1. 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

2. 9.1 Permanent Magnet Synchronous Machines
Surface mounted magnet machine
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

3. 9.1 Permanent Magnet Synchronous Machines
Interior permanent magnet machine
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

4. 9.2 Operating Char. of PMAC Machines
Machine connections
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

5. 9.2 Operating Char. of PMAC Machines
Machine model in QD variables
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

6. 9.2 Operating Char. of PMAC Machines
Flux linkage equations
Torque equation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

7. 9.2 Operating Char. of PMAC Machines
Steady-state analysis
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

8. 9.2 Operating Char. of PMAC Machines
Three-phase bridge inverter
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

9. 9.2 Operating Char. of PMAC Machines
Inverter voltage limit
Semiconductor conduction loss
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

10. 9.2 Operating Char. of PMAC Machines
Derivation of semiconductor conduction loss
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

11. 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

12. 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

13. 9.2 Operating Char. of PMAC Machines
Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

14. 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

15. 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

16. 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

17. 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

18. 9.2 Operating Char. of PMAC Machines
Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

19. 9.2 Operating Char. of PMAC Machines
Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

20. 9.2 Operating Char. of PMAC Machines
Reason to inject d-axis current
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

21. 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

22. 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

23. 9.2 Operating Char. of PMAC Machines
Approach: Treat as optimization problem
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

24. 9.2 Operating Char. of PMAC Machines
Result
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

25. 9.3 Machine Geometry Machine dimensions
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

26. 9.3 Machine Geometry Stator tooth
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

27. 9.3 Machine Geometry Tooth fraction and tooth tip fraction
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

28. 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

29. 9.3 Machine Geometry Rectangular slot approximation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

30. 9.3 Machine Geometry Rectangular slot approximation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

31. 9.3 Machine Geometry Derivation notes
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

32. 9.3 Machine Geometry Function arrangement
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

33. 9.4 Stator Winding Assumed conductor density
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

34. 9.4 Stator Winding Discrete conductor layout
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

35. 9.4 Stator Winding Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

36. 9.4 Stator Winding Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

37. 9.4 Stator Winding Additional slot conductor calculations
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

38. 9.4 Stator Winding End conductor calculations We’ll assume
which yields
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

39. 9.4 Stator Winding Conductor size calculations
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

40. 9.4 Stator Winding Coil calculations
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

41. 9.4 Stator Winding Functional form of calculations
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

42. 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

43. 9.6 Stator Currents and Control Philosophy
Current selection information
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

44. 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

45. 9.7 Radial Field Analysis Stator MMF. Using
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

46. 9.7 Radial Field Analysis We obtain
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

47. 9.7 Radial Field Analysis Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

48. 9.7 Radial Field Analysis Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

49. 9.7 Radial Field Analysis Radial field variation. We will have
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

50. 9.7 Radial Field Analysis Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

51. 9.7 Radial Field Analysis Air gap MMF drop. We can show
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

52. 9.7 Radial Field Analysis Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

53. 9.7 Radial Field Analysis Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

54. 9.7 Radial Field Analysis Permanent magnet MMF. We have
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

55. 9.7 Radial Field Analysis PM characteristics versus position
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

56. 9.7 Radial Field Analysis We can show
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

57. 9.7 Radial Field Analysis Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

58. 9.7 Radial Field Analysis Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

59. 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

60. 9.7 Radial Field Analysis Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

61. 9.8 Lumped Parameters Flux linkage components Leakage flux linkage
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

62. 9.8 Lumped Parameters Derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

63. Derivation (continued)
9.8 Lumped Parameters
Derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

64. Derivation (continued again)
9.8 Lumped Parameters
Derivation (continued again)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

65. 9.8 Lumped Parameters Magnetizing flux linkage
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

66. 9.8 Lumped Parameters Partial derivation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

67. 9.8 Lumped Parameters Partial derivation (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

68. 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

69. 9.9 Ferromagnetic Field Analysis
Stator tooth flux
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

70. 9.9 Ferromagnetic Field Analysis
Notes
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

71. 9.9 Ferromagnetic Field Analysis
Stator tooth flux (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

72. 9.9 Ferromagnetic Field Analysis
Explanation of symmetry
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

73. 9.9 Ferromagnetic Field Analysis
Explanation of symmetry (continued)
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

74. 9.9 Ferromagnetic Field Analysis
Stator tooth flux densities
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

75. 9.9 Ferromagnetic Field Analysis
Stator backiron flux
We have
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

76. 9.9 Ferromagnetic Field Analysis
We can show
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

77. 9.9 Ferromagnetic Field Analysis
continuing …
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

78. 9.9 Ferromagnetic Field Analysis
We define
Similar to the stator tooth
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

79. 9.9 Ferromagnetic Field Analysis
Stator core loss
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

80. 9.9 Ferromagnetic Field Analysis
Rotor peak tangential back iron flux density
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

81. 9.9 Ferromagnetic Field Analysis
Rotor peak radial flux density
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

82. 9.9 Ferromagnetic Field Analysis
The peak radial flux density is given by
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

83. 9.9 Ferromagnetic Field Analysis
Notes
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

84. 9.9 Ferromagnetic Field Analysis
More notes
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

85. 9.9 Ferromagnetic Field Analysis
Observation on peak rotor flux density
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

86. 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

87. 9.9 Ferromagnetic Field Analysis
Functional representation
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

88. 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

89. 9.10 Formulation of Design Problem
Design parameters (continued)
nspp
atar
aso
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

90. 9.10 Formulation of Design Problem
Design metrics
Mass
Loss
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

91. 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

92. 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

93. 9.10 Formulation of Design Problem
Design constraints (continued)
Operating point field constraints
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

94. 9.10 Formulation of Design Problem
Design constraints (continued)
Torque
Power loss
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

95. 9.10 Formulation of Design Problem
Fitness
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

96. 9.10 Formulation of Design Problem
Fitness pseodo-code
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

97. 9.10 Formulation of Design Problem
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

98. 9.10 Formulation of Design Problem
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

99. 9.10 Formulation of Design Problem
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

100. 9.10 Formulation of Design Problem
Pseudo-code for check of constraints
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

101. 9.11Case Study Design specifications
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

102. 9.11Case Study Parameter ranges
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

103. 9.11Case Study Pareto-optimal front
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

104. 9.11Case Study Parameter distribution
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

105. 9.11Case Study Material selection
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

106. 9.11Case Study Power loss components
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

107. 9.11Case Study Component mass
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

108. 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

109. 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

110. 9.11Case Study
Design 38
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

111. 9.11Case Study Design 38 cross section
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

112. 9.11Case Study Design 38 flux density waveforms c
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach

113. 9.11Case Study
Comments
S.D. Sudhoff, Power Magnetic Devices: A Multi-Objective Design Approach