Читать книгу Power Magnetic Devices - Scott D. Sudhoff - Страница 4

1 Chapter 1Figure 1.1 A manual design process.Figure 1.2 Optimization‐based design process.Figure 1.3 Function properties.Figure 1.4 Definition of a convex set.Figure 1.5 Definition of a convex function.Figure 1.6 Deoxyribonucleic acid (DNA).Figure 1.7 Meiosis.Figure 1.8 Canonical genetic algorithm.Figure 1.9 Chromosome crossover, segregation, and mutation in Example 1.5B....Figure 1.10 Single‐point crossover.Figure 1.11 Single‐point simple‐blend crossover.Figure 1.12 Total mutation.Figure 1.13 Fitness and gene values for Example 1.6A.Figure 1.14 Enhanced real‐coded genetic algorithm.Figure 1.15 Motor performance objective space.Figure 1.16 Pareto‐optimal set and front.Figure 1.17 Calculation of Pareto‐optimal front with ε‐constraint method.Figure 1.18 Application of Kung’s method.Figure 1.19 Crowding distance.Figure 1.20 Elitist nondominated sorting genetic algorithm (NSGA‐II).Figure 1.21 Constraint functions.Figure 1.22 UI‐core inductor.Figure 1.23 Single‐objective optimization study.Figure 1.24 UI‐core design.Figure 1.25 Multi‐objective optimization results.Figure 1.26 Sample design from Pareto‐optimal front.Figure 1.27 Sample design from Pareto‐optimal front.

2 Chapter 2Figure 2.1 Ampere’s law.Figure 2.2 Calculation of flux.Figure 2.3 Atomic magnetic moment arrangements.Figure 2.4 B–H characteristic of ferromagnetic and ferrimagnetic mater...Figure 2.5 B − H Characteristic of a M47 silicon steel.Figure 2.6 Permeability functions for a M47 silicon steel.Figure 2.7 r(B) for a M47 silicon steel sample.Figure 2.8 Fields in a material sample “a.”Figure 2.9 UI‐core inductor.Figure 2.10 Construction of the MEC.Figure 2.11 Simplified magnetic equivalent circuit for a UI‐core inductor.Figure 2.12 Flux linkage versus current.Figure 2.13 Measured and predicted λ − i characteristics.Figure 2.14 Measurement of λ − i characteristics.Figure 2.15 Fringing Flux.Figure 2.16 Field components at air‐core interface.Figure 2.17 Calculation of fringing flux.Figure 2.18 Measured and predicted λ − i characteristics including frin...Figure 2.19 Leakage flux.Figure 2.20 Toroidal geometry.Figure 2.21 Horizontal and vertical slot leakage flux.Figure 2.22 Exterior adjacent leakage flux (approach 1).Figure 2.23 Exterior adjacent leakage flux (approach 2).Figure 2.24 Exterior isolated leakage flux.Figure 2.25 Magnetic equivalent circuit with leakage flux permeances.Figure 2.26 A standard branch.Figure 2.27 Sample MEC.Figure 2.28 Sample MECFigure 2.29 Simple nonlinear MEC.Figure 2.30 Residual for nodal analysis.Figure 2.31 Residual using mesh analysis.Figure 2.32 Measured and predicted λ − i characteristics including frin...Figure 2.33 B‐H and M‐H Characteristics of PM Material.Figure 2.34 Permanent magnet MEC element.Figure 2.35 Permanent magnet configuration.

3 Chapter 3Figure 3.1 Common inductor architectures.Figure 3.2 Example of a coil.Figure 3.3 Cross‐section of coil.Figure 3.4 Bobbin wound coil.Figure 3.5 UI‐Core inductor.Figure 3.6 UI‐Core inductor Pareto‐optimal front.Figure 3.7 Final population gene distribution.Figure 3.8 Current density versus mass.Figure 3.9 Conductor count versus mass.Figure 3.10 Dimensions versus mass.Figure 3.11 Design 50.

4 Chapter 4Figure 4.1 Field energy and co‐energy.Figure 4.2 Excitation of a single branch.

5 Chapter 5Figure 5.1 Possible electromagnet arrangements.Figure 5.2 EI‐core electromagnet.Figure 5.3 EI‐core magnetic equivalent circuit.Figure 5.4 Slot leakage path.Figure 5.5 Reduced magnetic equivalent circuit.Figure 5.6 Flux linkage versus current.Figure 5.7 Force versus current.Figure 5.8 Force over power loss versus current.Figure 5.9 Electromagnetic door latch.Figure 5.10 Pareto‐optimal front between volume and loss.Figure 5.11 Gene distribution plot for the electromagnet.Figure 5.12 Current density versus volume for electromagnet.Figure 5.13 Conductor count versus volume for electromagnet.Figure 5.14 Core widths versus volume for electromagnet.Figure 5.15 Geometrical parameters versus volume for electromagnet.Figure 5.16 Geometrical parameters versus volume for electromagnet.Figure 5.17 Effects of wire size descritization on Pareto‐optimal front.Figure 5.18 Effects of wire size discretization on current density.

6 Chapter 6Figure 6.1 Calculation of eddy current losses.Figure 6.2 Top view of test configuration.Figure 6.3 Excitation‐normalized power loss versus frequency.Figure 6.4 Magnetic domains.Figure 6.5 B–H characteristics of a ferrite material MN80C.Figure 6.6 Large uniformly wound toroid.Figure 6.7 Hysteresis characteristic.Figure 6.8 Minor loop behavior.Figure 6.9 Flux density waveforms.Figure 6.10 Loss components versus frequency.Figure 6.11 Epstein frame.Figure 6.12 Single‐ and double‐sheet testers.Figure 6.13 Toroidal tester.Figure 6.14 Impact of laser cutting.Figure 6.15 Determining the anhysteretic characteristic.Figure 6.16 Characterization waveforms in example 6.5A.Figure 6.17 Sense winding flux linkage versus magnetizing current in example...Figure 6.18 B–H characteristic in example 6.5A.Figure 6.19 Example 6.5B characterization of μ_B(B).Figure 6.20 Example 6.8A measured and fitted losses.Figure 6.21 Hysteron behavior.Figure 6.22 Example magnetization states.Figure 6.23 Incremental magnetization.Figure 6.24 Trajectories predicted by the extended Jiles–Atherton model.Figure 6.25 Alternate path for eddy current derivation.

7 Chapter 7Figure 7.1 Transformer types.Figure 7.2 Cross section of one leg of core type transformer.Figure 7.3 Elementary transformer.Figure 7.4 Transformer magnetic equivalent circuit.Figure 7.5 T‐equivalent circuit.Figure 7.6 Circuit for Example 7.3A.Figure 7.7 Modified T‐equivalent circuit.Figure 7.8 Core‐type transformer cross section.Figure 7.9 End leg cross section with coils.Figure 7.10 Coil construction.Figure 7.11 Core type transformer magnetic equivalent circuit.Figure 7.12 Reduced magnetic equivalent circuit.Figure 7.13 Core type transformer leakage paths.Figure 7.14 Division of winding into interior and exterior portions.Figure 7.15 Consideration of a vertical leakage path.Figure 7.16 Leakage flux paths.Figure 7.17 Exterior secondary leakage flux paths.Figure 7.18 Transformer design Pareto‐optimal front.Figure 7.19 Parameter distribution.Figure 7.20 Design 100 cross sections.Figure 7.21 Primary flux linkage versus current.Figure 7.22 No‐load flux density waveforms.

8 Chapter 8Figure 8.1 Distributed winding stator.Figure 8.2 Definition of position measurements.Figure 8.3 P‐pole machines.Figure 8.4 Slot structure.Figure 8.5 Developed diagram.Figure 8.6 End conductors.Figure 8.7 Stator winding for a 4‐pole 36‐slot machine.Figure 8.8 Winding arrangements.Figure 8.9 Calculation of the winding function.Figure 8.10 Conductor distribution and winding functions.Figure 8.11 Path of integration.Figure 8.12 Calculation of flux linkage.Figure 8.13 Carter’s coefficient.Figure 8.14 Slot leakage inductance.Figure 8.15 End leakage inductance.Figure 8.16 Slot leakage permeance due to paths 1–4.Figure 8.17 Slot leakage permeance due to paths 5–7.Figure 8.18 End winding permeance—exterior path.Figure 8.19 Geometric interpretation of Park’s transformation.

9 Chapter 9Figure 9.1 Surface‐mounted permanent magnet synchronous machine.Figure 9.2 Two interior magnetic arrangements.Figure 9.3 Wye and delta connections.Figure 9.4 Three‐phase bridge inverter and machine.Figure 9.5 Voltage source fed PMAC machine characteristics.Figure 9.6 Current source fed PMAC machine characteristics.Figure 9.7 Surface‐mounted permanent magnet synchronous machine.Figure 9.8 Slot and tooth dimensions.Figure 9.9 Rectangular slot approximation.Figure 9.10 Thin sector of machine.Figure 9.11 Radial magnetization.Figure 9.12 Backiron flux calculation.Figure 9.13 Backiron flux.Figure 9.14 Flux density in rotor backiron.Figure 9.15 Pareto‐optimal front.Figure 9.16 Parameter distribution.Figure 9.17 Material selection versus electromagnetic mass.Figure 9.18 Power loss components versus electromagnetic mass.Figure 9.19 Component mass versus electromagnetic mass.Figure 9.20 Current‐related parameters versus electromagnetic mass.Figure 9.21 Machine parameters versus electromagnetic mass.Figure 9.22 Design 38 cross section.Figure 9.23 Design 38 flux density versus rotor position.

10 Chapter 10Figure 10.1 An elemental cuboid.Figure 10.2 One‐dimensional heat flow example.Figure 10.3 Thermal equivalent circuit for one‐dimensional heat flow.Figure 10.4 Mean temperature versus time.Figure 10.5 Heat transfer rate versus time.Figure 10.6 Temperature profile versus time.Figure 10.7 Special case for one‐dimensional heat flow.Figure 10.8 Thermal equivalent circuit of a cuboidal region. (Based on [1].)...Figure 10.9 Cylindrical region.Figure 10.10 Thermal equivalent circuit of cylindrical region.Figure 10.11 Representation of homogenized region. (Based on [2].)Figure 10.12 Spatial temperature dependence.Figure 10.13 Standard branch.Figure 10.14 Concise circuit symbols.Figure 10.15 Thermal equivalent circuit elements.Figure 10.16 Cuboids of EI core electromagnet arrangement.Figure 10.17 Corner element.Figure 10.18 Core‐winding interface.Figure 10.19 Electromagnet thermal equivalent circuit.Figure 10.20 Pareto‐optimal fronts.Figure 10.21 Gene distribution.Figure 10.22 Current density versus volume.Figure 10.23 Conductor counts versus volume.Figure 10.24 Widths versus volume.Figure 10.25 Assorted dimensions versus volume.Figure 10.26 Peak winding temperature versus volume.

11 Chapter 11Figure 11.1 Strip conductor.Figure 11.2 Current density distribution in a strip conductor.Figure 11.3 Impedance characteristics of a strip conductor.Figure 11.4 Cylindrical conductor.Figure 11.5 Impedance characteristic of a cylindrical conductor.Figure 11.6 Rectangular conductor exposed to a magnetic field.Figure 11.7 Round conductor exposed to a magnetic field.Figure 11.8 Current density in a symmetric conductor.Figure 11.9 Gapped closed slot conductors.Figure 11.10 Slot geometry.Figure 11.11 Predicted and measured resistance of a coil in an open slot.Figure 11.12 UI‐core inductor.Figure 11.13 Assumed current waveform.Figure 11.14 Buck converter.Figure 11.15 Conductor losses.

12 Chapter 12Figure 12.1 Inductor equivalent circuit.Figure 12.2 Electric field at a conductor’s surface.Figure 12.3 Parallel plate capacitor.Figure 12.4 Cylindrical plate capacitor.Figure 12.5 Conductor and quasi‐conductor.Figure 12.6 Capacitance of conductive cylinders.Figure 12.7 Turn‐to‐turn capacitance of a simple coil.Figure 12.8 Symmetry conditions for capacitance.Figure 12.9 Turn‐to‐turn capacitance in multilayer windings.Figure 12.10 Calculation of layer‐to‐layer capacitance.Figure 12.11 Core‐type transformer.Figure 12.12 Transformer equivalent circuit.Figure 12.13 Photograph of inductors for Examples 12.3A (leftmost), 12.4 A (...Figure 12.14 Full impedance frequency response of a two‐layer inductor.Figure 12.15 Measured and fitted impedance frequency responses.

13 Chapter 13Figure 13.1 Buck converter.Figure 13.2 Buck converter operation.Figure 13.3 Buck converter average‐value model.Figure 13.4 Input filter waveforms.Figure 13.5 Output filter waveforms.Figure 13.6 Semiconductor/heat‐sink thermal‐equivalent circuit.Figure 13.7 Semiconductor loss versus current ripple.Figure 13.8 Required heat‐sink mass versus current ripple.Figure 13.9 Input inductor mass versus inductance.Figure 13.10 Input inductor loss versus inductance.Figure 13.11 UI‐core inductor.Figure 13.12 Cross‐section of the winding bundle.Figure 13.13 Winding bundle thermal‐equivalent circuit.Figure 13.14 Simplified winding bundle thermal‐equivalent circuit.Figure 13.15 Buck converter parameter distribution.Figure 13.16 Buck converter Pareto‐optimal front.Figure 13.17 Efficiency versus specific power density.Figure 13.18 Switching frequency versus mass.Figure 13.19 UI‐core output inductor cross section.

14 Chapter 14Figure 14.1 A dc–ac converter.Figure 14.2 Phase leg of three‐phase bridge converter.Figure 14.3 Sine‐triangle modulation.Figure 14.4 Inductor topology.Figure 14.5 Time‐domain waveforms with L_d = L_q .Figure 14.6 Time‐domain waveforms with L_d ≠ L_q .Figure 14.7 Elementary three‐phase inductor MEC.Figure 14.8 The three‐phase inductor MEC.Figure 14.9 Interior and exterior fringing and leakage paths.Figure 14.10 Face fringing and leakage permeances.Figure 14.11 Test points.Figure 14.12 Case study assumed current waveforms.Figure 14.13 Three‐Phase I‐Core inductor parameter distribution.Figure 14.14 Three‐Phase I‐Core inductor pareto‐optimal front.Figure 14.15 Design 100. Dimensions in meters.

15 Chapter 15Figure 15.1 Differential‐ and common‐mode currents.Figure 15.2 Dc‐to‐ac converter.Figure 15.3 Power block.Figure 15.4 Common‐mode equivalent circuit.Figure 15.5 Simplified common‐mode equivalent circuits.Figure 15.6 Common‐mode flux‐linkage waveform.Figure 15.7 Peak common‐mode flux linkage versus duty cycle.Figure 15.8 Original and proxy common‐mode flux‐linkage waveforms.Figure 15.9 CMI circuit diagram.Figure 15.10 UR‐core common‐mode inductor.Figure 15.11 Winding cross section.Figure 15.12 UR core magnetic analysis.Figure 15.13 UR‐core common‐mode inductor parameter distribution.Figure 15.14 UR‐core inductor Pareto‐optimal front.Figure 15.15 Design 75.Figure 15.16 Design 75 BH trajectories based on proxy waveform.Figure 15.17 Design 75 BH trajectories using original flux‐linkage waveform....

16 Chapter 16Figure 16.1 Selection of boundary conditions.Figure 16.2 Two domain problem.Figure 16.3 Triangular element.Figure 16.4 Simple domain.Figure 16.5 Rectangular–cuboid core inductor mesh.Figure 16.6 Rectangular–cuboid core inductor fields.Figure 16.7 FEA predictions for λ − i characteristic.

17 Appendix BFigure B.1 B–H characteristics of the selected ferrites.

18 Appendix CFigure C.1 B–H characteristics of selected steels.