Anomaly Detection with Machine Learning Algorithms in Large-Scale Power Grids

We apply several machine learning algorithms to the problem of anomaly detection in operational data for large-scale, high-voltage electric power grids. We observe important differences in the performance of the algorithms. Neural networks typically outperform classical algorithms such as k-nearest neighbors and support vector machines, which we explain by the strong contextual nature of the anomalies. We show that unsupervised learning algorithm work remarkably well and that their predictions are robust against simultaneous, concurring anomalies.

Model Reduction of Swing Equations with Physics Informed PDE

This manuscript is the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. We suggest, following Seymlyen (1974) and Thorpe, Seyler and Phadke (1999), to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. The continuous two-dimensional spatial domain is defined by a geographical map of the area served by the power grid, and associated with the PDE coefficients derived from smoothed graph-Laplacian of susceptances, machine inertia and damping. Inhomogeneous source terms represent spatially distributed injection/consumption of power. We illustrate our method on PanTaGruEl (Pan-European Transmission Grid and ELectricity generation model). We show that, when properly coarse-grained, i.e. with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based reduced modeling will initialize a physics-informed machine learning approach for real-time modeling, $n-1$ feasibility assessment and transient stability analysis of power systems.