Power systems handbook. Vol. 1, Short-circuits in AC and DC systems: ANSI, IEEE, and IEC standards

This book provides an understanding of the nature of short-circuit currents, current interruption theories, circuit breaker types, calculations according to ANSI/IEEE and IEC standards, theoretical and practical basis of short-circuit current sources, and the rating structure of switching devices. The book aims to explain the nature of short-circuit currents, the symmetrical components for unsymmetrical faults, and matrix methods of solutions, which are invariably used on digital computers. It includes innovations, worked examples, case studies, and solved problems. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Contents 6 Series Preface 16 Preface to Volume 1: Short-Circuits in AC and DC Systems 18 Author 20 1. Design and Analyses Concepts of Power Systems 22 1.1 Static and Dynamic Systems 23 1.2 State Variables 24 1.3 Linear and Nonlinear Systems 26 1.3.1 Property of Decomposition 27 1.4 Linearizing a Nonlinear System 27 1.5 Time-Invariant Systems 30 1.6 Lumped and Distributed Parameters 32 1.7 Optimization 33 1.8 Planning and Design of Electrical Power Systems 33 1.9 Electrical Standards and Codes 35 1.10 Reliability Analyses 36 1.10.1 Availability 37 1.10.1.1 Exponential Distribution 38 1.10.2 Data for Reliability Evaluations 39 1.10.3 Methods of Evaluation 39 1.10.4 Reliability and Safety 43 1.11 Extent of System Modeling 46 1.11.1 Short-Circuit Calculations 47 1.11.2 Load Flow Calculations 49 1.11.3 Harmonic Analysis 49 1.12 Power System Studies 49 1.13 Power System Studies Software 50 1.14 System of Units 51 Problems 51 References 53 2. Modern Electrical Power Systems 56 2.1 Classicafition 56 2.1.1 Utility Companies in the USA 57 2.1.2 North American Power System Interconnections 58 2.2 Deregulation of Power Industry 59 2.2.1 Generation Company (GENCO) 59 2.2.2 Transmission Company (TRANSCO) 60 2.2.3 Distribution Company (DISTCO) 60 2.3 The New Energy Platform 60 2.3.1 Sustainable, Renewable, and Green Energy 61 2.3.2 Green Energy 62 2.3.3 Hydroelectric Plants 62 2.3.4 Pumped Storage Hydroelectric Plants 64 2.3.5 Nuclear Power 64 2.3.5.1 Breeder Reactors 68 2.3.5.2 Nuclear Fusion 68 2.3.5.3 Nuclear Power around the Globe 69 2.3.5.4 Is Nuclear Power Green Energy? 69 2.3.6 Geothermal Plants 70 2.3.7 Solar and Wind Energy 71 2.3.8 Biofuels and Carbon-Neutral Fuels 71 2.3.9 Local Green Energy Systems 72 2.3.10 Fuel Cells 72 2.3.11 Reducing Caron Emissions 73 2.4 Large Power Stations of the World 74 2.5 Smart Grid 78 2.5.1 Legislative Measures 79 2.5.2 Technologies Driving Smart Grid 79 2.6 Microgrids and Distributed Generation 80 2.7 Energy Storage 84 2.7.1 Flywheel Storage 85 2.7.2 Superconductivity 88 2.7.2.1 Applications in Electrical Systems 89 2.8 Transmission Systems 89 2.9 Industrial Systems 90 2.10 Distribution Systems 92 2.10.1 The Radial System 93 2.10.2 The Parallel or Loop System 94 2.10.3 Network or Grid System 94 2.10.4 Primary Distribution System 96 2.11 Future Load Growth 98 2.12 Underground versus OH Systems 98 2.12.1 Spot Network 99 2.13 HV DC Transmission 101 2.13.1 HV DC Light 101 2.13.2 H VDC Congfiurations and Operating Modes 101 Problems 103 Bibliography 103 IEEE Color Books 105 3. Wind and Solar Power Generation and Interconnections with Utility 106 3.1 Prospective of Wind Generation in the USA 106 3.2 Characteristics of Wind Power Generation 108 3.2.1 Maximum Transfer Capability 112 3.2.2 Power Reserves and Regulation 113 3.2.3 Congestion Management 114 3.3 Wind Energy Conversion 114 3.3.1 Drive Train 115 3.3.2 Towers 117 3.3.3 Rotor Blades 117 3.4 The Cube Law 118 3.5 Operation 120 3.5.1 Speed Control 122 3.5.2 Behavior under Faults and Low-Voltage Ride Through 123 3.6 Wind Generators 124 3.6.1 Induction Generators 124 3.6.2 Direct Coupled Induction Generator 126 3.6.3 Induction Generator Connected to Grid through Full Size Converter 126 3.6.4 Doubly Fed Induction Generator 127 3.6.5 Synchronous Generators 128 3.7 Reactive Power and Wind Turbine Controls 128 3.8 Power Electronics and Harmonics 132 3.8.1 Power Electronics 132 3.8.2 Harmonics 133 3.9 Computer Modeling 134 3.9.1 A Wind Turbine Controller 134 3.10 Solar Power 136 3.11 CSP Plants 137 3.11.1 Solar Energy Collectors 137 3.11.1.1 Parabolic Dish Concentrators 138 3.11.1.2 Solar Tower 139 3.11.2 Trackers 139 3.11.2.1 Photovoltaic Trackers 140 3.12 Direct Conversion of Solar Energy through PV Cells 141 3.12.1 Cells, Modules, Panels, and Systems 141 3.12.1.1 PV Module 141 3.12.1.2 PV Panel 142 3.12.1.3 PV Array 142 3.12.1.4 PV Array Subefild 142 3.13 Classicfiation of Solar Cells 142 3.14 Utility Connections of Distributed Resources 144 3.14.1 Voltage Control 144 3.14.2 Grounding 144 3.14.3 Synchronizing 144 3.14.4 Distribution Secondary Spot Networks 145 3.14.5 Inadvertent Energization 145 3.14.6 Metering 145 3.14.7 Isolation Device 145 3.14.8 EMI Interference 145 3.14.9 Surge Withstand 146 3.14.10 Paralleling Device 146 3.14.11 Area Faults 146 3.14.12 Abnormal Frequencies 146 3.14.13 Reconnection 146 3.14.14 Harmonics 146 Problems 147 References 148 4. Short-Circuit Currents and Symmetrical Components 152 4.1 Nature of Short-Circuit Currents 153 4.2 Symmetrical Components 156 4.3 Eigenvalues and Eigenvectors 159 4.4 Symmetrical Component Transformation 160 4.4.1 Similarity Transformation 160 4.4.2 Decoupling a Three-Phase Symmetrical System 162 4.4.3 Decoupling a Three-Phase Unsymmetrical System 166 4.4.4 Power Invariance in Symmetrical Component Transformation 167 4.5 Clarke Component Transformation 167 4.6 Characteristics of Symmetrical Components 171 4.7 Sequence Impedance of Network Components 174 4.7.1 Construction of Sequence Networks 174 4.7.2 Transformers 176 4.7.2.1 Delta–Wye or Wye–Delta Transformer 176 4.7.2.2 Wye–Wye Transformer 178 4.7.2.3 Delta–Delta Transformer 179 4.7.2.4 Zigzag Transformer 179 4.7.2.5 Three-Winding Transformers 180 4.7.3 Static Load 184 4.7.4 S ynchronous Machines 184 4.8 Computer Models of Sequence Networks 189 Problems 191 Bibliography 192 5. Unsymmetrical Fault Calculations 194 5.1 Line-to-Ground Fault 194 5.2 Line-to-Line Fault 196 5.3 Double Line-to-Ground Fault 198 5.4 Three-Phase Fault 200 5.5 Phase Shift in Three-Phase Transformers 201 5.5.1 Transformer Connections 201 5.5.2 Phase Shifts in Winding Connections 201 5.5.3 Phase Shift for Negative Sequence Components 204 5.6 Unsymmetrical Fault Calculations 207 5.7 System Grounding 214 5.7.1 Solidly Grounded Systems 216 5.7.2 Resistance Grounding 217 5.7.2.1 High-Resistance Grounded Systems 218 5.7.2.2 Coefcfiient of Grounding 224 5.8 Open Conductor Faults 225 5.8.1 Two-Conductor Open Fault 225 5.8.2 One-Conductor Open 225 Problems 230 Bibliography 232 References 232 6. Matrix Methods for Network Solutions 234 6.1 Network Models 234 6.2 Bus Admittance Matrix 235 6.3 Bus Impedance Matrix 240 6.3.1 Bus Impedance Matrix from Open-Circuit Testing 241 6.4 Loop Admittance and Impedance Matrices 242 6.4.1 Selection of Loop Equations 244 6.5 Graph Theory 244 6.6 Bus Admittance and Impedance Matrices by Graph Approach 247 6.6.1 Primitive Network 247 6.6.2 Incidence Matrix from Graph Concepts 249 6.6.3 Node Elimination in Y-Matrix 253 6.7 Algorithms for Construction of Bus Impedance Matrix 254 6.7.1 Adding a Tree Branch to an Existing Node 255 6.7.2 Adding a Link 257 6.7.3 Removal of an Uncoupled Branch 259 6.7.4 Changing Impedance of an Uncoupled Branch 259 6.7.5 Removal of a Coupled Branch 259 6.8 Short-Circuit Calculations with Bus Impedance Matrix 267 6.8.1 Line-to-Ground Fault 267 6.8.2 Line-to-Line Fault 267 6.8.3 Double Line-to-Ground Fault 268 6.9 Solution of Large Network Equations 277 Problems 278 Bibliography 279 7. Current Interruptions in AC Networks 280 7.1 Rheostatic Breaker 280 7.2 AC Arc Interruption 282 7.2.1 Arc Interruption Theories 282 7.2.1.1 Cassie’s Theory 282 7.2.1.2 Mayr’s Theory 283 7.2.1.3 Cassie-Mayr Theory 283 7.3 Current-Zero Breaker 284 7.4 Transient Recovery Voltage 285 7.4.1 First Pole to Clear Factor 287 7.5 The Terminal Fault 290 7.5.1 Four-Parameter Method 290 7.5.2 Two-Parameter Representation 291 7.6 The Short-Line Fault 292 7.7 Interruption of Low Inductive Currents 294 7.7.1 Virtual Current Chopping 296 7.8 Interruption of Capacitance Currents 297 7.9 TRV in Capacitive and Inductive Circuits 299 7.10 Prestrikes in Circuit Breakers 300 7.11 Overvoltages on Energizing HV Lines 301 7.11.1 Overvoltage Control 303 7.11.2 Synchronous Operation 304 7.11.3 Synchronous Capacitor Switching 304 7.11.4 Shunt Reactors 305 7.11.4.1 Oscillation Modes 308 7.12 Out-of-Phase Closing 309 7.13 Resistance Switching 310 7.14 Failure Modes of Circuit Breakers 314 7.15 Stresses in Circuit Breakers 316 7.16 Classicfiation of Circuit Breakers according to Interrupting Medium 316 7.16.1 SF[sub(6)] Circuit Breakers 317 7.16.1.1 Electronegativity of SF[sub(6)] 318 7.16.2 Operating Mechanisms 320 7.16.3 Vacuum Interruption 321 7.16.3.1 Current Chopping and Multiple Ignitions 322 7.16.3.2 Switching of Unloaded Dry-Type Transformers 324 7.17 Part Winding Resonance in Transformers 325 7.17.1 Snubber Circuits 327 7.18 Solid-State Circuit Breakers 327 Problems 329 Bibliography 330 References 331 8. Application and Ratings of Circuit Breakers and Fuses according to ANSI Standards 334 8.1 Total and Symmetrical Current Basis 335 8.2 Asymmetrical Ratings 337 8.2.1 Contact Parting Time 337 8.3 Voltage Range Factor K 338 8.4 Circuit Breaker Timing Diagram 341 8.5 Maximum Peak Current 342 8.6 Permissible Tripping Delay 343 8.7 Service Capability Duty Requirements and Reclosing Capability 343 8.7.1 Transient Stability on Fast Reclosing 344 8.8 Shunt Capacitance Switching 347 8.8.1 Switching of Cables 352 8.9 Line Closing Switching Surge Factor 356 8.9.1 Switching of Transformers 357 8.10 Out-of-Phase Switching Current Rating 358 8.11 T ransient Recovery Voltage 358 8.11.1 Circuit Breakers Rated Below 100 kV 359 8.11.2 Circuit Breakers Rated 100 kV and Above 359 8.11.3 Short-Line Faults 363 8.11.4 Oscillatory TRV 365 8.11.4.1 Exponential (Overdamped) TRV 365 8.11.5 Initial TRV 366 8.11.6 Adopting IEC TRV Profiles in IEEE Standards 366 8.11.7 Definite-Purpose TRV Breakers 371 8.11.8 T RV Calculation Techniques 371 8.12 Generator Circuit Breakers 374 8.13 Specicfiations of High-Voltage Circuit Breakers 379 8.14 Low-Voltage Circuit Breakers 379 8.14.1 Molded Case Circuit Breakers 379 8.14.2 Insulated Case Circuit Breakers (ICCBs) 380 8.14.3 Low-Voltage Power Circuit Breakers (LVPCBs) 380 8.14.3.1 Single-Pole Interrupting Capability 382 8.14.3.2 Short-Time Ratings 382 8.14.3.3 Series Connected Ratings 383 8.15 Fuses 384 8.15.1 Current-Limiting Fuses 385 8.15.2 Low-Voltage Fuses 386 8.15.3 High-Voltage Fuses 386 8.15.4 Interrupting Ratings 387 Problems 388 References 389 9. Short Circuit of Synchronous and Induction Machines and Converters 392 9.1 Reactances of a Synchronous Machine 393 9.1.1 Leakage Reactance X''[sub(d)] 393 9.1.2 Subtransient Reactance X'[sub(d)] 393 9.1.3 Transient Reactance X'[sub(d)] 393 9.1.4 Synchronous Reactance X[sub(d)] 393 9.1.5 Quadrature Axis Reactances X''[sub(q)], X'[sub(q)], and X[sub(q)] 394 9.1.6 Negative Sequence Reactance X[sub(2)] 395 9.1.7 Zero Sequence Reactance X[sub(0)] 395 9.1.8 Potier Reactance X[sub(p)] 395 9.2 Saturation of Reactances 396 9.3 Time Constants of Synchronous Machines 396 9.3.1 Open-Circuit Time Constant T''[sub(do)] 396 9.3.2 Subtransient Short-Circuit Time Constant T'[sub(d)] 396 9.3.3 Transient Short-Circuit Time Constant T'[sub(d)] 396 9.3.4 Armature Time Constant T[sub(a)] 396 9.4 Synchronous Machine Behavior on Short Circuit 396 9.4.1 Equivalent Circuits during Fault 401 9.4.2 Fault Decrement Curve 404 9.5 Circuit Equations of Unit Machines 407 9.6 Park’s Transformation 411 9.6.1 Reactance Matrix of a Synchronous Machine 411 9.6.2 Transformation of Reactance Matrix 414 9.7 Park’s Voltage Equation 416 9.8 Circuit Model of Synchronous Machines 418 9.9 Calculation Procedure and Examples 420 9.9.1 Manufacturer’s Data 427 9.10 Short Circuit of Synchronous Motors and Condensers 429 9.11 Induction Motors 430 9.12 Capacitor Contribution to the Short-Circuit Currents 434 9.13 Static Converters Contribution to the Short-Circuit Currents 435 9.14 Practical Short-Circuit Calculations 438 Problems 438 References 440 Bibliography 440 10. Short-Circuit Calculations according to ANSI Standards 442 10.1 Types of Calculations 442 10.1.1 Assomptions 443 10.1.2 Maximum Peak Current 443 10.2 Accounting for Short-Circuit Current Decay 444 10.2.1 Low-Voltage Motors 445 10.3 Rotating Machine Model 446 10.4 Type and Severity of System Short Circuits 447 10.5 Calculation Methods 448 10.5.1 Simplified Method X/R ≤ 17 448 10.5.2 Simplified Method X/R > 17 448 10.5.3 E/X Method for AC and DC Decrement Adjustments 448 10.5.4 Fault Fed from Remote Sources 449 10.5.5 Fault Fed from Local Sources 451 10.5.6 Weighted Multiplying Factors 456 10.6 Network Reduction 456 10.6.1 E/X or E/Z Calculation 457 10.7 Breaker Duty Calculations 458 10.8 Generator Source Asymmetry 458 10.9 Calculation Procedure 460 10.9.1 N ecessity of Gathering Accurate Data 460 10.9.2 Ca lculation Procedure 461 10.9.3 Analytical Calculation Procedure 462 10.9.4 Hand Calculations 462 10.9.5 Dynamic Simulation 462 10.9.6 Circuit Breakers with Sources on Either Side 462 10.9.7 Switching Devices without Short-Circuit Interruption Ratings 464 10.9.8 Adjustments for Transformer Taps and Ratios 464 10.10 Examples of Calculations 465 10.10.1 Calculation of Short-Circuit Duties 465 10.10.2 K-Rated 15 kV Breakers 469 10.10.3 4.16 kV Circuit Breakers and Motor Starters 473 10.10.4 Transformer Primary Switches and Fused Switches 473 10.10.5 Low-Voltage Circuit Breakers 473 10.10.6 Bus Bracings 473 10.10.7 Power Cables 476 10.10.8 Overhead Line Conductors 477 10.10.9 Generator Source Symmetrical Short-Circuit Current 481 10.10.10 Generator Source Asymmetrical Current 482 10.10.11 System Source Symmetrical Short-Circuit Current 482 10.10.12 System Source Asymmetrical Short-Circuit Current 483 10.10.13 Required Closing Latching Capabilities 483 10.10.14 Selection of the Generator Breaker 484 10.11 Deriving an Equivalent Impedance 485 10.12 Thirty-Cycle Short-Circuit Currents 490 10.13 Fault Current Limiters 491 10.13.1 Superconducting Fault Current Limiters 494 Problems 495 References 498 11. Short-Circuit Calculations according to IEC Standards 500 11.1 Conceptual and Analytical Differences 500 11.1.1 Breaking Capability 500 11.1.2 Rated Restriking Voltage 501 11.1.3 Rated Making Capacity 501 11.1.4 Rated Opening Time and Break Time 501 11.1.5 Initial Symmetrical Short-Circuit Current 501 11.1.6 Peak Making Current 502 11.1.7 Breaking Current 502 11.1.8 Steady-State Current 502 11.1.9 Highest Short-Circuit Currents 503 11.2 Prefault Voltage 504 11.3 Far-From Generator Faults 504 11.3.1 Nonmeshed Sources 506 11.3.2 Meshed Networks 508 11.3.2.1 Method A: Uniform Ratio R/X or X/R Ratio Method 508 11.3.2.2 Ratio R/X or X/R at the Short-Circuit Location 508 11.3.2.3 Method C: Equivalent Frequency Method 509 11.4 Near-to-Generator Faults 510 11.4.1 Generators Directly Connected to Systems 510 11.4.2 Generators and Unit Transformers of Power Station Units 511 11.4.3 Motors 512 11.4.4 Short-Circuit Currents Fed from One Generator 512 11.4.4.1 Breaking Current 512 11.4.4.2 Steady-State Current 513 11.4.5 Short-Circuit Currents in Nonmeshed Networks 514 11.4.6 Short-Circuit Currents in Meshed Networks 515 11.5 Inuflence of Motors 516 11.5.1 Low-Voltage Motor Groups 517 11.5.2 Calculations of Breaking Currents of Asynchronous Motors 517 11.5.3 Static Converter Fed Drives 518 11.6 Comparison with ANSI/IEE Calculation Procedures 518 11.7 Examples of Calculations and Comparison with ANSI Methods 520 11.8 Electromagnetic Transients Program Simulation of a Generator Terminal Short Circuit 534 11.8.1 The Effect of PF 534 Problems 538 References 540 12. Calculations of Short-Circuit Currents in Direct Current Systems 542 12.1 DC Short-Circuit Current Sources 542 12.2 Calculation Procedures 544 12.2.1 IEC Calculation Procedure 544 12.2.2 Matrix Methods 546 12.3 Short-Circuit of a Lead Acid Battery 546 12.4 Short-Circuit of DC Motors and Generators 552 12.5 Short-Circuit of a Rectiefir 558 12.6 Short-Circuit of a Charged Capacitor 564 12.7 Total Short-Circuit Current 565 12.8 DC Circuit Breakers 566 12.9 DC Rated Fuses 569 12.10 Protection of the Semi-Conductor Devices 569 12.11 High-Voltage DC Circuit Breakers 571 Problems 574 References 574 Appendix A: Matrix Methods 576 Appendix B: Sparsity and Optimal Ordering 608 Appendix C: Transformers and Reactors 616 Appendix D: Solution to the Problems 650 Index 730 "This book provides an understanding of the nature of short-circuit currents, current interruption theories, circuit breaker types, calculations according to ANSI/IEEE and IEC standards, theoretical and practical basis of short-circuit current sources, and the rating structure of switching devices.©є℗¡The book aims to explain the nature of short-circuit currents, the symmetrical components for unsymmetrical faults, and matrix methods of solutions, which are invariably used on digital computers. It includes innovations, worked examples, case studies, and solved problems."--Provided by publisher