A non-contact power supplying appliance (100, 101) configured to contactlessly transmit power to a non-contact power receiving appliance (200, 200a, 200c) having a load (7, 509), the non-contact power supplying appliance (100, 101) comprising: a plurality of power supply units configured to transmit the power; a power-supply side communication unit configured to send and receive a communication packet; and a power-supply side controller configured to control the power supply units and the power-supply side communication unit, characterized in that the power-supply side communication unit is configured to complete placement detection of the non-contact power receiving appliance (200, 200a, 200c) when the power-supply side communication unit sends a first response-request message for placement detection of the non-contact power receiving appliances (200, 200a, 200c), and thereafter receives a corresponding first response message including a magnitude of the power under reception by the non-contact power receiving appliance (200, 200a, 200c), the power-supply side controller configured to identify a combination of the non-contact power receiving appliance (200, 200a, 200c) and some of the power supply units when the power-supply side communication unit sends second and third response-request messages for identifying a placement location of the non-contact power receiving appliance (200, 200a, 200c) and thereafter respectively receives corresponding second and third response messages including the magnitude of the power under reception by the non-contact power receiving appliance (299, 2a, 20c), and the power-supply side controller is configured to control the said identified power supply units in accordance with a corresponding fourth response message that is received by the power-supply side communication unit and includes a difference between the magnitude of the power under reception by the non-contact power receiving appliance (200, 200a, 200c) and rated power of the load (7, 509) after the power-supply side communication unit sends a fourth response-request message for power control. a plurality of power supply units configured to transmit the power; a power-supply side communication unit configured to send and receive a communication packet; and a power-supply side controller configured to control the power supply units and the power-supply side communication unit, characterized in that the power-supply side communication unit is configured to complete placement detection of the non-contact power receiving appliance (200, 200a, 200c) when the power-supply side communication unit sends a first response-request message for placement detection of the non-contact power receiving appliances (200, 200a, 200c), and thereafter receives a corresponding first response message including a magnitude of the power under reception by the non-contact power receiving appliance (200, 200a, 200c), the power-supply side controller configured to identify a combination of the non-contact power receiving appliance (200, 200a, 200c) and some of the power supply units when the power-supply side communication unit sends second and third response-request messages for identifying a placement location of the non-contact power receiving appliance (200, 200a, 200c) and thereafter respectively receives corresponding second and third response messages including the magnitude of the power under reception by the non-contact power receiving appliance (299, 2a, 20c), and the power-supply side controller is configured to control the said identified power supply units in accordance with a corresponding fourth response message that is received by the power-supply side communication unit and includes a difference between the magnitude of the power under reception by the non-contact power receiving appliance (200, 200a, 200c) and rated power of the load (7, 509) after the power-supply side communication unit sends a fourth response-request message for power control.