A power supply apparatus for use in a vehicle

The power supply device for use in a vehicle includes an alternator (2) driven by an engine (1) mounted on a vehicle is driven to generate electric power according to a command value, a battery (3) is electrically connected to the alternator to be charged by the alternator (2), and with electrical loads (11) which are mounted on the vehicle, connected to apply a power supply voltage to the electrical loads. The power supply device for use in a vehicle further includes a first function for determining an increase in amount of fuel to the engine (1) for the AC generator (2) used to generate electric power as a power generation cost and a second function for transferring the command value to the AC generator (2) wherein the second function is configured to determine the command value on the basis of which is determined by the first function of the power generating effort, such that a rate of change of the power supply voltage does not exceed a predetermined limit.