W.-Toke Franke, student member, Malte Mohr, Friedrich W. Fuchs, senior member

Transcription

1 omparson of a Z-ource Inerter and a oltage-ource Inerter ked wth a D/D- Boost-onerter for Wd urbes oncerng her Effcency and Installed emconductor ower W.-oke Franke, student member, Malte Mohr, Fredrch W. Fuchs, senor member Insttute of ower Electroncs and Electrcal Dres hrstan-albrechts-unersty Kel Germany Abstract In ths paper the power losses of both Z-sourceerter ( and oltage-source erter lked wth a dc/dc boost erter (IB are compared. heore the crcuts are smulated tme doma by means of numercal methods whereas the swtchg and conductg losses are calculated separately and parallel. A ma focus s on mathematcal descrpton of the current rms through the s of the to dere the conductg losses. It s shown that the losses of the dode the dc lk of the has a hgh percentage of the al power losses and cannot be neglected. Besdes that the choce of the modulaton method has a hgh fluence on the power losses of the as well. Based on the calculated power losses the effcency and the stalled semconductor power are estgated and compared for dfferent put oltages. he results show that for an output oltage of 4 the IB topology outperforms the almost all operatg pots. he reason s that for low put oltages the IB topology boosts the put oltage to lmted 6 and the I works wth a modulaton dex of about ery effcently. Howeer the has to boost the put oltage to much hgher alues, sce for hgh oltage gas long shootthrough-states are essental. Howeer, long shoot-throughstates are comg along wth long zero-states whch causes a buck behaor. I. INODUION he Z-ource-Inerter ( s a promsg new erter that has been dscussed seeral papers [][][3]. It s sutable for smlar applcatons as a three phase oltage source erter lked wth dc to dc boost conerter (IB [4][5]. Both topologes are able to boost a low dc oltage and ert t to a three phase oltage. ossble applcatons for both erters are connectg fuel cells, photooltac cell or wd turbes wth synchronous maches to the grd. In [4], [5] and [6] comparsons between these two topologes hae been presented. In addton, ths paper deals wth the power losses of all semconductor deces, cludg the dode the dc lk. A new approach of calculatg the effecte power losses of IB and the are presented, respectely. Based on these results the effcency and the necessary stalled semconductor power of both topologes s dered for a wde range of dfferent put oltages and fally compared to each other. For the deraton of the equatons whch are descrbg the losses of the ery extense calculaton hae been done whch cannot be presented ths paper due to the lmted space. he deratons wll be presented another publcaton. he paper s organzed as follows: In secton II the system confguraton and control s descrbed. he thrd secton deals wth general modelg of power losses semconductors. In sectons I and the power losses of the IB and the are ealuated respectely. In the next secton effcency and stalled power semconductor ratg are troduced. In secton II the method of smulaton s descrbed whle III the possblty of comparg both topologes s dscussed. After that the s compared to the IB concerng power losses effcency and stalled semconductor power. Fally the results are summarzed secton X. II. YEM ONFIGUAION AND ONO In ths paper the benefts of the IB and the are compared. he estgated applcaton s to feed energy from a dc source (, represented by a wd power generator wth rectfer for example, to the three phase ac grd. her topologes are shown fgures and. he oltage source erter s controlled by means of ector modulaton. he boost conerter the dc lk prodes a oltage that s hgh enough to let the I prode the requred output oltage wth a modulaton dex near to achee ts best effcency [7]. he s controlled by a modfed ector modulaton and outputs a requred oltage by adjustg the length of the shootthrough duty cycles [5][8]. he shoot-through states are placed stead of the zero states whle the acte states are the same as for tradtonal oltage source erter. he length of the shoot through states creases wth the rato between the put and the output oltage so that a oltage ga can be acheed. If a buck behaor s desred

2 stead of the shoot-through state normal zero states are appled III. GENEA MODEING OF HE OWE OE OF HE EMIONDUO here are four dfferent kds of losses whch occur as semconductors are used swtchg mode. hese losses are conducton and off-state losses as well as swtchg and drg losses. ompared wth the conducton and swtchg losses the off-state and drg losses are ery small and can be neglected [9]. In the followg the forward or conductg characterstcs of the semconductors hae been learzed. he conducton losses are calculated by ( and ( for one and one dode and depend on the mean and the rms alues of the current through the ales. E, and F, descrbe the threshold oltages and r E and r F the dfferental ohmc resstances of the and the dode, respectely. = E, re ( = r ( D 7 D Fgure. ower crcut of IB D D 7 D F, Fgure. ower crcut F he swtchg losses are a functon of the swtchg frequency, oltage and current. Howeer they depend also on the chosen WM-method and the swtchg loss energes of the (E on, E off and the dode (E rec. In datasheets these formaton are only gen for a erence oltage and a current. In (3 and (4 the swtchg power losses are gen for the contuous WM dependg on actual oltage and current. [9][]. ( E E = f π, con on off (3 π f E, con = rec (4 o reduce the swtchg losses a dscontuous WM mght be used. In ths case the ale that s carryg the greatest current s permanently turned on for a sxth of a le perod. In accordance to [] and as long as cosϕ < π the swtchg losses are haled to the standard 6 WM because the number of swtchg eents and swtchg power s reduced: ( E E = f π, dsc on off (5 f E, dsc = rec (6 π I. OWE O DEIAION FO HE IB he deraton of the power losses for the IBtopology are performed [7]. heore only the fal results are presented here. Based on equaton ( and ( the conductg losses shown equatons (7 and (8 are dered. hey depend on the le current and the modulaton dex M as well as on the power factor cos ϕ., I, I E, Mπ = cos( ϕ π 4 r π E M cos( ϕ π 4 3 F, Mπ = cos( ϕ π 4 r π F M cos( ϕ π 4 3 For calculatg the swtchg losses for each semconductor of the oltage source erter equatons (3 and (4 for the contuous WM and (5 and (6 for the dscontuous WM are adapted to the current and the oltage of the ale as presented (9 and (. he blockg oltage corresponds to the dc-lk oltage D and the current to the peak le current î. he factor N con/dsc s for the contuous and ½ for the dscontuous modulaton. D ( Eon Eoff Ncon dsc, I = f / π D, I f Erec Ncon/ dsc π (7 (8 (9 = ( he losses of the boost conerter depend on the put current and the modulaton dex a that s defed as: a on = = ( s he modulaton dex s a functon of the rato of the put oltage to the output oltage that s ths case the D

3 dc-lk oltage. he of the boost conerter s turned on for the tme on. he conductg losses are calculated by means of equaton ( and (3 for the and the dode, respectely. = r (, B, B ( E, E a ( U r ( a = F, F (3 he swtchg losses of the semconductors of the boost conerter are smlar to the swtchg losses of the oltage source erter, sce the blockg oltage s also the dc-lk oltage, just the commutaton current needs to be substtuted by the put current: ( E E = f D, B on off (4 = f E D, B rec (5. OWE O DEIAION FO HE A. onductg osses Whle the put oltage s aboe > the Z- source erter operates lke a I and the losses of the s and the freewheelg dodes are calculated lke for the I (see aboe and []. Howeer the smoothed dc lk current causes conductg losses wth the dc dode D 7 [9]: = r (6, F, F If the put oltage drops below <, another state, the so called shoot-through state s mplemented to boost the put oltage [] et al. Durg a shoot-throughstate all sx s are conductg smultaneously and the dc-lk s short-crcuted [], [8] et al.. In ths case the current through one s the supermposton of the susodal grd current and the hgh-frequent shootthrough current (see fgure 3. In ths sketch and for the calculatons t s assumed that the le flter s large enough that the rpple of the le current caused by the swtchg frequency can be neglected. For the calculaton of the power losses both the mean alue and the rms alue are requred and theore a mathematcal descrpton of the waeform s needed. he mean alue s the sum of the mean alues of half a fundamental perod of the le current (7 and the shoot-through-current (8: = M cos( ϕ (7 3 out, l l D 3 = (8 M s the modulaton dex and D s the shoot-throughduty-cycle. For the deraton of the rms of the current through one a mathematcal descrpton of the al waeform s requred. But sce the shoot-throughcurrent s added dscontuously to the le current, a mathematcal descrpton s ery dffcult. For the followg estgatons an approxmaton s made: For small put oltages the rms of the shoot-through-current s much larger than that of the le current. In ths case the deaton s acceptable small f just the rms of the shoot-through-current s dered and added to the aerage alue of the le current. For hgher put oltages the rato of the shoot-through-current to the current through one decreases. In ths case t s acceptable to add the rms of the le current to the mean alue of the shootthrough-current. he decson f the put oltage s hgh or low s done by comparg,, and, h, whch are the power losses for low and hgh put oltages. hey are calculated (9 and (, respectely. If the alue of equaton (9 s greater than the alue of ( the put oltage s defed as low and equaton (9 s appled and ce ersa. = r (9 here,,, h, E, E, ( ( E ( r ( = ( and E are the rms alues of the shootthrough and the le current, whch are calculated equatons ( followg [7] and (, separately. out π = M cos( ϕ π 4 3 =, out ( ( he freewheelg dodes only carry the grd current durg the zero-states and are blockg durg the shootthrough states. hs leads to followg conductg losses of one sgle dode [9]:, F, Mπ = cos π 4 rf π cos π M 4 3 ( ϕ ( ϕ ( 3 π 3M 3 3M π (3 Fgure 3. ketched current waeform of one In all preous publcatons as far as the authors know the losses of the dc-dode are neglected. Howeer the results deeloped here wll show that these losses cannot be omtted. he dode s only blockg durg the shoot-

4 through-states. Fgure 4 shows the smplfed waeform of the current through the dc dode where the current transents due to swtchg occasons are unconsdered. he resultg deaton when calculatg the conductg losses caused by ths smplfcaton s small because these transents amount to less than percent of the al current and are on aerage zero, so that only the rms-alue would be affected. Durg the shoot-through-state the current flows through the ductances (, and ts stored energy creases as mentoned aboe. Whle the dode s conductg the current s lmted by the ductances whch are connected seres. he current through the dode s slopg down due to the decreasg of the stored energy the ductances. he waeform s descrbed (4 where s the put power: D ( ( < t < 7 ( t = t ( (4 ( else hs yeld to the conductg losses of the dc-dode :, = F, 3 r ( ( ( ( F ( ( B. wtchg osses 3 (5 he swtchg losses of all deces the depend as for the I on the modulaton method. If stead of the contuous the dscontuous modulaton s used, the swtchg losses concerng the le current are haled the same way as for I []. But also the losses eoked by the shoot-through-states are haled compared to the contuous WM, because the number of zero-states and hence the number of shoot-through-states s haled as well but they appear twce as long. he followg equatons show the swtchg losses of one, one freewheelg dode and the dc dode separately. Aga the factor N con / dsc s one for the contuous and ½ for the dscontuous WM. dc dc ( Eon Eoff N con dsc, = f / u 3, π (6 = (7 dode dc, f Erec N con / dsc π = f E rec, ( ( N con / dsc (8 he factor /3 (6 arses because twce the dc-current s swtched smultaneously three phase legs. I. DEFINIION OF EFFIIENY, OWE EMIONDUO AING egardg losses and effcency, only the fluence of the power semconductors s taken to account. he al losses of both topologes are the sum of the swtchg and conductg losses of all semconductors as shown (9 and (3. I B = 6 (, B, I, I, B, B, I, I, B ( (9 = 6,,,,,, (3 he effcency for the IB and for the s defed as followg: I B η I B =, η = (3 he costs for semconductors are a small power range nearly lear to ther current carryg capablty, as long as they hae the same maxmum blockg oltage and a smlar loss performance [7]. he last pot can be acheed by usg the same type of semconductors. o compare the IB and the topologes concerng ther requred semconductor power, an stalled semconductor power has been establshed and defed as followg for the, the free-wheelg and dc-dode, separately: = I, = I (3 B E B I s the rated dc collector current of the s, I F the maxmum dc forward current of the dodes and E s the maxmum blockg oltage accordg to the datasheets. E F - / Fgure 4. ketched current waeform of the dc dode t II. MEHOD OF IMUAION he tenton of ths paper s to present a comparson of the IB and for dfferent dc put oltages and a constant three phase 5 Hz output oltage that s

5 choosen to 4 le to le. At the same tme eery sgle semconductor both s and (freewheelg- dodes s chosen as small as possble for any operatg pot. Because the maxmum permtted juncton temperature s the lmtg factor for the choce of sze of the deces, the juncton temperature s calculated for all semconductors and workg pots separately. he sze of the deces s chosen accordg to the maxmum alue of the datasheet thus the juncton temperature s J =5 at a case temperature of = 8. he statonary relatonshp between juncton temperature and power losses s gen by equaton (33 where th,j s the thermal resstance between juncton and case. J = th, J ( (33 he dmenson of the power semconductors by ther juncton temperature can lead to (theoretcal fractonal numbers of power semconductors or rather szes that are not aalable on the market. heore t s necessary to terpolate between the releant data gen able I and ABE I. EEAN DAA OF HE HOEN (FXXKE3, INFINEON I [A] E on [mj] E off [mj] 6,5 9, U E, [],,,,,, r E [mω],5 4,7, 7,3 3,6,8 th,j [K/W],45,35,6,8,85,6 E rec [mj] 4, 5, U F, [],65,65,65,65,65,65 r F [mω],4 8,5 6,3 4,,4 th,j [K/W],75,58,48,34,5, ABE II. EEAN DAA OF HE HOEN (FXX7KE3, INFINEON, 7 I [A] E on [mj] E off [mj] 5,5 3,5 3, II whch are based on [][3]. III. OMAABIIY OF AND IB ONENING OE AND INAED OWE ce the operatg prcples of the and IB are ery dfferent, a global comparson s dffcult. he ma ssue s that both the I and the dc-dc conerter work well wth s and dodes. Howeer the requres 7 modules for put oltages less than 4 [8]. he reason theore s that peak oltage across the s D creases wth small put oltages as shown equaton (34 [8]. out 3 (34 D = wth M = 3M out Fgure 5 shows the maxmum oltage across the s dependg on the put oltage and neglectg oershoots caused by stray ductances. haracterstc of the hgholtage deces s that they feature comparable threshold oltages, dfferental resstances and thermal resstances of the s as shown able I and II. hat s why the results for both topologes are presented wth and 7 s and dodes. For all results an put power of kw and cos(φ= s assumed. At an put oltage exceedg 575 both erters operate as Is. hat means that the of the boost conerter s conductg contuously and that the stops prodg any shoot-through state. For all calculatons t s supposed that the dc lk oltages and currents are deal and wthout any rpple. All results are presented for the contuous and dscontuous WM sce the swtchg losses of the hae been emphaszed as the major losses and thus can be reduced by the dscontuous WM. IX. OMAION OF OE, EFFIIENY AND INAED EMIONDUO OWE Fgures 6 and 7 show the effcency of both topologes for the contuous and dscontuous WM. he green dotted le descrbes unrealzable workg pots of the wth s. It can be seen that the IB topology (black dotted le has a better U E, [],4,4,4,4,4,4 r E [mω] 6 5 9,5 5 3,3 th,j [K/W],36,7,5,,75,55 E rec [mj] 3,5,5 7,5 36 7,5 [] U F, [],9,9,9,9,9,9 r F [mω] 6,3,6 7,9 5,3 3,7,6 th,j [K/W],63,48,39,,3, [] Fgure 5. oltage across the s of the s. put dc oltage for a grd oltage of 4

6 performance for almost eery put oltage. Only for an put oltage around 5 the s toppg ts counterpart by usg the dscontuous WM and ensurg a mmum put oltage of 4 (sold green le. Especally for low put oltages the performance of the s worse because of the opposed behaor by acheg a hgh oltage ga by extendg the shootthrough-states and consequently as well extendg the zero states whch hae a buck effect. hat results hgh oltages across the semconductors and large current through the s durg the shoot-through states. he reason for the dfferent behaor of the topologes s on the one hand that the I of the IB system works wth a modulaton dex of M= and has consequently only a small buck behaor compared to the. here the length of the shoot-through-states and consequently as well the duraton of the zero-states hae to be extended for low put oltages. On the other hand there s the dsadantage of only one transstor (the one of the boost conerter the IB that has to cope wth the shoot-through current compared to sx transstors wth the. hat leads to the rated semconductor power that s presented fgures 8 and 9 for a contuous and for a dscontuous WM. Aga the IB system wth semconductors has the best performance all operatg pots. hat means that ths topology needs the least amount of slcon. For a workg the full put oltage range three and fe tmes as much stalled semconductor power for the dscontuous and contuous WM s requred respectely. he reason for that s aga the buck behaor of the erter of the where long shoot-through-states are requred. hat causes ery hgh oltages across the power semconductors and ery large current through sx deces stead of one for the IB erter. Neertheless the power losses of the passe components are dsregarded. Howeer a close look at the waeforms of the current through the ductances and capactors of both the topologes pots to the fact that the power losses of the passe elements of the are clearly hgher than for IB. Howeer these results are only ald for the 4 grd. he cures may look somewhat dfferent for lower grd oltages. X. ONUION In wd power statons there are conerter confguratons where the generator current s rectfed by dodes. he resultg oltage depends on the arable rotor speed of the wd turbe and has to be boosted and erted to feed power to the grd. he Z-source erter s a new soluton for ths task. Here ts power losses, effcency and stalled semconductor power are compared to the conentonal soluton wth oltage source erter lked wth a dc/dc boost conerter. hs s done by calculatg the rms of the current through the s of the Z-source erter. Based on the mean and rms alues of current and oltage of the ales the power losses of all semconductors are calculated for the as well as for the oltage source erter lked wth dc/dc boost conerter. ce these two topologes hae the same put and output Fgure 6. Effcency at contuous WM for dfferent put oltages Fgure 7. Effcency at dscontuous WM for dfferent put oltages Fgure 8. ated semconductor power at contuous WM for dfferent put oltages Fgure 9. ated semconductor power at dscontuous WM for dfferent put oltages

7 characterstcs they hae been compared to each other concerng ther power losses of the semconductors, ther effcency and ther rated power. he results show that the power losses of the semconductors of the Z-source erter are sgnfcant hgher than for the IB topology although the has one dece less. Because of that also the effcency of the s worse compared to the IB system. o achee a hgh oltages ga by applyg long shootthrough-states a lot of semconductor power s requred because the buck conertg zero states hae to be extended at the same tme. It s also shown that the WM method has hgher fluences on the losses of the compared to the IB sce the swtchg losses are domatg the al semconductor losses of the. EFEENE [] Fang Zheng eng, Z-ource Inerter IEEE rans. Ind. Applcatons, ol. 39, no., pp. 54-5, March-Aprl 3 [] oh hang oh, Mahda lathgamuwa, Yue en a, Geok hua and Yunwe, ulse-wdth Modulaton of Z-ource Inerters, IEEE rans. On ower Electroncs ol., No. 6, pp , No. 5 [3].. oh,. J. Gajajayake, D. M. lathgamuwa and F. Blaabjerg, Ealuaton of esonant Dampg echnques for Z- ource urrent-ype Inerter IEEE Appled ower Electroncs onference and Exposton, March 6 [4] Maosen hen, Alan Joseph, J Wang, Fang Z. eng and Donald J. Adams, omparson of radtonal Inerters and Z-ource Inerter for Fuel ell ehcles IEEE ower Electroncs ransportaton, pp. 5-3, October 4 [5] Maosen hen, Alan Joseph, Wang, Fang Z. eng and Donald J. Adams, omparson of radtonal Inerters and Z-ource Inerter, IEEE ower Electronc pecalsts onference, pp.69-8, June 5 [6] B Justus ab and. Arumugan, Harmoncs tudy and omparson of Z-ource Inerter wth radtonal Inerters, Amercan Journal of Appled cences, ol., pp. 48-3, 5 [7] Malte Mohr and Fredrch W. Fuchs, omparson of three phase current source erters and oltage source erters lked wth dc to dc boost conerters for fuel cell generaton systems European conference on ower Electroncs and Applcatons, roceedgs on D, Dresden, ept. 5 [8] W.-oke Franke, Malte Mohr and Fredrch W. Fuchs Betrebserhalten des Z-ource-Wechselrchters (Operatg Behaor of the Z-ource Inerter. ymposum Martme Elektrotechnk, pp. 4-46, Oct. 7 [9] Ulrch Ncola, obas emann, Jürgen etzold, Josef utz, Applcaton Manual: and MOFE Modules, IE teuerungstechnk und estungselektronk, June [] Berhoff, M.H.; Fuchs, F.W.: ower emconductor osses oltage ource and urrent ource onerters based on omplete Analytcal Deraton, roceedgs of the E 4, Aachen [] D. Grahame Holmes and. A. po, ulse wdth modulaton for power conerters prcples and practce, IEEE press seres on power engeerg, scataway, 3 [] Datasheets eupec for FxxKE3, [3] Datasheets eupec for FxxKE3,