Complex-Value Spatiotemporal Graph Convolutional Neural Networks and Its Applications to Electric Power Systems AI

The effective representation, processing, analysis, and visualization of large-scale structured data over graphs, especially power grids, are gaining a lot of attention. So far most of the literature considered exclusively real-valued graph signals. However, graph signals are often sparse in the Fourier domain, and more informative and compact representations for them can be obtained using the complex envelope of their spectral components, as opposed to the original real-valued signals. This is the case for the AC carrier, and motivates its complex phasor representation. Focusing on applications in power systems, in this paper we generalize graph convolutional neural networks (GCN) to the complex domain, incorporating a complex-valued graph shift operators (GSO) based on the admittance matrix of power grids in the definition of graph filters (GF) and process complex-valued voltage phasor graph signals (GS). The theory developed is generalized to handle spatio-temporal complex network processes. We prove that complex-valued GCNs can be stable with respect to perturbations of the underlying graph support, by bounding of the error propagation through multiple NN layers. The paper showcases the benefits of complex GCN relative to several benchmarks, in power grid state forecasting and cyber-attack detection and localization.