Transformer Design Principles

Robert M. Del Vecchio received the BS degree in physics from the Carnegie Institute of Technology, Pittsburgh, Pennsylvania, the MS degree in electrical engineering, and the Ph.D. degree in physics from the University of Pittsburgh in 1972. He was a Lecturer in physics at Princeton University, New Jersey, from 1972 to 1976, and an Assistant Professor at the University of Pittsburgh from 1976 to 1978. He then joined the Westinghouse R&D Center, Pittsburgh, where he worked on modeling magnetic materials and electrical devices. He joined North American Transformer (now Waukesha Electric Systems) in 1989, where he developed computer models and transformer design tools. He is a member of the IEEE Power and Energy Society and Magnetics Society. He has served on the IEEE Transformers Committee, the IEC, and a Cigre committee. 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 carreer 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 holds currently 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 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 is currently 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 the M.S. University of Baroda (India) in 1964 and his MSEE degree in Power Systems from the Illinois Institute of Technology (Chicago, Illinois) in 1967. Since 1967 until 1977, he worked as a transfomer design engineer at Westinghouse Electric, Delta Star, and Aydin Energy Systems. He joined North American Transformer in 1977 as a senior design engineer and then the engineering manager. He left in 2002 and has been working as a transformer consultant for utilities world wide, covering areas such as design reviews, diagnosing transformer failures, and advising transformer manufacturers on improving their designs and manufacturing practices. Rajendra Ahuja graduated from the Univ. of Indore in India where he received a B.Engg. 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 Waukesha Electric Systems) in 1994 as a principal design engineer and became the manager of the testing and development departments. He is currently the vice president of engineering. He is an active member of the Power and Energy Society, the IEEE Transformers Committee, and the IEC.

Introduction


Historical Background


Uses in Power Systems


Core-Form and Shell-Form Transformers


Stacked and Wound Core Construction


Transformer Cooling


Winding Types


Insulation Structures


Structural Elements


Modern Trends





Magnetism and Related Core Issues


Basic Magnetism


Hysteresis


Magnetic Circuits


Inrush Current


Distinguishing Inrush from Fault Current


Optimal Core Stacking





Circuit Model of a Two-Winding Transformer with Core


Circuit Model of the Core


Two-Winding Transformer Circuit Model with Core


Approximate Two-Winding Transformer Circuit Model without Core


Vector Diagram of a Loaded Transformer with Core


Per-Unit System


Voltage Regulation





Reactance and Leakage Reactance Calculations


General Method for Determining Inductances and Mutual Inductances


Two-Winding Leakage Reactance Formula


Ideal Two-, Three-, and Multiwinding Transformers


Leakage Reactance for Two-Winding Transformers Based on Circuit Parameters


Leakage Reactances for Three-Winding Transformers





Phasors, Three-Phase Connections, and Symmetrical Components


Phasors


Wye and Delta Three-Phase Connections


Zig-Zag Connection


Scott Connection


Symmetrical Components





Fault Current Analysis


Fault Current Analysis on Three-Phase Systems


Fault Currents for Transformers with Two Terminals per Phase


Fault Currents for Transformers with Three Terminals per Phase


Asymmetry Factor





Phase-Shifting and Zig-Zag Transformers


Basic Principles


Squashed Delta Phase-Shifting Transformer


Standard Delta Phase-Shifting Transformer


Two-Core Phase-Shifting Transformer


Regulation Effects


Fault Current Analysis


Zig-Zag Transformer





Multi-terminal Three-Phase Transformer Model


Theory


Transformers with Winding Connections within a Phase


Multiphase Transformers


Generalizing the Model


Regulation and Terminal Impedances


Multiterminal Transformer Model for Balanced and Unbalanced Load Conditions





Rabins’ Method for Calculating Leakage Fields, Leakage Inductances, and Forces in Transformers


Theory


Rabins’ Formula for Leakage Reactance


Application of Rabins’ Method to Calculate the Self-Inductance of and Mutual Inductance between Coil Sections


Determining the B-Field


Determination of Winding Forces


Numerical Considerations





Mechanical Design


Force Calculations


Stress Analysis


Radial Buckling Strength


Stress Distribution in a Composite Wire-Paper Winding Section


Additional Mechanical Considerations





Electric Field Calculations


Simple Geometries


Electric Field Calculations Using Conformal Mapping


Finite Element Electric Field Calculations





Capacitance Calculations


Distributive Capacitance along a Winding or Disk


Stein’s Disk Capacitance Formula


General Disk Capacitance Formula


Coil Grounded at One End with Grounded Cylinders on Either Side


Static Ring on One Side of Disk


Terminal Disk without a Static Ring


Capacitance Matrix


Two Static Rings


Static Ring Between the First Two Disks


Winding Disk Capacitances with Wound-in Shields


Multistart Winding Capacitance





Voltage Breakdown and High-Voltage Design


Principles of Voltage Breakdown


Geometric Dependence of Transformer-Oil Breakdown


Insulation Coordination


Continuum Model of Winding Used to Obtain the Impulse-Voltage Distribution


Lumped-Parameter Model for Transient Voltage


Distribution





Losses


No-Load or Core Losses


Load Losses


Tank and Shield Losses Due to Nearby Busbars


Tank Losses Associated with the Bushings





Thermal Design


Thermal Model of a Disk Coil with Directed Oil Flow


Thermal Model for Coils without Directed Oil Flow


Radiator Thermal Model


Tank Cooling


Oil Mixing in the Tank


Time Dependence


Pumped Flow


Comparison with Test Results


Determining m and n Exponents


Loss of Life Calculation


Cable and Lead Temperature Calculation


Tank Wall Temperature Calculation


Tieplate Temperature


Core Steel Temperature Calculation





Load Tap Changers


General Description of Load Tap Changer


Types of Regulation


Principles of Operation


Connection Schemes


General Maintenance





Miscellaneous Topics


Setting the Impulse Test Generator to Achieve Close to Ideal Waveshapes


Impulse or Lightning Strike on a Transformer through a Length of Cable


Air Core Inductance


Electrical Contacts





References





Index