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عدد المساهمات : 18961 التقييم : 35389 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Electric Machines - Steady State and Performance with MATLAB الخميس 21 أكتوبر 2021 - 22:26 | |
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أخواني في الله أحضرت لكم كتاب Electric Machines - Steady State and Performance with MATLAB Second Edition Ion Boldea and Lucian N. Tutelea
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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