Abstract
In this paper, the modal series method is revisited and an extension on the method to include higher order terms is proposed. This proposal is based on the introduction of the multidimensional Laplace transform and association of variables theorems to deduce the analytical closed-form solution when it is applied to the analysis of a nonlinear power system model. The method is systematic and can incorporate higher order terms to the modal analysis to determine nonlinear modal interaction. When the power system is operating under stressed conditions, such as an increase in load demand, it results very important to consider the oscillations due to its nonlinear nature. Thus, the method is carefully exemplified with the application to the synchronous machine-infinite busbar power system operating under stress conditions. The oscillations produced during changes in its operation are analyzed as well as the nonlinear interaction through nonlinear indices and nonlinear participation factors. The time domain responses are compared between linear approximation, modal series, normal forms method and the direct numerical full solution of the nonlinear power system model.
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