612 Pages
    by CRC Press

    612 Pages
    by CRC Press

    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, Bertrand Poulin, Pierre T. Feghali, Dilipkumar Shah, Rajendra Ahuja

    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