Chapter
3.1 Element-Node Incidence Matrix
3.3 Branch-Path Incidence Matrix K
3.4 Basic Cut-Set Incidence Matrix
3.5 Augmented Cut-Set Incidence Matrix B̃
3.6 Basic Loop Incidence Matrix
3.7 Augmented Loop Incidence Matrix
3.8 Network Performance Equations
4.2.1 Network Matrices by Singular Transformations
4.2.1.1 Bus Admittance Matrix and Bus Impedance Matrix
4.2.1.2 Branch Admittance and Branch Impedance Matrices
4.2.1.3 Loop Impedance and Loop Admittance Matrices
4.2.2 Network Matrices by Nonsingular Transformation
4.2.2.1 Branch Admittance Matrix
4.2.2.2 Loop Impedance and Loop Admittance Matrices
4.3 Bus Admittance Matrix by Direct Inspection
5 Building of Network Matrices
5.3.1 Calculation of Mutual Impedances
5.3.2 Calculation of Self-Impedance of Added Branch Zab
5.4.1 Calculation of Mutual Impedances
5.4.2 Computation of Self-Impedance
5.4.3 Removal of Elements or Changes in Element
5.5 Removal or Change in Impedance of Elements with Mutual Impedance
6.2 Symmetrical Components of Unsymmetrical Phases
6.3 Power in Sequence Components
6.4 Unitary Transformation for Power Invariance
7.1 Three-Phase Network Element Representation
7.1.1 Stationary Network Element
7.1.2 Rotating Network Element
7.1.3 Performance Relations for Primitive Three-Phase Network Element
7.2 Three-Phase Balanced Network Elements
7.2.1 Balanced Excitation
7.2.2 Transformation Matrices
7.3 Three-Phase Impedance Networks
7.3.1 Incidence and Network Matrices for Three-Phase Networks
7.3.2 Algorithm for Three-Phase Bus Impedance Matrix
7.3.2.1 Performance Equation of a Partial Three-Phase Network
7.3.2.2 Addition of a Branch
7.3.2.3 Addition of a Link
8.1 The Two-Axis Model of Synchronous Machine
8.2 Derivation of Park’s Two-Axis Model
8.3 Synchronous Machine Analysis
8.3.1 Voltage Relations—Stator or Armature
8.3.1.2 Direct Axis Damper Windings
8.3.1.3 Quadrature Axis Damper Windings
8.3.2 Flux Linkage Relations
8.3.2.3 Direct Axis Damper Winding
8.3.2.4 Quadrature Axis Damper Winding
8.3.3 Inductance Relations
8.3.3.1 Self-Inductance of the Armature Windings
8.3.3.2 Mutual Inductances of the Armature Windings
8.3.3.3 Mutual Inductances Between Stator and Rotor Flux
8.3.4 Flux Linkage Equations
8.3.4.2 Direct Axis Damper Winding
8.3.4.3 Quadrature Axis Damper Winding
8.5 Stator Voltage Equations
8.6 Steady-State Equation
8.7 Steady-State Vector Diagram
8.9 Equivalent Circuits and Phasor Diagrams
8.9.1 Model for Transient Stability
8.10 Transient State Phasor Diagram
8.12 Synchronous Machine Connected Through an External Reactance
9.2.1 Transformer with Nominal Turns Ratio
9.2.2 Phase Shifting Transformers
9.3.1 Constant Current Model
9.3.2 Constant Impedance Model
9.3.3 Constant Power Model
9.4.1 Dynamic Characteristics
9.5 Induction Machine Modeling
9.6 Model with Mechanical Transients
9.6.1 Power Torque and Slip
9.6.2 Reactive Power and Slip
9.7 Rectifiers and Inverter Loads
9.7.1 Static Load Modeling for Load Flow Studies
9.7.2 Voltage Dependence of Equivalent Loads
9.7.3 Derivation for Equivalent Load Powers
10.1 Necessity for Power Flow Studies
10.2 Conditions for Successful Operation of a Power System
10.3 The Power Flow Equations
10.4 Classification of Buses
10.5 Bus Admittance Formation
10.6 System Model for Load Flow Studies
10.8 Gauss–Seidel Iterative Method
10.8.1 Acceleration Factor
10.8.2 Treatment of a PV Bus
10.9 Newton–Raphson Method
10.9.1 Rectangular Coordinates Method
10.9.2 The Polar Coordinates Method
10.10 Sparsity of Network Admittance Matrices
10.11 Triangular Decomposition
10.14 Fast Decoupled Methods
10.15 Load Flow Solution Using Z-Bus
10.15.1 Bus Impedance Formation
10.15.2 Addition of a Line to the Reference Bus
10.15.3 Addition of a Radial Line and New Bus
10.15.4 Addition of a Loop Closing Two Existing Buses in the System
10.15.5 Gauss–Seidel Method Using Z-Bus for Load Flow Solution
10.16 Convergence Characteristics
10.17 Comparison of Various Methods for Power Flow Solution
11 Short Circuit Analysis
11.2 Advantages of Per Unit System
11.3 Three-Phase Short Circuits
11.7 Importance of Short Circuit Currents
11.8 Analysis of R–L Circuit
11.9 Three-Phase Short Circuit on Unloaded Synchronous Generator
11.10 Effect of Load Current or Prefault Current
11.11.1 Construction of Reactors
11.11.2 Classification of Reactors
12 Unbalanced Fault Analysis
12.2 Balanced Star Connected Load
12.4 Sequence Impedances of Transformer
12.5 Sequence Reactances of Synchronous Machine
12.6 Sequence Networks of Synchronous Machines
12.6.1 Positive Sequence Network
12.6.2 Negative Sequence Network
12.6.3 Zero Sequence Network
12.7 Unsymmetrical Faults
12.8 Assumptions for System Representation
12.9 Unsymmetrical Faults on an Unloaded Generator
12.11 Double Line-to-Ground Fault
12.12 Single Line-to-Ground Fault with Fault Impedance
12.13 Line-to-Line Fault with Fault Impedance
12.14 Double Line-to-Ground Fault With Fault Impedance
13 Power System Stability
13.2 Illustration of Steady State Stability Concept
13.3 Methods for Improcessing Steady State Stability Limit
13.4 Synchronizing Power Coefficient
13.5 Short Circuit Ratio and Excitation System
13.7 Stability of a Single Machine Connected to Infinite Bus
13.9 Equal Area Criterion and Swing Equation
13.10 Transient Stability Limit
13.11 Frequency of Oscillations
13.12 Critical Clearing Time and Critical Clearing Angle
13.13 Fault on a Double-Circuit Line
13.14 Transient Stability When Power Is Transmitted During the Fault
13.15 Fault Clearance and Reclosure in Double-Circuit System
13.16 First Swing Stability
13.17 Solution to Swing Equation Step-by-Step Method
13.18 Factors Affecting Transient Stability
13.18.1 Effect of Voltage Regulator
13.19 Excitation System and the Stability Problem
13.20.1 Power System Stabilizer
13.21 Small Disturbance Analysis
13.22 Node Elimination Methods
13.23 Other Methods for Solution of Swing Equation
13.23.1 Modified Euler’s Method
Power Systems Analysis
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