Mathematical Foundations for Balancing Single-Phase Residential Microgrids Connected to a Three-Phase Distribution System

With the increased installation of single-phase rooftop PV systems, in-house battery storage units, and high-power plug-in loads (i.e., EVs) at single-phase residential sites, it is prevalent that an increasing number of residential distribution systems are becoming severely unbalanced, causing power quality problems and thermal risks at distribution sub-stations. While different techniques have been investigated to resolve this issue, there is still a lack of adequate theoretical foundations to guide these approaches. In this study, a detailed analytical analysis is carried out for a typical North American residential community with single-phase power generation, storage, and high-power random plug-in loads. This analysis has laid the foundation for a class of operating scenarios and provides an essential theoretical basis to unify different techniques for dynamically balancing single-phase microgrids connected to three-phase distribution systems. Detailed formulations have been developed for the first time to draw explicit power transfer relationships among power surplus and power-deficient phases to achieve an overall dynamic balance. A user-friendly, free interactive online tool has also been developed for potential users to evaluate their own application scenarios.