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Synchronized measurements of a large power grid enable an unprecedentedopportunity to study the spatialtemporal correlations. Statistical analyticsfor those massive datasets start with high-dimensional data matrices.Uncertainty is ubiquitous in a future's power grid. These data matrices arerecognized as random matrices. This new point of view is fundamental in ourtheoretical analysis since true covariance matrices cannot be estimatedaccurately in a high-dimensional regime. As an alternative, we considerlarge-dimensional sample covariance matrices in the asymptotic regime toreplace the true covariance matrices. The self-adjoint polynomials oflarge-dimensional random matrices are studied as statistics for big dataanalytics. The calculation of the asymptotic spectrum distribution (ASD) forsuch a matrix polynomial is understandably challenging. This task is madepossible by a recent breakthrough in free probability, an active researchbranch in random matrix theory. This is the very reason why the work of thispaper is inspired initially. The new approach is interesting in many aspects.The mathematical reason may be most critical. The real-world problems can besolved using this approach, however.

A New Approach of Exploiting Self-Adjoint Matrix Polynomials of Large Random Matrices for Anomaly Detection and Fault Location