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