Modern power gird is one of the most complex engineering systems in existence. Data of the grid, however, are not similar to big data such as image data. Power grid data are sampled by various sensors deployed within the network, such as phase measurement units (PMUs). The massive data set is in high-dimensional vector space, and in the form of time series: the temporal variations (T sampling instants) are simultaneously observed together with spatial variations (N grid nodes). The extraction of statistical information, especially temporal-spatial correlations, from the preceding data sets is a challenge that does not meet the prerequisites of most classical mathematical tools. Also, the mining task is inappropriate for supervised training algorithms such as neural networks due to the lack or the asymmetry of the labeled data. Unifying time and space through their ratio c= T/N, random matrix theory (RMT) deals with such kind of data mathematically rigorously. Moreover, linear eigenvalue statistics (LESs) built from data matrices follow Gaussian distributions for very general conditions, and other statistical variables are studied due to the latest breakthroughs in probability on the central limit theorems of those LESs.

In this chapter, we firstly model spatial-temporal data sets as random matrix sequences. Secondly, some basic principles of RMT, such as asymptotic spectrum laws, transforms, convergence rate, and free probability, are introduced briefly for a better understanding of the applications of RMT. Lastly, the case studies based on synthetic data and real data are developed to evaluate the performance of the RMT-based schemes in different application scenarios (ie, state evaluation and situation awareness).