On the Ability of Eigensystem Realization Algorithm to Identify the Dominant System Modes

Eigensystem 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.