Investigation of Lyapunov Modal Analysis Framework Using the Two-Area Test Power System

This paper investigates the possible advantages of the recently proposed framework of Lyapunov modal analysis compared to the conventional modal analysis. In particular, using a two-area Kundur test power system, we investigate two novel indicators: Lyapunov participation factors (PFs) and Lyapunov modal interaction energy (LMIE). Lyapunov PFs characterize the relative participation of the system modes in the perturbation energy accumulated in the state variables over time. We have observed that in contrast to conventional PFs, the Lyapunov PFs show an increase in the participation of those modes that approach the boundary of their stability. Therefore, this indicator combines information on the relationship of eigenmodes with state variables and on the stability of these modes. In contrast to conventional modal analysis, the averaged LMIE allows to characterize the interaction between two modes in a system in terms of total perturbation energy produced by their mutual actions over time. The experiment showed that the LMIE values allow one to detect and characterize the processes of merging and separation of eigenmodes in the system.