An observable microgrid may become unobservable when sensors are at fault, sensor data is missing, or data has been tampered by malicious agents. In those cases, state estimation cannot be performed using traditional approaches without pseudo-measurements. To address the lack of observability, this article presents the design and implementation of a novel three-phase state estimation method for unobservable and unbalanced AC microgrids, using machine learning techniques, without pseudo-measurements, and under heteroscedastic (i.e., non-constant variance) noise. The proposed machine learning state estimation (MLSE) makes full use of multiple candidate models trained with a small number of power flow simulations via OpenDSS, through random levels of demand and renewable generation in every simulation, enhanced through a proposed Tikhonov regularization operator. To deal with the heteroscedastic nature of measurements, a recursive average model is proposed to accurately estimate the state variables. Results are obtained using real data from a microgrid located on the main campus of the State University of Campinas (UNICAMP), in Brazil. The method can be easily adapted to microgrids with different configurations, distributed energy resources, and measurements. It is shown that the proposed MLSE outperforms the traditional weighted least square (WLS) state estimator.INDEX TERMS Machine learning, microgrids, Moore-Penrose left pseudoinverse, Tikhonov regularization operator, recursive average model.

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