Power System Analysis

Cover
About the Author
Contents
Preface
Chapter 1: Introduction
	1.1 Power System Studies
		1.1.1 Network Modelling Stage
		1.1.2 Mathematical Modelling Stage
		1.1.3 Solution Stage
	1.2 Organisation of Text Book
	1.3 Computer’s Role in Power System Studies
	1.4 Matlab Fundamentals
		1.4.1 Basics of MATLAB
Chapter 2: Power System Network Matrices—1
	2.1 Introduction
	2.2 Graph of a Power System Network
	2.3 Definitions
		2.3.1 Graph
		2.3.2 Planar and Non-Planar Graphs
		2.3.3 Rank of a Graph
		2.3.4 Oriented Graph
		2.3.5 Sub-Graph
		2.3.6 Path
		2.3.7 Connected Graph
		2.3.8 Tree
		2.3.9 Co-Tree
		2.3.10 Basic Loops or Fundamental f -Loops
		2.3.11 Basic Cutsets or Fundamental f -Cutsets
	2.4 Incidence Matrices
		2.4.1 Element Node Incidence Matrix (Â )
		2.4.2 Bus Incidence Matrix (A)
		2.4.3 Branch Path Incidence Matrix (P)
		2.4.4 Basic Cutset (or) Fundamental Cutset Incidence Matrix (C)
		2.4.5 Augmented or Tie Cutset Incidence Matrix (C)
		2.4.6 Basic or Fundamental f -loop Incidence Matrix (L)
		2.4.7 Augmented Loop Incidence Matrix L
	2.5 Primitive Network
		2.5.1 Primitive Network in Impedance Form
		2.5.2 Primitive Network in Admittance Form
	2.6 Network Equations and Network Matrices
	2.7 Bus Admittance Matrix
		2.7.1 Direct Inspection Method
		2.7.2 Step-by-Step Procedure
	2.8 Network Matrices by Singular Transformation Method
		2.8.1 Bus Admittance Matrix
		2.8.2 Branch Admittance Matrix
		2.8.3 Loop Impedance Matrix or Admittance Matrix
	2.9 Network Matrices by Non-Singular Transformation
Method
		2.9.1 Branch Admittance Matrix
		2.9.2 Loop Impedance and Loop Admittance Matrix
		2.9.3 Bus Admittance and Bus Impedance Matrices
		2.9.4 Algorithm for Singular and Non-Singular Transformation Methods
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 3: Power System Network Matrices—2
	3.1 Introduction
	3.2 Partial Network
	3.3 Case Studies in Zbus Algorithm
	3.4 Algorithm for Formation of Bus Impedance Matrix—No Mutual Coupling between the Elements
		3.4.1 Type-1 Modification
		3.4.2 Type-2 Modification
		3.4.3 Type-3 Modification
		3.4.4 Type-4 Modification
		3.4.5 MATLAB Program for Zbus Formation
	3.5 Algorithm for the Formation of Zbus— Consideration of Mutually Coupled Elements
		3.5.1 Type-1 and Type-2 Modifications
		3.5.2 Type-3 and Type-4 Modifications
		3.5.3 Summary of Formulas
	3.6 Modifications In Zbus for Changes in the Network
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 4: Power Flow Studies—1
	4.1 Introduction
		4.1.1 Basic Applications of Power Flow Studies and its Significance in Power System Operation and Control:
		4.1.2 Data Preparation:
	4.2 Network Modelling
	4.3 Mathematical Modelling
		4.3.1 Mathematical Model for Stage-1 Quantities
		4.3.2 Mathematical Modeling for Stage-2 Quantities
	4.4 Gauss–Seidel Iterative Method
	4.5 Classification of Buses
		4.5.1 PQ Bus or Load Bus
		4.5.2 PV Bus or Generator Bus
		4.5.3 Voltage Controlled Buses
		4.5.4 Slack Bus/Swing Bus/Reference Bus
	4.6 Case Studies in Power Flow Problem
	4.7 Algorithm for Power Flow Solution by the Gauss–Seidel Method
		4.7.1 Case-1: GS Method to obtain Bus Quantities when the PV Buses are Absent
		4.7.2 Case-2: GS Method to obtain Bus Quantities when the PV Buses are Present
		4.7.3 Flow Chart: Power Flow Solution by GS Method
	4.8 Conclusion
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 5: Power Flow Studies—2
	5.1 Introduction
	5.2 Newton–Raphson Method
		5.2.1 NR Method for Single-Valued Functions
		5.2.2 NR Method for Multi-Valued Function
	5.3 Power Flow Solution by Newton–Raphson Method
		5.3.1 NR Method when Bus Voltages are Expressed in the Polar Form
		5.3.4 NR Method when Bus Voltages are Expressed in the Rectangular Form
		5.3.5 Comparison of Gauss–Seidel and Newton–Raphson Method
	5.4 Decoupled Newton Method
		5.4.1 Algorithm for Decoupled Power Flow Method
	5.5 Fast Decoupled Power Flow Method
		5.5.1 Algorithm for Fast-Decoupled Power Flow Method
		5.5.2 Comparison of NR, Decoupled and Fast Decoupled Power Flow Methods
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 6: Short-Circuit Analysis—1 (Symmetrical Fault Analysis)
	6.1 Introduction
		6.1.1 Applications of Short Circuit Study
	6.2 Power System Representation
		6.2.1 Description of the Single Line Diagram Representation
		6.2.2 Assumptions made in Fault Calculations
		6.2.3 Network Modeling
	6.3 Per Unit Method
		6.3.1 Selection of Base Values
		6.3.2 Base Quantities
		6.3.3 Advantages of the Per Unit Method
	6.4 Symmetrical Fault Caculation
		6.4.1 Thevenin’s Equivalent Circuit
		6.4.2 Calculation of Symmetrical Fault Currents
	6.5 Current-Limiting Series Reactors
		6.5.1 Generator Reactors
		6.5.2 Feeder Reactors
		6.5.3 Bus Bar Reactors
	6.6 Consideration of Pre-Fault Load Current
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 7: Short-Circuit Analysis—2 (Unbalanced Fault Analysis)
	7.1 Introduction
	7.2 Symmetrical Components
		7.2.1 Operator a
		7.2.2 Sequence Components in Terms of Operator a
	7.3 Sequence Impedances
		7.3.1 Sequence Impedances of Individual Components
		7.3.1 Summary of Sequence Components
	7.4 Sequence Networks
		7.4.1 Generator Representation in Three-Sequence Networks.
		7.4.2 Transformer Representation in the Three Sequence Networks
		7.4.3 Transmission Line Representation
		7.4.4 Summary of Sequence Networks
	7.5 Unbalanced or Unsymmetrical Fault Analysis
		7.5.1 Single Line-to-Ground Fault (SLG Fault)
		7.5.2 Double Line Fault (LL Fault)
		7.5.3 Double Line-to-Ground (LLG) Fault
		7.5.4 Three-Phase Symmetrical Fault in Terms of Sequence Components
	7.6 Comparison of SLG and 3-Phase Faults
	7.7 Consideration of Pre-Fault Load Currents
	7.8 Fault Calculations Using Bus Impedance Matrix
		7.8.1 Three-Phase Symmetrical Fault
		7.8.2 Single Line-to-Ground Fault
		7.8.3 Double Line Fault (LL Fault)
		7.8.4 Double Line-to-Ground Fault
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 8: Power System Steady—State Stability Analysis
	8.1 Introduction
	8.2 Forms of Power System Stability
		8.2.1 Small Signal Analysis
		8.2.2 Large Signal Analysis—Transient Stability
	8.3 Physical Concept of Torque and Torque Angle
	8.4 Power Angle Curve and Transfer Reactance
	8.5 The Swing Equation
	8.6 Modelling Issues in the Stability Analysis
		8.6.1 Synchronous Machine Model
		8.6.2 Power System Model
		8.6.3 Multi-Machine System
	8.7 Assumptions made in Steady-State Stability Analysis
	8.8 Steady-State Stability Analysis
	8.9 Methods to Improve Steady-State Stability
	Questions from Previous Question Papers
	Competitive Examination Questions
Chapter 9: Transient Stability
	9.1 Transient Stability—Equal Area Criterion
		9.1.1 Mathematical Approach to EAC
		9.1.2 Application of Equal Area Criterion
		9.1.3 Determination of Critical Clearing Angle
		9.1.4 Determination of Critical Clearing Time [tcr]
		9.1.5 Determination of Transfer Reactance Before, During and After Fault Conditions
	9.2 II Solution of the Swing Equation: Point-By-Point
Method
	9.3 Methods to Improve Transient Stability
	Questions from Previous Question Papers
	Competitive Examination Questions
Answers to Selected Competitive Examination Questions
Index