كتاب Electric Machines - Steady State and Performance with MATLAB
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 كتاب Electric Machines - Steady State and Performance with MATLAB

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Electric Machines - Steady State and Performance with MATLAB
Second Edition
Ion Boldea and Lucian N. Tutelea

كتاب Electric Machines - Steady State and Performance with MATLAB  E_m_s_10
و المحتوى كما يلي :


Contents
Preface .xi
Authors xiv
Chapter 1 Introduction 1
1.1 Electric Energy and Electric Machines .1
1.2 Basic Types of Transformers and Electric Machines 3
1.3 Losses and Efficiency 11
1.4 Physical Limitations and Ratings 14
1.5 Nameplate Ratings .17
1.6 Methods of Analysis 19
1.7 State of the Art and Perspective .20
1.8 Summary 22
1.9 Proposed Problems 23
References 24
Chapter 2 Electric Transformers .27
2.1 AC Coil with Magnetic Core and Transformer Principles 28
2.2 Magnetic Materials in EMs and Their Losses .34
2.2.1 Magnetization Curve and Hysteresis Cycle .34
2.2.2 Permanent Magnets 37
2.2.3 Losses in Soft Magnetic Materials .38
2.3 Electric Conductors and Their Skin Effects 40
2.4 Components of Single- and Three-Phase Transformers 46
2.4.1 Cores .47
2.4.2 Windings .50
2.5 Flux Linkages and Inductances of Single-Phase
Transformers 53
2.5.1 Leakage Inductances of Cylindrical Windings .55
2.5.2 Leakage Inductances of Alternate Windings 57
2.6 Circuit Equations of Single-Phase Transformers with Core
Losses 58
2.7 Steady State and Equivalent Circuit 60
2.8 No-Load Steady State (I2 = 0)/Lab 2.1 61
2.8.1 Magnetic Saturation under No Load 64
2.9 Steady-State Short-Circuit Mode/Lab 2.2 .65
2.10 Single-Phase Transformers: Steady-State Operation on
Load/Lab 2.3 68
2.11 Three-Phase Transformers: Phase Connections 72vi Contents
2.12 Particulars of Three-Phase Transformers on No Load 75
2.12.1 No-Load Current Asymmetry .75
2.12.2 Y Primary Connection for the Three-Limb Core .77
2.13 General Equations of Three-Phase Transformers 78
2.13.1 Inductance Measurement/Lab 2.4 79
2.14 Unbalanced Load Steady State in 3-Phase
Transformers/Lab 2.5 80
2.15 Paralleling 3-Phase Transformers 84
2.16 Transients in Transformers 86
2.16.1 Electromagnetic (R,L) Transients 87
2.16.2 Inrush Current Transients/Lab 2.6 88
2.16.3 Sudden Short Circuit from No Load V2  0/
Lab 2.7 89
2.16.4 Forces at Peak Short-Circuit Current .90
2.16.5 Electrostatic (C,R) Ultrafast Transients 92
2.16.6 Protection Measures Against Overvoltage
Electrostatic Transients 95
2.17 Instrument Transformers .95
2.18 Autotransformers .96
2.19 Transformers and Inductances for Power Electronics .98
2.20 Preliminary Transformer Design (Sizing) by Example .100
2.20.1 Specifications .101
2.20.2 Deliverables 101
2.20.3 Magnetic Circuit Sizing .101
2.20.4 Windings Sizing .102
2.20.5 Losses and Efficiency .104
2.20.6 No-Load Current 105
2.20.7 Active Material Weight .105
2.20.8 Equivalent Circuit .106
2.21 Summary 106
2.22 Proposed Problems 108
References 110
Chapter 3 Energy Conversion and Types of Electric Machines 111
3.1 Energy Conversion in Electric Machines 111
3.2 Electromagnetic Torque .112
3.3 Passive Rotor Electric Machines .114
3.4 Active Rotor Electric Machines .117
3.4.1 DC Rotor and AC Stator Currents 117
3.4.2 AC Currents in the Rotor and the Stator 118
3.4.3 DC (PM) Stator and AC Rotor .119
3.5 Fix Magnetic Field (Brush–Commutator) Electric
Machines 120Contents vii
3.6 Traveling Field Electric Machines .122
3.7 Types of Linear Electric Machines 123
3.8 Flux – Modulation Electric Machines: A New Breed .129
3.9 Summary 135
3.10 Proposed Problems 136
References 137
Chapter 4 Brush–Commutator Machines: Steady State 139
4.1 Introduction .139
4.1.1 Stator and Rotor Construction Elements 139
4.2 Brush–Commutator Armature Windings .141
4.2.1 Simple Lap Windings by Example:
Ns
= 16, 2p1 = 4 .144
4.2.2 Simple Wave Windings by Example:
Ns
= 9, 2p1 = 2 .146
4.3 The Brush–Commutator 148
4.4 Airgap Flux Density of Stator Excitation MMF 149
4.5 No-Load Magnetization Curve by Example 150
4.6 PM Airgap Flux Density and Armature Reaction by
Example .156
4.7 The Commutation Process .160
4.7.1 The Coil Commutation Inductance 162
4.8 EMF .163
4.9 Equivalent Circuit and Excitation Connections .165
4.10 D.C. Brush Motor/Generator with Separate (or PM)
Excitation/Lab 4.1 .166
4.11 D.C. Brush PM Motor Steady-State and Speed
Control Methods/Lab 4.2 .169
4.11.1 Speed Control Methods 171
4.12 D.C. Brush Series Motor/Lab 4.3 177
4.12.1 Starting and Speed Control 178
4.13 A.C. Brush Series Universal Motor .179
4.14 Testing Brush–Commutator Machines/Lab 4.4 .182
4.14.1 D.C. Brush PM Motor Losses, Efficiency, and
Cogging Torque 183
4.15 Preliminary Design of a D.C. Brush PM Automotive
Small Motor by Example .186
4.15.1 PM Stator Geometry .186
4.15.2 Rotor Slot and Winding Design 188
4.16 Summary 190
4.17 Proposed Problems 192
References 194viii Contents
Chapter 5 Induction Machines: Steady State 195
5.1 Introduction: Applications and Topologies 195
5.2 Construction Elements .195
5.3 AC Distributed Windings .197
5.3.1 Traveling MMF of AC Distributed Windings .198
5.3.2 Primitive Single-Layer Distributed Windings
(q ≥ 1, Integer) .201
5.3.3 Primitive Two-Layer Three-Phase Distributed
Windings (q = Integer) .202
5.3.4 MMF Space Harmonics for Integer q
(Slots/Pole/Phase) .203
5.3.5 Practical One-Layer AC Three-Phase
Distributed Windings 207
5.3.6 Pole Count Changing AC Three-Phase
Distributed Windings 211
5.3.7 Two-Phase AC Windings 211
5.3.8 Cage Rotor Windings .212
5.3.9 EMF of AC Windings .215
5.4 Induction Machine Inductances .216
5.4.1 Main Inductance .216
5.4.2 Leakage Inductance 218
5.5 Rotor Cage Reduction to the Stator .221
5.6 Wound Rotor Reduction to the Stator 221
5.7 Three-Phase Induction Machine Circuit Equations .222
5.8 Symmetric Steady State of Three-Phase IMs 224
5.9 Ideal No-Load Operation/Lab 5.1 .226
5.10 Zero Speed Operation (S = 1)/Lab 5.2 228
5.11 No-Load Motor Operation (Free Shaft)/Lab 5.3 .232
5.12 Motor Operation on Load (1 > S > 0)/Lab 5.4 234
5.13 Generating at Power Grid (n > f1/p1,S < 0)/Lab 5.5 .235
5.14 Autonomous Generator Mode (S < 0)/Lab 5.6 236
5.15 Electromagnetic Torque and Motor Characteristics 237
5.16 Deep-Bar and Dual-Cage Rotors .243
5.17 Parasitic (Space Harmonics) Torques 244
5.18 Starting Methods .247
5.18.1 Direct Starting (Cage Rotor) 248
5.18.2 Reduced Stator Voltage 249
5.18.3 Additional Rotor Resistance Starting .250
5.19 Speed Control Methods .251
5.19.1 Wound Rotor IM Speed Control 251
5.20 Unbalanced Supply Voltages .255
5.21 One Stator Phase Open by Example/ Lab 5.7 .257
5.22 One Rotor Phase Open 260
5.23 Capacitor Split-Phase Induction Motors/ Lab 5.8 .262Contents ix
5.24 Linear Induction Motors 267
5.24.1 End and Edge Effects in LIMs .267
5.25 Regenerative and Virtual Load Testing of IMs/Lab 5.7 .271
5.26 Preliminary Electromagnetic IM Design by Example .273
5.26.1 Magnetic Circuit .274
5.26.2 Electric Circuit .278
5.26.3 Parameters 279
5.26.3.1 Leakage Reactances .281
5.26.4 Starting Current and Torque .282
5.26.5 Breakdown Slip and Torque .283
5.26.6 Magnetization Reactance, Xm, and Core Losses,
piron 283
5.26.7 No-Load and Rated Currents, I0 and In .285
5.26.8 Efficiency and Power Factor .286
5.26.9 Final Remarks 286
5.27 Dual Stator Windings Induction Generators (DWIG) .287
5.28 Summary 290
5.29 Proposed Problems 293
References 294
Chapter 6 Synchronous Machines: Steady State .297
6.1 Introduction: Applications and Topologies 297
6.2 Stator (Armature) Windings for SMs 300
6.2.1 Nonoverlapping (Concentrated) Coil SM
Armature Windings 304
6.3 SM Rotors: Airgap Flux Density Distribution and EMF .310
6.3.1 PM Rotor Airgap Flux Density 314
6.4 Two-Reaction Principle via Generator Mode 315
6.5 Armature Reaction and Magnetization Reactances,
X
dm and Xqm 318
6.6 Symmetric Steady-State Equations and Phasor Diagram 320
6.7 Autonomous Synchronous Generators 322
6.7.1 No-Load Saturation Curve/Lab 6.1 322
6.7.2 Short-Circuit Curve: (Isc(IF))/Lab 6.2 .322
6.7.3 Load Curve: V
s(Is)/Lab 6.3 .325
6.8 Synchronous Generators at Power Grid/Lab 6.4 .328
6.8.1 Active Power/Angle Curves: Pe(δV) .329
6.8.2 V-Shaped Curves 330
6.8.3 Reactive Power Capability Curves .331
6.9 Basic Static- and Dynamic-Stability Concepts 332
6.10 Unbalanced Load Steady State of SGs/Lab 6.5 .336
6.10.1 Measuring Xd, Xq, Z−, and X0/Lab 6.6 .337
6.11 Large Synchronous Motors .341
6.11.1 Power Balance 341x Contents
6.12 PM Synchronous Motors: Steady State .342
6.13 Load Torque Pulsations Handling by Synchronous
Motors/Generators .346
6.14 Asynchronous Starting of SMs and Their
Self-Synchronization to Power Grid 348
6.15 Single-Phase and Split-Phase Capacitor PM
Synchronous Motors 350
6.15.1 Steady State of Single-Phase Cageless-Rotor
PMSMs .350
6.16 Preliminary Design Methodology of a Three-Phase Small
Automotive PMSM by Example .354
6.17 Single Phase PM Autonomous A.C. Generator with Step–
Capacitor Voltage Control: A Case Study 361
6.17.1 Introduction 361
6.17.2 The Proposed Configuration Characterization .363
6.17.3 Sample Step Capacitor Results 365
6.17.4 Experimental Effort 365
6.17.5 Experimental Effort 370
6.18 Summary 370
6.19 Proposed Problems 376
References 378
Index 381
Index
A
AC distributed windings, 197–198, 370
cage rotor windings, 212
airgap flux density, 16, 121, 133, 149–165,
186–215, 237, 269–294, 310–318,
374–376
bar and ring resistances, 214
chording and distribution factor, 207
end ring and cage-bar currents, 214
factor components, 216
rotor cage geometry, 214
skewing factor, 214
total winding factor, 215
MMF space harmonics, integer q
chording factor, 212
linear current density, 122, 204
mmf distribution, 201, 203, 222, 312
peak value, 15, 33, 90, 204
winding distribution factor, 204
pole count changing ac 3-phase, 211
winding, 215–222, 244–251, 260–279,
287–375
practical one-layer ac 3-phase winding
bar (single turn) coils, 208
concentric coil phase belt, 208
identical (chain) coil phase, 208
self-induced emf angle shift, 207, 210
single-layer 24-slot, 4-pole winding, 207
slot-emf phasor star, 210
traveling magnetomotive force (MMF)
airgap flux density, 211–215, 237,
269–276, 294, 310–318, 356, 374–376
brush–commutator windings, 200
ideal multiphase MMF, 200
integer, 200–209, 279, 290
number of slots, 143, 146, 156, 193, 197,
200, 204, 290
two-phase ac windings, 211
active power, 11, 13, 16, 23, 44, 67–72, 76, 99,
109, 225–227, 235–236, 266, 271–272,
290–293, 317–321, 326, 328–332, 342,
363, 365, 374–375
active rotor electric machines
dc rotor and ac stator currents, 117
magnetic conergy, 117
matrix form, 87
motion equations, 333
primitive active rotor single-phase electric
machine, 117
rotor cage, 333–337, 347, 363, 375
airgap flux density
armature reaction, 132–134, 156, 163,
192–193, 318–320
leakage factor, 156
leakage flux, 32, 53–55, 90, 153–158,
216–218
linear curve, 159
magnetic field, 5–7, 19, 27–44, 51–57,
102–114, 120–126, 136, 139, 149–153,
158, 165, 190, 197, 216, 219–220, 244,
289–291, 332
mmf, 37, 53–55, 77, 81–82, 96, 118, 121–123,
132–135, 149–165, 198–222, 244–266,
283, 306–336, 374
electric machine design, 186
electromagnetic force (EMF), 30, 141
stator diameter, 192, 276, 355, 358
stator excitation MMF, 149
Ampere’s law
flux linkages and inductances, 53
magnetic field, 5–7, 19, 27–39, 44, 51–57,
112–123, 136, 158, 190, 216, 244, 289,
332
no-load magnetization curve, 62, 150–155,
217, 237
autonomous induction generator, 236–238, 326
autonomous synchronous generators, 322
characteristic curves, 177, 323
load curve, 322–330, 373–374
voltage equation, 127, 160, 174–177,
180–184, 325, 329, 350
voltage regulation, 51–52, 58, 68, 97, 107,
175, 291, 309, 326–328, 362–374, 377
Vs
(Is) load curves, 325–326, 373–374
no-load saturation curve, 322, 376
phasor diagram, 31, 66–83, 182, 227, 263,
317, 324–327, 343, 359–363, 377
rated current, 24, 33, 54, 63–67, 101–109,
171, 183, 205, 240, 253, 274, 285, 326,
352–366, 374
short-circuit curve, 322–324
test rig, 183–184, 227, 323–325
autotransformers, 4, 28, 96, 106
B
brush-commutator machines, 6, 20, 120, 139–149,
199
airgap flux density, 16, 121, 133, 149–159,
165, 192, 211, 237, 269, 294, 318, 356,
374
armature reaction, 132, 156, 163, 192,
318–320
stator excitation MMF, 149
armature windings
coil span, 146, 202, 209, 278382 Index
double winding, 142
phase shift angle, 144, 315, 329
simple lap windings, Ns = 16, 2p1 = 4,
144–156
simple wave windings, Ns = 9, 2p1 = 2,
146–156
commutation process, 158–160
brush-segment contact resistance, 160
definition, 44, 63, 182, 199, 234, 256, 344
efficiency, 11–24, 67–70, 98–108, 126,
159, 171–174, 182, 240–293, 342–378
electromagnetic power, 17, 97, 166–194,
224, 293, 343
electromagnetic torque, 12–17, 112,
166–194, 224, 271, 291–294, 321, 334,
343, 351, 377
excitation circuit equation, 167
excitation losses, 159, 167
rotor coil current reversal, 160
separate excitation, 171, 178
transient inductance, 167
dc brush PM motor, 183
artificial loading, 184, 272
characteristic curves, 177, 323
closed-loop control, 183
cogging torque, 113, 156, 183–191, 351
countercurrent braking, 171–174
electromagnetic power, 97, 166, 191–194,
224, 343
equivalent circuit, 32, 60–70, 93–107, 165,
221, 288, 321
iron losses, 59, 105, 181, 285, 343
pole flux, 141, 151, 166, 177, 215
self-excitation regenerative braking, 177
speed control methods, 169, 251
starting and speed control, 171
steady-state, 7, 31, 60, 89, 127, 180, 240,
288, 315, 354, 374
twin motors, 183
electromagnetic force (EMF)
armature reaction, 134, 156, 192, 318
brush emf, 165
compensation winding, 163–165
motion emf, 112, 163, 180
resultant nonuniform flux density, 164
electromagnetic torque, 224–225, 237, 291,
321, 334, 351, 374
electromagnetic transients, 87–88
sudden short circuit, 27, 51, 87, 91
equivalent circuit and excitation connection, 165
handheld universal contemporary motor, 182
instantaneous steady-state torque, 180
machine voltage equation, 180, 350
no-load magnetization curve, 62, 150, 217, 237
Ampere’s law, 54, 151, 199, 219
current density, 16, 33, 61, 122, 155, 204,
268, 357
magnetic flux line path, 151
pole body mmf, 154
rotor tooth mmf, 152
rotor yoke, 152, 187, 274, 282, 300
stator back iron, 149, 154, 276
torque, 6–24, 112–200, 235–306, 348–378
orthogonal (dq) model, 290
parameter estimation, 354, 375
preliminary design, 106, 186, 274, 354, 365
coil wire diameter, 189
copper losses, 24, 41, 62, 97, 189, 227,
299, 309, 359, 378
current density, 16, 38, 68, 101, 122, 155,
186, 192, 268, 357
PM stator geometry, 186
rotor diameter, 152, 186, 274
slot active area, 189
slot height left, 188
specifications, 274, 354
stack length, 24, 151, 186, 276, 294, 376
turns per rotor periphery, 188
silver-copper segments, 149
speed control, 181–182, 250, 291, 322, 350,
370
stator and rotor construction elements, 139
automobile engine-starter motors, 140
universal motor, 145–146
testing, 182, 271, 354
artificial loading, 184, 272
cogging torque, 113, 156, 183, 306, 351, 371
iron losses, 59, 105, 181, 227, 285, 294,
343
pole flux, 141, 150, 184, 215, 322
torque speed curve, 181, 243, 255
C
cage rotor windings, 212
airgap flux density, 121, 133, 149–186,
211–237, 269–318, 356
applications and topologies, 195, 297, 356
bar and ring resistances, 214
chording and distribution factor, 207
end ring and cage-bar currents, 214
factor components, 216
rotor cage geometry, 214
skewing factor, 214
total winding factor, 215
circuit models, 19, 22
cyclic inductance, 79, 320
D
dc brush PM motor, 183
artificial loading, 184, 272
characteristic curves, 177, 323Index 383
closed-loop control, 183
cogging torque, 113, 156, 183, 191, 306, 351,
365, 371
countercurrent braking, 171, 183
electromagnetic power, 97, 166, 171–194,
224, 256, 293, 343
equivalent circuit, 60, 93, 165, 221–295, 321
iron losses, 59, 105, 167, 181, 222, 227,
285, 341
pole flux, 184, 215, 322
self-excitation regenerative braking, 177
speed control methods, 169–171, 251
starting and speed control, 171–178
steady-state, 31, 60, 72–89, 127, 180, 226,
288, 320, 346, 374
current/speed curve, 169
ideal no-load speed, 169–193, 226
short-circuit torque, 169
speed/torque curve, 169
transients, 107, 169, 346, 354
twin motors, 183
distributed power systems, 22
structural diagram, 88
axis, 121, 157, 160–190, 315, 366, 377
E
electric machines
automotive electric motor applications, 21
electric energy, 111, 190, 328
coupled electric and magnetic circuits, 19
electric motor drive applications, 3
Faraday’s law, 22, 30, 39, 58, 106–112
generator/motor operation mode, 3
electromagnetic torque, 5, 12, 24, 112–116,
132, 194, 224, 271, 343, 374
fixed magnetic field machines, 5
brush-commutator machines, 20, 120, 135
magnetic flux density, 152, 190, 217
speed and power limitations, 6
high-frequency electric transformers, 22, 99
IEEE and IEC standards, 20
losses and efficiency, 101, 186
magnetic composite soft materials, 22
methods of analysis, 19
induction machine (IM), 6
nameplate ratings, 17
physical limitations and ratings, 14
electromagnetic rotor shear stress, 15
global cost function, 16
insulation materials, 23
power grid, 18, 46, 77, 86, 198, 228, 235, 262,
309, 336, 374
types of transformers, 3
electric transformers
autotransformers, 28, 96, 106
cores, 15, 34, 43, 113, 195, 234, 290, 356
Ampere’s and Faraday’s laws, 49
copper conductor, 45
critical conductor height, 51
dc current conductors, 45
laminated magnetic core vicinity, 48
magnetic field, 49–50
Poynting vector, 50
Roebel bar, 51–52
single-phase distribution transformer, 49
single-phase power transformer, 47
slot leakage and ac resistance, 50
stacking pattern, 49
three-phase power transformer, 47
instrument transformers, 102–103
magnetic core ac
coil airgap, 32
emf ratio, 35
equivalent magnetic circuit, 33–34
Faraday’s law, 34–35
flux (Gauss) law, 33
inductance, 34
magnetic circuit (Ampere’s) law, 32–33
magnetic core, 33
magnetic permeability, 35
soft magnetic materials, 33
magnetization curve and hysteresis cycle
differential permeability, 40–41
frequency and graphical representation, 39
incremental permeability, 40–41
magnetic permeability, 38, 40
normal permeability, 40–41
no-load steady state (I2 = 0)
core loss, 68
equivalent circuit, 67
magnetic saturation, 70–71
no-load magnetization curve, 69
no-load power, 68
phasor diagram and power breakdown, 67
permanent magnets, 41–42
power electronics
boost dc-dc converter, 106–107
contact-less battery charging system,
107–108
galvanic separation, 106
series-connected transformer, 107
static-power semiconductor-controlled
switches, 106
two stage ac-ac power electronics
converter, 107
preliminary transformer design
active material weight, 113
deliverables, 109
equivalent circuit, 113
losses and efficiency, 112
magnetic circuit sizing, 101–102
no-load current, 112384 Index
specifications, 108–109
windings sizing, 102–105
single-phase transformer, 31–32
circuit equations, core losses, 64–65
flux linkages and leakage inductances,
59–63
steady-state operation on load, 74–77
soft magnetic material losses
B-H curve, 45–46
core loss, 45, 47
eddy current losses, 43–44
hysteresis losses, 42–43
steady state and equivalent circuit
complex variables, 65
core loss series resistance, 66
input voltage, 65
load equation, 66
primary and secondary winding losses, 67
steady-state short-circuit mode, 71–73
three-phase transformers
general equations, 84–86
no-load current asymmetry, 82–83
paralleling, 91–92
phase connections, 78–81
unbalanced load steady state, 87–89
Y primary connection, 3-limb core, 83–84
transients
anti-overvoltage electrostatic transients,
102
electromagnetic (R,L) transients, 94–95
electrostatic (C,R) ultrafast transients,
99–102
forces, peak short-circuit current, 97–98
inrush current transients, 95–96
no load sudden short circuit, 96–97
windings
alternate windings, 57
concentric and biconcentric cylindrical
windings, 57
conductor strand, insulation paper lapping,
54–55
continuously transposed cable, 54–55
corrugated tank, 58
disc windings, 55–56
foil windings, 56
layer and helical windings, 55–56
oil circulation, 57
transformer tank and oil conservator, 57–58
turn-ratio limited range regulation, 56
types, 55
electromagnetic (active) power, 321
boundary conditions, 44, 94, 271
electromagnetic (R,L) transients, 87
electro-magneto-mechanical energy conversion,
112
electromechanical time constant, 248
electrostatic (C,R) ultrafast transients, 92
distributed capacitor model, 93–94
microsecond front voltage propagation, 93
single-layer winding, 93
wave equation, 94
end-connection leakage inductance, 218
energy conversion, 251, 298, 370
active rotor electric machines, 117
dc rotor and ac stator currents, 117
magnetic conergy, 117
primitive active rotor single-phase electric
machine, 117
coupling magnetic field, 111
cogging torque, 183
Faraday’s law, 31, 43, 58, 106–112
mechanical energy conversion, 112–113
stored magnetic energy, 112, 135, 190
electromagnetomotive force (emf), 112
linear electric machines, 123, 129
linear compressor coil-mover PM linear
motor, 128
linear oscillatory motor/generator, 125
loudspeaker/microphone, 126
three-phase linear flat synchronous
machine, 124
passive rotor electric machines, 114
coenergy, 113–116, 190
constant instantaneous torque, 123
magnetic saliency, 114
reluctance synchronous machine, 116
stepper reluctance motor, 116
switched reluctance machines, 297
traveling field electric machines, 122
equivalent bar resistance, 214, 280
F
Faraday’s law, 31, 43, 58, 106–112
electromagnetic induction, 2, 22, 97, 112
field circuit losses, 342
finite element method (FEM), 314
analysis, 19, 57–101, 251
electric machines, 314
magnetic flux lines, 55
fixed magnetic field machines, 5
brush-commutator machines, 120, 139–199, 322
magnetic flux density, 5, 62, 152, 190, 217
speed and power limitations, 6
G
Gauss law, 29, 267
H
hybrid electric vehicle (HEV), 22, 99
actuators, 22, 149, 298, 303Index 385
I
induction generator, 235, 253, 287, 326, 362
induction machines (IMs), 195
AC distributed windings, 197–198, 370
cage rotor windings, 212, 370
applications and topologies, 195, 297
autonomous generator mode, 236
capacitor split-phase induction motors, 262
dual capacitor IM, 263
equivalent impedances, 264
source voltage, 263
symmetrical components theory, 262
construction elements, 300
ball bearings, 197
single-phase supply capacitor, 196
slots, 196–221, 230, 268, 293, 304, 351,
370
wound rotor, 3-phase, 195
deep-bar and dual-cage rotors, 243–244
electromagnetic torque and motor
characteristics, 237
electromagnetic power, 224, 240, 293, 343
rated current, 24, 54, 63–71, 86, 171, 183,
205, 240, 274, 285, 327, 361, 376
rated slip, 234, 275, 293
rated speed, 171–175, 211, 262, 348
rotor cage losses, 240
stator resistance, 240, 279, 321, 354
steady-state characteristics, 241
torque vs. slip S, 239
electromagnetic transients, 87
ideal no-load operation, 226, 236
active power, 23, 44, 68, 225, 235, 266,
290, 321, 363
iron losses, 59, 105, 167, 181, 227–228
phasor diagram, 263, 317, 343
supersynchronous operation, 226
leakage inductance, 228
airgap flux density, 270
differential leakage stator inductance, 218
double-layer, full-pitch windings, 268
dynamic end effect, 269–271
end-connection leakage inductance, 218
end effect thrust, 271, 294
equivalent goodness factor, 270
flat geometry, 267
primary length, 270
rectangular slot leakage field, 219
secondary current density path, 269
single layer windings, 200, 220
slot geometrical permeance coefficient,
219
static end effect, 267
transverse edge effect, 268
on load operation, 27, 234
main inductance, 59–61, 216, 358
Carter coefficient, 149, 217, 276, 376
cyclic main (magnetization) inductance,
217
magnetic saturation factor, 199, 217
magnetization characteristics, 218
no-load motor operation, 232
one rotor phase, 260
one stator phase, 257, 292
copper losses, 260, 299, 344, 359, 371,
378
parasitic (space harmonics) torques, 244
asynchronous parasitic torques, 245
complex number variables, 224
electromagnetic power, 97, 293, 343
electromagnetic torque, 112, 115, 135,
166, 224
flux linkages, 53–54, 113, 222, 247
mmf space harmonics, 200
reduced rotor windings, 222
slot skewing, 245, 291
symmetric steady state, 224, 259, 320
synchronous parasitic torques, 245–247,
290
preliminary electromagnetic design, 28, 58,
375
efficiency and power factor, 241, 271, 279,
353, 375
electric circuit, 19, 46, 60, 106, 190, 216,
287
magnetic circuit, 27, 41, 76, 101, 120, 274,
292, 323
main specifications, 274
parameters, 287–290
starting current and torque, 194
realistic analytical model, 232, 274
regenerative and virtual load testing, 271
frequency mixing method, 272
speed control methods, 251
breakdown torque, 220, 230, 240, 276
critical rotor frequency, 254
short-circuit reactance, 293
soft starter, 181, 249
torque–speed curves, 255
variable frequency and voltage, 293
wound rotor, 253
split-phase capacitor, 263, 350
starting methods, 247
additional rotor resistance, 237, 250
direct starting (cage rotor), 248
two-phase ac windings, 211
unbalanced supply voltages, 255, 291
zero speed operation, 228
rotor (slip) frequency, 228, 285
short circuit impedance, 66, 81–85
single-phase zero-speed testing, 229
starting current, 230, 249, 282, 291
starting torque, 140, 230386 Index
interaction torque, 117, 237, 321
iron loss resistance, 285
L
lagging power factor, 318, 325, 363–370
asynchronous starting, 292, 346
linear compressor coil-mover PM linear motor,
128
linear electric machines, 129, 136
airgap flux density, 133
double-layer, full-pitch windings, 268
dynamic end effect, 269
end effect thrust, 271
equivalent goodness factor, 270
linear compressor coil-mover PM linear
motor, 128
loudspeaker/microphone, 126
BIL force, 126
mechanical resonance conditions, 127
steady-state harmonic motion, 127
tubular configuration, 123
primary length, 270
single layer windings, 200
load torque pulsations, 346
asynchronous torque, 346
damping coefficient, 348
mechanical resonance module, 347
proper (eigen) angular frequency, 347
M
magnetic fields
airgap, 2–34, 62, 99, 120, 132–140, 186–196,
215, 269–326, 356, 363, 374–376
magnetic circuit (Ampere’s) law, 29
magnetic core, 29–55, 96, 101–104, 167, 195,
300, 356
magnetic permeability, 29, 54
magnetic field distribution, 19, 149, 219
magnetic materials, 15, 29, 34–40
magnetization curve and hysteresis cycle, 34
differential permeability, 36
graphical representation, 35
incremental permeability, 36
magnetic permeability, 40, 54
normal permeability, 35
permanent magnets, 37, 114, 121, 132
soft magnetic material losses, 38
B-H curve, 41
core loss, 285
eddy current losses, 38, 77, 107–111,
285, 310
hysteresis losses, 35–38
motion equation, 333, 335
induction machine (IM)
anisotropic rotor, 9–10
asynchronous machine, 6
heteropolar magnetic flux density, 5–8
self-synchronization, 8, 348–350, 375
wound rotor, 6–9, 195–197, 227, 244–260,
287
mutual inductance, 117, 317
O
optimal design, 155, 190, 354
dc brush PM motor (ωb = 0), 183
active and reactive power, 44, 68, 326,
342, 365
instantaneous torque, 118, 123, 182
magnetic saturation, 251, 256, 276–278,
283–286, 291, 319, 336, 358, 363
motion-induced voltage, 161, 222
motion emf, 112, 163, 180
motion equation, 333
stator equation, 224
P
Passive rotor electric machines, 114
coenergy, 113–116
constant instantaneous torque, 123
magnetic saliency, 321
switched reluctance machines, 10, 116, 297
permanent magnet synchronous generators
(PMSGs), 298
phase coordinate model, 19
phase leakage inductance, 218, 320
phase voltage unbalance index, 256
phasor diagram, 35–36
PM synchronous and switched reluctance motors,
22
PM synchronous motors, 342, 350
electromagnetic torque, 343
interior PM rotor, 310, 319, 344
phasor diagram, 31, 66, 83, 182, 263,
317–327, 343, 359–364
pole changing winding, 211, 251, 291
pole pitch, 122, 145, 152, 163, 190, 198, 244, 276,
376
preliminary electromagnetic design, 28, 58, 116,
375
efficiency and power factor, 241, 271, 279,
353, 375
electric circuit, 19, 46, 60, 106–112, 190, 216,
274, 287
magnetic circuit, 19, 27, 76, 120, 274, 292,
323
airgap flux density, 275
Carter coefficient, 276
magnetic saturation, 276Index 387
magnetization reactance, 283
rated torque, 283
rotor diameter, 121, 152, 186, 274
rotor yoke, 284
stator back iron (yoke) height, 276
stator stack length, 276, 355, 376
stator wire diameter, 284
stator yoke weight, 284
tangential specific force, 15, 155, 186,
274, 355
tooth/slot pitch ratio, 276
top and bottom widths, 277
main specifications, 274
parameters
leakage reactances, 107, 281, 288, 374
reduction factor, 280
rotor aluminum bar resistance, 279
stator resistance, 236, 242, 279, 286, 321,
354
starting current and torque, 194, 282
preliminary transformer design
active material weight, 16, 105
equivalent circuit, 60, 87, 99, 106, 165, 177,
221, 229, 235–244, 288, 321–322
losses and efficiency, 11, 101, 186
magnetic circuit sizing, 101
no-load current, 62, 89, 96, 101, 217, 285
windings sizing, 102
filling factor, 102, 152, 192, 357
leakage reactance, 374
number of turns, 376
primary and secondary resistances, 104
primary emf, 102
radial width, 103
short-circuit rated voltage, 67, 97, 104
primitive active rotor single-phase electric
machine, 117
R
reactive power, 363, 374
reluctance synchronous machine (RSM), 9
S
secondary winding, 59–61, 74, 92, 112, 195
shaft power, 12–14, 234, 286, 334, 342, 374
single-phase and split-phase capacitor PM, 350
single-phase transformer, 27–28, 53–54, 58, 68,
87, 95
alternate windings, 52, 55, 57–58
Ampere’s law, 54, 151, 199, 219
cylindrical windings, 50, 55–58
definition, 44, 63, 182, 199, 234, 256, 344
primary and secondary mmfs, 53–55
resultant magnetic reluctance, 54
steady-state operation on load, 68
active and reactive power break down, 68
dual voltage single-phase residential
transformer, 71
skewing leakage inductance, 218, 220, 282
skin effect parameter, 282
soft magnetic material losses, 38
B-H curve, 41
core loss, 48, 52, 58–69, 76, 95–107, 171,
194, 225, 257, 283–285, 331, 352
eddy current losses, 38, 77, 107, 310
hysteresis losses, 35–38
soft starter, 179, 247–252
electromagnetic torque, 12–17, 112–116, 135,
166–180, 224, 235, 237, 271, 321, 351,
374, 377
phase coordinate model, 19
star–delta switch, 249
stator copper losses, 24, 227, 248
stator teeth weight, 285
stator winding factor, 278
stator (armature) windings, 300
four-pole PMSM windings, 308, 310
LCM, Ns and, 310, 312
single-phase tooth-wound machines, 312–313
switched reluctance motor (SRM), 310–312
TF-PMSMs, 312–313
types, 306–307
super high-frequency models, 375
airgap flux density, 16, 121, 133, 149–165,
186–199, 211–215, 269–276, 294,
310–318, 356, 374–376
parameters, 78–79, 98–107, 175–191, 228,
236, 244–245, 261–291, 315, 337, 358,
376–377
synchronous inductances, 306, 320
applications and topologies, 195
automobile alternators, 297
hard disks, 299
linear SMs, 299, 303
open cross section, 305
permanent magnet synchronous generators
(PMSGs), 298
power systems, 298, 318
special configuration PMSMs, 302
stepper machines, 297
switched reluctance machines, 297
armature reaction and magnetization
reactances, 318
d and q axes, 318
magnetization inductances, 319
nonsinusoidal airgap flux densities, 318
synchronous inductances, 320
autonomous synchronous generators, 322
load curve, 322–330, 373
no-load saturation curve, 322, 376
short-circuit curve, 322388 Index
basic static-and dynamic-stability concepts,
332
attenuation, 334
short-circuit clearing time, 334
synchronizing power, 333
torque, 334
large synchronous motors, 341
power balance, 68, 166–168, 232–234
speed/torque curve, 169, 175
load torque pulsations, 346
asynchronous torque, 245, 334, 346, 377
damping coefficient, 348
mechanical resonance module, 347–348
proper (eigen) angular frequency, 347
PM synchronous motors, 342
electromagnetic torque, 343
interior PM rotor, 319, 344
phasor diagram, 343
reluctance synchronous motor (RSM), 344
preliminary design methodology, 354
base current, 360
general specifications, 354
machine parameters, 358
maximum phase voltage, 355
maximum speed torque, 360
number of turns, 359
phasor diagram, 360
PM flux, 356–357
stator phase winding, 314
single-phase and split-phase capacitor PM, 350
classification, 120, 218
efficiency, 353
electromagnetic torque, 352
phasor diagram, 352–353
two-pole split-phase capacitor, 352
voltage equation, 350
stator (armature) windings, 300
digital synchronizers, 328
field current, 329
four-pole PMSM windings, 306, 308
reactive power capability curves, 329
single-phase tooth-wound machines, 309
SRM, 309
TF-PMSMs, 309
types, 304–305
V-shaped curves, 329–332
synchronous reactances, 330, 374
emfs and current phasors, 316
load, 316
mutual inductance, 19, 114–119, 216, 221,
291, 317, 359
phasor diagram, 317, 320–327, 343,
352–360, 377
unbalanced 3-phase current loads
impedance, 339
phase-to-phase short circuit, 339
pole-slipping method, 337
slip, 338
symmetrical components, 264, 336
total voltage, 337
T
three-phase linear flat synchronous machine, 124
three-phase transformers, 72
airgap flux density, 16, 121, 157, 199, 270,
294, 314, 376
brush–commutator windings, 200
general equations, 78
ideal multiphase MMF, 200
no-load current asymmetry, 75
number of slots, 143, 193, 290
paralleling, 66, 84
phase connections, 72, 234
connection schemes, 74
primary line voltage, 74
stator connection, 376
zig-zag (Z) connections, 72
unbalanced load steady state
direct and inverse components, 81
inverse transformation, 80
secondary neutral point potential, 82
symmetrical components superposition, 80
zero sequence current, 81
zero sequence impedance, 81–82
U
unbalanced load steady state
impedance, 339
phase-to-phase short circuit, 339
pole-slipping method, 337
slip, 196, 232, 251–262, 337, 346
symmetrical components, 80, 262, 336
total voltage, 337
V
voltage and current measurement transformers, 4
V-shaped curves, 329–332
W
wound rotor, 221
Z
zig-zag leakage inductance, 218


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