  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.
