Transient Analysis of Power Systems

About the Editor xv List of Contributors xvii Preface xix About the Companion Website xxi 1 Introduction to Transients Analysis of Power Systems with ATP 1 Juan A. Martinez-Velasco 1.1 Overview 1 1.2 The ATP Package 3 1.3 ATP Documentation 5 1.4 Scope of the Book 6 References 8 2 Modelling of Power Components for Transients Studies 11 Juan A. Martinez-Velasco 2.1 Introduction 11 2.2 Overhead Lines 12 2.2.1 Overview 12 2.2.2 Multi-conductor Transmission Line Equations and Models 13 2.2.2.1 Transmission Line Equations 13 2.2.2.2 Corona Effect 15 2.2.2.3 Line Constants Routine 15 2.2.3 Transmission Line Towers 16 2.2.4 Transmission Line Grounding 17 2.2.4.1 Introduction 17 2.2.4.2 Low-Frequency Models 17 2.2.4.3 High-Frequency Models 18 2.2.4.4 Treatment of Soil Ionization 20 2.2.5 Transmission Line Insulation 21 2.2.5.1 Voltage-Time Curves 21 2.2.5.2 Integration Methods 22 2.2.5.3 Physical Models 22 2.3 Insulated Cables 23 2.3.1 Overview 23 2.3.2 Insulated Cable Designs 24 2.3.3 Bonding Techniques 25 2.3.4 Material Properties 26 2.3.5 Discussion 27 2.3.6 Cable Constants/Parameters Routines 27 2.4 Transformers 28 2.4.1 Overview 28 2.4.2 Transformer Models for Low-Frequency Transients 31 2.4.2.1 Introduction to Low-Frequency Models 31 2.4.2.2 Single-Phase Transformer Models 32 2.4.2.3 Three-Phase Transformer Models 36 2.4.3 Transformer Modelling for High-Frequency Transients 37 2.4.3.1 Introduction to High-Frequency Models 37 2.4.3.2 Models for Internal Voltage Calculation 39 2.4.3.3 Terminal Models 41 2.5 Rotating Machines 45 2.5.1 Overview 45 2.5.2 Rotating Machine Models for Low-Frequency Transients 46 2.5.2.1 Introduction 46 2.5.2.2 Modelling of Induction Machines 46 2.5.2.3 Modelling of Synchronous Machines 51 2.5.3 High-Frequency Models for Rotating Machine Windings 55 2.5.3.1 Introduction 55 2.5.3.2 Internal Models 56 2.5.3.3 Terminal Models 58 2.6 Circuit Breakers 58 2.6.1 Overview 58 2.6.2 Circuit Breaker Models for Opening Operations 59 2.6.2.1 Current Interruption 59 2.6.2.2 Circuit Breaker Models 60 2.6.2.3 Gas-Filled Circuit Breaker Models 61 2.6.2.4 Vacuum Circuit Breaker Models 62 2.6.3 Circuit Breaker Models for Closing Operations 64 2.6.3.1 Introduction 64 2.6.3.2 Statistical Switches 65 2.6.3.3 Prestrike Models 66 Acknowledgement 66 References 66 3 Solution Techniques for Electromagnetic Transient Analysis 75 Juan A. Martinez-Velasco 3.1 Introduction 75 3.2 Modelling of Power System Components for Transient Analysis 76 3.3 Solution Techniques for Electromagnetic Transients Analysis 78 3.3.1 Introduction 78 3.3.2 Solution Techniques for Linear Networks 78 3.3.2.1 The Trapezoidal Rule 78 3.3.2.2 Companion Circuits of Basic Circuit Elements 79 3.3.2.3 Computation of Transients in Linear Networks 85 3.3.2.4 Example: Transient Solution of a Linear Network 86 3.3.3 Networks with Nonlinear Elements 87 3.3.3.1 Introduction 87 3.3.3.2 Compensation Methods 87 3.3.3.3 Piecewise Linear Representation 89 3.3.4 Solution Methods for Networks with Switches 90 3.3.5 Numerical Oscillations 91 3.4 Transient Analysis of Control Systems 96 3.5 Initialization 97 3.5.1 Introduction 97 3.5.2 Initialization of the Power Network 97 3.5.2.1 Options for Steady-State Solution Without Harmonics 97 3.5.2.2 Steady-State Solution 98 3.5.3 Load Flow Solution 99 3.5.4 Initialization of Control Systems 100 3.6 Discussion 100 3.6.1 Solution Techniques Implemented in ATP 101 3.6.2 Other Solution Techniques 101 3.6.2.1 Transient Solution of Networks 101 3.6.2.2 Transient Analysis of Control Systems 102 3.6.2.3 Steady-State Initialization 102 Acknowledgement 103 References 103 To Probe Further 106 4 The ATP Package: Capabilities and Applications 107 Juan A. Martinez-Velasco and Jacinto Martin-Arnedo 4.1 Introduction 107 4.2 Capabilities of the ATP Package 108 4.2.1 Overview 108 4.2.2 The Simulation Module – TPBIG 109 4.2.2.1 Overview 109 4.2.2.2 Modelling Capabilities 110 4.2.2.3 Solution Techniques 117 4.2.3 The Graphical User Interface – ATPDraw 120 4.2.3.1 Overview 120 4.2.3.2 Main Functionalities 120 4.2.3.3 Supporting Modules for Power System Components 123 4.2.4 The Postprocessor – TOP 125 4.2.4.1 Data Management 125 4.2.4.2 Data Display 126 4.2.4.3 Data Processing 127 4.2.4.4 Data Formatting 127 4.2.4.5 Graphical Output 127 4.3 Applications 128 4.4 Illustrative Case Studies 129 4.4.1 Introduction 129 4.4.2 Case Study 1: Optimum Allocation of Capacitor Banks 130 4.4.3 Case Study 2: Parallel Resonance Between Transmission Lines 132 4.4.4 Case Study 3: Selection of Surge Arresters 133 4.5 Remarks 136 References 136 To Probe Further 138 5 Introduction to the Simulation of Electromagnetic Transients Using ATP 139 Juan A. Martinez-Velasco and Francisco González-Molin 5.1 Introduction 139 5.2 Input Data File Using ATP Formats 140 5.3 Some Important Issues 142 5.3.1 Before Simulating the Test Case 142 5.3.1.1 Setting Up a System Model 142 5.3.1.2 Topology Requirements 142 5.3.1.3 Selection of the Time-Step Size and the Simulation Time 143 5.3.1.4 Units 143 5.3.1.5 Output Selection 144 5.3.2 After Simulating the Test Case 144 5.3.2.1 Verifying the Results 144 5.3.2.2 Debugging Suggestions 144 5.4 Introductory Cases. Linear Circuits 145 5.4.1 The Series and Parallel RLC Circuits 145 5.4.2 The Series RLC Circuit: Energization Transient 145 5.4.2.1 Theoretical Analysis 145 5.4.2.2 ATP Implementation 147 5.4.2.3 Simulation Results 148 5.4.3 The Parallel RLC Circuit: De-energization Transient 150 5.4.3.1 Theoretical Analysis 150 5.4.3.2 ATP Implementation 152 5.4.3.3 Simulation Results 153 5.5 Switching of Capacitive Currents 155 5.5.1 Introduction 155 5.5.2 Switching Transients in Simple Capacitive Circuits – DC Supply 155 5.5.2.1 Energization of a Capacitor Bank 155 5.5.2.2 Energization of a Back-to-Back Capacitor Bank 157 5.5.3 Switching Transients in Simple Capacitive Circuits – AC Supply 159 5.5.3.1 Energization of a Capacitor Bank 159 5.5.3.2 Energization of a Back-to-Back Capacitor Bank 160 5.5.3.3 Reclosing into Trapped Charge 162 5.5.4 Discharge of a Capacitor Bank 164 5.6 Switching of Inductive Currents 168 5.6.1 Introduction 168 5.6.2 Switching of Inductive Currents in Linear Circuits 168 5.6.2.1 Interruption of Inductive Currents 168 5.6.2.2 Voltage Escalation During the Interruption of Inductive Currents 170 5.6.2.3 Current Chopping 172 5.6.2.4 Making of Inductive Currents 175 5.6.3 Switching of Inductive Currents in Nonlinear Circuits 176 5.6.4 Transients in Nonlinear Reactances 178 5.6.4.1 Interruption of an Inductive Current 180 5.6.4.2 Energization of a Nonlinear Reactance 181 5.6.5 Ferroresonance 184 5.7 Transient Analysis of Circuits with Distributed Parameters 187 5.7.1 Introduction 187 5.7.2 Transients in Linear Circuits with Distributed-Parameter Components 187 5.7.2.1 Energization of Lines and Cables 187 5.7.2.2 Transient Recovery Voltage During Fault Clearing 191 5.7.3 Transients in Nonlinear Circuits with Distributed-Parameter Components 195 5.7.3.1 Surge Arrester Protection 195 5.7.3.2 Protection Against Lightning Overvoltages Using Surge Arresters 196 References 201 Acknowledgement 202 To Probe Further 202 6 Calculation of Power System Overvoltages 203 Juan A. Martinez-Velasco and Ferley Castro-Aranda 6.1 Introduction 203 6.2 Power System Overvoltages: Causes and Characterization 204 6.3 Modelling for Simulation of Power System Overvoltages 206 6.3.1 Introduction 206 6.3.2 Modelling Guidelines for Temporary Overvoltages 207 6.3.3 Modelling Guidelines for Slow-Front Overvoltages 208 6.3.3.1 Lines and Cables 208 6.3.3.2 Transformers 208 6.3.3.3 Switchgear 208 6.3.3.4 Capacitors and Reactors 209 6.3.3.5 Surge Arresters 209 6.3.3.6 Loads 210 6.3.3.7 Power Supply 210 6.3.4 Modelling Guidelines for Fast-Front Overvoltages 210 6.3.4.1 Overhead Transmission Lines 210 6.3.4.2 Substations 212 6.3.4.3 Surge Arresters 213 6.3.4.4 Sources 214 6.3.5 Modelling Guidelines for Very Fast-Front Overvoltages in Gas Insulated Substations 214 6.4 ATP Capabilities for Power System Overvoltage Studies 216 6.5 Case Studies 216 6.5.1 Introduction 216 6.5.2 Low-Frequency Overvoltages 216 6.5.2.1 Case Study 1: Resonance Between Parallel Lines 217 6.5.2.2 Case Study 2: Ferroresonance in a Distribution System 219 6.5.3 Slow-Front Overvoltages 225 6.5.3.1 Case Study 3: Transmission Line Energization 227 6.5.3.2 Case Study 4: Capacitor Bank Switching 238 6.5.4 Fast-Front Overvoltages 243 6.5.4.1 Case Study 5: Lightning Performance of an Overhead Transmission Line 244 6.5.5 Very Fast-Front Overvoltages 261 6.5.5.1 Case Study 6: Origin of Very Fast-Front Transients in GIS 262 6.5.5.2 Case Study 7: Propagation of Very Fast-Front Transients in GIS 263 6.5.5.3 Case Study 8: Very Fast-Front Transients in a 765 kV GIS 267 References 270 To Probe Further 274 7 Simulation of Rotating Machine Dynamics 275 Juan A. Martinez-Velasco 7.1 Introduction 275 7.2 Representation of Rotating Machines in Transients Studies 275 7.3 ATP Rotating Machines Models 276 7.3.1 Background 276 7.3.2 Built-in Rotating Machine Models 276 7.3.3 Rotating Machine Models for Fast Transients Simulation 278 7.4 Solution Methods 278 7.4.1 Introduction 278 7.4.2 Three-Phase Synchronous Machine Model 278 7.4.3 Universal Machine Module 281 7.4.4 WindSyn-Based Models 284 7.5 Procedure to Edit Machine Data Input 284 7.6 Capabilities of Rotating Machine Models 285 7.7 Case Studies: Three-Phase Synchronous Machine 287 7.7.1 Overview 287 7.7.2 Case Study 1: Stand-Alone Three-Phase Synchronous Generator 288 7.7.3 Case Study 2: Load Rejection 288 7.7.4 Case Study 3: Transient Stability 298 7.7.5 Case Study 4: Subsynchronous Resonance 302 7.8 Case Studies: Three-Phase Induction Machine 309 7.8.1 Overview 309 7.8.2 Case Study 5: Induction Machine Test 310 7.8.3 Case Study 6: Transient Response of the Induction Machine 313 7.8.3.1 First Case 314 7.8.3.2 Second Case 314 7.8.3.3 Third Case 318 7.8.4 Case Study 7: SCIM-Based Wind Power Generation 323 References 328 To Probe Further 331 8 Power Electronics Applications 333 Juan A. Martinez-Velasco and Jacinto Martin-Arnedo 8.1 Introduction 333 8.2 Converter Models 334 8.2.1 Switching Models 334 8.2.2 Dynamic Average Models 334 8.3 Power Semiconductor Models 335 8.3.1 Introduction 335 8.3.2 Ideal Device Models 335 8.3.3 More Detailed Device Models 335 8.3.4 Approximate Models 336 8.4 Solution Methods for Power Electronics Studies 337 8.4.1 Introduction 337 8.4.2 Time-Domain Transient Solution 337 8.4.3 Initialization 338 8.5 ATP Simulation of Power Electronics Systems 338 8.5.1 Introduction 338 8.5.2 Switching Devices 339 8.5.2.1 Built-in Semiconductor Models 339 8.5.2.2 Custom-made Semiconductor Models 340 8.5.3 Power Electronics Systems 342 8.5.4 Power Systems 343 8.5.5 Control Systems 343 8.5.6 Rotating Machines 344 8.5.6.1 Built-in Rotating Machine Models 344 8.5.6.2 Custom-made Rotating Machine Models 344 8.5.7 Simulation Errors 345 8.6 Power Electronics Applications in Transmission, Distribution, Generation and Storage Systems 345 8.6.1 Overview 345 8.6.2 Transmission Systems 346 8.6.3 Distribution Systems 346 8.6.4 DER Systems 347 8.7 Introduction to the Simulation of Power Electronics Systems 349 8.7.1 Overview 349 8.7.2 One-Switch Case Studies 350 8.7.3 Two-Switches Case Studies 351 8.7.4 Application of the GIFU Request 355 8.7.5 Simulation of Power Electronics Converters 361 8.7.5.1 Single-phase Inverter 361 8.7.5.2 Three-phase Line-Commutated Diode Bridge Rectifier 362 8.7.6 Discussion 365 8.8 Case Studies 367 8.8.1 Introduction 367 8.8.2 Case Study 1: Three-phase Controlled Rectifier 367 8.8.3 Case Study 2: Three-phase Adjustable Speed AC Drive 369 8.8.4 Case Study 3: Digitally-controlled Static VAR Compensator 373 8.8.4.1 Test System 375 8.8.4.2 Control Strategy 375 8.8.5 Case Study 4: Unified Power Flow Controller 382 8.8.5.1 Configuration 382 8.8.5.2 Control 382 8.8.5.3 Modelling 384 8.8.5.4 ATPDraw Implementation 385 8.8.5.5 Simulation Results 385 8.8.6 Case Study 5: Solid State Transformer 386 8.8.6.1 Introduction 386 8.8.6.2 SST Configuration 388 8.8.6.3 Control Strategies 388 8.8.6.4 Test System and Modelling Guidelines 393 8.8.6.5 Case Studies 396 Acknowledgement 399 References 399 To Probe Further 404 9 Creation of Libraries 405 Juan A. Martinez Velasco and Jacinto Martin-Arnedo 9.1 Introduction 405 9.2 Creation of Custom-Made Modules 406 9.2.1 Introduction 406 9.2.2 Application of DATA BASE MODULE 406 9.2.3 Application of MODELS 411 9.2.4 The Group Option 417 9.3 Application of the ATP to Power Quality Studies 419 9.3.1 Introduction 419 9.3.2 Power Quality Issues 419 9.3.3 Simulation of Power Quality Problems 422 9.3.4 Power Quality Studies 423 9.4 Custom-Made Modules for Power Quality Studies 426 9.5 Case Studies 426 9.5.1 Overview 426 9.5.2 Harmonics Analysis 426 9.5.2.1 Case Study 1: Generation of Harmonic Waveforms 428 9.5.2.2 Case Study 2: Harmonic Resonance 431 9.5.2.3 Case Study 3: Harmonic Frequency Scan 434 9.5.2.4 Case Study 4: Compensation of Harmonic Currents 441 9.5.3 Voltage Dip Studies in Distribution Systems 447 9.5.3.1 Overview 447 9.5.3.2 Case Study 5: Voltage Dip Measurement 449 9.5.3.3 Case Study 6: Voltage Dip Characterization 454 9.5.3.4 Case Study 7: Voltage Dip Mitigation 462 References 466 To Probe Further 470 10 Protection Systems 471 Juan A. Martinez-Velasco and Jacinto Martin-Arnedo 10.1 Introduction 471 10.2 Modelling Guidelines for Protection Studies 472 10.2.1 Line and Cable Models 472 10.2.1.1 Models for Steady-State Studies 473 10.2.1.2 Models for Transient Studies 473 10.2.2 Transformer Models 473 10.2.2.1 Low-frequency Transformer Models 474 10.2.2.2 High-frequency Transformer Models 475 10.2.3 Source Models 475 10.2.4 Circuit Breaker Models 475 10.3 Models of Instrument Transformers 476 10.3.1 Introduction 476 10.3.2 Current Transformers 476 10.3.3 Coupling Capacitor Voltage Transformers 478 10.3.4 Voltage Transformers 479 10.3.5 Case Studies 480 10.3.5.1 Case Study 1: Current Transformer Test 480 10.3.5.2 Case Study 2: Coupling Capacitor Voltage Transformer Test 482 10.3.6 Discussion 484 10.4 Relay Modelling 484 10.4.1 Introduction 484 10.4.2 Classification of Relay Models 485 10.4.3 Implementation of Relay Models 486 10.4.4 Applications of Relay Models 488 10.4.5 Testing and Validation of Relay Models 488 10.4.6 Accuracy and Limitations of Relay Models 490 10.4.7 Case Studies 490 10.4.7.1 Overview 490 10.4.7.2 Case Study 3: Simulation of an Electromechanical Distance Relay 491 10.4.7.3 Case Study 4: Simulation of a Numerical Distance Relay 497 10.5 Protection of Distribution Systems 508 10.5.1 Introduction 508 10.5.2 Protection of Distribution Systems with Distributed Generation 508 10.5.2.1 Distribution Feeder Protection 508 10.5.2.2 Interconnection Protection 508 10.5.3 Modelling of Distribution Feeder Protective Devices 509 10.5.3.1 Circuit Breakers – Overcurrent Relays 509 10.5.3.2 Reclosers 511 10.5.3.3 Fuses 511 10.5.3.4 Sectionalizers 512 10.5.4 Protection of the Interconnection of Distributed Generators 513 10.5.5 Case Studies 514 10.5.5.1 Case Study 5: Testing the Models 514 10.5.5.2 Case Study 6: Coordination Between Protective Devices 524 10.5.5.3 Case Study 7: Protection of Distributed Generation 525 10.6 Discussion 531 Acknowledgement 533 References 533 To Probe Further 537 11 ATP Applications Using a Parallel Computing Environment 539 Javier A. Corea-Araujo, Gerardo Guerra and Juan A. Martinez-Velasco 11.1 Introduction 539 11.2 Bifurcation Diagrams for Ferroresonance Characterization 540 11.2.1 Introduction 540 11.2.2 Characterization of Ferroresonance 540 11.2.3 Modelling Guidelines for Ferroresonance Analysis 541 11.2.4 Generation of Bifurcation Diagrams 541 11.2.5 Parametric Analysis Using a Multicore Environment 542 11.2.6 Case Studies 544 11.2.6.1 Case 1: An Illustrative Example 544 11.2.6.2 Case 2: Ferroresonant Behaviour of a Voltage Transformer 545 11.2.6.3 Case 3: Ferroresonance in a Five-Legged Core Transformer 545 11.2.7 Discussion 550 11.3 Lightning Performance Analysis of Transmission Lines 550 11.3.1 Introduction 550 11.3.2 Lightning Stroke Characterization 551 11.3.3 Modelling for Lightning Overvoltage Calculations 552 11.3.4 Implementation of the Monte Carlo Procedure Using Parallel Computing 554 11.3.5 Illustrative Example 555 11.3.5.1 Test Line 555 11.3.5.2 Line and Lightning Stroke Parameters 555 11.3.5.3 Simulation Results 559 11.3.6 Discussion 562 11.4 Optimum Design of a Hybrid HVDC Circuit Breaker 563 11.4.1 Introduction 563 11.4.2 Design and Operation of the Hybrid HVDC Circuit Breaker 563 11.4.3 ATP Implementation of the Hybrid HVDC Circuit Breaker 565 11.4.4 Test System 566 11.4.5 Transient Response of the Hybrid Circuit Breaker 567 11.4.6 Implementation of a Parallel Genetic Algorithm 568 11.4.7 Simulation Results 570 11.4.8 Discussion 574 Acknowledgement 575 References 575 A Characteristics of the Multicore Installation 579 B Test System Parameters for Ferroresonance Studies 579 To Probe Further 580 Index 581