Extraction of State Matrix Eigenvalues for Resistive Companion Nodal Power System Model in Shifted-Frequency Domain

The state-space and the resistive companion (RC) nodal methods are two common techniques for dynamic modeling and simulation of power systems. The eigenvalues of a state-space model’s state matrix encapsulate important information about the dynamics of a power system. These eigenvalues play a key role in small-signal stability analysis, oscillation mode identification, and design of control systems. The RC nodal model in shifted-frequency domain is specifically suitable for efficient offline and real-time simulations of large power systems. However, this modeling method does not directly provide access to the state matrix eigenvalues. In this paper we derive equations and formulate an algorithm for the extraction of the state matrix eigenvalues from the RC nodal model of a power system in shifted-frequency domain. The integration of the algorithm with the RC nodal method in the open-source simulator DPsim allows for the extraction of eigenvalues at every simulation time step, a capability that has been numerically demonstrated.