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Dynamic model of magnetic materials applied on softferrites

Pierre Tenant, Jean-Jacques Rousseau

To cite this version:Pierre Tenant, Jean-Jacques Rousseau. Dynamic model of magnetic materials applied on soft ferrites.IEEE Transactions on Power Electronics, Institute of Electrical and Electronics Engineers, 1998, 13(2), pp.372-379. �hal-00141594�

IEEE TILkUSACTIONS ON POII'ER ELECTROhqCS. VOL. 13. NO. 2. MARCH 1998

Dynamic Model of Magnetic Materials Applied on Soft Ferrites

P. Tenant and J. J. Rousseau

Abstract-A behavioral model of magnetic materials is pw- sentetl. This motlel takes into account both hysteresis ant1 dy- namic phenomena. It predict< B ( H ) . ~ ( f 3 , and d ; ( f ) / d # rl1al.a~- tcristics, and a few pieces of experimental data are net led ta identify itF parameters. In this paper, the authors propose to validate the model for some t q i c a l applications encountered in power electronics. Results ohfaincrl a r r very satisfactory.

Index T ~ r m s 4 o r e losses, dynamic effect, hysteresis, inductor, soft ferrites. transformer.

D UlUNG tlie last few years In the field of power electron- ics, improvements in switching devices and power con-

verter topologies have enabled important increases in switch- ing frequencies. These recent advances have allowed major reductions of cost, weight, and volume of inapetic coin- ponents such as inductom and transformers On the other hand, high switching f'requencies have brought new difficulties concerning the design of magnetic components. It is the same for the computer-aided design (CAD) tools development. The increase in frequency requires taking into account a lot of phenomena which are negli9ible at lower frequencies. The decrease in volun~e imposes to better take illto account thermal problems. That means that magnetic components designers need thermal model to evaluate the temperature in few points Both iron and copper losses constitute essential data for any thermal model. Unlortunately, losses are not easy to accurately determine. Copper losses calculation requires considering both skill and proxiniity effects. For maglietic components with alr gap, addit~onal losses are due to the leakage flux, wh~ch cause eddy currents in conductors. Core losses calculation in magnetic material are also difficult In power electronics, operating conditions are specific. In most cases, flux densities are triangular or trapezoidal.

For inductors, an important dc level is observed. However, ferrite nranufkcturers only give losses tor sinusoidal-applied flux densities. Moreover, CAD tools in power electronics re- quire fast, simple, and easy-to-use models in order to calculate waveforms A magnetic component is one component in a converter. So, simple methods must be used to model it. It is a d~fficult task Magnetic character~stics are nonl~ilear because of' hysteresis phenomena and tiine dependent because of dynamic

Manuscript recei~ed December 23, 1995: rer-ised January 29, 1997 Rec- ommended 1,y Associate Fd~tor, W J Sajeant. This work was suppn+ted by the French Mimster of Research and Space and Shneidpr-Electric.

The authors am with CEGELY-ECPA-INSA d*: LYON. 69621, V~llcur- hanne, Ccdex, France (e-mail routrcau@~cegely insa-lyon fr)

Plihlisher Item Identifier S 0885-899:(98)0 1940- 1

effects such as eddy currents. Tl~e temperature inust be taken into account, and the model inust also consider air gap and windings.

Magnetic properties modeling is a first important step of nragnetic component modeling. We are working on a heliav- ioral model for the predetermination of dectrical and magnetic characteristics. This model takes into account liysteresis and dynamic phenomena. Initially applied on FeSi and FeNi ma- tenals, its application has been extended to soft ferrites.

The purpose of this article is to present the performance of this model. In Section 11, the model is briefly described. In Section III, ident~fication n~odel parameters are presented in the specific case of soft ferrites In Section IV, the model is validated for some typical applications encountered in power electronics.

TI. THE BEHAWORAL MODEL

We only consider toroid circuits, without air gap. However, tlte pnnciples of the model can be easily extended to other peoinetnes, mcludmg air gaps. We assume that both the flux density B and the magnetlc field H are uniforms throughout the material We also assume that the temperature is constant. The parameters of the model are then identified for a given temperature. The base of the model is the following: the real magnetic circuit is replaced by a fictitious equivalent circuit of tlte same geometry without any dynamic properties [ I ] . These dynam~c properties are represented by an add~tional w~nding of n turns closed on a resistor r (Fig. 1). The Ampere's law applied to this eq~~lvalent cirmit of effective length 1, gives

We can define the current I by

Equation (2) is relative to a material without any dynamic properties. Its magnetic properties correspond to a str~ctly static behavior. So, we can state

where p is the flux in cross-sectional area. Equation (3 ) is graphically illustrated by all the static magnetic characteristics of the material. The current Id flowing the fictitious winding IS defined by

-00 0 1998 IEEE

TENANT AhV ROUSSEAU MAGhTTIC MATERTALS APPLIED ON SOFT FERRITE3

b i t h myric effects] [ ~ i f h o e t Dynamic effects

(a) Cb) Fig 1. Pr~ncipIe of the model. (a) the real magnehc c ~ r c u ~ t 1s replaced by a (b) fict~tious eq~rix-alent c~rcu~t of the same geometly w~thmit any dynam~c properties Dynamic propertleq are represented hy a additional ~vjnding of n turns closed on a reqistor T

+ + Expcrimcntal: static virgin curve Experimental dynamic virgin curve

* . - - Simulated dynamic virgin curve

Applied field H (Alrn) 0 . I I I I 0 34 69 1'04 138 173

Fig. 2. Identification of the parameter -, in the field of application of the material, which is between the range 10b200 mT

Staring y = n2/r and substituting (2) in (5 ) . we finally obtained the following equation linking the applied current I,,, to the flux p.

To solve this equation, ~t is necessary to identlfy both the coefficient y, assumed to he constant, representative of the dynamic behavior of the sample, aiid tlie relatioil 1 = ki-ltp), wllicll characterizes the hysteresis pllenomena.

A. Identification of llje Pol-alneter y

When this criterkon is minimum, the parameter y is correctly estimated. Peak flux density generally observed in power electronic applications is in the range 50-300 nrT. So, i t is not usefill to apply the criterion until saturation. Particularly, this criterion must he minimized in tlie field of application of the material. Fig. 2 concenls a rnapnetlc mater~al whose field of application is between 100-200 mT. The parameter y has been set so that the criterioii is minimnt in the field 0-200 mT. Measurements have beell carried out with different ring cores in order to study the variation of the y parameter versus core sizes. The saine value of this parameter has been obta~ned. That ineans this parameter character~zes dynamlc eKects for a given material. No dimension effect has been shown. Nevertheless it would be advisable to limit these concIusions for snlall cores (d~ameter less than 30 nun). For important dimensions, no measurement has been carr~ed out For this study, the y parameter is kept constant far a given material.

In order to identify the parameter y, the static virgin curve and one of the dynam~c v~rgin curves are reqllired [2]. The B. Ide1~r!ficcrrioj7 of rhe 6n1wss Sm1lc Fz~nciion I = F-'(P) experimental dynamic virgin curve is used as a reference. The The inverse static function 1 = P-"(rp characterizes the correct value of the paralneter 1s obtained when the following static bchavlor of the material, i.e., the hysteresis phenomena error crkterion is minimized. According to the considered applicatbon, static hysteresis loops

H max Jd (Bnleas~red - 3~*nulated) dH can be symmetric or non. So, it is necessary to have a

E = I3 I Y I ~ K . (7) hysteresis model, which generates any type of staric hysteresis SO &ea~~rerldH loops. Currently, two models are often used. the Jiles and

IEEE TRPINSACTIONS ON POWER ELECTRONICS. YOL 13. KO 2. MARCH I$!%

t .._.- - - Uninrproved Preisach model - -. + - -

Applied field H (Alm) 27 ' .B -I

FIE. 3. Illustration of irnplovements brought by the dzvmt~on model. Companson bcracm simuIated and measured minor Ioops obtained 1v1t11 a rect~fied sinuso~dal magnetic field H of IO-Hz frequency and 27-A/m magnitude

Thealotkmt rmrgne#ization curve

--- I" -

Fig. 4. Dynamic model and required experimentd results

Atherton model [?I, [4] and Pre~sach model [5] The Preisach nod el has been chosen for its great siniplicity. It allows the generation of all static magnetic characteristics without major dlfficulttes, and ~ t s parameters can be easily identified Amongst numerous identification techniques that can be used to identify the Preisach model parameters [h]-[9], a simple method has been used This is the rndhod proposed by Biorci and Pescetti [7]. Unfortunately, and particularly when the Biorci and Pescetti identification technique is used, the Preisach model has important shortcomings [ 101 The Preisach inodel is very accurate when peak flux density is close to sam- ration, either for major loops or for minor loops. Unfortunately, it constderably deteriorates when peak flux density is far froin saturation. Hysterews losses are overestlinated.

Classical solutions proposed to improve the Preisach model have been tested [11]-[17]. But these solutions are not re- ally adapted to the context of power electronics and results obtained are unsatisfactory. Consequently, a new method has been developed in order to improve significantly the Preisach

model. This method IS based on the predict~on of the deviations observed between simulation and experiment. It has been s h o w that deviation characteristtcs can be eaaly interpolated using very simple laws (parabolas and straight lines). Only the knowledpe of the reinanence versus the peak flux deiisity of symmetrical loops is sufficient. Improvements brought to the Preisach model are very good. In Fig 3, a comparison between simulation and experinlent is presented. The applied field 1s smusoidal, rectified, and of a 10-Hz frecluei~cy One can see that the predicted hysteresis loop is in accordance with experimental data. In this figure, oiily static hysteresis loops are compared because the first magnetization curve do not set problem. Both the Preisach model and the improved Preisach model compute very well the first magnetization curve (the first magnetlzatlon curve IS one of the two expenmental curves which are required to calculate the Preisach function).

Fig. 4 shows the presented dynamic model and specifies the set of experimental results which are required to generate

T M A K T AND ROUSSEAU. MAGNETIC MATERIALS APPLIED ON SOFT FERRITES 375

Push-Pull configuration Fly-Back configuration

Fig 5 Waveforms of the flux versus time according to the converter topology

Forward configuration

Fig. 6. Waveforms o f the applied field H versus time considered for our validntlon.

a model for a given material H(t ) is the input of the model, provides the desired waveforms of the magnetkc field H. and U ( t ) and dp /d t represent the outputs. By integrating stat~c AcquisItloii of data l,,,(t) and Uz( t ) 1s made by a TDS540 and dynamic hysteres~s [oops, bo~h statlc and total core losses scope Data are transferred to a calculator, and the voltage are obtained. W2(t) is numerically integrated after an offset correction. The

result of this liltegrat~oil gives the flux dennity B as

IV. DYNAMIC VALIDATION OF THE MODEL

The field of application of soft ferrites is wide It covers a frequency range between 10 lcHt aiid 1 MHz. Accarding to tlie topology of the converter, flux dens~ty U is syrnmetr~c or asymmetric, with magnitudes wh~ch are between 50-300 mT. Waveforms are rarely sinusoidal, but rather more triangular and trapezoidal as shown in Fig. 5. In Fig. 6, the three waveforms which have been chosen for our validation are presented. sinusoidal magnetic field H, triangular magnetic field H, and umpolar tr~angular magnetic field H w ~ t h a supenn~posed dc level Except for the case of' mductors, the flux is imposed by applying a voltage on the primary winding. For our validation, it is important to notice that we lmpose the field H and not the flux. Nevertheless, we assume that chosen waveforms are sufEc~ently close to real operating conditions and that the model w11l be validated in the context of power electronics

Experimental data is obtained with a magnetic component, which includes a primary wlnding of nl turns crossed by a current Iapp(t). A secondary open winding of n2 turns is also rounded in order to measure tlie voltage Uz(t ) , which 1s equivalent of the derivative of the flux y. A current generator

A noninductive shunt is used to measure the applied current I,,(t). Currelit probes should not be used as erroneous measurements are observed w~th them. T h ~ s is confirmed by a complete study made by Thottuvelil et a!. (181. The current generator prov~des current impulses which allow us to used high-value shunts and eliminates problems due to material heating.

The choice of materials inust be sufficiently representative. Four of them 11ave hem chosen Their usual appl~cation fields are given in Table I.

R. Core Losses P~rdictirion

Core losses are predicted by integrating magnetic character- istics at the steady state. It is interesting to coinpare simulated losses versus experimental losses measured with a wattmeter. In order to quantifi the perfor~nances of the model. we used an error criterion defined by

Experimental losses - Simulated losses E = l

Experimental losses I * 100. (9)

Flg. 7 shows error criterion versus frequency. The appIied field is sinl~soidal. Frequencies are between 10-300 kHz. The

JEEE TRkUSACTIONS ON POWER ELECTROhICS. VOL. 13. NO. 2 . W R C H 1998

TABLE I FIELD OF APPLICATION OF THE SO!T FERRIES RETAJNED FOR OUR STUDY (THOMSON-LCC bhTERIALS) TYPE OF MATERUL

Frequency (kHz)

Type o f material

Fig 7. Errors made on the predicted iron losses by the model for a sinusoidal magnetic field H versus frequency The magnitude of the flux density is equal to 100 mT.

S loo c

IJsual frequency range

1 10 100 loo0

Frequency (KHz]

Usual perk flux density

range

- B3

B4

Fig. 8. Cornpanson between measured Iron losses by manufacturer and s~mulattd iron loss- versus frequency.

magnitude of the peak flux denaty IS equal to 100 mT, and In Fig. 8, sim~~lated and measured lnanufacturer core losses three materials are considered. As one cart see, iron Iosses have been compared. Both static and dynamic effects are taken are estimated accurately, generally wit11 errors less than 10%. ~n to account. At low frequencies, core Iosses are only due to With respect to manufach~rer data, performances of the model hysteresis phenomena. When the frequency increases, dynamic are excellent too. effects occur and core losses depeiid on both hysteresis and

fOKHz-50KHz

IQ KHz- 70 KHz

200 mT - 300 mT

100 mT - 250 mT

- 100 mT - 200 mT

SQ mT - 100 mT

B2

F2

50 KHz - 250 KHz

100 KHz - 506 KHz

TENAhT AKD ROUSSEAU: MAGh2TIC MATERIALS APPLIED ON SOFT FERRITES

~imulated dynamic curve

- ~2'6. 7

I I I - 1 8 . 3 -9.39 -0.73 7.92 16.6 25.2

H (AMPERE/METRE)

Ftg 9 Cmpafison henveen stmulation and experiment Triangular applied field af 160 kHz and 25-Alm magn~rude 0 4 matefial

a - Applied field H (Alm) - I

Fig 10 Cornpanson between sfmrlation and experiment Rectsfied triangular magnetic field H of 300-kHz frequency and 42-Alm magn~h~de 8 2 material

Comparison between srmulat~on and expenment. Rect~ficd triangular magnehc field H of 300-kHz frequency and 42-A!m magn~tudc.

EEE TRANSACTIONS ON POWER ELECTROh?CS. VOL. 15. NO. 2 . MARCH 1998

ti' I I ,'- < >< - / -S? -

A zkxpe!imen 1 \, t a 1 c!%d:ld/ k l Simulation

STEADY STATE

Applied field H (Nm)

Fig 12. Comparison between simulation and experiment for a rectified triangular applied field H of 385-kHz frequency with a transient state

dynamic losses. One notes a very good accordance with errors less than 10%. These results show that the model covers perfectly the applicatioii fieId of each inatenal.

For the case of push-pull conveflers, magnetic character- istics obtained are symmetric. Fig. 9 presents a coinparison between simulation and experiment The presented magnetic characteristics have been obfained with a triangular magnetic field H of 160-kHz frequency and 25-Nm magnitude. The magmtltde of the flux denslty B is equal to 150 mT In order to judge the rrnportance of dynarnlc effects, we have super~inposed the corresponding statlc curve. Tlie constdered magnetrc material is the 8 4 material, ust~ally used at a frequency less than 70 kIIz Core losses are larger to 1. W/cm9 It is clear that this application does not cortespoiid to a real appl~catlon. But the proposed example ~llustrates perfectly the performances of the model which are not limited to the appltcatlon field of each matenal. For t h ~ s example, error made on the prediction of iron losses is equal to 5%. Fig. 10 shows a comparison between simulation and experiment for a unipolar ininor loop such as miiior loops encountered in forward and fly-hack cnnverterq We have applied a rectified triangular

field H of a 300-kHz frequency and 42-Nm magnitude. The magnitude of the flux density 1s equal to 200 mT. Here too, the behavior of the model is excelrent. Error made on the prediction of iron losses is equal to 6% GlobaIly, the inodel predicts iron losses with errors less than 15% for such applications. The derivarive of the flux, corresponding to the previous magnetic characteristic presented, is well predicted too as shown in Fig. 11.

It ts also i~nportai~t to control the behavior of the model for transient states An improper account of transient states can give nse to bad results on the steady state. As one can see in Fig 12, transient stares are sufficiently well predicted to obtain very good results on the steady state.

A behavioral model of ma_metic material has been pre- sented This model predicts B(H), p(t), and d.g(t)/dt charac- teristics and iron losses. Initially developed for FeSi and FeNi material, this model has been improved in order to increase its performances for soft femtes. The accuracy obtained on the prediction of waveforms is quite good, and, obviously, iron losses are predicted well too. Peribrmances of the inodel are not limited to the steady state. Important transient states are taken into account too. The Darameters of the model are easily ~dent~fied, and t h ~ s ident~ficat~on needs a few experimental data which are quickly and easily obtained. Siinulation t~mes require around 3 s with a PC4176. This model constin~tes an important advance In nlagnetic component modeling. More- over, the next srep concerns the implementation of the models in circuit simulation software.

[I] I. J. Rouswau, J. P. Masson, and B. Lefeb~w, "Behavioral model of ~ron losses," In hw I W r S . 1990

[Z] P. Tenant and J. I. Roimscau, "'Dymrn~c model for -soft fcrntts," In PIVC PESC Atlanta. GA, 1995. 7-01 2

[3] 13 C hIer and D L Athaton. ''Theory of fmamagnc~ic h y ~ t m i s . " J .Mog.n ,Mug .l.lare~. , 1-01 6 I , pp 4 8 6 0 , 1986

141 D. C. Jiles and B. Thoclke, ''Thcorv of f m m a a n e t ~ c hysteresis. lletermination of model parameters from experimental hysteresis loop," IEEE Eons. . lhgr~., vol 25. pp. 3928-393.30. 1989

[5] F h s a c h , "'Uher die rnagnet~~che nack~virkung." Ze~frchr~fr$~r Phvs~k, 1.01 94, pp 277-302, 19<5

I G l 1: D Mavewovz ,Uatl~e~notrcal .Uodeis of Hi rfewsrs Berlin Ger- - . . - - , . many. Springer-Verlag, 199 1 .

[7] G R~orci aitd D Pescetti, "Analytical theory of the hehavinr of ferromagnetic materials," I! .I'lrola Cimento, tol- 7, pp. 829-281, 1958.

[&I S. Y. R. Hul and J Zhu, "Maqetic hystcresls model~ng and simulat~on usinp: the Prer~acb t h e m and the TLM teclmniciue *' IFFE Pons .Mup.n . ~ 0 1 . ~ 5 , pp. 833-842, 1694.

[91 G Kadar. "On the Preisach function of ferromapnetic hysteresis." J dpyt. Phvs., vol 61, no. 8, pp. 4013-4015, 1987.-

[ lo] 0 Renda, "To the question of the reversible processes In the Preisach model," Elect Eng. J Sio~ ak .4cademt. SCF., ~ 0 1 . 3. 199 1 .

[ I I ] G Kadar. E Kl~di-Koszo. L Potocky, P J Safatlk. and E D Totre, "Rtlinear product Preisach modeling of magnetic hystereqis cun7er." I I T K Eanr .Wflgn, rol 25, pp 3931-?.9::, 1989

TENAW AKD ROUSSEATJ MAGKETIC MATERIALS APPLIED OV SOFT FERRITES 3 79

[I21 E. D. Tom and F. Va~da, "Paramctrr ~dcntification of the completc- moving hyteresis model ming major loop data." IEEE Pons ,Lfagn, \-o-ol 70, pp 4987-5000. 1994

[13] D L Atherton. F3 57punar, and J A Szpunar, "A new approach to Prelssch d~agrams." IEEE firtns. ,Map , vol. 23, pp. 1856- 1865, 1987.

[ Id] G Kadat and E D Torre, "Deta-mination of the bilinear pmduct Frelwcb functlm," J .+,of. Pi~vs , tol. 63. pp. 3001-3003, 1988.

[I51 E D T o m . J Oti, and G Kadar, "Preisacl~ modeling and rer,ers~hle magnetization," IEEE Stwns Mugtr., vo1. 26, pp. 3052-3058, 1990.

[16] F Vajdjda. E D Twre, and M Pardaxri-Hm-r,ath, "Analysis of re- versible magnetization-dependent h i s a c h models for recmding media," 1 .MO~IS ,Wag mare^ , vol. 11 5, pp. 187-1 89, 1992

[IT] F. Val& and E. D. Tom, "ElKcient numcncal ~mplcmenrat~on of complctr moving h y s t m ~ ~ s modcl." JEEE hens .Vngn, l o1 29. pp 15:2-1537, 199;

[IX] V J Thottur-el~l, T G Wilron, and H A Omen, "H~gh frequency mearurement technicper for magnetic core$." PEEF h a n s .Mop , xol 5, pp. 41-53, 1990.

P. Tenant was born in 1966. He received the

Q Ph D degree from the Inrtirut Nat~onal des Scimces Appliques (MSA). Lyon, rrance, In 1995

He was m~tlt Ccgely from 1991 to 1995 HIS

t. =)C research Interest 1s inagnet~c phenomena modeling 4 Smcr 1996. lie lies bets1 !v~ll~ ISOLSEC, Viller~i- - hanne. Cedex, France, and currently ~vorks on the

- ,l. .J. Rousqeru mas horn In 1953. He rccelvcd the Eng degree in 1978 and the Ph.D degree in elec~rical engineering in 1983, both from the Unlvers~ty of Clcrmont-Ferrand, Clmnont-Fcrrand, France.

He 1s cumntly an Associate Professor at hoth the Inshhlt Nat~onal der Sciences Appliques (IKSA), Lym, France, and Inst~tut Un~versltalrede TcchnoIo- gie (IUT). St. Etlmne. France Hr bat bem w ~ t h the Cegely Electrical Engineering Center. Lyon, slncc 1987. HIS current research ~ntcrests arc power

e l e ~ t l i n ~ l ~ s and lllagi~etic component modeling.

design of transformers. AY.