Windings For Permanent Magnet Machines

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21 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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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

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 K
w




5

Overall design procedure

Rated design
specifications
:
15
KW
1800
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


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


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 performance

Calculation

Meet specifications and constraints ?

Output

9

Proposed Improved Design Process

reduce the number of design variables



Magnet Design:


Permanent magnet material


NdFeB35


Magnet thickness


design variable




*
* *
1
r leak
m
r carter
m
B k
B
g k
h



where

B
m
: average airgap flux density

h
m
: magnet thickness

B
r
: the residual flux density.

g
: the minimum airgap length, 1 mm


r
: relative recoil permeability.

k
leak
: leakage factor.

k
carter
: 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



75
o

11

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

12

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/mm
2

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




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

DiaSYoke
DiaSGap
DiaSRGap
DiaRYoke
h
m
Bs
1
Bs
2
Hs
0
Hs
1
Hs
2
Bs
0
Rs
Tw
DiaSGap
Length
AirGap Flux
Density
Back EMF
Inductance
Number of
turns per
phase
Tooth Width
Stator and Rotor
Yoke Thickness
Current
Current
Desnity
Slot Fill Factor
Output
Power
Design
Parameters
Weigth
Volume
Loss
ThichMag
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 m
3


Efficiency
: typically in the range of 0 to 1.




*10000 10*(100 *100)
obj weight volume eff
   
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.

g
best
(t)

P
best
(t)

inertia

x(t
-
1)

v(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









x
(
t
-
1
)
x
(
t
)
V
i
(
t
-
1
)
V
i
(
t
)
p
g
p
i
1 1,2,
* ()*( ) ()*( )
n n best n n best n n
v v c rand p x c rand g x


    
where



: inertia constant


p
best,n
: the best position the individual particle has found so far




at the n
-
th iteration


c
1
: self
-
acceleration constant


g
best,n:
the best position the swarm has found so far at the n
-
th iteration


c
2
: social acceleration constant

22

Position of each particle

23

Output of particles

Iteration No.

0

20

40

60

80

100

g
best

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

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


*10 *10000 10*(100 *100)
obj weight volume eff
   
*10000 5*(100 *100) *10 *10
obj weight volume eff WtMagnet TperA
     
where


WtMagnet
: weight of the permanent magnet, Kg


TperA
: torque per ampere, Nm/A

25

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 *10
obj weight volume eff WtMagnet TperA
     
From
obj1

obj2

Weight

31.4

28.8

10000*Volum
e

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

26

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

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



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 / m
3

0.0031

0.0032

0.003
8

0.0037

0.0043

0.0041

0.004
8

0.0047

Efficiency

93.3%

93.3%

94.7%

93.7%

95.1%

94.9%

95.9%

95.9%

Torque/Amper
e (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

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