The work is based on a collaboration between Hiroshima University and Kure KOSEN College. This paper presents the design concept, hardware, and applications of a single-phase synchronous inverter (SSI), a specially designed grid-forming inverter (GFM) for single-phase micro-grid (SMGs). The SSI is designed for the conventional 100/200 V distribution network and is based on the concept of “Non-Interference Core (NIC) dynamic model”. Novel contributions of this paper are: (1) A root mean square (RMS) model of NIC-SSI was developed, combined with the conventional power system model, and verified through the comparison with the hardware-in-the-loop (HIL) simulation and SSI hardware experiments; (2) using the developed RMS simulation tool, the stabilization effect of the SSIs was investigated in condition under which the SSIs are massively installed in a distribution system; (3) off-grid SMG operations using SSIs under various ill-conditioned loads were demonstrated. The results show that the SSI has the considerable ability of grid stability enhancements for frequency, transient, and small-signal stabilities. The proposed SMG using SSIs is promising.