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Windings For Permanent Magnet Machines Yao Duan, R. G. Harley and T. G. Habetler Georgia Institute of Technology. OUTLINE. Introduction Overall Design Procedure Analytical Design Model Optimization Comparison Conclusions. Introduction.

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slide1
Windings For Permanent Magnet Machines

Yao Duan, R. G. Harley and T. G. Habetler

Georgia Institute of Technology

outline
OUTLINE
  • Introduction
  • Overall Design Procedure
  • Analytical Design Model
  • Optimization
  • Comparison
  • Conclusions
introduction
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
distributed and concentrated winding
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)

overall design procedure
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

surface mount pm machine design variables and constraints
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
surface mount pm machine design variables and constraints7
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

current pm machine design process
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
proposed improved design process reduce the number of design variables
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.

proposed improved design process reduce the number of design variables10
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

design of prototypes
Design of Prototypes
  • Maxwell 2D simulation and verification
    • Transient simulation

Rated torque = 79.5 Nm

design specifications and constraints
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
analytical design model 1
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
analytical design model 3
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
verification of the analytical model 1
Verification of the analytical model -1
  • Finite Element Analysis used to verify the accuracy of the analytical model(time consuming)
particle swarm optimization 1
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
particle swarm optimization 2
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.
particle swarm optimization 3
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)

particle swarm optimization 4
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

different objective functions 1
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

comparison of two winding types
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
comparison of optimization result
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
conclusion
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.
acknowledgement
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.
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Thanks!

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