Power system controlled islanding is an emergency control to stop the propagation of disturbances and to avoid blackouts. This paper presents a three-stage method for intentional controlled islanding of power systems. It enables to search out reasonable islanding cutsets, which have the minimum load-generation imbalance or the minimal power flow disruption, without low-voltage problems. In the first stage, a self-adaptive graph simplification algorithm is proposed to obtain a two-terminal graph as a suitable islanding cutset search area from the original power network graph model. In the second stage, an islanding cutset search algorithm is designed to find all of islanding cutsets, including the minimum load-generation imbalance cutset, in the two-terminal graph. In the third stage, an islanding scheme checking algorithm is developed to examine the outputs of stage two. It uses the depth first search algorithm to determine reasonable islanding cutsets without low-voltage problems. The IEEE 30-bus system and the IEEE 118-bus system are utilized to demonstrate the proposed method. The simulation results show its validity and accuracy in large-scale power systems.