Spotlight on Modern Transformer Design (eBook)

Pavlos S. Georgilakis is currently assistant professor in the production engineering and management department of the Technical University of Crete, Greece. He received a diploma in electrical and computer engineering and a PhD from the National Technical University of Athens, Greece in 1990 and 2000 respectively. In his doctoral thesis, entitled "Contribution of Artificial Intelligence Techniques in the Reduction of Distribution Transformer Iron Losses", he introduced the concept of artificial intelligence in transformer design. He worked in the transformer industry for 10 years before joining academia. From 1994 to 2003 he was with Schneider Electric AE, where he worked as transformer quality control engineer for one year, transformer design engineer for four years, transformer research and development manager for three years, and marketing manager for two years. He has considerable experience in the design, development, and manufacturing of transformers. Assistant Professor Georgilakis has designed and supervised eight research projects in the field of transformer design, which have been funded by the government and the private sector. He is the author of two books, 40 papers in international journals, and 70 papers in international conference proceedings. His current research interests include transformer design and modeling, artificial intelligence techniques in transformer design and power systems, numerical techniques in the analysis and design of power transformers, and renewable energy sources. He is a member of the IEEE, the CIGRE, and the Technical Chamber of Greece.

Foreword 6
Preface 8
Contents 13
1 Transformers 20
1.1 Introduction 20
1.2 Magnetic Circuits 1.2.1 General 21
1.2.2 Analysis of Magnetic Circuits 24
1.2.3 Flux Linkage 26
1.2.4 Magnetic Materials 27
1.3 Transformer Fundamentals 1.3.1 Equivalent Circuit 29
1.3.2 Derivation of Equivalent Circuit Parameters 31
1.3.3 Voltage Regulation 35
1.3.4 Efficiency 40
1.4 Transformer Electrical Characteristics 1.4.1 Rated Power 44
1.4.2 Temperature Rise 45
1.4.3 Ambient Temperature 45
1.4.4 Altitude of Installation 46
1.4.5 Impedance Voltage 46
1.4.6 No-Load Losses 46
1.4.7 Load Losses 47
1.4.8 Rated Voltages 48
1.4.9 Vector Group 48
1.4.10 Frequency 49
1.4.11 Noise 49
1.4.12 Short-Circuit Current 49
1.4.13 No-Load Current 49
1.5 Transformer Operation 1.5.1 Overloading 50
1.5.2 Parallel Operation 50
1.5.3 Load Distribution to Transformers in Parallel Operation 51
1.6 Transformer Standards and Tolerances 1.6.1 Transformer Standards 52
1.6.2 Tolerances 53
1.7 Transformer Tests 54
1.7.1 Type Tests 54
1.7.2 Routine Tests 54
1.7.3 Special Tests 56
1.8 Transformer Types 56
1.8.1 Classification According to Transformer Use 57
1.8.2 Classification According to Transformer Cooling Method 57
1.8.3 Classification According to Transformer Insulating Medium 58
1.8.4 Classification According to Transformer Core Construction 58
1.9 Transformers Studied in this Book 59
References 60
2 Conventional Transformer Design 61
2.1 Nomenclature 61
2.2 Introduction 65
2.3 Problem Formulation 65
2.3.1 Objective Function 66
2.3.2 Constraints 68
2.3.3 Mathematical Formulation of the TDO Problem 73
2.3.4 Characteristics of the TDO Problem 74
2.4 Conventional Transformer Design Optimization Method 2.4.1 Methodology 75
2.4.2 Case Study 78
2.4.3 Repetitive Transformer Design Process 82
2.5 Example of Transformer Design Data 84
2.5.1 Values of Description Variables 86
2.5.2 Values of Special Variables 86
2.5.3 Values of Default Variables 86
2.5.4 Values of Cost Variables 86
2.5.5 Values of Various Variables 87
2.5.6 Values of Conductor Cross-Section Calculation Variables 87
2.5.7 Values of Design Variables 87
2.6 Calculation of Volts per Turn and Thickness of Core Leg 2.6.1 Calculation of Volts per Turn 90
2.6.2 Calculation of Thickness of Core Leg 90
2.6.3 Example 2.1 92
2.7 Calculation of Layer Insulation 93
2.7.1 Layer Insulation of LV Winding 94
2.7.2 Layer Insulation of HV Winding 94
2.7.3 Example 2.2 94
2.8 Calculation of Winding and Core Dimensions 95
2.8.1 Example 2.3 95
2.9 Calculation of Core Weight and No-Load Loss 100
2.9.1 Example 2.4 102
2.10 Calculation of Inductive Part of Impedance Voltage 103
2.10.1 Example 2.5 105
2.11 Calculation of Load Loss 110
2.11.1 Example 2.6 110
2.12 Calculation of Impedance Voltage 115
2.12.1 Example 2.7 116
2.13 Calculation of Coil Length 116
2.13.1 Example 2.8 117
2.14 Calculation of Tank Dimensions 118
2.14.1 Example 2.9 118
2.15 Calculation of Winding Gradient and Oil Gradient 119
2.15.1 Example 2.10 119
2.16.1 Example 2.11 124
2.17 Calculation of the Weight of Insulating Materials 126
2.17.1 Example 2.12 126
2.18 Calculation of the Weight of Ducts 130
2.18.1 Example 2.13 130
2.19 Calculation of the Weight of Oil 131
2.19.1 Example 2.14 131
2.20 Calculation of the Weight of Sheet Steel 132
2.20.1 Example 2.15 133
2.21 Calculation of the Weight of Corrugated Panels 133
2.21.1 Example 2.16 133
2.22 Calculation of the Cost of Transformer Main Materials 133
2.22.1 Example 2.17 134
2.23 Calculation of Transformer Manufacturing Cost 135
2.23.1 Example 2.18 136
References 138
3 Numerical Analysis 140
3.1 Introduction 3.1.1 Magnetostatic Problems 140
3.1.2 Methods for the Solution of Magnetostatic Problems 142
3.2 Finite Element Method 3.2.1 Introduction 143
3.2.2 Applications to Power Engineering 144
3.2.3 Solution of Linear Magnetostatic Problems 145
3.2.4 Solution of Nonlinear Magnetostatic Problems 161
References 168
4 Classification and Forecasting 172
4.1 Introduction 172
4.2 Automatic Learning 173
4.3 Data Mining 173
4.3.1 Representation 174
4.3.2 Attribute Selection 174
4.3.3 Model Selection 174
4.3.4 Interpretation and Validation 174
4.3.5 Model Use 175
4.4 Learning Set and Test Set 175
4.4.1 Classification 175
4.4.2 Forecasting 176
4.5 Decision Trees 4.5.1 Introduction 177
4.5.2 Applications to Power Systems 178
4.5.3 General Characteristics 179
4.5.4 Top Down Induction 180
4.5.5 Optimal Splitting Rule 182
4.5.6 Stop Splitting Rule 185
4.5.7 Overview of Decision Tree Building Algorithm 188
4.5.8 Example 4.1 189
4.5.9 Example 4.2 194
4.6 Artificial Neural Networks 4.6.1 Introduction 200
4.6.2 Applications to Power Systems 201
4.6.3 ANN Types 202
4.6.4 Neuron Mathematical Model 203
4.6.5 ANN Architectures 204
4.6.6 ANN Training 206
4.6.7 ANN Configuration 220
4.6.8 Example 4.5 222
4.7 Hybrid Decision Tree–Neural Network Classifier 225
4.7.1 Example 4.6 226
References 227
5 Optimization 233
5.1 Introduction 233
5.2 Quadratic Programming 5.2.1 Methodology 236
5.2.2 Applications to Power Systems 239
5.2.3 Example 5.1 239
5.3 Sequential Quadratic Programming 5.3.1 Methodology 245
5.3.2 Applications to Power Systems 247
5.3.3 Example 5.2 247
5.4 Branch-and-Bound 5.4.1 Methodology 253
5.4.2 Applications to Power Systems 255
5.4.3 Example 5.3 255
5.5 Genetic Algorithms 5.5.1 Methodology 258
5.5.2 Applications to Power Systems 262
5.5.3 Example 5.4 263
References 270
6 Evaluation of Transformer Technical Characteristics 277
6.1 Introduction 277
6.2 No-Load Loss Classification with Decision Trees and Artificial Neural Networks 6.2.1 Introduction 278
6.2.2 Individual Core 279
6.2.3 Transformer 293
6.3 No-Load Loss Forecasting with Artificial Neural Networks 6.3.1 Introduction 304
6.3.2 Forecasting Accuracy 306
6.3.3 Individual Core 306
6.3.4 Transformer 310
6.4.2 Finite Element Model 314
6.4.3 Results and Discussion 329
References 337
7 Transformer Design Optimization 342
7.1 Introduction 342
7.2 No-Load Loss Reduction with Genetic Algorithms 7.2.1 Introduction 343
7.2.2 Conventional Core Grouping Process 343
7.2.3 Genetic Algorithm Solution to the TNLLR Problem 345
7.2.4 Results 352
7.3 Winding Material Selection with Decision Trees and Artificial Neural Networks 7.3.1 Introduction 354
7.3.2 Creation of Knowledge Base 355
7.3.3 Decision Trees 357
7.3.4 Adaptive Trained Neural Networks 360
7.3.5 Synthesis 370
7.4 Transformer Design Optimization with Branch-and-Bound 7.4.1 Introduction 370
7.4.2 MIP-FEM Methodology 371
7.4.3 Results and Discussion 375
7.5 Transformer Design Optimization with Genetic Algorithms 7.5.1 Introduction 379
7.5.2 Recursive GA-FEM Methodology 379
7.5.3 Results and Discussion 383
References 385
8 Transformer Selection 388
8.1 Introduction 388
8.2 Total Owning Cost for Industrial and Commercial Users 8.2.1 Cost Evaluation Method 389
8.2.2 Example 8.1 393
8.2.3 Example 8.2 396
8.2.4 Example 8.3 396
8.3 Total Owning Cost for Electric Utilities 8.3.1 Cost Evaluation Method 402
8.3.2 Example 8.4 405
8.3.3 Example 8.5 407
8.4 Proposed TOC Incorporating Environmental Cost 8.4.1 Introduction 411
8.4.2 Cost Evaluation Method 413
8.4.3 Example 8.6 418
8.4.4 Example 8.7 419
8.4.5 Example 8.8 420
8.4.6 Example 8.9 422
8.4.7 Example 8.10 428
References 430
Index 433