Improved Research on the Transformer-Inductor Simulation Model of Magnetics

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1 Jounal of Eletoni Reeah and Appliation OPEN Impoved Reeah on the Tanfome-Induto Simulation Model of Magneti Jiang Liyuan, Liu Baoyuan, Zhang Li Beijing Jiaotong Univeity Haibin College, Hebei 0600, China Abtat: Tanfome-induto imulation model not only eflet the haateiti of magneti path and iuit, but alo bing in magneti omponent that efleted the paaiti apaitane. Thee ae futhe eeah, tit deivation and magneti iuit equivalent fo the model in thi atile. Unde the ondition of onideing hyteei, atuation effet we an onlude a new modeling and it equivalent, whih an make the magneti uve and haateiti get bette fitting. It how that the tanfome-indutane imulation model i eay to pead and ue. Key wod: Momponent; Simulation model; Nonlinea; Hyteei B-H uve Publihed online: 30 th Nov 07 Coeponding autho: Jiang Liyuan, @qq.om Intodution At peent, baed on the magneti dual iuit method, the mathematial model of magneti devie an be divided into two ategoie: magneti iuit-dual iuit equivalent model and gyoope-apaitane equivalent iuit model. In the two model, the fome annot eflet the magneti path paamete, and the latte an eflet the eleti iuit and the magneti iuit haateiti of magneti omponent, but beaue it i a magneti guide with apaitive imulation, it i eay to be onfued with the onept of the tay apaitane of apaitane imulation in high fequeny. In thi pape, a new model - tanfome-indutane imulation model (T-I model) i tudied, and thi model not only utilize the magneti iuit-dual iuit tanfom method, whih an fully and lealy eflet the magneti iuit of magneti omponent and the magneti iuit haateiti, but alo the paamete that eflet the paaiti effet an be onveniently joined. In thi pape, the magneti dual iuit method i adopted to ondut modeling and theoy onluion on the imulation of the magneti hyteei effet of magneti omponent and atuation effet on T-I model. [] The Impoved T-I Model of Magneti Component. The Impoved T-I Model of Magneti Component The igue i the impoved T-I model. Aoding to the magneti iuit-dual iuit analogou elation, the magneti potential in the magneti omponent an be ompaed with patial eleti uent of magneti iuit in the model, and the magneti ondutane of magneti omponent an be ompaed with the patial nonlinea eitane of magneti iuit in the model. The haateiti of magneti hyteei in the model ae imulated by the eie onnetion (getting nonlinea eitane) of the fixed eitane R and the ontolled voltage oue. Nonlinea haateiti ae imulated by the paallel onnetion of the fixed indutane L and ontolled uent oue; Satuation haateiti ae imulated by the paallel onnetion of the fixed ondutane G and ontolled uent oue. [] Ditibuted unde eative ommon liene 4.0 Volume, Iue 3 9

2 igue Impoved T-I model igue T-I model by nonlinea eitane.. Nonlinea Indutane T-I Model Conideing Magneti Hyteei On the imulation of the haateiti of magneti hyteei of magneti omponent, nonlinea ontolled voltage oue (by z ontol) and R the eie onnetion ae led in the model fo the pupoe of eduing the influene of exitation oue ize on the hyteei loop width, a hown in igue [3-5]. The funtional equation of ontolled voltage oue i hown in the following fomula, whih i the eult of the implified equation in efeene [6]. m m ( ) ( ) ( R ) () z z When the hyteei popety i onideed only, the following elation an be obtained fom igue. ( R ) m R () Theefoe, the equivalent nonlinea eitane obtaining f banh an be woked out: R R R (3) m m eq Simulating haateiti of magneti hyteei of the magneti omponent by eitane onfom to the phyial mehanim. Beaue the eitane voltage and z meet the elative efeene dietion, the patial peue of the eitane will hinde the hange of the flux, whih i hown a the magneti hyteei haateiti... Nonlinea Indutane T-I Model Conideing Magneti Satuation On the veifiation of the atuation haateiti of the model, the hange of inentive magneti potential andom, o the nonlinea ontolled uent oue ontolled by g (diffeent fom ) and the ondutane G paallel ae timulated in thi pape, a hown in igue 3. [6] i igue 3 T-I model by nonlinea ondutivity 0 Ditibuted unde eative ommon liene 4.0 Volume, Iue 3

3 The nonlinea ontolled uent oue an be deibed in the following fomula: 3. The Simulation of Input Paamete A mentioned above, a nonlinea ontolled uent oue ( ) ( ) n ( ) n g g g G (4) f i ued to imulate the nonlinea haateiti of the The following elation an be obtained fom igue 3: ( G) n (5) G g g So the equivalent nonlinea ondutane of G banh i (6) ( ) n Geq G g G G When the voltage value of the both end of the ondutane G i le and the flux i le, the ontolled uent oue i oepondingly mall, and the magneti potential i almot alway on the ondutane G, o the equivalent magneti guide i G eq. Natually, when the voltage value of the both end of the ondutane i moe and the flux i moe, the figue of ( ) will ineae exponentially. Beaue the magneti potential i mainly povided by the ontolled oue, if the i appoximately zeo, the magneti omponent i at the atuation tate. 3 The Calulation of the Paamete in the Model The input paamete of the model an be divided into two type: the mateial paamete and geometi paamete of magneti oe. The mateial paamete inlude atuation magneti flux denity field intenity foe B at g, atuation magneti H at, eidual flux denity B, oeive H, elative pemeability B H egment of uve, of linea uve and B H o on. And the geometial paamete inlude the aea effetive magneti iuit, and the length Ae le of the of the effetive magneti iuit. The following paamete ae ued to ondut the model paamete, whih inlude the paamete influening magneti hyteei haateiti R,, m and the paamete influening the atuation haateiti G,, n. [6] magneti omponent model. The b ( i 3,5, 7, ) of an adopt the alulation method of data fitting. Within a etain ange of peiion, the fomula an be implified to the fomula (7), and that i, a etain highe tem i olely ued to imulate the nonlinea of magneti oe. Namely, a b a n n = f + n f (7) The patial imulation of thi ontolled oue will be diued below to how that thee i little diffeene uing fomula (7) to ondut the implified analyi. Aoding to the magnetization uve tandad in the magneti oe manual, the fomula (7) i onveted to the elational fomula, between H and B whih i a follow: a A b a A H B B l l n n = e + n e n (8) e In the fomula, aea and the e Ae i i the effetive magneti ondutive l e i the effetive magneti iuit length. [3] 3. The Conluion of Magneti Hyteei Paamete Beaue the and follow the iuit theoy in the model, the equation and the olving diffeential equation among the and eah banh an be lited dawing on Ampee' ule, the elationhip between and an be woked out, and the magneti hyteei paamete an be alulated by ombining with the point ( B, H ), ( B, H ), the oeponding (, ), and (, ), of the fundamental magnetization uve. 3.. Calulation R om the igue 4 imulating indutane magneti hyteei effet: = + f + L (9) Namely, Ditibuted unde eative ommon liene 4.0 Volume, Iue 3

4 a b a n n = + f + n f (0) When the magneti oe i unatuated, it atifie the following fomula: R () Without lo of geneality, ha n n R a bn a int () = inw t Beaue the non-odd nonlinea diffeential equation olving i tivial, the numeial value i not eay to obtain, and it' alo beaue when the hyteei effet i imulated, the main paamete ae the emanene (oeponding (oeponding B ) and the oeive foe H ), and at the ame time, beaue the highe powe of the nonlinea equation i vey mall in the viinity of zeo, it an be appoximately believed and ( a R ) ( a ) (7) R Then, the equivalent nonlinea eitane Req in the banh i ued to eplae R in equation (7) and the value of R i detemined by 0. R a (8) 3.. Selet m A an be een fom equation (3), the thee paamete of R, and m all influene the value of. To enue that the value of Req i not negative, the value of m hall be the odd numbe. om the above analyi, a m ineae, the impat of timulated magneti hyteei of magneti piee will be malle, o the eletion of m hall be a lage a poible. [5] 3..3 Calulate Replae R in equation (7) with the equivalent nonlinea i only influened by L = af when the hyteei effet i imulated. Theefoe, the expeion an be obtained: eitane though 0. Req of, and the value of i detemined R a int (3) Solve the diffeential equation, and the eult i hown in equation (4): R ( ar in t o t) a R (4) Theefoe, the magneti potential and flux have etablihed a paameti equation with the paamete t, and if t i emoved, the equation expeing the elationhip between and an be obtained ( a R a R ) (5) R Subtitute equation (3): int a (6) The following equation an be obtained by emoving the intemediate vaiable t fom equation (4) and equation () a R R R (9) m m ar 3.3 Calulation of Paamete of Satuation 3.3. Calulation of G The following magneti potential elationhip an be dedued fom the intodution of the nonlinea ondutane T-I model (igue 3): = G + f + L (0) Among them, G epeent the um of the uent flowing by the ondutane and the ontolled uent oue in paallel theewith. If linea ondutane i ued fo imulation alulation, then G a int () Equation () i a diffeential equation, and the following an be obtained by olving it: Ditibuted unde eative ommon liene 4.0 Volume, Iue 3

5 a ( int o t) G G a G () Magneti potential and ontitute a et of paameti equation in t a ( in t o t) G G a G (3) The following an be obtained by eliminating the paamete t fom the above equation ( g ) ( a ( G ) g ) G G a a a (4) The following an be obtained fom 0 G= a w - (5) g g 3.3. Seletion of n A an be een fom equation (6), a flux ineae, G g n g n a ( G) G (6) The expeion of paamete an be obtained fom equation (6) G a G n n (7) 4 Simulation Realization and Reult of the Model 4. Simulation of Nonlinea Indutane Model Ue the elationhip between magneti field intenity H and magneti indution intenity B in the above equation (8) to ay out theoetial imulation. To failitate analyi, take effetive magneti ondutivity ( ) g ineae exponentially, and when eahing a aea m = ), A e = m (oeponding to e 000 etain degee, the magneti potential will mainly fall on the ontolled oue, while the magneti piee will be atuated. om alulation, we an ee that to enue that the value of numbe. [7] Calulation of Geq i non-negative, n hall take the odd Ue the equivalent nonlinea eitane G eq of G banh to eplae G in equation (3), and the value of an be alulated fom G = f= 0 g. Theefoe - 9 b n = 3. 0 (hee, n b i a given value) to ondut quantitative analyi, and the bai magneti uve i hown in igue 4 (a). [8] Uing the equivalent iuit in igue 3 to imulate, and analog paamete ae et a follow: (t) = 500in(34t) A, L =.53mH. The bai magneti uve obtained by model analog i hown in igue 4 (b), howing that analog eult ae onitent with the theoetial analyi. (a) Theoetial analyi uve (b) Simulation uve igue 4 Bai magneti popetie of imulation Ditibuted unde eative ommon liene 4.0 Volume, Iue 3 3

6 4. Hyteei Model Simulation The eleted imulation paamete ae a follow: = φ 0.4Wb, = 500A, = 0, m = 7 and othe paamete ae the ame a befoe. Though alulation, it an be obtained that eitane R = 0.65Ω, = and value of amplitude of exitation ae 500, 750 and 000. The hyteei effet uing nonlinea eitane imulation and the eult oeponding to the analog hyteei uve ae hown in igue 5. It an be een fom the figue that, with the intodution of the T-I model of non-linea eitane, the imulation oeivity and eidual magnetim will not be geatly affeted by m. [9] Diffeent ae given, the value of will be alulated aoding to equation (9) fo imulation aoding to the alulated and imulation eult ae hown in Table. By ompaing theoetial and analog value, it an be een that the analog fowad magneti value i lightly lage than the theoetial value while the evee magneti value i lightly malle than the theoetial value. Theefoe, it an be poved that analog eult ae baially onitent with the theoetial analyi eult. Theefoe, paamete an be fully detemined by uing equation (9). Table Compaion between theoetial and imulation value of unde vaiou paamete Given Calulated C Simulated igue 5 Simulation hyteei uve unde vaiou exitation Anothe impotant paamete that eflet the haateiti of the hyteei loop i the eidual magnetim B (i.e. the oeponding ). With futhe 4 Ditibuted unde eative ommon liene 4.0 Volume, Iue 3

7 analyi of the yntheti hyteei uve and in tem of non-etangula magneti mateial, the paamete a an be detemined by the following equation a (8) A fo etangula hyteei mateial, a the magneti pemeability i vey lage, it an be dietly detemined aoding to a l A (9) e e 0 e By efeing to the B H uve in the magneti oe data manual, tuning point exit fom the linea to atuation egment. Selet a value of magneti flux denity B at tuning point, whih oepond to two magneti field intenity Hmin and H max, and the aveage value H of the two ae taken a the magneti field intenity in the bai magneti uve, theefoe H = ( H + H ) (30) min max B and H ae equivalent to and, whih will be ubtituted into equation (7) along with and to obtain value of paamete n and b n. ln( a ) ln( a ) n ln ln a bn n n a (3) 4.3 Chaateiti of Satuation Simulation By efeing to the magneti oe manual, ue the lope and oeponding to vaiable of the B H uve to imulate the haateiti of atuation. Duing alulation, the taken paamete ae the ame a befoe, take the deivative of the paamete in equation (3), and the following an be obtained d a G d G a G ( ) (3) Set the above equation d d 0, and atuated magneti potential obtained. at and magneti indution intenity Hat an be 3 3 G a at a G a G a G a at a G Simulation uve Data manual uve igue 6 Simulation of atuation model In equation (33), a a G i muh malle than the peviou value, whih an be omitted in alulation. Calulated value of the atuated magneti potential and atuated magneti indution intenity an be dedued, and it an be een that theoetial and alulated value ae vey loe. [0] Ditibuted unde eative ommon liene 4.0 Volume, Iue 3 at at 0.5( NegativeRounding) (34) When veifying, the equation an be egaded a the quadati equation with G a the unknown element. 5

8 d d G G a a 0 (35) d d A G 0, it an be known that in the equation, 0, and the oeponding elationhip between d φd and an be obtained. d d 4 0 a a (36) d d Set = 0, and in thi ituation, G ha the unique anwe, and the d d expeion an be obtained. d a d (37) 4 4 d (0. 0 5) 30 5 (38) 4 d By uing the above paamete of a 399 and 500, G =0.387, o d φd and an be obtained. Compaed it with uve value in the magneti oe data manual to pove that thi model i patial and appliable. [] Table Compaion between theoetial and imulation value of d d unde vaiou paamete theoetial value d / d theoetial value ɸ theoetial value manual value d / d manual value ɸ manual value Conluion ion oe elet pial film magneti piee, and it winding ai gap i g =0.4mm; the amount of leakage The expeimental platfom i a fou-phae (two-phae high) VRM tet platfom, it ontol hip i ISL6558EVALZ, the input voltage i VDC, the output voltage i.5vdc, the ontol hip i ISL6558, and the with tube MOSET elet HU7643S3S; the indutane of the integated magnet piee i L =00.4µH and L =0.µH; the indutane i about 4.µH. Afte veifiation, eveal eult in the following figue an be obtained. The igue 7 i the tigge wavefom of with tube, igue 8 i the indutane uent of ingle hannel, igue 9 i the uent wavefom of two-phae indutane and igue 0 i the total output uent. [] igue 7 The tigge wavefom of with tube igue 8 The indutane uent of ingle hannel 6 Ditibuted unde eative ommon liene 4.0 Volume, Iue 3

9 igue 9 The uent wavefom of two-phae indutane igue 0 The total output uent 6 Conluding Remak In thi atile, a new T-I imulation model of magneti piee i dedued theoetially, whih olve the poblem that effet degee of the exitation on the width of hyteei uve when the linea eitane imulate hyteei. At the ame time, the method of detemining the model and it paamete ae given. The B-H imulation uve i obtained by giving etain exitation and mateial paamete, and be ompaed with the data manual uve. The eult how the auay of the model and model paamete. Refeene [] Zengyi Lu, Wei Chen. Multi-Phae Induto Coupling Sheme with Balaning Winding in VRM Appliation[C]. Po. IEEE APEC, 007: [] Qianhong Chen, Yang eng, Linquan Zhou, et,al.. Ative Clamp Poitive Exitation Integated Convete with Minimized Output Ripple[J]. Poeeding of the CSEE, 009,(03). [3] Hongzhu Li, Liyuan Jiang, Wei Jia, et,al. Reeah on the tanfome-induto imulation model of magneti[j]. Jounal of Powe Soue Tehnology, 0, -. [4] Cheng D K, Wong L, Lee Y S. Deign, Modeling, and Analyi of Integated Magneti fo Powe Convete[C]. IEEE Powe Eletoni Speialit Confeene, 000,: [5] Liyuan Jiang. Reeah on the Equivalent Ciuit Model of Thin ilm Magneti Component Unde the Magneti Integation Tehnology[D]. Liaoning: Liaoning Tehnial Univeity, 0. [6] Yugang Yang, Hongzhu Li, Jianlin Wang, et,al. Appliation of Integated Magneti Piee Whoe DC-bia an be Redued in DC/DC Convete[J]. Poeeding of the CSEE, 005,5(): [7] Qianhong Chen, Ligang Xu, Zhuyun Li, et,al. Impoved Gyoope-Capaitane Nonlinea Magneti Coe Simulation Model[J]. Tanation of China Eletotehnial Soiety, 009,4(4): 4-. [8]Liang Yan, Bad Lehman, Bette. Undetanding and Synthei of Integated Magneti with Simplified Gyato Model Method[J]. Canada, IEEE-PESC, Vanouve, Bitih Columbia, 00: [9] R.T. Chen, Y.Y. Chen. Synthei and Deign of Integated-Magneti-Ciuit Tanfome fo VRM Appliation[J]. IEE Po.-Elet. Powe Appl. 006,53(3): [0] Wong L P, Lee Y S, Cheng D K. A New Appoah to the Analyi and Deign of Integated Magneti[C]. IEEE Powe Eletoni Speialit Confeene, 00:96-0. [] Jieli Li, Anthony Statako, Aaon Shultz, et,al. Uing Coupled Induto to Enhane Tanient Pefomane of Multi-Phae Buk Convete[C]. Po. IEEE APEC, 004:89-93 [] Yong Zhou, Zhimin Zhou, Ying Cao. abiation and Pefomane of e-baed Magneti Thin ilm Induto fo High-equeny Appliation. Jounal of Magnetim and Magneti Mateial, Ditibuted unde eative ommon liene 4.0 Volume, Iue 3 7