Topology identification (TI) is a key task for state estimation (SE) in distribution grids, especially the one with high-penetration renewables. The uncertainties, initiated by the time-series behavior of renewables, will almost certainly lead to bad TI results without a proper treatment. These uncertainties are analytically intractable under conventional framework--they are usually jointly spatial-temporal dependent, and hence cannot be simply treated as white noise. For this purpose, a hybrid framework is suggested in this paper to handle these uncertainties in a systematic and theoretical way; in particular, big data analytics are studied to harness the jointly spatial-temporal statistical properties of those uncertainties. With some prior knowledge, a model bank is built first to store the countable typical models of network configurations; therefore, the difference between the SE outputs of each bank model and our observation is capable of being defined as a matrix variate--the so-called random matrix. In order to gain insight into the random matrix, a well-designed metric space is needed. Auto-regression (AR) model, factor analysis (FA), and random matrix theory (RMT) are tied together for the metric space design, followed by jointly temporal-spatial analysis of those matrices which is conducted in a high-dimensional (vector) space. Under the proposed framework, some big data analytics and theoretical results are obtained to improve the TI performance. Our framework is validated using IEEE standard distribution network with some field data in practice.
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