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Dedication
by Marek Turowski, Janusz Turowski
Engineering Electrodynamics
Cover Page
Half Title
Title Page
Copyright Page
Dedication
Preface
Authors
List of Symbols
Abbreviations of Names of Computer Methods
1 Methods of Investigation and Constructional Materials
1.1 Methods of Investigations
1.2 Constructional Materials
1.2.1 Structure and Physical Properties of Metals
1.2.1.1 Atomic Structure
1.2.1.2 Ionization
1.2.1.3 Crystal Structure of Metals
1.2.1.4 Electrical Conductivity and Resistivity of Metals
1.2.1.5 Influence of Ingredients on Resistivity of Metals
1.2.1.6 Resistivity at Higher Temperatures
1.2.1.7 Thermoelectricity
1.2.1.8 Thermal Properties
1.2.1.9 Mechanical Properties
1.2.1.10 Hall Effect and Magnetoresistivity of Metals
1.2.2 Superconductivity
1.2.2.1 Superconductor Era in Electric Machine Industry
1.2.3 Magnetic Properties of Bodies (Ferromagnetism)
1.2.3.1 Magnetic Polarization and Magnetization
1.2.3.2 Ferromagnetics, Paramagnetics, and Diamagnetics
1.2.3.3 Atomic Structure of Ferromagnetics
1.2.3.4 Zones of Spontaneous Magnetization
1.2.3.5 Form of the Magnetization Curve
1.2.3.6 Hysteresis
1.2.3.7 Superposition of Remagnetization Fields
1.2.3.8 Amorphous Strips
1.2.3.9 Rotational Hysteresis
1.2.3.10 Types of Magnetization Curves
1.2.3.11 Curie Point
1.2.3.12 Nonmagnetic Steel
1.2.3.13 Influence of Various Factors on Properties of Magnetic Materials
1.2.3.14 Types of Magnetic Permeability
1.2.3.15 Permeability at High Frequencies
1.2.3.16 Magnetic Anisotropy
1.2.3.17 Magnetostriction
1.2.3.18 Demagnetization Coefficient
1.2.4 Semiconductors and Dielectrics
1.2.4.1 Hall Effect in Semiconductors
Example
2 Fundamental Equations of Electromagnetic Field
2.1 Primary Laws and Equations of Electromagnetism
2.2 Formulation and Methods of Solution of Field Differential Equations
2.2.1 Finding of Field Function
2.2.2 Classification of Field Equations
2.2.3 Boundary and Initial Value Problems of Electrodynamics
2.2.4 Auxiliary Functions and Vectors
2.2.4.1 Electric and Magnetic Scalar Potentials
2.2.4.2 Magnetic Vector Potential A and the Scalar Potential V of Electromagnetic Field (Electrodynamic Potentials)
2.2.4.3 Electric Vector Potential T
2.2.4.4 Hertz Vector P
2.2.4.5 Maxwell’s Stress Tensor
Example
2.2.5 Methods of Solution of Field Equations
2.3 Anisotropic Media
2.4 Nonlinear Media
2.4.1 Nonlinear Permittivity and Resistance
2.4.2 Nonlinear Magnetic Permeability
2.5 Fundamental Equations of Magnetohydrodynamics and Magnetogasdynamics
2.5.1 Mhd Generators
2.5.2 Electric Machines and Apparatus
2.6 Electrodynamics of Superconductors
2.7 Electrodynamics of Heterogeneous Media
2.8 Electrodynamics of Semiconductor Devices
2.9 Electrodynamics of Electrochemical Systems
2.10 General Wave Equations
2.10.1 Wave Equations in Metal
2.11 Fourier’s Method
2.12 Wave Equations in Cylindrical Coordinates
2.13 Plane Wave
2.13.1 Plane Wave in a Dielectric
2.13.2 Plane Wave in a Conducting Half-Space
2.13.3 Equivalent Depth of Wave Penetration and Impedance of Solid Conductors
Example
2.13.4 Field Diffusion Into a Conductor
2.14 Reflection and Refraction of Plane Wave
2.14.1 Boundary Conditions
2.14.2 Reflection and Refraction of a Perpendicular Plane Wave
2.14.3 Near and Far Fields
2.14.4 Oblique Reflection, Refraction, and Guiding of a Wave
3 Transfer and Conversion of Field Power
3.1 Poynting’s Theorem: Poynting Vector*
3.2 Penetration of the Field Power into a Solid Conducting Half-Space
Example
3.3 Power Flux at Conductors Passing through a Steel Wall
3.4 Power Flux in a Concentric Cable and Screened Bar
3.4.1 Factors of Utilization of Constructional Space
3.5 Power Flux in a Capacitor, Coil, and Transformer
3.6 Power Fluxes and Their Conversion in Rotating Machines
3.6.1 Power Flux of Electromagnetic Field in Gap of Induction Machine
3.6.2 Power Flux of Electromagnetic Field in Air Gap of Synchronous Machine
Example
4 Screening of Constructional Parts
4.1 Types and Goals of Screening and Shunting
4.2 Magnetic Screens
4.2.1 Spherical and Crosswise Cylindrical Screens
4.2.1.1 Magnetic Screening of a Double-Conductor Line
4.2.2 Longitudinal Magnetic Screens
4.3 Electromagnetic Screens: Wave Method of Modeling and Calculation
4.3.1 Practical Convenience at Application of Wave Method of Calculation
4.3.2 Penetrable (Translucent) Screen with a One-Sided Incident Wave
4.3.2.1 Thin Screens
4.3.2.2 Thin Screens in Dielectric
4.3.2.3 Thin Screens on the Surface of Iron
4.3.2.4 Thick Screens
4.3.3 Penetrable Screen at Wave Incident from Both Sides
4.4 Power Losses in Screens
4.4.1 Poynting Vector and Power Losses in a One-Sided Screen
4.4.1.1 Screen Surrounded by Dielectric
4.4.1.2 Screen Adhering to Iron
Screening coefficient of power
4.4.2 Poynting Vector and Power Loss at Double-Sided Symmetric Incidence of Waves
4.5 Screening of Transformer Tanks
4.5.1 Magnetic Screening (Shunting) of Tanks
4.5.1.1 Influence of Eddy Currents and Saturation on Magnetic Screens (Shunts)
EXAMPLE
4.5.2 Electromagnetic Screening of a Transformer Tank
4.5.3 Three-Dimensional Computer Analysis and Interactive Design of Screens
4.6 Induction Motors with a Screened and Multilayer Rotor
4.6.1 General Characteristics
4.6.2 Fundamental Equations of Stratified Induction Motors
4.6.2.1 Field Equations
The computation programs
4.7 Screening in Large Generators
4.7.1 Magnetic Screening and Shaping the Field
4.7.1.1 Magnetic Screening in Large Generators
4.7.1.2 Screening of Windings and Conductors
4.7.2 Electromagnetic Screening in Generators
4.8 Screening at Induction Heating
4.9 Screening of Bars and Conductor Wires
4.9.1 Cylindrical Screen of a Single Conductor Wire
4.9.1.1 Electromagnetic Screens
4.9.1.2 Power Losses in Screen
Example
Example
4.9.2 Cylindrical Screen in a Transverse, Uniform Field
4.9.3 Screens of Busbars in Generator Unit Systems of Power Stations
4.9.3.1 Isolated Screens
4.9.3.2 Connected Screens
4.10 Electromagnetic Field in Multilayer Screens
4.10.1 Two-Layer Conductor
4.10.2 Influence of Insulation Under the Screen
5 Magnetic Fields Near Iron Surfaces
5.1 Method of Mirror Images
5.1.1 Singular Images of Direct Current
5.1.1.1 Analogy in Electrostatic Fields
5.1.2 Application of the DC Field Theory to AC Fields
5.1.2.1 Mirror Image Coefficients of Alternating Currents in Metal Surfaces
5.1.3 Magnetic Images of Current in an Iron Cylinder
5.1.4 Multiple Mirror Images
5.1.4.1 Mirror Images of Current in Crossing Flat Iron Surfaces
5.1.4.2 Conductor Placed between Two Iron Surfaces
5.1.4.3 Conductor Encircled by Steel from Three Sides
5.1.5 Mirror Images of Magnets and Circuits with Direct Currents
5.2 Field of Endwindings in Electric Machines
5.2.1 Mirror Image in Solid Steel Wall
5.2.2 Influence of Air Gap
5.2.3 Influence of Constructional Elements
5.3 Field of Bushings
5.3.1 Dynamic Mirror Image of Currents
5.3.2 Field on the Cover Surface
5.4 Field of Bars Nearby a Steel Surface
5.5 Leakage Field in Transformers and in Slots of Electric Machines
5.5.1 Application of the Method of Multiple Mirror Images
5.5.2 Method of Approximate Solution of a Field in a Transformer Window with the Help of Fourier Series
5.5.2.1 Method of Analytical Prolongation
5.5.3 Numerical Methods: Mesh Methods of Solution of Leakage Magnetic Field in Power Transformers
5.5.3.1 Reluctance Network Method
5.5.4 Slot in a Deep-Slot Induction Machine
5.5.4.1 Rectangular Slot
5.5.4.2 Trapezoidal and Bulb Slots
5.5.5 Field in the Gap of Electric Machine
5.5.5.1 Analytical Methods
5.5.5.2 Meshed Numerical Methods
5.5.5.3 Graphical-Numerical Methods
5.5.5.4 Determination of the Magnetomotive Force (mmf) of Sources
5.6 Field of Conductors Nearby a Steel Wall
5.7 Additional Losses in Foil Windings of Transformer
6 Electromagnetic Phenomena in Metals with Constant Permeability
6.1 Application of Multiple Reflections of Electromagnetic Wave
6.2 Electrical Steel
6.2.1 Insulation Coefficient, ai
6.2.2 Coefficient of Flux Expulsion, aS
6.2.3 Hysteresis Losses
6.2.4 Losses Caused by Eddy Currents (Eddy-Current Losses)
6.2.5 Reactive Power Consumption
6.3 Power Losses at Current Intersections Through a Screen
6.3.1 Single-Phase Bushing System
6.3.2 Three-Phase Bushing System
6.4 Power Losses in Steel Covers with Gaps and Nonmagnetic Inserts Between Bushing Holes
6.5 Transient-Induced Processes
6.5.1 Eddy Currents
6.5.2 Mirror Image Coefficients
6.6 Solid Rotor of Induction Motor
6.7 Cup-Type Rotor
6.8 Principles of Induction Heating
6.9 High-Current Lines
6.9.1 Impedance
6.9.2 Proximity Effect
6.9.3 Power Translocation
6.9.4 Currents Induced in Steel Walls
7 Electromagnetic Phenomena in Ferromagnetic Bodies
7.1 Approximation of Magnetization Characteristics
7.1.1 Approximation of Recalculated Characteristics
7.2 Methods of Considering a Variable Magnetic Permeability
7.2.1 Rosenberg’s Method for Steel Conductors (1923)
7.2.2 Method of Rectangular Waves
7.2.3 Neiman’s Method (1949)
7.2.4 Substitute Permeability
7.2.5 Computer Method
Example
7.3 Dependence of Stray Losses in Solid Steel Parts of Transformers on Current and Temperature
7.4 Power Losses in Steel Covers of Transformers
7.5 Calculation of Stray Losses in Solid Steel Walls by Means of Fourier’s Series
7.5.1 General Method
7.5.1.1 Three-Dimensional Field
7.5.1.2 Two-Dimensional Field
7.5.2 Analytical Formulae in Case of Sinusoidal Distribution of a Field on the Steel Surface
7.5.3 Computer Calculation of Power Losses in a Steel Plate Placed in the Field of Parallel Bars
EXAMPLE
7.6 Power Losses in a Transformer Tank
7.6.1 Two-Dimensional Numerical Solution
7.6.2 Three-Dimensional Analytical Calculations of a Stray Field and Losses in Tanks at Constant Permeability
7.6.2.1 Field on the Tank Surface
7.6.2.2 Power Losses in a Tank
7.6.2.3 Influence of Flux in a Tank
7.6.3 Parametric Analytical-Numerical (ANM-3D) Calculation of Stray Losses in a Tank of a Transformer
Example
7.6.4 Three-Dimensional Numerical Calculation of Stray Fields and Losses in Large, Three-Phase, Power Transformers
7.6.4.1 FEM-3D
7.6.4.2 Three-Dimensional, Equivalent Reluctance Network Method: RNM-3D
7.6.5 Industrial Implementation and Verification of the RNM-3D
7.6.5.1 Industrial Implementation of the RNM-3D Package
7.6.5.2 Transformers without Screens, Almost Symmetric
7.6.5.3 Large Transformers with an Extensive Asymmetry
7.6.5.4 Influence of the Structure and Screens Configuration
7.6.5.5 Screening Mistake Risk
8 Forces in Electrodynamic Systems
8.1 Principles of Calculation of Forces Acting on Buses and Windings of Transformers
8.1.1 Interaction Force of Parallel Conductors
8.2 Forces Acting on bus Bars Located Near Steel Constructional Elements
8.3 Forces Acting on Conductor Surfaces
8.4 Forces in Slot Parts of Windings of Electric Machines
Example 8.1
Example 8.2
8.5 Reluctance Forces and Torques
8.5.1 Dynamics of Thyristor-Controlled Reversible Motors
8.5.2 Torque of Hybrid Stepping Motors with Permanent Magnets in Slots
9 Local Heating of Structural Parts
9.1 Electromagnetic Criteria of Local Excessive Heating
9.2 Methods of Prevention of Local Overheating of a Metal Construction
9.2.1 Coefficient of Irregularity of Heat Distribution, K (J. Turowski [9.10])
9.3 Heating of Transformer Cover Plates
9.4 Permissible Current in Bushings
9.4.1 Eddy-Current Loss and hot Spots in Bushing Turrets
9.4.2 Computer Calculation
9.4.3 Single-Phase Turrets
9.5 Three-Phase Turrets, Simulated by a Rapid, Equivalent-Circuit Rnm Model
9.5.1 Calculation of Reluctances for RNM
10 Methods of Experimental Investigations
10.1 Experimental Verification of Theoretical Calculations
10.2 Principles of Theory of Electrodynamic Similarity
10.3 Principle of Induction Heating Device Modeling
10.4 Modeling of High Current Lines
10.5 Modeling of Transformers and Their Elements
10.6 Thermometric Method of Per-Unit Power Losses Measurement
10.6.1 Method of Initial Rise of Body Temperature
10.6.2 Method of Switching on or off of the Investigated Object
10.6.3 Accuracy of the Method
10.6.4 Computer Recalculation of the Measured Power Losses in Solid Steel
10.6.5 Measurement Techniques
10.6.6 Approximate Formulae
10.7 Investigation of Permissible Over-Excitation of Power Transformers
10.8 Measurement of Power at Very Small Power Factors (Cos φ) and/or Small Voltages
10.8.1 Bridge Systems
10.8.2 Compensatory Measurement of Additional Losses
10.9 Other Methods of Measurements
10.9.1 Measurement of Magnetic Field Intensity
10.9.2 Measurement of Electric Field Intensity
10.9.3 Measurement of the Poynting Vector with the Help of Probes
10.9.4 Measurement of Power Flux*
10.10 Diagnostics of Metal Elements
10.11 Critical Distance of Tank Wall from Transformer Windings
10.11.1 Critical Distance of Electromagnetically Screened Tank Walls
10.12 Influence of Flux Collectors
11 Conclusion
11.1 Final Complex Example
Appendix
References
Index
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