Spatiotemporal Big Data Analysis for Smart Grids Based on Random Matrix Theory

This chapter gives a tutorial account of existing mathematical works that are relevant to the statistical analysis of random matrices arising in smart grids. It aims to build a model for spatiotemporal phasor measurement unit (PMU) data using large dimensional random matrices. Representation of the spatiotemporal PMU data as a sequence of large random matrices is a crucial part for power state evaluation, as it turns the big PMU data into tiny data for practical uses. To improve the understanding and application of random matrix theory (RMT) technologies, the chapter then introduces some basic principles of RMT, such as asymptotic spectrum laws, transforms, convergence rate, and free probability. It also presents a brief introduction to the main development of RMT. Motivated by the immediate demands of tackling the tricky problems raised from large‐scale smart grids, the chapter further explores RMT‐based schemes for spatiotemporal big data analysis.