book

Engineering Electrodynamics

by Janusz Turowski, Marek Turowski

December 2017

Intermediate to advanced

568 pages

15h 45m

English

CRC Press

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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 Investigations1.2 Constructional Materials1.2.1 Structure and Physical Properties of Metals1.2.1.1 Atomic Structure1.2.1.2 Ionization1.2.1.3 Crystal Structure of Metals1.2.1.4 Electrical Conductivity and Resistivity of Metals1.2.1.5 Influence of Ingredients on Resistivity of Metals1.2.1.6 Resistivity at Higher Temperatures1.2.1.7 Thermoelectricity1.2.1.8 Thermal Properties1.2.1.9 Mechanical Properties1.2.1.10 Hall Effect and Magnetoresistivity of Metals1.2.2 Superconductivity1.2.2.1 Superconductor Era in Electric Machine Industry1.2.3 Magnetic Properties of Bodies (Ferromagnetism)1.2.3.1 Magnetic Polarization and Magnetization1.2.3.2 Ferromagnetics, Paramagnetics, and Diamagnetics1.2.3.3 Atomic Structure of Ferromagnetics1.2.3.4 Zones of Spontaneous Magnetization1.2.3.5 Form of the Magnetization Curve1.2.3.6 Hysteresis1.2.3.7 Superposition of Remagnetization Fields1.2.3.8 Amorphous Strips1.2.3.9 Rotational Hysteresis1.2.3.10 Types of Magnetization Curves1.2.3.11 Curie Point1.2.3.12 Nonmagnetic Steel1.2.3.13 Influence of Various Factors on Properties of Magnetic Materials1.2.3.14 Types of Magnetic Permeability1.2.3.15 Permeability at High Frequencies1.2.3.16 Magnetic Anisotropy1.2.3.17 Magnetostriction1.2.3.18 Demagnetization Coefficient1.2.4 Semiconductors and Dielectrics1.2.4.1 Hall Effect in SemiconductorsExample

2 Fundamental Equations of Electromagnetic Field
2.1 Primary Laws and Equations of Electromagnetism2.2 Formulation and Methods of Solution of Field Differential Equations2.2.1 Finding of Field Function2.2.2 Classification of Field Equations2.2.3 Boundary and Initial Value Problems of Electrodynamics2.2.4 Auxiliary Functions and Vectors2.2.4.1 Electric and Magnetic Scalar Potentials2.2.4.2 Magnetic Vector Potential A and the Scalar Potential V of Electromagnetic Field (Electrodynamic Potentials)2.2.4.3 Electric Vector Potential T2.2.4.4 Hertz Vector P2.2.4.5 Maxwell’s Stress Tensor Example2.2.5 Methods of Solution of Field Equations2.3 Anisotropic Media2.4 Nonlinear Media2.4.1 Nonlinear Permittivity and Resistance2.4.2 Nonlinear Magnetic Permeability2.5 Fundamental Equations of Magnetohydrodynamics and Magnetogasdynamics2.5.1 Mhd Generators2.5.2 Electric Machines and Apparatus2.6 Electrodynamics of Superconductors2.7 Electrodynamics of Heterogeneous Media2.8 Electrodynamics of Semiconductor Devices2.9 Electrodynamics of Electrochemical Systems2.10 General Wave Equations2.10.1 Wave Equations in Metal2.11 Fourier’s Method2.12 Wave Equations in Cylindrical Coordinates2.13 Plane Wave2.13.1 Plane Wave in a Dielectric2.13.2 Plane Wave in a Conducting Half-Space2.13.3 Equivalent Depth of Wave Penetration and Impedance of Solid ConductorsExample2.13.4 Field Diffusion Into a Conductor2.14 Reflection and Refraction of Plane Wave2.14.1 Boundary Conditions2.14.2 Reflection and Refraction of a Perpendicular Plane Wave2.14.3 Near and Far Fields2.14.4 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-SpaceExample3.3 Power Flux at Conductors Passing through a Steel Wall3.4 Power Flux in a Concentric Cable and Screened Bar3.4.1 Factors of Utilization of Constructional Space3.5 Power Flux in a Capacitor, Coil, and Transformer3.6 Power Fluxes and Their Conversion in Rotating Machines3.6.1 Power Flux of Electromagnetic Field in Gap of Induction Machine3.6.2 Power Flux of Electromagnetic Field in Air Gap of Synchronous MachineExample
4 Screening of Constructional Parts
4.1 Types and Goals of Screening and Shunting4.2 Magnetic Screens4.2.1 Spherical and Crosswise Cylindrical Screens4.2.1.1 Magnetic Screening of a Double-Conductor Line4.2.2 Longitudinal Magnetic Screens4.3 Electromagnetic Screens: Wave Method of Modeling and Calculation4.3.1 Practical Convenience at Application of Wave Method of Calculation4.3.2 Penetrable (Translucent) Screen with a One-Sided Incident Wave4.3.2.1 Thin Screens4.3.2.2 Thin Screens in Dielectric4.3.2.3 Thin Screens on the Surface of Iron4.3.2.4 Thick Screens4.3.3 Penetrable Screen at Wave Incident from Both Sides4.4 Power Losses in Screens4.4.1 Poynting Vector and Power Losses in a One-Sided Screen4.4.1.1 Screen Surrounded by Dielectric4.4.1.2 Screen Adhering to IronScreening coefficient of power4.4.2 Poynting Vector and Power Loss at Double-Sided Symmetric Incidence of Waves4.5 Screening of Transformer Tanks4.5.1 Magnetic Screening (Shunting) of Tanks4.5.1.1 Influence of Eddy Currents and Saturation on Magnetic Screens (Shunts)EXAMPLE4.5.2 Electromagnetic Screening of a Transformer Tank4.5.3 Three-Dimensional Computer Analysis and Interactive Design of Screens4.6 Induction Motors with a Screened and Multilayer Rotor4.6.1 General Characteristics4.6.2 Fundamental Equations of Stratified Induction Motors4.6.2.1 Field EquationsThe computation programs4.7 Screening in Large Generators4.7.1 Magnetic Screening and Shaping the Field4.7.1.1 Magnetic Screening in Large Generators4.7.1.2 Screening of Windings and Conductors4.7.2 Electromagnetic Screening in Generators4.8 Screening at Induction Heating4.9 Screening of Bars and Conductor Wires4.9.1 Cylindrical Screen of a Single Conductor Wire4.9.1.1 Electromagnetic Screens4.9.1.2 Power Losses in ScreenExampleExample4.9.2 Cylindrical Screen in a Transverse, Uniform Field4.9.3 Screens of Busbars in Generator Unit Systems of Power Stations4.9.3.1 Isolated Screens4.9.3.2 Connected Screens4.10 Electromagnetic Field in Multilayer Screens4.10.1 Two-Layer Conductor4.10.2 Influence of Insulation Under the Screen
5 Magnetic Fields Near Iron Surfaces
5.1 Method of Mirror Images5.1.1 Singular Images of Direct Current5.1.1.1 Analogy in Electrostatic Fields5.1.2 Application of the DC Field Theory to AC Fields5.1.2.1 Mirror Image Coefficients of Alternating Currents in Metal Surfaces5.1.3 Magnetic Images of Current in an Iron Cylinder5.1.4 Multiple Mirror Images5.1.4.1 Mirror Images of Current in Crossing Flat Iron Surfaces5.1.4.2 Conductor Placed between Two Iron Surfaces5.1.4.3 Conductor Encircled by Steel from Three Sides5.1.5 Mirror Images of Magnets and Circuits with Direct Currents5.2 Field of Endwindings in Electric Machines5.2.1 Mirror Image in Solid Steel Wall5.2.2 Influence of Air Gap5.2.3 Influence of Constructional Elements5.3 Field of Bushings5.3.1 Dynamic Mirror Image of Currents5.3.2 Field on the Cover Surface5.4 Field of Bars Nearby a Steel Surface5.5 Leakage Field in Transformers and in Slots of Electric Machines5.5.1 Application of the Method of Multiple Mirror Images5.5.2 Method of Approximate Solution of a Field in a Transformer Window with the Help of Fourier Series5.5.2.1 Method of Analytical Prolongation5.5.3 Numerical Methods: Mesh Methods of Solution of Leakage Magnetic Field in Power Transformers5.5.3.1 Reluctance Network Method5.5.4 Slot in a Deep-Slot Induction Machine5.5.4.1 Rectangular Slot5.5.4.2 Trapezoidal and Bulb Slots5.5.5 Field in the Gap of Electric Machine5.5.5.1 Analytical Methods5.5.5.2 Meshed Numerical Methods5.5.5.3 Graphical-Numerical Methods5.5.5.4 Determination of the Magnetomotive Force (mmf) of Sources5.6 Field of Conductors Nearby a Steel Wall5.7 Additional Losses in Foil Windings of Transformer
6 Electromagnetic Phenomena in Metals with Constant Permeability
6.1 Application of Multiple Reflections of Electromagnetic Wave6.2 Electrical Steel6.2.1 Insulation Coefficient, ai6.2.2 Coefficient of Flux Expulsion, aS6.2.3 Hysteresis Losses6.2.4 Losses Caused by Eddy Currents (Eddy-Current Losses)6.2.5 Reactive Power Consumption6.3 Power Losses at Current Intersections Through a Screen6.3.1 Single-Phase Bushing System6.3.2 Three-Phase Bushing System6.4 Power Losses in Steel Covers with Gaps and Nonmagnetic Inserts Between Bushing Holes6.5 Transient-Induced Processes6.5.1 Eddy Currents6.5.2 Mirror Image Coefficients6.6 Solid Rotor of Induction Motor6.7 Cup-Type Rotor6.8 Principles of Induction Heating6.9 High-Current Lines6.9.1 Impedance6.9.2 Proximity Effect6.9.3 Power Translocation6.9.4 Currents Induced in Steel Walls
7 Electromagnetic Phenomena in Ferromagnetic Bodies
7.1 Approximation of Magnetization Characteristics7.1.1 Approximation of Recalculated Characteristics7.2 Methods of Considering a Variable Magnetic Permeability7.2.1 Rosenberg’s Method for Steel Conductors (1923)7.2.2 Method of Rectangular Waves7.2.3 Neiman’s Method (1949)7.2.4 Substitute Permeability7.2.5 Computer MethodExample7.3 Dependence of Stray Losses in Solid Steel Parts of Transformers on Current and Temperature7.4 Power Losses in Steel Covers of Transformers7.5 Calculation of Stray Losses in Solid Steel Walls by Means of Fourier’s Series7.5.1 General Method7.5.1.1 Three-Dimensional Field7.5.1.2 Two-Dimensional Field7.5.2 Analytical Formulae in Case of Sinusoidal Distribution of a Field on the Steel Surface7.5.3 Computer Calculation of Power Losses in a Steel Plate Placed in the Field of Parallel BarsEXAMPLE7.6 Power Losses in a Transformer Tank7.6.1 Two-Dimensional Numerical Solution7.6.2 Three-Dimensional Analytical Calculations of a Stray Field and Losses in Tanks at Constant Permeability7.6.2.1 Field on the Tank Surface7.6.2.2 Power Losses in a Tank7.6.2.3 Influence of Flux in a Tank7.6.3 Parametric Analytical-Numerical (ANM-3D) Calculation of Stray Losses in a Tank of a TransformerExample7.6.4 Three-Dimensional Numerical Calculation of Stray Fields and Losses in Large, Three-Phase, Power Transformers7.6.4.1 FEM-3D7.6.4.2 Three-Dimensional, Equivalent Reluctance Network Method: RNM-3D7.6.5 Industrial Implementation and Verification of the RNM-3D7.6.5.1 Industrial Implementation of the RNM-3D Package7.6.5.2 Transformers without Screens, Almost Symmetric7.6.5.3 Large Transformers with an Extensive Asymmetry7.6.5.4 Influence of the Structure and Screens Configuration7.6.5.5 Screening Mistake Risk
8 Forces in Electrodynamic Systems
8.1 Principles of Calculation of Forces Acting on Buses and Windings of Transformers8.1.1 Interaction Force of Parallel Conductors8.2 Forces Acting on bus Bars Located Near Steel Constructional Elements8.3 Forces Acting on Conductor Surfaces8.4 Forces in Slot Parts of Windings of Electric MachinesExample 8.1Example 8.28.5 Reluctance Forces and Torques8.5.1 Dynamics of Thyristor-Controlled Reversible Motors8.5.2 Torque of Hybrid Stepping Motors with Permanent Magnets in Slots
9 Local Heating of Structural Parts
9.1 Electromagnetic Criteria of Local Excessive Heating9.2 Methods of Prevention of Local Overheating of a Metal Construction9.2.1 Coefficient of Irregularity of Heat Distribution, K (J. Turowski [9.10])9.3 Heating of Transformer Cover Plates9.4 Permissible Current in Bushings9.4.1 Eddy-Current Loss and hot Spots in Bushing Turrets9.4.2 Computer Calculation9.4.3 Single-Phase Turrets9.5 Three-Phase Turrets, Simulated by a Rapid, Equivalent-Circuit Rnm Model9.5.1 Calculation of Reluctances for RNM
10 Methods of Experimental Investigations
10.1 Experimental Verification of Theoretical Calculations10.2 Principles of Theory of Electrodynamic Similarity10.3 Principle of Induction Heating Device Modeling10.4 Modeling of High Current Lines10.5 Modeling of Transformers and Their Elements10.6 Thermometric Method of Per-Unit Power Losses Measurement10.6.1 Method of Initial Rise of Body Temperature10.6.2 Method of Switching on or off of the Investigated Object10.6.3 Accuracy of the Method10.6.4 Computer Recalculation of the Measured Power Losses in Solid Steel10.6.5 Measurement Techniques10.6.6 Approximate Formulae10.7 Investigation of Permissible Over-Excitation of Power Transformers10.8 Measurement of Power at Very Small Power Factors (Cos φ) and/or Small Voltages10.8.1 Bridge Systems10.8.2 Compensatory Measurement of Additional Losses10.9 Other Methods of Measurements10.9.1 Measurement of Magnetic Field Intensity10.9.2 Measurement of Electric Field Intensity10.9.3 Measurement of the Poynting Vector with the Help of Probes10.9.4 Measurement of Power Flux*10.10 Diagnostics of Metal Elements10.11 Critical Distance of Tank Wall from Transformer Windings10.11.1 Critical Distance of Electromagnetically Screened Tank Walls10.12 Influence of Flux Collectors
11 Conclusion
11.1 Final Complex Example
Appendix
References
Index

Content preview from Engineering Electrodynamics

5 Magnetic Fields Near Iron Surfaces

5.1 Method of Mirror Images

5.1.1 Singular Images of Direct Current

The method of images is based on the analogy with optics. The analogy of electrostatic E = −grad V and magnetostatic H = −grad V_m fields gives us the possibility to consider them in the same way. Let us start with the magnetostatics, where B = μH. The method of mirror images, in the case of constant magnetic permeability μ_i of two adjacent media, consists of substitution of two media I and II (Figure 5.1a) by only one medium I (Figure 5.1b) or II (Figure 5.1c) and an auxiliary fictitious, image current i₁. The value of this fictitious current i₁ is determined by the rule of uniqueness of the field, specified by the boundary conditions (2.191) ...

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Engineering Electrodynamics

by Janusz Turowski, Marek Turowski