Direct methods for stability analysis of electric power systems : theoretical foundation BCU methodologies and applications Widely accepted around the world the BCU method is the only direct method used in the power industry. Direct Methods for Stability Analysis of Electric Power Systems presents a comprehensive theoretical foundation of the method and its numerical implementation. This book provides graduate students researchers and practitioners with theoretical foundations of direct methods energy functions and the BCU method as well as the group based BCU method and its applications. Numerical studies on industrial models and data are also included System Modeling and Stability Problems. Lyapunov Stability and Stability Regions of Nonlinear Dynamical Systems. Quasi Stability Regions: Analysis and Characterization. Energy Function Theory and Direct Methods. Constructing Analytical Energy Functions for Transient Stability Models. Construction of Numerical Energy Functions for Lossy Transient Stability Models. Direct Methods for Stability Analysis: An Introduction. Foundation of the Closest UEP Method. Foundations of the Potential Energy Boundary Surface Method. Controlling UEP Method: Theory. Controlling UEP Method: Computations. Foundations of Controlling UEP Methods for Network Preserving Transient Stability Models. Network Reduction BCU Method and Its Theoretical Foundation. Numerical Network Reduction BCU Method. Network Preserving BCU Method and Its Theoretical Foundation. Numerical Network Preserving BCU Method. Numerical Studies of BCU Methods from Stability Boundary Perspectives. Study of the Transversality Conditions of the BCU Method. The BCU Exit Point Method. Group Properties of Contingencies in Power Systems. Group Based BCU Exit Method. Group Based BCU CUEP Methods. Group Based BCU Method. Perspectives and Future Directions This book describes the BCU method (Boundary of Stability Region Based Controlling Unstable Equilibrium Point method)