Post on 27-Sep-2020
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
214/06/2016
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
314/06/2016
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,…:
414/06/2016
►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
514/06/2016
Huge potential for improvement:
► In typical converters, inductive elements account for significant amount of space and
losses!
614/06/2016
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:
714/06/2016
• 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
814/06/2016
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…
914/06/2016
Are we able to model those?
1014/06/2016
► 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):
1114/06/2016
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!!
1214/06/2016
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
1314/06/2016
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
1414/06/2016
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
1514/06/2016
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)
1614/06/2016
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
1714/06/2016
► 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 !
1814/06/2016
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.
1914/06/2016
Copper(ρCu, ACu)
Insulation
Average resistivity
ρavg = ρCu *Acu / Ages
Litz-wire windings with many turns:2 possible approaches
2014/06/2016
►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
2114/06/2016
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.
2214/06/2016
->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.
2314/06/2016
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.
2414/06/2016
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.
2514/06/2016
Sum of losses model 3D approach: 3,3WCaloric measurement LLC-choke (model unmodified): 3,6W
Thank you for your attention!
2614/06/2016
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)
2714/06/2016