Matrix Analysis of Electrical Machinery (eBook)

Front Cover 1
Matrix Analysis of Electrical Machinery 4
Copyright Page 5
Table of Contents 6
Preface to the second edition 12
Preface to the first edition 14
Chapter 1. Introduction 16
Conventions 16
Units 19
Parameters 19
Chapter 2. Elements of matrix algebra 20
Matrix Representation of Simultaneous Equations 20
Multiplication of Matrices 21
Application of Matrices to the Solution of Simultaneous Linear Equations—Inversion 23
Singular Matrices 26
The Transpose and Inverse of a Product 26
Alternative Methods of Inversion 27
Compound Matrices 27
Linear Transformation 31
Reduction to Diagonal Form 32
The Advantages of Matrices 33
Types of Matrix 34
Differentiation and Integration of a Matrix 35
Chapter 3. Application of matrix algebra to static electrical networks 36
Laplace Transform Equations 36
Notation 38
Linear Transformation in Electrical Circuit Analysis 39
Choice of Transformations—Invariance of Power 48
Transformation of Voltage and Impedance for Invariant Power with a Given Current Transformation 49
Chapter 4. Transformers 52
The Two-winding Transformer 52
The Three-winding Transformer 59
More Complicated Magnetic Circuits 64
Chapter 5. The matrix equations of the basic rotating machines 68
The Matrix Equation of the Basic Commutator Machine 68
Matrix Equations of Slip-ring and Squirrel-cage Machines 70
The Matrix Equation of the Balanced Two-phase Machine with a Uniform Air-gap (Induction Machine) 72
The Matrix Equation of the Balanced Two-phase Revolving-armature Salient-pole Machine (Synchronous Machine) 80
The Form of the Transformed Impedance Matrix 88
Limitations of the Method 91
Chapter 6. The torque expressions 95
The Energy stored in the Magnetic Fields 96
Torque Expressions 99
Derivation of the Torque Expression from the Equation v = Ri+/> (Li)
The Transformation of dL/ 
103 
Derivation of the Torque Expression from the Equation v = Ri+L/> i + G0i
The Mean Steady-state Torque in A.C. Machines 107
Direction of Torque 107
Chapter 7. Linear transformations in circuits and machines 109
Resolution of Rotor M.M.F. 112
Transformation between Two Sets of Stationary Axes (Brush-shifting Transformation) 113
The Equivalence of Three-phase and Two-phase Systems 115
The Transformation from Three-phase to Two-phase Axes (a, b, c to a, a,ß o) 117
The Transformation from Three-phase Axes to Symmetrical Component Axes (a, b, c to p, n, o) 121
The Transformation from Two-phase Axes to Symmetrical Component Axes (a, a,ß o to p, n, o) 124
Steady-state and Instantaneous Symmetrical Components 127
Transformation from Two-phase Rotating Axes to Stationary Axes (a, a,ß otod, q, o) 129
Transformation from Three-phase Rotating Axes to Stationary Axes (a, b, ctod, q, o) 132
The Transformation from Stationary Axes to Forward and Backward Axes (d, q, o to f, b, o) 133
The Transformation of Stator Winding Axes 134
Physical Interpretation of Various Sets of Axes 134
Chapter 8. The application of matrix techniques to routine performance calculations 138
The Establishment of the Transient Impedance Matrix 138
Phasor Diagrams and Equivalent Circuits 141
Interconnections between Machines or between Machines and other Circuit Elements 143
Closed Circuits 144
Specific Types of Problem 144
The Analysis of Three-phase Machines 147
Chapter 9. D.C. and single-phase commutator machines 154
The Series Commutator Machine 154
The Shunt Commutator Machine 158
Parameters of D.C. Machines 166
The Repulsion Motor 168
Chapter 10. The steady-state performance of polyphase machines 177
The Balanced Polyphase Induction Machine 177
The Unbalanced Two-phase Induction Machine 192
Single-phase Operation of Induction Machine 200
The Polyphase Synchronous Machine with a Uniform Air-gap and no Damper Windings 204
The Polyphase Synchronous Machine with Salient Poles and no Damper Windings 212
Chapter 11. Transient and negative-sequence conditions in A.C. machines 234
Balanced Induction Machine Transients 234
The Synchronous Machine with Salient Poles and no Damper Windings 239
The Synchronous Machine with Salient Poles and Damper Windings 258
Chapter 12. Small oscillations 269
Separately Excited D.C. Machine 272
Balanced Induction Machine 275
Synchronous Machine 283
Chapter 13. Miscellaneous machine problems 289
The Metadyne Generator with its Quadrature Brushes displaced 289
The Ferraris–Arno Phase Converter 294
The Polyphase Induction Machine with a Single-phase Secondary Circuit 300
Power Selsyns 307
The Single-phase Performance of the Synchronous Generator with a Uniform Air-gap and no Damping Circuits 320
Chapter 14. Conclusion 324
Appendices 326
A. Restriction on Rotor Windings 326
B. Torque under Saturated Conditions 329
C. Definitions of Systems of Axes 336
D. Trigonometric Formulae 339
Exercises 341
Hints and answers to exercises 348
References 360
Index 362