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This paper presents a comparative study of three real-time algorithms for power system model identification, parameter estimation and state prediction using real-time Phasor Measurement (PMU) data available from various selected nodes in a power system. Current modeling and state estimation algorithms in power control centers only use limited amount of data, leading to local observability. Our approach, on the other hand, is to use data from wide regions in the grid to gain insight on the global health of the system. The two main challenges for our approach are, therefore, the large size of the system and the large amount of measured data. Three specific algorithms, namely the Eigenvalue Realization Algorithm, linear least squares and state observer method, are used for this purpose. The first algorithm identifies the global system dynamics from PMU data in real-time, the second relaxes the identification problem as a parameter estimation problem, while the third generates estimate of the global state and, thereafter, computes the impulse response of a selected oscillation mode depending on the participation of that mode on the chosen output. The performance of these three methods is then compared in terms of their computational time delays and accuracy of prediction.