Ferrite Loss Measurement and Models in Half Bridge and Full Bridge Waveforms

Transcription

1 Feite Loss Measuement and Models in Half idge and Full idge Wavefoms Alex P. an den ossche Ghent Univesity, EELA SINT-PIETERSNIEUWSTRAAT 4 ELGIUM, 9 GENT David M. an de Sype Ghent Univesity, EELA SINT-PIETERSNIEUWSTRAAT 4 ELGIUM, 9 GENT encislav Cekov alchev Technical Univesity of ana Depatment of Electonics ana 9, ULGARIA Abstact The Steinmetz equation is applied in a pue hysteesis pat and a emaining pat following a d/ behavio. A double natual Steinmetz extension method fo non-sinusoidal wavefoms is poposed (DNSE). Tests have been done at khz squae waves fo half bidges with vaiable duty atio and full bidges with vaiable phase shift. I. INTRODUCTION The classical Steinmetz equation (), fo the powe loss/volume, coesponds to a linea fitting in a double logaithmic gaph []. It is sufficiently accuate fo a small fequency ange o fo two distinct fequencies. P k f β v = () Fo feites, at low fequencies (khz), the powe is close to wheeas at highe fequencies (khz-5khz) it tends to be close to. The powe = coesponds to pue hysteesis, whee the losses ae mainly dependent on the peak-peak induction. A powe = would coespond to a pue Foucault loss, which would coespond with a low fequency model of macoscopic eddy cuents. As the esistivity of feites is quite high, these macoscopic eddy cuents (=) ae quite small and this type of model is not ealistic. Also a model has been poposed which is exact fo = and = which is called modified Steinmetz equation [], [3]. It uses the ms value of the voltage to calculate an equivalent fequency. It also gives good esults if the is fitted between the fundamental and the dominant hamonics [4],[5]. The dawback of the method is that measuements have to be made at the fundamental fequency and the dominant hamonics. The fundamental fequency might not be known in advance and the dominant hamonics ae somewhat dependent on the wavefom, fo instance a half bidge o a full bidge type of wavefom. The usual wavefoms in powe electonics ae squae waves o a supeposition of squae waves athe than sine waves. Thoughout the pape, we keep the same peak-peak induction but we vay the fequency and the wavefom. As a ule, the losses ae also dependent on the wavefom and not only the peak-peak induction. A solution is to intoduce a dependence of the losses on d/. In the pevious aticles [4],[5] and [6], a Natual Steinmetz Extension (NSE) has been poposed, based on a given powe. Pv = P β T k N T d T : efeence peiod (hee μs) : efeence induction (hee.t) P : efeence powe/vol (loss at khz,.t) In eq. () k N is given by: k k N = π ( π) cosθ dθ Since in non-linea magnetic mateials, hamonic supeposition is not allowed, the solution was to fit on a efeence fequency (the fundamental) and on a fequency in the egion of the most dominant hamonics. The disadvantage is that although the oveall accuacy can be satisfactoy, the modeling is somewhat dependent on the dominant hamonics. II. DOULE NATURAL STEINMETZ EXTENSION It is clea that a highe numbe of paametes usually fits bette, but it is valuable if the paametes can be detemined and if it impoves the modeling. We sum two Steinmetz equations one tem with =, which means pue hysteesis and one tem with >. Fo convenience we define a efeence fequency, a efeence induction and a efeence powe, we give them the index : β β f f P sin = P γ + P ( γ ) (4) f f f : efeence fequency (hee khz) γ : faction of hysteesis losses at the efeence case We expect that < γ <, >, β and β > > The efeence powe can be one of the measuement points, we did take it at khz,.t. The paamete and γ can be detemined by fitting the expeimental data o manufactue data. We fit it with expeimental data. Fo γ = we ae in the pue hysteesis situation; wheeas γ = coesponds to a taditional Steinmetz with constant. Fo = we would have a loss type known as Foucault losses. In this aticle the paamete is only used as a cuve () (3) /5/$. 5 IEEE. 535

2 fitting, even an > is possible. The used mateial was 3F3, the shape ETD44, the induction. T peak (. T peak to peak). We pefomed the measuements in sine wave, shown in Table. TALE I PERFORMED THE MEASUREMENTS IN SINE WAE f, [khz] P [W] The function κ() is defined in such way that it satisfies the sine wave solution: κ( ) = π ( π ) cosθ dϑ Note that κ() is only depending on, this is shown in fig.. Coesponding to hysteesis losses, fo =, the function κ() = /4. Coesponding to Foucault losses, fo =, the function κ() = /( π ) =.57. (6) [W].5. measued: PP model: Ps κ( ).5. All the measuements ae done at C as this coesponds to a minimum loss fo the mateial. in this way stable and epeatable measuements can be done. A good match is obtained fo =.6 and γ=.5 as shown in Fig.. We attibute the powe pat to a dependency on d/. This pat is simila to the poposed Natual Steinmetz Extension NSE [4],[5],[6]. The pupose is to match also non-sinusoidal cases. We will efe to the following equation as the Double Natual Steinmetz Extension (DNSE). The wod double efes that the Steinmetz extension is applied two times, once with = in the fist tem whee only the peak value influences the losses and once fo > in the second tem:, gg, gg f [Hz] Fig.. Measuing points: sinusoidal losses at.t and C, cuve: double Steinmetz with =.6 and γ=.5, P =.8W Fig.: Facto κ() as function of Note also that in this aticle we keep the peak inductance constant, so that the values of β and β ae not impotant. We can sepaate the losses in: P DNSE = Physt + PNSE (7) with: β f Physt = γ P f (8) β T PNSE = P κ( ) ( γ ) d T Fo special wavefoms we can fill in the integal. Fo a squae wave with duty atio D (half bidge), we have y using (), () and (8) yield Pv = γ P f f β β T + κ( ) ( γ ) P d T (5) The paamete γ is the pat of the losses at the efeence fequency, which follows the hysteesis losses. 536

3 Fig.3. Measued oltage, cuent and powe fo a half bidge at D=.5, /div 5mA/div, W/div Fig.4. Measued oltage, cuent and powe fo a full bidge at D=.5, /div 5mA/div, W/div T d + = f D T D D This is also T d = f T and substituted in (7): ( D) ( D + ( D) ) (9) () β f P = γ DNSE P f β f + ( γ ) P κ( ) D f () ( D + ( ) ) We show the cuent, voltage and powe wavefoms fo khz and with a duty atio of 5% in fig. 3 and 4. At this exteme duty atio, a notch in the cuent is clealy visible duing the high voltage pulse. kw m 3 DNSE ( d) Measued measued n PS DNSE ( d, f) m Measued n PS kw 3 m Fig.5. Feite losses/volume fo half d, nbidge +, d measuement as function of D,.T, khz DNSE, measued and nomal Steinmetz Fig.6. Feite losses/volume fo full d, bidge dd n measuement as function of D,.T, khz DNSE, measued and nomal Steinmetz 537

4 We conside a full bidge wavefom with a phase shift D; D= coesponds with no phase shift; D= with a phase shift of a full peiod. Fo this condition, the double Steinmetz equation. becomes β f P = DNSE γ P + f β f + ( γ ) P κ( ) D f D () The following measuements wee made with 3F3 mateial fo a half bidge (fig.5) and a full bidge (fig. 6), using a test platfom [7]. The test object is an ETD44 coe with 5 pimay tuns (two Litz wies in paallel of 6 stands of.mm) and 5 seconday tuns fo flux and powe measuement of.3mm, see figue 7. simila to [6] shows a typical deviation in powe measuement of 3% and 5% in exteme duty atios. III. INTERPRETATION At low fequency, the losses ae quite independent of the wavefom when no exteme d/ is pesent, the losses seem to be mainly detemined by hysteesis effects []. If we look at the wavefom of the cuent and the exponent on d/, which is close to, it is likely to conside a macoscopic esistive cuent fo high fequency. The voltage of one tun is: = A d min (3) A min : section of the mid-leg 7mm The E field at the cicumfeence of the mid-leg is E = A d min π d c (4) d c : diamete of the cente leg The E-field in the feite inceases in a linea way with the adius. This esults in an aveage E-field loss/volume, which is times lowe than the loss/volume at the cicumfeence. This model is allowed as even fo MHz the penetation depth [8],[9] in the feite is still.3mm (bigge than the adius) if you conside a esistivity of Ωm, a elative pemeability of 4 and a fequency of MHz, which contains aleady a big pat of the hamonics. The expected losses/volume with this field patten ae d A min d π t dc P = E (5) ρ Fig.7. Test object Cae has been taken to obtain a low capacitance between pimay and seconday windings, and a low leakage inductance. Note that the powe loss fo D=5% is in full and half bidge is almost equal as it concens the same wavefom. At D=5%, the losses in the full bidge ae almost twice the losses in the half bidge, although the peak-peak induction is the same! A wide band cuent pobe has been used (5Hz- 5MHz) [4], togethe with an oscilloscope powe measuement. A voltage pobe was constucted with almost the same chaacteistic as the cuent pobe, to obtain a phase shift close in the ode of ns at 5MHz. A compaison with caloimetic powe measuements ρ: esistivity: Ωm at DC and 5 C (data) Fo the half bidge we can calculate d ms = T + D D (6) If we conside a duty atio of.5 fo the half bidge, we get 8kW/m 3, which is only % of the measued losses. We know that the E-field in the yoke and side legs is smalle, so that the aveage eddy cuent losses/volume in the total coe will be even less than the cente leg. So we can say that the bulk eddy cuents caused by DC esistivity ae not sufficient to explain the d/ losses. 538

5 I. CONCLUSION Fo a given peak induction, the sinusoidal losses of feites can be modeled with a double extended Steinmetz equation, fo common fequencies in powe electonics. The dependency of the wavefom in half bidge and full bidge configuations can be well modeled using a hysteesis pat and a pat dependent on d/. The losses at exteme duty atio of the full bidge can be almost twice the losses of a half bidge, fo the same peak-peak induction. Although the d/ losses ae close to a esistive effect, a simple model with using the DC esistivity does not explain the losses. High losses ae pesent at exteme duty atios, but in pactical applications, fotunately the peak-peak induction will be lowe in such cases. ACKNOWLEDGMENT The thid autho paticipated in the famewok of the NATO Reseach Poject EAP.RIG.98.48, and wants to expess his gatitude. REFERENCES [] Snelling, E.C., Soft Feites Popeties and Applications, nd edition, London, UK., uttewoth, 988. [] A. ockmeye, Dimensionieungswekzeug fü magnetische auelemente in Stomichteanwendungen, PhD thesis, Aachen Univesity of Technology, Gemany, 997. [3] Jieli Li, Taek Abdallah and Chales Sullivan, Impoved calculation of coe loss with nonsinusoidal wavefoms IEEE, IAS 36-th Annual Meeting, Chicago, USA, Septembe 3 Octobe 4,, pp. 3-. [4] Alex an den ossche, Geogi Geogiev, encislav alchev, Feite losses with squae wave wavefoms, OPTIM 4, Optimization of Electical and Electonical Equipment, asov, Romania, -, OL I, pp49-54, May, 4. [5] Alex an den ossche, encislav alchev, Geogi Geogiev, Measuement and loss model of feites in non-sinusoidal waves, PESC, Powe electonics specialist confeence, Aachen, pp , -4 June, 4 [6] Alex an den ossche, encislav Cekov alchev, Inductos and tansfomes fo powe electonics, CRC-pess, oca Raton, Floida, ISN pp. [7] Alex an den ossche, Todo Filchev, encislav alchev, Dimite Yudov, Test Platfom fo Resonant Convetes, EPE Toulouse, 3-4 Sept. 3, cdom. [8] Alex an den ossche, Flow Caloimete fo Powe Electonic Convetes, EPE confeence, Gaz,, august 7-9, cdom. [9] Lammeane J, Stafl M., Eddy cuents, Iliffe ooks, London, UK,