3rd Edition
Transformer Design Principles, Third Edition
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.
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 Fault Current Waveform and Peak Amplitude
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
4.3 Two Winding Leakage Reactance Formula
4.4 Ideal Two, Three, and Multi-Winding Transformers
4.5 Leakage Reactance for Two Winding Transformers Based on Circuit Parameters
4.6 Leakage Reactance for Three Winding Transformers
5 PHASORS, THREE PHASE CONNECTIONS, AND SYMMETRICAL COMPONENTS
5.1 Phasors
5.2 Y 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
6.3 Fault Currents for Transformers with Two Terminals per Phase
6.4 Fault Currents for Transformers with Three Terminals per Phase
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
7.4 Standard Delta Phase Shifting Transformer
7.5 Two Core Phase Shifting Transformer
7.6 Regulation Effects
7.7 Fault Current Analysis
7.8 Zig-Zag Transformer
8 MULTI-TERMINAL THREE PHASE TRANSFORMER MODEL
8.1 Introduction
8.2 Theory
8.3 Transformers with Winding Connections within a Phase
8.4 Multi-Phase Transformers
8.5 Generalizing the Model
8.6 Regulation and Terminal Impedances
8.7 Multi-Terminal Transformer Model for Balanced and Unbalanced Load Conditions
8.8 Two Core Analysis
9 RABINS’ METHOD FOR CALCULATING LEAKAGE FIELDS, INDUCTANCES, AND FORCES IN IRON CORE TRANSFORMERS, INCLUDING AIR CORE METHODS
9.1 Introduction
9.2 Theory
9.3 Rabins’ Formula for Leakage Reactance
9.4 Rabins’ Method Applied to Calculate the Self
Inductance of and Mutual Induction between Coil Sections
9.5 Determining the B-Field
9.6 Determining the Winding Forces
9.7 Numerical Considerations
9.8 Air Core Inductance
10 MECHANICAL DESIGN
10.1 Introduction
10.2 Force Calculations
10.3 Stress Analysis
10.4 Radial 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
11.2 Electric Field Calculations Using Conformal Mapping
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 Disk
12.7 Terminal Disk without a Static Ring
12.8 Capacitance Matrix
12.9 Two End Static Rings
12.10 Static Ring between the First Two Disks
12.11 Winding Disk Capacitances with Wound-in-Shields
12.12 Multi-Start Winding Capacitance
13 VOLTAGE BREAKDOWN THEORY AND PRACTICE
13.1 Introduction
13.2 Principles of Voltage Breakdown
13.3 Geometric Dependence of Transformer Oil Breakdown
13.4 Insulation Coordination
13.5 Continuum Model of Winding Used to Obtain the Impulse Voltage Distribution
14 HIGH VOLTAGE IMPULSE ANALYSIS AND TESTING
14.1 Introduction
14.2 Lumped Parameter Model for Transient Voltage Distribution
14.3 Setting the Impulse Test Generator to Achieve Close to Ideal Waveshapes
15 NO-LOAD AND LOAD LOSSES
15.1 Introduction
15.2 No-Load or Core Losses
15.3 Load Losses
15.4 Tank and Shield Losses Due to Nearby Busbars
15.5 Tank Losses Associated with the Bushings
16 STRAY LOSSES FROM 3D FINITE ELEMENT ANALYSIS
16.1 Introduction
16.2 Stray Losses on Tank Walls and Clamps
16.3 Nonlinear Impedance Boundary Correction for the Stray Losses
17 THERMAL DESIGN
17.1 Introduction
17.2 Thermal Model of a Disk Coil with Directed Oil Flow
17.3 Thermal Model for Coils without Directed Oil Flow
17.4 Radiator Thermal Model
17.5 Tank Cooling
17.6 Oil Mixing in the Tank
17.7 Time Dependence
17.8 Pumped Flow
17.9 Comparison with Test Results
17.10 Determining m and n Exponents
17.11 Loss of Life Calculation
17.12 Cable and Lead Temperature Calculation
17.13 Tank Wall Temperature Calculation
17.14 Tieplate Temperature Calculation
17.15 Core Steel Temperature Calculation
18 LOAD TAP CHANGERS
18.1 Introduction
18.2 General Description of LTC
18.3 Types of Regulation
18.4 Principles of Operation
18.5 Connection Schemes
18.6 General Maintenance
19 CONSTRAINED NONLINEAR OPTIIZATION WITH APPLICATION TO TRANSFORMER DESIGN
19.1 Introduction
19.2 Geometric Programming
19.3 Nonlinear Constrained Optimization
19.4 Application to Transformer Design
REFERENCES
INDEX
Biography
Robert M. Del Vecchio received the BS degree in physics from the Carnegie Institute of Technology, Pittsburgh, PA, the MS degree in electrical engineering, and the PhD degree in physics from the University of Pittsburgh, Pittsburgh, PA in 1972. He served in several academic positions from 1972 to 1978. He then joined the Westinghouse R&D Center, Pittsburgh, PA, where he worked on modeling magnetic materials and electrical devices. He joined North American Transformer (now SPX Transformer Solutions), Milpitas, CA, in 1989, where he developed computer models and transformer design tools. Currently, he is a Consultant.
Bertrand Poulin, received his Bachelor of Engineering degree in Electrical Engineering from École Polytechnique Université de Montréal in 1978 and his MS degree in High Voltage Engineering in 1988 from the same University. Bertrand started his career in a small repair facility for motors, generators, and transformers in Montréal in 1978 as a technical advisor. In 1980, he joined the transformer division of ASEA in Varennes, Canada as a test engineer and later as a design and R&D engineer. In 1992, he joined North American Transformer, where he was involved in testing and R&D and finally manager of R&D and testing. In 1999, he went back to ABB in Varennes where he held the position of Technical Manager for the Varennes facility and Senior Principal Engineer for the Power Transformer Division of ABB worldwide. He is a member of IEEE Power and Energy Society, an active member of the Transformers Committee, and a registered Professional Engineer in Québec, Canada.
Pierre T. Feghali, PE, MS received his bachelor’s degree in Electrical Engineering from Cleveland State University in 1985 and his Master's degree in Engineering Management in 1996 from San Jose State University. He has worked in the transformer industry for over 23 years. He started his career in distribution transformer design at Cooper Power Systems in Zanesville, Ohio. In 1989, he joined North American Transformer in Milpitas, CA, where he was a Senior Design Engineer. Between 1997 and 2002, he held multiple positions at the plant including: production control manager, quality and test manager, and plant manager. He became Vice President of Business Development and Engineering at North American Substation Services, Inc. He is a Professional Engineer in the state of California and an active member of the IEEE and PES.
Dilipkumar M. Shah received his BSEE degree from India in 1964 and his MSEE degree from IIT (Chicago, IL) in 1967. From 1967 to 1977, he worked as a transformer design engineer at Westinghouse Electric and Delta Star. He joined Waukesha Electric Systems in 1977 as a senior design engineer and then the engineering manager. Since 2002, he has been working as a transformer consultant for utilities in Argentina, Brazil, and US, covering areas such as design reviews, diagnosing transformer failures, and for transformer manufacturers in Argentina, Brazil India and US on improving their designs and manufacturing practices for transformer up to 500KV. Presently, he is working as a consultant for Auriga Corporation as a transformer specialist.
Rajendra Ahuja graduated from the Univ. of Indore in India, where he received a B.Eng. Hons. (Electrical) degree in 1975. He worked at B.H.E.L. and GEC Alsthom India and was involved in design and development of EHV transformers and in the development of wound-in-shield type windings. He also has experience in the design of special transformers for traction, furnace, phase shifting, and rectifier applications. He joined North American Transformer (now SPX Transformer Solutions) in 1994 as a principal design engineer and became the manager of the testing and development departments. He became the vice president of engineering at SPX Transformer Solutions. He is an active member of the Power and Energy Society, the IEEE Transformers Committee, and the IEC. He is currently a consultant.
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
