1. An appliance control system comprising: plural electrical appliances configured to operate with electrical power supplied from an external power source; and an appliance control device connected to said plural electrical appliances, wherein said appliance control device comprises an external interface unit, and a control unit, and said external interface unit is configured to receive an energy conservation instruction indicative of a total reduction amount of power consumption of said plural electrical appliances from an external device, and said control unit is configured to, upon acknowledging that said external interface unit receives the energy conservation instruction, send, to at least one of said plural electrical appliances, a control signal including a common control order indicative of an individual reduction amount of the power consumption of said at least one of said plural electrical appliances based on the total reduction amount indicated by the energy conservation instruction, each of said plural electrical appliances comprises: a functional unit having plural operation states with different power consumption; a control instruction storage unit configured to store plural control instructions for changing the plural operation states of said functional unit; an individual storage unit configured to store individual control information indicative of a correspondence relation between the individual reduction amount and the plural control instructions; a time period storage unit; a time period judging unit; and an operation control unit configured to, upon receiving the control signal, refer to the individual control information stored in said individual storage unit, and select, from the plural control instructions stored in said control instruction storage unit, a control instruction corresponding to the individual reduction amount indicated by the common control order included in the received control signal, and provide the selected control instruction to said functional unit, and said functional unit is configured to, upon receiving the control instruction from said operation control unit, perform an energy conservation control process of changing its operation state in accordance with the received control instruction, wherein the energy conservation instruction further includes an energy conservation time period indicative of a continuous time period of the energy conservation control process, the energy conservation time period included in the control signal, and said time period storage unit is configured to store an allowed continuous time period for which said functional unit is allowed to continue the energy conservation control process corresponding to the common control order, said time period judging unit is configured to, upon receiving the control signal, refer to said time period storage unit, and retrieve the allowed continuous time period associated with the energy conservation control process which is performed by said functional unit in accordance with the energy conservation instruction, and prohibit said functional unit from performing the energy conservation control process upon acknowledging that the allowed continuous time period is equal to or less than the energy conservation time period included in the energy conservation instruction by not providing the control instruction to the functional unit.