On the Uniqueness of Participation Factors in Nonlinear Dynamical Systems

Abstract: In the modal analysis and control of nonlinear dynamical systems, the participation factors of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables. For linear systems, the participation factors of state variables regarding a mode are uniquely determined by the mode's composition and shape, defined by the system's left and right eigenvectors, respectively. However, the uniqueness of other types of participation factors necessitates further investigation. This paper establishes a sufficient condition for the uniqueness of nonlinear participation factors and five other variants of participation factors, accounting for uncertain scaling factors in a mode's shape and composition. These scaling factors arise from variations in the selection of physical units or the value ranges of state variables when analyzing and controlling real-world dynamical systems. Understanding the sufficient condition of the uniqueness is therefore crucial for the correct application of participation factors in practical scenarios. Additionally, the paper explores the relationship between perturbation magnitudes in state variables and the selection of optimal scaling factors.