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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 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

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Distributed and Concentrated Winding

A-A+

C-

C+

B+B-

B+B-

C+

C-

A-A+

Distributed Winding(DW)

Concentrated Winding(CW)

• 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

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Overall design procedureRated design specifications:

15 KW1800 rpm

60 Hz

Optimization Optimization

Comparison

Weight

Volume

Harmonics

Efficiency

Torque ripples

Inverter requirements

Weight

Volume

Harmonics

Efficiency

Torque ripples

Inverter requirements

Concentrated Winding Distributed Winding

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 MagnetizationRadial 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

Manually input design variables

Machine performanceCalculation

Meet specifications and constraints ?

Output

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Proposed Improved Design Process—reduce the number of design variables

• Magnet Design: Permanent magnet material – NdFeB35 Magnet thickness – design variable

** *

1

r leakm

r carter

m

B kB

g k

h

where Bm: average airgap flux densityhm: magnet thicknessBr: the residual flux density. g: the minimum airgap length, 1 mmr: relative recoil permeability. kleak: leakage factor.kcarter: Carter coefficient.

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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

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Design of Prototypes

• Maxwell 2D simulation and verification 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

Rated torque = 79.5 Nm

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Design specifications and constraints

Distributed winding Concentrated winding

Slot number 12, 24, 36 (full pitched) 3, 6 (short pitched)

Number of layers Double Double

Flux density in teeth and back iron

1.45 T (steel_1010) 1.45 T (steel_1010)

Covered wire slot fill factor Around 60% Around 80%

Current density Around 5 A/mm2 Around 5 A/mm2

• 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

DiaSYoke

DiaSGap

DiaSRGap

DiaRYokehm

Bs1

Bs2

Hs0Hs1

Hs2

Bs0

Rs

Tw

DiaSGapLength

AirGap Flux Density

Back EMF

Inductance

Number of turns per

phase

Tooth WidthStator and Rotor Yoke Thickness

Current

Current Desnity

Slot Fill Factor

Output Power

Design Parameters

Weigth VolumeLoss

ThichMag

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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.

*10000 10*(100 *100)obj weight volume eff

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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.

gbest(t)

Pbest(t)

inertiax(t-1)

v(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

x(t-1)

x(t)Vi(t-1)

Vi(t) pg

pi

1 1 , 2 ,* ()*( ) ()*( )n n best n n best n nv v c rand p x c rand g x

where

: 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

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 31.4

10000*Volume 53.3 41.62 40.2 43.0 42.5 42.5

1000*(1-eff) 37.6 51.2 50.2 46.2 46.9 46.9

Efficiency 96.2% 94.9% 95.0%

95.4% 95.3% 95.3%

Objective 128.4 123.1 121.3 121.0 120.9 120.9

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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

*10 *10000 10*(100 *100)obj weight volume eff

*10000 5*(100 *100) *10 *10obj weight volume eff WtMagnet TperA

where

WtMagnet: weight of the permanent magnet, Kg

TperA: torque per ampere, Nm/A

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Different Objective Function - 2

1 *10000 10*(100 *100)obj weight volume eff

2 *10 *10000 10*(100 *100)obj weight volume eff

3 *10000 10*(100 *100) *10 *10obj weight volume eff WtMagnet TperA

From obj1

obj2

Weight 31.4 28.8

10000*Volume

42.5 47.7

1000*(1-eff) 46.9 48.2

Efficiency 95.3% 95.2%

Objective 403.4 384.4

From obj1 obj3

Weight 31.4 31.0

10000*Volume 42.5 43.4

Efficiency 95.3% 95.4%

WtMagnet 0.88 0.92

TperA 3.56 3.58

Objective 94.2 93.8

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Comparison of two winding types

• Objective function

1 *20000 2* (1 )*200

*5 *5

obj output volume Weight Eff

WtMagnet TperA

2 *10000 (1 )*1000

*5 *20

obj output volume Weight Eff

WtMagnet TperA

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

  Objective Function 1 Objective Function 2

CW DW CW DW

Des. 1 Des. 2 Des. 1 Des. 2 Des. 1 Des. 2 Des. 1 Des. 2

Weight / kg 28.5 27.9 30.0 29.4 32.12 32.39 32.02 33.23

Volume / m3 0.0031 0.0032 0.0038

0.0037 0.0043 0.0041 0.0048

0.0047

Efficiency 93.3% 93.3% 94.7% 93.7% 95.1% 94.9% 95.9% 95.9%

Torque/Ampere (Nm/Arms)

2.79 2.79 3.54 2.79 3.79 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

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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