A method for controlling power of a display apparatus of a display system, the method comprising: sensing, while a portable device operates in a standby mode, a movement of the portable device using a motion sensor of the portable device; switching a mode of the portable device from the standby mode to a normal mode based on the movement of the portable device being sensed; generating, by the portable device, a pre-power on signal based on the standby mode being switched to the normal mode; and transmitting, by the portable device, the pre-power on signal to the display apparatus; characterised in that the method further comprises: activating, by the display apparatus, some elements of the display apparatus among all elements of the display apparatus in a pre-power on mode based on the pre-power on signal being received, wherein the pre-power on mode is a mode in which the some elements of the display apparatus are activated; switching based on a power on signal being received from the portable device, the pre-power on mode of the display apparatus to a normal mode by activating all elements of the display apparatus, the power on signal being generated by the portable device and transmitted from the portable device to the display apparatus based on a user command being received through the portable device; wherein the method further comprises: switching, by the display apparatus, the pre-power on mode of the display apparatus to the standby mode based on a signal not being received within a predetermined time after the display apparatus switches to the pre-power on mode; and maintaining, by the display apparatus, the standby mode even when the pre-power on signal is received from the portable device based on the display apparatus being switched from the pre-power on mode to the standby mode for a predetermined number of times due to the signal not being received within the predetermined time. sensing, while a portable device operates in a standby mode, a movement of the portable device using a motion sensor of the portable device; switching a mode of the portable device from the standby mode to a normal mode based on the movement of the portable device being sensed; generating, by the portable device, a pre-power on signal based on the standby mode being switched to the normal mode; and transmitting, by the portable device, the pre-power on signal to the display apparatus; characterised in that the method further comprises: activating, by the display apparatus, some elements of the display apparatus among all elements of the display apparatus in a pre-power on mode based on the pre-power on signal being received, wherein the pre-power on mode is a mode in which the some elements of the display apparatus are activated; switching based on a power on signal being received from the portable device, the pre-power on mode of the display apparatus to a normal mode by activating all elements of the display apparatus, the power on signal being generated by the portable device and transmitted from the portable device to the display apparatus based on a user command being received through the portable device; activating, by the display apparatus, some elements of the display apparatus among all elements of the display apparatus in a pre-power on mode based on the pre-power on signal being received, wherein the pre-power on mode is a mode in which the some elements of the display apparatus are activated; switching based on a power on signal being received from the portable device, the pre-power on mode of the display apparatus to a normal mode by activating all elements of the display apparatus, the power on signal being generated by the portable device and transmitted from the portable device to the display apparatus based on a user command being received through the portable device; wherein the method further comprises: switching, by the display apparatus, the pre-power on mode of the display apparatus to the standby mode based on a signal not being received within a predetermined time after the display apparatus switches to the pre-power on mode; and maintaining, by the display apparatus, the standby mode even when the pre-power on signal is received from the portable device based on the display apparatus being switched from the pre-power on mode to the standby mode for a predetermined number of times due to the signal not being received within the predetermined time. switching, by the display apparatus, the pre-power on mode of the display apparatus to the standby mode based on a signal not being received within a predetermined time after the display apparatus switches to the pre-power on mode; and maintaining, by the display apparatus, the standby mode even when the pre-power on signal is received from the portable device based on the display apparatus being switched from the pre-power on mode to the standby mode for a predetermined number of times due to the signal not being received within the predetermined time.