DESIGN OF ROTATING ELECTRICAL MACHINES

1 Principal Laws and Methods in Electrical Machine Design 1
1.1 Electromagnetic Principles 1
1.2 Numerical Solution 9
1.3 The Most Common Principles Applied to Analytic Calculation 12
1.3.1 Flux Line Diagrams 17
1.3.2 Flux Diagrams for Current-Carrying Areas 22
1.4 Application of the Principle of Virtual Work in the Determination
of Force and Torque 25
1.5 Maxwell’s Stress Tensor; Radial and Tangential Stress 33
1.6 Self-Inductance and Mutual Inductance 36
1.7 Per Unit Values 40
1.8 Phasor Diagrams 43
Bibliography 4

2 Windings of Electrical Machines 47
2.1 Basic Principles 48
2.1.1 Salient-Pole Windings 48
2.1.2 Slot Windings 52
2.1.3 End Windings 53
2.2 Phase Windings 54
2.3 Three-Phase Integral Slot Stator Winding 56
2.4 Voltage Phasor Diagram and Winding Factor 63
2.5 Winding Analysis 71
2.6 Short Pitching 72
2.7 Current Linkage of a Slot Winding 81
2.8 Poly-Phase Fractional Slot Windings 92
2.9 Phase Systems and Zones of Windings 95
2.9.1 Phase Systems 95
2.9.2 Zones of Windings 98

2.10 Symmetry Conditions 99
2.11 Base Windings 102
2.11.1 First-Grade Fractional Slot Base Windings 103
2.11.2 Second-Grade Fractional Slot Base Windings 104
2.11.3 Integral Slot Base Windings 104
2.12 Fractional Slot Windings 105
2.12.1 Single-Layer Fractional Slot Windings 105
2.12.2 Double-Layer Fractional Slot Windings 115
2.13 Single- and Two-Phase Windings 122
2.14 Windings Permitting a Varying Number of Poles 126
2.15 Commutator Windings 127
2.15.1 Lap Winding Principles 131
2.15.2 Wave Winding Principles 134
2.15.3 Commutator Winding Examples, Balancing Connectors 137
2.15.4 AC Commutator Windings 140
2.15.5 Current Linkage of the Commutator Winding and
Armature Reaction 142
2.16 Compensating Windings and Commutating Poles 145
2.17 Rotor Windings of Asynchronous Machines 147
2.18 Damper Windings 150
Bibliography 15

3 Design of Magnetic Circuits 153
3.1 Air Gap and its Magnetic Voltage 159
3.1.1 Air Gap and Carter Factor 159
3.1.2 Air Gaps of a Salient-Pole Machine 164
3.1.3 Air Gap of Nonsalient-Pole Machine 169
3.2 Equivalent Core Length 171
3.3 Magnetic Voltage of a Tooth and a Salient Pole 173
3.3.1 Magnetic Voltage of a Tooth 173
3.3.2 Magnetic Voltage of a Salient Pole 177
3.4 Magnetic Voltage of Stator and Rotor Yokes 177
3.5 No-Load Curve, Equivalent Air Gap and Magnetizing Current
of the Machine 180
3.6 Magnetic Materials of a Rotating Machine 183
3.6.1 Characteristics of Ferromagnetic Materials 187
3.6.2 Losses in Iron Circuits 193
3.7 Permanent Magnets in Rotating Machines 200
3.7.1 History and Characteristics of Permanent Magnets 200
3.7.2 Operating Point of a Permanent Magnet Circuit 205
3.7.3 Application of Permanent Magnets in Electrical Machines 213
3.8 Assembly of Iron Stacks 219
3.9 Magnetizing Inductance 221
Bibliography 22

4 Flux Leakage 225
4.1 Division of Leakage Flux Components 227
4.1.1 Leakage Fluxes Not Crossing an Air Gap 227
4.1.2 Leakage Fluxes Crossing an Air Gap 228
4.2 Calculation of Flux Leakage 230
4.2.1 Air-Gap Leakage Inductance 230
4.2.2 Slot Leakage Inductance 234
4.2.3 Tooth Tip Leakage Inductance 245
4.2.4 End Winding Leakage Inductance 246
4.2.5 Skewing Factor and Skew Leakage Inductance 250
Bibliography 25

5 Resistances 255
5.1 DC Resistance 255
5.2 Influence of Skin Effect on Resistance 256
5.2.1 Analytical Calculation of Resistance Factor 256
5.2.2 Critical Conductor Height 265
5.2.3 Methods to Limit the Skin Effect 266
5.2.4 Inductance Factor 267
5.2.5 Calculation of Skin Effect Using Circuit Analysis 267
5.2.6 Double-Sided Skin Effect 274
Bibliography 28

6 Main Dimensions of a Rotating Machine 281
6.1 Mechanical Loadability 291
6.2 Electrical Loadability 293
6.3 Magnetic Loadability 294
6.4 Air Gap 297
Bibliography 300
7 Design Process and Properties of Rotating Electrical Machines 301
7.1 Asynchronous Motor 313
7.1.1 Current Linkage and Torque Production of an
Asynchronous Machine 315
7.1.2 Impedance and Current Linkage of a Cage Winding 320
7.1.3 Characteristics of an Induction Machine 327
7.1.4 Equivalent Circuit Taking Asynchronous Torques and Harmonics
into Account 332
7.1.5 Synchronous Torques 337
7.1.6 Selection of the Slot Number of a Cage Winding 339
7.1.7 Construction of an Induction Motor 342
7.1.8 Cooling and Duty Types 343
7.1.9 Examples of the Parameters of Three-Phase Industrial
Induction Motors