Theory and Calculation of Electrical Apparatus (1917) — part 1 of 21

THEORY AND CALCULATIONS

OF

ELECTRICAL APPARATUS

BY

CHARLES PROTEUS STEINMETZ, A. M., Ph. D.

First Edition Second Impression

McGRAW-HILL BOOK COMPANY, Inc. 239 WEST 39TH STREET. NEW YORK

LONDON: HILL PUBLISHING CO., Ltd.

6 & 8 BOUVERIE ST.. E. C.

1017

PREFACE

In the twenty years since the first edition of “ Theory and Cal- culation of Alternating Current Phenomena” appeared, elec- trical engineering has risen from a small beginning to the world’s greatest industry; electricity has found its field, as the means of universal energy transmission, distribution and supply, and our knowledge of electrophysics and electrical engineering has in- creased many fold, so that subjects, which twenty years ago could be dismissed with a few pages discussion, now have expanded and require an extensive knowledge by every electrical engineer.

In the following volume I have discussed the most important characteristics of the numerous electrical apparatus, which have been devised and have found their place in the theory of electrical engineering. While many of them have not yet reached any industrial importance, experience has shown, that not infre- quently apparatus, which had been known for many years but had not found any extensive practical use, become, with changes of industrial conditions, highly important. It is therefore necessary for the electrical engineer to be familiar, in a general way, with the characteristics of the less frequently used types of apparatus.

In some respects, the following work, and its companion vol- ume, “Theory and Calculation of Electric Circuits,” may be considered as continuations, or rather as parts of “ Theory and Calculation of Alternating Current Phenomena.” With the 4th edition, which appeared nine years ago, “Alternating Current Phenomena” had reached about the largest practical bulk, and when rewriting it recently for the 5th edition, it became necessary to subdivide it into three volumes, to include at least the most necessary structural elements of our knowledge of electrical engineering. The subject matter thus has been distributed into three volumes: “Alternating Current Phenomena,” “Electric Circuits,” and “Electrical' Apparatus.” -

Charles Proteus Steinmetz,

Camp Mohawk, Viele’s Creek,

July , 1917 .

CONTENTS

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Preface v

Chapter I. — Speed Control of Induction Motors.

I. Starting and Acceleration

1. The problems of high torque over wide range of speed, and of

constant speed over wide range of load — Starting by armature rheostat 1

2. A. Temperature starting device — Temperature rise increasing

secondary resistance with increase of current — Calculation of motor 2

3. Calculation of numerical instance — Its discussion — Estimation

of required temperature rise 4

4. B. Hysteresis starting device — Admittance of a closed mag- •

netic circuit with negligible eddy current loss — Total secondary impedance of motor with hysteresis starting device 5

5. Calculation of numerical instance — Discussion — Similarity of

torque curve with that of temperature startin gdevice — Close speed regulation — Disadvantage of impairment of power factor and apparent efficiency, due to introduction of reactance — Re- quired increase of magnetic density 6

6. C. Eddy current starting device — Admittance of magnetic cir-

cuit with high eddy current losses and negligible hysteresis — Total secondary impedance of motor with eddy current starting device — Numerical instance 8

7. Double maximum of torque curve — Close speed regulation —

High torque efficiency — Poor power factor, requiring increase of magnetic density to get output — Relation to double squirrel cage motor and deep bar motor 10

II. Consent Speed Operation

8. Speed control by armature resistance — Disadvantage of in-

constancy of speed with load — Use of condenser in armature or secondary — Use of pyro-electrie resistance 12

9. Speed control by variation of the effective frequency: con-

catenation — By changing the number of poles: multispeed motors 13

10. A. Pyro-electric speed control — Characteristic of pyro-

electric conductor — Close speed regulation of motor — Limita- tion of pyro-electric conductors 14

11. B. Condenser speed control — Effect of condenser in secondary,

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giving high current and torque at resonance speed — Calcula- tion of motor 1G

12. Equations of motor — Equation of torque— -Speed range of

maximum torque 17

13. Numerical instance — Volt-ampere capacity of required con- denser IS

14. C. Multispeed motors — Fractional pitch winding, and switch-

ing of six groups of coils in each phase, at a change of the num- ber of poles 20

15. Discussion of the change of motor constants due to a change of

the number of poles, with series connection of all primary turns — Magnetic density and inferior performance curves at lower speeds 21

16. Change of constants for approximately constant maximum

torque at all speeds — Magnetic density and change of coil connection 22

17. Instance of 4 -5- G -5- 8 pole motor — Numerical calculation and

discussion 23

Chapter II. Multiple Squirrel Cage Induction Motor.

18. Superposition of torque curves of high resistance low reactance,

and low resistance high reactance squirrel cage to a torque curve with two maxima, at high and at low speed 27

19. Theory of multiple squirrel cage based on the use of the true

induced voltage, corresponding to the resultant flux which passes beyond the squirrel cage — Double squirrel cage induc- tion motor 28

20. Relations of voltages and currents in the double squirrel cage

induction motor 29

21. Equations, and method of calculation 30

22. Continued: torque and power equation 31

23. Calculation of numerical instance of double squirrel cage

motor, speed and load curves — Triple squirrel cage induction motor 32

24. Equation between the voltages and currents in the triple

squirrel cage induction motor 34

25. Calculation of voltages and currents 35

26. Equation of torque and power of the three squirrel cages, and

their resultant . . . ; : ' . . 37

27. Calculation of numerical instance of triple squirrel cage induc- tion motor — Speed and load curves 37

Chapter III. Concatenation.

Cascade or Tandem Control of Induction Motors

28. Synchronizing of concatenated couple at half synchronism — The two speeds of a couple of equal motors and the three

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Pack

speeds of a couple of unequal motors — Internally concatenated motor 40

29. Generator equation of concatenated couple above half syn-

chronism — Second range of motor torque near full synchron- ism — Generator equation above full synchronism — Ineffi- ciency of second motor speed range — Its suppression by resistance in the secondary of the second motor 41

30. General equation and calculation of speed and slip of con- catenated couple 42

31. Calculation of numerical instances 44

32. Calculation of general concatenated couple 45

33. Continued 46

34. Calculation of torque and power of the two motors, and of the

couple 47

35. Numerical instance 48

36. Internally concatenated motor — Continuation of windings into

one stator and one rotor winding — Fractional pitch — No inter- ference of magnetic flux required — Limitation of available speed — Hunt motor 49

37. Effect of continuation of two or more motors on the character- istic constant and the performance of the motor 50.

Chapter IV. Induction Motor w t ith Secondary Excitation.

38. Large exciting current and low power factor of low speed in-

duction motors and motors of high overload capacity — Instance 52

39. Induction machine corresponding to synchronous machine ex-

cited by armature reaction, induction machine secondary corre- sponding to synchronous machine field — Methods of secondary excitation: direct current, commutator, synchronous machine, commutating machine, condenser 53

40. Discussion of the effect of the various methods of secondary

excitation on the speed characteristic of the induction motor . 55

Induction Motor Converted to Synchronous

41. Conversion of induction to synchronous motor — Relation of

exciting admittance and self-inductive impedance as induction motor, to synchronous impedance and coreloss as synchronous motor — Danielson motor . 57

42. Fundamental equation of synchronous motor — Condition of

unity power 'factor — Condition of constant field excitation . . 60

43. Equations of power input and output, and efficiency .... 61

44. Numerical instance of standard induction motor converted to synchronous — Load curves at unity power factor excitation and

at constant excitation (52

• 45. Numerical instance of low speed high excitation induction motor converted to synchronous motor — Load curves at unity

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power factor and at constant field excitation — Comparison

with induction motor 67

46. Comparison of induction motor and synchronous motor regard- ing armature reaction and synchronous impedance — Poor induction motor makes good, and good induction motor makes poor synchronous motor 69

Induction Motor Concatenated with Synchronous 47. Synchronous characteristic and synchronizing speed of con-

catenated couple — Division of load between machines — The synchronous machine as small exciter 71

48. Equation of concatenated couple of synchronous and induction

motor — Reduction to standard synchronous motor equation . 72

49. Equation of power output and input of concatenated couple . 74

50. Calculation of numerical instance of 56 polar high excitation

induction motor concatenated to 4 polar synchronous .... 75

51. Discussion. High power factor at all loads, at constant

synchronous motor excitation 76

Induction Motor Concatenated with Commutating Machine

52. Concatenated couple with commutating machine asynchronous

— Series and shunt excitation — Phase relation adjustable — Speed control and power factor control — Two independent variables with concatenated commutating machine, against one with synchronous machine — Therefore greater variety of speed and load curves 78

53. Representation of the commutating machine by an effective

impedance, in which both components may be positive or negative, depending on position of commutator brushes ... 80

54. Calculation of numerical instance, with commutating machine

series excited for reactive anti-inductive voltage— Load curves and their discussion 82

Induction Motor with Condenser in Secondary Circuit

55. Shunted capacity neutralizing lagging current of induction motor — Numerical instance — Effect of wave shape distortion— Condenser in tertiary circuit of single-phase induction motor—

Condensers in secondary circuit — Large amount of capacity required by low frequency 84

56. Numerical instance of low speed high excitation induction

motor with capacity in secondary — Discussion of load curves and of speed * 86

57. Comparison of different methods of secondary excitation, by

power factor curves: low at all loads; high at all loads, low at light, high at heavy loads — By speed : synchronous or constant speed motors and asynchronous motors in which the speed decreases with increasing load 88

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Induction Motor with Commutator

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58. Wave shape of commutated full frequency current in induction

• motor secondary — Its low frequency component — Full fre- quency reactance for rotor winding — The two independent variables: voltage and phase — Speed control and power factor correction, depending on brush position 89

59. Squirrel cage winding combined with commutated winding —

Heyland motor — Available only for power factor control — Its limitation 91

Chapter V. Single-phase Induction Motor.

60. Quadrature magnetic flux of single-phase induction motor pro- duced by armature currents — The torque produced by it —

The exciting ampere- turns and their change between synchron- ism and standstill 93

61. Relations between constants per circuit, and constants of the

total polyphase motor — Relation thereto of the constants of the motor on single-phase supply — Derivation of the single- phase motor constants from those of the motor as three-phase or quarter-phase motor 94

62. Calculation of performance curves of single-phase induction

motor — Torque and power 96

63. The different methods of starting single-phase induction motors

— Phase splitting devices; inductive devices; monocyclic de- vices; phase converter 96

64. Equations of the starting torque, starting torque ratio, volt-

ampere ratio and apparent starting torque efficiency of the single-phase induction motor starting device 98

65. The constants of the single-phase induction motor with starting

device 100

66. The effective starting impedance of the single-phase induction

motor — Its approximation — Numerical instance 101

67. Phase splitting devices — Series impedances with parallel con-

nections of the two circuits of a quarter-phase motor — Equa- tions 103

6S. Numerical instance of resistance in one motor circuit, with motor of high and of low resistance armature 104

69. Capacity and inductance as starting device— Calculation of

values to give true quarter-phase relation 106

70. Numerical instance, applied to motor of low, and of high arma- ture resistance 108

71. Series connection of motor circuits with shunted impedance—

Equations, calculations of conditions of maximum torque ratio — Numerical instance 109

72. Inductive devices — External inductive devices— -Internal in- ductive devices ...Ill

73. Shading coil — Calculations of voltage ratio and phase angle . 112

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74. Calculations of voltages, torque, torque ratio and efficiency . . 114

75. Numerical instance of shading coil of low, medium and high

resistances, with motors of low, medium and high armature resistance 116

76. Monocyclic starting device — Applied to three-phase motor — Equations of voltages, currents, torque, and torque efficiency . 117

77. Instance of resistance inductance starting device, of condenser

motor, and of production of balanced three-phase triangle by

capacity and inductance 120

78. Numerical instance of motor with low resistance, and with high resistance armature — Discussion of acceleration .... 121

Chapter VI. Induction Motor Regulation and Stability.

1. Voltage Regulation and Output

2. Effect of the voltage drop in the line and transformer im- pedance on the motor — Calculation of motor curves as affected

by line impedance, at low, medium and high line impedance . 123

80. Load curves and speed curves — Decrease of maximum torque

and of power factor by line impedance — Increase of exciting current and decrease of starting torque — Increase of resistance required for maximum starting torque 126

2. Frequency Pulsation

3. Effect of frequency pulsation — Slight decrease of maximum

torque — Great increase of current at light load 131

3. Load and Stability

4. The two motor speed at constant torque load — One unstable

and one stable point — Instability of motor, on constant torque load, below maximum torque point 132

83. Stability -at all speeds, at load requiring torque proportional to square of speed: ship propellor, centrifugal pump — Three speeds at load requiring torque proportional to speed — Two stable and one unstable speed — The two stable and one un- stable branch of the speed curve on torque proportional to

speed 134

84. Motor stability function of the character of the load — General conditions of stability and instability — Single-phase motor . . 136

85. Generator Regulation and Stability

86. Effect of the speed of generator regulation on maximum output of induction motor, at constant voltage — Stability coefficient of motor — Instance 137

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Page

86. Relation of motor torque curve to voltage regulation of system — Regulation coefficient of system — Stability coefficient of

system 138

87. Effect of momentum on the stability of the motor — Regulation of overload capacity — Gradual approach to instability . . . . 141

Chapter VII. Higher Harmonics in Induction Motors.

88. Component torque curves due to the higher harmonics of the

impressed voltage wave, in a quarter-phase induction motor; their synchronous speed and their direction, and the resultant torque curve 144

89. The component torque curves due to the higher harmonics of the impressed voltage wave, in a three-phase induction motor — True three-phase and six-phase winding — Ti e single-phase

torque curve of the third harmonic 147

90. Component torque curves of normal frequency, but higher

number of poles, due to the harmonics of the space distribu- tion of the winding in the air-gap of a quarter-phase motor — Their direction and synchronous speeds 150

91. The same in a three-phase motor — Discussion of the torque

components due to the time harmonics of higher frequency and normal number of poles, and the space harmonics of normal frequency and higher number of poles 154

92. Calculation of the coefficients of the trigonometric series repre-

senting the space distribution of quarter-phase, six-phase and three-phase, full pitch and fractional pitch windings 155

93. Calculation of numerical values for 0, 34 > 34 pitch defi- ciency, up to the 21st harmonic 157

Chapter VII. Synchronizing Induction Motors.

94. Synchronizing induction motors when using common secondary

resistance 159

95. Equation of motor torque, total torque and synchronizing

torque of two induction motors with common secondary rheo- stat 160

96. Discussion of equations — Stable and unstable position — Maxi-

mum synchronizing power at 45° phase angle — Numerical instance 163

Chapter IX. Synchronous Induction Motor.

97. Tendency to drop into synchronism, of single circuit induction motor secondary — Motor or generator action at synchronism — Motor acting as periodically varying reactance, that is, as reaction machine — Low power factor — Pulsating torque below synchronism, due to induction motor and reaction machine torque superposition 166

XIV

CONTENTS

Chapter X. Hysteresis Motor.

Pack

1)8. Rotation of iron disc in rotating magnetic field— Equations—

Motor below, generator above synchronism 168

99. Derivation of equations from hysteresis law — Hysteresis torque

of standard induction motor, and relation to size 169

100. General discussion of hysteresis motor — Hysteresis loop

collapsing or expanding 170

Chapter XI. Rotary Terminal Single-phase Induction Motors.

101. Performance and method of operation of rotary terminal

single-phase induction Motor — Relation of motor speed to brush speed and slip corresponding to the load 172

102. Application of the principle to a self -starting single-phase power

motor with high starting and accelerating torque, by auxiliary motor carrying brushes ' 173

Chapter XII. Frequency Converter or General Alternating Current Transformer.

103. The principle of the frequency converter or general alternating

current transformer — Induction motor and transformer special cases — Simultaneous transformation between primary elec- trical and secondary electrical power, and between electrical and mechanical power — Transformation of voltage and of fre- quency — The air-gap and its effect 176

104. Relation of e.m.f., frequency, number of turns and exciting

current 177

105. Derivation of the general alternating current transformer —

Transformer equations and induction motor equations, special cases thereof 178

106. Equation of power of general alternating current transformer . 182

107. Discussion: between synchronism and standstill — Backward driving — Beyond synchronism — Relation between primary electrical, secondary electrical and mechanical power .... 184

108. Calculation of numerical instance 185

109. The characteristic curves: regulation curve, compounding

curve — Connection of frequency converter with synchronous machine, and compensation for lagging current — Derivation of equation and numerical instance 186

110. Over-synchronous operation — Two applications, as double

synchronous generator, and as induction generator, with low frequency exciter 190

111. Use as frequency converter — Use of synchronous machine or induction machine as second machine — Slip of frequency — Advantage of frequency converter over motor generator . . .191

112. Use of frequency converter — Motor converter, its advantages and disadvantages — Concatenation for multispeed operation . 192

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Chapter XIII. Synchronous Induction Generator.

Page

113. Induction machine as asynchronous motor and asynchronous

generator 194

114. Excitation of induction machine by constant low frequency

voltage in secondary — Operation below synchronism, and above synchronism 195

115. Frequency and power relation — Frequency converter and syn- chronous induction generator 196

1 16. Generation of two different frequencies, by stator and by rotor . 198

117. Power relation of the two frequencies — Equality of stator and rotor frequency: double synchronous generator — -Low rotor frequency: induction generator with low frequency exciter,

Stanley induction generator 198

118. Connection of rotor to stator by commutator — Relation of fre-

quencies and powers to ratio of number of turns of stator and rotor 199

119. Double synchronous alternator — General equation — Its arma- ture reaction 201

120. Synchronous induction generator with low frequency excita-

tion — (a) Stator and rotor fields revolving in opposite direc- tion — ( b ) In the same direction — Equations 203

121. Calculation of instance, and regulation of synchronous induc- tion generator with oppositely revolving fields 204

122. Synchronous induction generator with stator and rotor fields

revolving in the same direction — Automatic compounding and over-compounding, on non-inductive load — Effect of inductive load 205

123. Equations of synchronous induction generator with fields re- volving in the same direction . . 207

124. Calculation of numerical instance 209

Chapter XIV. Phase Conversion and Single-phase Generation.

125. Conversion between single-phase and polyphase requires energy

storage — Capacity, inductance and momentum for energy storage— Their size and cost per Kva . . . .* 212

126. Industrial importance of phase conversion from single-phase to polyphase, and from balanced polyphase to single-phase . . . 213

127. Monocyclic devices — Definition of monocyclic as a system of

polyphase voltages with essentially single-phase flow of energy — Relativity of the term — The monocyclic triangle for single- phase motor starting 214

128. General equations of the monocyclic square 216

129. Resistance — inductance monocyclic square — Numerical in- stance on inductive and on non-inductive load — Discussion . 218

130. Induction phase converter — Reduction of the device to the

simplified diagram of a double transformation 220

131. General equation of the induction phase converter 222

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132. Numerical instance — Inductive load — Discussion and com- parisons with monocyclic square 223

133. Series connection of induction phase converter in single-phase induction motor railway — Discussion of its regulation .... 220

134. Synchronous phase converter and single-phase generation — Control of the unbalancing of voltage due to single-phase load, by stationary induction phase balancing with reverse rotation

of its polyphase system — Synchronous phase balancer. . . . 227

135. Limitation of single-phase generator by heating of armature coils — By double frequency pulsation of armature reaction —

Use of squirrel cage winding in field — Its size — Its effect on the momentary short circuit current 229

136. Limitation of the phase converter in distributing single-phase

load into a balanced polyphase system — Solution of the problem by the addition of a synchronous phase balancer to the synchronous phase converter — Its construction 230

137. The various methods of taking care of large single-phase loads —

Comparison of single-phase generator with polyphase generator and phase converter — Apparatus economy 232

Chapter XV.. Synchronous Rectifiers.

138. Rectifiers for battery charging — For arc lighting — The arc ma- chine as rectifier — Rectifiers for compounding alternators —

For starting synchronous motors — Rectifying commutator — Differential current and sparking on inductive load — Re- sistance bipass — Application to alternator and synchronous motor 234

139. Open circuit and short circuit rectification — Sparking with

open circuit rectification on inductive load, and shift of brushes 237

140. Short circuit rectification on non-inductive and on inductive

load, and shift of brushes — Rising differential current and flash- ing around the commutator — Stability limit of brush position, between sparking and flashing — Commutating c.m.f. resulting from unsymmetrical short circuit voltage at brush shift- — Sparkless rectification 239

141. Short circuit commutation in high inductance, open circuit commutation in low inductance circuits — Use of double brush to vary short circuit — Effect of load — Thomson Houston arc machine — Brush arc machine — Storage battery charging . . 243

142. Reversing and contact making rectifier — Half wave rectifier and its disadvantage by unidirectional magnetization of trans- former — The two connections full wave contact making recti- fiers 1 - Discussion of the two types of full wave rectifiers —

The mercury arc rectifier 245

143. Rectifier with intermediary segments — Polyphase rectifica- tion — Star connected,. ring connected and independent phase

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rectifiers — Y connected three-phase rectifier — Delta connected three-phase rectifier — Star connected quarter-phase rectifier — Quarter-phase rectifier with independent phases — Ring con- nected quarter-phase rectifier — Wave shapes and their discus- sion — Six-phase rectifier 250

144. Ring connection or independent phases preferable with a large

number of phases — Thomson Houston arc machine as con- stant current alternator with three-phase star connected rectifier — Brush arc machine as constant current alternator with quarter-phase rectifiers in series connection 254

145. Counter e.m.f. shunt at gaps of polyphase ring connected

rectifier — Derivation of counter e.m.f. from synchronous mo- tor — Leblanc’s Panchahuteur — Increase of rectifier output with increasing number of phases 255

146. Discussion: stationary rectifying commutator with revolving brushes — Permutator — Rectifier with revolving transformer —

Use of synchronous motor for phase splitting in feeding rectifying commutator: synchronous converter — Conclusion . 257

Chapter XVI. Reaction Machines.

147. Synchronous machines operating without field excitation . . 260

148. Operation of synchronous motor without field excitation de-

pending on phase angle between resultant m.m.f. and magnetic, flux, caused by polar field structure — Energy component of reactance 261

149. Magnetic hysteresis as instance giving energy component of

reactance, as effective hysteretic resistance 262

150. Make and break of magnetic circuit — Types of reaction machines — Synchronous induction motor — Reaction machine

as converter from d.-c. to a.-c 263

151. Wave shape distortion in reaction machine, due to variable

reactance, and corresponding hysteresis cycles 264

152. Condition of generator and of motor action of the reactance

machine, as function of the current phase 267

153. Calculation of reaction machine equation — Power factor and

maximum power 268

154. Current, power and power factor — Numerical instance . . .271

155. Discussion — Structural similarity with inductor machine . . 272

Chapter XVII. Inductor Machines.

156. Description of inductor machine type— Induction by pulsating

unidirectional magnetic flux 274

157. Advantages and disadvantages of inductor type, with regards

to field and to armature - . . . 275

158. The magnetic circuit of the inductor machine, calculation of

magnetic flux and hysteresis loss 27 (3

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159. The Stanley type of inductor alternator — The Alexanderson

high frequency inductor alternator for frequencies of 100,000 cycles and over 279

160. The Eickemeyer type of inductor machine with bipolar field —

The converter from direct current to high frequency alternating current of the inductor type 280

161. Alternating current excitation of inductor machine, and high

frequency generation of pulsating amplitude. Its use as amplifier — Amplification of telephone currents by high fre- quency inductor in radio communication 281

162. Polyphase excitation of inductor, and the induction motor

inductor frequency converter 282

163. Inductor machine with reversing flux, and magneto communi-

cation — Transformer potential regulator with magnetic com- mutation 284

164. The interlocking pole type of field design in alternators and

commutating machines 286

165. Relation of inductor machine to reaction machine — Half syn-

chronous operation of standard synchronous machine as inductor machine 287

Chapter XVIII. Surging of Synchronous Motors.

166. Oscillatory adjustment of synchronous .motor to changed con-

dition of load — Decrement of oscillation — Cumulative oscil- lation by negative decrement 288

167. Calculation of equation of electromechanical resonance . . . 289

168. Special cases and example 292

169. Anti-surging devices and pulsation of power 293

170. Cumulative surging — Due to the lag of some effect behind its cause — Involving a frequency transformation of power . . . 296

Chapter XIX. Alternating Current Motors in General.

171. Types of alternating-current motors 300

172. Equations of coil revolving in an alternating field 302

173. General equations of alternating-curreat motor 304

174. Polyphase induction motor, equations 307

175. Polyphase induction motor, slip, power, torque 310

176. Polyphase induction motor, characteristic constants . . . .312

177. Polyphase induction motor, example 313

178. Singlephase induction motor, equations 314

179. Singlephase induction motor, continued 316

180. Singlephase induction motor, example 318

181. Polyphase shunt motor, general 319

182. Polyphase shunt motor, equations 320

183. Polyphase shunt motor, adjustable speed motor 321

184. Polyphase shunt motor, synchronous speed motor 323

185. Polyphase shunt motor, phase control by it 324

186. Polyphase shunt motor, short-circuit current under brushes . 327

187. Polyphase series motor, equations 327

188. Polyphase series motor, example . . . , , 330

CONTENTS xix

Chapter XX. Single-phase Commutator Motors.

Page

189. General: proportioning of parts of a.-c. commutator motor

different from d.-c 331

190. Power factor: low field flux and high armature reaction re-

quired — Compensating winding necessary to reduce armature self-induction 332

191. The three circuits of the single-phase commutator motor —

Compensation and over-compensation — Inductive compen- sation — Possible power factors 336

192. Field winding and compensating winding: massed field

winding and distributed compensating winding — Under-com- pensation at brushes, due to incomplete distribution of com- pensating winding, 338

193. Fractional pitch armature winding to secure complete local

compensation — Thomson’s repulsion motor — Eickemeyer in- ductively compensated series motor *. 339

194. Types of varying speed single-phase commutator motors: con-

ductive and inductive compensation; primary and secondary excitation; series and repulsion motors — Winter — Eichberg — Latour motor — Motor control by voltage variation and by change of type 341

195. The quadrature magnetic flux and its values and phases in the

different motor types 345

196. Commutation: e.m.f. of rotation and e.m.f. of alternation —

Polyphase system of voltages — Effect of speed 347

197. Commutation determined by value and phase of short circuit current — High brush contact resistance and narrow brushes . 349

198. Commutator leads — Advantages and disadvantages of resist- ance leads in running and in starting 351

199. Counter e.m.f. in commutated coil: partial, but not com- plete neutralization possible 354

200. Commutating field — Its required intensity and phase rela- tions: quadrature field 356

201. Local commutating pole — Neutralizing component and revers-

ing component of commutating field — Discussion of motor types regarding commutation 358

202. Motor characteristics : calculation of motor — Equation of cur- rent, torque, power 361

203. Speed curves and current curves of motor — Numerical instance

— Hysteresis loss increases, short circuit current decreases power factor 364

204. Increase of power factor by lagging field magnetism, by

resistance shunt across field 366

205. Compensation for phase displacement and control of power

factor by alternating current commutator motor with lagging field flux, as effective capacity — Its use in induction motors and other apparatus 370

206. Efficiency and losses : the two kinds of core loss 370

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207. Discussion of motor types: compensated series motors: con-

ductive and inductive compensation — Their relative advan- tages and disadvantages 371

208. Repulsion motors: lagging quadrature flux — Nob adapted to

speeds much above synchronism — Combination type: series repulsion motor 373

209. Constructive differences — Possibility of changing from type to

type, with change of speed or load 375

210. Other commutator motors: shunt motor — Adjustable speed

polyphase induction motor — Power factor compensation: Heyland motor — Winter-Eichberg motor . . ' 377

211. Most general form of single-phase commutator motor, with two stator and two rotor circuits and two brush short circuits . . . 381

212. General equation of motor * 382

213. Their application to the different types of single-phase motor

■ with series characteristic 383

214. Repulsion motor: Equations 385

215. Continued 388

216. Discussion of commutation current and commutation factor . 391

217. Repulsion motor and repulsion generator 394

218. Numerical instance ' 395

219. Series repulsion motor: equations 3Q7

220. Continued 398

221. Study of commutation — Short circuit current under brushes . 403

222. Commutation current 404

223. Effect of voltage ratio and phase, on commutation 406

224. Condition of vanishing commutation current 408

225. Numerical example 411

226. Comparison, of repulsion motor and various series repulsion

motor 414

227. Further example — Commutation factors 415

228. Over-compensation — Equations 418

229. Limitation of preceding discussion — Effect and importance of

transient in short circuit current 419

Chapter XXI. Regulating Pole Converter.

230. Change of converter ratio by changing position angle between

brushes and magnetic flux, and by change of wave shape . . 422 A. Variable ratio by change of position angle between com- mutator brushes and resultant magnetic flux 422

231. Decrease of a.-c. voltage by shifting the brushes — By shifting the magnetic flux — Electrical shifting of the magnetic flux by varying the excitation of the several sections of the field pole . 422

232. Armature reaction and commutation — Calculation of the re-

sultant armature reaction of the converter with shifted mag- netic flux 426

233. The two directions “of shift flux, the one spoiling, the other

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xxi

Pa<; k

improving commutation — Demagnetizing armature reaction

and need of compounding by series field 429

B. Variable ratio by change of the wave shape of the Y voltage. 429

234. Increase and decrease of d.-c. voltage by increase or decrease of maximum a.-c. voltage by higher harmonic — Illustration

by third and fifth harmonic 430

235. Use of the third harmonic in the three-phase system — Trans- former connection required to limit it to the local converter circuit — Calculation of converter wave as function of the pole

arc • ■ • 432

236. Calculation of converter wave resulting from reversal of

middle of pole arc 435

237. Discussion 436

238. Armature reaction and commutation — Proportionality of

resultant armature reaction to deviation of voltage ratio from normal 437

239. Commutating flux of armature reaction of high a.-c. voltage — Combination of both converter types, the wave shape distor- tion for raising, the flux shift for lowering the a.-c. voltage —

Use of two pole section, the main pole and the regulating pole . 437

240. Heating and rating — Relation of currents and voltages in

standard converter 439

241. Calculation of the voltages and currents in the regulating pole

converter 440

242. Calculating of differential current, and of relative heating of

armature coil 442

243. Average armature heating of n phase converter 444

244. Armature heating and rating of three-phase and of six-phase

regulating pole converter 445

245. Calculation of phase angle giving minimum heating or maxi- mum rating 446

246. Discussion of conditions giving minimum heating — Design —

Numerical instance 448

Chapter XXII. Unipolar Machines.

Homo'polar Machines — Acyclic Machines

247. Principle of unipolar, homopolar or acyclic machine — The

problem of high speed current collection — Fallacy of unipolar induction in stationary conductor — Immaterial whether mag- net standstill or revolves — The conception of lines of magnetic force 450

248. Impossibility of the coil wound unipolar machine — All electro- magnetic induction in turn must be alternating — Illustration

of unipolar induction by motion on circular track 452

249. Discussion of unipolar machine design — Drum type and disc type — Auxiliary air-gap — Double structure — Series connec- tion of conductors with separate pairs of collector rings . . . 454

XXII

CONTENTS

Pack

250. Unipolar machine adapted for low voltage, or for large size high

speed machines — Theoretical absence of core loss — Possibility of large core loss by eddies, in core and in collector rings, by pulsating armature reaction 456

251. Circular magnetization produced by armature reaction—

Liability to magnetic saturation and poor voltage regulation — Compensating winding — Most serious problem the high speed collector rings 457

252. Description of unipolar motor meter 458

Chapter XXIII. Review.

253. Alphabetical list of machines: name, definition, principal

characteristics, advantages and disadvantages 459

Chapter XXIV. Conclusion.

254. Little used and unused types of apparatus — Their knowledge important due to the possibility of becoming of great industrial importance — Illustration by commutating pole machine . . 472

255. Change of industrial condition may make new machine types

important — Example of induction generator for collecting numerous small water powers 473

256. Relative importance of standard types and of special types of

machines 474

257. Classification of machine types into induction, synchronous,

commutating and unipolar machines — Machine belonging to two and even three types 474

Index 477

THEORY AND CALCULATION OF ELECTRICAL APPARATUS

CHAPTER I •

SPEED CONTROL OF INDUCTION MOTORS I. STARTING AND ACCELERATION