Power and Distribution Transformers. Practical Design Guide

499 Pages·2021·9.304 MB·English

by  K.R.M. Nair

Power and Distribution
Transformers

Power and Distribution
Transformers
Practical Design Guide
K.R.M. Nair
First edition published 2021
by CRC Press
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© 2021 K.R.M. Nair
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Contents
Preface.............................................................................................................................................xix
Acknowledgments ...........................................................................................................................xxi
Author ..........................................................................................................................................xxiii
Chapter 1 Transformer Design ......................................................................................................1
1.1 Introduction .......................................................................................................1
1.2 Definition of Transformer ..................................................................................1
1.3 Design Objectives ..............................................................................................1
1.4 Basic Theory of Transformer ............................................................................2
1.4.1 Electromagnetic Terms and Concepts ..................................................2
1.4.2 Charges, Electric Field and Magnetic Field .........................................3
1.4.3 Maxwell’s Equations ............................................................................4
1.5 Power Transfer Capacity of Transformer ..........................................................5
Chapter 2 Brief History of Transformers and the Emerging Trends ............................................7
2.1 Brief History of the Transformer .......................................................................7
2.2 Development of Materials for Transformer production .....................................7
2.2.1 Conducting Material.............................................................................7
2.2.2 Cooling Medium ..................................................................................7
2.2.3 Magnetic Material (Electrical Steel) ....................................................8
2.2.4 New and Emerging Technologies .........................................................8
2.2.5 New Technologies in Commercial Use ................................................9
2.2.5.1 Amorphous Core Transformers ............................................9
2.2.5.2 Symmetrical Wound Core (3D Core) Transformer...............9
2.2.5.3 Biodegradable Oil-Filled Transformer ...............................10
2.2.5.4 Gas-Insulated Transformers ...............................................10
2.2.6 Application of Emerging Technologies to Transformer
Design and Manufacture ....................................................................10
2.2.6.1 Transformers Using High-Temperature Superconductors ......10
2.2.6.2 Intelligent Transformer for Smart Grid ..............................12
2.3 Replacement of Copper/Aluminium by Carbon Nanotube .............................12
2.4 Use of Artificial Intelligence (AI) for Transformer Design and Diagnostics .....13
2.5 Use of Additive Manufacturing (3D Printing) for Transformer Production ...13
Chapter 3 Design Procedures ......................................................................................................15
3.1 Design Input Data ............................................................................................15
3.2 Design Flow Chart [For Design with LV Parallel Conductors and HV
Layer Windings] ..............................................................................................16
Chapter 4 Core Design: Core Area Calculation ..........................................................................19
4.1 Calculation of Core Diameter and Core Area .................................................19
4.1.1 Selection of Core Circle .....................................................................19
4.1.2 Selection of Core Step Widths ...........................................................20
4.1.2.1 Optimum Width of Core Steps to Get Maximum
Core Area ............................................................................20
4.1.3 Calculation of Gross Area and Net Area of Core ..............................22
v
vi Contents
Chapter 5 Winding Design..........................................................................................................27
5.1 Calculation of Volts per Turn ..........................................................................27
5.2 Calculation of Phase Volts and Phase Currents ..............................................27
5.3 Calculation of Number of Turns ......................................................................29
5.3.1 Calculation of Voltage and Turns of Extended Delta Winding ..........29
5.3.2 Calculation of Tap Turns ....................................................................32
5.3.2.1 Categories of Voltage Variation ..........................................33
5.4 Calculation of the Cross Section Area of Conductor ......................................34
5.5 Selection of Current Density ...........................................................................34
5.6 Selection of Conductor Sizes ...........................................................................35
5.7 Selection of Types of Windings .......................................................................36
5.8 Tap CHANGERS and Tap Changer Connections ...........................................39
5.8.1 Off-Circuit Tap Changer ....................................................................39
5.8.2 Off-Load Tap Changer .......................................................................39
5.8.3 On-Load Tap Changer ........................................................................40
5.9 Calculation of Axial Height of Winding .........................................................42
5.9.1 Spiral Winding ...................................................................................43
5.9.2 Foil Winding ......................................................................................43
5.9.3 Crossover Coils...................................................................................43
5.9.4 Disc Winding .....................................................................................43
5.10 Electrical Clearances of Oil-Filled Three-Phase Transformers ......................45
5.11 Calculation of Electrical Stresses for Different Configurations ......................55
5.11.1 Two Bare Uniform Electrodes (Parallel Electrodes)
(One Dielectric) ................................................................................55
5.11.2 Multidielectric (Parallel Electrodes) ..................................................56
5.11.3 Concentric Cylindrical Electrodes (One Dielectric) ..........................56
5.11.4 Concentric Cylindrical Electrodes with Multiple Dielectrics ............57
5.11.5 Cylindrical Conductor to Plane Electrode .........................................57
5.11.6 Insulated Cylindrical Conductor to Plane Electrode .........................58
5.11.7 Factors Affecting Insulation Strength ................................................59
5.12 Insulation between Layers ...............................................................................60
5.13 Calculation of Winding Diameter and Radial Depth ......................................63
5.14 Weight of Bare Conductor, Covered Conductor and Resistance of Winding .......64
Chapter 6 Calculation of Load Loss ...........................................................................................65
6.1 Calculation of I 2R Loss ...................................................................................65
6.2 Calculation of Eddy Current Losses and Stray Losses ...................................65
6.2.1 Eddy Current Loss in Winding ..........................................................66
6.2.2 Stray Loss in Bushing plate ................................................................67
6.2.3 Stray Losses in Flitch Plate (Tie Plate) ..............................................68
6.2.4 Circulating Current Loss in Continuous Disc Winding .....................68
6.2.5 Empirical Formula for Tank Loss Calculation ...................................69
6.2.6 Loss on Transformer Tank Due to High-Current Busbars .................72
6.2.7 Empirical Formula for Calculating Total Stray Loss .........................72
6.3 Calculation of Load Loss ................................................................................73
Contents vii
Chapter 7 Calculation of Reactance ............................................................................................77
7.1 Reactance Calculation of Two-Winding Transformer .....................................77
7.1.1 Alternate Formula for Reactance Calculation ....................................80
7.2 Reactance Calculation of Zigzag Connected two-winding Transformers ......81
7.2.1 Effective Reactance of Zigzag Connected Transformers ...................81
7.3 Reactance Calculation with Different Ampere-Turn Distributions .................84
7.3.1 LV–HV–LV Arrangement or Similar .................................................84
7.3.2 Winding with Ducts inside or Windings Made in Two Separate
Layers with Gaps ................................................................................85
7.3.3 Reactance of Layer Winding with Reduced Layer Height
towards Outer Layers .........................................................................86
7.4 Reactance Calculations Based on Total Inductance ........................................90
7.5 Reactance Calculation of Extended Winding..................................................93
7.6 Zero Sequence Impedance of Zigzag Earthing Transformer ..........................94
7.7 Reactance Calculation of Neutral Earthing Transformer with
Auxiliary Winding ..........................................................................................95
7.8 Reactance of Autotransformer with Tertiary Winding ...................................96
7.9 Effective Reactance of Windings in Series (Autotransformer) .......................98
7.10 Reactance Calculation of Split Winding .......................................................101
7.11 Calculation of Reactance of Individual Windings ........................................103
7.12 Calculation of Reactance by Finite Element Method ....................................103
7.13 Zero Sequence Impedance of Three-Phase Transformers ............................107
7.14 Zero Sequence Impedance Calculation .........................................................107
Chapter 8 Calculation of Core Frame Size, Core Losses, Efficiency and Regulation ..............111
8.1 Core Frame Size and Core Weight Calculation .............................................111
8.2 Core Loss Calculation ...................................................................................112
8.2.1 Loss Calculation Based on Average Building Factor .......................113
8.2.2 Loss Calculation by Adding of Losses Across the Grain and
Along the Grain ................................................................................113
8.3 Specific Losses of Different Grades of CRGO Materials .................................114
8.4 Core Losses of Symmetrical Core Transformers ..........................................114
8.4.1 Advantages of Symmetrical Wound Core ........................................114
8.4.2 Manufacturing Process of Symmetrical Wound Core .....................115
8.4.3 Symmetrical Wound Core Designs ..................................................119
8.5 Calculation of No-Load Current (Excitation Current) ..................................120
8.6 Suggested Changes of Design Parameters to Get Desired Losses .....................121
8.7 Calculation of Efficiency and Regulation ......................................................123
8.7.1 Calculation of Efficiency ..................................................................123
8.7.1.1 Calculation of Efficiency as per ANSI Standard ..............123
8.7.1.2 IEC 60076 Standard and ANSI C57.12 Standard .............123
8.7.1.3 Calculation of Efficiency as per IEC 60076 and
ANSI C57.12 .....................................................................124
8.7.2 Calculation of Regulation .................................................................126
8.8 Calculation of Equivalent Circuit Parameters of Transformer ......................127
viii Contents
Chapter 9 Lightning and Switching Surges on Transformers ...................................................129
9.1 Introduction ...................................................................................................129
9.2 Effect of Surges on Transformer Winding ....................................................129
9.3 Capacitive Equivalent Circuit of Transformer ...............................................130
9.4 Calculation of Capacitances ..........................................................................130
9.5 Calculation of Initial Voltage Distribution of a Capacitive Ladder Circuit ......132
9.6 Impulse and Switching Surge Waves as per IEC 60076-4 ............................136
9.7 Simulation of Waveform for Analytical Calculations ...................................137
9.8 Design Techniques to Reduce Non-linear Impulse Voltage Distribution .....137
9.9 Power Frequency Breakdown and Impulse Breakdown ................................139
9.10 Selection of Surge Arrester for Transformer .................................................139
9.10.1 Surge Arresters Parameters ..............................................................140
9.10.2 Calculation of Arrester Rating of Solidly Grounded
three-Wire System ............................................................................140
Chapter 10 Inrush Current in Transformers ...............................................................................143
10.1 Introduction ...................................................................................................143
10.2 Problems of Transformer Inrush Current ......................................................144
10.2.1 Mechanical Stresses .........................................................................144
10.2.2 Overvoltage Due to Harmonic Resonance .......................................144
10.2.3 Nuisance Tripping of Transformer ...................................................144
10.2.4 Temporary Voltage Dip ....................................................................144
10.2.5 Sympathetic Inrush ..........................................................................144
10.3 Calculation of Inrush Current .......................................................................144
10.3.1 Approximate Value of the First Peak of Inrush Current ..................144
10.3.2 First Peak of Inrush Current Considering Switching Angle
and Circuit Resistance ......................................................................146
10.3.3 Estimation of Initial Few Peaks of Inrush Current ..........................146
10.3.4 Calculation Example ........................................................................147
10.4 Frequency Range of Inrush Current and Other Transients ...........................148
10.5 Influence of Design on Inrush Current ..........................................................148
10.6 Methods for Reduction of Inrush Current .....................................................149
10.7 Effect of System and Switching Parameters on Inrush Current ...................149
10.7.1 Source Resistance .............................................................................149
10.7.2 Switching Angle ...............................................................................150
10.7.3 Effect of Remnant Flux on the First Cycle Peak Current ................150
Chapter 11 Calculation of Core and Coil Assembly Dimensions, Tank Size and Tank Weight ....151
11.1 Calculation of the Dimensions of Core and Coil Assembly (CCA) ..............151
11.2 Calculation of Dimensions of Tank ..............................................................152
11.3 Calculation of the Size of Wooden Beam (Core Clamp) ...............................153
11.4 Calculation of Weight of Tank [Radiator-Type Tank] ...................................155
11.4.1 Weight of Top Cover ........................................................................155
11.4.2 Weight of Sidewalls ..........................................................................155
11.4.3 Bottom Plate .....................................................................................156
11.4.4 Tank Curb .........................................................................................156
11.4.5 Horizontal Stiffeners ........................................................................156
11.4.6 Vertical Stiffeners .............................................................................156
Contents ix
11.4.7 Base Channel ....................................................................................156
11.5 Design of Conservator ...................................................................................156
11.5.1 Size of the Conservator ....................................................................157
11.6 Air Cell for Conservator ................................................................................157
11.7 Dehydrating Breathers for Transformers .......................................................158
11.7.1 Regeneration of Saturated Silica Gel ...............................................158
11.7.2 Design Parameters of Breather ........................................................158
11.7.3 Calculation of Quantity of Silica Gel Required ...............................159
11.7.4 Self-Dehydrating Breather................................................................160
11.7.5 Calculation of Desiccant in Breather Alternate Method ..................160
Chapter 12 Calculation of Winding Gradient, Heat Dissipation Area and Oil Quantity ...........163
12.1 Radiation and Convection from Surface .......................................................163
12.2 Heat Dissipation Data for Radiator ...............................................................164
12.3 Calculation of Winding Gradient ..................................................................165
12.4 Calculation of Winding Gradient: Alternate Method....................................167
12.5 Calculation of Mean Oil Temperature Rise ..................................................169
12.6 Calculation of Weight of Radiator Panels .....................................................169
12.7 Calculation of Weight of Corrugated Fins ....................................................170
12.8 Effect of Ambient Temperature on the Top Oil Temperature Rise ...............171
12.9 Heat Dissipation by Forced Air Cooling .......................................................172
12.10 Reference Ambient as per IEC ......................................................................173
12.11 Calculation of Weighted Average Ambient Temperature ..............................174
12.12 Calculation of Oil Quantity ...........................................................................174
Chapter 13 Calculation of Pressure Rise, Stresses and Strength of Tank ..................................177
13.1 Calculation of Pressure Rise in Sealed Tanks ...............................................177
13.1.1 Tank with Pressed Steel Radiators with Air/Gas Cushion...............178
13.1.2 Corrugated Tank with Air/Gas Cushion ..........................................179
13.1.3 Corrugated Tank with Complete Filling of Oil (No Air/
Gas Cushion) ....................................................................................179
13.2 Calculation of Pressure and Stresses on Corrugated Fins for
Completely Filled Transformer .....................................................................179
13.3 Gas Pressure Calculation of Sealed Transformers, Considering
Solubility Changes of Gas with Temperature and Pressure ..........................182
13.4 Calculations of Strength of Rectangular Tank When Pressure Tested .........184
13.4.1 Tank Dimensions and Constants ......................................................184
13.4.2 Calculation of Section Modulus Required for Stiffeners .................185
13.5 Fastener Spacing and Tightening Torque of Gasket Joints of
Oil-Filled Transformers .................................................................................186
13.5.1 Introduction ......................................................................................186
13.5.2 Leakage Rate through Gasket Joint .................................................187
13.5.3 Properties of Gasket Required for a Good Joint ..............................188
13.5.4 Types of Gaskets Used and Comparison of Properties ....................188
13.5.5 Fastener Spacing ...............................................................................189
13.5.6 Bolt Torque .......................................................................................190
13.5.7 Joining/Splicing of the Gasket .........................................................190
13.5.8 Thickness of Gaskets for Distribution Transformers .......................191