Local mode-in-state participation factors for nonlinear systems

Abstract

The paper studies an extension to nonlinear systems of a recently proposed approach to the concept of modal participation factors. First, a definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. The definition is general, and, unlike in the more traditional approach, the resulting participation measures depend on the assumed uncertainty law governing the system initial condition. The work follows Hashlamoun, Hassouneh and Abed (2009) in taking a mathematical expectation (or settheoretic average) of a modal contribution measure with respect to an assumed uncertain initial state. As in the linear case, it is found that a symmetry assumption on the distribution of the initial state results in a tractable calculation and an explicit and simple formula for mode-in-state participation factors. * Boumediene Hamzi is with the

Data-Driven Participation Factors for Nonlinear Systems Based on Koopman Mode Decomposition

“…Finally, following [10], the most excited nonlinear modes are usually those that are combinations of the linear inter-area modes. In this sense, the frequency of µ 12,13 is approximately twice the frequency of the linear inter-area mode. III MODE-IN-STATE PARTICIPATION FACTORS BASED ON THE KOOPMAN MODE DECOMPOSITION µ1 µ2 µ3 µ4 µ5 µ6 µ7 µ8 µ9 µ10 µ11 µ12 µ13 µ14 µ15 µ16 µ17 µ18 µ19 µ20 µ21 µ22 µ23…”

Local modal participation analysis of nonlinear systems using Poincaré linearization

“…Another extension is to consider any possible relationship of nonlinear eigenvalues and eigenvectors for nonlinear systems [23,24] to modal participation analysis for nonlinear systems. A preliminary version of this work appeared in [25].…”

Lyapunov modal analysis and participation factors with applications to small-signal stability of power systems

“…Accordingly, the original definition of PFs was retained for the mode-in-state PFs; however, a new definition was proposed for the state-in-mode PFs (or SIMPFs). Subsequently, similar SIMPF concepts were considered for dynamical nonlinear systems (Hamzi, Abed, 2014) and for systems described by algebraic equations such as power flow equations (Song et al, 2019).…”

“…Attempts to account for nonlinear effects and intermodal interactions within the framework of modal analysis developed mainly in two directions. The model-based approach is associated with taking into account the higher-order terms of the Taylor expansion in the system approximation and using normal Poincaré forms (Vittal et al, 1991;Hamzi, Abed, 2014;Tian et al, 2018). A study in (Sanchez-Gasca et al, 2005) showed that accounting for these terms becomes significant, for example, when studying inter-area oscillations in stressed power systems following large disturbances.…”

“…Unlike works on nonlinear modal analysis (Vittal et al, 1991;Hamzi, Abed, 2014;Tian et al, 2018), this paper proposes a new principle for evaluating modal indicators and modal interactions. This principle is not based on the instantaneous dynamics of variables, but on variation of their energy over a time interval.…”