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Ned Mohan. Analysis and Control of Electric Drives
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
ANALYSIS AND CONTROL OF ELECTRIC DRIVES. Simulations and Laboratory Implementation
PREFACE
A NEW APPROACH
ACKNOWLEDGMENT
ABOUT THE COMPANION SITE
1 Electric Drives: Introduction and Motivation
1‐1 THE CLIMATE CRISIS AND THE ENERGY‐SAVING OPPORTUNITIES
1‐2 ENERGY SAVINGS IN GENERATION OF ELECTRICITY
1‐2‐1 Energy‐Saving Potential in Harnessing of Wind Energy
1‐3 ENERGY‐SAVING POTENTIAL IN THE END‐USE OF ELECTRICITY
1‐3‐1 Energy‐Saving Potential in the Process Industry
1‐3‐2 Energy‐Saving Potential in the Residential and Commercial Sectors
1‐4 ELECTRIC TRANSPORTATION
1‐5 PRECISE SPEED AND TORQUE CONTROL APPLICATIONS IN ROBOTICS, DRONES, AND THE PROCESS INDUSTRY
1‐6 RANGE OF ELECTRIC DRIVES
1‐7 THE MULTIDISCIPLINARY NATURE OF DRIVE SYSTEMS
1‐8 USE OF SIMULATION AND HARDWARE PROTOTYPING
1‐9 STRUCTURE OF THE TEXTBOOK
1‐10 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS
Note
2. Understanding Mechanical System Requirements for Electric Drives. 2‐1 INTRODUCTION
2‐2 SYSTEMS WITH LINEAR MOTION
2‐3 ROTATING SYSTEMS
EXAMPLE 2‐1
Solution
EXAMPLE 2‐2
Solution
EXAMPLE 2‐3
Solution
EXAMPLE 2‐4
Solution
EXAMPLE 2‐5
Solution
2‐4 FRICTION
EXAMPLE 2‐6
Solution
2‐5 TORSIONAL RESONANCES
2‐6 ELECTRICAL ANALOGY
EXAMPLE 2‐7
Solution
2‐7 Coupling Mechanisms
2‐7‐1 Conversion Between Linear and Rotary Motion
EXAMPLE 2‐8
Solution
2‐7‐2 Gears
Optimum Gear Ratio
2‐8 TYPES OF LOADS
2‐9 FOUR‐QUADRANT OPERATION
2‐10 STEADY‐STATE AND DYNAMIC OPERATIONS
2‐11 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS
Belt‐and‐Pulley Systems
Gears
Lead‐Screw Mechanism
Wind Turbines and Electric Vehicles
Simulation Problems
Note
3. Basic Concepts in Magnetics and Electromechanical Energy Conversion. 3‐1 INTRODUCTION
3‐2 MAGNETIC CIRCUIT CONCEPTS
3‐3 MAGNETIC FIELD PRODUCED BY CURRENT‐CARRYING CONDUCTORS
3‐3‐1 Ampere’s Law
EXAMPLE 3-1
Solution
3‐4 FLUX DENSITY B AND THE FLUX ϕ
3‐4‐1 Ferromagnetic Materials
3‐4‐2 Flux ϕ
3‐4‐3 Flux Linkage
EXAMPLE 3-2
Solution
3‐5 MAGNETIC STRUCTURES WITH AIR GAPS
EXAMPLE 3-3
Solution
3‐6 INDUCTANCES
EXAMPLE 3-4
Solution
3‐7 MAGNETIC ENERGY STORAGE IN INDUCTORS
EXAMPLE 3-5
Solution
3‐8 FARADAY’S LAW: INDUCED VOLTAGE IN A COIL DUE TO TIME‐RATE OF CHANGE OF FLUX LINKAGE
EXAMPLE 3-6
Solution
3‐8‐1 Relating e(t), ϕ(t), and i(t)
EXAMPLE 3-7
Solution
3‐9 LEAKAGE AND MAGNETIZING INDUCTANCES
3‐10 MUTUAL INDUCTANCES
3‐11 BASIC PRINCIPLES OF TORQUE PRODUCTION AND VOLTAGE INDUCTION
3‐11‐1 Basic Structure of ac Machines
3‐11‐2 Production of Magnetic Field
EXAMPLE 3-8
Solution
3‐11‐3 Basic Principles of Torque Production and EMF Induction
Electromagnetic Force
EXAMPLE 3-9
Solution
Induced EMF
EXAMPLE 3-10
Solution
Magnetic Shielding of Conductors in Slots
3‐11‐4 Application of the Basic Principles
3‐11‐5 Energy Conversion
EXAMPLE 3-11
Solution
Regenerative Braking
3‐11‐6 Power Losses and Energy Efficiency
3‐12 REVIEW QUESTIONS. 3‐12‐1 Magnetic Circuits
3‐12‐2 Electromechanical Energy Conversion
FURTHER READING
PROBLEMS. Magnetic Circuits
Electromechanical Energy Conversion
Note
4. Basic Understanding of Switch‐Mode Power Electronic Converters. 4‐1 INTRODUCTION
4‐2 OVERVIEW OF POWER ELECTRONIC CONVERTERS
4‐2‐1 Switch‐Mode Conversion: Switching Power‐Pole as the Building Block
4‐2‐2 PWM of the Switching Power‐Pole (Constant fs)
4‐2‐3 Bidirectional Switching Power‐Pole
4‐2‐4 PWM of the Bidirectional Switching Power‐Pole
4‐3 CONVERTERS FOR dc MOTOR DRIVES ()
EXAMPLE 4-1
Solution
EXAMPLE 4-2
Solution
4‐3‐1 Switching Waveforms in a Converter for dc Motor Drives
EXAMPLE 4-3
Solution
4‐4 SYNTHESIS OF LOW‐FREQUENCY ac
4‐5 THREE‐PHASE INVERTERS
4‐5‐1 Switching Waveforms in a Three‐Phase Inverter with Sine‐PWM
EXAMPLE 4-4
Solution
4‐6 POWER SEMICONDUCTOR DEVICES [2]
4‐6‐1 Device Ratings
4‐6‐2 Power Diodes
4‐6‐3 Controllable Switches
MOSFETs
Insulated‐Gate Bipolar Transistors
4‐6‐4 “Smart Power” Modules Including Gate Drivers and Wide Bandgap Devices
4‐7 HARDWARE PROTOTYPING OF PWM
4‐8 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS
dc–dc Converters (Four‐Quadrant Capability)
dc‐to‐Three‐Phase ac Inverters
Simulation Problems
dc–dc Converters
dc‐Three‐Phase ac Inverters
Note
5. Control in Electric Drives. 5‐1 INTRODUCTION
5‐2 dc MOTORS
5‐2‐1 Requirements Imposed by dc Machines on the PPU
5‐3 DESIGNING FEEDBACK CONTROLLERS FOR MOTOR DRIVES. 5‐3‐1 Control Objectives
EXAMPLE 5-1
Solution
5‐3‐2 Cascade Control Structure
5‐3‐3 Steps in Designing the Feedback Controller
5‐3‐4 System Representation for Small‐Signal Analysis
The Average Representation of the PPU
The Modeling of the dc Machine and the Mechanical Load
5‐4 CONTROLLER DESIGN
5‐4‐1 Proportional‐Integral Controllers
5‐4‐2 Example of a Controller Design
Design of the Torque (Current) Control Loop
EXAMPLE 5-2
Solution
The Design of the Speed Loop
EXAMPLE 5-3
Solution
5‐4‐3 The Design of the Position Control Loop
EXAMPLE 5-4
Solution
5‐5 THE ROLE OF FEED‐FORWARD
5‐6 EFFECTS OF LIMITS
5‐7 ANTI‐WINDUP (NON‐WINDUP) INTEGRATION
5‐8 HARDWARE PROTOTYPING OF dc MOTOR SPEED CONTROL
5‐9 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS AND SIMULATIONS. dc Motors
Controller Design
Note
6. Using Space Vectors to Analyze ac Machines. 6‐1 INTRODUCTION
6‐2 SINUSOIDALLY DISTRIBUTED STATOR WINDINGS
EXAMPLE 6‐1
EXAMPLE 6‐2
Solution
6‐2‐1 Three‐Phase, Sinusoidally Distributed Stator Windings
EXAMPLE 6‐3
Solution
6‐3 THE USE OF SPACE VECTORS TO REPRESENT SINUSOIDAL FIELD DISTRIBUTIONS IN THE AIR GAP
EXAMPLE 6‐4
Solution
6‐4 SPACE‐VECTOR REPRESENTATION OF COMBINED TERMINAL CURRENTS AND VOLTAGES
6‐4‐1 Physical Interpretation of the Stator Current Space Vector
EXAMPLE 6‐5
Solution
6‐4‐2 Phase Components of Space Vectors and
EXAMPLE 6‐6
Solution
6‐5 BALANCED SINUSOIDAL STEADY‐STATE EXCITATION (ROTOR OPEN‐CIRCUITED)
6‐5‐1 Rotating Stator MMF Space Vector
EXAMPLE 6‐7
Solution
6‐5‐2 Rotating Stator MMF Space Vector in Multipole Machines
6‐5‐3 The Relationship Between Space Vectors and Phasors in Balanced Three‐Phase Sinusoidal Steady State ( and )
6‐5‐4 Induced Voltages in Stator Windings
EXAMPLE 6‐8
Solution
6‐6 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS
Note
7. Space Vector Pulse‐Width‐Modulated (SV‐PWM) Inverters. 7‐1 INTRODUCTION
7‐2 SYNTHESIS OF STATOR VOLTAGE SPACE VECTOR
7‐3 COMPUTER SIMULATION OF SV‐PWM INVERTER
EXAMPLE 7-1
Solution
7‐4 LIMIT ON THE AMPLITUDE OF THE STATOR VOLTAGE SPACE VECTOR
7‐5 Hardware Prototyping of Space Vector Pulse Width Modulation
7‐6 SUMMARY
REFERENCE
FURTHER READING
PROBLEMS
Note
8. Sinusoidal Permanent‐Magnet ac (PMAC) Drives in Steady State. 8‐1 INTRODUCTION
8‐2 THE BASIC STRUCTURE OF PMAC MACHINES
8‐3 PRINCIPLE OF OPERATION. 8‐3‐1 Rotor‐Produced Flux‐Density Distribution
8‐3‐2 Torque Production
Generator Mode
8‐3‐3 Mechanical System of PMAC Drives
8‐3‐4 Calculation of the Reference Values , , and of the Stator Currents
EXAMPLE 8‐1
Solution
8‐3‐5 Induced EMFs in the Stator Windings During Balanced Sinusoidal Steady State
Induced EMF in the Stator Windings Due to Rotating
Induced EMF in the Stator Windings Due to Rotating : Armature Reaction
Superposition of the Induced EMFs in the Stator Windings
Per‐Phase Equivalent Circuit
EXAMPLE 8‐2
Solution
8‐3‐6 Generator‐Mode of Operation of PMAC Drives
8‐4 THE CONTROLLER AND THE PPU
8‐5 HARDWARE PROTOTYPING OF PMAC MOTOR HYSTERESIS CURRENT CONTROL
8‐6 REVIEW QUESTIONS
REFERENCE
FURTHER READING
PROBLEMS
Note
9. Induction Motors in Sinusoidal Steady-State. 9‐1 INTRODUCTION
9‐2 THE STRUCTURE OF THREE‐PHASE, SQUIRREL‐CAGE INDUCTION MOTORS
9‐3 THE PRINCIPLES OF INDUCTION MOTOR OPERATION
9‐3‐1 Electrically Open‐Circuited Rotor
EXAMPLE 9‐1
Solution
9‐3‐2 The Short‐Circuited Rotor
Transformer Analogy
The Assumption of Rotor Leakage
EXAMPLE 9‐2
Solution
Revisiting the Transformer Analogy
The Slip Frequency, fslip, in the Rotor Circuit
EXAMPLE 9‐3
Solution
Electromagnetic Torque
EXAMPLE 9‐4
Solution
The Generator (Regenerative Braking) Mode of Operation
EXAMPLE 9‐5
Solution
Reversing the Direction of Rotation
Including the Rotor Leakage Inductance
9‐3‐3 Per‐Phase Steady‐State Equivalent Circuit (Including Rotor Leakage)
EXAMPLE 9‐6
Solution
Including the Stator Winding Resistance Rs and Leakage Inductance L
9‐4 TESTS TO OBTAIN THE PARAMETERS OF THE PER‐PHASE EQUIVALENT CIRCUIT
9‐4‐1 dc‐Resistance Test to Estimate Rs
9‐4‐2 The No‐Load Test to Estimate Lm
9‐4‐3 Blocked‐Rotor Test to Estimate and the Leakage Inductances
9‐5 INDUCTION MOTOR CHARACTERISTICS AT RATED VOLTAGES IN MAGNITUDE AND FREQUENCY
9‐6 INDUCTION MOTORS OF NEMA DESIGN A, B, C, AND D
9‐7 LINE START
9‐8 HARDWARE PROTOTYPING OF INDUCTION MOTOR PARAMETER ESTIMATION
9‐9 REVIEW QUESTIONS
REFERENCES
FURTHER READING
PROBLEMS
Note
10. Induction‐Motor Drives: Speed Control. 10‐1 INTRODUCTION
10‐2 CONDITIONS FOR EFFICIENT SPEED CONTROL OVER A WIDE RANGE
EXAMPLE 10‐1
Solution
10‐3 APPLIED VOLTAGE AMPLITUDES TO KEEP
EXAMPLE 10‐2
Solution
10‐4 STARTING CONSIDERATIONS IN DRIVES
EXAMPLE 10‐3
Solution
10‐5 CAPABILITY TO OPERATE BELOW AND ABOVE THE RATED SPEED
10‐5‐1 Rated Torque Capability Below the Rated Speed (With )
10‐5‐2 Rated Power Capability Above the Rated Speed by Flux‐Weakening
10‐6 INDUCTION‐GENERATOR DRIVES
10‐7 SPEED CONTROL OF INDUCTION‐MOTOR DRIVES
10‐7‐1 Limiting of Acceleration/Deceleration
10‐7‐2 Current‐Limiting
10‐7‐3 Slip Compensation
10‐7‐4 Voltage Boost
10‐8 PULSE‐WIDTH‐MODULATED PPU
10‐9 Harmonics in the PPU Output Voltages
10‐9‐1 Modeling the PPU‐Supplied Induction Motors in Steady State
10‐10 REDUCTION OF AT LIGHT LOADS
10‐11 HARDWARE PROTOTYPING OF CLOSED‐LOOP SPEED CONTROL OF INDUCTION MOTOR
10‐12 SUMMARY/REVIEW QUESTIONS
REFERENCE
FURTHER READING
PROBLEMS
SIMULATION PROBLEM
Note
11. Induction Machine Equations in Phase Quantities: Assisted by Space Vectors. 11‐1 INTRODUCTION
11‐2 SINUSOIDALLY DISTRIBUTED STATOR WINDINGS
11‐2‐1 Three‐Phase, Sinusoidally Distributed Stator Windings
11‐3 STATOR INDUCTANCES (ROTOR OPEN‐CIRCUITED)
11‐3‐1 Stator Single‐Phase Magnetizing Inductance Lm,one‐phase
11‐3‐2 Stator Mutual‐Inductance Lmutual
11‐3‐3 Per‐Phase Magnetizing‐Inductance Lm
11‐3‐4 Stator‐Inductance Ls
11‐4 EQUIVALENT WINDINGS IN A SQUIRREL‐CAGE ROTOR
11‐4‐1 Rotor‐Winding Inductances (Stator Open‐Circuited)
11‐5 MUTUAL INDUCTANCES BETWEEN THE STATOR AND THE ROTOR PHASE WINDINGS
11‐6 REVIEW OF SPACE VECTORS
11‐6‐1 Relationship Between Phasors and Space Vectors in Sinusoidal Steady State
11‐7 FLUX LINKAGES
11‐7‐1 Stator Flux Linkage (Rotor Open‐Circuited)
11‐7‐2 Rotor Flux Linkage (Stator Open‐Circuited)
11‐7‐3 Stator and Rotor Flux Linkages (Simultaneous Stator and Rotor Currents)
11‐8 STATOR AND ROTOR VOLTAGE EQUATIONS IN TERMS OF SPACE VECTORS
11‐9 MAKING A CASE FOR A dq‐WINDING ANALYSIS
EXAMPLE 11‐1
Solution
EXAMPLE 11-2
Solution
EXAMPLE 11-3
Solution
11‐10 SUMMARY
PROBLEMS
Note
12. Dynamic Analysis of Induction Machines in Terms of dq‐Windings. 12‐1 INTRODUCTION
12‐2 dq‐WINDING REPRESENTATION
12‐2‐1 Stator dq‐Winding Representation
12‐2‐2 Rotor dq‐Windings (Along the Same dq‐Axes as in the Stator)
12‐2‐3 Mutual Inductance Between dq‐Windings on the Stator and the Rotor
12‐3 MATHEMATICAL RELATIONSHIPS OF THE dq‐WINDINGS (AT AN ARBITRARY SPEED ωd)
12‐3‐1 Relating dq‐Winding Variables to Phase Winding Variables
12‐3‐2 Flux Linkages of dq‐Windings in Terms of Their Currents
Stator Windings
Rotor Windings
12‐3‐3 dq‐Winding Voltage Equations. Stator Windings
Rotor Windings
12‐3‐4 Obtaining Fluxes and Currents with Voltages as Inputs
12‐4 CHOICE OF THE dq‐WINDING SPEED ωd
12‐5 ELECTROMAGNETIC TORQUE. 12‐5‐1 Torque on the Rotor d‐Axis Winding
12‐5‐2 Torque on the Rotor q‐Axis Winding
12‐5‐3 Net Electromagnetic Torque Tem on the Rotor
12‐6 ELECTRODYNAMICS
12‐7 d‐ AND q‐AXIS EQUIVALENT CIRCUITS
12‐8 RELATIONSHIP BETWEEN THE dq‐WINDINGS AND THE PER‐PHASE PHASOR‐DOMAIN EQUIVALENT CIRCUIT IN BALANCED SINUSOIDAL STEADY STATE
12‐9 COMPUTER SIMULATION
12‐9‐1 Calculation of Initial Conditions
12‐10 Phasor Analysis
EXAMPLE 12‐1
Solution
EXAMPLE 12‐2
Solution
EXAMPLE 12‐3
Solution
EXAMPLE 12‐4
Solution
EXAMPLE 12‐5
Solution
EXAMPLE 12‐6
Solution
EXAMPLE 12‐7
Solution
12‐11 SUMMARY
FURTHER READING
PROBLEMS
Test Machine
Note
13 Mathematical Description of Vector Control in Induction Machines. 13‐1 INTRODUCTION
13‐2 MOTOR MODEL WITH THE d‐AXIS ALIGNED ALONG THE ROTOR FLUX LINKAGE ‐AXIS
13‐2‐1 Calculation of ωdA
13‐2‐2 Calculation of Tem
13‐2‐3 d‐Axis Rotor Flux‐Linkage Dynamics
13‐2‐4 Motor Model
EXAMPLE 13‐1
Solution
13‐3 VECTOR CONTROL
13‐3‐1 Speed and Position Control Loops
EXAMPLE 13‐2
Solution
13‐3‐2 Initial Startup
13‐3‐3 Calculating the Stator Voltages to be Applied
13‐3‐4 Designing the PI Controllers
EXAMPLE 13‐3
Solution
13‐4 HARDWARE PROTOTYPING OF VECTOR CONTROL OF INDUCTION MOTOR
13‐5 SUMMARY
REFERENCE
PROBLEMS
Note
14. Speed‐Sensorless Vector Control of Induction Motor. 14‐1 INTRODUCTION
14‐2 OPEN‐LOOP SPEED ESTIMATOR
EXAMPLE 14‐1
Solution
14‐3 MODEL‐REFERENCE ADAPTIVE SYSTEM (MRAS) ESTIMATOR
14‐3‐1 Rotor Speed Estimation
14‐3‐2 Stator d‐ and q‐Axis Current Reference
14‐3‐3 Estimation of ωdA and θda
EXAMPLE 14‐2
Solution
14‐3‐4 Designing the PI controller
EXAMPLE 14‐3
Solution
14‐4 PARAMETER SENSITIVITY OF OPEN‐LOOP ESTIMATOR AND MRAS ESTIMATOR
EXAMPLE 14‐4
Solution
14‐5 PRACTICAL IMPLEMENTATION
14‐6 SUMMARY
REFERENCES
FURTHER READING
PROBLEMS
14‐A APPENDIX. 14‐A‐1 MRAS Linearized Error Function
15 Analysis of Doubly Fed Generators (DFIGs) in Steady State and Their Vector Control. 15‐1 INTRODUCTION
15‐2 STEADY‐STATE ANALYSIS
15‐3 UNDERSTANDING DFIG OPERATION IN dq AXIS
15‐3‐1 Stator Voltages
15‐3‐2 Flux Linkages and Currents
15‐3‐3 Rotor Voltages
15‐3‐4 Stator and Rotor Power Inputs
15‐3‐5 Electromagnetic Torque
15‐3‐6 Relationships of Stator and Rotor Real and Reactive Powers
EXAMPLE 15‐1
Solution
EXAMPLE 15‐2
Solution
15‐4 DYNAMIC ANALYSIS OF DFIG
15‐5 VECTOR CONTROL OF DFIG
15‐5‐1 Rotor Current Controller
15‐5‐2 Rotor Speed Controller
15‐5‐3 Stator Reactive Power Controller
15‐5‐4 Rotor Position Estimator
EXAMPLE 15‐3
Solution
15‐6 SUMMARY
REFERENCES
FURTHER READING
PROBLEMS
Note
16. Direct Torque Control (DTC) and Encoder‐Less Operation of Induction Motor Drives. 16‐1 INTRODUCTION
16‐2 SYSTEM OVERVIEW
16‐3 PRINCIPLE OF ENCODER‐LESS DTC OPERATION
16‐4 CALCULATION OF s, r, Tem, AND ωm. 16‐4‐1 Calculation of the Stator Flux
16‐4‐2 Calculation of the Rotor Flux
16‐4‐3 Calculation of the Electromagnetic Torque Tem
16‐4‐4 Calculation of the Rotor Speed ωm
16‐5 CALCULATION OF THE STATOR VOLTAGE SPACE VECTOR
EXAMPLE 16‐1
Solution
16‐6 DIRECT TORQUE CONTROL USING dq‐AXES
16‐7 SUMMARY
REFERENCE
FURTHER READING
PROBLEMS
TEST MACHINE
16‐A APPENDIX. 16‐A‐1 Derivation of Torque Expressions
Note
17. Vector Control of Permanent‐Magnet Synchronous Motor Drives. 17‐1 INTRODUCTION
17‐2 dq‐ANALYSIS OF PERMANENT‐MAGNET SYNCHRONOUS MACHINES
17‐2‐1 Flux Linkages
17‐2‐2 Stator dq‐Winding Voltages
17‐2‐3 Electromagnetic Torque
17‐2‐4 Electrodynamics
17‐3 NON‐SALIENT POLE SYNCHRONOUS MACHINES
17‐3‐1 Relationship Between the dq Circuits and the Per‐Phase Phasor‐Domain Equivalent Circuit in Balanced Sinusoidal Steady State
Relationship Between kE and λfd
17‐3‐2 dq‐Based Dynamic Controller for “Brush‐less dc” Drives
Flux Weakening
EXAMPLE 17‐1
Solution
17‐4 SALIENT‐POLE SYNCHRONOUS MACHINES
17‐4‐1 Rotor Position Estimation Using High‐Frequency Injection
17‐4‐2 Speed‐Sensorless Dynamic Controller for IPM Motor
17‐4‐3 Designing PID Controller
EXAMPLE 17‐2
Solution
EXAMPLE 17‐3
Solution
17‐4‐4 Electromagnetic Torque
EXAMPLE 17‐4
Solution
17‐5 HARDWARE PROTOTYPING OF VECTOR CONTROL OF SPM SYNCHRONOUS MOTOR
17‐6 SUMMARY
REFERENCES
PROBLEMS
17‐A APPENDIX. 17‐A‐1 Transformation of Stator Flux‐Linkage From Rotating dq Frame to Stationary Frame
Note
18. Reluctance Drives: Stepper‐Motors and Switched‐Reluctance Drives. 18‐1 INTRODUCTION
18‐2 THE OPERATING PRINCIPLE OF RELUCTANCE MOTORS
18‐3 STEPPER‐MOTOR DRIVES
18‐3‐1 Variable‐Reluctance Stepper‐Motors
18‐3‐2 Permanent‐Magnet Stepper‐Motors
18‐3‐3 Hybrid Stepper‐Motors
18‐3‐4 Equivalent‐Circuit Representation of a Stepper‐Motor
18‐3‐5 Half‐Stepping and Micro‐Stepping
18‐3‐6 Power Electronic Converters for Stepper‐Motors
18‐4 SRM DRIVES
18‐4‐1 Switched‐Reluctance Motor
18‐4‐2 Electromagnetic Torque Tem
18‐4‐3 Induced Back‐EMF ea
18‐5 INSTANTANEOUS WAVEFORMS
18‐6 ROLE OF MAGNETIC SATURATION [1]
18‐7 POWER ELECTRONIC CONVERTERS FOR SRM DRIVES
18‐8 DETERMINING THE ROTOR POSITION FOR ENCODER‐LESS OPERATION
18‐9 CONTROL IN MOTORING MODE
18‐10 SUMMARY/REVIEW QUESTIONS
REFERENCE
FURTHER READING
PROBLEMS
Note
INDEX
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