Fast SVD Computations for Synchrophasor Algorithms

Abstract

Many singular value decomposition (SVD) problems in power system computations require only a few largest singular values of a large-scale matrix for the analysis. This letter introduces two fast SVD approaches recently developed in other domains to power systems for speeding up phasor measurement unit (PMU) based online applications. The first method is a randomized SVD algorithm that accelerates computation by introducing a low-rank approximation of a given matrix through randomness. The second method is the augmented Lanczos bidiagonalization, an iterative Krylov subspace technique that computes sequences of projections of a given matrix onto low-dimensional subspaces. Both approaches are illustrated on SVD evaluation within an ambient oscillation monitoring algorithm, namely stochastic subspace identification (SSI).

Improved SVD-based data compression method for synchronous phasor measurement in distribution networks

“…Since the voltage and current data are threephase signals, these three-phase signals are built in the same matrix with the dimension of 39 × 30000, whereas the dimensions of other matrices are 13 × 30000. The horizontal and vertical dimensions of the measurement data matrices are extremely unbalanced, which may affect the efficiency of SVD [34]. To reduce the time cost of SVD, the matrices are sequentially rearranged into 1170 × 1000 and 390 × 1000, respectively.…”

Robust and Efficient Harmonics Denoising in Large Dataset Based on Random SVD and Soft Thresholding

“…How to extract features from a large dataset efficiently and effectively becomes gradually important for signal denoising and data analysis. In recent years, with the development of random projection method in linear algebra [18], [19], random sampling and probabilistic methods were applied for signal denoising [20], [21]. In 2014, rQRd (random QR denoising) algorithm [20] was proposed to solve low rank approximation problem for very large matrix.…”

Estimating electromechanical oscillation modes from synchrophasor measurements in bulk power grids using FSSI

“…For ambient data, Anderson et al [15] and Dosiek and Pierre [16] used an autoregressive moving average exogenous (ARMAX) to estimate the electromechanical modes, and two extended ARMAX methods, robust recursive least square (RRLS) and regularised RRLS, were further developed by Zhou et al [17,18]. Ghasemi et al [19], Ni et al [20] and Wu et al [21] applied stochastic subspace identification (SSI) for electromechanical mode estimation. Since the SSI costs high computational burden in singular value decomposition (SVD) of a large-dimensional matrix, a recursive adaptive SSI (RASSI) is proposed in [22] to overcome this drawback by recursively updating the estimations that avoid computation of SVD in each instance of estimation.…”