Current sharing between parallel turns of a planar transformer: prediction and improvement using a circuit simulation software

Transcription

1 Current sharing etween parallel turns of a planar transformer: predition and improvement using a iruit simulation software Xavier Margueron, Jean-Pierre Kerade, Adelhadi Besri To ite this version: Xavier Margueron, Jean-Pierre Kerade, Adelhadi Besri. Current sharing etween parallel turns of a planar transformer: predition and improvement using a iruit simulation software. IEEE Industrial Appliation Soiety 7, Sep 7, New Orléans, United States. 7. <hal-8969> HAL Id: hal Sumitted on 3 Fe 9 HAL is a multi-disiplinary open aess arhive for the deposit and dissemination of sientifi researh douments, whether they are pulished or not. The douments may ome from teahing and researh institutions in Frane or aroad, or from puli or private researh enters. L arhive ouverte pluridisiplinaire HAL, est destinée au dépôt et à la diffusion de douments sientifiques de niveau reherhe, puliés ou non, émanant des étalissements d enseignement et de reherhe français ou étrangers, des laoratoires pulis ou privés.

2 Current Sharing Between Parallel Turns of a Planar Transformer: Predition and Improvement Using a Ciruit Simulation Software X. Margueron, J-P. Kerade, A. Besri GEla UMR 569-INPG-UJF-CNRS ENSIEG, B.P. 46, 384 St Martin d'hères Cedex, Frane Jean-Pierre.Kerade@gela.inpg.fr Astrat With the inrease of power needs in low voltage appliations, wiring several windings in parallel to sustain large urrents eomes ommon. This operation often has a dangerous impat on transformer reliaility eause additional urrents, we all "irulation urrents", reate extra losses, generally not taken into aount y analytial approahes. Yet, hot points whih result from these urrents an destroy the omponent. In planar transformers, windings are made of PCB layers and irulation urrents lead to severe unalane of urrent sharing etween parallel layers. This paper presents an analytial method whih enales urrents in all layers to e evaluated using only a iruit simulation software suh as Pspie or PSIM. For a designer, this method is very intuitive and fast ompared with the use of fem simulations. Keywords-planar transformers; PCB parallel windings; irulation urrent; model; analytial alulation. I. INTRODUCTION Frequeny rise in power eletroni onverters has indued a diminution of ative and passive omponent sizes. Aove khz, traditional round winding transformers are often replaed y planar ones whih use low profile magneti ores and printed iruit oard (PCB for turns. For atual appliations whih need high output urrents, the use of PCB ondutors 5-5µm thik is prolemati. Even if it is some m wide, ross setion of one layer remains small so several layers have to e wired in parallel to sustain several hundredths of Amps []. Unfortunately, paralleling several layers doesn t result automatially in a alaned urrent sharing. Indeed, flux flowing through these parallel turns is slightly different and so are indued voltages. As a result, additional urrents, here alled "irulation urrents", are reated y these low differential voltages. These internal extra urrents are only limited y turn impedanes so they seriously impat omponent losses and reliaility. Consequently, aounting for them is not optional for the designer. At first sight, to design a transformer and predit the urrent distriution etween parallel layers, fem simulations an e used []. In pratie, planar transformers are quite omplex-we studied one inluding 44 ondutive layers-so detailed desription of shape and physial properties is time onsuming. Worst, to orretly aount for eddy urrents, meshing must e fine enough so a very large memory omputer is needed to arry out a simulation at around MHz and suh a simulation lasts several hours. In order to short the "engineer-time" needed to study suh a planar transformer intended for an industrial appliation and to ease optimization proess, we developed a method, ased on an analytial approah, whih enales the designer to otain the needed results y using any iruit simulation software [3]. Suh software is among the familiar tools of the designer and related simulations last seonds rather hours, even for omplex multi-layer planar transformer. II. PROBLEM DUE TO PARALELL WINDINGS Impat of eddy urrents on opper losses of a high frequeny has een widely studied. Several analytial methods have een proposed to aount for these effets, espeially when windings an e represented as staks of ondutive layers insulated from eah other [4, 5]. They all start from the solution of propagation equation in an infinite plan layer made of ondutive linear homogenous and isotropi material. For one layer, total losses split into skin and proximity losses. In a transformer, when wires are onneted in parallel, adding skin and proximity losses of all wires leads to total opper losses only if urrents flowing in all wires onneted in parallel have not een supposed equal from the eginning. Indeed, as explained aove, irulation urrents add to the mean urrent per wire so skin losses must e alulated with the real urrent that flows in it. Reently we presented the effet of irulating urrents into a 9 kva, 5-kHz, planar transformer (Fig. [6]. This industrial transformer inludes 44 ondutive layers. Its PQ ore [7] is made of ferrite PC4. This omponent has two seondaries, eah made of paralleled layers. Its primary is made of pairs of layers. Eah pair is wired in parallel, then, all these pairs are onneted in series. Due to external iruit, while one seondary is loaded (output urrent : 75 A eff, the other is in open iruit. The loaded is modeled y a. Ω resistane. This work is supported y THALES Airorne System Centre Amiral Nomy, Avenue de la ère DFL, 983 Brest, Frane

3 III. HOW TO PREDICT CIRCULATION CURRENTS? The impat of irulating urrents may e destrutive for transformer. Designers have to predit them while they are dimensioning their omponents. Figure. 44-ondutive layers, 3 windings planar transformer Eleven primary layers are loated aove and eleven under the seondaries. The urrent alulated in the different layers, as it is otained with D fem. simulation software [8], is presented in Fig st seondary (loaded fem simulation Nominal value nd seondary (open iruit Figure. Current repartition in seondary layers. Current modulus is plotted versus seondary layer numer For the loaded seondary, nominal urrent should e of 5 A eff per layer. The maximal urrent value (8 A eff, whih appears for the external layer of the loaded winding, is more than three times higher so, power losses in this layer is ten times than expeted. For the open iruit winding, despite nominal urrent is null (Fig. shows only modulus!, urrents in layers and reah 4 A eff. Even if it doesn't impat on transformer effiieny (still aove 98.5 %, this atastrophi urrent sharing results in strongly loalized extra losses (Fig. 3, even in the open iruit seondary. That reates hot points into PCB and, sometimes, destroys the transformer. nd seondary (Open iruit st seondary (Loaded Figure 3. Power repartition in seondary layers. The Clearer the olor is, the higher the power density is A. Limits of fem Simulations Traditional method for determining irulation urrent is ased on fem simulation. Introduing planar transformer geometry in software is quite easy ut it is a long task. Besides, meshing of suh a omponent (for example the 44 layers one must plae mashes in a skin depth to properly aount for eddy urrents. As a onsequene, alulation requires a large memory size omputer. In pratie, the major prolem arises when geometrial optimizations are arried out. In order to find the est topology for loss redution, numerous simulations have to e run [9, ] and oth desription and omputation times are often prohiitive. In order to redue transformer's development and optimization time, we looked for an analytial method onvenient to easily and quikly hek different topologies. B. Analytial Method : -D propagation assumption Prinipe Looking at its D ross setion, a planar transformer an e seen as a stak of different types of layers made of onduting, insulating or magneti material (Fig. 4. Eah material is onsidered as linear, homogeneous, isotropi and it is desried y its omplex permeaility and its omplex permittivity. Magneti Condutor : primary ( Condutor : primary ( Condutor : seondary ( Condutor : seondary ( Condutor : seondary (3 Magneti Figure 4. Example of layer stak Assuming energy propagation is -D (normal to the layers [, ], power exhange of a layer is defined, y 6 parameters linearly linked: eletri and magneti fields on eah faes, and supplied urrent and voltage (if the layer is ondutive. Suh an approah leads to a 3-port equivalent iruit that synthetially represents all energy transfers of a layer. In order to develop this unidiretional approah, let s onsider an infinite plane layer of thikness a, perpendiular to Oz axis. A portion of this layer (height and depth is taken into aount (Fig. 5. This plate is exposed to plane waves (inident and refleted on its two faes. Magneti field H is parallel to Oy while eletri field E is direted toward

4 Ox. If this plate is a ondutive one, a ondution ourant an flow inside. This layer is sumitted to three power flux: one at the input, one at the output and the third is injeted. Impedane formulation Analytial expressions of impedanes Z and Z (Fig. 7 depend on omplex phase φ (4 and on attenuation A (5 introdued y the plate of thikness a. They depend also on harateristi impedane Z of this media (6. φ = ω µ ε a (4 jφ A = e (5 Figure 5. One layer Relations etween the six external variales ( E and g H g at the input, E d and H d at the output, V and I an e written as a 3x3 matrix whih is assoiated to a passive 3-port iruit. However, Ampere s theorem shows that urrent I is linked to magneti exitation ( H g and H d on oth faes (. H H d J ( g = As a onsequene, matrix relation is redued to a ouple of equations ( [] that an e represented y a -port iruit (Fig. 6. with E E g Es = Z H g + Z E = Z H + Z d s d I J = and E g H g E s V = Z Z J E s J J ( V Es Z = = (3 I J Z H d Ed Figure 6. Equivalent -port iruit (quadripolar form Owing to relation (3, this iruit an e modified to introdue potential V and urrent I (Fig. 7 Z Z µ Z = (6 ε Z and Z an then simply e written with (7 and (8. Z Z A φ = Z = Z j tan (7 + A A = Z = Z (8 A j sin( φ These formulas are general and they need to e personalized to any type of material present in transformers. For example, only ondutive layers need an eletrial supply. Other types of material, not supplied, are represented y a serial impedane ( Z. To study a transformer, three different types of material need to e desried: ondutive, insulating and magneti ones. a Condutive layer (opper A ondutive layer is defined y its resistivity (or its ondutivity σ ρ = and its thikness ep. For a ondutor, σ permittivity ε is diretly linked to ondutivity σ (9 so φ and Z are expressed as ( and (. σ ε = (9 j ω σ ep φ = ω µ ep = ( j ( j ω δ Z = j ω ρ µ = + j ( ( σδ V I Z With ep x =, Z and Z eome : δ ( x sin( x + j [ sinh( x + sin( x ] osh( x + os( x sinh Z = r x ( Figure 7. Equivalent iruit for a ondutive layer

5 Z = r j + sinh( x os( x + osh( x sin( x x osh( x os( x [ sinh( x os( x osh( x sin( x ] osh( x os( x with r = σ a Air layer (or insulating An insulating layer (thikness : simple indutane (4. Z a ep _ a (3 is modelled y a = i ω µ ep _ a µ ep _ a = L (4 Magneti layer (ferrite A magneti layer is haraterized y its thikness ep _ f and its permeaility µ r. The simplest model for suh a layer is an indutane (5. If neessary, losses an e taken into aount y adding a parallel resistane and even more sophistiated models have een developed [3]. However, at long as we fous essentially on opper losses suh sophistiated models are useless. For the same reasons, fem simulations will e arried out assuming permeaility is real. Z f = i ω µ µ r ep _ f µ µ r ep _ f = L (5 3 Example Let's take a simple two windings EP transformer as an example. Eah winding is assumed to e made of only one layer. Axial symmetry of this devie enales to otain a layer stak after unrolling the transformer (Fig. 8. Depth is taken equal to average turn length. Height is equal to layer's width. Eah layer is separated from the others y an insulating zone whih has the same permeaility than air. Turns numer of primary and seondary are introdued in the equivalent iruit y the mean of oupler ratios [] whih links the layer to its power supply. Finally, the equivalent iruit otained this way is presented on Fig. 8. Z a3 3 Z p p Z p p Ferrite insulator Primary Seondary Ferrite Z a Z s s Z s s Z a Z Z f p Z s s Z f n t n t V p V s Figure 8. Equivalent iruit for a two winding transformer After some elementary transformations, this equivalent iruit looks more familiar, as one an see on Fig. 9. All impedanes depend on frequeny parameter. Open iruit impedane of this transformer depends essentially of magneti Z + Z + Z. In this expression, ferrite impedane ( ( p a3 f impedane Z f is dominating. V p Z p Z p Z p Z a3 Z f Z a Z s Z s Z a Z f Z s = n t Figure 9. Classial model (similar to Fig. 8 nt nt Impedanes that an e negleted in omparison with magnetizing impedane 4 Appliation to 44-layers transformer Geometry of 44-layers transformer (Fig. 3 seems very interesting to hek the equivalent iruit representation introdued aove. In fat, all ondutors have the same width and they are separated y idential insulating layers. In order to implement this model in iruit simulation software [3], 39 impedanes (3 resistanes and 3 reatanes per layer and 44 ouplers must e introdued. Results otained with this model are presented in Fig st seondary (loaded fem simulation Nominal value nd seondary (open iruit Figure. Comparison of urrent repartition in seondary layers This simulation gives very good results. Current in the load is equal to 75 A eff and the repartition otained with fem software is quite similar to that dedued from our equivalent iruit representation introdued in iruit simulation software (differene less than 5%. The most interesting aspet of this "analytial simulation" is that it is very fast. Computing time is less than s and this an e advantageously ompared to the min neessary to run an fem simulation. Introdution of suh model into a iruit software is also simpler (and faster eause numerous idential ells an e repeated. In the final part of this paper, different layer staks will e ompared in order to redue irulation urrents and to improve transformer reliaility. Vs

6 IV. PLANAR TRANSFORMER STUDIES A. Redution of irulation urrents Cirulation urrents are due to leakage flux enlosed y parallel layers and these flux inrease with the distane separating two ondutive layers. So, est solution appears to e the use only one thik layer with the total opper thikness! In standard transformers, one alternative solution onsists in twisting wires suh as in Litz wires. This does redue the flux emraed y eah pair of wires ut it is not appliale for PCB windings. The seond solution onsists in modifying winding arrangement to redue the leakage indutane of the transformer [4]. This is ahieved y interleaving primary and seondary to loally anel Ampere-turns. This solution, whih redues rms indution in the transformer window when one winding is shorted, dereases stored energy and leakage indutane. It also redues eddy urrent losses whih are roughly proportional to this rms indution. B. Layer stak improvements Impat of interleaving is now tested using our equivalent iruit method. All layers stay at the loation oupied in the 44-layer transformer ut they are onneted differently. This leads to the three different layer staks shown in Fig.. P P P3 P4 P5 SA SA SA3 SA4 SA5 SA6 SA7 SA8 SA9 SA SA SB SB SB3 SB4 SB5 SB6 SB7 SB8 SB9 SB SB P6 P7 P8 P9 P P P P SA SA SB SB P3 P4 SA3 SA4 SB3 SB4 P5 P6 SA5 SA6 SB5 SB6 P7 P8 SA7 SA8 SB7 SB8 P9 P SA9 SA SB9 SB P SA SB P SA SB P SA SB P3 SA3 SB3 P4 SA4 SB4 P5 SA5 SB5 P6 SA6 SB6 P7 SA7 SB7 P8 SA8 SB8 P9 SA9 SB9 P SA SB P SA SB (a ( ( Figure. Connetions of the 44 ondutive layers of the 3-winding transformer. (a : initial design ( : arrangement ( : arrangement The first one (Fig. -a desries the initial planar devie. Eah primary layer in the figure is omposed of two parallel layers. Seondaries are oth plaed etween the two halfprimaries. The seond design (Fig. - is otained y interleaving primary layers, "A" seondary layers and "B" seondary layers. The third one (Fig. - onsists in interleaving the three winding layers one y one. Aording to our guiding idea, this last arrangement seems to e the ideal one ut an not always e done eause of manufaturing reasons. Comparison etween theses different arrangements an e realized very quikly with the use of iruit simulation software. Only onnetions etween plates must e modified to ahieve different arrangements. Fig. presents the omparison of urrents in seondary A (loaded winding. Both arrangements and lead to quite equal urrents in parallel layers Initial design Arrangement Arrangement Figure. Current distriution in loaded winding (seondary A For the open iruit winding (Seondary B, urrents values otained with iruit simulation are presented on Fig. 3. Cirulations urrents are redued to 5 A eff with the arrangement. This value an e ompare to the 45 A eff reahed in the initial devie. Arrangement enales to still redue urrents to A eff (nominal values may e null Initial design Arrangement Arrangement Figure 3. Current repartition in open iruit winding (seondary B Total power dissipated in opper an also e ompared: for the initial design, it is evaluated to 7 W, for arrangement, losses are redued to 9 W and, for arrangement, losses still

7 derease slightly to 7.8 W. This values doesn t inlude losses in the PCB vias and in the magneti ore. C. Final optimized transformer Owing to our equivalent iruit method, onnetion etween layers as well as thikness of insulating and ondutive layers an e hanged easily and quikly. However, the solution showing lowest losses is not neessary the one that engineers adopt. Other industrial onsiderations are taken into aount suh as volume, weight, ost,. The study of this 44- layers planar transformer has een proposed y Thales and it gave us the opportunity of working with Thales engineers to improve their omponent. After alaning est effiieny solution with ost and ease of manufaturing, they uilt the omponent desried elow (Fig. 4. This omponent is made of a smaller numer of layers. Both seondary are made of 6 parallel layers. Thikness of PCB layers have een inreased (surfae x.5 to sustain 75/6 = 45.8 A eff. Arrangement of primary and oth seondary is a mix ( primaries- seondary A- seondary B etween Fig. - and Fig. -. Final performanes are presented elow. Current in loaded windings is inluded etween 3 A eff and 55 A eff. This values must e ompared to the nominal value : 45.8 A eff. In the open iruit seondary, urrent is inluded etween A eff and 3 A eff. Copper losses are lose to.6 W and, aording to measurements, power effiieny seems to e slightly aove 99 %. Compared to the first prototype, etter performanes and reliaility are otained (lower opper losses, redue hot spots and this omponent is easier to manufature fem simulation Analytial model Nominal value Figure 6. Currents repartition in optimized 4-layer planar transformer (Seondary B Figure 4. 4-layers optimized transformer Currents repartitions in seondary layers are presented in Fig. 5 for the loaded seondary, and in Fig. 6 for the open iruit seondary. On these figures, results otained with fem software are ompared with those dedued using iruit simulation software. Results are in very good agreement fem simulation Analytial model Nominal value Figure 5. Currents repartition in optimized 4-layer planar transformer (Seondary A V. CONCLUSION In this paper, we investigated the impat of irulation urrents on high frequeny transformers. These urrents appear as soon as at least one winding is made of strands onneted in parallel. They are never taken into aount in analytial approahes. They an e studied y f.e.m. simulations providing equality of urrents irulating in parallel strands is not imposed from the eginning. Despite paralleling winding seems to e a good solution to redue eddy urrent effets while sustaining high frequeny strong urrents, impat of irulation urrents must e evaluated to avoid destrutive hot spots. This evaluation is long and quite inompatile with an optimization proess when it is done using traditional approah (analytial and f.e.m. simulation. In this paper, an exat analytial approah has een formatted to appear as a iruit prolem that an e solved using standard iruit simulation software. This method, ased on the -D propagation assumption, leads to an equivalent iruit suitale to determine all layer urrents, inluding irulation ones. Owing to this tool, heking onurrent topologies for a planar transformers with given speifiation is easy and fast. Using it, engineers an save a lot of time. Sine this paper have een proposed, equivalent iruit method has een extended and it is now usale with non harmoni waveforms. This will e pulished soon.

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