Rao, K.Shubhanga, K.N.2026-02-0620252025 International Conference on Advances in Renewable Energy and Electric Vehicles, AREEV 2025, 2025, Vol., , p. 101-106https://doi.org/10.1109/AREEV64307.2025.10925199https://idr.nitk.ac.in/handle/123456789/28728Eigensystem realization algorithm (ERA) is a popular ring-down mode identification algorithm used for power system identification from wide area measurement systems. This essentially involves construction of a state matrix from the measured ring-down response signal through some matrix manipulation. The eigenvalues of the state matrix thus obtained are known to match with the dominant system modes excited upon the occurrence of a disturbance. However, a mathematical proof for the similarity of the state matrix thus constructed from the response signal to the reduced-rank state matrix obtained through detailed modelling of the system is not available. This paper ventures successfully in this direction by relating the Vandermonde- and singular value-decompositions of the data matrix pertaining to pulse response. © 2025 IEEE.Eigensystem realization algorithm (ERA)electromechanical mode identificationright equivalencesingular value decomposition (SVD)Vandermonde decomposition