Index
A
Acceptors, 71
ACs, see see Alternating currents (ACs)
ADC, see see Analog to-digital converter (ADC)
Agarwal method of linearization, 297, 342
AI, see see Artificial Intelligence (AI)
Air gap
cup-type rotor, 315
demagnetization action, 68
electromagnetic field power flux in, 161–163
endwindings in permeable wall, 263
real and ideal, 278
Alternating currents (ACs), 12
electromagnetic screens, 217
hysteresis loop, 44
mirror image coefficients, 248–250
nonmagnetic metal mass, 404
proximity effect, 323
quasi-permeability, 64
solid steel elements, 475
conductivity, 15
electromagnetic screens, 200
properties, 22
recrystallization, 14
thick screens, 182
wavelength and equivalent depth, 134
Amorphous strips, 40, 44, 52, 53
ASM, 434
division of transformer, 371
Ampere-turns shifting method (ASM), 434
Ampere’s law, 80, 234, 395, 447
Analog to-digital converter (ADC), 481
Analytical-numerical methods (ANM), 98, 370
classical and modern, 403
power transformer steel parts, 376
single-phase turrets, 433, 434
stray losses calculation, 375
Analytical methods, electric machine, 277–288
Analytical prolongation method, 269–271
Epstein iron loss measurement, 451, 454
FEM, 98
interactive design, 99, 203, 205, 288
MFN, 98
powder figures, 37
wave for screen calculation, 175, 273
Anisotropic media, 99–103; see see also Nonlinear media
Anisotropic transformer sheets, 65
metallic glass amorphous strips, 48
per-unit iron losses plots, 47
symmetric hysteresis loops, 45
Anisotropy
constant, 66
of crystals, 10
ANM, see see Analytical-numerical methods (ANM)
Annealing design, 14, 20, 44, 425
“Anomaly” of eddy currents, 226
Approximation
of magnetization characteristics, 331–335
of magnetization curve, 49, 420, 448
of recalculated characteristics, 335–337
Artificial Intelligence (AI), 4, 272
ASM, see see Ampere-turns shifting method (ASM)
Atomic structure of metals, 5–9
Austenite, 56
Auxiliary functions, 90
electric and magnetic scalar potentials, 90–91
electric vector potential, 95
magnetic vector and scalar potential, 91–95
Maxwell’s stress tensor, 96–97
Azimuthal quantum number, 6, 7, 34
B
Band, 10
energy, 10
forbidden, 70
semiconductor, 71
Bar field, 264
flux density distribution, 266
Bars and conductor wires
busbar screen connections, 237
coefficient of reflexive interaction, 230
conformal mapping method, 233
cylindrical screen, 229
design programs, 224
Eddy currents, 220
electromagnetic screens, 220
in generator unit systems, 231
geometric dependences, 234
Hankel’s functions, 221
isolated screens, 233
power losses in screen, 225–228
proximity effect, 232
relative current densities, 235
screen damping, 231
screening of, 219
BEM, see see Boundary element method (BEM)
Bessel function, 275
equations, 123
Bloch walls, 37
Bohr magneton, 35
Boltzmann constant, 15
Boltzmann transport equation (BTE), 115
Boundary element method (BEM), 437
Boundary layers, see see Bloch walls
Bridge systems
high-voltage, 472
with mutual inductance, 471
power and induction impedances, 470
power factor, 473
Turowski’s compensation wattmeter, 470
BTE, see see Boltzmann transport equation (BTE)
Bushing field, 261
currents dynamic mirror image, 261–262
field on cover surface, 262–264
Bushing turrets, 432
C
CAD, see see Computer-aided design (CAD)
CAE system, see see Computer-aided engineering system (CAE system)
CAM system, see see Computer-aided manufacturing system (CAM system)
Carlit layer, 65
Carter’s coefficient, 277, 315
Characteristic of magnetization, 27
demagnetization, 46, 332, 337, 354
Chemical diffusion processes, 104, 107
Closed screens, 165
Coefficient of thermal expansion (CTE), 18, 20
Cold-rolled transformer sheets, 65, 66
Collision resistivity, see see Phonon resistivity
Commutation magnetization curve, 44
Compensation wattmeter, 467, 468, 470
Competitiveness, 2
Complex permeability, 62
Complex permeability, equivalent, 63
Computer-aided design (CAD), 3
Computer-aided digital measurement methods, 481
Computer-aided engineering system (CAE system), 3
Computer-aided manufacturing system (CAM system), 3
Concentric cable, power flux in, 156, 157
Concurrent engineering, 4
Conduction band, 10
Conductivity
equation, 86
Conductor
cryoconductive, 30
Conformal mapping method, 233
Constructional materials, 4
atomic structure, 5
crystal structure of metals, 9
electrical conductivity and resistivity, 10
hall effect and magnetoresistivity, 22
influence of ingredients on resistivity, 13
ionization, 9
mechanical properties, 18
metals, structure and physical properties, 4, 5
resistivity at higher temperatures, 14
semiconductors and dielectrics, 69–73
thermal properties, 17
thermoelectricity, 15
Contributed resistance, 320
Copper
electrical, thermal, and chemical properties, 18
Cost effectiveness of abandoning, 440–441
Cost of risk (CR), 439
Coulomb forces, 107
Cover plate
with nonmagnetic slits inserts, 302–305
CR, see see Cost of risk (CR)
Critical distance of tank wall, 483, 488
Cryogenic liquids, 28
Crystal structure of metals, 9–10
CTE, see see Coefficient of thermal expansion (CTE)
Curie motor, 54
permanent magnets, 57, 73, 414, 416
temperature, 54
Cylindrical conductor skin effect coefficient, 321
Cylindrical coordinate systems, 121–123
D
d’Alambert’s equation, 92
DC, see see Direct current (DC)
DC field theory to AC application, 247
AC mirror image coefficients, 248–250
experimental verification, 248
quasi-permeability, 247
Dead phase, 327
Debye temperature, 12
Deep-slot induction machine
trapezoidal and bulb slots, 275–277
de l’Hospitale rule, 364
Demagnetization, 54
factor, 68
Diamagnetic bodies, 34
Differential permeability, 61
Dipole, 261
impedance, 320
loops of, 256
Dirichlet, 88
Domains, 36
complementary, 443
curie point, 54
ferromagnetic materials, 36, 37
Donors, 71
Doping-based conductivity, 71
Double-layer conductor, 237
Double Fourier’s series, 270, 358
Drude’s model of conductivity, 11
Dynamic images, 248
Dynamic permeability, see see Differential permeability
E
anomalies, 50
flow, 371
linear density, 329
methods, 482
Effective complex permeability, see see Complex permeability, equivalent
Electrical steel, 289
flux expulsion coefficient, 290–293
insulation coefficient, 289–290
reactive power consumption, 296–298
Electric charge images method, 246
Electric field intensity measurement, 477–479; see see also Magnetic field intensity measurement
Electric machines
commutator bars of, 20
field in gap, 277
graphical-numerical methods, 278–279
manganic steels, 56
rotational remagnetization, 53
vector potential T, 95
Electric scalar potentials, 90–91
Electric vector potential, 95
Electrodynamic systems, forces in, 395
calculation of, 395
circumferential flux density, 409
course of flux density lines, 405
Euler–Lagrange equations, 397
examples, 411
field and forces calculation, 406
flux density in slot, 410
forces in slot, 407
Hamilton’s Principle equations, 397
iron saturation influence, 408
Maxwell’s stress tensor, 398
nonlinear 2-D FEM model, 409
ponderomotive forces, 399
reluctance forces and torques, 412–416
slotted part of windings, 405
virtual work, 396
Electrodynamics
of electrochemical systems, 115–117
heterogeneous media, 114
of semiconductor devices, 114–115
Electroflow field, 84
Electromagnetic compatibility (EMC), 115
Electromagnetic field
field differential equations solution, 84–97
MHD and magnetogasdynamics, 106–112
reflection and refraction, 141–145
Electromagnetic field power flux, 161
capacitive load, 162
ideal inductive load, 162, 163
motion in synchronous machine, 162
Electromagnetic screens, 165; see see also Magnetic screens
current density distribution, 180
eddy-current reaction, 176
field and current density distribution, 184
internal reflections, 183
magnetic field distribution, 178
magnetic field strength, 177
penetrable double-sided screens, 182
penetrable screen, 175
reflection of, 179
thick screens, 182
Electromagnetic tail, 111
Electromagnetism, 77
Biot–Savart law, 81
Faraday’s formulation, 81
Green’s Theorem, 83
Stokes’ theorem, 80
Electromotive force (EMF), 158, 279, 482
Electron-dominated n-type semiconductor, 71, 72
electron-volts (eV), 9
Electron conductivity, 10
intrinsic conductivity, 71
of semiconductor, 70
Electron gas, 9
metal conductors, 17
permeability, 62
valence electrons, 11
Electron octet, 70
Electron thermoemission, 11
Electronic work function, 11
Electrostatics, 83
EMC, see see Electromagnetic compatibility (EMC)
EMF, see see Electromotive force (EMF)
Endwinding field in electric machines, 258
constructional elements influence, 261
mirror image, 259
Energy methods, 98
Error function, 137
Euler-Lagrange equations, 395, 396, 397, 403
eV, see see electron-volts (eV)
Experimental investigation methods, 439
cost-effectiveness dependence, 441
electrodynamic similarity theory, 442–448
electromagnetic coupled systems, 443
electromechanical coupled systems, 443
experimental verification, 439
high current lines modeling, 450–451
induction heating device modeling, 448–450
industrial investigations profitability, 440
metal elements diagnostics, 481–482
transformers modeling, 451–454
Expert approach
industrial power transformers, 272
RNM-3Dshell program, 437
F
Faraday’s formulation, 81
Far radiation field, 142
FDM, see see Finite difference method (FDM) FEM-2D tool, 99
analytical methods, 98
calculations effect, 489
differential approach, 273
physical models, 281
three-dimensional computer analysis, 203
FEM, see see Finite element method (FEM)
Ferraris motors, 315
comparative scale, 69
demagnetization curve, 48
permanent magnets, 49
Ferromagnetic bodies, electromagnetic phenomena in
magnetization characteristics approximation, 331–337
power losses in transformer steel covers, 352–354
stray loss calculation, 354–367
stray loss dependence, 349–352
Ferromagnetics
atomic structure, 31
bodies, 33
materials, 31
resonance, 67
Ferromagnetism, see see Magnetic properties of bodies
Fick’s law of diffusion, 116
Field differential equation solution, 84
auxiliary functions and vectors, 90–97
example, 97
finding of field function, 84–85
Field power, transfer and conversion of
field components, 153
penetration into solid conducting half-space, 150–152
power flow through, 155
Poynting vector distribution, 156
Finite difference method (FDM), 98, 281
Finite element method (FEM), 98
Flow, see see Magnetomotive force (MMF); Flow network method (FNM), 98
FNM, see see Flow network method (FNM) Foerster’s probe, 482
experimental verification, 439
double, 358
RNM-3D method, 272
Fredholm’s equations, 321
Frölich–Kenelly law, 48
G
Gauss error function, see see Error function
Gauss errors integral, 137
Gaussotrons, 72
General electric co. (GEC), 382
Generalized Power Density Vector, 149
Generators, screening in
electromagnetic screening, 217, 218
isotropic sheets, 65
periphery flange, 218
windings and conductors, 217
Gibbs’s correction coefficient, 314
Grain-oriented sheets, see see Anisotropic transformer sheets
Graphical-numerical methods, 278–279
Green’s Theorem, 83
H
Half-closed screens, 165
magnetic circuit, 73
magnetoresistance, 12
in metals, 24
Hamilton-84 program, 403
Hamilton package, 443
electrodynamic transient forces, 403
mathematical modeling, 442
principle, 98, 395, 396, 397, 443
Hamilton’s differential operator, 78
Hankel functions, 123
Hankel problem, 89
Hard magnetic materials, 33
Hard superconductor, see see Soft superconductor Hardening coil design, 425
Heat distribution
irregularity coefficient of, 427
power losses and temperature, 427
thermal conductivity, 428
transformer cover, 429
Heat irregularity coefficient, 427–430
Heisenberg quantum theory, 36
Helmholtz equation, 86
Hermite’a FEM solution, 393
Heterogeneous media, electrodynamics of, 114
High-current lines, 320
currents induced in steel walls, 328–330
High-temperature superconductors, 28
High current bus-bars, 431
leads, 432
High voltage (HV), 280
Hole-dominated p-type semiconductor, 71, 72
Holes, 70
Hydrodynamic equations, 109–110
Hydrogen atom, 5
Hysteresis loop, 39
coefficient, 52
demagnetization characteristics, 46
in electronics and power electronics, 42–43
energy factor, 47
flux density of saturation, 39, 40–41
hard magnetic material, 45, 46
hysteresis losses, 51
magnetization curve shape, 49
metallic glass amorphous strips, 48
plots of per-unit iron losses, 47
symmetric family, 45
working process of iron, 44
Hysteresis losses, 51, 293–294
rotational, 53
I
IACS, see see International Annealed Copper Standard (IACS)
Ideal magnetization curve, 54
Ideal permeability, 61
Ideal resistivity, 12
Ideal superconductor, 25; see see also Nonideal superconductor
IEC, see see International Electrotechnical Commission (IEC)
Impenetrable screens, 166
IMT, see see Institute of Material Technology (IMT)
Induction heating device modeling
losses and effective power, 450
objective of modeling, 448, 449
principles of, 448
Induction heating principles, 317
curie point, 320
current density distribution, 318
current density ratio, 319
power density volumetric distribution, 318
Induction machine, electromagnetic field, 160, 161
Induction motor
current density in, 214
deep-slot, 192
power losses, 215
radial flux density, 214
rotation torque, 215
two-phase, 315
Induction motors cap motor, 315
computation programs, 213
current density in, 214
density of forces, 212
double-layer screened rotor, 210
equivalent circuit of, 314
field equations, 211
fundamental equations, 209
Maxwell’s equation, 313
radial flux density, 214
in rotating field, 309
rotation torque and power losses, 215
rotor parameters calculation, 310
six-layer motor calculations, 213
solid rotor, 308
Inductivity, 324
Industrial verification, 496–497
Innovativeness, 2
Institute of Material Technology (IMT), 49
Interactive design, 99, 203, 205, 288
International Annealed Copper Standard (IACS), 14
International Electrotechnical Commission (IEC), 401
Intern. Sympos. on Electromagn Fields (ISEF), 413, 414, 422
Inverse synthesis design, 425
Inverted transformer model, 451, 452, 453
Investigation methods, 1
classification of, 2
structure and physical properties, 4
J
K
Kirchhoff’s equations, 84
base, 4
engineer, 3
Kramp’s function, 334
L
Lagrange state function, 443
Laplace function
single-harmonic function, 89
Laplacian operator, 79
Laser irradiation, 50
Law of flow, see see Ampere’s law
Łazarz M. ASEA formula of tank loss, 374, 379–380
Leakage field
analytical prolongation method, 269–271
in electric machine gap, 277–281
multiple mirror images application, 267–269
slot in deep-slot induction machine, 273–277
in transformers, 267
Legendre transformation, 396
Lehman’s method, 98
Linearization of steel, 136–137
Local heating, 417
coefficient of heat removal, 419
detection of, 422
electromagnetic criteria, 417
irregularity coefficient of heat distribution, 427–430
J. Turowski’s approximation, 420
permissible current in bushings, 431–434
permitted current determination, 425
permitted values, 421
perpendicular penetration of field lines, 424
thermal dissipation of eddy-current, 418
transformer cover plates, 430
Local overheating
bushing turrets, 432
lack of screens, 194
Longitudinal magnetic screens, 171
lines of magnetic field, 171
magnetic screening power coefficient, 173
reluctance of solid conductor, 172
of solid steel, 171
Lorentz number, 17
condition, 92
forces of volume density, 78
Low-temperature superconducting generator (LTS generator), 31
Low voltage (LV), 280
M
MacDonald function, 123
Machine learning, 3
Magnetic anisotropy, 64, 65, 66
Magnetic constant, 32
Magnetic field intensity measurement, 477
Magnetic flux lines diagram, 247
Magnetic hysteresis
demagnetization curves, rare earth, 44, 54, 67
materials properties, 31
Magnetic materials
anisotropy, 102
in electronics and power electronics, 42–43
Magnetic permeability
nonlinear, 104
permalloys, 46
thick metal plates, 419
variability of, 337
demagnetization field intensity, 68
in hard magnetic materials, 39
rotation of, 45
rotational hysteresis, 53
Magnetic properties of bodies, 31
demagnetization coefficient, 67, 68–69
distribution, 35
in electronics and power electronics, 42–43
energy of exchange dependence, 36
ferromagnetic and paramagnetics, 32–34
flux density reduction, 60
hysteresis loop, 39, 44, 45, 46, 47, 48–52
magnetic anisotropy, 64, 65, 66
magnetic material properties, 57, 58, 59
magnetic polarization and magnetization, 31–32
magnetization curve, 37, 38–39, 54
nonmagnetic steel, 56
permeability at high frequencies, 62–64
remagnetization field, 52
Magnetic quantum number, 6
Magnetic scalar potentials, 90–91
Magnetic screens, 165
calculation of spherical, 168
crosswise, 170
curves, 195
double-conductor line, 170
effectiveness of, 169
empty iron sphere, 167
in external magnetic field, 166
longitudinal magnetic screens, 171–174
non-linear, 5
Magnetic strap, 476
Magnetic vector potential, 91–95
Magnetic voltage measurement, 475
Magnetization characteristics approximation, 331
approximating equations, 333
approximation, 331
Kramp’s function, 334
recalculated characteristics, 335–337
standard magnetization characteristic, 332
Magnetization curve, 37, 38–39
approximation formulae, 49
measurement, 476
Magnetohydrodynamics (MHD), 106–107
electric machines and apparatus, 111–112
hydrodynamic equations, 109–110
Reynold’s Magnetic Number, 110
Magnetomotive force (MMF), 80, 279
Magnetoresistance, 12
Magnetostatics, 83
Manganese (Mn), 36
Manganic steels, 56
Matlab, 443
Matthiessen’s rule, 12
Maxwell theory, 375
steel linearization by Agarwal, 297, 342
thermometric loss measurement, 458
Maxwell’s stress tensor, 96–97, 398
Maxwell’s surface equations, 140–141
Mechanical properties of metals, 4, 18–22
Mechatronic engineering, 4
Mechatronics, 4
Metal resistivity, see see Resistivity, metal
Metallic glass, 46
Metals, electromagnetic phenomena in
electromagnetic wave reflection application, 289
induction heating principles, 317–320
induction motor solid rotor, 308–315
power losses in steel covers, 302–305
single-phase bushing system, 298–300
three-phase bushing system, 300–301
transient induced processes, 305–308
Metals, structure and physical properties
atomic structure, 5, 6, 7, 8, 9
average thermoelectric force, 17
characteristics of, 11
copper at temperature, 21
Cu conductivity, 14
electrical conductivity, 10–11, 12–13
electromagnetic properties, 4, 5
electrons energy levels, 7
Hall effect, 23
influence of ingredients on resistivity, 13, 14
ionization, 9
mechanical properties, 18
mechanical strength on temperature, 19
periodic classification, 8
quantization of orbits, 6
recrystallization temperature, 20
resistivity at higher temperatures, 14, 15
tensile forces vs. elongation, 19
thermaland mechanical properties, 5
METGLASS, see see Metallic glass
Method of finite boxes (MFB), 98
MFB, see see Method of finite boxes (MFB)
MHD, see see Magnetohydrodynamics (MHD)
Mirror image methods, 243
analogy in electrostatic fields, 246–247
current magnetic images, 251–252
DC field theory to AC application, 247–250
direct current singular images, 243–245
magnets and circuits mirror images, 254–258
multiple mirror images, 252–254
MMF, see see Magnetomotive force (MMF)
Model laws, 451
Modeling
Mono-coherent superconductor, 112
Monochromatic wave, 124
Multilayer screens
electromagnetic field in, 236
insulation influence, 240
long transmission line theory, 241
magnetic field intensity, 238
two-layer conductor, 236
wave impedance, 239
Multiple mirror image approach, 252, 269
conductor encircled, 254
current mirror images in flat iron surfaces, 252
N
Natural wave, see see Plane unpolarized wave
Navier-Stokes equation, 109, 443
Near induction field, 142
Non-magnetic materials, 427
Nonideal superconductor, 26; see see also Ideal superconductor
Nonlinear magnetic permeability, 104–106, 346
Nonlinear media, 103; see see also Anisotropic media
current–voltage characteristic, 104
nonlinear magnetic permeability, 104–106
permittivity, nonlinear, 103
resistance, nonlinear, 104
Nonlinear permittivity, 103
Nonmagnetic cast iron, 56
Nonmagnetic steel, 56
Normal magnetization characteristic, see see Standard magnetization characteristic
Numerical methods, 271–273, 278
Numerical solution, two-dimensional, 369–370
O
Oil cooling, 422
Open screens, 165
Orthogonal right-handed system, 125
Overheating hazard, 417
P
Parallel conductors, interaction force of determination, 400
forces in transformer windings, 401, 402
Hamilton-84
program, 403
magnetic field intensity, 400
short-circuit forces in switching stations, 401
Paramagnetic bodies, 34
Paramagnetics, diamagnetics, 32–34
Pauli exclusion principle, 7
Peltier effect, 17
Thomson functions, 192, 221, 222, 223
Penetrable screens, 166
Permalloys, 46
Permanent magnets, 57, 73, 414, 416
DC current, 248
demagnetization characteristics, 46
hard magnetic materials, 47
motor design, 416
with rare earth, 55
Permitted field on metal surface, 430
P. Hammond concept, 322
Phonon resistivity, 11
Photon, 9
Piezoelectricity, 72
Plane polarized wave, 123, 124
Plane unpolarized wave, 124
near and far fields, 142
in conducting half-space, 129, 130, 131–133
electromagnetic penetration, 130
field diffusion into conductor, 137, 138, 139
reflection and refraction, 141–142
solid conductors, 133, 134, 135–136
spherical coordinate system, 128
Plasma, 9
Poisson’s equation, 86
Ponderomotive forces, 399
Potassium seeding, 106
Powder method, 482
Power density volumetric distribution, 318
Power flux
in capacitor and coil, 157
at conductors passing, 153, 154–156
field components, 153
in parallel-plate capacitor, 158
synchronous machine, 161, 162–163
Power losses; see see also Screens, power losses in
bar pairs geometrical proportionality, 367
computer calculation, 364
in core iron, 50
de l’Hospitale rule, 364
example and solution, 368
opacity, 366
parallel bar magnetic field distribution, 365
in transformers steel covers, 352–354
Power measurement
angle-errors, 469
compensation wattmeter, 468
electrodynamic systems, 466
double-sided symmetric, 189–193
measurement, 479
and power losses, 184
Preisach’s model of hysteresis, 44, 51
Principles of mechatronics, 4, 437, 492
coefficient for bars, 324, 325
in nearby conductors, 323
Q
Quantization of orbits, 5
Quasi-static sinusoidal processes, 345
Quasi-stationary alternating fields, 94
R
Radio frequencies (RFs), 62
Rapid design, 224
complementary domains of, 443
Reactive power consumption, 296–298
Real system, 255
AC leakage flux in, 174
mapping, 254
Recoil permeability, 61
Rectangular anisotropy, 102
Rectangular waves method, 338–342
Reluctance forces, 412
field and electrodynamic forces, 413
hybrid stepping motors torques, 414–416
linear reversible actuator, 415
magnet sort in slots, 415
permanent magnet motors, 416
thyristor-controlled reversible motors, 412–414
Reluctance network method (RNM), 271–273, 412, 434
calculation of reluctances, 435, 436
magnetic shunts, 436
shell-type transformers, 437
3D modeling, 435
three-phase bushing system, 435
Reluctance network method three-dimensional (RNM-3D), 272, 383
industrial implementation, 384–386
RNM-3Dshell program, 437
screening mistake risk, 390–393
structure and screens configuration, 389–390
transformers without screens, 386–388
user’s input questionnaire, 203
Remagnetization field superposition, 52
Resistivity, metal, 10
formula for, 13
ideal, 12
influence of ingredients on, 13–14
phonon, 11
Return permeability, 61
Reversible permeability, 60–61
Reynold’s magnetic number, 109, 110
RFs, see see Radio frequencies (RFs)
RNM-3D, see see Reluctance network method three-dimensional (RNM-3D)
RNM, see see Reluctance network method (RNM)
Rogowski’s method, 270
Rogowski’s strap, see see Magnetic strap
Rosenberg’s method, 338
S
Scalar Poisson’s equation, 93
Scale of power, 445
Screening
electromagnetic field in multilayer screens, 236–241
Screens,
cross wise cylindrical, 167–170
longitudinal magnetic, 171–174
thick, 182
Screens, power losses in, 184; see see also Transformer tank, power losses in
active and reactive power, 187, 190
by dielectric, 186
double-sided symmetric, 189
electric power factor, 191
impedances, 185
magnetic field intensity, 192
power density distribution, 193
Poynting vector, 184
screen adhering to iron, 187
screen per unit surface, 185
screening coefficient of power, 188
Secondary quantum number, see see Azimuthal quantum number
Semiconductors, 69
dopants, 71
electron-dominated n-type, 71, 72
hall effect in semiconductors, 72, 73
properties, 70
Shunting, see see Magnetic screening Shunt thermocompensators, 55, 75
SI, see see Signal integrity (SI)
Signal integrity (SI), 115
Silicon carbide (SiC), 70
Similarity theory, 441
based electrodynamic similarity theory, 442
Single-phase bushing system, 298–300
Skin-effect, 12, 133, 317, 465
Slot in deep-slot induction machine, 273
trapezoidal and bulb slots, 275–277
Soft ferromagnetics, 33
Soft superconductor, see see Ideal superconductor
Solid conductors, 133, 134, 135–136
conductor radius, 136
equivalent depth of penetration, 133, 134
solid metal half-space, 135
wavelength, 134
Source-free flux density field, 82
Spin magnetic quantum number, 6
Spontaneous magnetization zones, 36, 37
Standard magnetization characteristic, 332
Steel linearization, 337
Steel surface, field on, 360
linear induction motors calculations, 364
theoretical system, 363
typical cases of, 361
Steel walls, currents induced in, 328–330
Steinmetz formula, 51
Stray field three-dimensional analytical calculations, 370
field on Tank Surface, 370–372
flux in tank influence, 374–375
Stray fields and losses three-dimensional numerical calculation, 381
Stray flux distribution, 487, 489
Stray losses calculation method, 354
losses in transformers steel covers, 355
three-dimensional field, 356–359
two-dimensional field, 359–360
Stray losses dependence, 349
analytical approximation, 350
magnetic field intensity, 351
Stray losses in ABB-ELTA transformers, 387
Strength, Weakness, Opportunity, Threat (SWOT), 4
Cammerlingh-Onnes, 24
critical flux density dependence, 26
cryoconductive conductors, 30
cryogenic liquid features, 28
in electric machine industry, 30–31
high temperature Bednorz & Müller, 28, 30
magnetization and flux density, 27
Olszewski and Wróblewski, 24, 30
stability of, 29
temperatures and critical fields, 27
Superconductors, 24
in electric machine industry, 30–31
hard, 26
magnetization in, 27
superconducting devices, 29
Swelling, 304
SWOT, see see Strength, Weakness, Opportunity, Threat (SWOT)
Synthesis design, 425
T
Tangential component, 207, 234, 260, 421, 426
Tank wall, critical distance of, 482
circuit tests, 483
determination, 484
electromagnetically screened tank walls, 485
experimental verification, 488
FEM-2D calculations, 489
geometric proportions, 485
leakage flux distribution, 486
tank screening influence and yoke beams, 488
from transformer windings, 482
Technology Computer-Aided Design (TCAD), 114
Temperature method, 425
Tensor permeability, 63
Textured sheets, see see Anisotropic transformer sheets
Thermal properties, 5
Thermal resistors, see Thermistors Thermistors, 70, 103
Thermomagnetics, 55
Thermometric method
coefficient, 460
heating and self-cooling, ideal curves of, 455
local losses and magnetic field intensity, 454, 456
measurement techniques, 462
power loss density distribution, 462
rise of body temperature method, 454–456
transformer core, heating curves of, 459
Thick screens, 182
Thin screens, 179
in dielectric, 181
exponential functions, 179
Third quantum number, see see Magnetic quantum number
Three-dimensional computer analysis, 203
interactive computer design, 204, 206
RNM-3D program user’s input questionnaire, 203
screw bolts bracing yoke beams, 208
two-dimensional analysis, 207
Three-dimensional field, 356–359
Three-phase bushing system, 300–301
Three-phase transformer, 374
computational dimensions of, 377
experimental verifications, 384
interactive computer design, 204
Thyristor-controlled reversible motors
dynamics of, 412
electromechanical transient processes, 413
RNM-3D calculations, 414
Transformation electromotive force, 82
Transformer cover plates, heating of, 430
Transformer modeling
Fe sheets packages, 453
magnetic screening, 454
model laws, 451
Turowski’s inverted model, 452, 453
Transformer tank, power losses in, 369
stray field 3D analytical calculations, 370–375
stray losses parametric ANM-3D calculation, 375–381
3D numerical calculation of stray fields, 381–384
two-dimensional numerical solution, 369–370
Transformer tanks, 375, 378, 380
Transformer tanks, screening of, 194
electromagnetic screening, 200–203
power losses in, 194
principle of operation, 195
strong leakage fields, 194
Transient induced processes, 305
Translucent screen, see see Penetrable screens
Transparency of sheet, 354
Two-dimensional field, 359–360
U
Uniqueness of field, 243
V
Valence band, 10
Variable magnetic permeability methods, 337
permeability substitution, 345–346
rectangular waves method, 338–342
Rosenberg’s method for steel conductors, 338
Varistors, 70
Vertex magnetization curve, see see Commutation magnetization curve
W
in cylindrical coordinates, 121–123
heterogeneous wave equation, 92
Wavelength, 5, 127, 134, 136, 172, 182, 446
Weierstrass theorem, 331
Wiedemann-Franz law, 17
Winding factor, 82
Y
Yokes measurement, 482