• Declaration of Authorship
• Abstract
• Acknowledgements
• List of Figures
• List of Tables
• Abbreviations
• Symbols
• 1 Introduction
  • 1.1 Definitions
  • 1.2 Transient Stability Analysis: Background
  • 1.3 Transient Stability Study Methods
    • 1.3.1 Time Domain Methods
    • 1.3.2 Probabilistic Methods
    • 1.3.3 Expert System Methods
    • 1.3.4 Database or Pattern Recognition Methods
    • 1.3.5 Equal Area Criterion: An Elementary View of Transient Stability
    • 1.3.6 Transient Energy Function Method
      • 1.3.6.1 Gorev's Energy Criteria
      • 1.3.6.2 Magnusson's Method
      • 1.3.6.3 Aylett's Method
      • 1.3.6.4 Tavora and Smith's Method
      • 1.3.6.5 Attay et al.'s Work
  • 1.4 Current Trends in the Direct Methods
  • 1.5 Dynamic Security Assessment in Restructured Power Systems
  • 1.6 Thesis Outline
• 2 Nonlinear Systems and Stability Theory
  • 2.1 Second-Order Systems
    • 2.1.1 Qualitative Behavior of Linear Systems
      • 2.1.1.1 Real and Distinct Eigenvalues
      • 2.1.1.2 Complex Eigenvalues
      • 2.1.1.3 Nonzero Multiple Eigenvalues
      • 2.1.1.4 One or Both Eigenvalues Equal to Zero
    • 2.1.2 Behavior of Nonlinear Systems about the Equilibrium Point
    • 2.1.3 Multiple Equilibria
    • 2.1.4 Qualitative Behavior Near Equilibrium Points
  • 2.2 Stability in the Sense of Lyapunov
  • 2.3 Domain of Attraction
    • 2.3.1 The Closest Unstable Equilibrium Point Method
    • 2.3.2 Controlling Unstable Equilibrium Point
    • 2.3.3 Potential Energy Boundary Surface
      • 2.3.3.1 Theoretical Foundation for the PEBS
    • 2.3.4 Accuracy of PEBS Method vs Controlling UEP Method
• 3 Transient Stability Assessment Using Transient Energy Function
  • 3.1 The Classical Power System Model
  • 3.2 System Conditions at Fault-Clearing Instant
  • 3.3 Motion Equations Relative to the Center of Inertia
  • 3.4 Derivation of Transient Energy Function
  • 3.5 Corrected Kinetic Energy
  • 3.6 Transient Stability Assessment and Concept of Controlling UEP
  • 3.7 Determination of the Controlling UEP
    • 3.7.1 Controlling UEP Determination Using MOD Method
      • 3.7.1.1 Obtaining Candidate UEPs
      • 3.7.1.2 Approximating the UEPs for the Candidate MODs
    • 3.7.2 Determination of the Controlling UEP Using the BCU Method
  • 3.8 Calculation of Exact Controlling UEP
    • 3.8.1 Calculation of the Jacobian Matrix for the Mismatch Function
    • 3.8.2 Calculation of the Hessian Matrix
    • 3.8.3 Case Study: Calculating the Exact Controlling UEP
      • 3.8.3.1 IEEE 17-Generator 162-Bus System
      • 3.8.3.2 IEEE 50-Generator 145-Bus System
• 4 Relieving Transient Stability Constraint
  • 4.1 Energy Margin and the its Functional Dependence
    • 4.1.1 Sensitivity of Reduced Admittance Matrix
    • 4.1.2 Sensitivity of Controlling UEP and Predisturbance SEP
    • 4.1.3 Sensitivity of Angle and Speed at Fault Clearing Instant
    • 4.1.4 Sensitivity of the Other Dependent Variables
  • 4.2 Sensitivity of Static Operational Parameters
    • 4.2.1 Complex Power Equations and the Jacobian Matrix
    • 4.2.2 Sensitivity of Voltage at Load Controlled Buses
    • 4.2.3 Sensitivity of Reactive Power of Generators and the Generation of Slack Bus
    • 4.2.4 Sensitivity of Generators' Internal Voltage
    • 4.2.5 Sensitivity of Transmission Lines' Flow
  • 4.3 Relieving Transient Stability Constraint in Electricity Markets
  • 4.4 Allocating the Cost of Transient Stability Relief in Bilateral Electricity Markets
    • 4.4.1 Nodal Method
    • 4.4.2 Proposed Method
    • 4.4.3 Shapley Value
    • 4.4.4 Case Study
      • 4.4.4.1 Single Constraint
      • 4.4.4.2 Multiple Constraints
  • 4.5 Incorporating the Static Constraints in Transient Stability Relief
    • 4.5.1 3-Machine System
    • 4.5.2 New England 10-Machine System
• 5 Conclusions
  • 5.1 Concluding Remarks
  • 5.2 Contributions
  • 5.3 Future Research
• A Numerical Methods for Solving the Differential Equations
  • A.1 Euler Method
  • A.2 Modified Euler Method
  • A.3 Runge-Kutta Methods
    • A.3.1 Second-Order R-K Method
    • A.3.2 Fourth-Order R-K Method
• B Line Search Methods in Unconstrained Optimization
  • B.1 Introduction: Overview of methods
  • B.2 Search Direction for Line Search Methods
    • B.2.1 Steepest Descent Direction
    • B.2.2 Newton Direction
  • B.3 Step Length
  • B.4 Termination Conditions in Line Search Methods
    • B.4.1 Wolfe Conditions and Strong Wolfe Conditions
    • B.4.2 Goldstein Condition
  • B.5 Interpolation
    • B.5.1 Quadratic Interpolation
    • B.5.2 Cubic Interpolation
  • B.6 Implementing Line Search Algorithm
• C Transient Stability Test Systems
  • C.1 Western System Coordinating Council Power System
  • C.2 17-Generator 162-Bus System
  • C.3 50-Generator 145-Bus System
• Bibliography

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