Theory and Calculation Alternating Current Phenomena
By
Charles Proteus.steinmetz
With the Assistance of
Ernst
J. Berg
Third Edition, Revised and Enlarged
Contents.
Chap. I. Introduction.
1, P. 1. Fundamental Laws of Continuous Current Circuits.
2, P. 2. Impedance, Reactance, Effective Resistance.
3, P. 3. Electro-magnetism as Source of Reactance.
4, P. 5. Capacity as Source of Reactance.
5, P. 6. Joule’s Law and Power Equation of Alternating Circuit.
6, P. 6. Fundamental Wave and Higher Harmonics, Alternating
Waves With and Without Even Harmonics.
7, P. 9. Alternating Waves as Sine Waves.
Chap. Ii. Instantaneous Values and
Integral Values.
8, P. 11. Integral Values of Wave.
9, P. 13. Ratio of Mean to Maximum to Effective Value of Wave.
Chap. Iii. Law of Electro-magnetic Induction.
11, P. 16. Induced E.m.f. Mean Value.
12, P. 17. Induced E.m.f. Effective Value.
13, P. 18. Inductance and Reactance.
Chap. Iv. Graphic Representation.
14, P. 19. Polar Characteristic of Alternating Wave.
15, P. 20. Polar Characteristic of Sine Wave.
16, P. 21. Parallelogram of Sine Waves, Kirchhoff’s Laws, and Energy
Equation.
17, P. 23. Non-inductive Circuit Fed Over Inductive Line, Instance.
18, P. 24. Counter E.m.f. And Component of Impressed E.m.f.
19, P. 26. Continued.
20, P 26. Inductive Circuit and Circuit With Leading Current Fed Over
Inductive Line.
Alternating-current Generator.
21, P. 28. Polar Diagram of Alternating-current Transformer, Instance.
22, P. 30. Continued.
Chap. V. Symbolic Method.
23, P. 33. Disadvantage of Graphic Method for Numerical Calculatioa
24, P. 34. Trigonometric Calculation.
25, P. 34. Rectangular Components of Vectors.
26, P. 36. Introduction of / as Distinguishing Index.
27, P. 36. Rotation of Vector by 180 and 90. J = V^ht.xii Contents.
Chap. V. Symbolic Method Continued.
28, P. 37. Combination of Sine Waves in Symbolic Expression.
29, P. 38. Resistance, Reactance, Impedance, in Symbolic Expression.
30, P. 40. Capacity Reactance in Symbolic Representation.
31, P. 40. Kirchhoffs Laws in Symbolic Representation.
32, P. 41. Circuit Supplied Over Inductive Line, Instance.
Chap. Vi. Topographic Method.
33, P, 43. Ambiguity of Vectors.
34, P. 44. Instance of a Three-phase System.
35, P. 46. Three-phase Generator on Balanced Load.
36, P. 47. Cable With Distributed Capacity and Resistance.
37, P. 49. Transmission Line With Self-inductive Capacity, Resistance,
And
Leakage.
Chap. Vii. Admittance, Conductance, Susceptance.
38, P. 52. Combination of Resistances and Conductances in Series and
In
Parallel.
39, P. 53. Combination of Impedances. Admittance, Conductance,
Susceptance.
40, P. 54. Relation Between Impedance, Resistance, Reactance, and
Admittance, Conductance, Susceptance.
41, P. 56. Dependence of Admittance, Conductance, Susceptance, Upon
Resistance and Reactance. Combination of Impedances and Admittances.
Chap. Viii. Circuits Containing Resistance, Inductance, and Capacity.
42, P. 58. Introduction.
43, P. 58. Resistance in Series With Circuit.
44, P. 60. Discussion of Instances.
45, P. 61. Reactance in Series With Circuit.
46, P. 64. Discussion of Instances.
47, P. 66. Reactance in Series With Circuit.
48, P. 68. Impedance in Series With Circuit.
49, P. 69. Continued.
50, P. 71. Instance.
51, P. 72. Compensation for Lagging Currents by Shunted Condensance.
52, P. 73. Complete Balance by Variation of Shunted Condensance.
53, P. 75. Partial Balance by Constant Shunted Condensance.
54, P. 76. Constant Potential Constant Current Transformation.
55, P. 79. Constant Current Constant Potential Transformation.
56, P. 81. Efficiency of Constant Potential Constant Current Transformation.
Chap. Ix. Resistance and Reactance of Transmission Lines.
57, P. 83. Introduction.
58, P. 84. Non-inductive Receiver Circuit Supplied Over Inductive Line.contents. Xiii
Chap. Ix. Resistance and Reactance of Transmission Lines. Continued.
59, P. 86. Instance.
60, P. 87. Maximum Power Supplied Over Inductive Line.
61, P. 88. Dependence of Output Upon the Susceptance of the Receiver Circuit.
62, P. 89. Dependence of Output Upon the Conductance of the Receiver Circuit.
63, P. 90. Summary.
64, P. 92. Instance.
65, P. 93. Condition of Maximum Efficiency.
6, P. 96. Control of Receiver Voltage by Shunted Susceptance.
67, P. 97. Compensation for Line Drop by Shunted Susceptance.
68, P. 97. Maximum Output and Discussion.
69, P. 98. Instances.
70, P. 101. Maxium Rise of Potential in Receiver Circuit.
71, P. 102. Summary and Instances.
Chap. X. Effective Resistance and Reactance.
72, P. 104. Effective Resistance, Reactance, Conductance, and Susceptance.
73, P. 105. Sources of Energy Losses in Alternating-current Circuits.
74, P. 106. Magnetic Hysteresis.
75, P. 107. Hysteretic Cycles and Corresponding Current Waves.
76, P. 111. Action of Air-gap and of Induced Current on Hysteretic
Distortion.
77, P. 111. Equivalent Sine Wave and Wattless Higher Harmonic.
78, P. 113. True and Apparent Magnetic Characteristic.
79, P. 115. Angle of Hysteretic Advance of Phase.
80, P. 116. Loss of Energy by Molecular Magnetic Friction.
81, P. 119. Effective Conductance, Due to Magnetic Hysteresis.
82, P. 122. Absolute Admittance of Ironclad Circuits and Angle of
Hysteretic Advance.
83, P. 124. Magnetic Circuit Containing Air-gap.
84, P. 125. Electric Constants of Circuit Containing Iron.
85, P. 127. Conclusion.
Chap. Xi. Foucault or Eddy Currents.
86, P. 129. Effective Conductance of Eddy Currents.
87, P. 130. Advance Angle of Eddy Currents.
88, P. 131. Loss of Power by Eddy Currents, and Coefficient of Eddy
Currents.
89, P. 131. Laminated Iron.
90, P. 133. Iron Wire.
91, P. 135. Comparison of Sheet Iron and Iron Wire.
92, P. 136. Demagnetizing or Screening Effect of Eddy Currents.
93, P. 138. Continued.
94, P. 138. Large Eddy Currents.contents.
Chap. Xi. Foucault or Eddy Currents. Continued.
95, P. 139. Eddy Currents in Conductor and Unequal Current Distribution.
96, P. 140. Continued.
97, P. 142. Mutual Inductance.
98, P. 144. Dielectric and Electrostatic Phenomena.
99, P. 145. Dielectric Hysteretic Admittance, Impedance, Lag, Etc.
100, P. 147. Electrostatic Induction or Influence.
101, P. 149. Energy Components and Wattless Components.
Chap. Xii. Power, and Double Frequency Quantities in General.
102, P. 150. Double Frequency of Power.
103, P. 151. Symbolic Representation of Power.
104, P. 153. Extra-algebraic Features Thereof.
105, P. 155. Combination of Powers.
106, P. 156. Torque as Double Frequency Product.
Chap. Xiii. Distributed Capacity, Inductance, Resistance, and Leakage.
107, P. 158. Introduction.
108, P. 159. Magnitude of Charging Current of Transmission Lines.
109, P. 160. Line Capacity Represented by One Condenser Shunted
Across Middle of Line.
110, P. 161. Line Capacity Represented by Three Condensers.
111, P. 163. Complete Investigation of Distributed Capacity, Inductance, Leakage, and Resistance.
112, P. 165. Continued.
113, P. 166. Continued.
114, P. 166. Continued.
115, P. 167. Continued.
116, P. 169. Continued.
117, P. 170. Continued.
118, P. 170. Difference of Phase at Any Point of Line.
119, P. 17-2. Instance.
120, P. 173. Further Instance and Discussion.
121, P. 178. Particular Cases, Open Circuit at End of Line, Line
Grounded at End, Infinitely Ong Conductor, Generator Feeding
Into Closed Circuit.
122, P. 181. Natural Period of Transmission Line.
123, P. 186. Discussion.
124, P. 190. Continued.
125, P. 191. Inductance of Uniformly Charged Line.
Chap. Xiv. The Alternating-current Transformer.
126, P. 193. General.
127, P. 193. Mutual Inductance and Self-inductance of Transformer.
128, P. 194. Magnetic Circuit of Transformer.contents.
.
Xv
Chap. Xiv. The Alternating-current Transformer Continued.
129, P. 195. Continued.
130, P. 196. Polar Diagram of Transformer.
131, P. 198. Instance.
132, P. 202. Diagram for Varying Load.
133, P. 203. Instance.
134, P. 204. Symbolic Method, Equations.
135, P. 206.
136, P. 208.
Continued.
Apparent Impedance of Transformer. Transformer
Equivalent to Divided Circuit.
137, P. 209. Continued.
138, P. 212. Transformer on Non-inductive Load.
139, P. 214. Constants of Transformer on Non-inductive Load.
140, P. 217. Numerical Instance.
Chap. Xv. General Alternating-current Transformer or Frequency
Converters.
141, P. 219. Introduction.
142, P. 220. Magnetic Cross-flux or Self-induction of Transformer.
143, P. 221. Mutual Flux of Transformer.
144, P. 221. Difference of Frequency Between Primary and Secondary
Of General Alternate-current Transformer.
145, P. 221. Equations of General Alternate-current Transformer.
146, P. 227. Power, Output, and Input, Mechanical and Electrical.
147, P. 228. Continued.
148, P. 229. Speed and Output.
149, P. 231. Numerical Instance.
150, P. 232. Characteristic Curves of Frequency Converter.
Chap. Xvi. Induction Machines.
151, P. 237. Slip and Secondary Frequency.
152, P. 238. Equations of Induction Motor.
153, P. 239. Magnetic Flux, Admittance, and Impedance.
154, P. 241. E.m.f.
155, P. 244. Graphic Representation.
156, P. 245. Continued.
157, P. 246. Torque and Power.
158, P. 248. Power of Induction Motors.
159, P. 250. Maximum Torque.
160, P. 252. Continued.
161, P. 252. Maximum Power.
162, P. 254. Starting Torque.
163, P. 258. Synchronism.
164, P. 258. Near Synchronism.
165, P. 259. Numerical Instance of Induction Motor.
166, P. 262. Calculation of Induction Motor Curves.
167, P. 265. Numerical Instance.xvi Contents.
Chap. Xvi. Induction Machines Continued.
168, P. 265. Induction Generator.
169, P. 268. Power Factor of Induction Generator.
170, P. 269. Constant Speed, Induction Generator.
171, P. 272. Induction Generator and Synchronous Motor.
172, P. 274. Concatenation or Tandem Control of Induction Motors.
173, P. 276. Calculation of Concatenated Couple.
174, P. 280. Numerical Instance.
175, P. 281. Single-phase Induction Motor.
176, P. 283. Starting Devices of Single-phase Motor.
177, P. 284. Polyphase Motor on Single-phase Circuit.
178, P. 286. Condenser in Tertiary Circuit.
179, P. 287. Speed Curves With Condenser.
180, P. 291. Synchronous Induction Motor.
181, P. 293. Hysteresis Motor.
Chap. Xvii. Alternate-current Generator.
182, P. 297. Magnetic Reaction of Lag and Lead.
183, P. 300. Self-inductance and Synchronous Reactance.
184, P. 302. Equations of Alternator.
185, P. 303. Numerical Instance, Field Characteristic.
186, P. 307. Dependence of Terminal Voltage on Phase Relation.
187, P. 307. Constant Potential Regulation.
188, P. 309. Constant Current Regulation, Maximum Output.
Chap. Xviii. Synchronizing Alternators.
189, P. 311. Introduction.
190, P. 311. Rigid Mechanical Connection.
191, P. 311. Uniformity of Speed
192, P. 312. Synchronizing.
193, P. 313. Running in Synchronism.
194, P. 313. Series Operation of Alternators.
195, P. 314. Equations of Synchronous Running Alternators, Synchronizing Power.
196, P. 317. Special Case of Equal Alternators at Equal Excitation.
197, P. 320. Numerical Instance.
Chap. Xix. Synchronous Motor.
198, P. 321. Graphic Method.
199, P. 323. Continued.
200, P. 325. Instance.
201, P. 326. Constant Impressed E.m.f. And Constant Current.
202, P. 329. Constant Impressed and Counter E.m.f.
203, P. 332. Constant Impressed E.m.f. And Maximum Efficiency.
204, P. 334. Constant Impressed E.m.f. And Constant Output.
205, P. 338. Analytical Method. Fundamental Equations and Power,
Characteristic.contents. Xvii
Chap. Xix. Synchronous Motor Continued.
206, P. 342. Maximum Output.
207, P. 343. No Load.
208, P. 345. Minimum Current.
209, P. 347. Maximum Displacement of Phase.
210, P. 349. Constant Counter E.m.f.
211, P. 349. Numerical Instance.
212, P. 351. Discussion of Results.
Chap. Xx. Commutator Motors.
213, P. 354. Types of Commutator Motors.
214, P. 354. Repulsion Motor as Induction Motor.
215, P. 356. Two Types of Repulsion Motors.
216, P. 358. Definition of Repulsion Motor.
217, P. 359. Equations of Repulsion Motor.
218, P. 360. Continued.
219, P. 361. Power of Repulsion Motor. Instance.
220, P. 363. Series Motor, Shunt Motor.
221, P. 366. Equations of Series Motor.
222, P. 367. Numerical Instance.
223, P. 368. Shunt Motor.
224, P. 370. Power Factor of Series Motor.
Chap. Xxi. Reaction Machines.
225, P. 371. General Discussion.
226, P. 372. Energy Component of Reactance.
227, P. 372. Hysteretic Energy Component of Reactance.
228, P. 373. Periodic Variation Reactance.
229, P. 375. Distortion of Wave-shape.
230, P. 377. Unsymmetrical Distortion of Wave-shape.
231, P. 378. Equations of Reaction Machines.
232, P. 380. Numerical Instance.
Chap. Xxii. Distortion of Wave-shape, and Its Causes.
233, P. 383. Equivalent Sine Wave.
234, P. 383. Cause of Distortion.
235, P. 384. Lack of Uniformity and Pulsation of Magnetic Field^
S 236, P. 388. Continued.
237, P. 391. Pulsation of Reactance.
238, P. 391. Pulsation of Reactance in Reaction Machine.
239, P. 393. General Discussion.
240, P. 393. Pulsation of Resistance Arc.
241, P. 395. Instance.
242, P. 396. Distortion of Wave-shape by Arc.
243.
P. 397. Discussion.xvili Co Ttents.
Chap. Xxiii. Effects of Higher Harmonics.
244, P. 393. Distortion of Wave-shape by Triple and Quintuple Harmonics. Some Characteristic
Wave-shapes.
245, P. 401. Effect of Self-induction and Capacity on Higher Harmonics.
246, P. 402. Resonance Due to Higher Harmonics in Transmission Lines.
247, P. 405. Power of Complex Harmonic Waves.
248, P. 405. Three-phase Generator.
249, P. 407. Decrease of Hysteresis by Distortion of Wave-shape.
250, P. 407. Increase of Hysteresis by Distortion of Wave-shape.
251, P. 408. Eddy Currents.
252, P. 408. Effect of Distorted Waves on Insulation.
Chap. Xxiv. Symbolic Representation of General Alternating Wave.
253, P. 410. Symbolic Representation.
254, P. 412. Effective Values.
255, P. 4l3. Power Torque, Etc. Circuit Factor.
256, P. 416. Resistance, Inductance, and Capacity in Series.
257, P. 419. Apparent Capacity of Condenser.
258, P. 422. Synchronous Motor.
259, P. 426. Induction Motor.
Chap. Xxv. General Polyphase Systems.
260, P. 430. Definition of Systems, Symmetrical and Unsymmetrical
Systems.
261, P. 430. Flow of Power. Balanced and Unbalanced Systems.
Independent and Interlinked Systems. Star Connection and Ring
Connection.
262, P. 432. Classification of Polyphase Systems.
Chap. Xxvi. Symmetrical Polyphase Systems.
263, P. 434. General Equations of Symmetrical Systems.
264, P. 435. Particular Systems.
265, P. 436. Resultant M.m.f. Of Symmetrical System.
266, P. 439. Particular Systems.
Chap. Xxvii. Balanced and Uunbalanced Polyphase Systems.
267, P. 440. Flow of Power in Single-phase System.
268, P. 441. Flow of Power in Polyphase Systems, Balance Factor of
System.
269, P. 442. Balance Factor.
270, P. 442. Three-phase System, Quarter-phase System.
271, P. 413. Inverted Three Phase System.
272, P. 444. Diagrams of Flow of Power.
273, P. 447. Monocyclic and Polycyclic Systems.
274, P. 447. Power Characteristic of Alternating-current System.
275, P. 448. The Same in Rectangular Coordinates.
276, P. 450. Main Power Axes of Alternating-current System.contents. Xix
Chap. Xxviii. Interlinked Polyphase Systems.
277, P. 452. Interlinked and Independent Systems.
278, P. 452. Star Connection and Ring Connection. Y Connection and
Delta Connection.
279, P. 454. Continued.
280, P. 455. Star Potential and Ring Potential. Star Current and Ring
Current. Y Potential and Y Current, Delta Potential and Delta
Current.
281, P. 455. Equations of Interlinked Polyphase Systems.
282, P. 457. Continued.
Chap. Xxix. Transformation of Polyphase Systems.
283, P. 460. Constancy of Balance Factor.
284, P. 460. Equations of Transformation of Polyphase Systems.
285, P. 462. Three-phase, Quarter-phase Transformation.
286, P. 463. Some of the More Common Polyphase Transformations.
287, P. 466.f Transformation With Change of Balance Factor.
Chap. Xxx.
Copper Efficiency of Systems.
288, P. 468. General Discussion.
289, P. 469. Comparison on the Basis of Equality of Minimum Difference of
Potential.
290, P. 474. Comparison on the Basis of Equality of Maximum Difference of
Potential.
291, P. 476. Continued.
Chap. Xxxi. Three-phase System.
292, P. 478. General Equations.
293, P. 481. Special Cases: Balanced System, One Branch Loaded,
Two Branches Loaded.
Chap. Xxxii.
Quarter-phase System.
294, P. 483. General Equations.
295, P. 484. Special Cases : Balanced System, One Branch Loaded.
Appendix I.
Algebra of Complex Imaginary Quantities.
296, P. 489. Introduction.
297, P. 489. Numeration, Addition, Multiplication, Involution.
298, P. 490. Subtraction, Negative Number.
299, P. 491. Division, Fraction.
300, P. 491. Evolution and Logarithmation.
301, P. 492. Imaginary Unit, Complex Imaginary Number.
302, P. 492. Review.
303, P. 493. Algebraic Operations With Complex Quantities.
304, P. 494. Continued.
305, P. 495. Roots of the Unit.
306, P. 495. Rotation.
307, P. 496. Complex Imaginary Plane.contents.
Appendix Ii. Oscillating Currents.
308, P. 497. Introduction.
309, P. 498. General Equations.
310, P. 499. Polar Coordinates.
311, P. 500. Loxodromic Spiral.
312, P. 501. Impedance and Admittance.
313, P. 502. Inductance.
314, P. 502. Capacity.
315, P. 503. Impedance.
316, P. 504. Admittance.
317, P. 505. Conductance and Susceptance.
318, P. 506. Circuits of Zero Impedance.
319, P. 506. Continued.
320, P. 507. Origin of Oscillating Currents.
321, P. 508. Oscillating Discharge.
322, P. 509. Oscillating Discharge of Condensers
323, P. 510. Oscillating Current Transformer.
324, P. 512. Fundamental Equations Thereof.
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