NOVELTY - The fuel cell power system comprises a fuel cell stack (1) in which cells having a membrane electrode assembly and a separator are stacked, a secondary battery (20), a power generation cell connection/disconnection mechanism (18) for individually connecting and disconnecting a conductor for electrical conduction between an anode and a cathode of each cell included in the fuel cell stack, a control unit to control connection/disconnection operation performed by the power generation cell connection/disconnection mechanism, and a voltage sensor (13) to measure a voltage of the fuel cell stack.    USE - The fuel cell power system such as a direct methanol fuel cell is useful as a power supply for portable devices such as telephones, notebook computers, audio/visual devices, camcorders and personal information terminals and electric vehicles.    ADVANTAGE - The fuel cell power system is capable of rapidly and efficiently generating the power with improved performance, has high volumetric energy density, and can be stably operated for a long period of time.    DETAILED DESCRIPTION - The fuel cell power system comprises a fuel cell stack (1) in which cells having a membrane electrode assembly and a separator are stacked, a secondary battery (20), a power generation cell connection/disconnection mechanism (18) for individually connecting and disconnecting a conductor for electrical conduction between an anode and a cathode of each cell included in the fuel cell stack, a control unit for controlling connection/disconnection operation performed by the power generation cell connection/disconnection mechanism, and a voltage sensor (13) for measuring a voltage of the fuel cell stack. The secondary battery is charged by power generated by the fuel cell stack, and is capable of supplying power from the fuel cell stack to an external device. The control unit: stops power generation by the fuel cell stack; stops air supply to the cathode of each cell included in the fuel cell stack; causes the power generation cell connection/disconnection mechanism to electrically connect the anode and cathode of each cell included in the fuel cell stack; breaks the electrical connection between the anode and cathode; resumes air supply to the cathode; and resumes power generation by the fuel cell stack when the power generation by the fuel cell stack is continued for a predetermined amount of time of 1-100 hours and when a voltage measured by the voltage sensor is lower than a predetermined voltage value. The anode and cathode of each cell included in the fuel cell stack are electrically connected for a period of time of 10 seconds to 10 minutes. The power is supplied from the secondary battery to the external device when the power generation by the fuel cell stack is stopped. The predetermined voltage value is 0.5-0.2 V per cell. An INDEPENDENT CLAIM is included for a method of operating a fuel cell power system.    DESCRIPTION OF DRAWING(S) - The diagram shows a block diagram of a direct methanol fuel cell system.    Fuel cell stack (1)    Voltage sensor (13)    Power generation cell connection/disconnection mechanism (18)    Secondary battery (20)    Temperature sensor. (21)