1 windings for permanent magnet machines yao duan, r. g. harley and t. g. habetler georgia institute...
TRANSCRIPT
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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