Equivalence of Matrix Pencil and HTLS Ring-Down Electromechanical Mode Identification Algorithms

Matrix pencil and Hankel total least squares (HTLS) are two popular ring-down electro- mechanical mode identification algorithms. The appeal of these algorithms can be attributed to faster execution due to the non-iterative procedure of model order determination based on singular value decomposition of the data matrix. In this paper, these two algorithms are shown to be equivalent – the data matrix in one being the transpose of that in the other. Although this equivalence is proved in the context of power systems, it is valid for other areas of system identification as well. Further, the performance of these algorithms is examined as noise level in the signal increases, and it is shown that these work right down to an SNR of 1 dB provided the signal has only poorly damped modes.