Teaching the Linked Use of Various Softwares for the Simulation of Magnetic Devices

Transcription

1 Intrnational Confrnc on Advancd Computr Scinc and Elctronics Information (ICACSEI 2013) Taching th Linkd Us of Various Softwars for th Simulation of Magntic Dvics Rosa Ana Salas, Jorg Plit Dpartamnto d Tcnología Elctrónica, Escula Politécnica Suprior, Univrsidad Carlos III d Madrid Avda. d la Univrsidad, 30, 28911, Lganés (Madrid), Spain rsalas@ing.uc3m.s Abstract - Th modling of frrit inductors is a difficult task du to th nonlinarity of th magntic filds and th grat varity of shaps, sizs of th cor and numbr of turns in th winding. This papr prsnts a procdur that intgrats various standard softwars, modling and simulation tchniqus and xprimntal masurmnts in ordr to simulat a soft frrit inductor for us in a circuit simulator. This procdur is applid to th modling and simulation of frrit inductors widly usd in th fild of powr lctronics. It can b applid to undrgraduat and postgraduat studnts and hlp thm to undrstand th bhavior of th circuits and th nonlinar physical phnomna involvd in powr lctronics. Indx Trms - Cor Saturation, Powr Losss, Magntic Dvics, Nonlinar Inductors, Frrit Cors, 2D Finit Elmnt Analysis. I. Introduction Inductors consist of a frrit cor, winding and somtims a coil formr and ar availabl in a grat varity of shaps, sizs and numbr of turns in th winding 1-4. As an xampl, Figurs 1(a) and 2(a) show two ral magntic componnts with diffrnt gomtris, i.. E and RM typ, rspctivly. Th cor matrial shows a nonlinar bhavior including saturation, hystrsis and powr losss and th magntic filds ar nonlinar, i.. th spatial distribution of th magntic filds in th cor is inhomognous. This inhomognity can b sn in Fig. 3 whr w show th distribution of th valus of th B-fild modul on th surfac of a saturatd RM cor, displaying a highr concntration on th cntral column. Thrfor, th modling of ths frrit inductors is a complicatd task 5-19 as it involvs solving nonlinar diffrntial quations which cannot b solvd by analytical quations. In ordr to modl thm it is ncssary to masur th magntic proprtis 7,8,9,12 and us dsign, simulation and Finit Elmnt Analysis programs 14,15,17,18. (a) Fig.1 (a) Ral magntic componnt with an E cor and two windings of 28 turns.(b) Triangular msh gnratd by th 2D simulations. (b) (a) Fig.2 (a) Ral magntic componnt with an RM cor and two windings of 15 turns. (b) Triangular msh gnratd by th 2D simulations. 3D (a) (b) 2D (b) Fig.3. Valus of th B-fild modul in 2D and 3D on th surfac of th RM8/I cor sn in Fig. 2(a). In this papr w prsnt a procdur that combins modling, simulation and xprimntal masurmnts on ral inductors. This procdur uss diffrnt programming and modling tchniqus coupld togthr: a Computr Aidd Dsign program (AutoCAD), a Finit Elmnt Analysis program (Maxwll), two scintific calculus programs for th numrical solving of drivativs and intgrals (Origin and Matlab), a numrical simulation program (Simulink) combind with Matlab and finally an lctronic circuit simulation program (PSIM). W dmonstrat how in th dvlopmnt of th modling procdur of frrits it is ncssary to rsort to th linkd us of diffrnt modling and simulation tchniqus (finit lmnts, mathmatical quations, circuit simulation, tc...). This procdur is applicabl to undrgraduat and postgraduat studnts and hlps us to show th studnts how diffrnt softwars can oprat togthr to solv th task of dsigning and modling a frrit inductor. As th procdur is long and complx w hav dividd it in lvls with growing complxity that can b applid to studnts at diffrnt ducational stags Th authors - Publishd by Atlantis Prss 537

2 Th papr is organizd as follows: In Sction II w giv a stp by stp squnc of th procdur. In Sction III w show th division of th procdur in lvls with growing complxity showing th ncssary supplis and softwars. Finally, in Sction IV som conclusions ar offrd. II. Stp by stp procdur Th objctiv is to obtain th voltag, currnt and powr wavforms of an inductor with a frrit cor corrsponding to its srial lctric circuit as can b sn in Fig. 4. xcitation currnt valu w obtain th spatial distribution valus of th magntic filds B and H (B-I and H-I Tabls) and th R-I rms -f curv for all working rgions of th frrit from th linar to saturation rgions. Using th program Origin and through intgration of th B fild, w obtain th Φ- I curv and from this w driv th L-I curv by diffrntiating Φ with rspct to I. Φ BdS S (1) Construction of th inductor and masuring of th magntic proprtis MAGNETIC MODELING Fig.4 Equivalnt Elctric Circuit of an inductor with a frrit cor. It consists of two nonlinar paramtrs: th inductanc L as a function of th xcitation currnt I (L-I curv) and th rsistanc R as a function of th rms currnt and frquncy f (R-I rms curv). Th procdur consists of two diffrnt parts: magntic modling (computation of th L-I and R-I rms curvs) and lctrical modling through a circuit simulator. Th calculation procss diagram is shown in Fig. 5. Th procss starts with th construction of th inductor that consists of a frrit cor and a coil formr on which a coppr wir is wound and th masuring of th magntic paramtrs undr dirct currnt that charactriz th frrit: prmability as a function of th magntic fild H (-H curv) and th magntic fild B as a function of H (B-H curv). Nxt, ithr th 2D (th quivalnt sction of th frrit plus its winding and coil formr) or th 3D domain is dsignd using th program AutoCAD. In Figs. 1(b) and 2(b) w show th 2D quivalnt domains of th ral inductors dsignd in AutoCAD. This dsign and th magntic proprtis ar introducd into th Finit Elmnt Analysis program Maxwll. Aftr that, th boundary conditions and xcitation currnt lvls ar assignd. In ordr to gnrat th msh both in 2D and 3D w chos to carry out an adaptativ rfinmnt of th msh consisting of making a finr msh at th spatial points whr th prviously stablishd rror lvl is xcdd (cornrs, rgions with irrgular bordrs, tc..). In ach itration th program computs th magntic filds, maks an rror stimat and rfins th msh. This adaptativ mshing rducs th computing tim and th convrgnc and tolranc. This algorithm is implmntd into th Maxwll program. In th adaptativ procdur th paramtrs corrsponding to th stopping critria and th prcnt rfinmnt pr pass ar introducd. Th first ons spcify th maximum numbr of passs and th maximum prcnt rror, also calld rror tolranc. Th prcnt rfinmnt pr pass spcifis what prcntag of finit lmnts (triangls in 2D or ttrahdra in 3D) should b rfind during ach itration in th initial msh. In Figs. 1(b) and 2(b) w show th msh gnratd in th 2D simulations. As th simulation program s outputs, for ach Φ BdS S L I d di Dsign of th 2D or 3D domains using AutoCAD Finit Elmnt Analysis program Maxwll B-I, H-I Tabls Solving numrically with Origin -I curv L-I curv Solving diffrntial and intgral quations numrically using Simulink v n Elctronic Circuit i n Simulation Program PSIM v(t), i(t) - Boundary conditions - Adaptativ mshing - Excitation lvl (voltag or currnt) p(t) v(t), i(t), p(t) R-I rms curv ELECTRICAL MODELING Fig.5 Calculation procss diagram. Solving mathmatical quations numrically using Matlab - Dsign of th circuit - Excitation lvl 538

3 Th procss starts with th construction of th inductor that consists of a frrit cor and a coil formr on which a coppr wir is wound and th masuring of th magntic paramtrs undr dirct currnt that charactriz th frrit: prmability as a function of th magntic fild H (-H curv) and th magntic fild B as a function of H (B-H curv). Nxt, ithr th 2D (th quivalnt sction of th frrit plus its winding and coil formr) or th 3D domain is dsignd using th program AutoCAD. In Figs. 1(b) and 2(b) w show th 2D quivalnt domains of th ral inductors dsignd in AutoCAD. This dsign and th magntic proprtis ar introducd into th Finit Elmnt Analysis program Maxwll. Aftr that, th boundary conditions and xcitation currnt lvls ar assignd. In ordr to gnrat th msh both in 2D and 3D w chos to carry out an adaptativ rfinmnt of th msh consisting of making a finr msh at th spatial points whr th prviously stablishd rror lvl is xcdd (cornrs, rgions with irrgular bordrs, tc..). In ach itration th program computs th magntic filds, maks an rror stimat and rfins th msh. This adaptativ mshing rducs th computing tim and th convrgnc and tolranc. This algorithm is implmntd into th Maxwll program. In th adaptativ procdur th paramtrs corrsponding to th stopping critria and th prcnt rfinmnt pr pass ar introducd. Th first ons spcify th maximum numbr of passs and th maximum prcnt rror, also calld rror tolranc. Th prcnt rfinmnt pr pass spcifis what prcntag of finit lmnts (triangls in 2D or ttrahdra in 3D) should b rfind during ach itration in th initial msh. In Figs. 1(b) and 2(b) w show th msh gnratd in th 2D simulations. As th simulation program s outputs, for ach xcitation currnt valu w obtain th spatial distribution valus of th magntic filds B and H (B-I and H-I Tabls) and th R-I rms -f curv for all working rgions of th frrit from th linar to saturation rgions. Using th program Origin and through intgration of th B fild, w obtain th Φ- I curv and from this w driv th L-I curv by diffrntiating Φ with rspct to I. Φ B ds (2) S In Figur 6 w show th valus of th B-fild modul in 2D and 3D on th surfac of th cor computd by th Finit Elmnt Analysis program Maxwll. As can b sn th softwar has a usr frindly and intractiv visual intrfac which maks it intrsting for studnts to us. In Fig. 7 w show an xampl of an L-I curv and in Fig. 8 an xampl of an R-I rms -f curv. Fig.7 Exprimntal (stars) and simulatd by Finit Elmnt Analysis (squars) L-I curvs. Fig.8 Exprimntal (stars) and simulatd by Finit Elmnt Analysis (squars) R-I rms curvs. Now w can start th lctrical modling with th joint us of thr programs. Th L-I and R-I rms curvs ar introducd into th Simulink program. With th hlp of th Matlab program th quation 2 that rprsnts th voltag of th inductor is solvd numrically. W draw th lctrical circuit to b simulatd in th circuit simulator PSIM and assign th voltag and/or currnt xcitation lvl. At ach instant in tim th Simulink program snds th xcitation currnt valu i that flows through th inductor to PSIM and PSIM snds th voltag v across th inductor to Simulink. v di dt t Li, f iri, f (3) In Fig. 9 w show an xampl of an lctrical circuit including th nonlinar inductor modl xcitd by a sinusoidal voltag. Fig.9 An xampl of lctrical circuit to b drawn in th PSIM program Finally, w obtain as outputs of th PSIM program th voltag and currnt wavforms (v(t), i(t)) and from ths data w driv th powr wavform p(t) using Origin. In Fig.10 w show an xampl of ths wavforms. Th rsults of Figs. (a), (b) and (c) corrspond to th linar rgion and (d), () and (f) to th saturation rgion. Fig.6 Valus of th B-fild modul in 2D and 3D on th surfac of th cor. 539

4 Fig.10 Exampl of xprimntal (dottd lin) and simulatd (solid lin) voltag, currnt and powr wavforms for th linar and saturation rgions. III. Us of th procdur in taching Th contnt of th procdur would b usful for any subjct daling with powr lctronics that ar tought at Univrsitis. As th full procdur is vry laborious, w hav optd to divid it into four lvls with growing complxity. A. First lvl In this lvl studnts carry out xprimntal masurmnts and analyz th magntic proprtis that charactriz th frrits studying thir bhavior from th linar to th saturation rgion of th matrial. This way, alrady known basic concpts of magntism ar rviwd and usd in a practical contxt. This lvl consists of four activitis: dsign and construction of th inductors and transformrs, prliminary xprimntal masurmnts at low currnt intnsity, DC currnt xprimnts and AC currnt xprimnts. Ths activitis would b usful for undrgraduat studnts and could b suggstd as optional additional work for th subjct. Th optimal organization would b individual or pairwork. 1) First activity of th first lvl: In this activity th inductors ar built by winding coppr wir and th ncssary numbr of turns and siz of th wir ar calculatd. Th optimal numbr of turns of th windings is stimatd using as paramtrs th spcifications of th masuring quipmnt, th ncssary B and H valus to saturat th magntic cor and, in th cas of AC currnt, th working frquncy to b studid. In th cas of an inductor xcitd by a sinusoidal voltag th studnts would us th following quations in ordr to driv N, bing f th frquncy, A th ffctiv cross-sctional ara of th cor, and th ffctiv magntic path lngth. V p I 2 f N A B (4) p p H p. (5) N As th varity of availabl frrits is vry big, it is possibl to study many variabls such as diffrnt matrials, gomtris and sizs, diamtrs of th wir and numbr of turns. As far as th gomtris go, w can study toroidal inductors (no gap) and inductors mad with two idntical frrit half-cors (typs EE, RM and POT) whr th thicknss of th air-gap can b varid dpnding on th applications. Diffrnt matrials and gomtris can b proposd in ordr to compar th rsults. Ncssary supplis: namld coppr wir, frrit cors, and in som cass a coil formr. 2) Scond activity of th first lvl: In this activity xprimntal masurmnts with an impdanc/gain-phas analyzr ar mad as a function of frquncy at low amplitud and linar rgion to calculat th rsonant frquncy and th inductanc and rsistanc. Through this xprimnt th studnts gt to know som charactristics of th inductors as wll as th corrct rang of th working frquncis. Ncssary supplis: prviously built inductors, impdanc/gain-phas analyzr and a prsonal computr with th program Labviw. This activity has th advantag of working with a low intnsity and thrfor not bing dangrous for th studnt. 3) Third activity of th first lvl: In this activity, xprimntal masurmnts ar takn undr DC currnt. Th objctivs of ths masurmnts ar to obtain th magntic proprtis of th frrit cor (B-H curv) using a toroidal cor and obtain also to obtain th L-I curv of th inductors. In ordr to obtain th B-H curv, a two-winding toroidal transformr with th sam matrial as th studid frrit is built and th -I curv is masurd for currnt valus from 0 to cor saturation. W hav chosn a toroidal gomtry as it liminats th ffct of th air-gap and th magntic fild lins tnd to b circular, thus rducing th dg ffct. Th B and H valus wr computd using Matlab as: B 1 vdt N A (6) N A s N p I H (7) whr N p and N s ar th numbr of turns of th primary and scondary winding rspctivly, A is th ffctiv ara of th frrit cor and l is th ffctiv lngth of th frrit. In ordr to obtain th L-I curv of th inductors, a twowinding transformr with th sam cor as th studid on is built and th -I curv is masurd for currnt valus from 0 up to cor saturation. From this, th L-I curv is drivd as: L I d. (8) di At this point th studnts can study th influnc of th numbr of turns and th ffct of th air-gap on th -I and L-I curvs by building diffrnt transformrs and comparing th masurmnts. Ncssary supplis: frrit transformrs with two windings, namld coppr wir, DC currnt sourc, digital s 540

5 multimtr, lctronic fluxmtr and AC currnt sourc. 4) Fourth activity of th first lvl: In this activity w propos xprimnts undr AC currnt by applying an xcitation voltag to th frrit inductors. Exprimntal masurmnts wr takn with variabl voltag at a fixd frquncy obtaining a st of voltag and currnt wavforms. From ths rsults studnts can comput th B-H hystrsis cycls of th matrial using th quations (8) and (9). From a saturatd hystrsis cycl studnts can obtain magntic paramtrs such as rmannc, saturation induction, and corcitiv fild. Also cor losss can b computd calculating th ara of th st of cycls. This procdur can b rpatd at diffrnt frquncis. 1 Bt vt dt. (9) N A H t t Ni. (10) This activity might hav som risk dpnding on th voltag and frquncy of th xprimnt. This activity has bn trid at th Carlos III Univrsity with undrgraduat studnts with good rsults. As an xampl, w show in Figur 11 a st of xprimntal hystrsis loops of th Frroxcub 3F3 matrial masurd at 20 khz by th studnts. Th procdur without losss (th inductor modl consists of an inductanc) can b implmntd in th PSIM softwar which in turn works with Matlab and Simulink. Ncssary supplis: Prsonal computr with th following softwars: AutoCAD to dsign th inductors, Maxwll softwar to modl, and th PSIM and Matlab- Simulink softwars to simulat. C. Third lvl This lvl can b applid to postgraduat studnts, for xampl as a final projct. Hr, th complt procdur is applid to diffrnt gommtris and sizs allowing th studnts to study th influnc of th gap-thicknss on th magntic proprtis. Th cor losss ar includd in th procdur (th inductor modl consists of inductanc and rsistanc) and th rsults ar validatd with xprimntal masurmnts for th cas of a sinusoidal wavform. Ncssary supplis: Prsonal computr with th following softwars: AutoCAD to dsign th inductors, Maxwll softwar to modl, and th PSIM and Matlab- Simulink softwars to simulat. Magntic componnts and powr sourc to supply th sinusoidal wavform and an oscilloscop to masur th wavforms. D. Fourth Lvl This lvl can b applid to postgraduat studnts that show intrst in rsarch in powr lctronics. Thy can carry out all th stps of th procdur (magntic and lctrical modling) and can validat it for th cas of a typical squar wavform as is widly usd in powr lctronics. Thy can vrify th complt modl of th inductor consisting of th L-I and R-I rms curvs, considring powr losss in th cor. To validat th wavforms studnts build a ral powr convrtr, for xampl a DC-DC powr convrtr as shown in Figur 12. Inductor with an RM cor Fig.11 Exprimntal hystrsis loops of a Frroxcub 3F3 matrial masurd at 20 khz for diffrnt maximum valus of th H and B magntic filds (Hp, Bp). B. Scond lvl This lvl focuss on th analysis and simulation of th inductors with frrit cors using Finit Elmnt Analysis. Through th us of th Maxwll softwar studnts can visualiz for ach xcitation currnt valu th flux lins, B and H fild distributions as shown in Figur 6 and comput from ths data th magntic flux from th linar to th saturation rgion. This softwar has a visual intrfac and provids a physical and xtrmly usful prspctiv which hlps undrstand concpts that ar difficult for th studnts. Th instructors can propos diffrnt gomtris and compar 2D to 3D rsults. Fig.12 Ral DC-DC powr convrtr. Th inductor includd in th powr convrtr should b a frrit cor of th sam typ as th on usd in th magntic modling, for xampl an RM frrit cor. Ncssary supplis: Prsonal computr with th following softwars: AutoCAD to dsign th inductors, Maxwll softwar to modl, Origin for th numrical calculations and th PSIM and Matlab-Simulink softwars to simulat. Magntic componnts and othr componnts to build 541

6 th powr convrtr and an oscilloscop to masur th wavforms. IV. Conclusions Powr lctronics is a difficult subjct for studnts as it is an intrdisciplinary subjct by natur, which rquirs knowldg of digital and analogu lctronics as wll as of simulation. Apart from this th matrials usd in powr lctronics includ inductors or transformrs with soft frrit cors that show a nonlinar bhavior and involv various variabls such as numbr of turns, gomtry and siz. Thus th modling of th frrit inductors is not an asy task. It is ncssary to rsort to th masuring of magntic proprtis, modling and simulating tchniqus and Finit Elmnt programs. In this papr w hav proposd a procdur in which diffrnt softwars ar usd togthr and which is suitd to th modling th inductors with frrit cors for us in circuit simulators. This procdur uss diffrnt programming and modling tchniqus coupld togthr: a Computr Aidd Dsign program (AutoCAD), a Finit Elmnt Analysis program (Maxwll), two scintific calculus programs for th numrical solving of drivativs and intgrals (Origin and Matlab), a numrical simulation program (Simulink) combind with Matlab and finally an lctronic circuit simulation program (PSIM). W hav dividd th papr in two parts. In th first part w hav shown our procdur and som illustrativ xampls. In th scond part w hav focusd on its application to studnts of diffrnt ducational stags (undrgraduat and postgraduat) and hav commntd on th rquird matrials. Th us of th procdur could motivat th studnts and hlp to undrstand th bhavior of th circuits and nonlinar physical phnomna involvd in powr lctronics. Rfrncs [1] E. C. Snlling. Soft Frrits, Proprtis and Applications, Buttrworths, London U.K. (1988). [2] G. E. Fish, Proc. IEEE, 78, [3] Frroxcub, Data Handbook Soft Frrits and Accssoris, 2008, [4] A. Goldman. Magntic Componnts for Powr Elctronics, Springr (2002). [5] D. C. Jils and D. L. Athrton, J. Magn. Magn. Matr. 61 (1986). [6] D. C. Jils and D. L. Athrton, J. Magn. Magn. Matr. 92 (1990). [7] V. J. Thottuvlil, T. G. Wilson, H. A. Own, Jr. IEEE Trans. Magn. 5, 1 (1990). [8] D. C. Jils, J. B. Tholk and M. K. Dvin, IEEE Trans. Magn. 28, 1 (1992). [9] L. Zgadi, J. J. Roussau, B. Allard, P. Tnant, and D. Rnault, IEEE Trans. Magn. 36, 4 (2000). [10] P. Nakmahachalasint, K. D. T. Ngo, and L. Vu-Quoc, IEEE Trans. Powr Elctron. 17, 4 (2002). [11] M. Sippola and R. E. Spponn, IEEE Trans. Powr Elctron. 17, 5, (2002). [12] P. R. Wilson, J. N. Ross, and A. D. Brown, IEEE Trans. Powr Elctron. 17, 1 (2002). [13] P. R. Wilson, J. N. Ross, and A. D. Brown, IEEE Trans. Magn. 40, 3 (2004). [14] D. Lin, P. Zhou, W. N. Fu, Z. Badics, and Z. J. Cnds, IEEE Trans. Magn. 4, 2 (2004). [15] Y. Zhai and L. Vu-Quoc, IEEE Trans. Magn. 41, 7 (2005). [16] W. A. Roshn, IEEE Trans. Powr Elctron. 22, 1 (2007). [17] R. A. Salas, J. Plit, E. Olías, and A. Barrado, IEEE Trans. Magn. 44, 7 (2008). [18] R. A. Salas and J. Plit, IEEE Trans. Magn. 47, 10 (2011). [19] D. Zhang and J. E. Fltchr, IEEE Trans. Instrum. Mas. (2012). 542