Short-Circuits in AC and DC Systems ANSI, IEEE, and IEC Standards Volume by 1 J.C. Das

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Short-Circuits in AC and DC Systems ANSI, IEEE, and IEC Standards Volume by 1 J.C. Das


Short-Circuits in AC and DC Systems ANSI, IEEE, and IEC Standards Volume by 1 J.C. Das is available for free download in PDF format

Contents

Series Preface …………………xv

Preface to Volume 1: Short-Circuits in AC and DC Systems ……….. xvii

Author…………………………. xix

1. Design and Analyses Concepts of Power Systems………………….1

1.1 Static and Dynamic Systems ……………2

1.2 State Variables….3

1.3 Linear and Nonlinear Systems…………5

1.3.1 Property of Decomposition ….6

1.4 Linearizing a Nonlinear System………6

1.5 Time-Invariant Systems …………………..9

1.6 Lumped and Distributed Parameters ……………………………. 11

1.7 Optimization …12

1.8 Planning and Design of Electrical Power Systems …………12

1.9 Electrical Standards and Codes …….. 14

1.10 Reliability Analyses………………………. 15

1.10.1 Availability………………………… 16

1.10.1.1 Exponential Distribution……………………… 17

1.10.2 Data for Reliability Evaluations…………………………. 18

1.10.3 Methods of Evaluation ………. 18

1.10.4 Reliability and Safety …………22

1.11 Extent of System Modeling…………….25

1.11.1 Short-Circuit Calculations….26

1.11.2 Load Flow Calculations ……..28

1.11.3 Harmonic Analysis…………….28

1.12 Power System Studies…………………….28

1.13 Power System Studies Software……..29

1.14 System of Units………………………………30

Problems………………….30

References ………………. 32

2. Modern Electrical Power Systems………….35

2.1 Classifcation….35

2.1.1 Utility Companies in the USA ……………………………36

2.1.2 North American Power System Interconnections. 37

2.2 Deregulation of Power Industry …….38

2.2.1 Generation Company (GENCO) …………………………38

2.2.2 Transmission Company (TRANSCO) …………………39

2.2.3 Distribution Company (DISTCO) ……………………….39

2.3 The New Energy Platform……………..39

2.3.1 Sustainable, Renewable, and Green Energy………..40

2.3.2 Green Energy…………………….. 41

2.3.3 Hydroelectric Plants………….. 41

2.3.4 Pumped Storage Hydroelectric Plants………………..43

2.3.5 Nuclear Power ……………………43

2.3.5.1 Breeder Reactors…..47

2.3.5.2 Nuclear Fusion……..47

2.3.5.3 Nuclear Power around the Globe …………48

2.3.5.4 Is Nuclear Power Green Energy? ………….48

2.3.6 Geothermal Plants ……………..49

2.3.7 Solar and Wind Energy………50

2.3.8 Biofuels and Carbon-Neutral Fuels…………………….50

2.3.9 Local Green Energy Systems……………………………… 51

2.3.10 Fuel Cells…………………………… 51

2.3.11 Reducing Caron Emissions .. 52

2.4 Large Power Stations of the World …53

2.5 Smart Grid……..57

2.5.1 Legislative Measures………….58

2.5.2 Technologies Driving Smart Grid ………………………58

2.6 Microgrids and Distributed Generation…………………………59

2.7 Energy Storage……………………………….63

2.7.1 Flywheel Storage………………..64

2.7.2 Superconductivity……………… 67

2.7.2.1 Applications in Electrical Systems………..68

2.8 Transmission Systems ……………………68

2.9 Industrial Systems………………………….69

2.10 Distribution Systems ……………………..71

2.10.1 The Radial System ……………..72

2.10.2 The Parallel or Loop System……………………………….73

2.10.3 Network or Grid System …….73

2.10.4 Primary Distribution System ……………………………..75

2.11 Future Load Growth………………………77

2.12 Underground versus OH Systems….77

2.12.1 Spot Network……………………..78

2.13 HVDC Transmission ……………………..80

2.13.1 HVDC Light……………………….80

2.13.2 HVDC Confgurations and Operating Modes ……80

Problems………………….82

Bibliography ……………82

IEEE Color Books…….84

3. Wind and Solar Power Generation and Interconnections with Utility…………………85

3.1 Prospective of Wind Generation in the USA ………………….85

3.2 Characteristics of Wind Power Generation…………………….87

3.2.1 Maximum Transfer Capability ………………………….. 91

3.2.2 Power Reserves and Regulation …………………………92

3.2.3 Congestion Management……93

3.3 Wind Energy Conversion……………….93

3.3.1 Drive Train…………………………94

3.3.2 Towers………………………………..96

3.3.3 Rotor Blades……………………….96

3.4 The Cube Law………………………………..97

3.5 Operation……….99

3.5.1 Speed Control………………….. 101

3.5.2 Behavior under Faults and Low-Voltage

Ride Through…………………… 102

3.6 Wind Generators …………………………. 103

3.6.1 Induction Generators……….. 103

3.6.2 Direct Coupled Induction Generator ……………….. 105

3.6.3 Induction Generator Connected to Grid through

Full Size Converter ………….. 105

3.6.4 Doubly Fed Induction Generator……………………… 106

3.6.5 Synchronous Generators….. 107

3.7 Reactive Power and Wind Turbine Controls………………… 107

3.8 Power Electronics and Harmonics ………………………………. 111

3.8.1 Power Electronics…………….. 111

3.8.2 Harmonics……………………….. 112

3.9 Computer Modeling ……………………. 113

3.9.1 A Wind Turbine Controller ……………………………… 113

3.10 Solar Power …. 115

3.11 CSP Plants …… 116

3.11.1 Solar Energy Collectors……. 116

3.11.1.1 Parabolic Dish Concentrators …………….. 117

3.11.1.2 Solar Tower………… 118

3.11.2 Trackers …………………………… 118

3.11.2.1 Photovoltaic Trackers…………………………. 119

3.12 Direct Conversion of Solar Energy through

PV Cells ………. 120

3.12.1 Cells, Modules, Panels, and Systems………………… 120

3.12.1.1 PV Module…………. 120

3.12.1.2 PV Panel…………….. 121

3.12.1.3 PV Array……………. 121

3.12.1.4 PV Array Subfeld………………………………. 121

3.13 Classifcation of Solar Cells …………. 121

3.14 Utility Connections of Distributed Resources………………123

3.14.1 Voltage Control…………………123

3.14.2 Grounding………………………..123

3.14.3 Synchronizing ………………….123

3.14.4 Distribution Secondary Spot

Networks…………………………. 124

3.14.5 Inadvertent Energization…. 124

3.14.6 Metering………………………….. 124

3.14.7 Isolation Device……………….. 124

3.14.8 EMI Interference ……………… 124

3.14.9 Surge Withstand ………………125

3.14.10 Paralleling Device…………….125

3.14.11 Area Faults……………………….125

3.14.12 Abnormal Frequencies……..125

3.14.13 Reconnection ……………………125

3.14.14 Harmonics………………………..125

Problems……………….. 126

References …………….. 127

4. Short-Circuit Currents and Symmetrical Components………. 131

4.1 Nature of Short-Circuit Currents…. 132

4.2 Symmetrical Components …………… 135

4.3 Eigenvalues and Eigenvectors……… 138

4.4 Symmetrical Component Transformation……………………. 139

4.4.1 Similarity Transformation .. 139

4.4.2 Decoupling a Three-Phase Symmetrical System ……………………………… 141

4.4.3 Decoupling a Three-Phase Unsymmetrical System …………………………. 145

4.4.4 Power Invariance in Symmetrical Component

Transformation………………… 146

4.5 Clarke Component Transformation …………………………….. 146

4.6 Characteristics of Symmetrical Components……………….. 150

4.7 Sequence Impedance of Network Components …………… 153

4.7.1 Construction of Sequence Networks ……………….. 153

4.7.2 Transformers……………………. 155

4.7.2.1 Delta–Wye or Wye–Delta Transformer . 155

4.7.2.2 Wye–Wye Transformer………………………. 157

4.7.2.3 Delta–Delta Transformer……………………. 158

4.7.2.4 Zigzag Transformer …………………………… 158

4.7.2.5 Three-Winding Transformers…………….. 159

4.7.3 Static Load……………………….. 163

4.7.4 Synchronous Machines……. 163

4.8 Computer Models of Sequence Networks……………………. 168

Problems……………….. 170

Bibliography …………. 171

5. Unsymmetrical Fault Calculations ……… 173

5.1 Line-to-Ground Fault ………………….. 173

5.2 Line-to-Line Fault………………………… 175

5.3 Double Line-to-Ground Fault………. 177

5.4 Three-Phase Fault ……………………….. 179

5.5 Phase Shift in Three-Phase

Transformers……………………………….. 180

5.5.1 Transformer Connections… 180

5.5.2 Phase Shifts in Winding Connections……………… 180

5.5.3 Phase Shift for Negative Sequence

Components…………………….. 183

5.6 Unsymmetrical Fault Calculations………………………………. 186

5.7 System Grounding ……………………… 193

5.7.1 Solidly Grounded Systems ………………………………. 195

5.7.2 Resistance Grounding……… 196

5.7.2.1 High-Resistance Grounded Systems ….. 197

5.7.2.2 Coeffcient of Grounding ……………………203

5.8 Open Conductor Faults ………………..204

5.8.1 Two-Conductor Open Fault………………………………204

5.8.2 One-Conductor Open……….204

Problems………………..209

Bibliography …………. 211

References …………….. 211

6. Matrix Methods for Network Solutions ……………………………… 213

6.1 Network Models………………………….. 213

6.2 Bus Admittance Matrix……………….. 214

6.3 Bus Impedance Matrix ………………… 219

6.3.1 Bus Impedance Matrix from Open-Circuit Testing…………………………..220

6.4 Loop Admittance and Impedance Matrices ………………… 221

6.4.1 Selection of Loop Equations……………………………..223

6.5 Graph Theory……………………………….223

6.6 Bus Admittance and Impedance Matrices by Graph

Approach……..226

6.6.1 Primitive Network ……………226

6.6.2 Incidence Matrix from Graph Concepts ……………228

6.6.3 Node Elimination in Y-Matrix …………………………. 232

6.7 Algorithms for Construction of Bus Impedance Matrix.233

6.7.1 Adding a Tree Branch to an Existing Node ………234

6.7.2 Adding a Link ………………….236

6.7.3 Removal of an Uncoupled Branch…………………….238

6.7.4 Changing Impedance of an Uncoupled Branch ..238

6.7.5 Removal of a Coupled Branch…………………………..238

6.8 Short-Circuit Calculations with Bus Impedance Matrix. 246

6.8.1 Line-to-Ground Fault ………. 246

6.8.2 Line-to-Line Fault ……………. 246

6.8.3 Double Line-to-Ground Fault ………………………….. 247

6.9 Solution of Large Network Equations…………………………..256

Problems……………….. 257

Bibliography ………….258

7. Current Interruptions in AC Networks ……………………………….259

7.1 Rheostatic Breaker ……………………….259

7.2 AC Arc Interruption ……………………. 261

7.2.1 Arc Interruption Theories… 261

7.2.1.1 Cassie’s Theory ….. 261

7.2.1.2 Mayr’s Theory……. 262

7.2.1.3 Cassie-Mayr Theory…………………………… 262

7.3 Current-Zero Breaker……………………263

7.4 Transient Recovery Voltage ………….264

7.4.1 First Pole to Clear Factor …..266

7.5 The Terminal Fault………………………. 269

7.5.1 Four-Parameter Method…… 269

7.5.2 Two-Parameter Representation………………………… 270

7.6 The Short-Line Fault ……………………. 271

7.7 Interruption of Low Inductive Currents………………………. 273

7.7.1 Virtual Current Chopping.. 275

7.8 Interruption of Capacitance Currents ………………………….. 276

7.9 TRV in Capacitive and Inductive Circuits……………………. 278

7.10 Prestrikes in Circuit Breakers ……… 279

7.11 Overvoltages on Energizing HV Lines…………………………280

7.11.1 Overvoltage Control ………… 282

7.11.2 Synchronous Operation ……283

7.11.3 Synchronous Capacitor Switching ……………………283

7.11.4 Shunt Reactors………………….284

7.11.4.1 Oscillation Modes ……………………………… 287

7.12 Out-of-Phase Closing……………………288

7.13 Resistance Switching ……………………289

7.14 Failure Modes of Circuit Breakers.. 293

7.15 Stresses in Circuit Breakers …………. 295

7.16 Classifcation of Circuit Breakers according to Interrupting

Medium ………. 295

7.16.1 SF6 Circuit Breakers …………. 296

7.16.1.1 Electronegativity of SF6 ……………………… 297

7.16.2 Operating Mechanisms…….299

7.16.3 Vacuum Interruption………..300

7.16.3.1 Current Chopping and Multiple Ignitions …………………………. 301

7.16.3.2 Switching of Unloaded Dry-Type Transformers………………….303

7.17 Part Winding Resonance in Transformers ……………………304

7.17.1 Snubber Circuits……………….306

7.18 Solid-State Circuit Breakers………….306

Problems………………..308

Bibliography ………….309

References …………….. 310

8. Application and Ratings of Circuit Breakers and Fuses according to ANSI

Standards……………… 313

8.1 Total and Symmetrical Current Basis ………………………….. 314

8.2 Asymmetrical Ratings…………………. 316

8.2.1 Contact Parting Time ………. 316

8.3 Voltage Range Factor K………………… 317

8.4 Circuit Breaker Timing Diagram…. 320

8.5 Maximum Peak Current ……………… 321

8.6 Permissible Tripping Delay ………….322

8.7 Service Capability Duty Requirements and Reclosing

Capability …….322

8.7.1 Transient Stability on Fast Reclosing ……………….. 323

8.8 Shunt Capacitance Switching………. 326

8.8.1 Switching of Cables …………. 331

8.9 Line Closing Switching Surge Factor……………………………335

8.9.1 Switching of Transformers ……………………………….336

8.10 Out-of-Phase Switching Current Rating………………………. 337

8.11 Transient Recovery Voltage …………. 337

8.11.1 Circuit Breakers Rated Below 100 kV ………………..338

8.11.2 Circuit Breakers Rated 100 kV and Above…………338

8.11.3 Short-Line Faults ………………342

8.11.4 Oscillatory TRV………………..344

8.11.4.1 Exponential (Overdamped) TRV ………..344

8.11.5 Initial TRV………………………..345

8.11.6 Adopting IEC TRV Profles in IEEE Standards …345

8.11.7 Defnite-Purpose TRV Breakers………………………..350

8.11.8 TRV Calculation Techniques ………..350

8.12 Generator Circuit Breakers …………..353

8.13 Specifcations of High-Voltage Circuit Breakers……………358

8.14 Low-Voltage Circuit Breakers……….358

8.14.1 Molded Case Circuit Breakers ………………………….358

8.14.2 Insulated Case Circuit Breakers (ICCBs)………….. 359

8.14.3 Low-Voltage Power Circuit Breakers (LVPCBs)… 359

8.14.3.1 Single-Pole Interrupting Capability……. 361

8.14.3.2 Short-Time Ratings…………………………….. 361

8.14.3.3 Series Connected Ratings…………………… 362

8.15 Fuses…………….363

8.15.1 Current-Limiting Fuses…….364

8.15.2 Low-Voltage Fuses ……………365

8.15.3 High-Voltage Fuses…………..365

8.15.4 Interrupting Ratings…………366

Problems……………….. 367

References ……………..368

9. Short Circuit of Synchronous and Induction Machines

and Converters …….. 371

9.1 Reactances of a Synchronous Machine………………………… 372

9.1.1 Leakage Reactance XI………. 372

9.1.2 Subtransient Reactance X d′′ ………………………………. 372

9.1.3 Transient Reactance X d′ ……. 372

9.1.4 Synchronous Reactance Xd………………………………. 372

9.1.5 Quadrature Axis Reactances X q′′, X q′ , and Xq …… 373

9.1.6 Negative Sequence Reactance X2……………………… 374

9.1.7 Zero Sequence Reactance X0 ……………………………. 374

9.1.8 Potier Reactance X

p………….. 374

9.2 Saturation of Reactances ……………… 375

9.3 Time Constants of Synchronous Machines………………….. 375

9.3.1 Open-Circuit Time Constant Tdo ′ ………………………. 375

9.3.2 Subtransient Short-Circuit Time ConstantTd′′…… 375

9.3.3 Transient Short-Circuit Time Constant Td′ ……….. 375

9.3.4 Armature Time Constant T

a ………………. 375

9.4 Synchronous Machine Behavior on Short Circuit………… 375

9.4.1 Equivalent Circuits during Fault………………………380

9.4.2 Fault Decrement Curve …….383

9.5 Circuit Equations of Unit Machines……………………………..386

9.6 Park’s Transformation ………………….390

9.6.1 Reactance Matrix of a Synchronous Machine …..390

9.6.2 Transformation of Reactance Matrix………………… 393

9.7 Park’s Voltage Equation……………….. 395

9.8 Circuit Model of Synchronous Machines…………………….. 397

9.9 Calculation Procedure and Examples………………………….. 399

9.9.1 Manufacturer’s Data…………406

9.10 Short Circuit of Synchronous Motors and Condensers…408

9.11 Induction Motors………………………….409

9.12 Capacitor Contribution to the Short-Circuit Currents….. 413

9.13 Static Converters Contribution to the Short-Circuit Currents………………………. 414

9.14 Practical Short-Circuit Calculations…………………………….. 417

Problems……………….. 418

References …………….. 419

Bibliography …………. 419

10. Short-Circuit Calculations according to ANSI Standards ….. 421

10.1 Types of Calculations ………………….. 421

10.1.1 Assomptions…………………….422

10.1.2 Maximum Peak Current …..422

10.2 Accounting for Short-Circuit Current Decay………………..423

10.2.1 Low-Voltage Motors…………. 424

10.3 Rotating Machine Model ……………..425

10.4 Type and Severity of System Short Circuits………………….426

10.5 Calculation Methods ……………………427

10.5.1 Simplifed Method X/R ≤ 17……………………………..427

10.5.2 Simplifed Method X/R > 17……………………………..427

10.5.3 E/X Method for AC and DC Decrement Adjustments………………………427

10.5.4 Fault Fed from Remote Sources ………………………..428

10.5.5 Fault Fed from Local Sources……………………………430

10.5.6 Weighted Multiplying Factors ………………………….435

10.6 Network Reduction………………………435

10.6.1 E/X or E/Z Calculation …….436

10.7 Breaker Duty Calculations…………… 437

10.8 Generator Source Asymmetry …….. 437

10.9 Calculation Procedure………………….439

10.9.1 Necessity of Gathering Accurate Data………………439

10.9.2 Calculation Procedure………440

10.9.3 Analytical Calculation Procedure …………………….441

10.9.4 Hand Calculations……………441

10.9.5 Dynamic Simulation…………441

10.9.6 Circuit Breakers with Sources on Either Side……441

10.9.7 Switching Devices without Short-Circuit

Interruption Ratings…………443

10.9.8 Adjustments for Transformer Taps and Ratios….443

10.10 Examples of Calculations……………..444

10.10.1 Calculation of Short-Circuit Duties……………….444

10.10.2 K-Rated 15 kV Breakers….448

10.10.3 4.16kV Circuit Breakers and Motor Starters …. 452

10.10.4 Transformer Primary Switches and Fused Switches…………. 452

10.10.5 Low-Voltage Circuit Breakers……………………….. 452

10.10.6 Bus Bracings…………………. 452

10.10.7 Power Cables…………………455

10.10.8 Overhead Line Conductors …………………………..456

10.10.9 Generator Source Symmetrical Short-Circuit Current…………..460

10.10.10 Generator Source Asymmetrical Current …….. 461

10.10.11 System Source Symmetrical Short-Circuit Current ………….. 461

10.10.12 System Source Asymmetrical Short-Circuit Current ………… 462

10.10.13 Required Closing Latching Capabilities ………. 462

10.10.14 Selection of the Generator Breaker………………..463

10.11 Deriving an Equivalent Impedance ……………………………..464

10.12 Thirty-Cycle Short-Circuit Currents …………………………….469

10.13 Fault Current Limiters…………………. 470

10.13.1 Superconducting Fault Current Limiters …………. 473

Problems……………….. 474

References ……………..477

11. Short-Circuit Calculations according to IEC Standards……… 479

11.1 Conceptual and Analytical Differences……………………….. 479

11.1.1 Breaking Capability…………. 479

11.1.2 Rated Restriking Voltage ….480

11.1.3 Rated Making Capacity ……480

11.1.4 Rated Opening Time and Break Time ………………480

11.1.5 Initial Symmetrical Short-Circuit Current ………..480

11.1.6 Peak Making Current………. 481

11.1.7 Breaking Current …………….. 481

11.1.8 Steady-State Current………… 481

11.1.9 Highest Short-Circuit Currents…………………………482

11.2 Prefault Voltage ……………………………483

11.3 Far-From Generator Faults……………483

11.3.1 Nonmeshed Sources…………485

11.3.2 Meshed Networks…………….487

11.3.2.1 Method A: Uniform Ratio R/X or X/R

Ratio Method ……..487

11.3.2.2 Ratio R/X or X/R at the Short-Circuit Location ………………….487

11.3.2.3 Method C: Equivalent Frequency Method ………………………….488

11.4 Near-to-Generator Faults ……………..489

11.4.1 Generators Directly Connected to Systems ………489

11.4.2 Generators and Unit Transformers of Power

Station Units …………………….490

11.4.3 Motors……………………………… 491

11.4.4 Short-Circuit Currents Fed from One Generator …………………. 491

11.4.4.1 Breaking Current.. 491

11.4.4.2 Steady-State Current ………………………….. 492

11.4.5 Short-Circuit Currents in Nonmeshed Networks…………………………….. 493

11.4.6 Short-Circuit Currents in Meshed Networks …… 494

11.5 Influence of Motors……………………… 495

11.5.1 Low-Voltage Motor Groups ……………………………… 496

11.5.2 Calculations of Breaking Currents of

Asynchronous Motors……… 496

11.5.3 Static Converter Fed Drives……………………………… 497

11.6 Comparison with ANSI/IEE Calculation Procedures….. 497

11.7 Examples of Calculations and Comparison with

ANSI Methods……………………………..499

11.8 Electromagnetic Transients Program Simulation of a

Generator Terminal Short Circuit… 513

11.8.1 The Effect of PF ……………….. 513

Problems……………….. 517

References …………….. 519

12. Calculations of Short-Circuit Currents in Direct Current Systems……………………. 521

12.1 DC Short-Circuit Current Sources.. 521

12.2 Calculation Procedures ……………….. 523

12.2.1 IEC Calculation Procedure ………………………………. 523

12.2.2 Matrix Methods……………….. 525

12.3 Short-Circuit of a Lead Acid Battery……………………………. 525

12.4 Short-Circuit of DC Motors and Generators ………………… 531

12.5 Short-Circuit of a Rectifer …………… 537

12.6 Short-Circuit of a Charged Capacitor……………………………543

12.7 Total Short-Circuit Current…………..544

12.8 DC Circuit Breakers……………………..545

12.9 DC Rated Fuses ……………………………548

12.10 Protection of the Semi-Conductor Devices …………………..548

12.11 High-Voltage DC Circuit Breakers..550

Problems………………..553

References ……………..553

Appendix A: Matrix Methods …………………….555

Appendix B: Sparsity and Optimal Ordering …………………………… 587

Appendix C: Transformers and Reactors…… 595

Appendix D: Solution to the Problems ……… 629

Index …………………………… 709

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