Windings For Permanent Magnet Machines

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

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OUTLINE

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

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Introduction

• The use of permanent magnet (PM) machines
  continues to grow and theres 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

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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)
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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
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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

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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
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Current PM Machine Design Process

• 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

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Proposed Improved Design Processreduce 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.
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Proposed Improved Design Processreduce 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
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Design of Prototypes

• Maxwell 2D simulation and verification
• Transient simulation

Rated torque 79.5 Nm
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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

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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

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Analytical design model - 2
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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

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Verification of the analytical model -1

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

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Verification of the analytical model - 2
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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

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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.

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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)
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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
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Position of each particle
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Output of particles
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Different Objective functions - 1

• Depending on users 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
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Different Objective Function - 2
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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

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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

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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.

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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!
• Questions and Answers