NOVELTY - The method involves determining whether to operate a fuel cell in a fuel cell stop mode by determining conditions for stopping power generation of the fuel cell. The fuel cell is operated in the fuel cell stop mode, so that current output from a fuel cell stack is cut off by stopping a supply of reactant gases to the fuel cell when the fuel cell stop mode is determined. The fuel cell is operated in a fuel cell restart mode by restarting the supply of air and hydrogen when conditions for restarting the fuel cell are satisfied in the fuel cell stop mode.    USE - Method for controlling an idle start-stop of a power system for a fuel cell hybrid vehicle i.e. fuel cell-supercapacitor hybrid vehicle. Uses include but are not limited to a motor vehicle e.g. passenger automobile such as sports utility vehicle (SUV), bus, truck, various commercial vehicle, watercraft such as boat and ship, and aircraft, hybrid vehicle, electric vehicle, plug-in hybrid electric vehicle and hydrogen-powered vehicle.    ADVANTAGE - The method enables consuming residual oxygen and hydrogen by the fuel cell to drop voltage of fuel cell stack, thus stopping operation of the fuel cell. The method enables utilizing a hydrogen purge valve to discharge impurities and condensed water in an anode, thus ensuring performance of the fuel cell stack. The method enables stopping an operation of fuel cell balance-of-plant (BOP) components during low power operation, thus improving fuel efficiency and efficiency of the fuel cell system. The method enables preventing automatic charging of a supercapacitor, thus preventing increase in voltage of the supercapacitor, and hence increasing an amount of regenerative braking. The method enables improving durability of the fuel cell by reducing open circuit voltage. The method enables preventing fuel cell stack deterioration that occurs when oxygen is introduced into the anode, thus improving durability of the fuel cell stack without a loss of improvement in fuel efficiency. The method enables immediately eliminating voltage unexpectedly generated in the fuel cell stack by driving the load device and cutting off the hydrogen supply.    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart illustrating a method for controlling a non-power generation region.