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The potential uses of the sub-second GPS-synchronized phasor data collected from various locations within an electric power system promise endless benefits for the applications targeting reliable operation of electric power systems. Despite the undisputable progress achieved in developing visualization tools, alarming tools, modal analysis tools, and statistical analysis tools based on synchrophasor data, there is an emerging need to develop more real-time phasor-based applications. This paper discusses a new idea of the characteristic ellipsoid approach to monitor the dynamic behavior of an interconnected power system using phasor measurements. This method will be a useful tool for providing wide-area situational awareness for grid operators, identification of system disturbances and detection of system stresses and their locations.