This paper summarizes our results of a study on the complete controllability of power systems. With a nonlinear dynamic power system model, it is shown that power systems are completely controllable within a region of the state space. In other words, with the available controls, a power system can be steered from one state to any other state within the complete controllability region. The study also provides a strategy for constructing the complete controllability region. The results imply that during emergencies, if the power system states are in the complete controllability region, the movement of the power system states can be directed toward a desired operating point so that events like a voltage collapse can be avoided.