Traditionally, a microgrid relies on electro-mechanical generators to achieve reliable and stable operations. With recent technical advancement in the fields of renewable energy and energy storage, a modern microgrid can operate autonomously with only inverter-based energy sources. While the three-phase microgrid has been extensively studied in recent years, the single-phase microgrid has been barely investigated. However, massive numbers of single-phase microgrids (or nanogrids in some references and this thesis) are now being deployed in conjunction with the introduction of electric vehicles (EVs) and household power generators (such as photovoltaic solar) to the 130 million single-phase consumers in North America. The lack of single-phase microgrid analysis represents a significant knowledge gap. The objective of this thesis is to advance the understanding of single-phase nanogrids consisting of both grid-supporting and grid-forming inverters. Three topics are covered in this thesis. • Integration of the EV in the nanogrid: a novel control and optimization strategy for On-board Battery Charger (OBC) is proposed. It is based on Direct Current Hysteretic Control (DCHC) with optimized switching patterns and dead time. The strategy can significantly reduce the switching losses of Silicon Carbide (SiC) based inverters. • A voltage control loop tuning approach for grid-forming inverters: by extending the Modulus Optimum algorithm to the stationary reference frame, the proposed approach provides a simple and reliable method when tuning the voltage control loop. • A systematic single-phase modelling methodology: a synchronous dq0 frame model of the single-phase inverters is developed. It allows the application of three phase stability analysis techniques/tools to single phase systems.