Energy Function Analysis for Power System Stability

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.