  A cornerstone of the smart grid is the advanced monitorability on its assets
and operations. Increasingly pervasive installation of the phasor measurement
units (PMUs) allows the so-called synchrophasor measurements to be taken
roughly 100 times faster than the legacy supervisory control and data
acquisition (SCADA) measurements, time-stamped using the global positioning
system (GPS) signals to capture the grid dynamics. On the other hand, the
availability of low-latency two-way communication networks will pave the way to
high-precision real-time grid state estimation and detection, remedial actions
upon network instability, and accurate risk analysis and post-event assessment
for failure prevention.
  In this chapter, we firstly modelling spatio-temporal PMU data in large scale
grids as random matrix sequences. Secondly, some basic principles of random
matrix theory (RMT), such as asymptotic spectrum laws, transforms, convergence
rate and free probability, are introduced briefly in order to the better
understanding and application of RMT technologies. 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 (i.e., state
evaluation and situation awareness).
