This paper describes the development of a three-phase line-interactive DVR with a new sag detection algorithm. The developed detection algorithm has a hybrid structure composed of an instantaneous detector and RMS-variation detectors. The source voltage passes through the sliding-window DFT and RMS calculator, and the instantaneous sag detector. If an instantaneous sag is detected, the RMS variation detector-1 is selected to calculate the RMS variation. The RMS variation detector-2 is selected when the instantaneous sag occurs under the operation of the RMS variation detector-1. The feasibility of the proposed algorithm is verified through computer simulations and experimental work with a prototype of a line-interactive DVR with a 3kVA rating. The line-interactive DVR with the proposed algorithm can compensate for an input voltage sag or an interruption within a 2ms delay. The developed DVR can effectively compensate for a voltage sag or interruption in sensitive loads, such as computers, communications equipment, and automation equipment.