Power Systems Analysis

Cover
Power Systems Analysis
Copyright
Dedication
Preface
1 Introduction
	1.1 The Electrical Power System
	1.2 Network Models
	1.3 Faults and Analysis
	1.4 The Primitive Network
	1.5 Power System Stability
	1.6 Deregulation
	1.7 Renewable Energy Resources
2 Graph Theory
	2.1 Introduction
	2.2 Definitions
	2.3 Tree and Cotree
	2.4 Basic Loops
	2.5 Cut-Set
	2.6 Basic Cut-Sets
	Worked Examples
	Problems
	Questions
3 Incidence Matrices
	3.1 Element-Node Incidence Matrix
	3.2 Bus Incidence Matrix
	3.3 Branch-Path Incidence Matrix K
	3.4 Basic Cut-Set Incidence Matrix
	3.5 Augmented Cut-Set Incidence Matrix B˜
	3.6 Basic Loop Incidence Matrix
	3.7 Augmented Loop Incidence Matrix
	3.8 Network Performance Equations
	Worked Examples
	Questions
	Problems
4 Network Matrices
	4.1 Introduction
	4.2 Network Matrices
		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
	Worked Examples
	Questions
	Problems
5 Building of Network Matrices
	5.1 Introduction
	5.2 Partial Network
	5.3 Addition of a Branch
		5.3.1 Calculation of Mutual Impedances
		5.3.2 Calculation of Self-Impedance of Added Branch Zab
		5.3.3 Special Cases
	5.4 Addition of a Link
		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
	Worked Examples
	Problems
	Questions
6 Symmetrical Components
	6.1 The Operator “a”
	6.2 Symmetrical Components of Unsymmetrical Phases
	6.3 Power in Sequence Components
	6.4 Unitary Transformation for Power Invariance
7 Three-Phase Networks
	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
	Summary of the Formulae
	Worked Examples
	Questions
	Problems
8 Synchronous Machine
	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
			8.3.1.1 Field or Rotor
			8.3.1.2 Direct Axis Damper Windings
			8.3.1.3 Quadrature Axis Damper Windings
		8.3.2 Flux Linkage Relations
			8.3.2.1 Armature
			8.3.2.2 Field
			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
			8.3.4.1 Field
			8.3.4.2 Direct Axis Damper Winding
			8.3.4.3 Quadrature Axis Damper Winding
	8.4 The Transformations
	8.5 Stator Voltage Equations
	8.6 Steady-State Equation
	8.7 Steady-State Vector Diagram
	8.8 Reactances
	8.9 Equivalent Circuits and Phasor Diagrams
		8.9.1 Model for Transient Stability
	8.10 Transient State Phasor Diagram
	8.11 Power Relations
	8.12 Synchronous Machine Connected Through an External Reactance
	Worked Examples
	Questions
	Problems
9 Lines and Loads
	9.1 Lines
		9.1.1 Short Lines
		9.1.2 Medium Lines
		9.1.3 Long Lines
	9.2 Transformers
		9.2.1 Transformer with Nominal Turns Ratio
		9.2.2 Phase Shifting Transformers
	9.3 Load Modeling
		9.3.1 Constant Current Model
		9.3.2 Constant Impedance Model
		9.3.3 Constant Power Model
	9.4 Composite Load
		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
		9.6.3 Synchronous Motor
	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
	Worked Examples
	Questions
	Problems
10 Power Flow Studies
	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
	10.7 Gauss–Seidel Method
	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
	10.12 Optimal Ordering
	10.13 Decoupled Methods
	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
	Worked Examples
	Problems
	Questions
11 Short Circuit Analysis
	11.1 Per Unit Quantities
	11.2 Advantages of Per Unit System
	11.3 Three-Phase Short Circuits
	11.4 Reactance Diagrams
	11.5 Percentage Values
	11.6 Short Circuit kVA
	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 Reactors
		11.11.1 Construction of Reactors
		11.11.2 Classification of Reactors
	Worked Examples
	Problems
	Questions
12 Unbalanced Fault Analysis
	12.1 Sequence Impedances
	12.2 Balanced Star Connected Load
	12.3 Transmission Lines
	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
	12.10 Line-to-Line Fault
	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
	Worked Examples
	Problems
	Questions
13 Power System Stability
	13.1 Elementary Concepts
	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
	13.6 Transient Stability
	13.7 Stability of a Single Machine Connected to Infinite Bus
	13.8 The Swing Equation
	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 Dynamic Stability
		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
	Worked Examples
	Problems
	Questions
Index
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