Table Of ContentENGINEERING
ELECTRODYNAMICS
Electric Machine, Transformer,
and Power Equipment Design
J a n u s z Tu row s k i
Ma re k Tu row s k i
ENGINEERING
ELECTRODYNAMICS
Electric Machine, Transformer,
and Power Equipment Design
Boca Raton London New York
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To Our Family
Contents
Preface....................................................................................................................xvii
Authors ................................................................................................................. xxiii
List of Symbols ....................................................................................................xxvii
Abbreviations of Names of Computer Methods ...................................................xxxi
Chapter 1 Methods of Investigation and Constructional Materials ......................1
1.1 Methods of Investigations ..........................................................1
1.2 Constructional Materials ...........................................................4
1.2.1 Structure and Physical Properties of Metals ................4
1.2.1.1 Atomic Structure ..........................................5
1.2.1.2 Ionization ......................................................9
1.2.1.3 Crystal Structure of Metals ..........................9
1.2.1.4 Electrical Conductivity and Resistivity
of Metals ..................................................... 10
1.2.1.5 Infuence of Ingredients on Resistivity
of Metals ..................................................... 13
1.2.1.6 Resistivity at Higher Temperatures ............ 14
1.2.1.7 Thermoelectricity ....................................... 15
1.2.1.8 Thermal Properties ..................................... 17
1.2.1.9 Mechanical Properties ................................ 18
1.2.1.10 Hall Effect and Magnetoresistivity of
Metals .........................................................22
1.2.2 Superconductivity .......................................................24
1.2.2.1 Superconductor Era in Electric
Machine Industry ........................................30
1.2.3 Magnetic Properties of Bodies (Ferromagnetism) ..... 31
1.2.3.1 Magnetic Polarization and Magnetization ....31
1.2.3.2 Ferromagnetics, Paramagnetics, and
Diamagnetics .............................................. 32
1.2.3.3 Atomic Structure of Ferromagnetics ..........34
1.2.3.4 Zones of Spontaneous Magnetization ........36
1.2.3.5 Form of the Magnetization Curve .............. 37
1.2.3.6 Hysteresis .................................................... 39
1.2.3.7 Superposition of Remagnetization Fields ... 52
1.2.3.8 Amorphous Strips ....................................... 52
1.2.3.9 Rotational Hysteresis .................................. 53
1.2.3.10 Types of Magnetization Curves ..................54
1.2.3.11 Curie Point ..................................................54
1.2.3.12 Nonmagnetic Steel ...................................... 56
vii
viii Contents
1.2.3.13 Infuence of Various Factors on
Properties of Magnetic Materials ............... 57
1.2.3.14 Types of Magnetic Permeability .................60
1.2.3.15 Permeability at High Frequencies .............. 62
1.2.3.16 Magnetic Anisotropy ..................................64
1.2.3.17 Magnetostriction .........................................66
1.2.3.18 Demagnetization Coeffcient ...................... 67
1.2.4 Semiconductors and Dielectrics .................................69
1.2.4.1 Hall Effect in Semiconductors .................... 72
Chapter 2 Fundamental Equations of Electromagnetic Field .............................77
2.1 Primary Laws and Equations of Electromagnetism ................77
2.2 Formulation and Methods of Solution of Field
Differential Equations .............................................................84
2.2.1 Finding of Field Function ...........................................84
2.2.2 Classifcation of Field Equations ................................85
2.2.3 Boundary and Initial Value Problems of
Electrodynamics .........................................................87
2.2.4 Auxiliary Functions and Vectors ...............................90
2.2.4.1 Electric and Magnetic Scalar
Potentials.....................................................90
2.2.4.2 Magnetic Vector Potential
A and the Scalar Potential
V of Electromagnetic Field
(Electrodynamic Potentials) ....................... 91
2.2.4.3 Electric Vector Potential T ..........................95
2.2.4.4 Hertz Vector P ............................................95
2.2.4.5 Maxwell’s Stress Tensor T . 96
2.2.5 Methods of Solution of Field Equations .....................97
2.3 Anisotropic Media ...................................................................99
2.4 Nonlinear Media .................................................................... 103
2.4.1 Nonlinear Permittivity and Resistance .................... 103
2.4.2 Nonlinear Magnetic Permeability ............................ 104
2.5 Fundamental Equations of Magnetohydrodynamics
and Magnetogasdynamics ..................................................... 106
2.5.1 MHD Generators ...................................................... 110
2.5.2 Electric Machines and Apparatus ............................ 111
2.6 Electrodynamics of Superconductors .................................... 112
2.7 Electrodynamics of Heterogeneous Media............................ 114
2.8 Electrodynamics of Semiconductor Devices ......................... 114
2.9 Electrodynamics of Electrochemical Systems ...................... 115
2.10 General Wave Equations ....................................................... 117
2.10.1 Wave Equations in Metal ......................................... 118
2.11 Fourier’s Method ................................................................... 119
2.12 Wave Equations in Cylindrical Coordinates ......................... 121
Contents ix
2.13 Plane Wave ............................................................................ 123
2.13.1 Plane Wave in a Dielectric ....................................... 125
2.13.2 Plane Wave in a Conducting Half-Space.................. 129
2.13.3 Equivalent Depth of Wave Penetration and
Impedance of Solid Conductors ............................... 133
2.13.4 Field Diffusion into a Conductor .............................. 137
2.14 Refection and Refraction of Plane Wave .............................. 139
2.14.1 Boundary Conditions ............................................... 139
2.14.2 Refection and Refraction of a Perpendicular
Plane Wave ............................................................... 141
2.14.3 Near and Far Fields .................................................. 142
2.14.4 Oblique Refection, Refraction, and Guiding
of a Wave .................................................................. 143
Chapter 3 Transfer and Conversion of Field Power .......................................... 147
3.1 Poynting’s Theorem: Poynting Vector ................................... 147
3.2 Penetration of the Field Power into a Solid Conducting
Half-Space ............................................................................. 150
3.3 Power Flux at Conductors Passing through a Steel Wall ...... 153
3.4 Power Flux in a Concentric Cable and Screened Bar............ 156
3.4.1 Factors of Utilization of Constructional Space ........ 157
3.5 Power Flux in a Capacitor, Coil, and Transformer ................ 157
3.6 Power Fluxes and Their Conversion in Rotating
Machines ............................................................................... 160
3.6.1 Power Flux of Electromagnetic Field in Gap
of Induction Machine ............................................... 160
3.6.2 Power Flux of Electromagnetic Field in Air Gap
of Synchronous Machine .......................................... 161
Chapter 4 Screening of Constructional Parts.................................................... 165
4.1 Types and Goals of Screening and Shunting ......................... 165
4.2 Magnetic Screens .................................................................. 167
4.2.1 Spherical and Crosswise Cylindrical Screens .......... 167
4.2.1.1 Magnetic Screening of a Double-
Conductor Line ......................................... 170
4.2.2 Longitudinal Magnetic Screens ............................... 171
4.3 Electromagnetic Screens: Wave Method of Modeling
and Calculation ...................................................................... 174
4.3.1 Practical Convenience at Application of
Wave Method of Calculation .................................... 174
4.3.2 Penetrable (Translucent) Screen with a One-
Sided Incident Wave ................................................. 175
4.3.2.1 Thin Screens ............................................. 179
4.3.2.2 Thin Screens in Dielectric ........................ 181
