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ELECTRICAL MACHINES
Contents
1 Introduction
Power converters and electrical machines
Rotating power converters
Static power converters
The role of electromechanical power conversion
Principles of operation
Magnetic and current circuits
Rotating electrical machines
Reversible machines
Significance and typical applications
Variables and relations of rotational movement
Notation and system of units
Target knowledge and skills
Basic characteristics of electrical machines
Equivalent circuits
Mechanical characteristics
Transient processes in electrical machines
Mathematical model
Adopted approach and analysis steps
Prerequisites
Notes on converter fed variable speed machines
Remarks on high efficiency machines
Remarks on iron and copper usage
2 Electromechanical energy conversions
Lorentz force
Mutual action of parallel conductors
Electromotive force in a moving conductor
Generator mode
Reluctant torque
Reluctant force
Force on conductors in electrical field
Change of permittivity
Piezoelectric effect
Magnetostriction
3 Magnetic and electrical coupling field
Converters based on electrostatic field
Charge, capacitance, and energy
Source work, mechanical work, and field energy
Force expression
Conversion cycle
Energy density of electrical and magnetic field
Coupling field and transfer of energy
Converter involving magnetic coupling field
Linear converter
Rotational converter
Rotational converter
Back electromotive force
4 Magnetic circuits
Analysis of magnetic circuits
Flux conversion law
Generalized relation between magnetic
Field H and induction B
The flux vector
Magnetizing characteristics of ferromagnetic materials
Magnetic resistance of the circuit
Energy in a magnetic circuit
Energy in a magnetic circuit
Reference direction of the magnetic circuit
Losses in magnetic circuits
Hysteresis losses
Losses due to eddy currents
Total losses in magnetic circuit
The methods of reduction of iron losses
Eddy current in laminated ferromagnetic
5 Rotating electrical machines
Magnetic circuit of rotating machines
Mechanical access
The windings
Slots in magnetic circuit
The position and notation of winding axis
Conversion losses
Magnetic field in air gap
Field energy, size, and torque
6 Modeling electrical machines
The need for modeling
Problems of modeling
Conclusion
Neglected phenomena
Distributed energy and distributed parameters
Neglecting parasitic capacitances
Neglecting iron losses
Neglecting iron nonlinearity
Power of electrical sources
Electromotive force
Voltage balance equation
Leakage flux
Energy of the coupling field
Power of electromechanical conversion
Torque expression
Mechanical subsystem
Kinetic energy
Model of mechanical subsystem
Balance of power in electromechanical converters
Equations of mathematical model
7 Single-fed and double-fed converters
Analysis of single-fed converter
Variation of self-inductance
The expressions for power and torque
Analysis of double-fed converter
Variation of mutual inductance
Torque expression
Average torque
Conditions for generating nonzero torque
Magnetic poles
Direct current and alternating current machines
Torque as a vector product
Position of the flux vector in rotating machines
Rotating field
Types of electrical machines
Direct current machines
Induction machines
Synchronous machines
8 Magnetic field in the air gap
Stator winding with distributed conductors
Sinusoidal current sheet
Components of stator magnetic field
Axial component of the field
Tangential component of the field
Radial component of the rotor field
Survey of components of the rotor
Magnetic field
Convention of representing magnetic
Field by vector
9 Energy, flux, and torque
Interaction of the stator and rotor fields
Energy of air gap magnetic field
Electromagnetic torque
The torque expression
Turn flux and winding flux
Flux in one stator turn
Flux in one rotor turn
Winding flux
Winding flux vector
Winding axis and flux vector
Vector product of stator and rotor flux vectors
Conditions for torque generation
Torque-size relation
Rotating magnetic field
System of two orthogonal windings
System of three windings
10 Electromotive forces
Transformer and dynamic electromotive forces
Electromotive force in one turn
Calculating the first derivative
Of the flux in one turn
Summing electromotive forces of individual
Conductors
Voltages balance in one turn
Electromotive force waveform
Root mean square value
Of electromotive forces
Electromotive force in a winding
Concentrated winding
Distributed winding
Chord factor
Belt factor
Harmonics suppression of winding belt
Electromotive force in distributed winding
Individual harmonics
Peak and rms of winding electromotive force
11 Introduction to DC machines
Construction and principle of operation
Construction of the stator
Separately excited machines
Current in rotor conductors
Mechanical commentator
Rotor winding
Communication
Operation of commentator
Making the rotor winding
Problems with commutation
Rotor magnetic field
Current circuits and magnetic circuits
Magnetic circuits
Direct and quadrature axis
Vector representation
Resultant fluxes
Resultant flux of the machine
Electromotive force and electromagnetic torque
Electromotive force in armature winding
Torque generation
Torque and electromotive force expressions
Calculation of electromotive force E
Calculation of torque
12 Modeling and supplying DC machines
Voltage balance equation for excitation winding
Voltage balance equation in armature winding
Changes in rotor speed
Mathematical model
DC machine with permanent magnets
Block diagram of the model
Torque control
Steady-state equivalent circuit
Mechanical characteristics
Stable equilibrium
Properties of mechanical characteristics
Speed regulation
DC generator
Topologies of DC machine power supplies
Armature power supply requirements
Four quadrants in T- and U-I diagrams
The four-quadrant power converter
Pulse-width modulation
Current ripple
Topologies of power converters
13 Characteristics of DC machines
Rated voltage
Mechanical characteristics
Natural characteristics
Rated current
Thermal model and intermittent operation
Rated flux
Rated speed
Field weakening
High-speed operation
Torque and power in field weakening
Flux change
Electromotive force change
Current change
Torque change
Power change
The need for field-weakening operation
Steady-state operating area
Power losses and power balance
Power of supply
Losses in excitation winding
Losses armature winding
Power of electromechanical conversion
Iron losses
Mechanical losses
Losses due to rotation
Mechanical power
Rated and declared values
Nameplate data
Current ripple
Frequency control
Field weakening
Reversal of frequency-controlled
Induction machines
Steady state and transient operating area
Steady state operating limits
RI compensation
Critical speed
Construction of induction machines
Mains-supplied machines
Variable frequency induction
Machines
14 Synchronous machines
Principle of operation
Stator windings
Revolving field
Torque generation
Construction of synchronous machines
Stator magnetic circuit
Construction of the rotor
Supplying the excitation winding
Excitation with rotating transformer
Permanent magnet excitation
Characteristics of permanent magnets
Magnetic circuits with permanent magnets
Surface mounts and buried magnets
Characteristics of permanent magnet machines
15 Mathematical model of synchronous machine
Modeling synchronous machines
Magneto motive force
Two-phase equivalent
Clarke 3 /2 transform
Inductance matrix and voltage balance equations
Park transform
Inductance matrix in dq frame
Vectors as complex numbers
Voltage balance equations
Electrical subsystem of isotropic machines
Torque in isotropic machines
Anisotropic rotor
Reluctant torque
Reluctance motor
16 steady-state operation
Voltage balance equations at steady state
Equivalent circuit
Peak and rms values of currents and voltages
Phasor diagram of isotropic machine
Phasor diagram of anisotropic machine
Torque in anisotropic machine
Torque change with power angle
Mechanical characteristics
Synchronous machine supplied from stiff network
Operation of synchronous generators
Increase of turbine power
Increase in line frequency
Reactive power and voltage changes
Changes in power angle
17 Transients in synchronous machines
Electrical and mechanical time constants
Hunting of synchronous machines
Damped LC circuit
Damping of synchronous machines
Damper winding
Short circuit of synchronous machines
DC component
Calculation of Isc1
Calculation of Isc2
Calculation of Isc3
Transient and sub transient phenomena
Interval 1
Interval 2
Interval 3
18 Variable frequency synchronous machines
Inverter-supplied synchronous machines
Torque control principles
Current control principles
Field weakening
Transient and steady-state operating area