A power supply apparatus comprising: a first battery; a second battery; the first battery and the second battery being configured to supply electric power to a load device and to a backupable auxiliary machine installed in a vehicle, a regeneration device configured to generate regenerative electric power to charge the first battery and the second battery; and an electronic control unit configured to determine the state of charge of the second battery, wherein the power supply apparatus is characterized in that the electronic control unit is configured to: a) determine whether a condition i) is satisfied, i) a degree of deterioration of the second battery is less than a first threshold, b) determine whether a condition ii) and a condition iii) are satisfied, ii) a state of charge of the second battery is lower than a second threshold, and iii) the state of charge of the second battery is equal to or higher than a third threshold, the second threshold being a value that is higher by a prescribed value than a lowest allowable value of the state of charge at which the second battery is able to function as a backup power for the backupable auxiliary machine, and the third threshold being the lowest allowable value, and c) execute single-battery-using control when the electronic control unit determines that the conditions i), ii), and iii) are all satisfied, the single-battery-using control being control in which regeneration control using the regenerative electric power is executed with use of the first battery, and the second battery is not used for the regeneration control, meaning that the second battery is neither charged by power generated by the regenerative device nor discharged to supply power to the load device. a first battery; a second battery; the first battery and the second battery being configured to supply electric power to a load device and to a backupable auxiliary machine installed in a vehicle, the first battery and the second battery being configured to supply electric power to a load device and to a backupable auxiliary machine installed in a vehicle, a regeneration device configured to generate regenerative electric power to charge the first battery and the second battery; and an electronic control unit configured to determine the state of charge of the second battery, wherein the power supply apparatus is characterized in that the electronic control unit is configured to: a) determine whether a condition i) is satisfied, i) a degree of deterioration of the second battery is less than a first threshold, b) determine whether a condition ii) and a condition iii) are satisfied, ii) a state of charge of the second battery is lower than a second threshold, and iii) the state of charge of the second battery is equal to or higher than a third threshold, the second threshold being a value that is higher by a prescribed value than a lowest allowable value of the state of charge at which the second battery is able to function as a backup power for the backupable auxiliary machine, and the third threshold being the lowest allowable value, and c) execute single-battery-using control when the electronic control unit determines that the conditions i), ii), and iii) are all satisfied, the single-battery-using control being control in which regeneration control using the regenerative electric power is executed with use of the first battery, and the second battery is not used for the regeneration control, meaning that the second battery is neither charged by power generated by the regenerative device nor discharged to supply power to the load device. a) determine whether a condition i) is satisfied, i) a degree of deterioration of the second battery is less than a first threshold, i) a degree of deterioration of the second battery is less than a first threshold, b) determine whether a condition ii) and a condition iii) are satisfied, ii) a state of charge of the second battery is lower than a second threshold, and iii) the state of charge of the second battery is equal to or higher than a third threshold, the second threshold being a value that is higher by a prescribed value than a lowest allowable value of the state of charge at which the second battery is able to function as a backup power for the backupable auxiliary machine, and the third threshold being the lowest allowable value, and ii) a state of charge of the second battery is lower than a second threshold, and iii) the state of charge of the second battery is equal to or higher than a third threshold, the second threshold being a value that is higher by a prescribed value than a lowest allowable value of the state of charge at which the second battery is able to function as a backup power for the backupable auxiliary machine, and the third threshold being the lowest allowable value, and the second threshold being a value that is higher by a prescribed value than a lowest allowable value of the state of charge at which the second battery is able to function as a backup power for the backupable auxiliary machine, and the third threshold being the lowest allowable value, and c) execute single-battery-using control when the electronic control unit determines that the conditions i), ii), and iii) are all satisfied, the single-battery-using control being control in which regeneration control using the regenerative electric power is executed with use of the first battery, and the second battery is not used for the regeneration control, meaning that the second battery is neither charged by power generated by the regenerative device nor discharged to supply power to the load device.