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Engineering Electrodynamics

Book Description

Due to a huge concentration of electromagnetic fields and eddy currents, large power equipment and systems are prone to crushing forces, overheating, and overloading. Luckily, power failures due to disturbances like these can be predicted and/or prevented.

Based on the success of internationally acclaimed computer programs, such as the authors’ own RNM-3D, Engineering Electrodynamics: Electric Machine, Transformer, and Power Equipment Design explains how to implement industry-proven modeling and design techniques to solve complex electromagnetic phenomena. Considering recent progress in magnetic and superconducting materials as well as modern methods of mechatronics and computer science, this theory- and application-driven book:

  • Analyzes materials structure and 3D fields, taking into account magnetic and thermal nonlinearities
  • Supplies necessary physical insight for the creation of electromagnetic and electromechanical high power equipment models
  • Describes parameters for electromagnetic calculation of the structural parts of transformers, electric machines, apparatuses, and other electrical equipment
  • Covers power frequency 50-60 Hz (worldwide and US) equipment applications
  • Includes examples, case studies, and homework problems

Engineering Electrodynamics: Electric Machine, Transformer, and Power Equipment Design provides engineers, students, and academia with a thorough understanding of the physics, principles, modeling, and design of contemporary industrial devices.

Table of Contents

  1. Cover Page
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Preface
  7. Authors
  8. List of Symbols
  9. Abbreviations of Names of Computer Methods
  10. 1 Methods of Investigation and Constructional Materials
    1. 1.1 Methods of Investigations
    2. 1.2 Constructional Materials
      1. 1.2.1 Structure and Physical Properties of Metals
        1. 1.2.1.1 Atomic Structure
        2. 1.2.1.2 Ionization
        3. 1.2.1.3 Crystal Structure of Metals
        4. 1.2.1.4 Electrical Conductivity and Resistivity of Metals
        5. 1.2.1.5 Influence of Ingredients on Resistivity of Metals
        6. 1.2.1.6 Resistivity at Higher Temperatures
        7. 1.2.1.7 Thermoelectricity
        8. 1.2.1.8 Thermal Properties
        9. 1.2.1.9 Mechanical Properties
        10. 1.2.1.10 Hall Effect and Magnetoresistivity of Metals
      2. 1.2.2 Superconductivity
        1. 1.2.2.1 Superconductor Era in Electric Machine Industry
      3. 1.2.3 Magnetic Properties of Bodies (Ferromagnetism)
        1. 1.2.3.1 Magnetic Polarization and Magnetization
        2. 1.2.3.2 Ferromagnetics, Paramagnetics, and Diamagnetics
        3. 1.2.3.3 Atomic Structure of Ferromagnetics
        4. 1.2.3.4 Zones of Spontaneous Magnetization
        5. 1.2.3.5 Form of the Magnetization Curve
        6. 1.2.3.6 Hysteresis
        7. 1.2.3.7 Superposition of Remagnetization Fields
        8. 1.2.3.8 Amorphous Strips
        9. 1.2.3.9 Rotational Hysteresis
        10. 1.2.3.10 Types of Magnetization Curves
        11. 1.2.3.11 Curie Point
        12. 1.2.3.12 Nonmagnetic Steel
        13. 1.2.3.13 Influence of Various Factors on Properties of Magnetic Materials
        14. 1.2.3.14 Types of Magnetic Permeability
        15. 1.2.3.15 Permeability at High Frequencies
        16. 1.2.3.16 Magnetic Anisotropy
        17. 1.2.3.17 Magnetostriction
        18. 1.2.3.18 Demagnetization Coefficient
      4. 1.2.4 Semiconductors and Dielectrics
        1. 1.2.4.1 Hall Effect in Semiconductors
    3. Example
  11. 2 Fundamental Equations of Electromagnetic Field
    1. 2.1 Primary Laws and Equations of Electromagnetism
    2. 2.2 Formulation and Methods of Solution of Field Differential Equations
      1. 2.2.1 Finding of Field Function
      2. 2.2.2 Classification of Field Equations
      3. 2.2.3 Boundary and Initial Value Problems of Electrodynamics
      4. 2.2.4 Auxiliary Functions and Vectors
        1. 2.2.4.1 Electric and Magnetic Scalar Potentials
        2. 2.2.4.2 Magnetic Vector Potential A and the Scalar Potential V of Electromagnetic Field (Electrodynamic Potentials)
        3. 2.2.4.3 Electric Vector Potential T
        4. 2.2.4.4 Hertz Vector P
        5. 2.2.4.5 Maxwell’s Stress Tensor
    3. Example
      1. 2.2.5 Methods of Solution of Field Equations
    4. 2.3 Anisotropic Media
    5. 2.4 Nonlinear Media
      1. 2.4.1 Nonlinear Permittivity and Resistance
      2. 2.4.2 Nonlinear Magnetic Permeability
    6. 2.5 Fundamental Equations of Magnetohydrodynamics and Magnetogasdynamics
      1. 2.5.1 Mhd Generators
      2. 2.5.2 Electric Machines and Apparatus
    7. 2.6 Electrodynamics of Superconductors
    8. 2.7 Electrodynamics of Heterogeneous Media
    9. 2.8 Electrodynamics of Semiconductor Devices
    10. 2.9 Electrodynamics of Electrochemical Systems
    11. 2.10 General Wave Equations
      1. 2.10.1 Wave Equations in Metal
    12. 2.11 Fourier’s Method
    13. 2.12 Wave Equations in Cylindrical Coordinates
    14. 2.13 Plane Wave
      1. 2.13.1 Plane Wave in a Dielectric
      2. 2.13.2 Plane Wave in a Conducting Half-Space
      3. 2.13.3 Equivalent Depth of Wave Penetration and Impedance of Solid Conductors
    15. Example
      1. 2.13.4 Field Diffusion Into a Conductor
    16. 2.14 Reflection and Refraction of Plane Wave
      1. 2.14.1 Boundary Conditions
      2. 2.14.2 Reflection and Refraction of a Perpendicular Plane Wave
      3. 2.14.3 Near and Far Fields
      4. 2.14.4 Oblique Reflection, Refraction, and Guiding of a Wave
  12. 3 Transfer and Conversion of Field Power
    1. 3.1 Poynting’s Theorem: Poynting Vector*
    2. 3.2 Penetration of the Field Power into a Solid Conducting Half-Space
    3. Example
    4. 3.3 Power Flux at Conductors Passing through a Steel Wall
    5. 3.4 Power Flux in a Concentric Cable and Screened Bar
      1. 3.4.1 Factors of Utilization of Constructional Space
    6. 3.5 Power Flux in a Capacitor, Coil, and Transformer
    7. 3.6 Power Fluxes and Their Conversion in Rotating Machines
      1. 3.6.1 Power Flux of Electromagnetic Field in Gap of Induction Machine
      2. 3.6.2 Power Flux of Electromagnetic Field in Air Gap of Synchronous Machine
    8. Example
  13. 4 Screening of Constructional Parts
    1. 4.1 Types and Goals of Screening and Shunting
    2. 4.2 Magnetic Screens
      1. 4.2.1 Spherical and Crosswise Cylindrical Screens
        1. 4.2.1.1 Magnetic Screening of a Double-Conductor Line
      2. 4.2.2 Longitudinal Magnetic Screens
    3. 4.3 Electromagnetic Screens: Wave Method of Modeling and Calculation
      1. 4.3.1 Practical Convenience at Application of Wave Method of Calculation
      2. 4.3.2 Penetrable (Translucent) Screen with a One-Sided Incident Wave
        1. 4.3.2.1 Thin Screens
        2. 4.3.2.2 Thin Screens in Dielectric
        3. 4.3.2.3 Thin Screens on the Surface of Iron
        4. 4.3.2.4 Thick Screens
      3. 4.3.3 Penetrable Screen at Wave Incident from Both Sides
    4. 4.4 Power Losses in Screens
      1. 4.4.1 Poynting Vector and Power Losses in a One-Sided Screen
        1. 4.4.1.1 Screen Surrounded by Dielectric
        2. 4.4.1.2 Screen Adhering to Iron
          1. Screening coefficient of power
      2. 4.4.2 Poynting Vector and Power Loss at Double-Sided Symmetric Incidence of Waves
    5. 4.5 Screening of Transformer Tanks
      1. 4.5.1 Magnetic Screening (Shunting) of Tanks
        1. 4.5.1.1 Influence of Eddy Currents and Saturation on Magnetic Screens (Shunts)
    6. EXAMPLE
      1. 4.5.2 Electromagnetic Screening of a Transformer Tank
      2. 4.5.3 Three-Dimensional Computer Analysis and Interactive Design of Screens
    7. 4.6 Induction Motors with a Screened and Multilayer Rotor
      1. 4.6.1 General Characteristics
      2. 4.6.2 Fundamental Equations of Stratified Induction Motors
        1. 4.6.2.1 Field Equations
          1. The computation programs
    8. 4.7 Screening in Large Generators
      1. 4.7.1 Magnetic Screening and Shaping the Field
        1. 4.7.1.1 Magnetic Screening in Large Generators
        2. 4.7.1.2 Screening of Windings and Conductors
      2. 4.7.2 Electromagnetic Screening in Generators
    9. 4.8 Screening at Induction Heating
    10. 4.9 Screening of Bars and Conductor Wires
      1. 4.9.1 Cylindrical Screen of a Single Conductor Wire
        1. 4.9.1.1 Electromagnetic Screens
        2. 4.9.1.2 Power Losses in Screen
    11. Example
    12. Example
      1. 4.9.2 Cylindrical Screen in a Transverse, Uniform Field
      2. 4.9.3 Screens of Busbars in Generator Unit Systems of Power Stations
        1. 4.9.3.1 Isolated Screens
        2. 4.9.3.2 Connected Screens
    13. 4.10 Electromagnetic Field in Multilayer Screens
      1. 4.10.1 Two-Layer Conductor
      2. 4.10.2 Influence of Insulation Under the Screen
  14. 5 Magnetic Fields Near Iron Surfaces
    1. 5.1 Method of Mirror Images
      1. 5.1.1 Singular Images of Direct Current
        1. 5.1.1.1 Analogy in Electrostatic Fields
      2. 5.1.2 Application of the DC Field Theory to AC Fields
        1. 5.1.2.1 Mirror Image Coefficients of Alternating Currents in Metal Surfaces
      3. 5.1.3 Magnetic Images of Current in an Iron Cylinder
      4. 5.1.4 Multiple Mirror Images
        1. 5.1.4.1 Mirror Images of Current in Crossing Flat Iron Surfaces
        2. 5.1.4.2 Conductor Placed between Two Iron Surfaces
        3. 5.1.4.3 Conductor Encircled by Steel from Three Sides
      5. 5.1.5 Mirror Images of Magnets and Circuits with Direct Currents
    2. 5.2 Field of Endwindings in Electric Machines
      1. 5.2.1 Mirror Image in Solid Steel Wall
      2. 5.2.2 Influence of Air Gap
      3. 5.2.3 Influence of Constructional Elements
    3. 5.3 Field of Bushings
      1. 5.3.1 Dynamic Mirror Image of Currents
      2. 5.3.2 Field on the Cover Surface
    4. 5.4 Field of Bars Nearby a Steel Surface
    5. 5.5 Leakage Field in Transformers and in Slots of Electric Machines
      1. 5.5.1 Application of the Method of Multiple Mirror Images
      2. 5.5.2 Method of Approximate Solution of a Field in a Transformer Window with the Help of Fourier Series
        1. 5.5.2.1 Method of Analytical Prolongation
      3. 5.5.3 Numerical Methods: Mesh Methods of Solution of Leakage Magnetic Field in Power Transformers
        1. 5.5.3.1 Reluctance Network Method
      4. 5.5.4 Slot in a Deep-Slot Induction Machine
        1. 5.5.4.1 Rectangular Slot
        2. 5.5.4.2 Trapezoidal and Bulb Slots
      5. 5.5.5 Field in the Gap of Electric Machine
        1. 5.5.5.1 Analytical Methods
        2. 5.5.5.2 Meshed Numerical Methods
        3. 5.5.5.3 Graphical-Numerical Methods
        4. 5.5.5.4 Determination of the Magnetomotive Force (mmf) of Sources
    6. 5.6 Field of Conductors Nearby a Steel Wall
    7. 5.7 Additional Losses in Foil Windings of Transformer
  15. 6 Electromagnetic Phenomena in Metals with Constant Permeability
    1. 6.1 Application of Multiple Reflections of Electromagnetic Wave
    2. 6.2 Electrical Steel
      1. 6.2.1 Insulation Coefficient, ai
      2. 6.2.2 Coefficient of Flux Expulsion, aS
      3. 6.2.3 Hysteresis Losses
      4. 6.2.4 Losses Caused by Eddy Currents (Eddy-Current Losses)
      5. 6.2.5 Reactive Power Consumption
    3. 6.3 Power Losses at Current Intersections Through a Screen
      1. 6.3.1 Single-Phase Bushing System
      2. 6.3.2 Three-Phase Bushing System
    4. 6.4 Power Losses in Steel Covers with Gaps and Nonmagnetic Inserts Between Bushing Holes
    5. 6.5 Transient-Induced Processes
      1. 6.5.1 Eddy Currents
      2. 6.5.2 Mirror Image Coefficients
    6. 6.6 Solid Rotor of Induction Motor
    7. 6.7 Cup-Type Rotor
    8. 6.8 Principles of Induction Heating
    9. 6.9 High-Current Lines
      1. 6.9.1 Impedance
      2. 6.9.2 Proximity Effect
      3. 6.9.3 Power Translocation
      4. 6.9.4 Currents Induced in Steel Walls
  16. 7 Electromagnetic Phenomena in Ferromagnetic Bodies
    1. 7.1 Approximation of Magnetization Characteristics
      1. 7.1.1 Approximation of Recalculated Characteristics
    2. 7.2 Methods of Considering a Variable Magnetic Permeability
      1. 7.2.1 Rosenberg’s Method for Steel Conductors (1923)
      2. 7.2.2 Method of Rectangular Waves
      3. 7.2.3 Neiman’s Method (1949)
      4. 7.2.4 Substitute Permeability
      5. 7.2.5 Computer Method
    3. Example
    4. 7.3 Dependence of Stray Losses in Solid Steel Parts of Transformers on Current and Temperature
    5. 7.4 Power Losses in Steel Covers of Transformers
    6. 7.5 Calculation of Stray Losses in Solid Steel Walls by Means of Fourier’s Series
      1. 7.5.1 General Method
        1. 7.5.1.1 Three-Dimensional Field
        2. 7.5.1.2 Two-Dimensional Field
      2. 7.5.2 Analytical Formulae in Case of Sinusoidal Distribution of a Field on the Steel Surface
      3. 7.5.3 Computer Calculation of Power Losses in a Steel Plate Placed in the Field of Parallel Bars
    7. EXAMPLE
    8. 7.6 Power Losses in a Transformer Tank
      1. 7.6.1 Two-Dimensional Numerical Solution
      2. 7.6.2 Three-Dimensional Analytical Calculations of a Stray Field and Losses in Tanks at Constant Permeability
        1. 7.6.2.1 Field on the Tank Surface
        2. 7.6.2.2 Power Losses in a Tank
        3. 7.6.2.3 Influence of Flux in a Tank
      3. 7.6.3 Parametric Analytical-Numerical (ANM-3D) Calculation of Stray Losses in a Tank of a Transformer
    9. Example
      1. 7.6.4 Three-Dimensional Numerical Calculation of Stray Fields and Losses in Large, Three-Phase, Power Transformers
        1. 7.6.4.1 FEM-3D
        2. 7.6.4.2 Three-Dimensional, Equivalent Reluctance Network Method: RNM-3D
      2. 7.6.5 Industrial Implementation and Verification of the RNM-3D
        1. 7.6.5.1 Industrial Implementation of the RNM-3D Package
        2. 7.6.5.2 Transformers without Screens, Almost Symmetric
        3. 7.6.5.3 Large Transformers with an Extensive Asymmetry
        4. 7.6.5.4 Influence of the Structure and Screens Configuration
        5. 7.6.5.5 Screening Mistake Risk
  17. 8 Forces in Electrodynamic Systems
    1. 8.1 Principles of Calculation of Forces Acting on Buses and Windings of Transformers
      1. 8.1.1 Interaction Force of Parallel Conductors
    2. 8.2 Forces Acting on bus Bars Located Near Steel Constructional Elements
    3. 8.3 Forces Acting on Conductor Surfaces
    4. 8.4 Forces in Slot Parts of Windings of Electric Machines
    5. Example 8.1
    6. Example 8.2
    7. 8.5 Reluctance Forces and Torques
      1. 8.5.1 Dynamics of Thyristor-Controlled Reversible Motors
      2. 8.5.2 Torque of Hybrid Stepping Motors with Permanent Magnets in Slots
  18. 9 Local Heating of Structural Parts
    1. 9.1 Electromagnetic Criteria of Local Excessive Heating
    2. 9.2 Methods of Prevention of Local Overheating of a Metal Construction
      1. 9.2.1 Coefficient of Irregularity of Heat Distribution, K (J. Turowski [9.10])
    3. 9.3 Heating of Transformer Cover Plates
    4. 9.4 Permissible Current in Bushings
      1. 9.4.1 Eddy-Current Loss and hot Spots in Bushing Turrets
      2. 9.4.2 Computer Calculation
      3. 9.4.3 Single-Phase Turrets
    5. 9.5 Three-Phase Turrets, Simulated by a Rapid, Equivalent-Circuit Rnm Model
      1. 9.5.1 Calculation of Reluctances for RNM
  19. 10 Methods of Experimental Investigations
    1. 10.1 Experimental Verification of Theoretical Calculations
    2. 10.2 Principles of Theory of Electrodynamic Similarity
    3. 10.3 Principle of Induction Heating Device Modeling
    4. 10.4 Modeling of High Current Lines
    5. 10.5 Modeling of Transformers and Their Elements
    6. 10.6 Thermometric Method of Per-Unit Power Losses Measurement
      1. 10.6.1 Method of Initial Rise of Body Temperature
      2. 10.6.2 Method of Switching on or off of the Investigated Object
      3. 10.6.3 Accuracy of the Method
      4. 10.6.4 Computer Recalculation of the Measured Power Losses in Solid Steel
      5. 10.6.5 Measurement Techniques
      6. 10.6.6 Approximate Formulae
    7. 10.7 Investigation of Permissible Over-Excitation of Power Transformers
    8. 10.8 Measurement of Power at Very Small Power Factors (Cos φ) and/or Small Voltages
      1. 10.8.1 Bridge Systems
      2. 10.8.2 Compensatory Measurement of Additional Losses
    9. 10.9 Other Methods of Measurements
      1. 10.9.1 Measurement of Magnetic Field Intensity
      2. 10.9.2 Measurement of Electric Field Intensity
      3. 10.9.3 Measurement of the Poynting Vector with the Help of Probes
      4. 10.9.4 Measurement of Power Flux*
    10. 10.10 Diagnostics of Metal Elements
    11. 10.11 Critical Distance of Tank Wall from Transformer Windings
      1. 10.11.1 Critical Distance of Electromagnetically Screened Tank Walls
    12. 10.12 Influence of Flux Collectors
  20. 11 Conclusion
    1. 11.1 Final Complex Example
  21. Appendix
  22. References
  23. Index