An alternating current uninterruptible power supply system includes a first power feed line, a second power feed line, a switchover relay, a converter, a power switch, a fuel cell, a system control board, a battery, and an inverter. If it is determined that electric power supply from a commercial alternating current power source has stopped for a first time or longer, a system control part of the system control board switches the switchover relay from a first state to a second state. Then, on the basis of the state of the electric power of the first power feed line, the system control part determines whether or not stopping of the electric power supply from the commercial alternating current power source has continued for a second time or longer. After that, if it is determined that the stopping of the electric power supply from the commercial alternating current power source has continued for the second time or longer, the system control part starts power generation of the stack.