1 Power System Stability in Single Machine System. - 1. 1 Introduction. - 1. 2 Statement of the Stability Problem. - 1. 3 Mathematical Formulation of the Problem. - 1. 4 Modeling Issues. - 1. 5 Motivation Through Single Machine Infinite Bus System. - 1. 6 Chapter Outline. - 2 Energy Functions for Classical Models. - 2. 1 Introduction. - 2. 2 Internal Node Representation. - 2. 3 Energy Functions for Internal Node Models. - 2. 4 Individual Machine and other Energy Functions. - 2. 5 Structure Preserving Energy Functions. - 2. 6 Alternative Form of the Structure Preserving Energy Function. - 2. 7 Positive Definiteness of the Energy Integral. - 2. 8 Tsolas-Araposthasis-Varaiya Model. - 3 Reduced Order Energy Functions. - 3. 1 Introduction. - 3. 2 Individual Machine and Group Energy Function. - 3. 3 Simplified Form of the Individual Machine Energy Function. - 3. 4 Cutset Energy Function. - 3. 5 Example of Cutset Energy Function. - 3. 6 Extended Equal Area Criterion (EEAC). - 3. 7 The Quasi Unstable Equilibrium Point (QUEP) Method. - 3. 8 Decomposition-Aggregation Method. - 3. 9 Time Scale Energies. - 4 Energy Functions with Detailed Models of Synchronous Machines and Its Control. - 4. 1 Introduction. - 4. 2 Single Machine System With Flux Decay Model. - 4. 3 Multi-Machine Systems With Flux Decay Model (Method of Parameter Variations). - 4. 4 Lyapunov Functions for Multi-Machine Systems With Flux Decay Model. - 4. 5 Multi-Machine Systems With Flux Decay Models and AVR. - 4. 6 Energy Functions With Detailed Models. - 4. 7 Lyapunov Function for Multi-Machine Systems With Flux Decay and Nonlinear Voltage Dependent Loads. - 5 Region of Stability in Power Systems. - 5. 1 Introduction. - 5. 2 Characterization of the Stability Boundary. - 5. 3 Region of Stability. - 5. 4 Method of Hyperplanes and Hypersurfaces. - 5. 5 Potential Energy Boundary Surface (PEBS) Method. - 5. 6 Hybrid Method Using the Gradient System. - 6 Practical Applications of the Energy Function Method. - 6. 1 Introduction. - 6. 2 The Controlling u. e. p. Method. - 6. 3 Modifications to the Controlling u. e. p. Method. - 6. 4 Potential Energy Boundary Surface (PEBS) Method. - 6. 5 Mode of Instability (MOI) Method. - 6. 6 Dynamic Security Assessment. - 7 Future Research Issues. - Appendix A 10 Machine 39 Bus System Data. - References. Language: English