space representation. It is known that the impedance criterion may lead to erroneous results if the grid frequency dynamics are not considered while eigenvalue analysis is considered as a reliable method for system stability assessment. The equivalence between these two methods has been recently explored, without considering the effect of network frequency variations. Additionally, the link of the impedance criterion with the power-frequency dynamics of power systems also remains largely unexplored. In this paper, the equivalency between the impedance method considering the grid frequency dynamics and the conventional eigenvalue analysis is demonstrated. In addition, the dynamic interaction between the apparent power flow and the network fundamental frequency is formulated and its link with the impedance representation is shown. It is demonstrated that, by using the impedance representation with the network frequency as an additional input port, the network frequency perturbation plot (NFP) can be intuitively expressed by using quantities consistent with the impedance analysis framework. The main findings are verified using detailed numerical simulations of two representative systems.

Josue Andino, Milan Prodanovic, Javier Roldan-Perez

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.