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This paper proposes a data-driven method to pinpoint the source of a new emerging dynamical phenomenon in the power grid, referred to “forced oscillations” in the difficult but highly risky case where there is a resonance phenomenon. By exploiting the low-rank and sparse properties of synchrophasor measurements, the localization problem is formulated as a matrix decomposition problem, which can be efficiently solved by the exact augmented Lagrange multiplier algorithm. An online detection scheme is developed based on the problem formulation. The data-driven nature of the proposed method allows for a very efficient implementation. The efficacy of the proposed method is illustrated in a 68-bus power system. The proposed method may possibly be more broadly useful in other situations for identifying the source of forced oscillations in resonant systems. Index Terms—Forced oscillations, resonant systems, phasor measurement unit (PMU), robust principal component analysis (RPCA), Big Data.
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e RPCA : Robust Principal Component Analysis for Exponential Family Distributions
Abstract Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient decomposition, under either its natural or canonical parametrization. The effectiveness of is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area.
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- PAR ID:
- 10518507
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Statistical Analysis and Data Mining: The ASA Data Science Journal
- Volume:
- 17
- Issue:
- 2
- ISSN:
- 1932-1864
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/sam.11670
