Analysis of Synchronous Machines, Second Edition

✍ Scribed by T.A. Lipo

• Publisher: CRC Press
• Year: 2012
• Tongue: English
• Leaves: 608
• Edition: 2nd
• Category: Library

✦ Synopsis

Analysis of Synchronous Machines, Second Edition is a thoroughly modern treatment of an old subject. Courses generally teach about synchronous machines by introducing the steady-state per phase equivalent circuit without a clear, thorough presentation of the source of this circuit representation, which is a crucial aspect. Taking a different approach, this book provides a deeper understanding of complex electromechanical drives. Focusing on the terminal rather than on the internal characteristics of machines, the book begins with the general concept of winding functions, describing the placement of any practical winding in the slots of the machine. This representation enables readers to clearly understand the calculation of all relevant self- and mutual inductances of the machine. It also helps them to more easily conceptualize the machine in a rotating system of coordinates, at which point they can clearly understand the origin of this important representation of the machine. Provides numerical examples Addresses Park’s equations starting from winding functions Describes operation of a synchronous machine as an LCI motor drive Presents synchronous machine transient simulation, as well as voltage regulation Applying his experience from more than 30 years of teaching the subject at the University of Wisconsin, author T.A. Lipo presents the solution of the circuit both in classical form using phasor representation and also by introducing an approach that applies MathCAD®, which greatly simplifies and expands the average student’s problem-solving capability. The remainder of the text describes how to deal with various types of transients—such as constant speed transients—as well as unbalanced operation and faults and small signal modeling for transient stability and dynamic stability. Finally, the author addresses large signal modeling using MATLAB®/Simulink®, for complete solution of the non-linear equations of the salient pole synchronous machine. A valuable tool for learning, this updated edition offers thoroughly revised content, adding new detail and better-quality figures.

✦ Table of Contents

Analysis of Synchronous Machines, Second Edition......Page 4
Contents......Page 6
Preface......Page 14
Acknowledgments......Page 16
1.1 Introduction......Page 18
1.2 Winding Function......Page 19
1.3 Calculation of the Winding Function......Page 25
1.4 Multipole Winding Configurations......Page 39
1.5 Inductances of an Ideal Doubly Cylindrical Machine......Page 42
1.6 Calculation of Winding Inductances......Page 46
1.7 Mutual Inductance Calculation—An Example......Page 49
1.8 Winding Functions for Multiple Circuits......Page 56
1.9 Analysis of a Shorted Coil—An Example......Page 63
1.10 General Case for C Circuits......Page 66
1.11 Winding Function Modifications for Salient-Pole Machines......Page 70
1.12.1 Synchronous Machine Stator......Page 81
1.12.2 Synchronous Machine Rotor......Page 86
1.13 Practical Winding Design......Page 87
1.15 References......Page 92
2.1 Introduction......Page 94
2.2 Rotating Reference Frames......Page 95
2.3.1 Vector Approach Applied to r–L Circuits......Page 98
2.3.2 Transformation Equations......Page 101
2.3.3 System Equations in the d–q–n Coordinate System......Page 109
2.3.4 Power Flow in the d–q–n Equivalent Circuits......Page 112
2.4 Stationary Three-Phase r–L Circuits Observed in a d–q–n Reference Frame......Page 113
2.4.1 Example......Page 121
2.5 Matrix Approach to the d–q–n Transformation......Page 129
2.5.1 Example......Page 134
2.6 The d–q–n Transformation Applied to a Simple Three-Phase Cylindrical Inductor......Page 138
2.7 Winding Functions in a d–q–n Reference Frame......Page 142
2.8 Direct Computation of d–q–n Inductances of a Cylindrical Three-Phase Inductor......Page 148
2.10 References......Page 151
3.2 Physical Description......Page 154
3.3 Synchronous Machine Equations in the Phase Variable or as-, bs-, cs- Reference Frame......Page 155
3.3.1 Voltage Equations......Page 157
3.3.2 Flux Linkage Equations......Page 159
3.4 Transformation of the Stator Voltage Equations to a Rotating Reference Frame......Page 160
3.5 Transformation of Stator Flux Linkages to a Rotating Reference Frame......Page 161
3.6 Winding Functions of the Three-Phase Stator Windings in a d–q–n Reference Frame......Page 163
3.7.1 d–Axis Amortisseur Winding Function......Page 165
3.7.2 q–Axis Amortisseur Circuit Winding Function......Page 172
3.7.3 Field Circuit Winding Function......Page 176
3.8 Calculation of Stator Magnetizing Inductances......Page 177
3.9 Mutual Inductances between Stator and Rotor Circuits......Page 181
3.10 d–q Transformation of the Rotor Flux Linkage Equation......Page 184
3.11 Power Input......Page 185
3.12 Torque Equation......Page 186
3.13 Summary of Synchronous Machine Equations Expressed in Physical Units......Page 188
3.14 Turns Ratio Transformation of the Flux Linkage Equations......Page 189
3.15 System Equations in Physical Units Using Hybrid Flux Linkages......Page 197
3.16.1 Base Quantities......Page 199
3.16.3 Flux Linkage Equations......Page 201
3.16.4 Electromagnetic Torque Equation......Page 202
3.16.5 Motional Equation......Page 203
3.16.6 Power Equation......Page 204
3.16.7 Summary......Page 205
3.18 References......Page 207
4.2 d–q Axes Orientation......Page 210
4.3 Steady-State Form of Park’s Equations......Page 213
4.4 Steady-State Torque Equation......Page 217
4.5 Steady-State Power Equation......Page 219
4.7 Graphical Interpretation of the Steady-State Equations......Page 221
4.8 Steady-State Vector Diagram......Page 224
4.9 Vector Interpretation of Power and Torque......Page 227
4.10 Phasor Form of the Steady-State Equations......Page 233
4.11 Equivalent Circuits of a Synchronous Machine......Page 234
4.12 Solutions of the Phasor Equations......Page 238
4.13 Solution of the Steady-State Synchronous Machine Equations Using MathCAD......Page 240
4.14 Open-Circuit and Short-Circuit Characteristics......Page 243
4.15 Saturation Modeling of Synchronous Machines under Load......Page 250
4.16 Construction of the Phasor Diagram for a Saturated Round-Rotor Machine......Page 254
4.17 Calculation of the Phasor Diagram for a Saturated Salient-Pole Synchronous Machine......Page 257
4.18 Zero Power Factor Characteristic and the Potier Triangle......Page 258
4.19 Other Reactance Measurements......Page 264
4.20 Steady-State Operating Characteristics......Page 267
4.21 Calculation of Pulsating and Average Torque during Starting of Synchronous Motors......Page 270
4.22 Conclusion......Page 279
4.23 References......Page 280
5.2 Theorem of Constant Flux Linkages......Page 282
5.3 Behavior of Stator Flux Linkages on Short-Circuit......Page 283
5.4 Three-Phase Short-Circuit, No Damper Circuits, Resistances Neglected......Page 284
5.5 Three-Phase Short-Circuit with Resistances and Damper Windings Neglected......Page 287
5.6 Short-Circuit from Loaded Condition, Stator Resistance and Dampers Neglected......Page 289
5.7 Three-Phase Short-Circuit, Effect of Resistances Included, No Dampers......Page 292
5.8 Extension of the Theory to Machines with Damper Windings......Page 299
5.9 Short-Circuit of a Loaded Generator, Dampers Included......Page 307
5.10 Vector Diagrams for Sudden Voltage Changes......Page 308
5.11 Effect of Exciter Response......Page 312
5.12 Transient Solutions Utilizing Modal Analysis......Page 314
5.13 Comparison of Modal Analysis Solution with Conventional Methods......Page 323
5.14 Unsymmetrical Short-Circuits......Page 327
5.16 References......Page 329
6.2 Assumptions......Page 332
6.3 Torque Angle Curves......Page 335
6.4 Mechanical Acceleration Equation in Per Unit Form......Page 337
6.5 Equal Area Criterion for Transient Stability......Page 339
6.6 Transient Stability Analysis......Page 340
6.7 Transient Stability of a Two Machine System......Page 348
6.8 Multi-Machine Transient Stability Analysis......Page 350
6.9 Types of Faults and Effect on Stability......Page 355
6.10 Step-by-Step Solution Methods Including Saturation......Page 357
6.11 Machine Model Including Saturation......Page 359
6.12 Summary Step-by-Step Method for Calculating Synchronous Machine Transients......Page 364
6.14 References......Page 365
7.1 Introduction......Page 366
7.2 Generator Response to System Disturbances......Page 367
7.3 Sources of System Damping......Page 369
7.4.2 Basic DC Exciter......Page 370
7.4.3 Modeling of Saturation......Page 374
7.4.4 AC Excitation Systems......Page 379
7.4.5 Static Excitation Systems......Page 380
7.5 IEEE Type 1 Excitation System......Page 381
7.6 Excitation Design Principles......Page 386
7.7.1 Generator Operating with Constant Field Flux Linkages......Page 391
7.7.2 Generator with Variable Field Flux Linkages......Page 397
7.7.3 Closed–Loop Representation......Page 403
7.7.4 Excitation Control of Other Terminal Quantities......Page 407
7.9 References......Page 409
8.2 Load Commutated Inverter (LCI) Synchronous Motor Drives......Page 412
8.3 Principle of Inverter Operation......Page 414
8.4.1 Phasor Diagram......Page 416
8.4.2 Inverter Operation......Page 418
8.4.3 Expression for Power and Torque......Page 422
8.5.1 Firing Angle Controller......Page 423
8.7 Detailed Steady-State Analysis......Page 425
8.7.1 Modes of Converter Operation......Page 428
8.7.2 State Equations......Page 430
8.7.3 Conduction Mode 1 State Equations......Page 431
8.7.4 Commutation Mode 2 State Equations......Page 434
8.7.5 Calculation of Initial Conditions......Page 438
8.8 Time Step Solution......Page 441
8.9 Sample Calculations......Page 442
8.10 Torque Capability Curves......Page 444
8.11 Constant Speed Performance......Page 449
8.12 Comparison of State Space and Phasor Diagram Solutions......Page 451
8.13 Conclusion......Page 453
8.14 References......Page 454
9.2 Source Voltage Formulation......Page 456
9.3 System Equations to Be Solved......Page 460
9.4 System Formulation with Non-Sinusoidal Stator Voltages......Page 463
9.5 Solution for Currents......Page 468
9.6 Solution for Electromagnetic Torque......Page 470
9.7 Example Solutions......Page 479
9.8 Conclusion......Page 481
10.2 Park’s Equations in Physical Units......Page 484
10.3 Linearization Process......Page 486
10.4.1 Transfer Function Inputs......Page 491
10.4.2 Transfer Function Outputs......Page 492
10.5 Solution of the State Space and Measurement Equations......Page 496
10.6 Design of a Terminal Voltage Controller......Page 502
10.7 Design of a Classical Regulator......Page 509
10.9 References......Page 513
11.2 Simulation Equations......Page 514
11.3 MATLAB® Simulation of Park’s Equations......Page 517
11.4 Steady-State Check of Simulation......Page 520
11.5 Simulation of the Equations of Transformation......Page 524
11.6 Simulation Study......Page 536
11.7 Consideration of Saturation Effects......Page 537
11.8 Air Gap Saturation......Page 542
11.9 Field Saturation......Page 546
11.10 Approximate Models of Synchronous Machines......Page 548
11.11 Conclusion......Page 560
Appendix 1: Identities Useful in AC Machine Analysis......Page 564
A2.1 Reduction to Explicit Form......Page 566
A2.2 Complex Eigenvalues......Page 569
A2.3 References......Page 570
Appendix 3: Three-Phase Fault......Page 572
Appendix 4: TrafunSM......Page 580
Appendix 5: SMHB—Synchronous Machine Harmonic Balance......Page 588
Index......Page 600