The Art and Science of Rotating Field Machines Design: A Practical Approach (eBook)

Vlado Ostovic has worked for leading machine manufacturers in Europe, as well as consulting for companies throughout the world, which hold electrical machine production as a part of their portfolio, such as those in the automobile, aerospace and wind industry. In theses roles he had an opportunity to gain insights into contemporary procedures for electromagnetic and thermal design of electric machines, and to improve them by applying more efficient computational algorithms.

Preface 6
Contents 12
List of Symbols 17
1 Introduction 19
1.1 General Considerations 20
1.2 Stationary Coils and Rotating Magnetic Field 21
1.3 Electromagnetic Field Equations and Boundary Conditions Field Distribution in Heteropolar Machines
1.4 Fluid Flow and Heat Transfer in Electric Machines Types of Cooling
1.5 Electric, Magnetic, and Thermal Properties of Materials for Electric Machines Classes of Insulation
1.6 Lumped Element Presentation of Electric, Magnetic, Thermal, and Fluid Flow Circuits 59
References 60
2 Windings 61
2.1 Active Part and End Winding Zone, Air Gap Winding Versus Coils in Slots, Slot Fill Factor 62
2.2 Single- and Double-Layer Windings, Coil Pitch, Skewing, Feasibility 66
2.3 Current Sheet and Air Gap MMF 73
2.4 Spatial Harmonics in Air Gap MMF, Slot-Opening Factor, Winding Factors 74
2.5 Air Gap Permeance, Carter Factor, Air Gap Flux Density Distribution 88
2.5.1 Uneven Air Gap and Homopolar Flux 95
2.5.2 Flux Density Distribution in Eccentric Air Gap of a Slotless Machine 97
2.5.3 Flux Density Distribution in the Air Gap of a Single-Slotted Machine 103
2.5.4 Magnetic Gears 124
2.5.5 Flux Density Distribution in the Air Gap of a Double-Slotted Machine 125
2.5.6 Flux Density Distribution in Eccentric Air Gap of a Single-Slotted Machine 134
2.5.7 The Influence of Saturation 135
2.6 Time-Dependent Excitation, Rotating Field Generation, MMF Wave Speed, Positive and Negative Sequence Components 137
2.6.1 MMF Waves Generated by Rotating DC-Fed Coil(s) on One Side of Air Gap 140
2.6.2 MMF Waves Generated by Symmetrically Wound Stationary Coils Carrying Symmetrical Alternating Currents on One Side of Air Gap 141
2.6.3 The Influence of the Number of Phases 150
2.6.4 MMF Waves Generated by Asymmetrically Wound Stationary Coils Carrying Asymmetrical Alternating Currents on One Side of Air Gap 153
2.6.5 MMF Waves Generated by Rotating Coil(s) Carrying Constant Frequency Current(s) 159
2.6.6 MMF Waves Generated by Rotating Coil(s) Carrying Variable Frequency Currents on One Side of Air Gap 161
2.6.7 Resulting MMF Waves Generated by Coils on Both Sides of Air Gap 163
2.6.8 Air Gap Flux Density Waves in a Single-Slotted Machine with Linear Magnetization Curve 165
2.6.9 Air Gap Flux Density Waves in a Double-Slotted Machine with Linear Magnetization Curve 167
2.6.10 Air Gap Flux Density Waves in a Slotless Machine with Nonlinear Magnetization Curve 169
2.7 Induced Voltage 171
2.7.1 Rotating Air Gap Flux Density 171
2.7.2 Elliptic Air Gap Flux Density 175
2.7.3 DC Flux Density Traveling at Angular Speed ? 177
2.8 Fractional Slot Windings: Fundamental and Principal Poles Single-Tooth Winding
2.9 Squirrel Cage Winding 189
2.10 Winding Failures 210
References 212
3 Magnetic Circuit 213
3.1 A Straightforward Method for the Solution of Flux Distribution in Current-Free Air Gap and Slots 213
3.2 A Straightforward Method for the Solution of Flux Distribution in Air Gap and Slots with Current-Carrying Conductors 221
3.3 A Straightforward Method for Determination of Magnetic Parameters of a Nonlinear Permeance 228
3.4 An Accelerated Procedure for the Solution of a System of Differential—Algebraic Equations 230
3.5 A Straightforward Method for the Solution of Flux Distribution in Magnets 235
References 243
4 Machine Parameters 245
4.1 DC Resistance of a Coil 246
4.2 Air Gap Inductance of a Coil in a Machine with Constant Air Gap Width 247
4.3 Air Gap Inductance of a Coil in a Machine with Variable Air Gap Width—Rotational Harmonics of Concatenated Flux 254
4.3.1 Salient Pole Rotor 264
4.3.2 Slotted Rotor 273
4.4 Mutual Inductance Between Windings in a Machine with Cylindrical Rotor 274
4.5 Slot Leakage Inductance Due to Transverse Field 278
4.5.1 Magnetic Energy Accumulated in One Slot 278
4.5.2 Magnetic Energy Accumulated in All N Slots 280
4.6 End Winding Leakage Inductance 282
References 283
5 Skin and Proximity Effect 284
5.1 Analytical Solution for Current Density Redistribution in a Solid Rectangular Conductor in a Slot as a Result of Alternating Leakage Flux: One-Dimensional Skin Effect 285
5.2 Analytical Solution for Current Density Redistribution in an Arbitrarily Shaped Solid Conductor in a Slot as a Result of Alternating Leakage Flux 297
5.2.1 Exact Solution 298
5.2.2 Approximate Solution 302
5.3 Analytical Solution for Current Density Redistribution in a Solid Rectangular Conductor in a Slot as a Result of Impressed Alternating Leakage Flux: One-Dimensional Proximity Effect 306
5.4 One-Dimensional Skin and Proximity Effect in Solid Conductors of a Coil in a Slot: Average Values of Skin Effect Factors for All Conductors in a Slot and for All Slots of a Phase 312
5.5 Coil Manufacturing Techniques for Suppression of Current Redistribution Due to Skin Effect: Roebel Bar, Ringland Bar, Willyoung Bar, Strand Transposition 314
5.5.1 Multi-turn Coil with Straight Strands 315
5.5.2 Multi-turn Coil with All Strands Twisted 318
5.5.3 Multi-turn Coil with Arbitrarily Twisted Strands 319
5.5.4 Transposed Strands Within a Slot: Roebel Bar, Ringland Bar, Willyoung Bar 323
5.6 Analytical Method for the Determination of Three-Dimensional Proximity Effect in Strands in the End Winding Zone Circulating Currents
5.7 Skin Effect in a Ferromagnetic, Conducting Half-Space 324
5.8 The Influence of Saturation on Skin Effect in Iron 328
5.9 Skin Effect in a Thin Plate 329
5.10 Skin Effect in a Solid Ferromagnetic Cylinder 330
5.11 Losses in Surface-Mounted Permanent Magnets 332
References 332
6 Force and Torque 333
6.1 Magnetic Field as a Medium in Which Electromechanical Energy Conversion Takes Place, the Role of Accumulated Magnetic Energy 334
6.2 Shear Force on Contact Surfaces Between Media with Different Permeabilities 335
6.3 Force Due to External Field Acting on Current-Carrying Conductors in Slots of Electric Machines 342
6.4 Torque as a Function of Air Gap Quantities 343
6.4.1 Constant Air Gap Width 344
6.4.2 Variable Air Gap Width 348
6.5 Spectral Components of Torque in a Constant Width Air Gap 351
6.5.1 Symmetrically Wound Polyphase Machine Fed Symmetrically with Sinusoidal Currents 351
6.5.2 Symmetrically Wound Machine Fed with Sinusoidal Unbalanced Currents 362
6.5.3 Single-Phase Operation of a Rotating Field Machine 367
6.6 Spectral Components of Torque in a Machine with Uneven Air Gap: Slotting, Salient Poles, and Rotor Eccentricity 372
6.7 Side Effects of Accumulated Magnetic Energy: Radial Air Gap Force, Forces on Conductors in Slots and on Slot Wedges 376
6.7.1 Unbalanced Magnetic Pull Caused by Rotor Eccentricity 380
6.7.2 Radial Forces on Conductors in Slots 381
6.8 Forces on Conductors in End Winding 383
6.9 Torque as a Function of Terminal Quantities 384
6.10 A Method for Direct Measurement of Electromagnetic Torque in Large Synchronous Machines 390
References 391
7 Thermal Design of Rotating Field Electric Machines 392
7.1 Types of Cooling 393
7.2 Rated Torque and Rated Power 394
7.3 Hydraulic Resistances and Fan Curves 395
7.3.1 Friction Factor for Coolant Expanding in Axial Direction Through Air Gap 396
7.3.2 Pressure Loss Coefficients for Radial Cooling Ducts 398
7.3.3 Pressure Loss Coefficients for End Winding with Form-wound Coils 399
7.3.4 Fan Curve 400
7.4 Coolant Distribution in Electric Machines, Pressure, and Volumetric Flow Rate in Elements of Its Hydraulic Network 401
7.5 Finite Difference Solution of Temperature Distribution in Electric Machines—Thermal Node Potential Equations 405
7.6 Thermal Networks of Electric Machines and Methods for Their Solution 408
7.7 Transient Heating of a Hollow Conductor 417
References 424
8 General Principles of AC Machine Design 425
8.1 Introduction 425
8.2 Sizing Equations of an Induction Machine 426
8.3 Sizing Equations of a Synchronous Machine 438
References 443
Appendix 444
A.1 Orthogonal Functions 444
A.2 Periodic Functions of Time 452
A.3 Power Factor 463
Outline placeholder 1
A.3.1 Field MMF Necessary to Operate Wound Rotor Synchronous Machine at a Given Power Factor 463
A.3.2 Power Factor and Magnetic Energy Demand of a Permanent Magnet Synchronous Machine 465
A.3.3 Power Factor of an Induction Machine—The Influence of the Number of Machine Poles 469
A.4 Efficiency 471
Index 473