Analogous deployment of phase measurement units (PMUs), the increase of data quantum and deregulation of energy market, all call for robust state evaluation in large scale power systems. Implementing model based estimators is impracticable as the complexity scale of solving the high dimension power flow equations. In this paper, we first represent massive streaming PMU data as big random matrix flow. Motivated by exploiting the variations in the covariance matrix of the massive streaming PMU data, a novel power state evaluation algorithm is then developed based on the multiple high dimensional covariance matrix test. The proposed test statistic is nonparametric without assuming a specific parameter distribution for the PMU data and of a wide range of data dimensions and sample size. Besides, it can jointly reveal the relative magnitude, duration and location of an system event. For the sake of practical application, we reduce the computation of the proposed test statistic from O(εn _g ⁴ ) to O(ηn _g ² ) by principal component calculation and redundant computation elimination. The novel algorithm is numerically evaluated utilizing the IEEE 30-, 118-bus system and a Polish 2383-bus system and a real 34-PMU system. The case studies illustrate and verify the superiority of proposed state evaluation indicator.