To appreciate the revolutionary nature of the space vector approach, one must first understand the limitations of the classical "per-phase" equivalent circuit model.
Preface
Acknowledgments
List of Symbols and Abbreviations
1. Introduction to Space Vector Theory
1.1 Limitations of per-phase equivalent circuits
1.2 The space vector definition: voltage, current, flux
1.3 Complex plane representation
1.4 Stationary and rotating reference frames
1.5 Relationship to symmetrical components
2. Fundamentals of Rotating Magnetic Fields
2.1 MMF distribution in AC machines
2.2 Space vector of stator and rotor fields
2.3 Resultant air-gap flux vector
2.4 Torque as cross product of flux and current vectors
3. Induction Machines in Space Vector Form
3.1 Dynamic equations in stator coordinates
3.2 Equivalent circuits via space vectors
3.3 Rotor flux estimation (voltage model, current model)
3.4 Steady-state operation: slip and torque
3.5 Transients: starting, load changes, and short-circuit
4. Synchronous and Permanent-Magnet Machines
4.1 Space vector model of salient-pole synchronous machines
4.2 PMSM: surface-mount vs. interior permanent magnet
4.3 Reluctance torque contribution
4.4 Damper windings and transient behavior
5. Reference Frame Transformations
5.1 Clarke transformation (αβ)
5.2 Park transformation (dq)
5.3 Transformation of machine equations
5.4 Invariance of power and torque
6. Voltage-Source Inverters and Space Vector PWM
6.1 Three-phase inverter as a voltage source
6.2 Active and zero voltage vectors
6.3 Space vector modulation (SVPWM) algorithm
6.4 Comparison with sinusoidal PWM
6.5 Overmodulation and six-step operation
7. Field-Oriented Control (FOC)
7.1 Principles of rotor flux orientation
7.2 Direct FOC (with flux sensors/estimators)
7.3 Indirect FOC (slip frequency control)
7.4 PI controller tuning in dq frame
7.5 Anti-windup and saturation handling
8. Direct Torque Control (DTC)
8.1 Hysteresis-based torque and flux control
8.2 Optimal switching table
8.3 DTC with space vector modulator (DTC-SVM)
8.4 Comparison with FOC To appreciate the revolutionary nature of the space
9. Sensorless Drives and Observers
9.1 Need for sensorless control
9.2 Model reference adaptive system (MRAS)
9.3 Sliding-mode observers in space vector form
9.4 Extended Kalman filter for speed estimation
9.5 Signal injection methods for zero/low speed
10. Stability and Harmonic Analysis
10.1 Small-signal stability of drive systems
10.2 Influence of PWM harmonics
10.3 Stator and rotor current harmonics
10.4 Acoustic noise and vibration
11. Case Studies and Experimental Validation
11.1 Induction motor drive with SVPWM (1.5 kW)
11.2 PMSM servo drive for position control
11.3 Doubly-fed induction generator (DFIG) for wind energy
11.4 Fault-tolerant operation under inverter faults
12. Advanced Topics
12.1 Multilevel inverters and their space vectors
12.2 Model predictive control (MPC) with space vectors
12.3 Finite control set MPC (FCS-MPC)
12.4 Machine learning in space vector control
Appendix A: Complex Numbers and Vector Calculus
Appendix B: Per-Unit System for Machines
Appendix C: Simulink Models and Code Listings
Appendix D: Answers to Selected Exercises
References
Index
According to Google Scholar (2024 estimates):
The space vector approach is now standard in industrial drive software (e.g., in Simulink, PLECS, and commercial VFDs).
End of Monograph Extract
The book "Electrical Machines and Drives: A Space-Vector Theory Approach" by Peter Vas, part of the Monographs in Electrical and Electronic Engineering series, is a comprehensive text that uses space-vector theory to analyze the steady-state and transient operation of AC and DC machines. Key Features of the Text
Universal Theory Application: Provides a general theory applicable to both steady-state and transient operation for a wide variety of AC and DC machines and variable-speed drives.
Simplified Modeling: Demonstrates how all major machine models (including those used in matrix models) can be derived from the simple space-vector model without requiring complex matrix transformations.
Inclusion of Modern Drives: Discusses a large number of variable-speed drives, including recently introduced modern types and electronically commutated machines.
Magnetic Saturation Integration: Uniquely incorporates the effects of magnetic saturation into different models for both smooth-air-gap and salient-pole machines.
Analytical and Simulation Readiness: Equations are presented in state-variable and analytical forms, making them directly usable for computer simulations or hand calculations.
Extended Machine Coverage: Applies the space-vector model to advanced configurations like the double-cage induction machine and the salient-pole synchronous machine.
Accessible Entry: The book is designed so it can be used without prior knowledge of space-vector theory, starting from fundamental principles to remain self-contained for students and researchers.
Rich Visuals: Includes approximately 200 figures to illustrate detailed physical and mathematical analyses. According to Google Scholar (2024 estimates):
Electrical Machines and Drives: A Space-Vector Theory Approach by Peter Vas is
a comprehensive technical monograph that provides a unified mathematical and physical analysis of AC and DC machines using space-vector theory . Published by Clarendon Press (Oxford University Press)
as the 25th volume in the "Monographs in Electrical and Electronic Engineering" series, the book is designed for researchers, academics, and advanced students. Oxford University Press Core Content and Themes
The book's primary goal is to present a general theory applicable to both steady-state operations of electrical machines. Amazon.com Electrical Machines and Drives - Peter Vas
| Book | Approach | Focus | Mathematical Depth | |------|----------|-------|---------------------| | Vas (this book) | Space vector unified | Drives + machines | High | | Krause et al. (Analysis of Electric Machinery) | $dq0$ transformation | Machines primarily | Medium-High | | Leonhard (Control of Electrical Drives) | Classical control | Drives | Medium | | Novotny & Lipo (Vector Control) | Field orientation | Induction drives | High | | Bose (Modern Power Electronics and AC Drives) | Application-oriented | Drives | Medium |
Vas is distinct in its exclusive space vector formulation and depth on saturation.
Classical AC machine analysis relies on representing a three-phase machine by a single-phase equivalent circuit. While adequate for steady-state calculations (e.g., torque, efficiency, power factor), this model collapses under dynamic conditions. It cannot explain:
Classical textbooks often focus on steady-state phasors. Vas provides full transient solutions, essential for drive control design.