Principles of Alternating Current Machinery
Ralph R. Lawrence
Associate Professor of Electrical Engineering of the Massachusetts
Institute of Technology; Member of the American
Institute of Electrical Engineers, Etc.
Table of Symbols Vi
Types of Alternators – frequency – armature Cores – field Cores – 1
Armature Insulation – field Insulation – cooling – filtering or
Washing Cooling Air – permissible Temperatures for Different
Types of Insulation.
Induced Electromotive Force
– phase Relation Between a Flux and the 20
Electromotive Force It Induces – shape of Flux and Electromotive-force Waves When Coil Sides Are 180 Electrical Degrees
Apart – calculation of the Electromotive Force Induced in a Coil
When the Coil Sides Are Not 180 Electrical Degrees Apart.
Open- and Closed-circuit Windings – bar and Coil Windings – con- 27
Centrated and Distributed Windings – whole- and Half-coiled
Windings – spiral, Lap and Wave Windings – single- and Polyphase Windings – pole Pitch – coil Pitch – phase Spread – breadth
– harmonics – pitch Factor – effect of Pitch on Harmonics –
Effect on Wave Form of Distributing a Winding – harmonics in
Rating – regulation – magnetomotive Forces and Fluxes Concerned 51
In the Operation of an Alternator – armature Reaction – armature
Reaction of an Alternator With Non-salient Poles – armature Reaction of an Alternator With Salient Poles
– armature Leakage Reactance – equivalent Leakage Reactance – effective Resistance –
Factors Which Influence the Effect and Magnitude of Armature
Reaction, Armature Reactance and Effective Resistance – conditions for Best Regulation.
Vector Diagram of an Alternator With Non-salient Poles – vector Dia- 84
Gram Applied as an Approximation to an Alternator With Salient
Poles – calculation of the Regulation of an Alternator From Vector Diagram – synchronous-impedance and Magnetomotive-force
Methods for Determining Regulation – data Necessary for the
Application of the Synchronous-impedance and the Magnetomotive-force Methods – examples of the Calculation of Regulation
By the Synchronous-impedance and Magnetomotive-force Methods
– potier Method – american Institute Method – example of the
Calculation of Regulation by the American Institute Method –
Value of a’ of the Magnetomotive-force Method for Normal
Saturation – example of the Calculation of Regulation by the
Magnetomotive-force Method Using the Value of a’ Obtained
From a Zero-power-factor Test – blondel Two-reaction Method
For Determining Regulation of an Alternator – example of Calculation of Regulation by the Two-reaction Method.
Short-circuit Method for Determining Leakage Reactance – zero- 118
Power-factor Method for Determining Leakage Reactance – potier
Triangle Method for Determining Reactance – determination of
Leakage Reactance From Measurements Made With Field Structure
– determination of Effective Resistance With Field
Losses – measurement of the Losses by the Use of a Motor – measure- 123
Ment of Effective Resistance
– retardation Method of Determining
The Losses – efficiency.
Short-circuit Current.. . 133
Conditions and Methods for Making Heating Tests of Alternators 136
Without Applying Load.
Calculation of Ohmic Resistance, Armature Leakage Reactance, 142
Armature Reaction, Air-gap Flux Per Pole, Average Flux Density
In the Air Gap and Average Apparent Flux Density in the Armature Teeth From the Dimensions of an Alternator – calculation of
Leakage Reactance and Armature Reaction From an Open-circuit
Saturation Curve and a Saturation Curve for Full-load Current at
Zero Power Factor – calculation of Equivalent-leakage Flux Per. Contents Xi
Unit Length of Embedded Inductor and Effective Resistance From
Test Data – calculation of Regulation, Field Excitation and Efficiency for Full-load Kv-a. At 0.8 Power Factor by the a. I. E. E.
Transformer – types of Transformers – cores – windings – insulation 151
– terminals – cooling – oil – breathers.
Induced Voltage – transformer on Open Circuit – reactance Coil 164
Determination of the Shape of the Flux Curve Wnich Corresponds to a 169
Given Electromotive-force Curve – determination of the Electromotive-force Curve From the Flux Curve – determination of the
Magnetizing Current and the Current Supplying the Hysteresis
Loss From the Hysteresis Curve and the Curve of Induced Voltage
– current Rushes.
Fluxes Concerned in the Operation of a Transformer and No-load 179
Vector Diagram – ratio of Transformation – reaction of Secondary Current – reduction Factors – relative Values of Resistances –
Relative Values of Reactances – calculation of Leakage Reactance
– load Vector Diagram – analysis of Vector Diagram – solution of
Vector Diagram and Calculation of Regulation.
True Equivalent Circuit of a Transformer – graphical Representation of 195
The Approximate Equivalent Circuit – calculation of Regulation
From the Approximate Equivalent Circuit.
Losses in a Transformer – eddy-current Loss – hysteresis Loss – 200
Screening Effect of Eddy Currents – efficiency – all-day Efficiency.
Measurement of Core Loss – separation of Eddy-current and Hystere- 213
Sis Losses – measurement of Equivalent Resistance – measurement
Of Equivalent Reactance, Short-circuit Method – measurement of
Equivalent Reactance, Highly-inductive-load Method – opposition
Method of Testing Transformers.xu Contents
Current Transformer – potential Transformer – constant-current Trans- 222
Former – auto-transformer – induction Regulation.
Transformers With Independently Loaded Secondaries; Parallel Opera- 241
Tion of Single-phase Transformers.
Transformer Connections for Three-phase Circuits Using Three Trans- 252
– three-phase Transformation With Two Transformers –
Three- to Four-phase Transformation and Vice Versa – three- to
Six-phase Transformation – two- or Four-phase to Six-phase Transformation
– three- to Twelve-phase Transformation.
Three-phase Transformers – third Harmonics in the Exciting Cur- 272
Rents and in the Induced Voltages of Y- and a-connected Transformers – advantages and Disadvantages of Three-phase Transformers – parallel Operation of Three-phase Transformers or
Three-phase Groups of Single-phase Transformers – v- and a-connected Transformers in Parallel.
Ratio of Transformation, Flux and Flux Density – primary and 288
Secondary Leakage Reactances, Equivalent Reactance, Primary and
Secondary Resistances Calculated From the Dimensions of a Transformer – core Loss – component of No-load Current Supplying
Core Loss, Magnetizing Current and No-load Current Calculated
From Dimensions of Transformer and Core Loss and Magnetization
Curves – equivalent Resistance and Equivalent Reactance From
– calculated Regulation and Efficiency.
– general Characteristics – power Factor – v-curves – 297
Methods of Starting – explanation of the Operation of a Synchronous Motor.
Vector Diagram – magnetomotive-force and Synchronous-impedance 304
Effect Diagrams of Change – change in Load in Normal and Field Excitation Excitation With, Change of Load – contents Xm
Maximum and Minimum Motor Excitation for Fixed Motor Power and 309
Fixed Impressed Voltage – maximum Motor Power With Fixed
Ea\ V , Re and Xs’, Maximum Possible Motor Excitation With Fixed
Impressed Voltage and Fixed Resistance and Reactance – maximum Motor Activity With Fixed Impressed Voltage and Fixed
Reactance and Resistance.
Hunting – damping – stability – methods of Starting Synchronous 314
Circle Diagram of the Synchronous Motor – proof of Diagram – con- 330
Struction of Diagram – limiting Operating Conditions – some
Uses of the Circle Diagram.
Losses and Efficiency – advantages and Disadvantages – uses 338
Parallel Operation of Alternators
– batteries and Direct-current Generators in 341
Parallel – alternators in Parallel – synchronizing Action, Two
Equal Alternators – synchronizing Current – reactance is Necessary for Parallel Operation – constants of Generators for Parallel
Operation Need Not Be Inversely Proportional to Their Ratings.
Synchronizing Action of Two Identical Alternators – effect of Paral- 353
Leling Two Alternators Through Transmission Lines of High Impedance – the Relation Between R and X for Maximum Synchronizing
Period of Phase Swinging or Hunting – damping – irregularity of 361
Engine Torque During Each Revolution and Its Effect on Parallel
Operation of Alternators – governors.
Power Output of Alternators Operating in Parallel and the Method of Ad- 370
Justing the Load Between Them – effect of Difference in the Slopes
Of the Engine Speed-load Characteristics on the Division of the
Load Between Alternators Which Are Operating in Parallel – effect
Of Changing the Tension of the Governor Spring on the Load Carried by an Alternator Which is in Parallel With Others.xiv Contents
Effect of Wave Form on Parallel Operation of Alternators, 377
A Resum6 of the Conditions for Parallel Operation of Alternators – 382
Difference Between Paralleling Alternators and Direct-current
Generators – synchronizing Devices – connections for Synchronizing Single-phase Generators – a Special Form of Synchronizing
Transformer – connections for Synchronizing Three-phase Generators Using Synchronizing Transformers – lincoln Synchronizer.
Means of Converting Alternating Current Into Direct Current 393
Voltage Ratio of an N-phase Converter – current Relations 396 ‘
Copper Losses of a Rotary Converter – inductor Heating – inductor 403
Heating of an N-phase Converter With a Uniformly Distributed
Armature Winding – relative Outputs of a Converter Operated as
A Converter and as a Generator – efficiency.
Armature Reaction – commutating Poles – hunting – methods of 414
– methods of Controlling Voltage – split-pole 422
Chapter Xl «
Inverted Converter – double-current Generator – 60-cycle Versus 429
25-cycle Converters – motor Generators Versus Rotary Converters.
Parallel Operation 435
Field Excitation and Efficiency Calculated From Armature Resistance, 437
Winding Data, Open-circuit Core Loss and Oped-circuit Saturn
Tion Curves.contents Xv
Polyphase Induction Motors
Asynchronous Machines – polyphase Induction Motor – operation of 443
The Polyphase Induction Motor – slip – revolving Magnetic Field
– rotor Blocked – rotor Free – load is Equivalent to a Noninductive Resistance on a Transformer – transformer Diagram of
A Polyphase Induction Motor – equivalent Circuit of a Polyphase
Effect of Harmonics in the Space Distribution of the Air-gap Flux 455
Analysis of the Vector Diagram – internal Torque – maximum Internal 460
Torque and the Slip Corresponding Thereto – effect of Reactance,
Resistance, Impressed Voltage and Frequency on the Breakdown
Torque and Breakdown Slip – speed-torque Curve – stability –
Starting Torque – fractional-pitch Windings – effect of Shape of
Rotor Slots on Starting Torque and Slip.
Rotors, Number of Rotor and Stator Slots, Air Gap – coil-wound Rotors 468
– squirrel-cage Rotors – advantages and Disadvantages of the
Two Types of Rotor.
Methods of Starting Polyphase Induction Motors – methods of Vary- 471
Ing the Speed of Polyphase Induction Motors – division of Power
Developed by Motors in Concatenation – losses in Motors in
Calculation of the Performance of an Induction Motor From Its Equiva- 484
Lent* Circuit – determination of the Constants for the Equivalent
Circle Diagram of the Polyphase Induction Motor – scales – maximum 490
Power, Power Factor and Torque – determination of the Circle
General Characteristics of the Induction Generator – circle Diagram 497
Of the Induction Generator
– changes in Power Produced by a
Change in Slip – power Factor of the Induction Generator – phasexvi Contents
Relation Between Rotor Current Referred to the Stator and
Rotor Induced Voltage, E2 – vector Diagram of the Induction
Generator – voltage, Magnetizing Current and Function of Synchronous Apparatus in Parallel With an Induction Generator –
Use of a Condenser Instead of a Synchronous Generator in
Parallel With an Induction Generator – voltage, Frequency and
Load of the Induction Generator
– short-circuit Current of the
– hunting of the Induction Generator –
Advantages and Disadvantages of Induction Generators – use of
Calculation of the Constants of a Three-phase Induction Motor for the 505
Equivalent Circuit – calculation of Output, Torque, Input, Efficiency, Stator Current and Power Factor From Equivalent Circuit
For a Given Slip.
Single-phase Induction Motors
Single-phase Induction Motor – windings – method of Ferraris for 511
Explaining the Operation of the Single-phase Induction Motor.
Quadrature Field of the Single-phase Induction Motor – revolving 516
Field of the Single-phase Induction Motor – explanation of the
Operation of the Single-phase Induction Motor – comparison of the
Losses in Single-phase and Polyphase Induction Motors.
Vector Diagram of the Single-phase Induction Motor – generator 527
Action of the Single-phase Induction Motor.
Commutator-type, Single-phase, Induction Motor – power-factor Com- 533
Pensation – vector Diagrams of the Compensated Motor – speed
Control of the Commutator-type, Single-phase, Induction Motor
– commutation of the Commutator-type, Single-phase, Induction Motor.
Methods of Starting Single-phase Induction Motors 545
The Induction Motor as a Phase Converter 551contents Xvii
Series and Repulsion Motors
Types of Single-phase Commutator Motors With Series Characteristics 555
– starting – doubly Fed Motors – diagrams of Connections for
Singly and Doubly Fed Series and Repulsion Motors – powerfactor Compensation.
Singly Fed Series Motor – vector Diagram – approximate Vector 559
Diagram – over- and Under-compensation – starting and Speed
Control – commutation – inter-poles – construction, Efficiency
And Losses of Series Motors.
Singly Fed Repulsion Motor – motor at Rest – motor Running – 570
Vector Diagram – commutation – comparison of the Series and
Compensated Repulsion Motor – diagram of Connections – phase 583
Relations Between Fluxes, Currents and Voltages – power-factor
Compensation – commutation – vector Diagram – speed Control
And Direction of Rotation – advantages and Disadvantages of the
Compensated Motor. *
Doubly Fed Series and Repulsion Motors – doubly Fed Series Motor – 595
Approximate Vector Diagram of the Doubly Fed Series Motor –
Commutation of the Doubly Fed Series Motor – starting and
Operating the Doubly Fed Series Motor – doubly Fed Repulsion
– doubly Fed Compensated Repulsion Motor – regeneration by the Doubly Fed Compensated Repulsion Motor – advantages of the Two Types of Doubly Fed Motors – compensation
And Commutation of the Doubly Fed Compensated Repulsion
Motor – starting and Speed Control of the Doubly Fed Compensated Repulsion Motor.
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Principles of Alternating Current Machinery