Power Systems Analysis

  1. Power System Stability
    1. Classification of Stability
      1. Rotor Angle Stability
        1. Small-Signal Stability
          1. Definition and Characteristics
            1. Oscillatory Stability
            2. Transient Stability
              1. Definition and Characteristics
                1. First Swing Stability
              2. Frequency Stability
                1. Definition and Characteristics
                  1. Load-Generation Balance
                  2. Voltage Stability
                    1. Definition and Characteristics
                      1. Voltage Collapse Phenomenon
                    2. Rotor Angle Stability
                      1. The Swing Equation
                        1. Derivation and Physical Meaning
                          1. Newton's Second Law Application
                            1. Mechanical and Electrical Torques
                            2. Per-Unit Form
                              1. Linearization for Small Disturbances
                              2. Single-Machine Infinite Bus System
                                1. System Representation
                                  1. Generator Model
                                    1. Transmission System Model
                                      1. Infinite Bus Representation
                                      2. Stability Analysis
                                        1. Power-Angle Relationship
                                          1. Synchronizing Power Coefficient
                                        2. The Equal Area Criterion
                                          1. Application to Disturbances
                                            1. Accelerating Area
                                              1. Decelerating Area
                                              2. Critical Clearing Angle
                                                1. Geometric Interpretation
                                                  1. Calculation Methods
                                                  2. Critical Clearing Time
                                                    1. Time Domain Analysis
                                                      1. Practical Applications
                                                    2. Numerical Solution of the Swing Equation
                                                      1. Euler's Method
                                                        1. Algorithm Implementation
                                                          1. Accuracy Considerations
                                                          2. Runge-Kutta Method
                                                            1. Fourth-Order Method
                                                              1. Accuracy and Stability
                                                              2. Time-Step Selection
                                                                1. Stability Criteria
                                                                  1. Accuracy Requirements
                                                                2. Multi-Machine System Stability
                                                                  1. Coupled Swing Equations
                                                                    1. System of Differential Equations
                                                                      1. Coherency Concepts
                                                                      2. Inter-Area Oscillations
                                                                        1. Mode Identification
                                                                          1. Damping Characteristics
                                                                      3. Voltage Stability
                                                                        1. Concept of Voltage Collapse
                                                                          1. Voltage Instability Mechanisms
                                                                            1. Cascading Voltage Collapse
                                                                            2. P-V and Q-V Curves
                                                                              1. P-V Curve Construction
                                                                                1. Q-V Curve Construction
                                                                                  1. Interpretation and Use
                                                                                    1. Voltage Stability Margins
                                                                                      1. Critical Points
                                                                                    2. Factors Affecting Voltage Stability
                                                                                      1. Load Characteristics
                                                                                        1. Constant Power Loads
                                                                                          1. Motor Load Dynamics
                                                                                          2. Reactive Power Support
                                                                                            1. Generator Reactive Power Limits
                                                                                              1. Transmission System Reactive Power
                                                                                              2. System Topology
                                                                                                1. Network Strength
                                                                                                  1. Load Centers
                                                                                                2. Methods for Voltage Stability Improvement
                                                                                                  1. Shunt Compensation
                                                                                                    1. Capacitor Banks
                                                                                                      1. Static Var Compensators
                                                                                                      2. Series Compensation
                                                                                                        1. Series Capacitors
                                                                                                          1. Power Flow Control
                                                                                                          2. Load Shedding
                                                                                                            1. Undervoltage Load Shedding
                                                                                                              1. Emergency Control Actions
                                                                                                          3. Frequency Stability
                                                                                                            1. Load-Frequency Control
                                                                                                              1. Primary Control
                                                                                                                1. Governor Response
                                                                                                                  1. Frequency Droop
                                                                                                                  2. Secondary Control
                                                                                                                    1. Automatic Generation Control
                                                                                                                      1. Load Dispatch Centers
                                                                                                                    2. Governor Control Systems
                                                                                                                      1. Governor Types
                                                                                                                        1. Droop Characteristics
                                                                                                                          1. Speed Droop Setting
                                                                                                                            1. Load Sharing
                                                                                                                          2. Automatic Generation Control
                                                                                                                            1. Area Control Error
                                                                                                                              1. Definition and Calculation
                                                                                                                                1. Control Objectives
                                                                                                                                2. Tie-Line Bias Control
                                                                                                                                  1. Bias Factor Selection
                                                                                                                                    1. Control Implementation
                                                                                                                                  2. Frequency Response of Power Systems
                                                                                                                                    1. System Inertia Effects
                                                                                                                                      1. Load Damping Effects
                                                                                                                                        1. Generation Response

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                                                                                                                                    5. Unsymmetrical Fault Analysis

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                                                                                                                                    7. Economic Operation of Power Systems