Power Magnetic Devices: A Multi-Objective Design Approach Chapter 9: Introduction to Permanent Magnet AC Machine Design S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.1 Permanent Magnet Synchronous Machines Surface mounted magnet machine S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.1 Permanent Magnet Synchronous Machines Interior permanent magnet machine S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Machine connections S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Machine model in QD variables S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Flux linkage equations Torque equation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Steady-state analysis S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Three-phase bridge inverter S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Inverter voltage limit Semiconductor conduction loss S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Derivation of semiconductor conduction loss S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Voltage source operation (abc) Voltage source operation (qd) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines For steady-state conditions we can show S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Example 9.2A. P = 4, Rs = 240 mW, Lq = Ld = 1.65 mH, lm = 115 mVs. Let’s plot operating characteristics with Vs =10.2 V and fv = 0. S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines We obtain Ismx = 40.8 A Pinmx = 1.25 kW Temx = 19.9 Nm S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Current source operation (abc) Current source operation (qd) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Selection of q- and d-axis currents in non-salient machine w/o voltage constraint S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Reason to inject d-axis current S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Reason to inject d-axis current (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Example 9.2B. Let’s look at capability curve of machine of Example 9.2A with current source operation. Assume a dc link a maximum current of 15.6 A rms and a dc link voltage of 200 V. S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Approach: Treat as optimization problem S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.2 Operating Char. of PMAC Machines Result S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Machine dimensions S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Stator tooth S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Tooth fraction and tooth tip fraction S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Independent geometry variables From GI we can completely describe the geometry using (9.3-4)-(9.3-28). This includes dimensions, areas, volumes S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Rectangular slot approximation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Rectangular slot approximation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Derivation notes S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.3 Machine Geometry Function arrangement S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Assumed conductor density S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Discrete conductor layout S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Additional slot conductor calculations S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding End conductor calculations We’ll assume which yields S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Conductor size calculations S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Coil calculations S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.4 Stator Winding Functional form of calculations S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.5 Material Parameters Material properties are looked up from catalogs represented as functions S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.6 Stator Currents and Control Philosophy Current selection information S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis In chapter 8 we showed that For our case S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Stator MMF. Using S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis We obtain S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Radial field variation. We will have S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Air gap MMF drop. We can show S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Permanent magnet MMF. We have S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis PM characteristics versus position S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis We can show S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Solution for radial field density. Using the results from this section, we can show Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.7 Radial Field Analysis Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Flux linkage components Leakage flux linkage S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
Derivation (continued) 9.8 Lumped Parameters Derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
Derivation (continued again) 9.8 Lumped Parameters Derivation (continued again) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Magnetizing flux linkage S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Partial derivation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Partial derivation (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.8 Lumped Parameters Finally, we express the flux linkages as In functional form S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Stator tooth flux S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Notes S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Stator tooth flux (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Explanation of symmetry S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Explanation of symmetry (continued) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Stator tooth flux densities S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Stator backiron flux We have S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis We can show S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis continuing … S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis We define Similar to the stator tooth S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Stator core loss S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Rotor peak tangential back iron flux density S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Rotor peak radial flux density S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis The peak radial flux density is given by S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Notes S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis More notes S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Observation on peak rotor flux density S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Permanent magnet field intensity in region of positive magnetization It follows that S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.9 Ferromagnetic Field Analysis Functional representation S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design space (w/o tooth tip) Design parameters (fixed) S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design parameters (continued) nspp atar aso S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design metrics Mass Loss S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design constraints Tooth aspect ratio Slot opening Current density Mass S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design constraints (continued) Voltage No current field constraints S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design constraints (continued) Operating point field constraints S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Design constraints (continued) Torque Power loss S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Fitness S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Fitness pseodo-code S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.10 Formulation of Design Problem Pseudo-code for check of constraints S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Design specifications S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Parameter ranges S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Pareto-optimal front S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Parameter distribution S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Material selection S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Power loss components S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Component mass S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Current related parameters Mean current: 22.7 A Mean area: 3.69 mm2 Mean current density: 6.28 A/mm2 S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Selected machine parameters Mean length: 10.9 cm Mead radius: 3.65 cm S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Design 38 S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Design 38 cross section S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Design 38 flux density waveforms c S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach
9.11Case Study Comments S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach