Handbook of Power Systems Engineering with Power Electronics Applications

YOSHIHIDE HASE, Power System Engineering Consultant, Tokyo, Japan

• PREFACE xxiACKNOWLEDGEMENTS xxiiiABOUT THE AUTHOR xxvINTRODUCTION xxvii1 OVERHEAD TRANSMISSION LINES AND THEIR CIRCUIT CONSTANTS 11.1 Overhead Transmission Lines with LR Constants 11.2 Stray Capacitance of Overhead Transmission Lines 101.3 Working Inductance and Working Capacitance 181.4 Supplement: Proof of Equivalent Radius req () for a Multi-bundled Conductor 252 SYMMETRICAL COORDINATE METHOD (SYMMETRICAL COMPONENTS) 292.1 Fundamental Concept of Symmetrical Components 292.2 Definition of Symmetrical Components 312.3 Conversion of Three-phase Circuit into Symmetrical Coordinated Circuit 342.4 Transmission Lines by Symmetrical Components 362.5 Typical Transmission Line Constants 462.6 Generator by Symmetrical Components (Easy Description) 492.7 Description of Three-phase Load Circuit by Symmetrical Components 523 FAULT ANALYSIS BY SYMMETRICAL COMPONENTS 533.1 Fundamental Concept of Symmetrical Coordinate Method 533.2 Line-to-ground Fault (Phase a to Ground Fault: 1fG) 543.3 Fault Analysis at Various Fault Modes 593.4 Conductor Opening 594 FAULT ANALYSIS OF PARALLEL CIRCUIT LINES (INCLUDING SIMULTANEOUS DOUBLE CIRCUIT FAULT) 694.1 Two-phase Circuit and its Symmetrical Coordinate Method 694.2 Double Circuit Line by Two-phase Symmetrical Transformation 734.3 Fault Analysis of Double Circuit Line (General Process) 774.4 Single Circuit Fault on the Double Circuit Line 804.5 Double Circuit Fault at Single Point f 814.6 Simultaneous Double Circuit Faults at Different Points f, F on the Same Line 855 PER UNIT METHOD AND INTRODUCTION OF TRANSFORMER CIRCUIT 915.1 Fundamental Concept of the PU Method 915.2 PU Method for Three-phase Circuits 975.3 Three-phase Three-winding Transformer, its Symmetrical Components Equations, and the Equivalent Circuit 995.4 Base Quantity Modification of Unitized Impedance 1105.5 Autotransformer 1115.6 Numerical Example to Find the Unitized Symmetrical Equivalent Circuit 1125.7 Supplement: Transformation from Equation 5.18 to Equation 5.19 1226 THE ab0 COORDINATE METHOD (CLARKE COMPONENTS) AND ITS APPLICATION 1276.1 Definition of ab0 Coordinate Method (ab0 Components) 1276.2 Interrelation Between ab0 Components and Symmetrical Components 1306.3 Circuit Equation and Impedance by the ab0 Coordinate Method 1346.4 Three-phase Circuit in ab0 Components 1346.5 Fault Analysis by ab0 Components 1397 SYMMETRICAL AND ab0 COMPONENTS AS ANALYTICAL TOOLS FOR TRANSIENT PHENOMENA 1457.1 The Symbolic Method and its Application to Transient Phenomena 1457.2 Transient Analysis by Symmetrical and ab0 Components 1477.3 Comparison of Transient Analysis by Symmetrical and ab0 Components 1508 NEUTRAL GROUNDING METHODS 1538.1 Comparison of Neutral Grounding Methods 1538.2 Overvoltages on the Unfaulted Phases Caused by a Line-to-ground fault 1588.3 Arc-suppression Coil (Petersen Coil) Neutral Grounded Method 1598.4 Possibility of Voltage Resonance 1609 VISUAL VECTOR DIAGRAMS OF VOLTAGES AND CURRENTS UNDER FAULT CONDITIONS 1699.1 Three-phase Fault: 3fS, 3fG (Solidly Neutral Grounding System, High-resistive Neutral Grounding System) 1699.2 Phase b–c Fault: 2fS (for Solidly Neutral Grounding System, High-resistive Neutral Grounding System) 1709.3 Phase a to Ground Fault: 1fG (Solidly Neutral Grounding System) 1739.4 Double Line-to-ground (Phases b and c) Fault: 2fG (Solidly Neutral Grounding System) 1759.5 Phase a Line-to-ground Fault: 1fG (High-resistive Neutral Grounding System) 1789.6 Double Line-to-ground (Phases b and c) Fault: 2fG (High-resistive Neutral Grounding System) 18010 THEORY OF GENERATORS 18310.1 Mathematical Description of a Synchronous Generator 18310.2 Introduction of d–q–0 Method (d–q–0 Components) 19110.3 Transformation of Generator Equations from a–b–c to d–q–0 Domain 19510.4 Generator Operating Characteristics and its Vector Diagrams on d- and q-axes Plane 20810.5 Transient Phenomena and the Generator’s Transient Reactances 21110.6 Symmetrical Equivalent Circuits of Generators 21310.7 Laplace-transformed Generator Equations and the Time Constants 22010.8 Measuring of Generator Reactances 22410.9 Relations Between the d–q–0 and a–b–0 Domains 22810.10 Detailed Calculation of Generator Short-circuit Transient Current under Load Operation 22810.11 Supplement 23411 APPARENT POWER AND ITS EXPRESSION IN THE 0–1–2 AND d–q–0 DOMAINS 24111.1 Apparent Power and its Symbolic Expression for Arbitrary Waveform Voltages and Currents 24111.2 Apparent Power of a Three-phase Circuit in the 0–1–2 Domain 24311.3 Apparent Power in the d–q–0 Domain 24612 GENERATING POWER AND STEADY-STATE STABILITY 25112.1 Generating Power and the P–d and Q–d Curves 25112.2 Power Transfer Limit between a Generator and a Power System Network 25412.3 Supplement: Derivation of Equation 12.17 from Equations 12.15st and 12.16 26113 THE GENERATOR AS ROTATING MACHINERY 26313.1 Mechanical (Kinetic) Power and Generating (Electrical) Power 26313.2 Kinetic Equation of the Generator 26513.3 Mechanism of Power Conversion from Rotor Mechanical Power to Stator Electrical Power 26813.4 Speed Governors, the Rotating Speed Control Equipment for Generators 27414 TRANSIENT/DYNAMIC STABILITY, P–Q–V CHARACTERISTICS AND VOLTAGE STABILITY OF A POWER SYSTEM 28114.1 Steady-state Stability, Transient Stability, Dynamic Stability 28114.2 Mechanical Acceleration Equation for the Two-generator System and Disturbance Response 28214.3 Transient Stability and Dynamic Stability (Case Study) 28414.4 Four-terminal Circuit and the Pd Curve under Fault Conditions and Operational Reactance 28614.5 PQV Characteristics and Voltage Stability (Voltage Instability Phenomena) 29014.6 Supplement 1: Derivation of DV/DP, DV/DQ Sensitivity Equation (Equation 14.20 from Equation 14.19) 29814.7 Supplement 2: Derivation of Power Circle Diagram Equation (Equation 14.31 from Equation 14.18 s) 29915 GENERATOR CHARACTERISTICS WITH AVR AND STABLE OPERATION LIMIT 30115.1 Theory of AVR, and Transfer Function of Generator System with AVR 30115.2 Duties of AVR and Transfer Function of Generator + AVR 30515.3 Response Characteristics of Total System and Generator Operational Limit 30815.4 Transmission Line Charging by Generator with AVR 31215.5 Supplement 1: Derivation of ed (s), eq(s) as Function of ef (s) (Equation 15.9 from Equations 15.7 and 15.8) 31315.6 Supplement 2: Derivation of eG(s) as Function of ef (s) (Equation 15.10 from Equations 15.8 and 15.9) 31416 OPERATING CHARACTERISTICS AND THE CAPABILITY LIMITS OF GENERATORS 31916.1 General Equations of Generators in Terms of p–q Coordinates 31916.2 Rating Items and the Capability Curve of the Generator 32216.3 Leading Power-factor (Under-excitation Domain) Operation, and UEL Function by AVR 32816.4 V–Q (Voltage and Reactive Power) Control by AVR 33416.5 Thermal Generators’ Weak Points (Negative-sequence Current, Higher Harmonic Current, Shaft-torsional Distortion) 33716.6 General Description of Modern Thermal/Nuclear TG Unit 34616.7 Supplement: Derivation of Equation 16.14 from Equation 16.9 35117 R–X COORDINATES AND THE THEORY OF DIRECTIONAL DISTANCE RELAYS 35317.1 Protective Relays, Their Mission and Classification 35317.2 Principle of Directional Distance Relays and R–X Coordinates Plane 35517.3 Impedance Locus in R–X Coordinates in Case of a Fault (under No-load Condition) 35817.4 Impedance Locus under Normal States and Step-out Condition 36517.5 Impedance Locus under Faults with Load Flow Conditions 37017.6 Loss of Excitation Detection by DZ-Relays 37117.7 Supplement 1: The Drawing Method for the Locus () of Equation 17.22 37217.8 Supplement 2: The Drawing Method for () of Equation 17.24 37418 TRAVELLING-WAVE (SURGE) PHENOMENA 37918.1 Theory of Travelling-wave Phenomena along Transmission Lines (Distributed-constants Circuit) 37918.2 Approximation of Distributed-constants Circuit and Accuracy of Concentrated-constants Circuit 39018.3 Behaviour of Travelling Wave at a Transition Point 39118.4 Surge Overvoltages and their Three Different and Confusing Notations 39518.5 Behaviour of Travelling Waves at a Lightning-strike Point 39618.6 Travelling-wave Phenomena of Three-phase Transmission Line 39818.7 Line-to-ground and Line-to-line Travelling Waves 40018.8 The Reflection Lattice and Transient Behaviour Modes 40218.9 Supplement 1: General Solution Equation 18.10 for Differential Equation 18.9 40518.10 Supplement 2: Derivation of Equation 18.19 from Equation 18.18 40719 SWITCHING SURGE PHENOMENA BY CIRCUIT-BREAKERS AND LINE SWITCHES 41119.1 Transient Calculation of a Single-Phase Circuit by Breaker Opening 41119.2 Calculation of Transient Recovery Voltages Across a Breaker's Three Poles by 3fS Fault Tripping 42019.3 Fundamental Concepts of High-voltage Circuit-breakers 43019.4 Current Tripping by Circuit-breakers: Actual Phenomena 43419.5 Overvoltages Caused by Breaker Closing (Close-switching Surge) 44419.6 Resistive Tripping and Resistive Closing by Circuit-breakers 44719.7 Switching Surge Caused by Line Switches (Disconnecting Switches) 45319.8 Supplement 1: Calculation of the Coefficients k1k4 of Equation 19.6 45519.9 Supplement 2: Calculation of the Coefficients k1k6 of Equation 19.17 45520 OVERVOLTAGE PHENOMENA 45920.1 Classification of Overvoltage Phenomena 45920.2 Fundamental (Power) Frequency Overvoltages (Non-resonant Phenomena) 45920.3 Lower Frequency Harmonic Resonant Overvoltages 46320.4 Switching Surges 46720.5 Overvoltage Phenomena by Lightning Strikes 46921 INSULATION COORDINATION 47521.1 Overvoltages as Insulation Stresses 47521.2 Fundamental Concept of Insulation Coordination 48121.3 Countermeasures on Transmission Lines to Reduce Overvoltages and Flashover 48321.4 Overvoltage Protection at Substations 48821.5 Insulation Coordination Details 50021.6 Transfer Surge Voltages Through the Transformer, and Generator Protection 51121.7 Internal High-frequency Voltage Oscillation of Transformers Caused by Incident Surge 52021.8 Oil-filled Transformers Versus Gas-filled Transformers 52621.9 Supplement: Proof that Equation 21.21 is the Solution of Equation 21.20 52922 WAVEFORM DISTORTION AND LOWER ORDER HARMONIC RESONANCE 53122.1 Causes and Influences of Waveform Distortion 53122.2 Fault Current Waveform Distortion Caused on Cable Lines 53423 POWER CABLES AND POWER CABLE CIRCUITS 54123.1 Power Cables and Their General Features 54123.2 Distinguishing Features of Power Cable 54523.3 Circuit Constants of Power Cables 55023.4 Metallic Sheath and Outer Covering 55723.5 Cross-bonding Metallic-shielding Method 55923.6 Surge Voltages: Phenomena Travelling Through a Power Cable 56323.7 Surge Voltages Phenomena on Cable and Overhead Line Jointing Terminal 56623.8 Surge Voltages at Cable End Terminal Connected to GIS 56824 APPROACHES FOR SPECIAL CIRCUITS 57324.1 On-load Tap-changing Transformer (LTC Transformer) 57324.2 Phase-shifting Transformer 57524.3 Woodbridge Transformer and Scott Transformer 57924.4 Neutral Grounding Transformer 58324.5 Mis-connection of Three-phase Orders 58525 THEORY OF INDUCTION GENERATORS AND MOTORS 59125.1 Introduction of Induction Motors and Their Driving Control 59125.2 Theory of Three-phase Induction Machines (IM) with Wye-connected Rotor Windings 59225.3 Squirrel-cage Type Induction Motors 61225.4 Supplement 1: Calculation of Equations (25.17), (25.18), and (25.19) 62726 POWER ELECTRONIC DEVICES AND THE FUNDAMENTAL CONCEPT OF SWITCHING 62926.1 Power Electronics and the Fundamental Concept 62926.2 Power Switching by Power Devices 63026.3 Snubber Circuit 63326.4 Voltage Conversion by Switching 63526.5 Power Electronic Devices 63526.6 Mathematical Backgrounds for Power Electronic Application Analysis 64327 POWER ELECTRONIC CONVERTERS 65127.1 AC to DC Conversion: Rectifier by a Diode 65127.2 AC to DC Controlled Conversion: Rectifier by Thyristors 66127.3 DC to DC Converters (DC to DC Choppers) 67127.4 DC to AC Inverters 68027.5 PWM (Pulse Width Modulation) Control of Inverters 68727.6 AC to AC Converter (Cycloconverter) 69127.7 Supplement: Transformer Core Flux Saturation (Flux Bias Caused by DC Biased Current Component) 69228 POWER ELECTRONICS APPLICATIONS IN UTILITY POWER SYSTEMS AND SOME INDUSTRIES 69528.1 Introduction 69528.2 Motor Drive Application 69528.3 Generator Excitation System 70428.4 (Double-fed) Adjustable Speed Pumped Storage Generator-motor Unit 70628.5 Wind Generation 71028.6 Small Hydro Generation 71528.7 Solar Generation (Photovoltaic Generation) 71628.8 Static Var Compensators (SVC: Thyristor Based External Commutated Scheme) 71728.9 Active Filters 72628.10 High-Voltage DC Transmission (HVDC Transmission) 73428.11 FACTS (Flexible AC Transmission Systems) Technology 73628.12 Railway Applications 74128.13 UPSs (Uninterruptible Power Supplies) 745APPENDIX A – MATHEMATICAL FORMULAE 747APPENDIX B – MATRIX EQUATION FORMULAE 751ANALYTICAL METHODS INDEX 757COMPONENTS INDEX 759SUBJECT INDEX 763