TY  - BOOK
AU  - Del Vecchio,Robert M
TI  - Transformer design principles: with applications to core-form power transformers 
SN  - 9781439805824
AV  - TK2551 .T765 2010
PY  - 2010///]
CY  - Boca Raton, FL
PB  - CRC Press/Taylor and Francis
KW  - Electric transformers
KW  - Design and construction
N1  - Includes bibliographical references and index; Contents;  	Preface	; 1	Introduction	; 1.1	Historical Background	; 1.2	Uses in Power Systems	; 1.3	Core-Form and Shell-Form Transformers	; 1.4	Stacked and Wound Core Construction	; 1.5	Transformer Cooling	; 1.6	Winding Types	; 1.7	Insulation Structures	; 1.8	Structural Elements	; 1.9	Modern Trends	; 2	Magnetism and Related Core Issues	; 2.1	Introduction	; 2.2	Basic Magnetism	; 2.3	Hysteresis	; 2.4	Magnetic Circuits	; 2.5	Inrush Current	; 2.6	Distinguishing Inrush from Fault Current	; 2.7	Optimal Core Stacking	; 3	Circuit Model of a Two-Winding Transformer with Core	; 3.1	Introduction	; 3.2	Circuit Model of the Core	; 3.3	Two-Winding Transformer Circuit Model with Core	; 3.4	Approximate Two-Winding Transformer Circuit Model without Core	; 3.5	Vector Diagram of a Loaded Transformer with Core	; 3.6	Per-Unit System	; 3.7	Voltage Regulation	; 4	Reactance and Leakage Reactance Calculations	; 4.1	Introduction	; 4.2	General Method for Determining Inductances and Mutual Inductances	; 4.2.1	Energy by Magnetic Field Methods	; 4.2.2	Energy from Electric Circuit Methods	; 4.3	Two-Winding Leakage Reactance Formula	; 4.4	Ideal Two-, Three-, and Multiwinding Transformers	; 4.4.1	Ideal Autotransformers	; 4.5	Leakage Reactance for Two-Winding Transformers Based on Circuit Parameters	; 4.5.1	Leakage Reactance for a Two-Winding Autotransformer	; 4.6	Leakage Reactances for Three-Winding Transformers	; 4.6.1	Leakage Reactance for an Autotransformer with a Tertiary Winding	; 4.6.2	Leakage Reactance between Two Windings Connected in Series and a Third Winding	; 4.6.3	Leakage Reactance of a Two-Winding Autotransformer with X-Line Taps	; 4.6.4	More General Leakage Reactance Calculations	; 5	Phasors, Three-Phase Connections, and Symmetrical Components	; 5.1	Phasors	; 5.2	Wye and Delta Three-Phase Connections	; 5.3	Zig-Zag Connection	; 5.4	Scott Connection	; 5.5	Symmetrical Components	; 6	Fault Current Analysis	; 6.1	Introduction	; 6.2	Fault Current Analysis on Three-Phase Systems	; 6.2.1	Three-Phase Line-to-Ground Fault	; 6.2.2	Single-Phase Line-to-Ground Fault	; 6.2.3	Line-to-Line Fault	; 6.2.4	Double Line-to-Ground Fault	; 6.3	Fault Currents for Transformers with Two Terminals per Phase	; 6.3.1	Three-Phase Line-to-Ground Fault	; 6.3.2	Single-Phase Line-to-Ground Fault	; 6.3.3	Line-to-Line Fault	; 6.3.4	Double Line-to-Ground Fault	; 6.3.5	Zero-Sequence Circuits	; 6.3.6	Numerical Example for a Single Line-to-Ground Fault	; 6.4	Fault Currents for Transformers with Three Terminals per Phase	; 6.4.1	Three-Phase Line-to-Ground Fault	; 6.4.2	Single-Phase Line-to-Ground Fault	; 6.4.3	Line-to-Line Fault	; 6.4.4	Double Line-to-Ground Fault	; 6.4.5	Zero-Sequence Circuits	; 6.4.6	Numerical Examples	; 6.5	Asymmetry Factor	; 7	Phase-Shifting and Zig-Zag Transformers	; 7.1	Introduction	; 7.2	Basic Principles	; 7.3	Squashed Delta Phase-Shifting Transformer	; 7.3.1	Zero-Sequence Circuit Model	; 7.4	Standard Delta Phase-Shifting Transformer	; 7.4.1	Zero-Sequence Circuit Model	; 7.5	Two-Core Phase-Shifting Transformer	; 7.5.1	Zero-Sequence Circuit Model	; 7.6	Regulation Effects	; 7.7	Fault Current Analysis	; 7.7.1	Squashed Delta Fault Currents	; 7.7.2	Standard Delta Fault Currents	; 7.7.3	Two-Core Phase-Shifting Transformer Fault Currents	; 7.8	Zig-Zag Transformer	; 7.8.1	Calculation of Electrical Characteristics	; 7.8.2	Per-Unit Formulas	; 7.8.3	Zero-Sequence Impedance	; 7.8.4	Fault Current Analysis	; 8	Multiterminal Three-Phase Transformer Model	; 8.1	Introduction	; 8.2	Theory	; 8.2.1	Two-Winding Leakage Inductance	; 8.2.2	Multiwinding Transformers	; 8.2.3	Transformer Loading	; 8.3	Transformers with Winding Connections within a Phase	; 8.3.1	Two Secondary Windings in Series	; 8.3.2	Primary Winding in Series with a Secondary Winding	; 8.3.3	Autotransformer	; 8.4	Multiphase Transformers	; 8.4.1	Delta Connection	; 8.4.2	Zig-Zag Connection	; 8.5	Generalizing the Model	; 8.6	Regulation and Terminal Impedances	; 8.7	Multiterminal Transformer Model for Balanced and Unbalanced Load Conditions	; 8.7.1	Theory	; 8.7.2	Admittance Representation	; 8.7.2.1	Delta Winding Connection	; 8.7.3	Impedance Representation	; 8.7.3.1	Ungrounded Y Connection	; 8.7.3.2	Series-Connected Windings from the Same Phase	; 8.7.3.3	Zig-Zag Winding Connection	; 8.7.3.4	Autoconnection	; 8.7.3.5	Three Windings Joined	; 8.7.4	Terminal Loading	; 8.7.5	Solution Process	; 8.7.5.1	Terminal Currents and Voltages	; 8.7.5.2	Winding Currents and Voltages	; 8.7.6	Unbalanced Loading Examples	; 8.7.6.1	Autotransformer with Buried Delta Tertiary and Fault on Low-Voltage Terminal	; 8.7.6.2	Power Transformer with Fault on Delta Tertiary	; 8.7.6.3	Power Transformer with Fault on Ungrounded Y Secondary	; 8.7.7	Balanced Loading Example	; 8.7.7.1	Standard Delta Phase-Shifting Transformer	; 8.7.8	Discussion	; 9	Rabins' Method for Calculating Leakage Fields, Leakage Inductances, and Forces in Transformers	; 9.1	Introduction	; 9.2	Theory	; 9.3	Rabins' Formula for Leakage Reactance	; 9.3.1	Rabins' Method Applied to Calculate the Leakage Reactance between Two Windings That Occupy Different Radial Positions	; 9.3.2	Rabins' Method Applied to Calculate the Leakage Reactance between Two Axially Stacked Windings	; 9.3.3	Rabins' Method Applied to Calculate the Leakage Reactance for a Collection of Windings	; 9.4	Application of Rabins' Method to Calculate the Self-Inductance of and Mutual Inductance between Coil Sections	; 9.5	Determining the B-Field	; 9.6	Determination of Winding Forces	; 9.7	Numerical Considerations	; 10	Mechanical Design	; 10.1	Introduction	; 10.2	Force Calculations	; 10.3	Stress Analysis	; 10.3.1	Compressive Stress in the Key Spacers	; 10.3.2	Axial Bending Stress per Strand	; 10.3.3	Tilting Strength	; 10.3.4	Stress in the Tie Bars	; 10.3.5	Stress in the Pressure Ring	; 10.3.6	Hoop Stress	; 10.3.7	Radial Bending Stress	; 10.4	Radial Buckling Strength	; 10.4.1	Free Unsupported Buckling	; 10.4.2	Constrained Buckling	; 10.4.3	Experiment to Determine Buckling Strength	; 10.5	Stress Distribution in a Composite Wire-Paper Winding Section	; 10.6	Additional Mechanical Considerations	; 11	Electric Field Calculations	; 11.1	Simple Geometries	; 11.1.1	Planar Geometry	; 11.1.2	Cylindrical Geometry	; 11.1.3	Spherical Geometry	; 11.1.4	Cylinder-Plane Geometry	; 11.2	Electric Field Calculations Using Conformal Mapping	; 11.2.1	Physical Basis	; 11.2.2	Conformal Mapping	; 11.2.3	Schwarz-Christoffel Transformation	; 11.2.4	Conformal Map for the Electrostatic Field Problem	; 11.2.4.1	Electric Potential and Field Values	; 11.2.4.2	Calculations and Comparison with a Finite Element Solution	; 11.2.4.3	Estimating Enhancement Factors	; 11.3	Finite Element Electric Field Calculations	; 12	Capacitance Calculations	; 12.1	Introduction	; 12.2	Distributive Capacitance along a Winding or Disk	; 12.3	Stein's Disk Capacitance Formula	; 12.4	General Disk Capacitance Formula	; 12.5	Coil Grounded at One End with Grounded Cylinders on Either Side	; 12.6	Static Ring on One Side of a Disk	; 12.7	Terminal Disk without a Static Ring	; 12.8	Capacitance Matrix	; 12.9	Two Static Rings	; 12.10	Static Ring between the First Two Disks	; 12.11	Winding Disk Capacitances with Wound-in Shields	; 12.11.1	Analytic Formula	; 12.11.2	Circuit Model	; 12.11.3	Experimental Methods	; 12.11.4	Results	; 12.12	Multistart Winding Capacitance	; 13	Voltage Breakdown and High-Voltage Design	; 13.1	Introduction	; 13.2	Principles of Voltage Breakdown	; 13.2.1	Breakdown in Solid Insulation	; 13.2.2	Breakdown in Transformer Oil	; 13.3	Geometric Dependence of Transformer-Oil Breakdown	; 13.3.1	Theory	; 13.3.2	Planar Geometry	; 13.3.3	Cylindrical Geometry	; 13.3.4	Spherical Geometry	; 13.3.5	Comparison with Experiment	; 13.3.6	Generalization	; 13.3.6.1	Breakdown for the Cylinder-Plane Geometry	; 13.3.6.2	Breakdown for the Disk-Disk-to-Ground Plane Geometry	; 13.3.7	Discussion	; 13.4	Insulation Coordination	; 13.5	Continuum Model of Winding Used to Obtain the Impulse-Voltage;  Distribution	; 13.5.1	Uniform Capacitance Model	; 13.5.2	Traveling Wave Theory	; 13.6	Lumped-Parameter Model for Transient Voltage Distribution	; 13.6.1	Circuit Description	; 13.6.2	Mutual and Self-Inductance Calculations	; 13.6.3	Capacitance Calculations	; 13.6.4	Impulse-Voltage Calculations and Experimental Comparisons	; 13.6.5	Sensitivity Studies	; 14	Losses	; 14.1	Introduction	; 14.2	No-Load or Core Losses	; 14.2.1	Building Factor	; 14.2.2	Interlaminar Losses	; 14.3	Load Losses	; 14.3.1	I2R Losses	; 14.3.2	Stray Losses	; 14.3.2.1	Eddy Current Losses in the Coils	; 14.3.2.2	Tieplate Losses	; 14.3.2.3	Tieplate and Core Losses Due to Unbalanced Currents	; 14.3.2.4	Tank and Clamp Losses	; 14.3.3	Stray Losses Obtained from 3D Finite Element Analyses	; 14.3.3.1	Shunts on the Clamps	; 14.3.3.2	Shunts on the Tank Wall	; 14.3.3.3	Effects of Three-Phase Currents on Losses	; 14.3.3.4	Stray Losses from the 3D Analysis versus Analytical and Test Losses	; 14.4	Tank and Shield Losses Due to Nearby Busbars	; 14.4.1	Losses Obtained with 2D Finite Element Study	; 14.4.2	Losses Obtained Analytically	; 14.4.2.1	Current Sheet	; 14.4.2.2	Delta Function Current	; 14.4.2.3	Collection of Delta Function Currents	; 14.4.2.4	Model Studies	; 14.5	Tank Losses Associated with the Bushings	; 14.5.1	Comparison with a 3D Finite Element Calculation	; 15	Thermal Design	; 15.1	Introduction	; 15.2	Thermal Model of a Disk Coil with Directed Oil Flow	; 15.2.1	Oil Pressures and Velocities	; 15.2.2	Oil Nodal Temperatures and Path Temperature Rises	; 15.2.3	Disk Temperatures	; 15.3	Thermal Model for Coils without Directed Oil Flow	; 15.4	Radiator Thermal Model	; 15.5	Tank Cooling	; 15.6	Oil Mixing in the Tank	; 15.7	Time Dependence	; 15.8	Pumped Flow	; 15.9	Comparison with Test Results	; 15.10	Determining m and n Exponents	; 15.11	Loss of Life Calculation	; 15.12	Cable and Lead Temperature Calculation	; 15.13	Tank Wall Temperature Calculation	; 15.14	Tieplate Temperature	; 15.15	Core Steel Temperature Calculation	; 16	Load Tap Changers	; 16.1	Introduction	; 16.2	General Description of Load Tap Changers	; 16.3	Types of Regulation	; 16.4	Principles of Operation	; 16.4.1	Resistive Switching	; 16.4.2	Reactive Switching with Preventive Autotransformers	; 16.5	Connection Schemes	; 16.5.1	Power Transformers	; 16.5.2	Autotransformers	; 16.5.3	Use of Auxiliary Transformers	; 16.5.4	Phase-Shifting Transformers	; 16.5.5	Reduced versus Full-Rated Taps	; 16.6	General Maintenance	; 17	Miscellaneous Topics	; 17.1	Setting the Impulse Test Generator to Achieve Close to Ideal Waveshapes	; 17.1.1	Impulse Generator Circuit Model	; 17.1.2	Transformer Circuit Model	; 17.1.3	Determining the Generator Settings for Approximating the Ideal Waveform	; 17.1.4	Practical Implementation	; 17.2	Impulse or Lightning Strike on a Transformer through a Length of Cable	; 17.2.1	Lumped Parameter Model	; 17.2.1.1	Numerical Example	; 17.2.2	Traveling Wave Theory	; 17.3	Air Core Inductance	; 17.4	Electrical Contacts	; 17.4.1	Contact Resistance	; 17.4.2	Thermal Considerations	; 17.4.3	Practical Considerations	;  	References	;  	Index
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