In recent years considerable progress has been achieved in power system transient stability assessment using the transient energy function (TEF) method. Due to the continued development and enhancement, the TEF method now provides accurate and reliable stability assessment;An inherent advantage of the TEF method is the availability of the relative degree of stability in terms of the transient energy margin. Moreover, the energy margin can be manipulated or analyzed as a function of important system parameters such as generation change, load change and transmission interface power flow change;In this dissertation a procedure to determine stability limits in terms of plant generation and transmission interface power flow for a particular contingency is presented using analytical sensitivity of the energy margin. This is evaluated from a single TEF run. In contrast, the conventional method involves repetitive runs of a time domain stability program and power flow study to determine the stability limits. This technique involves an analytic sensitivity equation and its solution method;The proposed procedure is tested on a 17-generator equivalent of the network of the State of Iowa. Test results show that proposed procedure determines the stability limit accurately when the generation change is small or when the energy margin changes approximately linearly. The proposed method can improve power system operations planning and permit real time transient stability limit calculation in power system operation.