Generalized Graph Laplacian Based Anomaly Detection for Spatiotemporal MicroPMU Data

Abstract

This letter develops a novel anomaly detection method using the generalized graph Laplacian (GGL) matrix to visualize the spatiotemporal relationship of distribution-level phasor measurement unit ( $\boldsymbol{\mu }$ PMU) data. The $\boldsymbol{\mu }$ PMU data in a specific time horizon are segregated into multiple segments. An optimization problem formulated as a Lagrangian function is utilized to estimate the GGL matrix. During the iterative process, an optimal update is constituted as a quadratic program problem. To perform the $\boldsymbol{\mu }$ PMU-based spatiotemporal analysis, normalized diagonal elements of GGL matrix are proposed as a quantitative metric. The effectiveness of the developed method is demonstrated through real-world $\boldsymbol{\mu }$ PMU measurements gathered from test feeders in Riverside, CA, USA.