Recently, while the installations of renewable energy sources and MG system to solve global environment issues are actively being performed, demonstration projects on community MG system to secure self-energy supply rate are being carried out in Jeollanam-do province in Korea. Where, the community MG system can be operated as a type of grid-connected or off-grid MG systems depending on the self-energy supply rate, and the power outage region may be expanded in the 3-phase short circuit or single line ground fault if proper time intervals of protection coordination between forward and backup protection devices is not secured. Therefore, this paper proposes operation method of protection coordination to secure the minimum time intervals of protection coordination not only between protection devices(CB, recloser) in primary feeder and MG customer relay in the grid-connected MG system, but also between MG customer relay in CVCF inverter(diesel generator) and other MG customer relay in the off-grid MG system. Furthermore, this paper performs the modeling of grid-connected and off-grid community MG systems, which is composed of distribution system, ESS, PV system and geothermal generator, using PSCAD/EMTDC S/W in order to analyze the fault current characteristics in the case of 3-phase short circuit and single line ground faults. From the simulation results based on the fault current characteristics and Off-DAS S/W of protection coordination analysis program, it is confirmed that the proposed operation method is useful tool to operate community MG system because the time intervals of protection coordination between forward and backup protection devices are properly secured in all contingency scenarios.