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Normal Mode Analysis of Inter-Area Oscillations

Normal Mode Analysis of Inter-Area Oscillations - Normal...

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Abstract —In this paper, a linear normal mode-based formulation for analyzing inter-area oscillations is presented. The method is based on the property of invariance of the modal subspaces and can be used to represent complex power system modal behavior by a set of uncoupled linear oscillators. Using the theory of modal subspaces, a new approach is outlined, for determining the linear Normal Modes (NMs) of motion of a general n- degree of freedom linear system. Within this framework, techniques to characterize modal behavior in terms of the linear NMs are explored, and procedures to compute the speed and displacement of the normal modes are proposed. A mechanical interpretation of NMs in terms of velocities and displacements is also provided. Numerical and symbolic examples are presented to illustrate the effectiveness and applicability of the proposed analysis technique. Specifically, we demonstrate and discuss the use of normal mode analysis as a basis for identifying modal parameters, including natural frequencies and damping ratios of general, linear systems with n degrees of freedom. Index Terms -- Linear normal modes of motion, Nonlinear oscillators, Power system dynamic stability. I. I NTRODUCTION ODAL analysis constitutes one of the most powerful techniques for the analysis and characterization of system oscillations. These techniques form an important part of current analysis methods and have become more extensively used in the last few years as the instances of system oscillations have increased. Several different approaches based on time or frequency, have been proposed to characterize modal behavior. These include spectral analyses, time-domain based methods and model-dependent analytical formulations. The characteristics of these methods are well described in the literature [1]-[4]. Despite these developments, the full issue of mode interaction between system modes has not been fully explored. This has motivated the development of relevant analytical techniques with the ability to characterize and interpret nonlinear modal interactions. The financial support of Mexican Council for Science and Technology under grant J-43279 is acknowledged. R. J. Betancourt, I. Martinez and A. Roman are with the Electrical Engineering Program, Cinvestav, Zapopan, Jal., 45010, Mexico. (e-mail: [email protected] gdl.cinvestav.mx). E. Barocio is with the Nuevo Leon Autonomous University, Monterrey Nuevo Leon, 12345, Mexico (e-mail: [email protected]). This paper explores the use of alternative methods for modal analysis based on the notion of Normal Modes (NMs) [6, 7]. These techniques have been successfully applied to numerous physical systems including the analysis of nonlinear vibrations [7], the movement of ocean platforms [8], and the study of micro cavities in quantum electronics [9].
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