Power System Dynamics with Computer-Based Modeling and Analysis

Yoshihide Hase is a power systems engineering consultant in Japan. Tanuj Khandelwal is CTO and Senior Principal Electrical Engineer at ETAP - Operation Technology, Inc. in the USA. Kazuyuki Kameda provides engineering and consulting services for Electrical and Control Systems at Eltechs Engineering & Consulting Co., Ltd, in Japan.

• About the Authors xxixPreface xxxiAcknowledgments xxxiiiPart A Power Systems Theories and Practices 11 Essentials of Electromagnetism 31.1 Overview 31.2 Voltage, Current, Electric Power, and Resistance 31.3 Electromagnetic Induction (Faraday’s Law) 41.4 Self Inductance and Mutual Inductance 61.5 Mutual Capacitance 72 Complex Number Notation (Symbolic Method) and the Laplace Transform 112.1 Euler’s Formula 112.2 Complex Number Notation of Electricity Based on Euler’s Formula 122.3 LR Circuit Transient Calculation Using Complex Number Notation and the Laplace Transform 142.4 LCR Circuit Transient Calculation 162.5 Resistive, Inductive, and Capacitive Load, and Phasor Expressions 213 Transmission Line Matrices and Symmetrical Components 253.1 Overhead Transmission Lines with Inductive LR Constants 253.2 Overhead Transmission Lines with Capacitive C Constants 303.3 Symmetrical Coordinate Method (Symmetrical Components) 323.4 Conversion of a Three-Phase Circuit into a Symmetrical Coordinated Circuit 393.5 Transmission Lines by Symmetrical Components 393.6 Generator by Symmetrical Components (Simplified Description) 473.7 Description of a Three-Phase Load Circuit by Symmetrical Components 494 Physics of Transmission Lines and Line Constants 514.1 Inductance 514.2 Capacitance and Leakage Current 594.3 Actual Configuration of Overhead Transmission Lines 664.4 Special Properties of Working Inductance and Working Capacitance 684.5 MKS Rational Unit System 715 The Per-Unit Method 775.1 Fundamental Concepts of the PU Method 775.2 PU Method for a Single-Phase Circuit 775.3 PU Method for Three-Phase Circuits 795.4 Base Quantity Modification of Unitized Impedance 805.5 Unitized Symmetrical Circuit: Numerical Example 816 Transformer Modeling 916.1 Single-Phase Three-Winding Transformer 916.2 − − Δ-Connected Three-Phase, Three-Winding Transformer 956.3 Three-Phase Transformers with Various Winding Connections 1016.4 Autotransformers 1056.5 On-Load Tap-Changing Transformer (LTC Transformer) 1076.6 Phase-Shifting Transformer 1096.7 Woodbridge Transformers and Scott Transformers 1136.8 Neutral Grounding Transformer 1166.9 Transformer Magnetic Characteristics and Inrush Current Phenomena 1187 Fault Analysis Based on Symmetrical Components 1277.1 Fundamental Concepts of Fault Analysis Based on the Symmetrical Coordinate Method 1277.2 Line-to-Ground Fault (Phase-a to Ground Fault: 1ϕG) 1277.3 Fault Analysis at Various Fault Modes 1327.4 Conductor Opening 1377.5 Visual Vector Diagrams of Voltages and Currents under Fault Conditions 1397.6 Three-Phase-Order Misconnections 1518 Fault Analysis with the αβ0-Method 1558.1 αβ0-Method (Clarke-Components) 1558.2 Fault Analysis with αβ0-Components 1668.3 Advantages of the αβ0-Method 1718.4 Fault-Transient Analysis with Symmetrical Components and the αβ0-Method 1719 Power Cables 1759.1 Structural Features of Power Cables 1759.2 Circuit Constants of Power Cables 1839.3 Metallic Sheaths and Outer Coverings 19010 Synchronous Generators, Part 1: Circuit Theory 19510.1 Generator Model in a Phase abc-Domain 19510.2 dq0 Method (dq0 Components) 20310.3 Transformation of Generator Equations from the abc-Domain to the dq0-Domain 20610.4 Physical Meanings of Generator Equations in the dq0-Domain 21010.5 Generator dq0-Domain Equations 21310.6 Generator dq0-Domain Equivalent Circuit 21810.7 Generator Operating Characteristics and Vector Diagram on the d- and q-Axes Plane 22010.8 Generator Transient Reactance 22310.9 Symmetrical Equivalent Circuits of Generators 22510.10 Laplace-Transformed Generator Equations and Time Constants 23110.12 Relations Between the dq0-Domain and αβ0-Domain 23910.13 Calculating Generator Short-Circuit Transient Current Under Load 23911 Synchronous Generators, Part 2: Characteristics of Machinery 25111.1 Apparent Power P + jQ in the abc-, 012-, dq0-Domains 25111.2 Mechanical (Kinetic) Power and Generating (Electrical) Power 25711.3 Kinetic Equation for Generators 25911.4 Generator Operating Characteristics with P-Q (or p-q) Coordinates 26911.5 Generator Ratings and Capability Curves 27111.6 Generator’s Locus in the pq-Coordinate Plane under Various Operating Conditions 27511.7 Leading Power-Factor (Under-Excitation Domain) Operation, and UEL Function by AVR 27711.8 Operation at Over-Excitation (Lagging Power-Factor Operation) 28211.9 Thermal Generators’ Weak Points (Negative-Sequence Current, Higher Harmonic Current, Shaft-Torsional Distortion) 28211.10 Transient Torsional Twisting Torque of a TG Coupled Shaft 28711.11 General Description of Modern Thermal/Nuclear TG Units 29012 Steady-State, Transient, and Dynamic Stability 29712.1 P-δ Curves and Q-δ Curves 29712.2 Power Transfer Limits of Grid-Connected Generators (Steady-State Stability) 29912.3 Transient Stability 30612.4 Dynamic Stability 30912.5 Four-Terminal Circuit and the P − δ Curve under Fault Conditions 31012.6 P-δ Curve under Various Fault-Mode Conditions 31212.7 PQV Characteristics and Voltage Instability (Voltage Avalanche) 31312.8 Generator Characteristics with an AVR 31912.9 Generator Operation Limit With and Without an AVR in PQ Coordinates 33012.10 VQ (Voltage and Reactive Power) Control with an AVR 33213 Induction Generators and Motors (Induction Machines) 33713.1 Introduction to Induction Motors and Generators 33713.2 Doubly Fed Induction Generators and Motors 33713.3 Squirrel-Cage Induction Motors 35513.4 Proportional Relations of Mechanical Quantities and Electrical Quantities as a Basis of Power-Electronic Control 36714 Directional Distance Relays and R–X Diagrams 37114.1 Overview of Protective Relays 37114.2 Directional Distance Relays (DZ-Ry) and R–X Coordinate Plane 37214.3 R–X Diagram Locus under Fault Conditions 37514.4 Impedance Locus under Ordinary Load Conditions and Step-Out Conditions 38114.5 Impedance Locus Under Faults with Load-Flow Conditions 38514.6 Loss of Excitation Detection by Distance Relays (40-Relay) 38615 Lightning and Switching Surge Phenomena and Breaker Switching 39115.1 Traveling Wave on a Transmission Line, and Equations 39115.2 Four-Terminal Network Equations between Two Arbitrary Points 39815.3 Examination of Line Constants 39915.4 Behavior of Traveling Waves at Transition Points 40115.5 Surge Overvoltages and Their Three Different, Confusing Notations 40415.6 Behavior of Traveling Waves at a Lightning-Strike Point 40615.7 Traveling Wave Phenomena of Three-Phase Transmission Lines 40815.8 Reflection Lattices and Transient Behavior Modes 41315.9 Switching Surge Phenomena Caused by Breakers Tripping 41515.10 Breaker Phase Voltages and Recovery Voltages after Fault Tripping 42415.11 Three-Phase Breaker TRVs across Independent Poles 42615.12 Circuit Breakers and Switching Practices 43215.13 Switching Surge Caused by Line Switches (Disconnecting Switches) 45215.14 Surge Phenomena Caused on Power Cable Systems 45415.15 Lightning Surge Caused on Cable Lines 45615.16 Switching Surge Caused on Cable Lines 45815.17 Surge Voltages Caused on Cables and GIS Jointed Points 45916 Overvoltage Phenomena 46316.1 Neutral-Grounding Methods 46316.2 Arc-Suppression Coil (Petersen Coil) Neutral-Grounded Method 46716.3 Overvoltages Caused by a Line-to-Ground Fault 46716.4 Other Low-Frequency Overvoltage Phenomena (Non-resonant Phenomena) 46916.5 Lower-Frequency Resonant Overvoltages 47216.6 Interrupted Ground Fault of a Cable Line in a Neutral-Ungrounded System 47516.7 Switching Surge Overvoltages 47516.8 Overvoltage Phenomena Caused by Lightning Strikes 47717 Insulation Coordination 48117.1 Overvoltages as Insulation Stresses 48117.2 Classification of Overvoltages 48317.3 Fundamental Process of Insulation Coordination 48617.4 Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover 48717.5 Tower-Mounted Arrester Devices 48917.6 Using Unequal Circuit Insulation (Double-Circuit Lines) 49017.7 Using High-Speed Reclosing 49017.8 Overvoltage Protection with Arresters at Substations 49117.9 Station Protection Using OGWs and Reduced Grounding Resistance 49917.10 Insulation Coordination Details 50117.11 Transfer Surge Voltages through Transformers, and Generator Protection 50917.12 Transformer Internal High-Frequency Voltage Oscillation Phenomena 51817.13 Oil-Filled Transformers Versus Gas-Filled Transformers 52418 Harmonics and Waveform Distortion Phenomena 52718.1 Classification of Harmonics and Waveform Distortion 52718.2 Impact of Harmonics 52718.3 Harmonic Phenomena Caused by Power Cable Line Faults 52919 Power Electronic Applications, Part 1: Devices 53519.1 Fundamental Concepts of Power Electronics 53519.2 Power Switching with Power Devices 53519.3 Snubber Circuit 53919.4 Voltage Conversion with Switching 54019.5 Power Electronics Devices 54219.6 Mathematical Background for Analyzing Power Electronics Applications 54720 Power Electronics Applications, Part 2: Circuit Theory 55320.1 AC-to-DC Conversion: A Rectifier with a Diode 55320.2 AC-to-DC Controlled Conversion: Rectifier with a Thyristor 56220.3 DC-to-DC Converters (DC-to-DC Choppers) 57120.4 DC-to-AC Inverters 57920.5 PWM Control of Inverters 58320.6 AC-to-AC Converters (Cycloconverters) 58721 Power Electronics Applications, Part 3: Control Theory 58921.1 Introduction 58921.2 Driving Motors 58921.3 Static Var Compensators (SVC: A Thyristor-Based Approach) 59721.4 Active Filters 60321.5 Generator Excitation Systems 60921.6 Adjustable-Speed Pumped-Storage Generator-Motor Units 61021.7 Wind Generation 61521.8 Small Hydro Generation 61821.9 Solar Generation (Photovoltaic Generation) 61921.10 High-Voltage DC Transmission (HVDC Transmission) 62121.11 FACTS Technology 62521.12 Railway Applications 62721.13 Uninterruptible Power Supplies 628Appendix A Mathematical Formulae 631Appendix B Matrix Equation Formulae 635Part B Digital Computation Theories 63922 Digital Computation Basics 64122.1 Introduction 64122.2 Network Types 64222.3 Circuit Elements 64522.4 Ohm’s Law 65322.5 Kirchhoff’s Circuit Laws 65522.6 Electrical Division Principle 65622.7 Instantaneous, Average, and RMS Values 65722.8 Nodal Formulation 65822.9 Procedure for Mesh Analysis 66222.10 Norton’s and Thévenin’s Equivalents 66422.11 Maximum Power Transfer Theorem 66822.13 Network Topology 67522.14 Power System Matrices 68122.15 Transformer Modeling 69222.16 Transmission Line Modeling 69623 Power-Flow Methods 70123.1 Newton–Raphson Method 70123.2 Gauss–Seidel Method 70223.3 Adaptive Newton–Raphson Method 70323.4 Fast-Decoupled Method 70324 Short-Circuit Methods 70524.1 ANSI/IEEE Calculation Methods 70524.2 IEC Calculation Methods 71925 Harmonics 72925.1 Problem Formulation 72925.2 Methodology and Standards 73325.3 Harmonic Indices 73525.4 Harmonic Component Modeling 74025.5 Power System Components 74125.6 System Resonance 74325.7 Harmonic Mitigation 74426 Reliability 74926.1 Methodology and Standards 74926.2 Performance Indices 75227 Numerical Integration Methods 75527.1 Accuracy 75527.2 Stability 75527.3 Stiffness 75727.4 Predictor–Corrector 75727.5 Runge–Kutta 75828 Optimization 76128.1 Power-Flow Injections 76128.2 Voltage Magnitude Constraints 76228.3 Line-Flow Thermal Constraints 76228.4 Line-Flow Constraints as Current Limitations 76328.5 Line-Flow Constraints as Voltage Angle Constraints 763Part C Analytical Practices and Examples using ETAP 76529 Introduction to Power System Analysis 76729.1 Planning Studies 76729.2 Need for Power-System Analysis 76829.3 Computers in Power Engineering 76829.4 Study Approach 76829.5 Operator Training 77229.6 System Reliability and Maintenance 77229.7 Electrical Transient Analyzer Program (ETAP) 77230 One-Line Diagrams 77730.1 Introduction 77730.2 Engineering Parameters 77730.3 One-Line Diagram Symbols 77830.4 Power-System Configurations 78030.5 Network Topology Processing 78730.6 Illustrative Example – Per-Unit and Single-Line Diagram 79031 Load Flow 79131.1 Introduction 79131.2 Study Objectives 79131.3 Problem Formulation 79231.4 Calculation Methodology 79431.5 Required Data for ETAP 79631.6 Data Collection and Preparation 79731.7 Model Validation 79731.8 Study Scenarios 79931.9 Contingency Analysis 80031.10 Optimal or Optimum Power Flow 80131.11 Illustrative Examples 80332 Short-Circuit/Fault Analysis 84132.1 Introduction 84132.2 Analysis Objectives 84132.3 Methodology and Standards 84632.4 Study Scenarios 85532.5 Results and Reports 85632.6 Illustrative Examples 85833 Motor Starting 88133.1 Methods 88133.2 Analysis Objectives 89333.3 Methodology and Standards 89433.4 Required Data 90233.5 Illustrative Examples 90333.6 Motor-Starting Plots and Results 91333.7 Motor-Starting Alerts 91634 Harmonics 91734.1 Introduction 91734.2 Analysis Objectives 91934.3 Required Data 92134.4 Harmonic Load Flow and Frequency Scan 92334.5 Illustrative Examples 92435 Transient Stability 93935.1 Introduction 93935.2 Analysis Objectives 94035.3 Basic Concepts of Transient Stability 94235.4 Dynamic Models 94435.5 User-Defined Models 96735.6 Parameter Tuning 96735.7 Single-Generator Power System Model 97135.8 Data Collection and Preparation 97335.9 Study Scenarios 97435.10 Stability Improvement 97735.11 System Simulation 97735.12 Illustrative Examples 97936 Reliability Assessment 100336.1 Introduction 100336.2 Analysis Objectives 100336.3 Problem Formulation 100436.4 Required Data 100536.5 Illustrative Examples 100537 Protective Device Coordination 101937.1 Introduction 101937.2 Relays 102237.3 Methodology 102837.4 Required Data 103537.5 Principle of Protection 103637.6 Principle of Selectivity/Coordination 103737.7 Art of Protection and Coordination >600 V 104037.8 Illustrative Examples 1048Appendix C Standards, Regulations, and Best Practice 1071Further Reading 1083Index 1085