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.

翻译：拓扑识别是配电网状态估计的关键任务，尤其对于高渗透率可再生能源接入场景。可再生能源时序行为引发的不确定性若未妥善处理，几乎必然导致拓扑识别性能恶化。这些不确定性在传统框架下难以解析处理——通常呈现时空联合依赖特性，因此无法简单视为白噪声。针对该问题，本文提出一种混合框架，以系统化理论化方式应对这些不确定性：重点研究利用大数据分析技术捕获不确定性数据的时空联合统计特性。基于先验知识，首先构建模型库以存储可枚举的典型网络拓扑模型；据此，各模型状态估计输出与实际观测的差异可定义为矩阵变量——即随机矩阵。为解析该随机矩阵，需构建精心设计的度量空间。通过融合自回归模型、因子分析与随机矩阵理论设计度量空间，继而在高维向量空间中对随机矩阵进行时空联合分析。在该框架下，本文推导了若干大数据分析理论成果以提升拓扑识别性能。基于IEEE标准配电网联合实测数据的验证实验证实了框架有效性。