A Comparative Analysis of Methodologies for the Representation of Nonlinear Oscillations in Dynamic Systems

Nonlinear oscillations in power systems have been extensively studied over the last years, to analyze and to determine their effects on the network. For that purpose, and based on analytical methodologies, normal forms of vector fields and modal series have been developed as a numerical tool, which allows the dynamic analysis of nonlinear systems. In this work, both methods are applied to analyze oscillations in two nonlinear systems. Observed differences between both methods are pointed out mainly those introduced by wrong selection of initial conditions. Time domain responses of a dynamical system used as a benchmark are analyzed in order to show this situation. Besides, a nine bus, three machines system is simulated to compare both nonlinear methodologies with respect to the numerical solution obtained with the direct solution of ordinary differential equations. The main differences observed between both methodologies when the power system is operated under a small perturbation and stress conditions are remarked.