High-frequency, High-power Magnetic Component Design … · with Maxwell 3D From Geometry ... – Steinmetz equation – Design primary voltage waveform • Winding loss: – Dc resistance

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

Monday, October 06, 2014 2014 Automotive Simulation World Congress 2

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


1:n

Transformer Electrical Parameters


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


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


• 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


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


Leakage Inductance Winding Resistance

Maxwell frequency sweep data to be added.

Determine Leakage and Magnetizing

• Mesh size =1.1 million tets


Leakage Inductance Calculation • Use total energy from convergence tab

– E = 9.51 uJ – Ip = 8 A – peak current

• Find inductance from:


E= 12𝐿 𝐼𝑝

2

2

𝐿𝑙𝑙𝑙𝑙 =2 ∗ 2 ∗ 𝐸𝐼𝑝2

Core Saturation Simulation

• Plot of inductance vs current • Field animation of saturation effects


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

Monday, October 06, 2014 2014 Automotive Simulation World Congress 13 10

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


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:


dccu

PBrP +=ρ

πω128

)2( 242

fπµρδ = δ<<d

2B

⋅

⋅

2

212

21

2

1

BBB

BBB

Inductor: Transformer:

Litz-wire Design Software


http://engineering.dartmouth.edu/inductor/index.shtml

User Supplied Magnetic Field Data

• Use magnetostatic simulations


Both windings conduct with equal and opposite unit N*I

Component Design Parameters


Magnetostatic Field Calculations


Winding Design Proposals

• Total winding loss = 2.5 W – Now tradeoff

• Cost • Loss • Temperature rise • Weight

– To pick the optimal stranding for design specifications


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


Integrate Results into Thermal Simulations

• Simulation running now


Conclusions


• 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


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


Documents

High-frequency, High-power Magnetic Component Design … · with Maxwell 3D From Geometry ... – Steinmetz equation – Design primary voltage waveform • Winding loss: – Dc resistance