Result: Static and dynamic eigenvalues in unified stability studies

A framework for unified analysis of small‐signal and large‐signal power system stability based on static and dynamic eigenvalues is proposed in this paper. The presented implementation is based on Gear's method, which is a two‐step integration method for numerical simulation with self‐adaptive time‐step. Furthermore, it can be easily configured for providing the state matrix as basis for calculating the system eigenvalues during simulation. Thus, the presented framework allows for eigenvalue‐based analysis of small‐signal dynamics and stability margin at any steady‐state operating point during a time‐domain simulation. Furthermore, Linear Time‐Varying system theory is utilized for modal analysis during large‐signal transients. For this purpose, dynamic eigenvalues and eigenvectors are calculated by solving a Riccati equation to generalize the modal analysis during transient conditions. The stability is evaluated by calculating the Lyapunov exponent of the mode‐vector of the system. The results from numerical analysis of three case studies are presented to evaluate and illustrate the characteristics of the presented approach for unified small‐signal and transient stability analysis.