Windings For Permanent Magnet Machines Yao Duan R

Windings For Permanent Magnet Machines Yao Duan, R. G. Harley and T. G. Habetler Georgia Institute of Technology 1

OUTLINE • Introduction • Overall Design Procedure • Analytical Design Model • Optimization • Comparison • Conclusions 2

Introduction • The use of permanent magnet (PM) machines continues to grow and there’s a need for machines with higher efficiencies and power densities. • Surface Mount Permanent Magnet Machine (SMPM) is a popular PM machine design due to its simple structure, easy control and good utilization of the PM material 3

Distributed and Concentrated Winding Distributed Winding(DW) • Advantages of CW § § § Modular Stator Structure Simpler winding Shorter end turns Higher packing factor Lower manufacturing cost Concentrated Winding(CW) • Disadvantages of CW More harmonics § Higher torque ripple § Lower winding factor Kw § 4

Overall design procedure Challenge: developing a SMPM design model which is accurate in calculating machine performance, good in computational efficiency, and suitable for multiobjective optimization 5

Surface Mount PM machine design variables and constraints • Stator design variables § Stator core and teeth • • • § Steel type Inner diameter, outer diameter, axial length Teeth and slot shape Winding • • Winding layer, slot number, coil pitch Wire size, number of coil turns • Major Constraints Flux density in stator teeth and cores § Slot fill factor § Current density § 6

Surface Mount PM machine design variables and constraints • Rotor Design Variables § § § Rotor steel core material Magnet material Inner diameter, outer diameter Magnet thickness, magnet pole coverage Magnetization direction Pole coverage • Major Rotor Design Constraints Flux density in rotor core § Airgap length § Radial Magnetization Parallel Magnetization 7

Current PM Machine Design Process • How commercially available machine design software works Manually input design variables Machine performance Calculation Output Meet specifications and constraints ? • Disadvantages: § § § Repeating process – not efficient and time consuming Large number of input variables: at least 11 for stator, 7 for rotor -- even more time consuming Complicated trade-off between input variables Difficult to optimize Not suitable for comparison purposes 8

Proposed Improved Design Process— reduce the number of design variables Magnet Design: • Permanent magnet material – Nd. Fe. B 35 § Magnet thickness – design variable § where Bm: average airgap flux density hm: magnet thickness Br : the residual flux density. g: the minimum airgap length, 1 mm mr: relative recoil permeability. kleak: leakage factor. kcarter: Carter coefficient. 9

Proposed Improved Design Process— reduce the number of design variables • Magnet Design: Minimization of cogging torque, torque ripple, back emf harmonics by selecting pole coverage and magnetization § Pole coverage – 83% § Magnetization direction. Parallel § 75 o 10

Design of Prototypes • Maxwell 2 D simulation and verification § Rated torque = 79. 5 Nm Transient simulation Concentrated winding Distributed winding Cogging Toque Peak-to-Peak value 4. 0 Nm = 5. 0 % of rated 4. 3 Nm = 5. 38% of rated Torque ripple Peak-to-Peak value 9. 2 Nm = 11. 25 % of rated 11. 3 Nm = 13. 75 % of rated 11

Design specifications and constraints Distributed winding Concentrated winding Slot number 12, 24, 36 (full pitched) 3, 6 (short pitched) Number of layers Double Flux density in teeth and back iron 1. 45 T (steel_1010) Covered wire slot fill factor Around 60% Around 80% Current density Around 5 A/mm 2 • Major parameters to be designed: Geometric parameters: Magnet thickness, Stator/Rotor inner/outer diameter, Tooth width, Tooth length, Yoke thickness § Winding configuration: number of winding turns, wire diameter § 12

Analytical Design Model - 1 • Build a set of equations to link all other major design inputs and constraints – analytical design model § With least number of input variables § Minimizes Finite Element Verification needed – high accuracy model 13

Analytical design model - 2 14

Analytical Design Model - 3 • Motor performance calculation § Active motor volume § Active motor weight § Loss • Armature copper loss • Core loss • Windage and mechanical loss § Efficiency § Torque per Ampere 15

Verification of the analytical model -1 • Finite Element Analysis used to verify the accuracy of the analytical model(time consuming) 16

Verification of the analytical model - 2 17

Particle Swarm Optimization - 1 • The traditional gradient-based optimization cannot be applied § Equation solving involved in the machine model § Wire size and number of turns are discrete valued • Particle swarm § Computation method, gradient free § Effective, fast, simplementation 18

Particle Swarm Optimization - 2 § Objective is user defined, multi-objective function • One example with equal attention to weight, volume and efficiency • Weight: typically in the range of 10 to 100 kg • Volume: typically in the range of 0. 0010 to 0. 005 m 3 • Efficiency: typically in the range of 0 to 1. 19

Particle Swarm Optimization - 3 • PSO is an evolutionary computation technique that was developed in 1995 and is based on the behavioral patterns of swarms of bees in a field trying to locate the area with the highest density of flowers. x(t-1) inertia gbest(t) Pbest(t) v(t) 20

Particle Swarm Optimization - 4 Implementation • § 6 particles, each particle is a three dimension vector: airgap diameter, axial length and magnet thickness § Position update where w: inertia constant pbest, n: the best position the individual particle has found so far at the n-th iteration c 1: self-acceleration constant gbest, n: the best position the swarm has found so far at the n-th iteration c 2: social acceleration constant 21

Position of each particle 22

Output of particles Iteration No. 0 20 40 60 80 100 gbest Particle No. 6 1 3 2 4 1 -6 Weight 37. 5 30. 3 30. 9 31. 7 31. 4 10000*Volume 53. 3 41. 62 40. 2 43. 0 42. 5 1000*(1 -eff) 37. 6 51. 2 50. 2 46. 9 Efficiency 96. 2% 94. 9% 95. 0 % 95. 4% 95. 3 % Objective 128. 4 123. 1 121. 3 121. 0 120. 9 23

Different Objective functions - 1 • Depending on user’s application requirement, different objective function can be defined, weights can be adjusted • More motor design indexes can be added to account for more requirement where Wt. Magnet: weight of the permanent magnet, Kg Tper. A: torque per ampere, Nm/A 24

Different Objective Function - 2 Weight From obj 1 obj 2 31. 4 28. 8 10000*Volum e 42. 5 1000*(1 -eff) 46. 9 Efficiency 95. 3% 95. 2% Objective 403. 4 From obj 1 obj 3 31. 4 31. 0 10000*Volume 42. 5 43. 4 Efficiency 95. 3% 95. 4% Wt. Magnet 0. 88 0. 92 Tper. A 3. 56 3. 58 Objective 94. 2 93. 8 Weight 47. 7 48. 2 384. 4 25

Comparison of two winding types • Objective function § obj 1 pays more attention to the weight and volume § obj 2 pays more attention to the efficiency and torque per ampere 26

Comparison of optimization Result Objective Function 1 CW Objective Function 2 DW CW DW Des. 1 Des. 2 Weight / kg 28. 5 27. 9 30. 0 29. 4 32. 12 32. 39 32. 02 33. 23 Volume / m 3 0. 0031 0. 0032 0. 003 8 0. 0037 0. 0043 0. 0041 0. 0048 0. 0047 Efficiency 93. 3% 94. 7% 93. 7% 95. 1% 94. 9% 95. 9% Torque/Amper e (Nm/Arms) 2. 79 3. 54 2. 79 3. 74 3. 73 3. 75 Magnet Weight / kg 0. 685 0. 780 0. 95 0. 600 1. 48 1. 26 1. 12 1. 04 Obj. Function 122. 5 123. 2 134. 3 134. 4 56. 38 56. 42 52. 39 52. 17 • • CW designs have smaller weight and volume, mainly due to higher packing factor CW designs have slightly worse efficiency than DW, mainly due to short end winding 27

Conclusion • Concentrated winding has modular structure, simpler winding and shorter end turns, which lead to lower manufacturing cost • Before optimization, the torque ripples and harmonics can be minimized by careful design of the magnet pole coverage, magnetization and slot opening • Analytical design models have been developed for both winding type machines and PSO based multi-objective optimization is applied. This tool, together with user defined objective functions, can be used for analysis and comparison of both winding type machines and different applications • Optimized result shows CW design have superior performance than convention DW in terms of weight, volume, and have comparable efficiencies. 28

Acknowledgement • Financial support for this work from the Grainger Center for Electric Machinery and Electromechanics, at the University of Illinois, Urbana Champaign, is gratefully acknowledged. 29

Thanks! Questions and Answers 30