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This paper proposes a moving window Prony method for power system oscillation detection. In the first step of batch Prony method, a discrete linear prediction model should be solved using pseudo inverse of the Toeplitz matrix, which can be realized by singular value decomposition (SVD). Considering the dimensions of data matrix are large than the effective rank which reflect the number of oscillation modes concerned, economic SVD rather than full SVD is sufficient. Thus, when a new data point enters the data window, the updating and downdating of SVD could be achieved by a well-established low rank modification. Based on economic SVD and its low rank modification, the Prony method can be implemented in a moving window manner. The algorithm proposed has been validated by a numerical example. Further investigation will be conducted to transform the second and the third steps of Prony into a moving window version, which will facilitate oscillation detection and on-line tracking.