DynamoPMU: A Physics Informed Anomaly Detection, Clustering, and Prediction Method Using Nonlinear Dynamics on μ PMU Measurements

The expansion in technology and attainability of a large number of sensors has led to a large amount of real-time streaming data. The real-time data in the electrical distribution system is collected through distribution-level phasor measurement units referred to as micro-PMU (
$\mu $
PMU) which report high-resolution phasor measurements comprising various event signatures that provide situational awareness and enable a level of visibility into the distribution system. These events are infrequent, unscheduled, and uncertain; it is a challenge to scrutinize, detect, and predict the occurrence of such events. In this article, we seek to address these problems by developing an unsupervised physics dynamics-based approach to detect anomalies in the
$\mu $
PMU data, then using an unsupervised clustering algorithm to categorize events based on their pattern and simultaneously predict the events using system governing equations. We propose a data-driven approach based on the Hankel alternative view of the Koopman (HAVOK) analysis and named it DynamoPMU, to analyze the underlying dynamics of the distribution system by representing them in a linear intrinsic space. The key technical idea is that the proposed method separates out the linear dynamical behavior pattern and intermittent forcing (anomalous events). Furthermore, we cluster the detected events using the Gaussian mixture model (GMM) and predict the measurement data and anomalous events using the sparse identification of nonlinear dynamic (SINDy) model. We demonstrate the efficacy of our proposed framework through analysis of real
$\mu $
PMU data taken from the Lawrence Berkeley National Laboratory (LBNL) distribution grid.