Modelling Attempts Litz-Wire in SMPS-Chokes: a comparison

Markus Mayrhofer, June 2016V1

Content

► Introduction: SwitchModePowerSupplies

►Losses & relative shares

►Litz-wire types

►Difficulties in Modelling attempts

►Practial example

►Homogenisation approaches

►Comparison

►Conclusions

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Introduction

►My Name is Markus Mayrhofer, working at Integrated Power Electronics / R&D at

Tridonic (http://www.tridonic.com)

►Tridonic is a global provider of smart and efficient lighting sol utions, manufacturing

LED-converters, controls & control-software, LED-modules & light-engines.

►Headquaters is located in Dornbirn, we have development- and manufacturing sites in

Jennersdorf (AT), Spennymoor (UK), Ennenda (CH), Shenzhen (CN).

►Gross sales is around 400Mill.€ (2015), with approx. 1750 employees.

►We belong to Zumtobel group, a worldwide operating lighting company

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Switch Mode Power Supplies (SMPS)

► In many applications, SMPS are widely used: Laptop- Desktop supply-units, chargers,

LED-converters,…

►Many varieties exist, can be divided depending on their properties, topologies, switching-

mode,…:

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►Forward or block-type converters

►Galvanic isolation

►Step up- or down converters

►Resonant types

►Design-Target: high efficient power conversion,

sinusoidal line-currents, low harmonics, low EMI

Common features

►Compared to line-frequency, high-frequency-switching (widely in the range of

20…200kHz)

►Alternate, periodic phases of Energy storage

► Inductive elements / „magnetics“

►Switching elements

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Huge potential for improvement:

► In typical converters, inductive elements account for significant amount of space and

losses!

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Low Power LED-converter: 100W (Tridonic)

Sources of losses in a typical 1kW converter: (from: I. Jitaru, APEC 2016)

Boost-choke LLC-Transformer

Major losses in a typical transformer:

►Neglecting the capacitive parasitics (winding-capacitances), a transformer can be

typically approximated by following equivalent circuit:

►Main losses come from those elements:

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• DC-winding losses• AC-winding losses (winding

exposed to changing magneticfield: skin- & proximity effects)

• Hysteresis losses (due to alternatingcore-magnetisation )

• Core-eddy-current-losses (corematerial non-ideal isolator)

No easy way of determination!

►Both the overall losses and the relative contribution of individual loss-mechanisms is

difficult to determine!

►AC-winding losses heavily depend on winding-geometry and magnetic field in the

winding-space!

►Only way of measuring: small-signal analysis (not depicting real load-conditions,

differentiation to resonance-impedance difficult)

►Differentiaion between winding- and core losses under real-load conditions difficult

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Reducing AC-wire losses: Litz-Wires

►At typical SMPS-switching frequencies, the AC-losses are way higher than the pure DC-

losses!

►Using litz-wires therefore is common sense

►As shown here, variety of litz-wires is near infinite…

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Are we able to model those?

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► In a solid wire, the magnetic field of an alternating current created by the current itselv,

will cause a very specific current distribution, which results in reduced diameter available

for the current, thus higher current-density and losses -> skin-effect, AC-losses

Classic, purely „inner“ skin-effect“ „Bundle-level“ skin-effect

►Substituting a solid wire by several thinner mutually insulated litz-wires will not show any

benefit, as long as the wires are not being somehow „twisted“!

Skin- & Proximity effects:

►Considering both internal and external fields (e.g. within a set of wires in a winding):

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Skin depth:δ ~ f^(1/2)

Skin-faktorFs ~ r/δ

Pskin ~ r/δ

Proximity-Faktor Ds

Pskin ~ Hext² * Ds

Modeling attempts:

Maxwell offers 2 settings:

►Conductor as „solid“: all eddy effects (skin- and proximity) of a single, solid conductor are

being calculated. However, a winding having eg. 70turns with a 50x0.1mm twisted litz-

wire cannot be exactly modeled!

►Conductor as „stranded“: „ideal“ litz-wire assumed, no eddy effects, entirely even

current distribution

►Reality: somewhere in between!

►Heavily depending on geometry and properties of the actual litz-wire!!

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2D-model: solid wires

Including frequency-sweep, this model takes between 5-15min of calculation

times (<50000 elements)

By looking to the field-appearance, quite some qualitative

conclusions can be drawn:

►Areas of low/high field stress (core saturation, proximity

effects)

►Dependency on frequencies, materials, geometry (f-

sweeps, core-material, winding-arrangement)

►Areas of high/low relative losses (steinmetz, eddy-

currents)

► This case:

overall flux-density is well acceptable

Try moving winding into areas of low field-strength

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Quantitative results:

Plot key-values as table, or as trends along selected lines, or integrated across selected

areas/volumes

Conclusions:

►AC-wire losses in W1 are dominant, and also far higher than DC-losses

►Further increase of copper will not yield lower losses

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Pure DC-losses

Potential for improvement has beenidentified: AC-losses

Although the model was not exactly showing the reality (e.g. no litz-wire), a trend could be

read from the results:

► Initial winding:

►34turns, 50*0.1mm litz-wire;

► Improved

►34turns, 20*0,1mm litz

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Cu area total area [mm²]0,39 26,60,16 10,7

DC-losses increase factor 2

AC losses decrease -64%

Could that be realized in temperature?

►Although the comparison was performed using a transformer prototype with 42 turns

instead 34, the improvement became evident

►Temperatures went down by ~9.6°(core), 5.3°C (W1) and 7°C (W2)

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3D approach: How does it compare to a 2D-model?

Including a lower number of sweep-frequencies, this model takes around 8 hours of calculation time (~450000 elements)

► If meshing is similarly precise, results are reasonably plausible and in accordance

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► In some details, precision is higher: DC- and AC-

losses of winding, coupling factor, field strength &

distribution within the core

Homogenisation approaches:

In order to save time and modelling-effort, substituting a winding by a bulky conducting-block was

investigated

AC-winding-losses are then not derived from explicitely calculated eddy-currents, but being

approximated by a virtual „loss-tangent“ of the conducting block.

It is important to note, that the current-density within the conductor is held constant and does not reflect

reality!

finding the numerical coefficients for the loss-tangent i s the key-issue and far from

trivial !

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Modeling an individual coated solid wire:

►Detailed model of both copper-wire and isolation: for

windings with many turns, this method yields large number

of blocks

►Simplification: Outer diameter of isolated wire, reduced

„average“ resistivity, to fit exactly the DC-impedance of the

real wire: electrically the same, simpler model

►However: even though the DC-behaviour is exactly the

same, the AC-behaviour & eddy effects are slightly different.

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Copper(ρCu, ACu)

Insulation

Average resistivity

ρavg = ρCu *Acu / Ages

Litz-wire windings with many turns:2 possible approaches

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►Full winding block: the entire winding with all ist litz-wires and turns is represented by one single block.

Maximum savings in model- and calculation expanses. Identification of the loss-parameters difficult

►Litz-level: each turn of the windings is still represented individually. However, not the time consuming

eddy currents are being calculated, but again by virtual loss-tangent approximation (representing the

litz-bundle of each turn). Less effort-savings, however, estimation of homogenisation-coefficient is

easier

„EM-losses“ for each individual conductor

„EM-losses“ for a bulky conductor

Loss tangent in different approaches:

► Loss tangent derived from:

► In the full-homogenised model, d is the diameter of the wire-bundle

► In the litz-level setting 1 approach, d is the diameter of one individual litz-strand

► 3D litz-level approach shows results with a tuned loss-tangent (deviating from calculation)

► The full-homogenised model fits best with the solid-wire explicit model

► The tuned litz-level tangent fits best with real-measurement

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From: „ProximityLosss Calculation Method“ (A. Bergquist, ANSYS Sweden)

Conformity with „real life“

► Comparing the AC-winding impedance: measuring the initial transformer-sample with the LRC-bridge

at different frequencies.

► The magnetic field-pattern is similar as in a real load case, as long as flux-densitiy is sufficiently away

from saturation.

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->as expected, losses areoverestimated in the explicit model, as it assumes a „solid wire“

-> the litz-level approximation can bedecently tuned by adjusting the loss-tangent-coefficient.

Remark : resonance frequency of the transformer isin the range of 850kHz. Therefore, at frequenciesabove ca.300kHz, resonance effects become visiblein the measurement, which is not reflected in thesimulation

Impedance [Ohm] vs frequency [kHz]

Conformity with a solid-wire prototype

► Best fit for the 3D-model to the the solid-wire prototype

► However, a certain deviation remains

► 3D-Litz-wire-homogenized model can be tuned to fit well to original (litzwire)-prototype

► geometrically tuning the 2D model (real 0.7mm copper-wire plus non-effective isolation instead of

„smeared“ impedance) also improves the fit.

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Measurements with shorted secondarywinding

► The 1st plot shows the reflected secondary-side impedance, which cannot

be modeled in the eddy-current solver (excitations are currents, no

voltages)

► When compensating for this, the fit improves, again, the 3D model lies

closer.

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2D-model 3D-model

Conclusions:

►2D model calculates fast, 3D model more precise (e.g. coupling matrix, core-eddy-

losses)

►Litz-wires difficult to consider: overestimation of losses in a „solid“-approach;

►homogenisation on litz-level promising, however, a-priori determination of equivalent

loss-tangent parameter not clear.

►Model gives a decent indication of the dominant source and absolute amount of losses,

allows to draw conclusions and optimisation potential.

►There is an unclear remaining deviation of the „solid“-model toward a dedicated solid-

wire prototype.

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Sum of losses model 3D approach: 3,3WCaloric measurement LLC-choke (model unmodified): 3,6W

Thank you for your attention!

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References

► Electronik power 2010 (Sonderdruck, Prof Dr-I M. Albach et al, Uni Erlangen)

► ProximityLosss Calculation Method (A. Bergquist, ANSYS Sweden)

► WirbelstromVerluste in Wicklungen magnet. Bauelemente (ETH-Z, Prof. Dr J. Biela)

► Exceeding 99% Efficiency, I Jitaru, APEC 2016 (Education Seminar)

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