To control power supply capacity to each electrical appliance, and to make it possible to be flexibly applicable to additional electrical appliances.

In a system 10 that controls power supply from a power source 11 to a plurality of the electrical appliances 12a-12d, ranking data representing the order of the degree of importance of securing power supply are given to each of the electrical appliances 12a-12d. The ranking date can be given redundantly to each electrical appliance 12a-12d. A communicating and controlling device 13 connected to each electrical appliances 12a-12d transmits power limiting data 'P' having the ranking data for stopping the power supply and data of limiting periods for stopping the power supply to each electrical appliances 12a-12d. The power supply is stopped to the electrical appliances 12a-12d to which the ranking data is given corresponding to the ranking data of the power limiting data 'P'.