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E-grāmata: Transformer Design Principles, Third Edition

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  • Formāts: 612 pages
  • Izdošanas datums: 09-Aug-2017
  • Izdevniecība: CRC Press Inc
  • ISBN-13: 9781498787543
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Transformer Design Principles, Third EditionPalielināt
  • Formāts: 612 pages
  • Izdošanas datums: 09-Aug-2017
  • Izdevniecība: CRC Press Inc
  • ISBN-13: 9781498787543
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In the newest edition, the reader will learn the basics of transformer design, starting from fundamental principles and ending with advanced model simulations. The electrical, mechanical, and thermal considerations that go into the design of a transformer are discussed with useful design formulas, which are used to ensure that the transformer will operate without overheating and survive various stressful events, such as a lightning strike or a short circuit event. This new edition includes a section on how to correct the linear impedance boundary method for non-linear materials and a simpler method to calculate temperatures and flows in windings with directed flow cooling, using graph theory. It also includes a chapter on optimization with practical suggestions on achieving the lowest cost design with constraints.

Recenzijas

This book focuses on providing an understanding of the technical details of designing traditional single-phase and multiphase power transformers. In this latest edition, which still includes funda­mental design equations and theory used to design power transformers, it also provides advanced modeling simulation to further optimize transformer designs. The reader will find this book very helpful for understanding transformer design theory including many practical considerations. - IEEE Electrical Insulation Magazine, March/April 2020 This book focuses on providing an understanding of the technical details of designing traditional single-phase and multiphase power transformers. In this latest edition, which still includes funda­mental design equations and theory used to design power transformers, it also provides advanced modeling simulation to further optimize transformer designs. The reader will find this book very helpful for understanding transformer design theory including many practical considerations. - IEEE Electrical Insulation Magazine, March/April 2020

Preface xiii
Authors xv
1 Introduction 1(20)
1.1 Historical Background
1(1)
1.2 Uses in Power Systems
2(5)
1.3 Core-Form and Shell-Form Transformers
7(1)
1.4 Stacked and Wound Core Construction
8(2)
1.5 Transformer Cooling
10(1)
1.6 Winding Types
11(2)
1.7 Insulation Structures
13(3)
1.8 Structural Elements
16(3)
1.9 Modern Trends
19(2)
2 Magnetism and Related Core Issues 21(22)
2.1 Introduction
21(1)
2.2 Basic Magnetism
22(3)
2.3 Hysteresis
25(2)
2.4 Magnetic Circuits
27(5)
2.5 Inrush Current
32(2)
2.6 Fault Current Waveform and Peak Amplitude
34(5)
2.7 Optimal Core Stacking
39(4)
3 Circuit Model of a 2-Winding Transformer with Core 43(16)
3.1 Introduction
43(1)
3.2 Circuit Model of the Core
43(3)
3.3 2-Winding Transformer Circuit Model with Core
46(4)
3.4 Approximate 2-Winding Transformer Circuit Model without Core
50(3)
3.5 Vector Diagram of a Loaded Transformer with Core
53(1)
3.6 Per-Unit System
54(2)
3.7 Voltage Regulation
56(3)
4 Reactance and Leakage Reactance Calculations 59(30)
4.1 Introduction
59(1)
4.2 General Method for Determining Inductances and Mutual Inductances
60(5)
4.2.1 Energy by Magnetic Field Methods
61(2)
4.2.2 Energy from Electric Circuit Methods
63(2)
4.3 2-Winding Leakage Reactance Formula
65(4)
4.4 Ideal 2-, 3-, and Multi-Winding Transformers
69(4)
4.4.1 Ideal Autotransformer
72(1)
4.5 Leakage Reactance for 2-Winding Transformers Based on Circuit Parameters
73(4)
4.5.1 Leakage Reactance for a 2-Winding Autotransformer
76(1)
4.6 Leakage Reactances for 3-Winding Transformers
77(12)
4.6.1 Leakage Reactance for an Autotransformer with a Tertiary Winding
81(4)
4.6.2 Leakage Reactance between 2 Windings Connected in Series and a Third Winding
85(1)
4.6.3 Leakage Reactance of a 2-Winding Autotransformer with X-Line Taps
86(3)
5 Phasors, 3-Phase Connections, and Symmetrical Components 89(18)
5.1 Phasors
89(3)
5.2 Y and Delta 3-Phase Connections
92(5)
5.3 Zig-Zag Connection
97(1)
5.4 Scott Connection
98(3)
5.5 Symmetrical Components
101(6)
6 Fault Current Analysis 107(28)
6.1 Introduction
107(1)
6.2 Fault Current Analysis on 3-Phase Systems
108(5)
6.2.1 3-Phase Line-to-Ground Fault
110(1)
6.2.2 Single-Phase Line-to-Ground Fault
111(1)
6.2.3 Line-to-Line Fault
112(1)
6.2.4 Double Line-to-Ground Fault
112(1)
6.3 Fault Currents for Transformers with Two Terminals per Phase
113(7)
6.3.1 3-Phase Line-to-Ground Fault
116(1)
6.3.2 Single-Phase Line-to-Ground Fault
116(1)
6.3.3 Line-to-Line Fault
117(1)
6.3.4 Double Line-to-Ground Fault
118(1)
6.3.5 Zero-Sequence Circuits
119(1)
6.3.6 Numerical Example for a Single Line-to-Ground Fault
120(1)
6.4 Fault Currents for Transformers with Three Terminals per Phase
120(14)
6.4.1 3-Phase Line-to-Ground Fault
123(1)
6.4.2 Single-Phase Line-to-Ground Fault
124(2)
6.4.3 Line-to-Line Fault
126(2)
6.4.4 Double Line-to-Ground Fault
128(2)
6.4.5 Zero-Sequence Circuits
130(1)
6.4.6 Numerical Example
131(3)
6.5 Asymmetry Factor
134(1)
7 Phase-Shifting and Zigzag Transformers 135(34)
7.1 Introduction
135(1)
7.2 Basic Principles
136(3)
7.3 Squashed Delta-Phase-Shifting Transformer
139(5)
7.3.1 Zero Sequence Circuit Model
142(2)
7.4 Standard Delta-Phase-Shifting Transformer
144(4)
7.4.1 Zero Sequence Circuit Model
147(1)
7.5 2-Core Phase-Shifting Transformer
148(5)
7.5.1 Zero Sequence Circuit Model
152(1)
7.6 Regulation Effects
153(1)
7.7 Fault Current Analysis
154(6)
7.7.1 Squashed Delta Fault Currents
156(1)
7.7.2 Standard Delta Fault Currents
157(2)
7.7.3 2-Core Phase-Shifting Transformer Fault Currents
159(1)
7.8 Zigzag Transformer
160(9)
7.8.1 Calculation of Electrical Characteristics
161(3)
7.8.2 Per-Unit Formulas
164(2)
7.8.3 Zero Sequence Impedance
166(1)
7.8.4 Fault Current Analysis
167(2)
8 Multiterminal 3-Phase Transformer Model 169(44)
8.1 Introduction
169(1)
8.2 Theory
170(4)
8.2.1 Two-Winding Leakage Inductance
170(1)
8.2.2 Multi-Winding Transformer
171(3)
8.2.3 Transformer Loading
174(1)
8.3 Transformers with Winding Connections within a Phase
174(4)
8.3.1 Two Secondary Windings in Series
174(1)
8.3.2 Primary Winding in Series with a Secondary Winding
175(1)
8.3.3 Autotransformer
176(2)
8.4 Multiphase Transformers
178(5)
8.4.1 Delta Connection
180(1)
8.4.2 Zigzag Connection
181(2)
8.5 Generalizing the Model
183(2)
8.6 Regulation and Terminal Impedances
185(2)
8.7 Multiterminal Transformer Model for Balanced and Unbalanced Load Conditions
187(19)
8.7.1 Theory
188(2)
8.7.2 Admittance Representation
190(3)
8.7.2.1 Delta Winding Connection
191(2)
8.7.3 Impedance Representation
193(6)
8.7.3.1 Ungrounded Y Connection
194(2)
8.7.3.2 Series-Connected Windings from the Same Phase
196(1)
8.7.3.3 Zigzag Connection
197(1)
8.7.3.4 Autoconnection
198(1)
8.7.3.5 Three Windings Joined
199(1)
8.7.4 Terminal Loading
199(1)
8.7.5 Solution Process
200(1)
8.7.5.1 Terminal Currents and Voltages
200(1)
8.7.5.2 Winding Currents and Voltages
201(1)
8.7.6 Unbalanced Loading Examples
201(3)
8.7.6.1 Autotransformer with Buried Delta Tertiary and Fault on LV Terminal
201(1)
8.7.6.2 Power Transformer with Fault on Delta Tertiary
202(1)
8.7.6.3 Power Transformer with Fault on Ungrounded Y Secondary
203(1)
8.7.7 Balanced Loading Example
204(1)
8.7.7.1 Standard Delta Phase Shifting Transformer
204(1)
8.7.8 Discussion
205(1)
8.8 2-Core Analysis
206(7)
8.8.1 2-Core Parallel Connection
207(1)
8.8.2 2-Core Series Connection
208(1)
8.8.3 Terminal Loading
209(1)
8.8.4 Example of a 2-Core Phase Shifting Transformer
209(3)
8.8.4.1 Normal Loading
210(1)
8.8.4.2 Single Line-to-Ground Fault
211(1)
8.8.5 Discussion
212(1)
9 Rabins' Method for Calculating Leakage Fields, Inductances, and Forces in Iron Core Transformers, Including Air Core Methods 213(30)
9.1 Introduction
213(1)
9.2 Theory
214(12)
9.3 Rabins' Formula for Leakage Reactance
226(6)
9.3.1 Rabins' Method Applied to Calculate the Leakage Reactance between Two Windings Which Occupy Different Radial Positions
226(3)
9.3.2 Rabins' Method Applied to Calculate the Leakage Reactance between Two Axially Stacked Windings
229(2)
9.3.3 Rabins' Method Applied to Calculate the Leakage Reactance for a Collection of Windings
231(1)
9.4 Rabins' Method Applied to Calculate the Self-Inductance of and Mutual Inductance between Coil Sections
232(2)
9.5 Determining the B-field
234(2)
9.6 Determining the Winding Forces
236(2)
9.7 Numerical Considerations
238(1)
9.8 Air Core Inductance
238(5)
10 Mechanical Design 243(40)
10.1 Introduction
243(2)
10.2 Force Calculations
245(1)
10.3 Stress Analysis
246(21)
10.3.1 Compressive Stress in the Key Spacers
248(1)
10.3.2 Axial Bending Stress per Strand
249(3)
10.3.3 Tilting Strength
252(3)
10.3.4 Stress in the Tie Bars
255(4)
10.3.5 Stress in the Pressure Ring
259(1)
10.3.6 Hoop Stress
260(1)
10.3.7 Radial Bending Stress
261(6)
10.4 Radial Buckling Strength
267(9)
10.4.1 Free Unsupported Buckling
268(2)
10.4.2 Constrained Buckling
270(2)
10.4.3 Experiment to Determine Buckling Strength
272(4)
10.5 Stress Distribution in a Composite Wire-Paper Winding Section
276(3)
10.6 Additional Mechanical Considerations
279(4)
11 Electric Field Calculations 283(42)
11.1 Simple Geometries
283(12)
11.1.1 Planar Geometry
283(3)
11.1.2 Cylindrical Geometry
286(2)
11.1.3 Spherical Geometry
288(1)
11.1.4 Cylinder-Plane Geometry
289(6)
11.2 Electric Field Calculations Using Conformal Mapping
295(23)
11.2.1 Mathematical Basis
295(1)
11.2.2 Conformal Mapping
296(3)
11.2.3 Schwarz-Christoffel Transformation
299(1)
11.2.4 Conformal Map for the Electrostatic Field Problem
300(31)
11.2.4.1 Electric Potential and Field Values
305(8)
11.2.4.2 Calculations and Comparison with a Finite Element Solution
313(1)
11.2.4.3 Estimating Enhancement Factors
314(4)
11.3 Finite Element Electric Field Calculations
318(7)
12 Capacitance Calculations 325(38)
12.1 Introduction
325(1)
12.2 Distributive Capacitance along a Winding or Disk
325(6)
12.3 Stein's Disk Capacitance Formula
331(7)
12.3.1 Determining Practical Values for the Series and Shunt Capacitances, Cs and Cdd
334(4)
12.4 General Disk Capacitance Formula
338(1)
12.5 Coil Grounded at One End with Grounded Cylinders on Either Side
339(2)
12.6 Static Ring on One Side of a Disk
341(1)
12.7 Terminal Disk without a Static Ring
342(1)
12.8 Capacitance Matrix
343(2)
12.9 Two End Static Rings
345(3)
12.10 Static Ring between the First Two Disks
348(1)
12.11 Winding Disk Capacitances with Wound-in-Shields
349(12)
12.11.1 Analytic Formula
349(3)
12.11.2 Circuit Model
352(5)
12.11.3 Experimental Methods
357(1)
12.11.4 Results
358(3)
12.12 Multi-Start Winding Capacitance
361(2)
13 Voltage Breakdown Theory and Practice 363(30)
13.1 Introduction
363(1)
13.2 Principles of Voltage Breakdown
364(8)
13.2.1 Breakdown in Solid Insulation
368(1)
13.2.2 Breakdown in Transformer Oil
369(3)
13.3 Geometric Dependence of Transformer Oil Breakdown
372(14)
13.3.1 Theory
373(1)
13.3.2 Planar Geometry
374(2)
13.3.3 Cylindrical Geometry
376(2)
13.3.4 Spherical Geometry
378(1)
13.3.5 Comparison with Experiment
379(1)
13.3.6 Generalization
380(5)
13.3.6.1 Breakdown for the Cylinder-Plane Geometry
381(1)
13.3.6.2 Breakdown for the Disk-Disk-to-Ground Plane Geometry
382(3)
13.3.7 Discussion
385(1)
13.4 Insulation Coordination
386(3)
13.5 Continuum Model of Winding Used to Obtain the Impulse Voltage Distribution
389(4)
13.5.1 Uniform Capacitance Model
389(3)
13.5.2 Traveling Wave Theory
392(1)
14 High-Voltage Impulse Analysis and Testing 393(22)
14.1 Introduction
393(1)
14.2 Lumped Parameter Model for Transient Voltage Distribution
393(9)
14.2.1 Circuit Description
393(3)
14.2.2 Mutual and Self-Inductance Calculations
396(1)
14.2.3 Capacitance Calculations
396(1)
14.2.4 Impulse Voltage Calculations and Experimental Comparisons
397(4)
14.2.5 Sensitivity Studies
401(1)
14.3 Setting the Impulse Test Generator to Achieve Close-to-Ideal Waveshapes
402(13)
14.3.1 Impulse Generator Circuit Model
404(3)
14.3.2 Transformer Circuit Model
407(1)
14.3.3 Determining the Generator Settings for Approximating the Ideal Waveform
408(4)
14.3.4 Practical Implementation
412(3)
15 No-Load and Load Losses 415(48)
15.1 Introduction
415(1)
15.2 No-Load or Core Losses
416(6)
15.2.1 Building Factor
418(1)
15.2.2 Interlaminar Losses
419(3)
15.3 Load Losses
422(26)
15.3.1 I2R Losses
422(2)
15.3.2 Stray Losses
424(24)
15.3.2.1 Eddy Current Losses in the Coils
426(3)
15.3.2.2 Tie Plate Losses
429(7)
15.3.2.3 Tie Plate and Core Losses due to Unbalanced Currents
436(5)
15.3.2.4 Tank and Clamp Losses
441(7)
15.4 Tank and Shield Losses due to Nearby Busbars
448(8)
15.4.1 Losses Obtained with 2D Finite Element Study
448(1)
15.4.2 Losses Obtained Analytically
449(7)
15.4.2.1 Current Sheet
449(1)
15.4.2.2 Delta Function Current
450(2)
15.4.2.3 Collection of Delta Function Currents
452(3)
15.4.2.4 Model Studies
455(1)
15.5 Tank Losses Associated with the Bushings
456(7)
15.5.1 Comparison with a 3D Finite Element Calculation
460(3)
16 Stray Losses from 3D Finite Element Analysis 463(18)
16.1 Introduction
463(1)
16.2 Stray Losses on Tank Walls and Clamps
463(8)
16.2.1 Shunts on the Clamps
464(2)
16.2.2 Shunts on the Tank Wall
466(3)
16.2.3 Effects of 3-Phase Currents on Losses
469(1)
16.2.4 Stray Losses from 3D Analysis versus Analytical and Test Losses
469(2)
16.3 Nonlinear Impedance Boundary Correction for the Stray Losses
471(10)
16.3.1 Linear Loss Calculation for an Infinite Slab
471(2)
16.3.2 Nonlinear Loss Calculation for a Finite Slab
473(2)
16.3.3 Application to Finite Element Loss Calculations
475(7)
16.3.3.1 Comparison with Test Losses
477(1)
16.3.3.2 Conclusion
478(3)
17 Thermal Design 481(48)
17.1 Introduction
481(1)
17.2 Thermal Model of a Disk Coil with Directed Oil Flow
482(16)
17.2.1 Governing Equations and Solution Process
482(5)
17.2.2 Oil Pressures and Velocities
487(3)
17.2.3 Disk Temperatures
490(3)
17.2.4 Nodal Temperatures and Duct Temperature Rises
493(3)
17.2.5 Comparison with Test Data
496(2)
17.3 Thermal Model for Coils without Directed Oil Flow
498(2)
17.4 Radiator Thermal Model
500(3)
17.5 Tank Cooling
503(1)
17.6 Oil Mixing in the Tank
504(2)
17.7 Time Dependence
506(2)
17.8 Pumped Flow
508(1)
17.9 Comparison with Test Results
508(4)
17.10 Determining m and n Exponents
512(2)
17.11 Loss of Life Calculation
514(3)
17.12 Cable and Lead Temperature Calculation
517(5)
17.13 Tank Wall Temperature Calculation
522(1)
17.14 Tie plate Temperature Calculation
523(2)
17.15 Core Steel Temperature Calculation
525(4)
18 Load Tap Changers 529(16)
18.1 Introduction
529(1)
18.2 General Description of LTC
529(1)
18.3 Types of Regulation
530(1)
18.4 Principle of Operation
531(3)
18.4.1 Resistive Switching
531(2)
18.4.2 Reactive Switching with Preventative Autotransformer
533(1)
18.5 Connection Schemes
534(7)
18.5.1 Power Transformers
534(2)
18.5.1.1 Fixed Volts/Turn
534(1)
18.5.1.2 Variable Volts/Turn
535(1)
18.5.2 Autotransformers
536(4)
18.5.3 Use of Auxiliary Transformer
540(1)
18.5.4 Phase Shifting Transformers
540(1)
18.5.5 Reduced versus Full-Rated Taps
541(1)
18.6 General Maintenance
541(4)
19 Constrained Nonlinear Optimization with Application to Transformer Design 545(32)
19.1 Introduction
545(1)
19.2 Geometric Programming
546(6)
19.3 Nonlinear Constrained Optimization
552(14)
19.3.1 Characterization of the Minimum
552(9)
19.3.2 Solution Search Strategy
561(4)
19.3.3 Practical Considerations
565(1)
19.4 Application to Transformer Design
566(11)
19.4.1 Design Variables
566(1)
19.4.2 Cost Function
567(2)
19.4.3 Equality Constraints
569(3)
19.4.4 Inequality Constraints
572(1)
19.4.5 Optimization Strategy
573(4)
References 577(6)
Index 583
Robert M. Del Vecchio, Bertrand Poulin, Pierre T. Feghali, Dilipkumar Shah, Rajendra Ahuja
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