This paper summarizes our recent work on Grid-Forming Inverter (GFM) application to power systems. We have developed a novel design of GFM, a single-phase synchronous inverter (SSI) for the conventional 100/200V distribution network based on the concept of "non-interference core (NIC) dynamic model." This paper first explains the design concept of NIC-SSI and a simulation model of SSI for power system analysis. Then the stabilization effect is investigated, where the installation of SSI on the single-phase consumer side is assumed as a new concept. The improvement of frequency and transient stability are evaluated. The SSI model is verified by comparing the developed root mean square (RMS) simulation, hardware-in-the-loop (HIL) simulation, and the experiment using SSI hardware. The simulation results show that the SSI has the considerable ability of grid stabilization. Singlephase micro-grid (SMG) operations using SSIs are also presented. The effectiveness of SMG operations is shown based on laboratory experiments.