Chapter
3 Synchronous Machine Modeling
3.1 Conventions and Notation
3.2 Three-Damper-Winding Model
3.3 Transformations and Scaling
3.4 The Linear Magnetic Circuit
3.5 The Nonlinear Magnetic Circuit
3.6 Single-Machine Steady State
3.7 Operational Impedances and Test Data
4 Synchronous Machine Control Models
4.1 Voltage and Speed Control Overview
4.3 Voltage Regulator Models
4.5 Speed Governor Models
5 Single-Machine Dynamic Models
5.2 The Multi-Time-Scale Model
5.3 Elimination of Stator/Network Transients
5.5 The One-Axis (Flux-Decay) Model
5.8 Single-Machine Infinite-Bus System
5.9 Synchronous Machine Saturation
6 Multimachine Dynamic Models
6.1 The Synchronously Rotating Reference Frame
6.2 Network and R-L Load Constraints
6.3 Elimination of Stator/Network Transients
6.3.1 Generalization of Network and Load Dynamic Models
6.3.2 The Special Case of “Impedance Loads”
6.4 Multimachine Two-Axis Model
6.4.1 The Special Case of “Impedance Loads”
6.5 Multimachine Flux–Decay Model
6.5.1 The Special Case of “Impedance Loads”
6.6 Multimachine Classical Model
6.6.1 The Special Case of “Impedance Loads”
6.7 Multimachine Damping Torques
6.8 Multimachine Models with Saturation
6.8.1 The Multimachine Two-Axis Model with Synchronous Machine Saturation
6.8.2 The Multimachine Flux-Decay Model with Synchronous Machine Saturation
6.9 Frequency During Transients
6.10 Angle References and an Infinite Bus
6.11 Automatic Generation Control (AGC)
7 Multimachine Simulation
7.1 Differential-Algebraic Model
7.2 Stator Algebraic Equations
7.2.3 Alternate Form of Stator Algebraic Equations
7.3.2 Real Power Equations
7.3.3 Reactive Power Equations
7.3.4 Current-Balance Form
7.5 Simplification of the Two-Axis Model
7.5.1 Simplification #1 (Neglecting Transient Saliency in the Synchronous Machine)
7.5.2 Simplification #2 (Constant Impedance Load in the Transmission System)
7.6 Initial Conditions (Full Model)
7.6.1 Load-Flow Formulation
7.6.3 Initial Conditions for Dynamic Analysis
7.6.4 Angle Reference, Infinite Bus, and COI Reference
7.7 Numerical Solution: Power-Balance Form
7.7.2 Review of Newton’s Method
7.7.3 Numerical Solution Using SI Method
7.7.4 Disturbance Simulation
7.8 Numerical Solution: Current-Balance Form
7.8.1 Some Practical Details
7.9 Reduced-Order Multimachine Models
7.9.2 Generator Equations
7.9.6 Structure-Preserving Classical Model
7.9.7 Internal-Node Model
8.2 Basic Linearization Technique
8.2.1 Linearization of Model A
8.2.2 Differential Equations
8.2.3 Stator Algebraic Equations
8.2.5 Linearization of Model B
8.2.6 Differential Equations
8.2.7 Stator Algebraic Equations
8.3 Participation Factors
8.4 Studies on Parametric Effects
8.4.3 Effect of Type of Load
8.5 Electromechanical Oscillatory Modes
8.5.1 Eigenvalues of A and A𝝎
8.6 Power System Stabilizers
8.6.2 Derivation of K1 - K6 Constants
8.6.4 Synchronizing and Damping Torques
8.6.5 Damping of Electromechanical Modes
8.6.7 Synchronizing Torque
8.6.9 Power System Stabilizer Design
8.6.10 Frequency-Domain Approach
8.6.11 Design Procedure Using the Frequency-Domain Method
9 Energy Function Methods
9.2 Physical and Mathematical Aspects of the Problem
9.5 Energy Function Formulation
9.6 Potential Energy Boundary Surface (PEBS)
9.6.1 Single-Machine Infinite-Bus System
9.6.2 Energy Function for a Single-Machine Infinite-Bus System
9.6.3 Equal-Area Criterion and the Energy Function
9.6.5 Initialization of VPE(𝜽) and its Use in PEBS Method
9.7 The Boundary Controlling u.e.p (BCU) Method
9.8 Structure-Preserving Energy Functions
10 Synchronized Phasor Measurement
10.2.1 Nominal Frequency Phasors
10.2.2 Off-Nominal Frequency Phasors
10.2.4 Positive-Sequence Signals
10.2.5 Frequency Estimation
10.2.6 Phasor Data Accuracy
10.3 Phasor Data Communication
10.4 Power System Frequency Response
10.5 Power System Disturbance Propagation
10.5.1 Disturbance Triggering
10.6 Power System Disturbance Signatures
10.6.1 Generator or Load Trip
10.6.3 Fault and Line Switching
10.6.4 Shunt Capacitor or Reactor Switching
10.7 Phasor State Estimation
10.8 Modal Analyses of Oscillations
10.9 Energy Function Analysis
10.10 Control Design Using PMU Data
10.11 Conclusions and Remarks
11.2 Power Flow Computation
11.2.2 Power Flow Formulation and Solution
11.2.3 Nonconvergent Power Flow
11.3.1 Dynamic Models and Per-Unit Parameter Values
11.3.4 Integration Methods
11.3.5 Disturbance Specifications
11.5 Conclusions and Remarks
A Integral Manifolds for Model Reduction
A.1 Manifolds and Integral Manifolds
A.2 Integral Manifolds for Linear Systems
A.3 Integral Manifolds for Nonlinear Systems
Power System Dynamics and Stability
：With Synchrophasor Measurement and Power System Toolbox
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