Power System Modelling and Scripting (eBook)

Title Page 1
Preface 6
Contents 11
List of Figures 19
List of Tables 26
List of Examples 30
List of Scripts 33
Notation 34
Part I Introduction 39
Power System Modelling 40
Background 40
Motivations 41
Modelling Physical Systems 42
Hybrid Dynamical Model 48
Power System Architecture 55
Structure of Software Projects 55
Classes and Procedures 57
Modularity 59
Architecture of a Power System Software Tool 63
Power System Scripting 67
Open and Closed Programming 67
Scripting 69
Scripting Languages for Computational Science 71
Suitable Computer Languages 72
Python Scripting Language 75
Part II Power System Analysis 95
Power Flow Analysis 96
Background 96
Taxonomy of Power Flow Problems 101
Classical Power Flow Equations 102
Power Flow Solvers 105
Jacobi and Gauss-Seidel's Method 105
Newton's Method 109
Power Flow Jacobian Matrix 112
Robust Newton's Method 117
Iwamoto's Method 119
Inexact and Dishonest Newton's Methods 120
Fast Decoupled Power Flow 121
DC Power Flow 127
Single and Distributed Slack Bus Models 130
A General Framework for Power Flow Solvers 131
Stability of the Continuous Newton's Method 132
Summary 135
Continuation Power Flow Analysis 137
Background 137
System Model 141
Direct Methods 142
Saddle-Node Bifurcation 143
Limit-Induced Bifurcation 145
Nonlinear Programming 147
Homotopy Methods 148
Continuation Power Flow 151
Predictor Step 151
Corrector Step 155
Continuous Newton's Method and Homotopy 160
N-1 Contingency Analysis 161
Summary 163
Optimal Power Flow Analysis 165
Background 165
Optimal Power Flow Model 167
Nonlinear Programming Solvers 173
Generalized Reduced Gradient Method 174
Interior Point Method 176
Summary of IPM Parameters 187
Eigenvalue Analysis 188
Background 188
Small Signal Stability Analysis 192
Bifurcation Points 194
Participation Factors 198
Analysis in the Z-Domain 202
Computing the Eigenvalues 203
Power Method 203
Inverse Iteration 205
Rayleigh's Iteration 205
Power Flow Modal Analysis 206
Singular Value Decomposition 207
Summary 210
Time Domain Analysis 212
Background 212
Power System Model 219
Current-Injection Model 220
Power-Injection Model 222
Numerical Integration Methods 225
Explicit Methods 225
Implicit Methods 228
Numerical Integration Routine 231
Step Length 233
Disturbances 235
Stop Criterion 237
Electro-magnetic Transients 244
Quasi-static Analysis 246
Summary 250
Part III Device Models 252
Device Generalities 253
General Device Model 253
Initialization of Device Internal Variables 255
Devices as Classes 258
Base Device Class 260
Methods of the Base Class 268
Specific Device Methods 273
Power Flow Devices 279
Topological Elements 279
Bus 279
Areas, Zones, Regions and Systems 281
Static Generators 282
PV Generator 282
Constant Voltage Phasor Generator 286
PQ Generator 288
Static Loads 289
PQ Load 289
Constant Power Factor Load 291
Shunt Admittance 292
Switched Shunt Admittances 292
Transmission Devices 294
Transmission Line 294
Line Sections 296
Tie Line 298
Distributed Transmission Line Models 299
Effect of Frequency Variation 301
Coupling Device and Zero-Impedance Line 302
Transformer 303
Two-Winding Transformer 303
Under Load Tap Changer 306
Phase Shifting Transformer 309
Three-Winding Transformer 310
Vectorial Implementation 313
Incidence Matrix 315
Jacobian and Hessian Matrices 316
Network Connectivity 318
OPF Devices 321
Network Constraints 321
Bus Voltage Limits 321
Transmission Line limits 321
Generator Constraints 322
Capability Curve 322
Supply Offer 323
Reactive Power Payment Function 326
Generator Power Reserve 328
Generator Power Ramp 329
Load Constraints 331
Demand Bid 331
Demand Daily Profile 332
Demand Power Ramp 333
Faults and Protections 335
Fault 335
Breaker 336
Relay 337
Phasor Measurement Unit 339
Bus Frequency Estimation 341
Loads 343
Voltage Dependent Load 343
ZIP Load 345
Frequency Dependent Load 346
Voltage Dependent Load with Dynamic Tap Changer 347
Exponential Recovery Load 350
Thermostatically Controlled Load 351
Jimma's Load 352
Mixed Load 353
Alternate-Current Machines 355
Synchronous Machine 355
Synchronous Machine Parameters 356
Initialization 357
Common Equations 358
Stator Electrical Equations 359
Magnetic Equations 359
Simplified Magnetic Equations 362
Synchronous Machine Model Taxonomy 366
Saturation 369
Center of Inertia 372
Dynamic Shaft 373
Sub-synchronous Resonance 375
Induction Machine 378
Initialization 378
Torque Model 379
Electromechanical Model 379
Detailed Single-Cage Model 380
Detailed Double-Cage Model 381
Synchronous Machine Regulators 384
Turbine Governor 384
Turbine Governor Type I 387
Turbine Governor Type II 388
Automatic Voltage Regulator 390
Automatic Voltage Regulator Type I 392
Automatic Voltage Regulator Type II 393
Automatic Voltage Regulator Type III 395
Power System Stabilizer 398
Simplified Power System Stabilizer Model 400
Power System Stabilizer Type I 400
Power System Stabilizer Type II 400
Power System Stabilizer Type III 402
Over-Excitation Limiter 402
Under-Excitation Limiter 405
Direct-Current Devices 407
Direct-Current Nodes 407
Common Interface Equations for Direct-Current Devices 407
Ideal Generators 409
Basic RLC Models 410
Direct-Current Machines 412
Other Direct-Current Devices 415
Solid Oxide Fuel Cell 415
Solar Photovoltaic Cell 418
Battery Energy System 419
AC/DC Devices 423
High-Voltage Direct-Current Transmission System 423
Per Unit System for DC Quantities 424
Rectifier Model 424
Inverter Model 425
HVDC Control 426
Voltage Source Converter 428
Simplified Dynamic VSC Model 436
Power Flow VSC Model 437
FACTS Devices 441
Static Var Compensator 441
SVC Type I 441
SVC Type II 442
SVC Initialization 443
Thyristor Controlled Series Compensator 445
TCSC Initialization 447
Static Synchronous Compensator 447
Detailed Model 448
Simplified Dynamic Model 449
Power Flow Model 450
STATCOM Initialization 451
Static Synchronous Series Compensator 451
Detailed Model 452
Simplified Dynamic Model 454
Power Flow Model 455
SSSC Initialization 455
Unified Power Flow Controller 456
Detailed Model 456
Simplified Dynamic Model 459
Power Flow Model 461
UPFC Initialization 462
Wind Power Devices 463
Wind Speed Models 463
Weibull's Distribution 464
Composite Wind Speed Model 466
Mexican Hat Wavelet Model 467
Wind Turbines 468
Single Machine and Aggregate Models 469
Wind Turbine Initialization 471
Turbine Model 471
Dynamic Shaft 474
Non-Controlled Speed Wind Turbine 476
Doubly-Fed Asynchronous Generator 477
Direct-Drive Synchronous Generator 481
Part IV Spare Material and Concluding Remarks 485
Data Formats 486
Data Format Taxonomy 486
Data Organization and Structures 486
Kind of Supported Data 488
Number of Files 489
Default Values, Prototypes and Data Manipulation 489
Canonical Model 490
Common Information Model 491
Consistent Data Schemes 494
Visualization Matters 502
Graphical Interface vs. Command Line Approach 502
Result Visualization 505
Standard Two-Dimensional Plots 505
Temperature Maps 509
Three-Dimensional Plots 511
Geographic Information System 512
Challenges of Scripting for Power System Education 516
Concepts and Definitions 516
Proprietary Software 516
Open Source Software 517
Free Software 517
Free Open Source Software 518
Education-Oriented FOSS 518
Pedagogical Issues 518
Failure of FOSS for Power System Analysis 519
Part V Appendices 521
Python Libraries 522
CVXOPT 522
NumPy 530
Matplotlib 532
System Classes 535
System Properties and Settings 535
Control Diagrams 538
Representation of Basic Functions 538
Hard Limits 539
IEEE 14-Bus System Data 545
Common Data 545
Static Data 545
Market Data 545
Dynamic Data 546
FACTS Data 546
Wind Turbine Data 548
Software Packages and Links 551
Software Packages Used in the Book 551
Links related to Power System Analysis 552
References 553