Transient stability analysis of a power system is concerned with the ability of the system to remain in synchronism following a disturbance. The synchronism of an interconnected network is, of course, fundamental for normal operation and as a result the study of transient stability plays a vital role in the planning and operation of electrical power systems. The time-domain simulation based on numerical integration methods used now by the utilities to conduct this study, although very effective in handling different models, are very expensive in terms of computation requirement. This has led to the search for a direct method which determines stability without explicitly solving the differential equations describ ing the power system dynamics. In this work, the efficiency and the accuracy of assessing power system transient stability using a direct method have been 188 investigated. This method is the Transient Energy Function method. The as sessment is based on the evaluation of the system transient energy components and does not involve any numerical integration. ln terms of the analytical bases, the following characteristics are observed The procedure combines computer-aided techniques with analytical tools in its formulation. The mathematical model describing the transient power system behaviour is the classical model. The energy function used for the analysis is derived from the system equation of motion, expressed in the inertial centre frame of reference and takes the system transfer conductance into consideration. Transient stability assessment using the TEF method is made by com paring the system transient energy at the end of the disturbance to the critical value of that energy. The success of the method depends upon the accurate evaluation of the energy components and also on the cost of the computational requirement. ln the work carried out in this project, both the above issues were of ma jor concern. The problems which arise when dealing with these issues have been analysed and a description of the approach to their solution has been proposed. A great deal of effort was devoted to the improvement of the TEF solution speed, which is very desirable for the planning as weil as operating studies. The main computational burden has appeared to be in the network reduction. Sparsity techniques and compact storage schemes have been used for construct" I ing , storing and reducing the admit tance matrices . Improving the accuracy of the TEF method is a challenging issue, which has been investigated in this project. It is related to the correct evaluation of the ! I transient critical energy, which in turn depends on how exact is the determination of the equilibrium points. Most of the problems encountered were associated with the computation of the unstable equilibrium points. Since the problem is a non linear one and many solutions are possible, obtaining the correct solution requires: ( a) an efficient and robust solution technique, and (b) select ion of a good starting point . Three equilibrium point solution techniques, namely the ewton-Raphson, the DFP minimisation technique and their combination, were formulated and in corporated into the implemented TEF program .Their algorithms have proved to be efficient in computing both stable and unstable equilibrium points of weIl behaved systems. A criteria, which determines the mode of instability, has been proposed for selecting the starting point for the unstable equilibrium point solution. It is based on identifying the group of critical generators from the knowledge of the rate of change of kinetic energies of the system generators. This criteria is easy to implement and has the advantage of providing the starting point with little computational effort .The numerical results of the various tests carried out have demonstrated tations of direct transient security assessment. Six power systems of different size have been used to assess the performance of the proposed algorithms . The use of sparsity techniques and the compact storage schemes in the network reduction procedure have been observed to be indispensable. Without the application of these techniques the TEF method would be inefficient. The computing time required by the network reduction procedure has been reduced to less than 20% of the total computing time of the TEF method. For a 118 bus 20-generator sytem, the ratio of the total computing time required by the TEF method to that by the step-by-step method is about 1/4 and the TEF program requires a memory storage of 1.94 Mb. The algorithms have proved to be practical in dealing with disturbances of different locations and very efficient in producing numerically stable results . The series of the transient stability runs have proved that there is a good correlation between the results obtained by the TEF method and the step-by step method. This can be attributed to the accurate determination of the mode of instability .