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TitleTransformer Engineering: Design and Practice
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Table of Contents
                            Transformer Engineering: Design and Practice
	Foreword
	Preface
	ACKNOWLEDGMENTS
	Contents
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 1: Transformer Fundamentals
	1.1 Perspective
	1.2 Applications and Types of Transformers
	1.3 Principles and Equivalent Circuit of a Transformer
		1.3.1 Ideal transformer
		1.3.2 Practical transformer
		1.3.3 Mutual and leakage inductances
		1.3.4 Simplified equivalent circuit
	1.4 Representation of Transformer in Power System
	1.5 Open Circuit and Short Circuit Tests
	1.6 Voltage Regulation and Efficiency
	1.7 Parallel Operation of Transformers
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 2: Magnetic Characteristics
	2.1 Construction
		2.1.1 Types of core
		2.1.2 Analysis of overlapping joints and building factor
	2.2 Hysteresis and Eddy Losses
	2.3 Excitation Characteristics
	2.4 Over-Excitation Performance
	2.5 No-Load Loss Test
		2.5.1 Asymmetrical magnetizing phenomenon
		2.5.2 Magnetic balance test
		2.5.3 Trouble-shooting by no-load loss test
		2.5.4 Effect of impulse test on no-load loss
	2.6 Impact of Manufacturing Processes on Core Performance
	2.7 Inrush Current
		2.7.1 Theory
		2.7.2 Estimation of magnitude of first peak
		2.7.3 Estimation of decay pattern
		2.7.4 Sympathetic inrush phenomenon
		2.7.5 Factors affecting inrush phenomenon
			A. Switching-on angle (Alpha)
			B. Residual flux density
			C. Series resistance
			D. Inrush under load
		2.7.5 Mitigation of inrush current
	2.8 Influence of Core Construction and Winding Connections on No-Load Harmonic Phenomenon
	2.9 Transformer Noise
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 3: Impedance Characteristics
	3.1 Reactance Calculation
		3.1.1 Concentric primary and secondary windings
		3.1.2 Sandwich windings
		3.1.3 Concentric windings with non-uniform distribution of ampere turns
	3.2 Different Approaches for Reactance Calculation
	3.3 Two-Dimensional Analytical Methods
		3.3.1 Method of images
		3.3.2 Roth’s method
		3.3.3 Rabin’s method
	3.4 Numerical Method for Reactance Calculation
		1. Classical method
		2. FEM analysis
		1. Classical method
		2. FEM analysis
	3.5 Impedance Characteristics of Three-Winding Transformer
	3.6 Reactance Calculation for Zigzag Transformer
	3.7 Zero-Sequence Reactance Estimation
		3.7.1 Open circuit zero-sequence reactance without delta connected winding
			A. Three-phase three-limb transformers
			B. Three-phase five-limb and single-phase three-limb transformers
		3.7.2 Open circuit zero-sequence reactance with delta connected winding
			A. Three-phase three-limb transformers
			B. Three-phase five-limb and single-phase three-limb transformers
		3.7.3 Short circuit zero-sequence reactance
			A. Three-phase three-limb transformers
			B. Three-phase five-limb and single-phase three-limb transformers
	3.8 Stabilizing Tertiary Winding
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 4: Eddy Currents and Winding Stray Losses
	4.1 Field Equations
	4.2 Poynting Vector
	4.3 Eddy Current and Hysteresis Losses
	4.4 Effect of Saturation
	4.5 Eddy Loss in Transformer Winding
		4.5.1 Expression for eddy loss
		4.5.2 Methods of estimation
		4.5.3 Optimization of losses and elimination of winding hot spots
		4.5.4 Eddy loss in foil windings
	4.6 Circulating Current Loss in Transformer Windings
		4.6.1 Analytical methods
		4.6.2 Method based on multi-winding transformer theory
		4.6.3 FEM analysis
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 5: Stray Losses in Structural Components
	5.1 Factors Influencing Stray Losses
		5.1.1 Type of surface excitation
		5.1.2 Effect of load, temperature and frequency
	5.2 Overview of Methods for Stray Loss Estimation
		5.2.1 Two-dimensional methods
		5.2.2 Three-dimensional analytical formulations
		5.2.3 Three-dimensional numerical methods
	5.3 Core Edge Loss
	5.4 Stray Loss in Frames
	5.5 Stray Loss in Flitch Plates
	5.6 Stray Loss in Tank
	5.7 Stray Loss in Bushing Mounting Plates
	5.8 Evaluation of Stray Loss Due to High Current Leads
	5.9 Measures for Stray Loss Control
		5.9.1 Magnetic shielding
		5.9.2 Eddy current shielding
	5.10 Methods for Experimental Verification
		5.10.1 Steady-state temperature rise
		5.10.2 Initial temperature rise
	5.11 Estimation of Stray Losses in Overexcitation Condition
	5.12 Load Loss Measurement
		5.12.1 Half-turn effect
		5.12.2 Single-phase load loss measurement on a three-phase transformer
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 6: Short Circuit Stresses and Strength
	6.1 Short Circuit Currents
	6.2 Thermal Capability at Short Circuit
	6.3 Short Circuit Forces
		6.3.1 Radial forces
		6.3.2 Axial forces
	6.4 Dynamic Behavior Under Short Circuits
	6.5 Failure Modes Due to Radial Forces
		6.5.1 Winding subjected to tensile stresses
		6.5.2 Windings subjected to compressive stresses
	6.6 Failure Modes Due to Axial Forces
		6.6.1 Bending between radial spacers
		6.6.2 Tilting under an axial load
	6.7 Effect of Pre-Stress
	6.8 Short Circuit Test
	6.9 Effect of Inrush Current
	6.10 Split-Winding Transformers
	6.11 Short Circuit Withstand
		6.11.1 System configuration and transformer specification
		6.11.2 Design
		6.11.3 Manufacturing processes
	6.12 Calculation of Electrodynamic Force Between Parallel Conductors
	6.13 Design of Clamping Structures
		Stresses in clamping ring
		Stresses in flitch plates and frames
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 7: Surge Phenomena in Transformers
	7.1 Initial Voltage Distribution
	7.2 Capacitance Calculations
	7.3 Capacitance of Windings
		7.3.1 Development of winding methods for better impulse response
		7.3.2 Turn-to-turn and disk-to-disk capacitances
		7.3.3 Continuous disk winding
		7.3.4 Continuous winding with SER and SR
		7.3.5 Interleaved winding
		7.3.6 Shielded-conductor winding
		7.3.7 Layer winding
		7.3.8 Interleaved tap winding
	7.4 Inductance Calculation
	7.5 Standing Waves and Traveling Waves
	7.6 Methods for Analysis of Impulse Distribution
	7.7 Computation of Impulse Voltage Distribution Using State Variable Method
		7.7.1 Derivation of differential equations
		7.7.2 Formation of circumflex matrix
		7.7.3 Formation of G matrix
		7.7.4 Formation of … matrix
		7.7.5 State space model
	7.8 Winding Design for Reducing Internal Overvoltages
		7.8.1 Part winding resonance
		7.8.2 Natural frequencies of windings
		7.8.3 Graded capacitance winding
		7.8.4 Location of windings
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 8: Insulation Design
	8.1 Calculation of Stresses for Simple Configurations
	8.2 Field Computations
		8.2.1 Analytical methods
		8.2.2 Numerical methods
	8.3 Factors Affecting Insulation Strength
		8.3.1 Effect of moisture and impurities
		8.3.2 Effect of time and frequency
		8.3.3 Effect of temperature
		8.3.4 Effect of thickness
		8.3.5 Stressed volume effects
		8.3.6 Creepage phenomenon
		8.3.7 Cumulative stress calculations
		8.3.8 Effect of oil velocity
		8.3.9 Processing of insulation
	8.4 Test Methods and Design Insulation Level (DIL)
	8.5 Insulation Between Two Windings
	8.6 Internal Insulation
	8.7 Design of End Insulation
	8.8 High Voltage Lead Clearances
	8.9 Statistical Analysis for Optimization and Quality Enhancement
		8.9.1 Parameter design
		8.9.2 Tolerance design
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 9: Cooling Systems
	9.1 Modes of Heat Transfer
		9.1.1 Conduction
		9.1.2 Radiation
		9.1.3 Convection
	9.2 Cooling Arrangements
		9.2.1 ONAN/OA cooling
		9.2.2 ONAF/FA cooling
		9.2.3 OFAF/FOA cooling
		9.2.4 Unit coolers
		9.2.5 OFWF cooling
	9.3 Dissipation of Core Heat
	9.4 Dissipation of Winding Heat
	9.5 Aging and Life Expectancy
	9.6 Direct Hot Spot Measurement
	9.7 Static Electrification Phenomenon
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 10: Structural Design
	10.1 Importance of Structural Design
	10.2 Different Types of Loads and Tests
		10.2.1 Loads
		10.2.2 Tests
	10.3 Classification of Transformer Tanks
	10.4 Tank Design
	10.5 Methods of Analysis
		10.5.1 Analytical method
		10.5.2 Numerical method
	10.6 Overpressure Phenomenon in Transformers
	10.7 Seismic Analysis
	10.8 Transformer Noise: Characteristics and Reduction
		10.8.1 Load-controlled noise
		10.8.2 Noise due to cooling equipment
		10.8.3 Noise level reduction
		10.8.4 Noise level measurement
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Contents
Chapter 11: Special Transformers
	11.1 Rectifier Transformers
		11.1.1 Bridge connection
		11.1.2 Interphase transformer connection
		11.1.3 Features of rectifier transformers
	11.2 Converter Transformers for HVDC
		11.2.1 Configurations
		11.2.2 Insulation design
		11.2.3 Other design aspects
	11.3 Furnace Transformers
	11.4 Phase Shifting Transformers
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Conents
Chapter 12: Recent Trends in Transformer Technology
	12.1 Magnetic Circuit
	12.2 Windings
	12.3 Insulation
	12.4 Challenges in Design and Manufacture of Transformers
	12.5 Computer-Aided Design and Analysis
	12.6 Monitoring and Diagnostics
	12.7 Life Assessment and Refurbishment
	References
	Appendix A: Fault Calculations
	Appendix B: Stress and Capacitance Formulae
Table of Conents
Appendix A: Fault Calculations
	A1 Asymmetrical Fault with No In-Feed from LV Side
		A1.1 Delta connected tertiary winding is present
		A1.2 Delta connected tertiary winding is absent
	A2 Asymmetrical Fault with In-Feed from LV Side
		A2.1 Delta connected tertiary winding is present
		A2.2 Delta connected tertiary winding is absent
	Appendix B: Stress and Capacitance Formulae
Table of Conents
Appendix B: Stress and Capacitance Formulae
	B1 Stress Calculations
	B2 Capacitance Calculations
		B2.1 Capacitance between two parallel cylindrical conductors
		B2.2 Capacitance of cylindrical conductor and plane at ground potential
	Appendix A: Fault Calculations
                        

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