Participation Factor Analysis of Nonlinear Systems: Beyond Equilibria

Participation factors are widely used in power system analysis to associate dynamic behavior to state variables. Participation factors account for both the appearance of the dynamic modes of interest in the response of the state variables, and the impact of state variables on the excitation of the dynamics, and they are calculated as the elementwise product of right- and left-eigenvectors associated with an eigenvalue. It is the purpose of this work to extend the use of participation factors beyond the analysis of constant fixed point solutions. We return to earlier work that attempted to extend participation factors to limit cycles through a nonlinear dynamic phasor transformation resulting in a system with a constant steady-state. In this paper we present additional analysis to support this extension by examining sensitivity involving limit cycle frequency of oscillation. We also compare to a data driven approach for calculating participation factors. We use the Rossler system which exhibits ordinary fixed points, limit cycles, and chaotic behavior depending on parameters.