Theory and Calculation of Alternating Current Phenomena (1900) — part 19 of 19

divided circuit 209

Equivalent sine wave of distorted

wave in

Evolution 491, 495

Exciting admittance of induction

motor 240

admittance of transformer . 204 current of magnetic circuit,

distorted by hysteresis. .111 current of transformer . . 195

Field characteristic of alternator . 304 First harmonic, or fundamental,

of general alternating wave, 8 Five-wire single-phase system, dis- tribution efficiency . . . 470

Flat-top wave 399

Flow of power in polyphase sys- tem 441

Foucault or Eddy currents, Ch. xi. 129 Four-phase, see quarter-phase.

Fraction 491

Free oscillations of circuit . . . 508 Frequency converter, Chap. xv. . 219 converter, calculation . . .232 converter, fundamental equa- tions 224

of alternating wave ... 7 ratio of general alternating current transformer or fre- quency converter . . . 221 Friction, molecular magnetic . . 106 Fundamental equations, see equa- tions, fundamental, frequency of transmission line discharge . . . .186

INDEX.

517

Fundamental equations, or first harmonic of general alter- nating wave 8

General alternating current trans- former, or frequency con- verter, Chap. xv. ... 219

alternating wave . . . . 7, 8

alternating wave, symbolic representation,Chap.xxiv. 410

equations, see equations, fun- damental.

polyphase systems, Chap.

xxv 430

Generator action of concatenated

couple 280

of reaction machine . . .377

alternating current, Chap. xvn 297

synchronous, operating with- out field excitation . . . 371

induction 265

induction, calculation for con- stant frequency .... 269

reaction, Chap. xxi. . . .371

vector diagram 28

Graphical construction of circuit

characteristic . . . . 48, 49 Graphic representation, Chap. iv. 19

limits of method .... 33

see polar diagram.

Harmonics, higher, effects of,

Chap, xxin 398

higher, resonance rise in

transmission lines . . . 402 of general alternating wave . 8 Hedgehog transformer .... 195 Hemisymmetrical polyphase sys- tem 439

Henry, definition of 18

Hexaphase, see six-phase.

Hysteresis, Chap, x 104

advance of phase . . . .115 as energy component of self- induction 372

Hysteresis, coefficient . . . .116

cycle or loop 107

dielectric, or electrostatic . 145 energy current of transformer 196 loss, effected by wave shape, 407 loss in alternating field . .114

magnetic 106

motor 293

of magnetic circuit, calcula- tion 125

or magnetic energy current . 115

Imaginary number 492

quantities, complex, algebra

of, App. 1 489

Impedance 2

in series with circuit ... 68 in symbolic representation . 39 primary and secondary, of

transformer 205

see, admittance.

series connection .... 57

total apparent, of transformer 208

Independent polyphase system . 431

Inductance 4

definition of 18

factors of distorted wave . . 415

mutual ' ... 142

Induction, electro-magnetic, law of 16

electrostatic 147

generator 265

generator, calculation for

constant frequency . . 269 generator, driving synchron- ous motor 272

motor, Chap, xvi 237

motor 281

motor, calculation .... 262 motor, concatenation or tan- dem control 274

motor, fundamental equa- tions 226, 242

motor, graphic representa- tion 244

motors in concatenation, cal- culation . .... 276

518

INDEX.

Induction motor, synchronous . 291 motor torque, as double fre- quency vector . . . .156 motor with distorted wave . 426 Inductive devices for starting sin- gle-phase induction motor 283 line, effect of conductance of receiver circuit on trans- mitted power 89

line, effect of susceptance of receiver circuit on trans- mitted power 88

line, in symbolic representa- tion 41

line, maximum efficiency of

transmitted power ... 93 line, maximum power sup- plied over 87

line, maximum rise of poten- tial by shunted suseeptance 101 line, phase control by shunted

susceptance 96

line, supplying non-inductive

receiver circuit .... 84 Influence, electrostatic . . . .147 Instantaneous values and inte- gral values, Chap. n. . . 11 value of alternating wave . 1 1 Insulation strength with distorted

wave 409

Integral values of alternating

wave 11

Intensity of sine wave .... 20 Interlinked polyphase systems,

Chap, xxvin 452

polyphase system .... 431 Internal impedance of trans- former 205

Introduction, Chap. 1 1

Inverted three-phase system . . 434 three-phase system, balance

factor 443, 446

three-phase system, distribu- tion efficiency 472

Involution 490,495

Iron, laminated, eddy currents . 131

Iron wire, eddy currents . . . 133 wire, unequal current distri- bution in alternating cir- cuit 142

Irrational number 492

f, as imaginary unit .... 37 introduction of, as distin- guishing index .... 36 Joules's law of alternating cur- rents 6

law of continuous currents . 1

Kirchhoff's laws in symbolic

representation .... 40 laws of alternating current

circuits 58

laws of alternating sine waves

in graphic representation . 22 laws of continuous current

circuits 1

Lagging currents, compensation for, by shunted conden-

sance 72

Lag of alternating wave ... 21 of alternator current, effect on armature reaction and

self-induction 298

Laminated iron, eddy currents . 131 Law of electro-magnetic induc- tion, Chap, in 16

L connection of three-phase, quar- ter-phase transformation . 465 connection of three-phase

transformation .... 464 Lead of alternating wave ... 21 of alternator current, effect on armature reaction and self-induction . . . . 298 Leakage current, see Exciting

current.

of electric current .... 148 Lightning discharges from trans- mission lines, frequencies

181, 188

INDEX.

519

Line, inductive, vector diagram . 23 with distributed capacity and

inductance 158

with resistance, inductance, capacity, and leakage, topographic circuit charac- teristic 49

Logarithmation 491

Long-distance lines, as distributed

capacity, and inductance 158

Loxodromic spiral 500

Magnetic circuit containing iron,

calculation 125

hysteresis 106

or hysteretic energy current . 116

Magnetizing current 115

current of transformer . . 196 effect of armature reaction in alternators and synchro- nous motors 298

Main and teazer connection of

three-phase transformation 464 Maximum output of synchronous

motor 342

power of induction motor . 252 power of synchronous motor 342 power supplied over induc- tive line 87

rise of potential in inductive line, by shunted suscep-

tance 101

to effective value .... 14

to mean value 13

torque of induction motor . 250

value of alternating wave . 11

Mean to maximum value ... 13

value 12

value, or average value of

alternating wave . . . . 11 Mechanical power of frequency

converter 227

Minimum current in synchronous

motor 345

M. M. F. of armature reaction

of alternator . . 297

M. M. F. rotating, of constant

intensity 436

's acting upon alternator ar- mature 297

Molecular magnetic friction . . 106 Monocyclic connection of three- phase-inverted three-phase transformation .... 464 devices for starting single- phase induction motors . 283

systems 447

Monophase, see Single-phase. Motor, action of reaction ma- chine 377

alternating series .... 363 alternating shunt .... 368 commutator, Chap. xx. . . 354

hysteresis 293

induction, Chap. xvi. . . . 237 reaction, Chap. xxi. . . .371

repulsion 354

single-phase induction . . 281 synchronous, Chap, xix . . 321 synchronous, driven by in- duction generator . . . 272 synchronous induction . . 291 Multiple frequency of transmis- sion line discharge . . . 185

Multiplication 490,494

Mutual inductance 142

inductance of transformer circuits 194

Natural period of transmission

line 181

Negative number 490

Nominal induced E.M.F. of alter- nator 302

Non-inductive load on trans- former 212

receiver circuit supplied over inductive line .... 84

N-phase system, balance fac- tor 443

phase system, symmetrical . 435

Numeration or counting . . . 489

520

INDEX.

Ohms law in symbolic represen- tation 40

of alternating currents . . 2

of continuous currents . . 1

Oscillating currents, App. n. . . 497

discharge 508

Oscillation frequency of transmis- sion line 181

Output, see Power.

Overtones, or higher harmonics

of general alternating wave 8

Parallel connection of conduc- tances 52

Parallelogram law of alternating

sine waves 21

of double-frequency vectors,

as power 153

Parallel operation of alternators,

Chap, xviir 311

Peaked wave 399

Period, natural, of transm. line 181 of alternating wave ... 7 Phase angle of transmission line 171 control, maximum rise of po- tential by 101

control of inductive line by

shunted susceptance . . 96 control of transmission line,

Chap, ix 83

difference of 7

displacement, maximum, in

synchronous motor . . . 347 of alternating wave ... 7

of sine wave 20

splitting devices for starting single-phase induction mo- tors 283

Plane, complex imaginary . . . 496 Polar coordinate of alternating

waves 19

diagram of induction motor 244 diagram of transformer . . 196 diagram of transmission line 191 diagrams, see Graphic repre- sentation.

PAGE

Polarization as capacity . . 6

distortion of wave shape by . 393

Polycyclic systems 447

Polygon of alternating sine waves 22 Polyphase system, balanced . . 431 systems, balanced and unbal- anced, Chap. xxvn. . . 440 . systems, efficiency of trans- mission, Chap. xxx. . . 468 systems, flow of power . . 441 systems, general, Chap. xxv. 430 systems, hemisymmetrical . 439 systems, interlinked, Chap.

xxvin 452

systems, symmetrical, Chap.

xxvi 435

systems, symmetrical . . . 430 systems, symmetrical, pro- ducing constant revolving

M.M.F 436

systems, transformation of,

Chap, xxix 460

systems, unbalanced . . . 431 systems, unsymmetrical . . 430 Power and double frequency quantities in general, Chap.

XII 150

characteristic of polyphase

systems 447

characteristic of synchronous

motor 341

equation of alternating cur- rents 6

equation of alternating sine waves in graphic represen- tation 23

equation of continuous cur- rents 1

factor of arc 395

factor of distorted wave . . 414 factor of reaction machine . 381 flow of, in polyphase system 441 flow of, in transmission line 177 maximum, of inductive line with non-inductive receiver circuit . . 86

INDEX.

521

PAGE

Power, maximum of synchronous

motor 432

maximum supplied over in- ductive line 87

of complex harmonic wave . 405 of distorted wave .... 413 of frequency converter . . 227 of general polyphase system 459 of induction motor .... 246 of repulsion motor .... 360 parallelogram of, in symbolic

representation .... 153 real and wattless, in symbol- ic representation . . . 151 Primary exciting admittance of

induction motor .... 240 exciting admittance of trans- former 204

impedance of transformer . 205 Pulsating wave, definition ... 11 Pulsation of magnetic field caus- ing higher harmonics of

E.M.F 384

of reactance of alternator ar- mature causing higher har- monics . 391

of resistance, causing higher harmonics 393

Quadriphase, see Quarter-phase. Quarter-phase, five-wire system,

distribution efficiency . . 471 system, Chap. xxxn. . . . 483

system 43^

system, balance factor . 442, 445 system, distribution efficiency 471 system, symmetry .... 436 system, transmission effi- ciency 474

three-phase transformation . 465

unitooth wave 388

Quintuple harmonic, distortion of

wave by 400

Ratio of frequencies in general alternating current trans- former . . 221

Ratio of frequencies of transfor- mation of transformer . . 207

Reactance 2

definition 18

effective, definition . . . 105 in series with circuit . . . 61 in symbolic representation . 39 periodically varying . . . 373 pulsation in alternator caus- ing higher harmonies . . 391

sources of 8

synchronous, of alternator . 301 see Susceptance. .

Reaction machines, Chap. xxi. . 371 machine, power-factor . . 381 armature, of alternator . . 297 Rectangular coordinates of alter- nating vectors .... 34 diagram of transmission

line 191

Reflected wave of transmission

line 169

Reflexion angle of transmission

line 169

Regulation curve of frequency

converter 232

of alternator for constant

current . 309

of alternator for constant

power 310

of alternator for constant

terminal voltage . . . 308 Reluctance, periodically varying . 373 pulsation of, causing higher harmonics of E.M.F. . . 384

Repulsion motor 354

motor, displacement angle . . . 361

motor, power 360

motor, starting torque . . 361

motor, torque 360

Resistance and reactance of transmission Lines,

Chap, ix 83

effective, definition . . . 104 effective, of alternating cur- rent circuit . 2

522

INDEX.

22

153

Resistance and reactance in alter- nating current circuits ... 2 in series with circuit ... 58 of induction motor secon- dary, affecting starting

torque 254

pulsation, causing higher har- monics 393

series connection .... 52 see Conductance. Resonance rise by series induc- tance, with leading cur- rent 65

rise in transmission lines with

higher harmonics . . . 402 Resolution of alternating sine waves by the parallelo- gram or polygon of vec- tors

of double frequency vectors,

as power

of sine waves by rectangular

components 35

of sine waves in symbolic

representation .... 38 Reversal of alternating vector by

multiplication with — 1 . 36 Revolving magnetic field . . . 436 M. M. F. of constant inten- sity 436

Ring connection of interlinked

polyphase system . . . 453 current of interlinked poly- phase system 455

potential of interlinked poly- phase system 455

Rise of voltage by inductance,

with leading current . . 62 of voltage by inductance in synchronous motor circuit 65

Roots of the unit 495

Rotating magnetic field .... 436 M.M.F. of constant intensity 436

Rotation 495

by 90°, by multiplication with ± j 37

Saturation, magnetic, effect on exciting current wave . .

Sawtooth wave

Screening effect of eddy currents Screw diagram of transmission

line

Secondary impedance of trans- former .

Self-excitation of alternator and synchronous motor by ar- mature reaction ....

Self-inductance

E.M.F. of

of transformer

of transformer for constant power or constant current

regulation

Self-induction, energy component

of

of alternator armature . .

reducing higher harmonics .

Series connection of impedances

of resistances

impedance in circuit . . . motor, alternating .... operation of alternators . . reactance in circuit . . . resistance in circuit Shunt motor, alternating Sine wave

circle as polar characteristic

equivalent, of distorted wave, definition

representation by complex

quantity

Single-phase induction motor

induction motor, calculation

induction motor, starting de- vices

induction motor, with con- denser in tertiary circuit .

system, balance factor . .

system, distribution efficiency

system, transmission effi- ciency

unitooth wave .

113 399 136

192 205

3

18

193

104

402 63 52 68

363

313 61 58

368

6

20

111

37 281 287

283

287 444 470

474

INDEX.

523

Six-phase system 434

three-phase transformation . 465 Slip of frequency converter or general alternating current

transformer 221

of induction motor . . . 238 Slots of alternator armature, af- fecting wave shape . . . 384 Space diagram of transmission

line 192

Star connection of interlinked

polyphase system . . . 453 current of interlinked poly- phase system 455

potential of interlinked poly- phase system 455

Starting of single-phase induction

motor 283

torque of induction motor . 254 torque of repulsion motor . 361 Stray field, see Cross flux.

Subtraction 490, 494

Suppression of higher harmonics

by self-induction . . . 402 Susceptance, definition . . . '. fii effective, definition .... 105 of receiver circuit with in- ductive line 88

shunted, controlling receiver

circuit 96

see Reactance.

Symbolic method, Chap. v. . . 33 method of transformer . . 204 representation of general alternating waves, Chap.

xxiV; 410

Symbolism of double frequency

vectors 151

Symmetrical n-phase system . . 435 polyphase system, Chap.

xxvi 435

polyphase systems .... 430 polyphase system, producing

constant revolving M.M.F. 436 Synchronism, at or near induc- tion motor . . 258

Synchronizing alternators, Chap.

xvm 311

power of alternators in par- allel operation . . . .317 Synchronous induction motor . 291

motor, also see Alternator.

motor, Chap xix 321

motor, action of reaction ma- chine 377

motor, analytic investiga- tion 338

motor and generator in single unit transmission . . . 324

motor, constant counter E.M.F . .349

motor, constant generator and motor E.M.F. . . .329

motor, constant generator E.M.F. and constant power 334

motor, constant generator E.M.F. and maximum effi- ciency 332

motor, constant impressed E.M.F. and constant cur- rent 326

motor driven by induction generator 272

motor, fundamental equa- tions 339

motor, graphic representa- tion 321

motor, maximum phase dis- placement 347

motor, maximum output . . 342

motor, minimum current at given power 345

motor, operating without field excitation . . . .371

motor, phase relation of cur- rent 325

motor, polar characteristic . 341

motor, running light . . . 343

motor, with distorted wave . 422

reactance of alternator and synchronous motor . . . 301

524

INDEX,

Tandem control of induction

motors 274

control of induction motors,

calculation 276

T-connection of three-phase, quar- ter-phase transformation . 465 connection of three-phase

transformation .... 464 Tertiary circuit with condenser, in single-phase induction

motor 287

Tetraphase, see Quarter-phase. Three-phase,four-wire system, dis- tribution efficiency . . . 471 quarter-phase transformation 465 six-phase transformation . . 465 system, Chap. xxxi. . . . 478

system 433

system, balance-factor 442, 446 system, distribution effi- ciency 470

system, equal load on phases,

topographic method . . 46 system, interlinked .... 44 system, symmetry .... 436 system, transmission effi- ciency 474

unitooth wave 389

Three-wire, quarter-phase system 483 single-phase system, distribu- tion efficiency 470

Time constant of circuit ... 3 Topographic construction of transmission line charac- teristic - 176

method, Chap, vi 43

Torque, as double frequency vec- tor 156

of distorted wave .... 413 of induction motor . . . 246 of repulsion motor .... 360 Transformation of polyphase

systems, Chap. xxix. . . 460 ratio of transformer . . . 207 Transformer, alternating current,

Chap, xiv 193

Transformer, equivalent to di- vided circuit 209

fundamental equations 208, 225 General alternating current, or frequency converter,

Chap, xv 219

oscillating current .... 510

polar diagram 196

symbolic method .... 204

vector diagram 28

Transmission efficiency of sys- tems, Chap. xxx. . . . 468 lines, as distributed capacity

and inductance .... 158 line, complete space diagram 192 line, fundamental equations . 169 line, natural period of . . 181 lines, resistance and re- actance of (Phase Con- trol), Chap, ix 83

line, resonance rise with

higher harmonics . . . 402 lines with resistance, induc- tance, capacity, topo- graphic characteristic . . 49 Trigonometric method .... 34 method, limits of .... 34 Triphase, see Three-phase. Triple harmonic, distortion of

wave by 398

Two-phase, see Quarter-phase.

Unbalanced polyphase system . 431

quarter-phase system . . . 485 three-phase system . . . .481 Unequal current distribution, eddy currents in conduc- tor 139

Uniphase, see Single-phase.

Unit, imaginary 494

Unitooth alternator waves . . . 388 alternator waves, decrease of

hysteresis loss .... 408 alternator waves, increase of

power 405

Unsymmetrical polyphase system 430

INDEX.

525

Vector, as representation of alter- nating wave 21

of double frequency, in sym- bolic representation . .151

Volt, definition 16

Wattless power 151

power of distorted wave . . 413

Wave length of transmission line 170 shape distortion and its

causes, Chap. xxn. . . .383 shape distortion by hyster- esis . .... 109

Wire, iron, eddy currents . . . 133

Y-connection of three-phase sys- tem 453

current of three-phase sys- tem 455

delta connection of three- phase transformation . . 463

potential of three-phase sys- tem 455

Zero impedance, circuits of . . 506

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