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چکیده
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Heavily loaded stressed power systems exhibit complex nonlinear dynamic behavior, which cannot be analyzed and described accurately by conventional linear methods, such as eigen-analysis. A normal form of the vector _elds theory, a well established mathematical method and the Modal Series technique (a relatively newly established approach) have been used as tools to analyze, characterize and quantify some of the stressed power system's sophisticated nonlinear behavior such as low frequency interarea oscillations. The normal form method has been used extensively in recent years for the analysis of nonlinear modal interaction and the role of this interaction in causing inter-area oscillations after the occurrence of large disturbances. However, the normal form has some shortcomings, which must be further highlighted. In this paper, some of these shortcomings are addressed by the use of simple examples. Linear modal, normal form and Modal Series methods are used to simulate a two-area, 4-machine power system test case and the results are compared with its accurate nonlinear simulation to asses the performance and accuracy of these three methods. It is shown that: 1) Normal form techniques cannot simulate stressed power systems well in some regions of its operating space, 2) In some regions of state space, even a linear modal method provides more accurate results than a normal form, and 3) Modal Series' results are consistently the most accurate of the three.
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