High-frequency, High-power Magnetic Component Design with Maxwell 3D
From Geometry Creation to Component Optimization
Dr. Jenna Pollock Tesla Motors
• Design magnetic components for automotive power conversion systems that are: – Light weight – Low cost – Reliable – Easy to build
• Meet electrical specs – Inductances, Resistances, Capacitances – Winding Loss, Core Loss
• Meet mechanical specs – Volume – Weight – Mounting
Objective
1:n
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Simulation-driven Design of an Isolation Transformer with Maxwell 3D • Challenges
– Flux distribution and saturation – Leakage fields and inductance – Minimize losses
• Optimize winding designs – Scripting winding geometry
• Makes iterating complex windings simple – Foil designs
• Find lowest loss design – determine foil thickness
• Understand current distribution in foil – Minimize Leakage Inductance – Litz-wire design
• Determine litz-wire standing • Determine fields and losses in near by
conductors – Housing and heat sinks
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1:n
Transformer Electrical Parameters
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Rac,p Rac,s Lleakage,all 1:n
Cw,p
Lm
Rcore
Cw,s
Cinterwinding
Transformer Design Example:
• Isolation transformer Parameter
Power level 3 kW Switching Frequency 120kHz Magnetizing inductance 1.3 mH Leakage inductance 4.2 uH Maximum power loss 1% Turns Ratio 8:1
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Preliminary Transformer Design
• Trade off core and windings losses to find an optimal design for given electrical specifications – Use FEA to support analytical methods – FEA can fine tune design
• Specific electrical parameters • Specific size requirements
• A free transformer design resource: – http://ecee.colorado.edu/copec/book/slides/slidedir.html
First Pass Design
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• Core Loss: – Steinmetz equation – Design primary voltage waveform
• Winding loss: – Dc resistance – Ratio of ac to dc resistance
• To be determined in coming slides
Use existing analytical methods
𝑃𝑐 = kc 𝑓𝛼𝐵𝛽V
Analytical Winding Loss Solutions
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Frequency Range
Loss Solution
Rectangular Cylindrical
Diameter less than skin
depth
Any Diameter
dccu
PBrP +=ρ
πω128
)2( 242
22 )()( el HGIFP λγ +=
+
−=
δδδρ hGHHhFHHbP babal 2)(
21 2
2,
42
45151 rmsacdcloss IRhpP
−
+=δ
2δγ d=
101
102
103
0
1
2
3
4
5
6
7
Frequency, kHz
Indu
ctan
ce, u
H
360/36100/38AWG 14
101
102
0
50
100
150
200
250
Frequency, kHz
Res
ista
nce,
moh
ms
360/36 wire100/38awg 14
Measured Inductance and Resistance
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Leakage Inductance Winding Resistance
Maxwell frequency sweep data to be added.
Determine Leakage and Magnetizing
• Mesh size =1.1 million tets
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Leakage Inductance Calculation • Use total energy from convergence tab
– E = 9.51 uJ – Ip = 8 A – peak current
• Find inductance from:
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E= 12𝐿 𝐼𝑝
2
2
𝐿𝑙𝑙𝑙𝑙 =2 ∗ 2 ∗ 𝐸𝐼𝑝2
Core Saturation Simulation
• Plot of inductance vs current • Field animation of saturation effects
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Foil Winding Design • Need Maxwell 3D to determine the ac resistance
– Often ac resistance is to low to measure – Analytical methods neglect edge effects, etc
• Use Optimetrics to find foil thickness with lowest ac resistance – This means the cost is the “ac resistance” – Use eddy current solver – Define mesh on foil winding to reflect the skin depth
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010
110
210
3-6
-4
-2
0
2
4
6
8
Frequency, kHz
Res
ista
nce,
moh
ms
foil1080/36foil 0.85mm
Foil Winding Resistance
Optimetrics Results • Results – minimize ac resistance
– Maxwell determines the response surface – Updates the design parameters with optimized values
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Evaluation
Foil thicknessmm
DC Resistance, mohms
AC Resistance, mohms
Volume, mm3 Maxwell 3D
Weight, g Cost, US dollar – CU prices
1 0.84 3.02 5693.5 51 0.341
2 0.85 5767.4 51.7 0.345
3 1.0 2.84 6886. 61.7 0.412
4 1.12 2.72 7803.5 69.9 0.467
5 1.16 2.71 8113.4 72.7 0.486
6 1.28 2.65 9056.4 81.1 0.542
7 1.32 2.63 9375.0 84.0 0.561
8 1.44 2.60 10343.9 92.7 0.619
9 1.48 2.59 10671.2 95.6 0.639
NEED RDC
Designing Litz-wire Windings
• Difficult to pick strand size and number of strands
– Valid where wire diameter is small compared to skin depth • Need the average value of magnitude of the flux density over a
winding region:
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dccu
PBrP +=ρ
πω128
)2( 242
fπµρδ = δ<<d
2B
⋅
⋅
2
212
21
2
1
BBB
BBB
Inductor: Transformer:
Litz-wire Design Software
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http://engineering.dartmouth.edu/inductor/index.shtml
User Supplied Magnetic Field Data
• Use magnetostatic simulations
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Both windings conduct with equal and opposite unit N*I
Component Design Parameters
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Magnetostatic Field Calculations
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Winding Design Proposals
• Total winding loss = 2.5 W – Now tradeoff
• Cost • Loss • Temperature rise • Weight
– To pick the optimal stranding for design specifications
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Compare Cost and Weight Windings design Weight, g
measured* Volume, mm3 Maxwell 3D
Rdc, mohms Rac ,at 120 kHz
N=2: 5 mil foil 12.63 1.8
N=2: 0.85 mm foil 61.23 0.224
N=2: 1080/36 37.94 0.310
N=16: 360/36 76.65 5.03
N=16: awg 14 25.52 8.65
N=16: 100/38 11.13 23.19
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Integrate Results into Thermal Simulations
• Simulation running now
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Conclusions
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• Maxwell 3D powerful tool for power magnetic component design
• Provides insight into field patterns and current distributions at high frequency
• Optimetrics package increase ability to design intelligently with FEA
• Parametric extremely useful for sweeping variables
Thanks and Questions?
• Specials thanks to: – Will Shultz, Pavani Gottipati, ANSYS – Lev Fedoseyev, Tesla Motors – My team, Tesla Motors – Thorben Schobre, Intern, Tesla Motors – Dr. Charles Sullivan, Dartmouth Magnetic Component and
Power Electronics Research Group
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References
• J. Pollock, T. Abdallah and C. R. Sullivan, “Easy-To-Use CAD Tools for Litz-Wire Winding Optimization”, IEEE Applied Power Electronics Conference, Feb. 2003, pp. 1157 -1163.
• Litzopt: Dartmouth Magnetic Components and Power Electronics http://engineering.dartmouth.edu/inductor/index.shtml
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