A Comparison of SVD-Augmented Prony Algorithms for Noisy Power System Signals
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Abstract
The conventional Prony algorithm, which is the most prominent power system ring-down mode identification method, fails if the test signal is noisy [with a signal-to-noise ratio (SNR) below 20 dB]. The performance of Prony algorithm can be improved through singular value decomposition (SVD)-based rank reduction of the data matrix. Principal eigenvector (PE)-Prony and total least squares (TLS)-Prony are two known formulations of SVD-augmented Prony algorithms. In both PE-Prony and TLS-Prony algorithms, the Toeplitz structure of the linear prediction data matrix is lost upon SVD-based noise filtering. On the other hand, structured total least squares (STLS)-Prony algorithm retains the Toeplitz structure even after SVD-based filtering and is hence expected to perform better. But a formulation of STLS-Prony algorithm for power systems is not available in the literature. Hence, the same is developed successfully in this paper. As a prelude to the formulation of STLS-Prony algorithm, PE-Prony and TLS-Prony analyses of power system signals are discussed in detail, bringing out their nuances. Further, through case studies on some benchmark power systems, it is demonstrated that all the three algorithms work successfully even at an SNR of 1 dB when the test signal has only inter-area modes. It is also shown that the performance of STLS-Prony algorithm is superior when the test signal has a highly damped local mode. Further, it is illustrated that by virtue of structure-preserving property, STLS-Prony algorithm is endowed with a unique filtering attribute although it has a longer execution time.