9505620 Chiang Despite its significant progress, the direct method still suffers from several limitations which prevent it from both off- line and on-line applications. These limitations may be classified into: modeling limitation, scenario limitation, function limitation and accuracy limitation. These limitations must be removed or significantly improved before direct methods can be actually used by power utilities. A major limitation of direct methods in the past has been the simplicity of the models used in various direct method implementations in software programs. Much of this limitation will be overcome by the work presented in this proposal. The second limitation has been that direct methods apply to first swing instability only. The proposed project will enhance direct methods in such a way to provide useful information for identifying multi-swing unstable cases. A third limitation has been the accuracy and reliability of direct methods. This limitation will be significantly improved by the work (BCU method) to be developed in this research for network-preserving power system models. This proposal seeks, from both computational and theoretical viewpoints, to remove or improve much of the limitations in direct methods and make them viable for on-line direct stability analysis of practical large-scale power systems ***