Power Magnetic Devices. Scott D. Sudhoff

href="#ulink_d67d98a1-265b-5b45-ba81-b428a3e9da1b">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