Transient stability is the ability of the power system to maintain synchronism when subjected to a severe transient disturbance such as transmission line shortage, loss of a transmission line, loss of generation, or loss of a large load. Loss of synchronism due to transient instability is very dangerous because it can lead to a widespread power outage, and moreover it is extremely fast to manifest and affect the system, usually within 2 to 3 seconds of the initial disturbance. As a result, the best approach to deal with transient instability is to detect and prevent it before it actually happens. The BCU ( Boundary of stability region based Controlling Unstable equilibrium point) method for direct analysis of power system transient st ability prevails over existing assessment methods due to (1) its fast computational speed, (2) its ability to provide conservative index for degree of stability, and (3) its ability to provide useful information regarding how to derive enhancement control actions. In this thesis work, we expand the applicability of the BCU method to a wider range of power system applications and models, by providing numerical illustrations, conducting critical evaluations, and developing new solution methods. We propose new BCU-based methods for enhancing power system transient stability based on the TSCOPF (transient stability constrained optimal power flow) and direct generation rescheduling frameworks. Our methods combine the advantages of the traditional transient stability enhancement/preventive control schemes with that of the dynamic and geometric characteristics of the stability regions of the corresponding power system transient stability model. Our methods were tested on several practical power systems with large contingency lists and the advantages of using this novel framework are clearly evident. This framework not only significantly improves the computational aspects of the algorithm (i.e. speed, and the ability to handle large -scale power systems with large contingency lists), but also enhances the overall accuracy in enforcing transient sta bility within the methods. Numerical studies of the stability regions for various power system models are also conducted to illustrate the CUEP method for DAE system, and to e valuate several CUEP-based direct methods in approximating relevant stability boundaries.