XII International PhD Workshop OWD 2010, October Modeling And Analysis Of Buck-Boost DC/DC Pulse Converter

Transcription

1 X nternatonal Ph Worshop OW, 3 6 October Moelng An Analyss Of Bc-Boost C/C Plse Converter Marcn Pawla, Kelce nversty of echnology Abstract he bc-boost C/C converter strctre has been analyze n the paper. Smplfe moel of converter was se for theoretcal analyss. Smplfcaton s base on assmpton that capactor voltage s nearly constant n molaton pero. Analyss was performe for both cases: Contnos Crrent Moe (CCM) an scontnos Crrent Moe (CM) together wth voltage step own an voltage step p. eslts of theoretcal analyss have been presente an were verfe by smlaton. CA crct smlator was se for smlaton. Smlatons confrm reslts of smplfe theoretcal analyss.. ntrocton Power converson technology wth the smallest possble loss s now a basc level of research n the fel of power electroncs. Strvng for effcent se of electrcty reslte n vrtally complete wthrawal from the se of lnear electronc power spples [] an replaces them wth systems of power electroncs plse converters [3]. here has been a tenency to apply hgher an hgher freqency of swtchng converters. hs allows a recton of the reactve elements of the system []. herefore, moern converters have been apple n all nstres, as well as n electronc an electrcal eqpment of everyay se. Power electronc converters are nonlnear systems. n esgnng converters an control systems there are se both mathematcal moelng of ther behavor, an software, capable of smlatng varos stages of wor n orer to verfy the correctness of the propose soltons to esgn an control algorthms. Plse C/C converters are wely se n power electronc systems, the C rve system, an are the basc blng blocs of complex strctres converters [4,5,7]. A goo nerstanng of the prncples of ther operaton s a prereqste for the analyss an esgn of moern plse power converters.. Analyss of the strctre of the bc-boost converter he sty aopte a smplfe methoology for moelng strctres of plse C/C converters. he analyss ses the followng smplfyng assmptons: Electronc connectors are eal: the voltage rop on the connector s zero (eal short crct), an at swtch off the crrent s zero (perfect pase); Elements of the reactance of the converter are eal: they are not n actve power losses of electrcty resstances of magnetc cols are zero an capactors o not show any leaage of the electrc charge; hans to losslessness electronc connectors an components an losslessness elements (resstance) the plse nverter n ts strctre s a lossless system - t leas to the assmpton that the coeffcent of energy effcency of the converter s eqal to nty; t was assme that capactances occrrng n the nverter crcts are of sch large vales that yo can set p ther voltage stablty rng the PWM molaton, whch allows replacng them wth the voltage sorces. We analyze the bc-boost converter voltage [4,7,8,9].. Analyss of the bc-boost voltage converter agram of the bc-boost s shown n Fg.. Fg.. he strctre of the bc-boost converter. 37

2 Fgre shows the sbsttton patterns corresponng to fferent states of ths nverter operaton. n cases of persstent states of the there are states of wor llstrate n a) an b), n the case of scontnos crrent of the magnetc col there appear states gven n ponts a), b) an c). Fg.. Eqvalent crcts corresponng to the bc-boost converter, wor states. n the operaton of the converter the smlarty of converters can be notce: ecreasng an ncreasng voltage [6]. Smlarly to the booster converter there appear the two stroe transfers of energy from the power sorce to the electrc loa. n the state of wor when the transstor connector s swtche on, shown n Fgre a process of storng energy from the power sorce taes place n a col magnetc fel. When yo swtch off the transstor connector, the E transstor taes over the crrent, as shown n Fgre b. nctance energy s transferre to the loa. Snce the crct n whch the transfer of energy to the loa occrs, has no seral connecton to the power sorce of the ecreasng magnetc col crrent, so t s possble to obtan the otpt voltages smaller than the npt voltage. hs s analogos to the operatng state of a converter lowerng the voltage when the transstor connector s swtche off. f the state of Fgre b lasts long enogh to come to a complete scharge of power nctors, then the E connector swtches off an there occrs the stats as llstrate n Fgre c. Fgres 3 an 4 llstrate the ealze voltage tme wave forms of the transstor voltage, oe voltage as well as the nctance an crrent voltages, for the case of contnos (pont a) an scontnos (pont b), resltng from the theoretcal analyss of the bc-boost converter for the case of lowerng voltage (Fg. 3a, Fg 3b) an for rasng the voltage (Fg. 4a, Fgre 4b). Fg.3. Voltage an crrent waveforms for the case of contnos (pont a) an scontnos (pont b) at the moe of voltage lowerng. 38

3 he average vale of the loa crrent: - n the moe of operaton wth contnos =, (6) - n the moe of operaton wth scontnos =. (7) he average vale of the : - n the moe of operaton wth contnos Fg.4. Voltage an crrent waveforms for the case of contnos (pont a) an scontnos (pont b) at the moe of the voltage ncrease. Below are the basc formlas whch characterze mathematcal relatonshp escrbng the scsse converter worng n contnos an scontnos moe wth whch rectly reslts from the analyss of nval states of ts wor. he parameters are set n a moe of a fxe wor of the converter. At the moe of the set wor the average nctance voltage vale an the average vale of the capactor crrent s zero. he fllng factor of PWM wave: ton = = ton f () where: f - means the PWM wave freqency. he relatve oe concton tme: - n the moe of operaton wth contnos (CCM), () - n the moe of operaton wth scontnos (CM) f =. (3) he average vale of voltage at the loa: - n the moe of operaton wth contnos =, (4) - n the moe of operaton wth scontnos =. (5) = ( ) (8) - n the moe of operaton wth scontnos ( + ) =. (9) f he average vale of the sorce crrent calclate assmng that there are no energy losses n the converter system: P = - n the moe of operaton wth contnos = P, () =, () - n the moe of operaton wth scontnos =. () he maxmm vale of the : - n the moe of operaton wth contnos ( ) f max = +, (3) - n the moe of operaton wth scontnos max = =. (4) f he mnmm vale of the : - n the moe of operaton wth contnos 39

4 ( ) f mn =, (5) - n the moe of operaton wth scontnos mn =. (6) he bonary vale of nctance resltng from the conton of contnty of the nctance crrent: ( ) mn =. (7) f he contnty of the oe crrent for mn. he rpple coeffcent of the otpt voltage: r = (8) - n the moe of operaton wth contnos r =, (9) Cf - n the moe of operaton wth scontnos ( f) r =. () f C he analyss of mathematcal relatonshps shows several mportant characterstcs of the converter ner conseraton. n the expresson (4) escrbng the relatonshp between the npt voltage an the otpt appears a factor responsble for lowerng the voltage an the factor responsble for ncreasng the voltage. Analogosly, yo can compose expresson efnng the relatonshp between the otpt an npt crrent [6]. he contnty of the crrent n the nctance epens on: the vale of nctance, the npt voltage, the fll factor, the loa an the PWM molaton freqency. he operatng moe shown n Fgre n c), occrs when the reaches a vale of zero rng the molaton. he relatve oe concton tme, can be etermne accorng to the relaton (3). he voltage rpple factor etermnes the qalty of the otpt voltage reglaton... Smlaton of the bc-boost converter he mathematcal moel of the converter an ts frther analyss were verfe sng smlatons performe wth the crct smlator of power electroncs systems CA. For ths smlaton moel was se to plse C/C converter shown n Fgre 5. he analyze crct s compose of the control component an the strong crrent component. he steerng part comprses: the plse generator controllng the transstor connector, crrent sensors:,,,, C. he strong crrent component comprses: the C voltage sorce, transstor connector, oe connector, nctance, capactance C an resstance. o regster, voltage an crrent wave forms on/n the varos components, crctry s eqppe wth measrement systems, whch ncle ammeters an voltmeters. Fg.5. Smlaton agram of C/C converter lowerng or rasng the voltage. Voltage an crrent waveforms, shown seqentally n Fgres 6, 7, 8 an 9 were obtane as a reslt of the smlaton system shown n Fgre 5. Fg.6. Waveforms of voltages an crrents of the bc-boost converter for the case of contnos crrent moe, recng nctance voltage. C C Fg.7. Waveforms of voltages an crrents of the bc-boost converter for the case of scontnos crrent moe, recng nctance n voltage. 4

5 Fg.8. Waveforms of voltages an crrents of the bc-boost converter for the case of contnos crrent moe nctance voltage ncrease. Fg.9. Waveforms of voltages an crrents of the bc-boost converter for the case of scontnos crrent moe nctance voltage ncrease. Waveforms of crrents an voltages obtane by smlaton are smlar to the ealze theoretcal waveforms. he corse shows the otpt voltage rpple, whch reslts from the aopte to smlate a fnte capactance. 3. Comparson of reslts of theoretcal analyss wth smlaton reslts ables an compare the parameter vales of the consere converters esgnate on the bass of theoretcal analyss wth the parameters obtane from the smlaton sng CA software. he average vales of voltages an crrents from the smlaton were obtane as a reslt of harmonc analyss. hs comparson ncates the accracy of the reslts of both methos of analyss of converters. ab.. Comparson of reslts of theoretcal analyss wth smlaton reslts of the bc-boost converter operatng n the moe of voltage recton KN OF ANAYSS Bc-boost converter n the moe of recng the otpt voltage Mathematca Smlator CA Physcal qantty C C nt CCM CM CCM CM nverter parameters f Hz s, C F,47 V 5,4 Ω H,4,,4, Calclaton Smlaton V 33,33 44,7 33, 44,65,666,36,656,3,,96,993, ,757 4,38 A max 5,77 5,46 9,999 mn,77,46 5 4,999 9,999 -,447 -,44 r,4,64,5,643 ab.. Comparson of reslts of the theoretcal analyss wth smlaton reslts of the epressve-boost converter operatng n the moe of voltage ncreases KN OF ANAYSS Bc-boost converter n the moe of rasng the otpt voltage Mathematca Smlator CA Physcal qantty nt CCM CM CCM CM nverter parameters f Hz s, C F,47 V 5.4 Ω H,7,4,7,4 Calclaton Smlaton V 6, 37,5 6, ,55 6,875 3,87 6,688 3,734 8,96 3,743 8,35 6,79 5,783 6,74 6,5 A max,88 68,75,793 68,739 mn,697,68,85 68,75,84 68,739 -, -,97 r,58,86,59,86 4. Conclson Smlaton sty of plse converter C/C confrms the reslts obtane by smplfe mathematcal analyss. hs means that the erve epenences are correct an can be se to correct the esgn elements of the nverter. Bblography [] BOKOWSK A.: Zaslane rzązeń eletroncznych, WKŁ, Warszawa 99 4

6 [] CKO.: Energoeletrona - łay wysoej częstotlwośc, WPB, Bałysto 7 [3] FEENCZ O.: Zaslane łaów eletroncznych zaslacze mplsowe, WN, Warszawa 989 [4] HAMAN M..: Welopozomowe falown napęca, Fnacja ozwoj Aaem Morsej w Gyn, Gyna 6 [5] NOWAK M. BAK.: Poran nżynera energoeletrona, WN, Warszawa 998 [6] PAWAK M.: Moelowane analza mplsowych przeształtnów C/C przeształtn obnżający powyższający napęce, Wyawnctwo Naowe nstytt echnolog Esploatacyjnej Państwowego nstytt Baawczego, aom, s [7] NA H., BAK.: eora przeształtnów, Ofcyna Wyawncza Poltechn Warszawsej, Warszawa 3 [8] NA H., BAK.: Energoeletrona, WN, Warszawa 994 [9] NA H., KAŹMEKOWSK M.: Atomatya napę przeształtnowego, PWN, Warszawa 987 Athor: Marcn Pawla MSc. Kelce nversty of echnology Al. ysącleca Państwa Polsego Kelce tel. (4) fax (4) emal: m.pawla@t.elce.pl 4