Windings For Permanent Magnet Machines Yao Duan, R. G. Harley and T. G. Habetler

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

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

3. 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

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

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

6. 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

7. 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 • Major Rotor Design Constraints • Flux density in rotor core • Airgap length Pole coverage Parallel Magnetization Radial Magnetization

8. Current PM Machine Design Process Manually input design variables Machine performance Calculation Output Meet specifications and constraints ? • How commercially available machine design software works • 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

9. Proposed Improved Design Process—reduce the number of design variables • Magnet Design: • Permanent magnet material – NdFeB35 • 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.

10. 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 75o

11. Design of Prototypes • Maxwell 2D simulation and verification • Transient simulation Rated torque = 79.5 Nm

12. Design specifications and constraints • 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

13. 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

14. Analytical design model - 2

15. 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

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

17. Verification of the analytical model - 2

18. 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, simple implementation

19. 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 m3 • Efficiency: typically in the range of 0 to 1.

20. 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) v(t) Pbest(t)

21. 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 c1: self-acceleration constant gbest,n: the best position the swarm has found so far at the n-th iteration c2: social acceleration constant

22. Position of each particle

23. Output of particles

24. 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 WtMagnet: weight of the permanent magnet, Kg TperA: torque per ampere, Nm/A

25. Different Objective Function - 2

26. 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

27. Comparison of optimization Result • 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

28. 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.

29. 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.

30. Thanks! Questions and Answers