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