It has been found that the transmission network and its electrical parameters play an important role in the transient performance of power systems. The transient angle instability of multi-machine power systems can be generally expressed by the network critical cutsets. When a system loses its synchronism, the angle differences of lines belonging to the corresponding critical cutsets will increase continuously and rapidly.So it is significant for power system planning and operation to effectively evaluate the influence of the network configuration upon the dynamic response, accurately identify the critical cutsets of post-fault network, and find vulnerable area of the network. Dynamic Security Region (DSR) in injection space is defined as a region in which a power system will be transient stable for a given fault. Compared with traditionalpoint wiseapproaches, the DSR concept is gradually being accepted by electrical power engineers for its advantage on dynamic security monitoring, assessment and optimal control of power systems. Based on the practical DSR (PDSR) theory, network critical cutsets are systematically and thoroughly studied in this dissertation, and some important theoretical and practical conclusions are derived as follows:1. The relationship between the number of critical cutsets and the type of unstable equilibrium point (UEP) with respect to transient angle stability is proved based on the Bergen-Hill structure-preserving model (SPM) of power systems and the application of matrix theories. Furthermore, this conclusion is developed to be applicable to the system expressed by a more complicated SPM and is used to propose the corrected cutset stability criterion, which can eliminate the old one's conservation resulting from the assumption that there exists just one unique critical cutset for a given fault.2. Based on the sufficient consideration of the dynamic response characteristics of the high voltage direct current (HVDC) system in the transient process of power systems, the HVDC system can be equivalent to be two injections. Then the differential topological characteristics of DSR for AC/DC systems are analyzed. The transient angle stabilities of several typical AC/DC parallel power systems are studied based on numerical simulation method. And the boundary characteristics of the PDSRfor AC/DC parallel power systems are investigated by changing the active powers, voltage magnitudes of generator nodes and active powers, reactive powers of load nodes, as well as HVDC power. The influences of HVDC control modes and load models on PDSR for AC/DC parallel power systems are considered.3. As applications of the PDSR theories for AC systems and AC/DC parallel power systems, the expressions for the power transfer limit of critical cutsets (PTLCC) are deduced for these two kinds of systems first, according to the relation of the UEP type to the critical cutset number. A simple and practical algorithm for solving the PTLCC maximization problem considering one contingency is proposed. Lastly, considering the multi-contingency, the mathematical models for determining the maximal PTLCC and transient stability-constrained generation economic dispatch are recommended respectively, which are linear programming problems and can be resolved on-line. Real bulk power systems have been used to test the proposed models and methods.