Novel Modulation Schemes Minimizing the Switching Losses of Sparse Matrix Converters

Transcription

1 Novel Modlton Shemes Mnmzng the Swthng Losses of Sprse Mtrx Converters Johnn W. Kolr nd Frnk Shfmester ETH Zrh, Power Eletron Systems Lortory ETH Zentrm / ETL H, Physkstr. 3, CH-9 Zrh/SWTZERLAND Tel.: Fx.: +--3 eml: kolr@lem.ee.ethz.h Astrt. The swthng losses of three-phse Sprse Mtrx Converter (SMC) opertng n the lower modlton rnge re mnmzed y employng the lowest nd the seond lrgest npt lne-to-lne voltge for the formton of the onverter DC lnk voltge. The resltng rrent stresses on the power semondtors nd the swthng freqeny rpple RMS vles of the flter ptor voltges nd otpt rrents re llted y dgtl smlton nd ompred to onventonl modlton. Fnlly, modlton sheme s ntroded whh llows the generton of retve npt power lso for mssng tve power trnsfer v the DC lnk nd/or prely retve lod. Ths s s reqrement for opertng the SMC n oost mode where the otpt flter ptor voltges hve to e ontrolled snsodlly lso for no-lod operton. ntrodton Sprse Mtrx Converter (SMC, f. Fg.) systems [] re fntonlly eqvlent to Conventonl Mtrx Converters (CMC) t re hrterzed y lower relzton effort nd lower ontrol omplexty nd re therefore espelly nterestng for n ndstrl pplton. p S p S D p D pn n S pa DAp Fg.: Topology of the Sprse Mtrx Converter (SMC) ordng to []. Wthn eh plse hlf perod two lne-to-lne voltges re swthed nto the DC lnk of the SMC y proper ontrol of the npt stge (f. Fg.). There, the npt stge ommtton s t zero rrent (f. n Fg., Fg. n [], []) wht llows to vod mlt-step ommtton sheme n dependeny on the sgn of the ommttng voltge or ommttng rrent s reqred for the CMC nd/or reslts n low swthng losses nd hgh onverter rellty. For employng the lrgest nd the seond lrgest postve lne-to-lne voltge for the formton of the DC lnk voltge mxmm otpt voltge rnge s heved, however, reltvely lrge swthng losses of the otpt stge do or. The s propertes of ths modlton sheme, whh wll e denoted s modlton sheme n the followng re shown n Fg.. For low otpt voltge mpltde therefore modfton of the modlton sheme hs to e onsdered whh redes the otpt stge swthng losses y swthng lne-to-lne npt voltges of low nstntneos vle nto the DC lnk. n ths pper novel SMC modlton sheme s proposed (denoted s modlton sheme ) where wthn eh plse hlf perod sseqently the lowest postve nd the seond lrgest npt lne-to-lne re swthed nto the DC lnk. n omnton wth the lmpng of the SMC otpt stge rdge legs wthn π/3-wde ntervl n the vnty of the mxm of the A B C orrespondng otpt phse rrents ths reslts n mnmm system swthng losses. n Seton the reltve on-tmes of the npt nd otpt stge swthng sttes re llted nd onept for shftng prt of the otpt stge swthng losses to the npt stge s desred. sp sp sp sn sn sn sa sb sc -π/3 t µ = - τ(), -C -C C τ τ(), -π/ τ(), τ(), t µ = -C -C τ τ(), τ τ τ(), TP TP τ τ +π/ C - τ(), T P τ τ(), τ(), τ(), τ τ(), τ(), +π/3 = ϕ Fg.: Modlton Sheme (f. Fg.9 n []); () tme ehvor of the mns phse voltges, the mns lne-to-lne voltges, the SMC DC lnk voltge nd of the lol verge vle of the DC lnk voltge nd the DC lnk rrent, ū nd ī, wthn π/3-wde ntervl of the npt perod (φ = π/3 + π/3); () tme ehvor of,, the mns phse rrents, =,,, wthn plse perod t µ = T P for φ n +π/ nd φ n +π/3 (φ denotes the phse of the referene vle of the otpt voltge spe vetor, f. Eq.()); frthermore shown: swthng fntons of the retfer nd the nverter stge (s p = ndtes dretonl onneton of phse npt nd the postve DC lnk s p, nd/or the trn-on stte of S nd S p ; s A = denotes the trn-on stte of S pa nd/or the trn-off stte of S na ). For the ske of lrty low plse freqeny s ssmed nd the rpple omponents of nd re negleted. C - T P () ()

2 n Seton 3 the modlton shemes nd re omprtvely evlted sed on the rrent stresses on the power semondtors nd the RMS vles of the rpple omponents of the flter ptor voltges nd otpt rrents. Fnlly, n Seton modfton of modlton sheme s proposed whh llows the generton of retve power t the onverter npt lso for prely retve lod,.e. wthot trnsfer of tve power v the DC lnk. Mnmzng Swthng Losses t Low Otpt Voltge As shown n Fg. the ommtton of the npt stge s wthn the free-wheelng ntervl of the otpt stge,.e. t zero DC lnk rrent =. Therefore, swthng losses do or only for the otpt stge nd re determned y the nstntneos vle of the DC lnk rrent nd the DC lnk voltge. The DC lnk rrent s dretly defned y the otpt rrent phse dsplement Φ for gven ϕ. Therefore, the only posslty for mnmzng the swthng losses s to employ setons of the npt lne-to-lne voltge wth mnmm nstntneos vle for the formton of the DC lnk voltge. sp sp sp sn sn sn sa sb sc -π/3 tµ = τ(), -C τ τ(), -π/ τ(), τ(), t µ = TP TP -C τ τ(), τ τ τ τ τ(), +π/ +π/3 = ϕ τ(), TP τ τ(), τ(), τ(), -C -C -C - τ τ(), C C - C Fg.3: Proposed modlton sheme (modlton sheme ); representton of the voltges, rrents nd swthng fntons s for modlton sheme n Fg.. n ontrst to modlton sheme the npt stge rdge leg s swthng wth plse freqeny etween the postve nd negtve DC lnk s. As the ommtton of the npt stge s t zero DC lnk rrent ths however does not reslt n swthng losses. - τ(), TP There, the omnton of the npt phses hs to e seleted sh tht the dstrton of the DC lnk rrent to the npt phses reslts n phse rrents eng proportonl to the orrespondng phse voltges,.e.,, ~,, (f. Eq.()). The resltng modlton sheme whh s denoted s modlton sheme n the followng s shown n Fg.3. n nlogy to Seton V n [] the llton of the reltve on-tmes of the power trnsstors of the npt stge n e lmted to π/-wde ntervl, φ = π/, of the mns perod. Bsed on ths the trn-on tmes for frther ntervls n e derved y symmetry onsdertons. Assmng onstnt lol verge vle ī of the DC lnk rrent for eh retfer swthng stte of plse hlf perod (tme ntervls τ nd τ, f. Eq.() n []) we hve for the lol verge vles of the npt phse rrents = d = ( d d ) = d. () Under onsderton of d d = () + Eq.() n e rewrtten s = ( d (3) ) nd/or d = +. () For ohm fndmentl mns ehvor of the SMC npt stge, φ =, (5) nd/or ~ Eq.() reslts n d = = + ~ ~ () where symmetr snsodl npt phse voltge system = os( ωt) = os( ωt π / 3). () = os( ω t + π / 3) s ssmed. Frthermore, Eqs.(), () nd () yeld d = + = (7). (9) The tme-dependent lol verge vle of the DC lnk voltge (f. Fg.3) now reslts s ˆ 3 U 3 ˆ = d + d = = U. () π os( ωt ) Wth referene to Eq.() the modlton lmt,.e. the mxmm vle of the mpltde of the otpt phse voltge fndmentl s ˆ,mx, = mn = / U ϕ = π = () 3 3 nd/or n omprson to modlton sheme,mx, =,mx,.5, mx,. () 3 De to the tme dependeny of ū the formton of onstnt mpltde Û of the otpt phse voltges reqres vrton of the SMC otpt stge modlton ndex

3 ˆ U m = = os( ωt π/ ). (3) 3 There, we hve for the solte trn-on tmes of the tve swthng sttes T ˆ p U π τ(), = os( ) ˆ ϕ + 3 U T ˆ p U τ(), = sn( ) 3 ˆ ϕ U ˆ () Tp U τ(), = ( )sn( ϕ ) 3 ˆ U T ˆ p U π τ(), = ( )os( ϕ + ) 3 ˆ U where φ denotes the phse of the otpt voltge spe vetor * ( * =Û, f. Fg. n []) whh hs to e formed n the verge over plse hlf perod (for Eq.() φ = π/3 nd φ = π/ s ssmed). n the followng the voltge trnsfer rto of the SMC shll e hrterzed sng M = =. (5) 3,mx, Besdes the DC lnk voltge the swthed rrent tkes dret nflene on the otpt stge swthng losses. Therefore, ordng to [3] n otpt stge rdge leg s dvntgeosly not swthed n the vnty of the mxm of the relted phse rrent; the phse otpt then remns lmped to the postve nd/or negtve DC lnk s wthn π/3-wde ntervl of the postve nd the negtve otpt hlf perod. For Φ = symmetr lmpng rond the mxmm of the otpt phse voltge fndmentl (f. Fg.() nd ()) reslts n mnmm swthng losses. For nresng rrent phse dsplement Φ the lmpng ntervl hs to e shfted ordngly, t hs to remn wthn n ngle ntervl of ±π/3 reltve to the phse voltge mxmm. Therefore, for Φ >π/ hgher otpt swthng losses s for Φ = wll or (f. Fgs.5(),(d) nd (g),(h)). For n optml postonng of the lmpng ntervl the tme ehvor of the phse rrent nd (ontrry to nverter systems wth onstnt DC lnk voltge s onsdered n [3]) the tme dependeny of the envelopes of the npt lne-to-lne voltges whh re employed n eh plse hlf perod for DC lnk voltge formton wold hve to e onsdered. Remrk: For hngng the npt stge swthng stte wthn the free-wheelng ntervl of the otpt stge (f. Fg.() nd Fg.3()) for modlton sheme nd swthng losses re lmted to the otpt stge. A prttonng of the swthng losses etween npt nd otpt stge s possle for postve DC lnk rrent >. There, y trnng off n npt stge power trnsstor, e.g. S n n Fg.5, the otpt stge s fored from n tve swthng stte nto (pssve) free-wheelng operton nd the trn-off losses re tken over y S n. At the end of the free-wheelng ntervl the sseqent lne-tolne npt voltge s ppled to the DC lnk y trnng on S n (f. Fg.5) nd the otpt stge retrns nto the pror tve swthng stte where gn no otpt stge swthng losses do or. A detled desrpton of ths ontrol onept wll e gven n ftre pper. sp sn sn spa spb spc τ(), -C τ(), t µ = τ(), FW -C τ(), τ(), T P Fg.5: Commtton of the SMC otpt stge nto pssve free-wheelng stte (free-wheelng ton despte the tve swthng stte ontrol sgnls remn ppled to the otpt stge power trnsstors) y trnng off power trnsstor (S n ) of the npt stge for postve DC lnk rrent >. For onventonl modlton (f. Fg.), the ommtton of the npt stge s t zero rrent nd/or swthng losses only do or for the otpt stge. 3 Comprtve Evlton of Modlton Shemes nd The reslts of smlton of the sttonry opertng ehvor of SMC employng the proposed modlton sheme re ompled n Fg. for mns freqeny f =5Hz otpt freqeny f =Hz swthng freqeny f P =5kHz lod ndtne L=mH npt flter ptne C=9µF (str onneton). n order to determne the swthng freqeny rpple of the flter ptor voltges ndependent of the nner mns mpedne p () SpA () SpA () SpA (d) n SpA SpA SpA s p s n ms ms ms ms ms ms ms ms p (e) SpA (f) SpA (g) SpA (h) n SpA SpA SpA s p Fg.: s n ms ms ms ms ms ms ms ms Fg.: Modlton of the SMC npt nd otpt stge for modlton sheme (f. ()-(d)) nd modlton sheme (f. (e)-(h)) for dfferent vles of the otpt rrent phse dsplement Φ = (),(f); Φ =π/ (),(g); Φ = π/ (d),(h). Representton of the potentl of the postve nd negtve DC lnk s, p nd n, wth referene to the mns str pont (f. () nd (e)) nd of the swthng fntons s p nd s n (f. Fg. nd Fg.3) of npt stge rdge leg ; frthermore shown: voltge, rrent nd swthng fnton of power trnsstor S pa of the SMC otpt stge. The postonng of the lmpng ntervls of S pa s nder onsderton of mnmzton of the trnsstor swthng losses.

4 () () () A A ms ms ms ms ms (e) (f) A ms (d) A ms ms ms ms ms ms Fg.: Smlton of the SMC opertng ehvor for modlton sheme (f. ()-()) nd modlton sheme (f. (d)-(f)); (), (d) DC lnk voltge, lol verge vle ū, otpt phse voltge A (wth referene to the ndtve lod str pont), lol verge vle ūa, otpt phse rrent ; (), (e) DC lnk rrent, lol verge vle ī, npt phse rrent, lol verge vle ī, npt phse voltge ; (), (f) npt phse voltge, rpple omponent, nd otpt phse rrent nd rpple omponent ; sles: V/dv, 5A/dv ( : V/dv, :.5A/dv); M=., Φ=. nd/or the dmensonng of n npt flter the system s fed y prely snsodl rrent. There, the rrent phse dsplement nd mpltde s djsted sh tht flter ptor voltge fndmentl mpltde of Û= 37V (eqvlent to U,RMS= 3V) s heved. Frthermore, lod voltge s mpressed t the otpt sde whh ensres lod rrent fndmentl mpltde of Î=7.75A ndependent of the seleted rrent phse dsplement Φ; for M= nd Φ= ths s eqvlent to PO=7.5kW. The lmpng ntervls of the otpt stge rdge legs re shfted wth nresng otpt rrent phse dsplement Φ s shown n Fg.5 n order to lwys heve mxmm redton of the otpt stge swthng losses. As shown n Fgs.(),() nd Fg.7 the proposed modlton sheme redes the verge DC lnk voltge nd therefore the otpt stge swthng losses y ftor of ot two s ompred to modlton sheme. However, for the formton of n otpt voltge of eql mpltde Û hgher modlton ndex of the otpt stge s reqred s for modlton sheme. Ths reslts n lrger wdth of the setons of the otpt rrents formng the DC lnk rrent nd/or n hgher ondton losses of the npt stge (f. Fg. nd Fg.9) nd n hgher rpple of the npt flter ptor voltges nd/or hgher RMS vle C,RMS of the flter ptor rrent (f. Fg.(f) nd Fg.() nd Fg.()). Frthermore, U,RMS nd C,RMS re nresed y the orrene of rrent plses of eql mgntde t opposte sgn n the vnty of the npt rrent zero rossngs (f. n Fg.3() nd n Fg.(e)). As shown n Fgs.() nd (f) nd Fg.(), modlton shemes nd reslt n n pproxmtely eql RMS vle,rms of the otpt rrent rpple for gven voltge trnsfer rto M. Ths s gn sed y the lrger on-tme of the tve swthng sttes of the otpt stge nd/or y the lrger wdth of the otpt voltge plses of modlton sheme whh led to n eql hnge of the otpt phse rrents s the voltge plses of smller wdth t hgher mpltde orrng for modlton sheme. An dvntge of modlton sheme over sheme s the lower vle of the swthed voltge whh reslts n lower mpltde of the ommon mode omponent of the otpt voltge nd/or n lower ondted eletromgnet emssons of the onverter system (Fg.()).. PSw,r.7 φ=π/ φ=..5. φ=π/ φ= M Fg.7: Normlzed swthng losses PSw,r of trnsstor of the otpt stge (e.g. of SpA). Assmng lner dependeny of the trnsstor swthng losses on the swthed voltge nd rrent, for determnng PSw,r the sm of the trnsstor voltge nd rrent prodts t the trn-on nd trn-off nstnts s llted over the lest ommon mltple Tm of the mns nd otpt perod, ΣTmSpASpA/(/3ÛÎTm/TP). The normlzton to /3ÛÎTm/TP (TP=/fP) reslts n qntty eng ndependent of the solte vle of the swthed voltge nd rrent nd the onsdered tme perod. The ftor /3 onsders tht there re n totl swthng tons of the otpt stge nd/or / swthng tons of sngle otpt stge power trnsstor wthn plse perod TP. φ = S,AVG S, + SpA, S, + SpA, S, S,.... M Fg.: Averge vles of the npt stge trnsstor S nd of the otpt stge trnsstor SpA n dependeny on the voltge trnsfer rto M (f. Eq.(5)) for Φ=. Sp does not ondt rrent for Φ= nd shows only very low rrent verge vle for Φ=π/ (f. Fg.7 n []), therefore, Sp s not shown. ndex refers to modlton sheme, ndex to modlton sheme. Smlton prmeters s for Fg., t f=5hz. nresng M reslts n n nresng wdth of the otpt rrent setons formng the DC lnk rrent nd therefore n lner nrese of the npt stge trnsstor rrent verge vle. nresng Φ reslts n lower nstntneos DC lnk rrent vles nd ordngly n lower npt stge ondton losses.

5 D,AVG D,AVG φ = DAp, + Dpn, + Dp, Dpn, + Dp, DAp, + Dpn, + Dp, Dp,.... M φ = π/ DAp, + Dpn, + Dp, Dpn, + Dp, DAp, + Dpn, + Dp, Dp,.... M Fg:9: Averge vles of the power dode rrents of the npt stge (dodes D p nd D pn ) nd of the otpt stge (dode D Ap ) n dependeny on the voltge trnsfer rto M (f. Eq.(5)) for Φ = nd Φ =π/. For detls of the representton nd n explnton of the hrterst of the dependeny on M see pton of Fg.... U,RMS,r A,RMS,r..3.., φ =, φ = π/, φ = π/, φ =.... M φ = φ =π/ φ = φ =π/.... M Fg.: Normlzed RMS vle of the npt flter ptor voltge rpple nd of the otpt rrent rpple, U,RMS,r nd A,RMS,r, for Φ = nd Φ =π/. normlzton wth referene to Û T P /(L) (f. [3]) nd/or Î T P /(C). For detls of the representton see pton of Fg.. As loser nlyss shows, the hrtersts shown n Fgs.7- whh hve een llted ssmng f /f = re lso vld n good pproxmton for wde vrton of the rto f /f of the npt nd otpt freqeny. Ths s proven y Fg. e.g. for S,AVG, U,RMS,r nd A,RMS,r. Conlsons For hevng low volme of the flter omponents mtrx onverter hs to e operted t hgh swthng freqeny. Therefore, the swthng losses re n generl onstttng lrge shre of the totl onverter losses. The modlton sheme proposed n ths pper llows to t the swthng losses of SMC opertng n the lower modlton rnge n hlf s ompred to onventonl modlton for eql RMS vle of the otpt rrent rpple. The onverter ondton losses re only slghtly nresed. Aordngly, the therml stress on the power semondtors s onsderly reded wht permts n nrese of the otpt rrent t low otpt fre- C,RMS U,RMS [V] 5 5, φ =, φ = π/, φ = π/, φ =.... M φ = φ =π/ φ = φ =π/.... M Fg.: RMS vles C,RMS,r nd U,RMS,r of the flter ptor rrent nd of the ommon-mode omponent of the SMC otpt voltge n dependeny on the voltge trnsfer rto M. 9 S,AVG U,RMS,r A,RMS,r φ = φ = φ = π/ φ = π/.... M φ = φ = π/.... M φ = π/.... M Fg.: Dependeny of npt stge trnsstor rrent verge vle S,AVG,r, of the normlzed RMS vle of the npt flter ptor voltge rpple U,RMS,r nd of the normlzed RMS vle of the otpt rrent rpple A,RMS,r on M for dfferent vles of the otpt freqeny f ; : f = 5Hz, : f = 5Hz, : f = Hz, : f = 5Hz, : f = 5Hz; f =5Hz, modlton sheme, normlzton s for Fgs. nd ; remnng prmeters s for Fg.. The ntegrton reqred for the llton of the verge nd RMS vles s performed over the lest ommon mltple of the npt nd otpt perods T =/f nd T =/f. qeny nd/or of the torqe of n AC drve t low speed. As dsdvntge hgher rpple of the npt flter ptor voltges hs to e epted. Alterntvely, the redton of the swthng losses n e tlzed for n nrese of the swthng freqeny. Ths llows to mntn

6 flter ptor voltge rpple gven for onventonl modlton nd fetres redton of the RMS vle of the otpt rrent rpple y ftor of two. n next step the proposed modlton sheme wll e expermentlly verfed for 7.5kW prototype of the SMC. There t s mportnt to onsder tht lrge rpple of the flter ptor voltges reslts n pssve free-wheelng operton n the vnty of whh ses dstorton of the otpt voltge formton. Therefore, ompenston sheme sed on otpt voltge mesrement hs to e employed or the modlton hs to e hnged over to modlton sheme n order to ensre hgh otpt rrent qlty. p NA A B C n Fg.3: Operton of SMC n oost mode. The defnton of the postve voltge nd rrent dretons s ssmed eql s for k-mode operton n Fg.. -B () generton of prely retve otpt power t no lod,.e. wthot tve power flow v the DC lnk (Φ = ±π/ nd Φ = ±π/). Ths s not possle for modlton sheme or (f. Seton V-B n []) s the DC lnk rrent shows zero lol verge vle wthn eh trn-on ntervl of lne-to-lne npt voltge for Φ = ±π/; Aordngly, no lol verge vle of the flter ptor rrent n e formed. The modfton of the modlton onept reqred for prely retve power operton s shown n Fg.() t the exmple of modlton sheme. There, the frst hlf of plse hlf perod, t µ = T P /, s tlzed for voltge formton (s gven for onventonl modlton). Wthn the seond hlf of the plse perod the flter ptor rrents (e.g. ) re formed, where the swthng stte trn-on tmes (e.g. τ (), * nd τ (), *) re determned sh tht no lol verge vle of the DC lnk power p=. does reslt. There, the DC lnk rrent n generl shows lol verge vle (f. Fg.5). The mxmm vle of the retve otpt rrent vlle for prely retve power operton (Φ = ±π/ nd Φ = ±π/) whh, e.g. old e tlzed for snsodl ontrol of the otpt flter ptor voltges t no (tve) lod s shown n Fg.. A detled dssson nd expermentl verfton of the novel ontrol onept wll e gven n pper to e plshed n ner ftre. A A A Fg.5: Dgtl smlton of the opertng ehvor of the SMC n oost mode for Φ =-π/ nd Φ =+π/; modlton s shown n Fg., prmeters s gven n Seton 3; sles: V/dv, A/dv. -C -C B ms ms AB - C -B - τ(), t µ = τ τ(), τ(), τ(), τ τ(), τ(), τ(), * τ* -B...f (τ(), < τ(), *) τ(), * τ(), * τ*...f (τ(), > τ(), *) -C -C...f B...f (τ(), < τ(), *) (τ(), > τ(), *) τ(), * T P () ms ms Î q,mx Î... Î q,mx = /.( - 3/ M ) Î..... M Fg.: Dependeny of the normlzed mxmm fndmentl mpltde of the retve otpt phse rrent, Î q,mx,r, on the voltge trnsfer rto M n se no tve power s trnsferred v the DC lnk; modlton s shown n Fg.. tµ = τ τ(), τ(), τ τ(), + Mn(τ(), ; τ(), *) TP τ(), - τ(), * τ(), - τ(), * τ(), + Mn(τ(), ; τ(), *) Fg.: Proposed modlton sheme () for genertng retve otpt rrent (flter ptor rrent, f. Fg.3) for zero tve power trnsfer v the DC lnk; the swthng stte seqene of plse perod T P (f. ()) n e omned n hlf plse perod s shown n (). n the orse of ftre reserh lso the operton of the SMC n oost mode (f. Fg.3) whh hs not een treted n the ltertre so fr wll e nlyzed n detl. There, the mn sjet s the Referenes [] Kolr, J.W., Bmnn, M., Shfmester, F., nd Ertl, H.: Novel Three-Phse AC-DC-AC Sprse Mtrx Converter, Prt nd. Proeedngs of the 7th Annl EEE Appled Power Eletrons Conferene, Dlls (Texs), USA, Mrh -, Vol., pp (). [] We, L., nd Lpo, T.A.: A Novel Mtrx Converter Topology wth Smple Commtton. Reord of the EEE ndstry Appltons Soety Annl Meetng, Chgo, Sept. 3 Ot., Vol. 3, pp (). [3] Kolr, J.W., Ertl, H., nd Zh, F.C.: nflene of the Modlton Method on the Condton nd Swthng Losses of PWM Converter System. EEE Trnstons on ndstry Appltons, Vol. 7, No., pp (99).