Modeling and Analysis of Active Front-End Induction Motor Drive for Reactive Power Compensation

Transcription

1 Unvrsty of Tnnss, Knoxvll Trac: Tnnss Rsarch an Cratv Exchang Mastrs Thss Grauat School Molng an Analyss of Actv Front-En Inucton Motor Drv for Ractv Powr Compnsaton Pankaj Prabhakar Pant Unvrsty of Tnnss - Knoxvll Rcommn Ctaton Pant, Pankaj Prabhakar, "Molng an Analyss of Actv Front-En Inucton Motor Drv for Ractv Powr Compnsaton. " Mastr's Thss, Unvrsty of Tnnss, Ths Thss s brought to you for fr an opn accss by th Grauat School at Trac: Tnnss Rsarch an Cratv Exchang. It has bn accpt for ncluson n Mastrs Thss by an authorz amnstrator of Trac: Tnnss Rsarch an Cratv Exchang. For mor nformaton, plas contact trac@utk.u.

2 To th Grauat Councl: I am submttng hrwth a thss wrttn by Pankaj Prabhakar Pant nttl "Molng an Analyss of Actv Front-En Inucton Motor Drv for Ractv Powr Compnsaton." I hav xamn th fnal lctronc copy of ths thss for form an contnt an rcommn that t b accpt n partal fulfllmnt of th rurmnts for th gr of Mastr of Scnc, wth a major n Elctrcal Engnrng. W hav ra ths thss an rcommn ts accptanc: Jack S. Lawlr, John N. Chasson (Orgnal sgnaturs ar on fl wth offcal stunt rcors.) Lon M. Tolbrt, Major Profssor Accpt for th Councl: Dx L. Thompson Vc Provost an Dan of th Grauat School

3 To th Grauat Councl: I am submttng hrwth a thss wrttn by Pankaj Prabhakar Pant nttl Molng an Analyss of Actv Front-En Inucton Motor Drv for Ractv Powr Compnsaton. I hav xamn th fnal lctronc copy of ths thss for form an contnt an rcommn that t b accpt n partal fulfllmnt of th rurmnts for th gr of Mastr of Scnc, wth a major n Elctrcal Engnrng. Lon M. Tolbrt Major Profssor W hav ra ths thss an rcommn ts accptanc: Jack S. Lawlr John N. Chasson Accpt for th Councl: Ann Mayhw Vc Chancllor an Dan of Grauat Stus (Orgnal sgnaturs ar on fl wth offcal stunt rcors)

4 Molng an Analyss of Actv Front-En Inucton Motor Drv for Ractv Powr Compnsaton A Thss Prsnt for th Mastr of Scnc Dgr Th Unvrsty of Tnnss, Knoxvll Pankaj Prabhakar Pant May 005

5 Copyrght 005 by Pankaj Prabhakar Pant All rghts rsrv.

6 Dcaton I wsh to cat ths thss to my famly: Shr. Prabhakar B. Pant Sau. Jayashr P. Pant Shara an Dpak Papa, Akka, Anna, an Dpu, thank you for your unnng lov, support, an abov all for bng my nspraton whch ma th complton of ths thss possbl.

7 Acknowlgmnts I wsh to thank all thos who hlp m complt my M.S. n Elctrcal Engnrng at th Unvrsty of Tnnss. I woul lk to thank Dr. Lon M. Tolbrt for gvng m an opportunty to work on ths thss by funng my rsarch, srvng as my major profssor, an provng valuabl avc from tm to tm. I woul lk to thank Dr. Chasson for srvng on my thss commtt, an tachng ECE 617 whch hlp m towars my rsarch. I woul lk to thank Dr. Lawlr for hs valuabl suggstons rgarng th rsarch, an srvng on my thss commtt. I am also gratful to Dr. Bmal K. Bos for gntng my ntrst n powr lctroncs, hs support, an guanc. I woul also lk to thank my lab mats, Surn, Bn, Wston, Nranjan, Mchal, Prr, an Grry for thr hartflt support, an makng my grauat school xprnc so much mor njoyabl. A spcal thanks to all my Inan frns at Th Unvrsty of Tnnss. v

8 Abstract In ths thss, an actv front n nucton motor rv for ractv powr compnsaton s analyz. Th classcal vctor control approach for hgh prformanc control of an nucton motor rv s a wll stablsh nustry stanar toay. Th sam a of coupl control s xtn to th ln-s PWM convrtr for achvng bttr ynamc prformanc. Th systm mol s obtan usng - rotatng fram thory. Th componnt of ln currnts s us to control th ractv powr. Th componnt s us to control th c-lnk voltag an also to supply actv powr rur by th motor. A hgh gan fback controllr wth nput-output lnarzaton s prsnt to rmov couplng btwn an currnts. A loa powr f-forwar loop s a to th c-lnk voltag controllr for fast ynamc rspons. Th rv prformanc s analyz to fn systm spcfcatons. Th motor acclraton, clraton, an varabl powr factor opraton (ractv powr compnsaton) of th actv rv systm ar monstrat. Th motor loa s var from no loa to full loa n stps of 10% ach. For ach stp th vc currnts, swtchng powr loss, ln harmoncs, an c-lnk rppls ar plott. Ths ata s us to rv conclusons that fn systm spcfcatons an also stat opratng lmts. Th control of th rv systm s mplmnt n MATLAB-SIMULINK. Th complt systm harwar s mplmnt n commrcally avalabl smulaton tool, PSIM. Th two softwar packags ar ntrlnk usng an ntrfac moul. v

9 Tabl of Contnts Chaptr Pag 1 Introucton Chaptr Ovrvw Thss Rsarch Actv Front-En Invrtrs Opratng Prncpl Ky Faturs of Actv Front-En Invrtrs Rsarch Goals Chaptr Summary an Thss Outln Backgoun Chaptr Ovrvw. 1. Powr Qualty Issus.1..1 Sourcs of Harmoncs Effcts of Harmoncs Rol of Powr Elctroncs n Improvng Qualty of AC Gr Powr Flxbl AC Transmsson Systms (FACTS) Opratng Prncpl Shunt-Connct Controllrs Srs-Connct Controllrs..0.4 Gnratng Rfrnc Currnts Usng Instantanous Powr p- Thory.3.5 Comparson btwn Tratonal Drvs an Actv Front-En Drvs v

10 .5.1 Tratonal Intrfac wth th Powr Gr Improv Powr Gr Intrfac wth Actv Front-En Invrtr 30.6 Chaptr Summary Systm Molng Chaptr Ovrvw Systm Confguraton Compnsaton Charactrstcs of an Actv Drv Stay-Stat Control Th - Thory Dynamc - Mol Drvng th - Mol Slctng th Rotatng Coornat Systm Powr Dfntons n - Coornat Systm Actv Rctfr Powr Loss Molng Estmatng Powr Loss Conucton Loss Mol Swtchng Loss Mol Chaptr Summary.55 4 Actv Front-En Motor Drv Control Chaptr Ovrvw Dynamc Euatons for an Actv Front-En Convrtr Control of Actv Drv F-Back Control v

11 4.3. Estmatng Angular Fruncy of Sourc Voltags Input-Output Lnarzaton Control F-Forwar Compnsaton Complt Control Schm for Actv Front-En Convrtr Inucton Motor Control Inucton Motor Dynamc Mol F-Back Control Chaptr Summary Smulaton Rsults Chaptr Ovrvw Mthoology us n Rsarch Stps Prform n Smulatng Systm Mos of Opraton Stps Prform n Analyzng Systm Prformanc Smulaton St-up Dmonstratng Systm Mos of Opraton Wthout Motor Loa Wth Motor Loa Actv Front-En Invrtr Systm Dsgn an Analyss Issus Systm Spcfcatons Dvc Powr Ratng Consratons Thrmal Managmnt Systm Issus Powr Qualty Consratons Lmts on Ractv Compnsaton.10 v

12 5.6 Chaptr Summary Summary an Conclusons Chaptr Ovrvw Thss Summary Conclusons from Rsarch Futur Rsarch Chaptr Summary Lst of Rfrncs.115 Vta.10 x

13 Lst of Tabls Tabl Pag.1 Voltag storton lmts A summary of FACTS controllrs confguratons Drv paramtrs at ffrnt motor loas Drv paramtrs urng ractv compnsaton at ffrnt motor loas x

14 Lst of Fgurs Fgur Pag 1.1 Actv front-n nucton motor rv systm Pr-phas uvalnt crcut Opratng prncpl Dstrbut nrgy sourc an utlty ntrfac Thr-phas thr-wr systm.4. Comparson btwn phas-controll an actv front-n rctfrs A smplf powr systm A voltag sourc rctfr Stay-stat control of PWM rctfr Thr-phas to two-phas transformaton Statonary to rotary rfrnc fram, Park s transformaton Crcut rprsntaton of systm mathmatcal mol Trackng θ Saturaton voltag charactrstcs for a 100 V, 100 A IGBT Forwar voltag charactrstcs for a 100 V, 100 A o Swtchng nrgy charactrstcs for a 100 V, 100 A IGBT Rvrs rcovry charactrstcs for a 100 V, 100 A o DC-lnk ynamcs controll by ln-s convrtr AC-s pr-phas uvalnt crcut 59 x

15 4.3 DC-s uvalnt crcut of an actv rv Hgh-gan fback controllr for ln-s convrtr Supply voltag fruncy stmaton F-forwar compnsaton for nput-output lnarzaton controllr Complt control schm for front-n convrtr Block agram of motor controllr Th harwar confguraton SIMULINK mol for actv front-n rv control componnt of ln currnt trackng th compnsaton comman Rvrsal of ln currnt DC-lnk varatons urng compnsaton trackng th rfrnc to mantan constant V c Stp rspons of c-lnk voltag controllr Dcoupl control of actv an ractv currnt componnts Ractv compnsaton an Motor Sp commans Unty an lang powr factor at th sourc Dcoupl control urng motorng opraton Motor currnts urng th motor acclraton an clraton Currnt flowng through IGBT an ant-paralll o at full motor loa Motor currnts for 3 Nm loa at 1100 rpm (50 hp) Ral an ractv currnt componnts IGBT collctor-mttr charactrstcs prov by th vc ata-sht IGBT collctor-mttr curv mol n MATLAB...97 x

16 5.18 IGBT powr losss at pak loa Fr whlng o powr losss at pak loa Total harmonc stortons n ln currnt at unty powr factor Ractv compnsaton lmts for actv rv Ln currnt THD an splacmnt powr factor urng compnsaton Dvc powr losss urng compnsaton.106 x

17 1 Introucton 1.1 Chaptr Ovrvw Th purpos of ths chaptr s to ntrouc th rsarch prsnt n ths thss. Scton 1. provs a brf ovrvw of th rsarch unrtakn. In Scton 1.3, th gnral a of Actv Front En Invrtrs s prsnt. Th crcut topology for th complt powr convrtr systm us for ractv powr compnsaton s xplan. Scton 1.4 scusss th basc opratng prncpl usng sngl-phas uvalnt crcut of th systm. Th ffrnt mos of opraton ar laborat usng phasor agrams. Scton 1.5 xamns th ky faturs an sutabl applcatons of th Actv Front En Invrtr systm. Scton 1.6 fns rsarch goals. Th scop of th rsarch s scuss hr. Scton 1.7 conclus Chaptr 1 by prsntng th thss outln. 1. Thss Rsarch In ths thss, an actv front-n nucton motor rv for ractv powr compnsaton s analyz. Th vctor control approach for hgh prformanc control of an nucton motor rv s now a wll accpt nustry stanar control. Th sam a of coupl control s xtn to th ln-s PWM convrtr for achvng bttr ynamc prformanc. Th sn-trangl PWM schm s us to control IGBT swtchs n both rctfr an nvrtr brgs. Th systm mol s obtan usng - rotatng fram thory. Th ln currnts ar compos nto an componnts. Th componnt s us to control th 1

18 ractv powr. Th componnt s us to control th c-lnk voltag an also to supply actv powr rur by th motor. A hgh gan fback wth nput-output lnarzaton control s prsnt to rmov couplng btwn an currnts. A loa powr f-forwar loop s a to th c-lnk voltag controllr for fast ynamc rspons. Usng th ynamc - mol, th rv prformanc s analyz to fn systm spcfcatons. Th motor acclraton, clraton, an varabl powr factor opraton (ractv powr compnsaton) of th actv systm ar monstrat. Th motor loa s var from no loa to full loa n stps of 10% ach. For ach stp th vc currnts, rvrs blockng voltag, swtchng powr loss, ln harmoncs, an c-lnk rppls ar plott. Ths ata s us to rv conclusons that fn systm spcfcatons an also stat opratng lmts. Th control of th rv systm s mplmnt n MATLAB-SIMULINK. Th complt systm harwar comprsng of swtchs, ln nuctors, c-lnk capactor bank, an th motor s mplmnt n commrcally avalabl smulaton tool, PSIM. Th two softwar packags ar ntrlnk usng an ntrfac moul. 1.3 Actv Front-En Invrtrs In ths work, th trm Actv Front En Invrtr rfrs to th powr convrtr systm consstng of th ln-s convrtr wth actv swtchs such as IGBTs, th clnk capactor bank, an th loa-s nvrtr. Th ln-s convrtr normally functons as a rctfr. But, urng rgnraton t can also b oprat as an nvrtr, fng powr back to th ln. Th ln-s convrtr s popularly rfrr to as a PWM rctfr

19 n th ltratur. Ths s u to th fact that, wth actv swtchs, th rctfr can b swtch usng a sutabl puls wth moulaton tchnu. Th PWM rctfr bascally oprats as a boost choppr wth ac voltag at th nput, but c voltag at th output. Th ntrmat c-lnk voltag shoul b hghr than th pak of th supply voltag [1]. Ths s rur to avo saturaton of th PWM controllr u to nsuffcnt c lnk voltag, rsultng n ln s harmoncs. Th rur c-lnk voltag ns b mantan constant urng rctfr as wll as nvrtr opraton of th ln s convrtr. Th rppl n c-lnk voltag can b ruc usng an appropratly sz capactor bank. Th actv front-n nvrtr topology for a motor rv applcaton s shown n Fgur 1.1 Ln-s Convrtr c V c M Loa-s Convrtr c Inucton Motor E 1 E E 3 L a V a b V b c V c C a' b' c' Fgur1.1 Actv front-n nucton motor rv systm 3

20 Th topology shown n Fgur 1.1 has two thr-phas, two-lvl PWM convrtrs, on on th ln s, an anothr on th loa s. Th confguraton uss 1 controllabl swtchs. Th ln-s convrtr s connct to th utlty through nuctor. Th nuctor s n for boost opraton of th ln-s convrtr. A transformr on th supply s wth approprat sconary mpanc also srvs th sam purpos. For a constant c-lnk voltag, th IGBTs n th ln-s convrtr ar swtch to prouc thr-phas PWM voltags at a, b, an c nput trmnals. Th ln-s PWM voltags, gnrat n ths way, control th ln currnts to th sr valu. Whn clnk voltag rops blow th rfrnc valu, th f-back os carry th capactor chargng currnts, an brng th c-lnk voltag back to rfrnc valu. 1.4 Opratng Prncpl A pr-phas uvalnt crcut of th thr-phas, ln-s PWM convrtr s shown n Fgur 1.. Th sourc voltag E S, an ln nuctanc L rprsnt th utlty systm. Th thr-phas voltags at th thr nput lgs of th ln s convrtr ar rprsnt by V. Th voltag V can b vw as a PWM voltag wav construct from th c lnk voltag V. Th magntu an phas of th funamntal componnt of V s controll by th ln-s convrtr. Th voltag V L, across nuctor L, s I S ωl whr, ω s th angular fruncy of supply voltag. Not that, th synchronous machn connct to an nfnt bus can also b rprsnt by th sam pr-phas uvalnt crcut shown n Fgur 1.. Smlar to an ovrxct or unr-xct synchronous machn, th PWM convrtr can also raw ln currnts at lang, laggng or unty powr factor. 4

21 V L E S L V I S Fgur 1. Pr-phas uvalnt crcut As llustrat n Fgur 1.3 (a), for unty powr factor opraton n rctfr mo of th ln-s convrtr, th PWM voltag V ns to b largr than th supply voltag phasor E S n magntu an lags E S by an angl δ. Ths maks E S an ln currnt I S, to b co-phasal. Th angl δ s call th powr angl bcaus t controls th powr flow btwn th two sourcs. Th rgnratv mo of th ln-s convrtr s shown n Fgur 1.3 (b). Th I S phasor now rvrss, causng rvrsal of I S ωl phasor. In orr to satsfy th phasor agram, th V phasor shoul la phasor E S by an angl δ. Thus th powr angl δ also rvrss. Lkws, th lang powr factor opraton s llustrat n Fgur 1.3 (c). Th actv powr P, an ractv powr Q, ar gvn by followng xprssons: P = E I S cosϕ (1.1) 3 S Q = E I S snϕ (1.) 3 S whr E S an I S ar supply voltag an ln currnt, whl φ s powr factor angl. 5

22 I S φ = 0 E S V I S ωl a) Unty powr factor urng motorng mo I S ωl I S φ = 180 b) Unty powr factor urng rgnratng mo I S ' φ' I S φ V V' c) Lang powr factor opraton urng motorng mo Fgur 1.3 Opratng prncpl 6

23 From Fgur 1.3 (b) w can wrt, I S ωl cosϕ = V snδ (1.3) I S ωlsnϕ = V cosδ (1.4) Substtutng th valus of I cosϕ an I snϕ n Euaton 1.1 an 1. S S rspctvly, V snδ P = 3 ES (1.5) ωl V cosδ ES Q = 3 ES (1.6) ωl Th uatons 1.1 through 1.6 ncat that th PWM voltag, V, an powr angl, δ, can b controll to control actv an ractv powr. It s also possbl to mantan ractv powr constant whl varyng actv powr. Ths s on by kpng phasors V cosδ constant an varyng phasor V snδ. An ffctv control stratgy for achvng ths ar scuss n tal n Chaptr Ky Faturs of Actv Front-En Invrtrs Th powr lctroncs upmnts ar oftn vw as a sourc of troublsom ln-s ntractons n th form of non-lnar ractv currnts an harmoncs. Howvr, wth th avnt of hgh powr smconuctor vcs capabl of swtchng auatly fast, many nw applcatons of powr lctroncs upmnts ar bng nvsag. On amongst thm s Actv front-n nvrtr, whch can prov a soluton to som powr ualty problms. Th ky faturs of ths topology ar scuss hr. 7

24 Rgnratv Capablts In normal motorng mo of th rv, powr flows from supply-s to th motor. Th ln-s convrtr oprats as rctfr, whras th loa-s convrtr oprats as an nvrtr. Durng rgnratv brakng mo, thr rspctv rols ar rvrs. Th systm can contnuously rgnrat powr f th machn s a gnrator, such as n wn gnraton systm. Unty Powr Factor Opraton Wth th ln currnts n phas wth th ln voltags, th unwant ractv currnts ar lmnat. Snc rgnraton s also possbl at unty powr factor, th ovrall powr ualty s mprov sgnfcantly. Th convrtr wll b abl to supply th sam actv powr but at ruc currnt ratngs. Thus an ncras cost of th convrtr on account of usng actv powr swtchs can b justf for hgh powr applcatons. Ractv Powr Compnsaton Altrnatvly, th kva ratngs sav u th unty powr factor opraton can b us to prov ractv powr compnsaton to th utlty systm. Th oubl-s powr convrtr thus acts as statc VAR compnsator whl rvng a varabl sp motor loa. Ths schm can b an attractv altrnatv to th ovrxct synchronous motor us as a VAR compnsator. As an Intrfac btwn Dstrbut Enrgy Sourc an Utlty Th lns PWM convrtrs ar applcabl whnvr a DC bus s to b connct to th AC gr. Usually ths s th cas for strbut nrgy sourcs such as ful clls, mcroturbns, or varabl sp wn nrgy plants mployng a c-lnk. 8

25 Utlty Supply Ln Transformr Ln-s Convrtr Dc-lnk Loa-s Convrtr Mcroturbn + Gnrator or Wn Gnrator Stp - up Choppr Solar Panl Fgur 1.4 Dstrbut nrgy sourc an utlty ntrfac Fgur 1.4 shows schmatc rprsntaton of strbut nrgy sourcs connct to th utlty gr. Th ln-s PWM convrtr facltats th flow of powr from strbut sourcs to th Utlty at fx fruncy, an at sr powr factor. 1.6 Rsarch Goals Evaluatng th systm prformanc by accurat smulatons s th frst mportant stp n th vlopmnt of any powr lctroncs systm prototyp. By smulatng th xpct prformanc of th systm, tchncal rsks n th actual vlopmnt can b ruc sgnfcantly. Thus to ntfy vc slcton, systm spcfcatons, an sgn 9

26 ssus pror to th actual sgn, s th prncpal motvaton bhn unrtakng ths rsarch. Th broar objctv stat abov s furthr artculat nto spcfc goals mnton blow. 1. Dmonstrat applcaton of an Actv Front En Motor Drv topology, shown n Fg. 1.1, for supplyng varabl ractv powr compnsaton to th utlty, whl rvng a varabl sp motor loa.. Obtan th systm ynamc mol an prsnt ffctv couplng control stratgs for bttr transnt prformanc. 3. Implmnt th systm mol an sutabl control schm n SIMULINK. 4. Evaluat th systm prformanc at varabl loa by plottng systm paramtrs such as ln currnts, ln harmoncs, c-lnk voltag rppl, vc pak currnts an voltags. Us th vc loss mol to plot conucton, an swtchng losss for th actv swtchs. 5. Draw conclusons about th systm opratng ffcncy, vc slcton, an scuss optmum systm sgn ssus. Th rsarch prsnt n ths thss ams to achv ths goals. 1.7 Chaptr Summary an Thss Outln In ths chaptr, svral topcs wr scuss. A brf ovrvw of th rsarch to b prsnt n ths thss s frst prov. A crcut topology us for an Actv Front En motor rv systm s scuss as wll. Furthr th prncpl of opraton for ths topology s xplan wth th hlp of phasor agrams. Svral ky faturs an som 10

27 potntal applcatons of Actv Front En Invrtrs ar xamn furthr. At th n, th prmary motvaton bhn ths rsarch an th prcs goals that ths rsarch st out to achv ar also stat. In Chaptr, a tal scusson on powr ualty, stablty, an ractv powr compnsaton wll b prsnt. In aton th Instantanous Actv an Ractv powr fntons wll b rvw. Furthr, ffrnt mthos for compnsaton wll b compar. In partcular, th powr compnsaton usng nucton motor rv wll b scuss. In Chaptr 3, th - rotatng fram thory as appl to th actv front n nvrtr systm wll b scuss. Th systm ynamc mol n - coornats wll b rv. Th actv an ractv powr fntons n -fram wll b rv as wll. Ths wll st up th control problm, whch wll b solv n th nxt chaptr. In Chaptr 4, th control stratgy s formulat. Th nput-output lnarzaton for coupl control of an currnt componnts wll b scuss. Th loa powr f-forwar compnsaton s also scuss to achv bttr transnt prformanc. Th man purpos of Chaptr 5 wll b to smulat all possbl mos of opraton of th complt rv systm. Th smulaton st up an mplmntaton ssus n SIMULINK as wll as PSIM wll b scuss. In aton, ths chaptr wll st own th approach for trmnng th systm spcfcatons, loss calculatons, an optmum systm prformanc. Th tal smulaton rsults wll also b prsnt. In Chaptr 6, a brf summary of th thss wll b gvn. Bas on th smulaton rsults, mportant conclusons rgarng th rsarch wll b ma. Lastly, svral suggstons on possbl futur rsarch wll b ma. 11

28 Backgroun.1 Chaptr Ovrvw In th prvous chaptr, th gnral a of actv front-n nvrtrs an th thss outln was prsnt. Th purpos of ths chaptr s to prov a tal backgroun prtanng to othr rsarch usful n analyzng th actv front-n rv. In Scton. powr ualty ssus nclung caus an ffcts of harmoncs ar scuss. In Scton.3 th rol of powr lctroncs n mprovng th ac gr powr s rvw. Th ntrstng ntrprtatons of nstantanous ral an ractv powr ar scuss n Scton.4. At th n, th comparson btwn tratonal rvs wth phas-controll rctfrs an rvs wth actv front-ns s prsnt. Ths comparson s th motvaton for prfrrng actv front-n rvs ovr tratonal rvs for som hgh powr applcatons.. Powr Qualty Issus An unntrrupt, snusoal voltag at rat magntu an fruncy rprsnts th powr supply of hghst ualty. Th factors that fn th ualty of lctrc powr ar harmonc storton, voltag rgulaton, voltag sag, an voltag unbalanc n aton to th contnuty of powr supply. Th unvrsal us of non-lnar loas, manly powr lctronc convrtrs, has ncras th prsnc of non-lnar an ractv currnts n th powr systm. In most applcatons, th swtchng of ths convrtrs s on synchronously wth th ln 1

29 voltag. Th harmonc componnts prouc n ths cas ar ntgr multpls of th funamntal fruncy, also rfrr to as suprharmoncs. Th prsnc of laggng, nonlnar currnts la to th ln voltag stortons, ncras transmsson losss, atonal transmsson an strbuton capacty, n aton to affctng powr systm stablty. In many othr nustral loas such as arc furnacs, spot wlng machns, rollng mlls, an mn hosts, th loa currnts ar raply changng an non-snusoal n shap. Th harmonc spctrum of th rctfr nput currnts for ths loas contan subharmonc componnts, whch ar not ntgr multpls of th funamntal ln fruncy, n aton to th suprharmoncs componnts []. Ths wavforms ar consr as non-proc. Ths ractv currnts along wth proc an non-proc harmonc currnts n to b lmnat from th powr systm to mprov th ovrall powr ualty to an accptabl lvl. Bfor scussng th tals of varous powr compnsaton mthos, t s usful to nvstgat th sourcs of harmoncs an thr ffcts n ffrnt typs of lctrcal loas...1 Sourcs of Harmoncs Any componnt of voltag or currnt wavform, othr than spcf fruncy snusoal componnt s rfrr to as harmoncs. Non-lnar loas chang th snusoal natur of th ac powr currnt, thrby, rsultng n th flow of harmonc currnts n an ac powr systm. A brf rvw of ths loas an harmoncs prouc by thm s prsnt hr [3]. 13

30 Statc Powr Convrtrs - Thyrstor an/or o bas powr convrtrs ar th largst non-lnar loas connct to th powr systm. Ths ar xtnsvly us n nustry to convrt powr from ac-to-c, c-to-ac, c-to-c, an ac-to-ac. Th currnt commutaton phnomnon rsults n voltag notchng an th poor splacmnt powr factor (DPF) raws atonal VAR from th sourc. Arc furnacs, mn hosts loas Th harmoncs prouc by ths loas ar hghly unprctabl bcaus of cycl-by-cycl varaton of th mchancal toru. Th ln currnt s non-proc. Th harmonc spctrum shows prsnc of both ntgr an non-ntgr orr of fruncs []. Ths typs of loas oftn rur a shunt compnsator to mantan voltag lvls, mprov powr factor, an ncras powr systm stablty. Swtch Mo Powr Suppls (SMPS) Most lctronc upmnt uss a SMPS to prov th stablz voltag to th upmnt. It fs th capactor that suppls voltag to th upmnt. Snc th loa, as sn from th powr systm, s a capactor, th currnt to th powr supply s scontnuous, proucng ln harmoncs. Puls Wth Moulat (PWM) Drv Th c lnk rv has a o at th nput an a larg capactor on th c lnk to rgulat th c voltag. For lght loas (30-50%), th currnt only flows whn th voltag output of th o rctfr s abov that of th capactor. Thus at lght loas currnt n th ac crcut s scontnuous. Utlty Intrfac wth Dstrbut Enrgy Sourcs Wth th ncrasng us of strbut nrgy sourcs such as ful clls, wn gnrators, mcro-turbns, an 14

31 solar clls, thr ar varous topologs avalabl to connct ths sourcs to th utlty. Ths ntrfacng powr convrtrs may act as currnt sourcs attach to th lctrc utlty or as voltag sourcs t to th utlty through a srs mpanc. Dpnng on th topology us, th outputs of ths powr convrtrs may contan harmoncs of varous orrs an powr factors that may caus unaccptabl powr ualty for th utlty gr... Effcts of Harmoncs Most powr upmnt ar sgn to oprat at fx fruncy snusoal voltags an currnts. Th prsnc of harmoncs wll naturally hav unwarrant ffcts on ths upmnts. Th gr to whch harmoncs can b tolrat pns on th typ of loa consumng ths harmoncs. In cas of hatng loas, such as ovn or furnacs, th harmonc currnts ar utlz for hatng an thus prsnc of harmoncs o not hav any avrs mpact. In rotatng machns, such as nucton motors an synchronous gnrators, th harmoncs caus ncras ron an coppr losss, rsultng n ncras hatng an ruc ffcncy. Harmonc currnts also gv rs to hghr aubl nos compar to th snusoal currnts. Th harmonc currnts can also caus or nhanc coggng (rfusal to start smoothly) or crawlng (hgh slp) phnomnon n an nucton motor. Th ntracton btwn harmonc currnts an funamntal fruncy stator currnt las to pulsatng toru an may caus mchancal oscllatons. In th cas of transformrs, th harmoncs caus hghr ron an cor losss rsultng n ncras hatng. 15

32 Powr cabls carryng harmonc currnts ar pron to hatng u to skn an proxmty ffcts. Powr cabls actng as paralll capactors may b nvolv n systm rsonanc. Du to magnf harmonc lvls, th cabls may b subjct to th voltag strss an corona, whch can la to lctrc falur. Atonally, th prsnc of harmoncs may caus mtrng an nstrumntaton vcs to prouc rronous rsults. In powr systm upmnt such as swtchgars, harmonc currnts ncras hatng an losss, thrby rucng stay stat currnt carryng capacty an shortnng th lf of nsulatng componnts. Fuss also suffr ratng bcaus of th hat gnrat by th harmoncs urng normal opraton. Th IEEE rcommn practcs an harmonc control gulns [3] lmt th harmonc contnts an th stortons caus by thm n th wavform to a crtan lvl. Th storton lvl s gaug n trms of total harmonc storton (THD), fn as, VRMS V1 THD = *100 (.1) V 1 Whr, V RMS s th root man suar valu of th total voltag wavform, comprsng all th harmoncs nclung th funamntal fruncy componnt. Whras, V 1 s th root man suar valu of th funamntal componnts of total voltag. Th storton lmts rcommn by IEEE 519 stanar ar lst n Tabl.1. Th lmts ar applcabl only at th pont of common couplng (PCC) of th utlty an plant ntrfac. Th lmts ar rcommn to b us as systm sgn valus for th worst cas for normal opraton. Normal opraton s th opratng conton lastng longr than an hour. For shortr pros, such as urng start-ups or unusual contons, th lmts may b xc by 50%. 16

33 Tabl.1: Voltag storton lmts Bus Voltag at Pont of Common Couplng (PCC) Invual Voltag Dstorton (%) Total Harmonc Dstorton (%) 69 kv an blow kv through 161 kv kv an abov Rol of Powr Elctroncs n Improvng Qualty of AC Gr Powr Powr lctroncs, whch s th major contrbutor to th troublsom ln-s ntractons n th form of ractv currnts an harmoncs, can also prov soluton for rmovng such ffcts. Th prospcts of usng a powr lctroncs bas systm to arss th powr ualty ssus proms to chang th lanscap of futur powr systms n trms of gnraton, transmsson an strbuton, opraton an control. Th vr ncrasng ntrst n ths applcatons can b attrbut to th svral factors as lst blow [4]: 1. Avalablty of powr smconuctor vcs wth hgh powr ratngs capabl of swtchng fast la to bttr convrson ffcncy an hgh powr nsty. 17

34 . Growng awarnss of powr ualty ssus an strctr norms st forth by th utlty compans an rgulatory authorts to control harmonc polluton an EMC ffcts. 3. Contnual us of xstng transmsson systm capacty for ncras powr transfr wthout compromsng transmsson systm stablty an rlablty. 4. N for ffctv control of powr flow n a rgulat nvronmnt. 5. Incras mphass on cntralz gnraton wth rnwabl nrgy sourcs to avo transmsson ln congston. Many typs of utlty applcatons bas on powr lctroncs controllrs ar bng nvsag. Ths nclu actv an ractv powr flow control, systm stablty, mprovng powr ualty by lmnatng harmoncs, mprovng transmsson ffcncy, an protcton. Thus, powr ualty solutons comprsng ractv compnsaton, compnsaton for th non-actv currnts, harmonc compnsaton, or actv fltrng s on of th many sgnfcant aras of utlty applcatons for ths controllrs, summarly rfrr to as flxbl ac transmsson systm (FACTS) controllrs. Th ffrnt typs of FACTS controllrs an th prncpl of opraton s rvw brfly n th followng subsctons..3.1 Flxbl AC Transmsson Systms (FACTS) Opratng Prncpl In xstng ac transmsson ntworks, lmtatons on constructng nw powr lns has l to svral ways to ncras powr transmsson capablty wthout sacrfcng th stablty rurmnts. Powr flow on a transmsson ln connctng two ac systms s gvn by, 18

35 P = E 1 E sn δ (.) X Whr E 1 an E ar magntus at th two ns of transmsson ln, X s th ln ractanc, an δ s th angl btwn th two bus voltags. Euaton. shows that powr flow on a transmsson ln pns on th voltag magntu E 1 an E, th ln ractanc X, an th powr angl δ. FACTS vcs bas on phas-controll thyrstors or actv swtchs such as IGBTs can b us to raply control on or mor of abov thr uantts. Th trm, FACTS vcs, can b formally fn as a collcton of powr convrtrs an controllrs that can b appl nvually or n coornaton wth othrs to control srs mpanc, shunt mpanc, currnt, voltag, phas angl, oscllaton ampng. By controllng on or all ths uantts, FACTS vcs nabl transmsson systm to b oprat closr to ts thrmal lmt wthout crasng th systm s rlablty n aton to provng mprov ualty powr. Dpnng on whthr thy ar connct n shunt or srs, th FACTS vcs can b catgorz as shuntconnct an srs-connct controllrs [5]..3. Shunt-Connct Controllrs Typcally, th shunt-connct controllrs raw or supply ractv powr from a bus, thus causng th bus voltag to chang u to th ntrnal systm ractanc. Som of th popular shunt controllrs ar scrb blow [6]. Statc synchronous compnsator (STATCOM) s a shunt-connct statc VAR compnsator, whch can control ts output currnt (nuctv/capactv) npnnt of 19

36 th ac systm voltag varatons. It uss slf commutat (actv) swtchs lk IGBTs, GTOs, or IGCTs. It may or may not n larg nrgy storag capacty pnng on what actv an/or ractv powr compnsaton s sr. Statc VAR compnsator (SVC) s anothr typ of powr compnsator, whos output s ajust to xchang capactv or nuctv currnt so as to mantan bus voltag constant. SVC s bas on vcs wthout turn-off capablty, lk thyrstors. SVC functons as a shunt-connct controll ractv amttanc. Som popular SVC confguratons ar thyrstor controll ractor (TCR), thyrstor swtch ractor (TSR), an thyrstor swtch capactor (TSC). Th TCR has an ffctv nuctv ractanc whch s var by frng angl control of th thyrstor valv. Th ffctv nuctv ractanc of a TSR, on th othr han, s var n stp-ws mannr by full or zro conucton of th thyrstor val. In cas of a TSC, th ffctv capactv ractanc s var n a stp-ws mannr by full or full conucton of th thyrstor valv..3.3 Srs-Connct Controllrs Ths typs of vcs ar connct n srs wth a transmsson ln, thrby, changng th ffctv transmsson ln ractanc. Ths fatur allows srs-connct controllrs to control th flow of powr through th transmsson ln. Varous forms of such vcs nclu statc synchronous srs compnsator (SSSC), thyrstor controll or swtch srs capactor (TCSC/TSSC), an thyrstor controll or swtch srs nuctor (TCSR/TSSR). Th output of SSSC s n uaratur wth th ln currnt, an s controll npnntly of th ln currnt. Th SSSC crass th ovrall ractv voltag rop 0

37 across th transmsson ln an controls flow of lctrc powr. Th SSSC may nclu transntly rat nrgy storag to compnsat tmporarly an atonal ral powr componnt. Th TCSC vars ts ffctv capactv ractanc smoothly by frng angl control of th thyrstor valv. Altrnatly, th ffctv capactv ractanc of a TSSC s var n stp-ws mannr, by full or zro conucton of th thyrstor val. Smlarly n cas of a TCSR an TSSR, th ffctv ractanc s var smoothly an n a stp-ws mannr rspctvly. Tabl. summarzs th abov scusson on ffrnt typs of controllrs, thr rspctv crcut schmatc, systm functons, an control prncpl [5]. Th actv frontn nucton motor rv analyz n ths thss work falls unr th catgory of statc synchronous compnsator (STATCOM). From powr ualty pont of vw, t s bascally a shunt-connct statc VAR compnsator whch can control ts output currnt (nuctv/capactv) npnnt of th ac systm voltag varatons or loa. It ns a tmporary nrgy storag lmnt n th form of a c-lnk capactor to ffctvly supply th sr powr compnsaton whl rvng th mchancal loa connct to th nucton motor. Aftr stablshng ffrnt mthos of compnsaton, t wll b worthwhl to know xactly how much an whch componnt of th sourc powr ns to b compnsat. In othr wors w n to stablsh th rfrnc commans for th powr controllrs scuss abov. Th nstantanous powr fntons prsnt n th nxt scton xplan how to choos compnsaton rfrncs. 1

38 Tabl.: A summary of FACTS controllrs confguratons Controllr Crcut confguraton Systm functons Control prncpl TCR/TSC - Thyrstor Controll or Swtch Ractor Rgulat voltag Improv stablty VAR control by varyng L n th shunt conncton TCC/TSC Thyrstor Rgulat voltag & VAR control by Controll or compnsat VAR varyng C n th Swtch Capactor Improv stablty shunt conncton TSSC Thyrstor Swtch Srs Capactor Control powr flow Improv stablty Powr an VAR control through varyng C. TCSR Thyrstor Controll Srs Capactor Control powr flow Improv stablty Lmt fault currnt Powr an VAR control through varyng C & L n shunt conncton TCSR Thyrstor Currnt control by Controll Srs Lmt fault currnt nsrtng L n Ractor srs. STATCOM Statc Synchronous Compnsator Rgulat voltag & compnsat VAR Improv stablty VAR control through currnt control n shunt conncton Actv Fltr (Shunt Connct) LOAD Harmonc currnt fltrng Injct canclng harmonc currnt nto th sourc SSSC Statc Srs Synchronous Compnsator Control powr flow Improv stablty VAR control through srs voltag control.

39 .4 Gnratng Rfrnc Currnts Usng Instantanous Powr p- Thory For sngl-phas an thr-phas powr systms wth snusoal voltags an snusoal currnts, th uantts such as actv powr, ractv powr, actv currnt, ractv currnt, an powr factor ar bas on th avrag concpt [7]. For compnsatng th non-actv currnts, howvr, nstantanous powr an currnt fntons ar rur. Akag t al [8] hav ntrouc an ntrstng thory of nstantanous powr n thr-phas crcuts, wthout zro sunc currnts. Th thory s also popularly rfrr to as p- thory. Th concpt stablshs an ffctv mtho to compnsat nstantanous componnts of actv an ractv powr of th thr-phas systm. Ths work s wly rgar as a classcal thortcal rsarch an s on of th most ct rfrncs n th fl of ractv powr compnsaton an actv fltrng []. Snc, t s also th bass for gnratng rfrnc commans for actv compnsator prsnt n ths thss, th brf summary of th nstantanous powr p- thory s prsnt blow. Th thr-phas, thr-wr systm s shown n Fgur.1. Th thrphas voltags an currnts ar transform to - coornats as shown blow. 0 = / 1/ 1/ 3 / 1/ 3 / 1/ a b c (.3) 0 = / 1/ 1/ 3 / 1/ 3 / 1/ a b c (.4) 3

40 4 Z a Z b Z c a c b b a c Fgur.1 Thr-phas thr-wr systm For balanc voltags = 0. Thus 0 uals to zro. For balanc currnts, 0 uals to zro as wll. Th transformaton matrx C 1 an ts nvrs matrx C 1-1 ar fn as, = 1/ 1/ 1/ 3 / 3 / 0 1/ 1/ C, = 3 / 3 1/ 3 1/ 3 / 3 1/ 3 1/ 3 / 0 3 / C Usng th matrcs C 1 an C 1-1 w can o followng coornat transformaton = c b a C 0, = C c b a, an = C c b a Not, C 1 an C 1-1 ar orthogonal matrcs, so that, C 1 T C 1 = C 1 C 1 T = (C 1-1 ) T C 1-1 = C 1-1 (C 1-1 ) T = I (.5) Whr, I rprsnt an ntty matrx.

41 5 Th nstantanous actv powr, p, n a-b-c coornats s fn by, [ ] = + + = c b a c b a c c b b a a p (.6) Convrtng voltags an currnts n - coornats, w can wrt, [ ] = 0 0 p p + = (.7) In th smlar way, an nstantanous ractv powr s fn as [9], = (.8) Not that, p, as shown n Euaton.7 s an nstantanous actv powr, bcaus t s fn as th sum of th prouct of th nstantanous voltag an nstantanous currnt n th sam phas. So, p has mnson of Watt (W). On th contrary, th xprsson for contans th prouct of nstantanous voltag n on phas an nstantanous currnt n anothr phas. Thrfor, cannot hav mnson of W, nsta, a nw mnson call as magnary watt wll b us []. Combnng Euaton.7 an.8, w can wrt, = p Altrnatvly, currnts n - coornats can b xprss as: = p 1 (.9)

42 6 Euaton.9 can b rwrttn as, = p = p p (.10) Whr, th p an componnts of -axs an -axs currnts ar gvn by, _ p p + = ; _ p p + = (.11) An _ + = ; _ + = (.1) Nxt, th nstantanous actv powr n trms of -axs powr p, an -axs powr p, s gvn by, p p p + = + = (.13) + = = p p p p (.14) Th two componnts of nstantanous actv powr n Euaton.14 ar rfrr to as, + = p p p p p p p p (.15) Also not that, p p p p L p p p p = = + = + = + (.16) R p p p = = + = + 0 (.17)

43 7 As can b sn, p L ( + ) s th nt powr lvr to th loa whl, p R s th rppl powr oscllatng btwn sourc an loa, such that nt p R s zro. In smlar fashon, w can also wrt nstantanous ractv powr n - coornats as, = + = = p p (.18) Th two componnts of nstantanous ractv powr n abov uaton ar rfrr to as, + = p p (.19) Not hr that, R p p p p = = = + 0 (.0) L = = = + (.) Euatons.15 through.17 an Euatons.19 through. la to th followng ntrstng ntrprtatons of nstantanous ral an magnary powr [9]. Th nstantanous actv powr has two componnts, p L an p R. p L s th actv powr lvr to th loa. Whl, p R s th rppl powr whch oscllats btwn sourc an loa, such that avrag p R s zro. Smlarly, th nstantanous ractv powr can b splt n two componnts, L an R. L s th ractv powr lvr to th loa. Whl, R s th rppl powr whch oscllats btwn sourc an loa, such that avrag R s zro. Th p- thory rvals xactly whch componnts of ral an ractv powr flow

44 to th loa an whch oscllats btwn sourc an loa. As rur by th utlty, th partcular powr/currnt componnts can b compnsat. Thus a shunt actv compnsator wthout nrgy-storag lmnt can b us to compnsat a rppl componnt of ractv powr, whch s flowng to-an-from btwn sourc an loa. On th othr han, th rppl componnt of th actv powr, whch s th rsult of harmonc currnts, can b compnsat by a shunt actv fltr wth nrgystorag lmnt. Th p- thory, howvr, os not tak nto account zro-sunc currnts. A gnralz thory of nstantanous actv an ractv powr propos by Png t al [10] fn nstantanous ral an ractv powr for all scnaros such as, snusoal or nonsnusoal, an balanc or unbalanc thr-phas systms, wth or wthout zrosunc currnts an/or voltags. Bas on abov gnralz powr fntons, ractv powr compnsaton rfrncs ar gnrat for th actv front-n rv smulatons prsnt n ths thss..5 Comparson btwn Tratonal Drvs an Actv Front-En Drvs Th scusson so far n ths chaptr las us to a coupl of ntrstng scnaros. Frst, th prsnc of non-lnar loas n a powr systm has bn sgnfcantly ncras, an bcaus of thr ablty to control lctrc powr prcsly an ffcntly, th wspra us of powr lctroncs convrtrs s nspnsabl. Sconly, utlts ar 8

45 ncrasng concrn about th non-lnar currnts n powr systm, rsultng nto strctr harmonc an powr ualty stanars. Ths stuaton calls for altrnatv solutons n th form of varous compnsaton tchnus. Dpnng on th compnsaton objctv, ffrnt topologs as scuss n scton.3 can b us. For larg varabl sp rvs such as thos us n mnng xcavators, th hug nflux of non-lnar currnts, srously affct th powr ualty at th pont of common couplng. To nsur powr gr compatblty, a ractv compnsator such as a capactor bank or a STATCOM vc s rur for such nstallatons. Altrnatvly, an nucton motor rv wth an actv front-n can b us. It can achv powrful ynamc prformanc, whl provng xcptonal compatblty wth th ln n trms of powr factor an total harmonc storton. Fgur. shows th two schms. Sourc Voltag E S Z 1 E 1 PCC Thyrstor Rctfr Dc-lnk Invrtr Inucton Motor L S Srs Ractanc Actv front-en Dc-lnk Invrtr Inucton Motor Fgur. Comparson btwn phas-controll an actv front-n rctfrs 9

46 .5.1 Tratonal Intrfac wth th Powr Gr As can b sn n Fgur. a rctfr conssts of a stanar phas-controll thyrstor. Th rv typcally oprats nar ts full loa at all th tm. Th ln-s rctfr controls n to prov a stabl c-lnk voltag unr all ln an loa contons or rv prformanc may suffr. Mantanng a stabl c-lnk voltag n th prsnc of w powr swngs s ffcult for phas-controll thyrstors bcaus of th poor powr factor to th ln. Thus, whn th strbuton systm voltag s wak, th voltag avalabl for rctfcaton s also ruc rsultng n poor tm rspons. Th poor powr factor an lmt tm rspons of phas-controll rctfrs rur a larg amount of capactanc n th clnk to mnmz th voltag fluctuatons sn by th nvrtr [11]..5. Improv Powr Gr Intrfac wth Actv Front-En Invrtr Th us of hgh powr IGBTs n actv front-n nvrtr (AFE) topology as shown n Fgur. lmnats th shortcomngs of tratonal rctfr front ns. Th actv front n boosts th ln voltag to a c-lnk voltag hghr than normally prouc wth a o brg. It taks an avantag of th ntwork s nhrnt ractanc to ncras c-lnk voltag gratr than th pak of th ln-to-ln supply voltag. Th ln ractanc s a savantag n a phas-controll rctfr rsultng n voltag notchng. Th systm can b sgn to oprat wth suffcnt control margns so that th sr c-lnk voltag can b mantan, vn n th prsnc of larg ps n th 30

47 ncomng ln voltag. Th currnt flow btwn th ln an th actv rctfr s rctly pnnt on th voltag ffrnc btwn ln voltag an PWM voltag gnrat by th actv rctfr. Ths voltag ffrnc s appl across th ln ractanc. Ajustng th magntu an phas of ths voltag gvs th actv rctfr contnuous control ovr th currnt ampltu an phas n all four uarants of opraton. Th controllr rgulats th c-lnk voltag by mantanng th balanc of actv powr suppl by th rctfr an th actv powr rur by th nvrtr/loa. At th sam tm, th controllr can npnntly control flow of ractv powr allowng unty powr factor at th prmary of th transformr or at any othr gvn pont n th ntwork, lk th pont of common couplng that fs th rctfr. Ths hlps n mprovng th voltag rgulatons an ovrall ffcncy. Howvr, thr s a lmt on th amount of powr that can b transfrr to or from th gr. Th voltag rato btwn th ln voltag pak an c-lnk voltag mposs ths lmt [11]. Atonally, th currnt ratng of actv front-n rctfr mposs constrants on both th actv an ractv powr to b transfrr to an from th powr gr. To fn out th lmts, frst th systm mol s rur whch s prsnt n Chaptr 3..6 Chaptr Summary In ths chaptr, a backgroun matral on ractv powr compnsaton an powr lctroncs controllrs us n utlty applcatons was prsnt. Powr ualty stanars an IEEE gulns on harmonc storton wr also scuss. 31

48 A brf rvw of FACTS vcs, thr rspctv crcut confguraton, systm functon an opratng prncpl was prsnt. Furthr, th nstantanous actv an ractv powr thory was scuss. Th powr fntons prov by p- thory ar th bass of compnsaton commans gnrat for th actv rv. Th bnfts of usng actv rv wr scuss by comparng t wth tratonal rv wth phas-controll rctfrs. In th nxt chaptr th mathmatcal mol for actv rv s rv. Bas on ths mathmatcal mol, a control approach s formulat n Chaptr 4. 3

49 3 Systm Molng 3.1 Chaptr Ovrvw In th prvous chaptr, th n for compnsatng non-actv currnts an a tal rvw of th compnsaton mthos usng powr lctronc vcs wr scuss. Th thortcal backgroun on nstantanous powr fntons was also prsnt. In ths chaptr, a ynamc - mol, n for fastr transnt rspons of an actv front n convrtr wll b rv. Latr n ths chaptr, th powr loss mol to stmat th total hat sspaton n a front-n rctfr wll b ntrouc. In Scton 3., th systm confguraton for usng actv rv as a shunt compnsator wll b prsnt. Th compnsaton charactrstcs an th stay-stat controllablty of an actv rv wll b scuss hr. Scton 3.3 wll ntrouc th - thory of transformng thr-phas paramtrs to uvalnt two-phas rotatng coornat systm. In Scton 3.4 th - thory wll b appl to th systm ffrntal uatons to rv th ynamc - mol. To prov sr ractv powr compnsaton, th actv an ractv powr masurmnts n - coornats ar rur. Ths powr fntons wll b prsnt n Scton 3.5. In Scton 3.6 th powr loss mol to stmat conucton an swtchng losss n IGBTs an ant-paralll os us n th front-n rctfr wll b prsnt. Th total hat sspaton stmat usng th powr loss mol can b us n sgnng an approprat thrmal systm. 33

50 3. Systm Confguraton Consr a smplf powr systm shown n Fgur 3.1. It s assum that th systm voltag E S s purly snusoal. E 1 an E ar th ntrmat ln voltags whch ar not snusoal, but ar stort at varyng grs. V pwm s th voltag gnrat by th actv front-n convrtr, whl Z 1 an Z ar transmsson ln mpancs. L S s th srs ractanc of an actv rv us for boost opraton. Th non-lnar loa, shown n fgur, raws currnts wth actv an non-actv componnts. If th non-actv currnts ar not compnsat, t wll rsult n sourc voltag storton. Th rol of an actv front-n convrtr, n ths stuaton, s to supply th non-actv currnts n to kp total harmonc storton (THD) at th sr lvl. At th sam tm, th convrtr must raw ral currnt to f ts own loa whch s nucton motor. Sourc Voltag Non-lnar Loa E S Z 1 Z I L1 + h1 E 1 E Utlty Ln 1 I L1 + L I L - h1 Utlty Ln L S V pwm Srs Ractanc Actv Drv Fgur 3.1 A smplf powr systm 34

51 Th funamntal ral currnt rawn by th actv rv pns on th applcaton. In applcatons lk mn hosts, th rv raws th ral powr from utlty to f th contnuously varyng mn loa. In othr applcatons such as, an nucton motor connct to an xtrnal nrgy sourc lk a wn powr gnrator or a mcroturbn, th nvrtr may f nt ral powr back nto th ntwork Compnsaton Charactrstcs of an Actv Drv As llustrat n Fgur 3.1, th actv front-n convrtr rprsnts a shuntconnct synchronous voltag sourc (STATCOM), prvously scrb n Chaptr. Th actv rv can b vw as a shunt compnsator wth an nrgy storag lmnt n th form of a c-lnk capactor. Du to nrgy storag capablty, th actv rv has svral bnfcal faturs, whch ar us to mantan sr powr gr compatblty. Ths faturs ar lst blow. Th maxmum attanabl compnsatng currnt of an actv rv s lmt only by th currnt ratngs of th actv swtchs an by th chosn rato of pak ln voltag to c-lnk voltag. Th actv rv can mantan th maxmum VAR compnsaton an th sr c-lnk voltag, vn n th prsnc of larg ps n th ncomng ln voltag [11]. Th actv front-n convrtr can b oprat ovr ts full currnt rang vn at th low ln voltag lvls. Somtm ln voltags as low as 0% of th rat can also b tolrat. 35

52 Opraton ovr full currnt rang hlp ncras th stablty margn n cas of a fault, an thus mprovs ovrall transnt stablty. Th rspons tm of an actv front-n convrtr for compnsaton purposs can b as fast as a fracton of a half cycl (~ 10ms) [1]. For thyrstor controll ractors, th ynamc rspons can b as slow as 5 to 6 cycls. Latr n Chaptr 5, th compnsator rspons to th stp nput s plott to llustrat ths. Th coupl control stratgy allows th compnsator to xchang ractv as wll as ral powr to an from th ac systm. Th two powr xchangs ar mutually xclusv. Du to ral powr xchang capablty, th compnsator can b us for powr oscllaton ampng. 3.. Stay-Stat Control Th stay stat charactrstcs as wll as ffrntal uatons scrbng th ynamcs of th front-n rctfr can b obtan npnnt of an nvrtr an motor loa. Ths s bcaus th c-lnk voltag can b vw as a voltag sourc, f V c s mantan constant for th full opratng rang. Th nvrtr s thus connct to th voltag sourc, whos trmnal voltag V c, rmans unaffct by any normal nvrtrmotor opraton. Furthrmor, as shown n Fgur 3., th rctfr can also b vw as connct to th voltag sourc V c. Thus, th rctfr s abl to control magntu an phas of PWM voltags V abc rrspctv of ln voltags E

53 Ln-s Convrtr c V c M c E 1 E E 3 L a V a b V b c Vc C Invrtr + Motor Loa Fgur3. A voltag sourc rctfr Th systm s an xact rplca of th nvrtr-motor systm. Th PWM voltags, V abc, ar now xctaton voltags smlar to th motor trmnal voltags. Th sourc voltags E 13 can b compar to th motor countr mf voltags. Whras, ln nuctanc s smlar to th motor lakag ractanc! Durng stay stat, th systm opraton can b scrb usng th phasor agram shown n Fgur 3.3. As xplan arlr n Chaptr 1, th ral an ractv powr ar rprsnt by, V snδ P = 3ES (3.1) ωl V cosδ ES Q = 3 ES (3.) ωl Euatons 3.1 an 3. suggst that an actv rctfr can gnrat a sr, fx valu ractv powr whl supplyng th varabl ral powr man by th motor. 37

54 I S φ φ' I S ' E I S ωl cosδ = I S ' ωl cosδ' δ δ' V V snδ V' snδ' V' Fgur 3.3 Stay-stat control of PWM rctfr As shown n Fgur 3.3, ths can b on by kpng V cosδ constant an varyng V snδ. Thus by controllng th magntu an phas rctfr voltag V, th stay stat control of actv an ractv powr s possbl. Howvr, th uatons fal to xplan smultanous control ovr ral an ractv powr, whch s rur for a ynamc opraton of an actv rv. Sconly, an mportant prrust for an actv rv opraton s a constant clnk voltag, V c. A varabl c-lnk wll ntrouc unsrabl fluctuatons n th magntu an phas of PWM voltags gnrat by th rctfr. It wll caus th actv an ractv currnts rawn by th rctfr to vary from th sr valus. Ths wll furthr ntrouc atonal nos n th c-lnk voltag, snc ths ln currnts charg an scharg th c capactor. To solv ths non-lnarty an at th sam tm achv 38

55 fast ynamc rspons, an ffctv control schm s n. Th voltag sourc rctfr connct to th utlty can b ffctvly controll usng th fl ornt approach, sam as us for controllng th voltag sourc nvrtr fng an nucton motor [13]. Th rotatng rfrnc fram - thory s frst us to obtan a ynamc - mol of a ln s convrtr. Th ynamc - mol s thn us to mplmnt fl ornt control. Th - thory s ntrouc n th nxt scton. 3.3 Th - Thory A systm of thr-phas, snusoal, tm-varyng voltags can b rprsnt by an uvalnt two-phas systm. Consr a balanc, thr-phas, Y-connct voltags, E 1, E, E 3, whch ar 10 lctrcal grs apart. Consr a statonary, two- axs coornat systm, whr th -axs s algn wth E 1, an -axs s orthogonal to th - axs. Th thr-phas voltags hav componnt on both th an axs. Th an axs componnts can b xprss as, E s E s E E3 = E1 E cos60 E3 cos 60 = E1 (3.3) 3 3 = 0 + E cos30 E3 cos30 = E E3 (3.4) In matrx form, E E E s 1 = 0 1/ 1/ 3 / 1/ E 3 / E 1/ E s 0s 1/ 1 3 (3.5) Howvr, n orr that th two coornat systms ar uvalnt, th nstantanous powr n both th coornat systms shoul b ual. 39

56 P = P 13 (3.6) whr P 13 s powr n thr-phas crcut, an P s powr n uvalnt two-phas systm. To mt ths rurmnt, th transformaton matrx ns to b multpl by a factor of / 3. Th nw transformaton matrx, C 1, s, 1 1/ 1/ C = / 3 /, 3 1/ 1/ 1/ / 3 0 / C 1 = 1/ 3 1/ 3 / 3 (3.7) 1/ 3 1/ 3 / 3 Th Euaton 3.5 s rwrttn as, E E E s = / 1/ 3 / 1/ E 3 / E 1/ E s 0s 1/ 1 3 (3.8) Not that paramtrs E s, E s n two-phas statonary rfrnc fram ar stll tm-varyng. Bcaus most of th lctrc crcuts ar assocat wth nuctancs, th tm varyng paramtrs such as snusoal currnts an voltags tns to mak th systm mol complx, an systm rspons s oftn sluggsh. R. H. Park propos n 190 [1] to transform ths varabls to a fcttous rfrnc fram rotatng at som angular sp. If ths sp of rotaton s th sam as th angular fruncy of tm-varyng paramtrs, thn all th paramtrs n ths rfrnc fram bcom tm nvarant or c uantts. Bcaus th ffct of nuctancs assocat wth varyng currnts an voltags s rmov, th systm mol s rlatvly smpl an systm rspons can b suffcntly fast. Fgur 3.4 an 3.5 llustrat Park s transformaton. 40

57 E 3 = E m sn (ωt ) 10 0 E 1 = E m sn ωt Es = E 1 - E / - E 3 / s - axs E s = E 3/ E3 3/ E = E m sn (ωt ) s - axs Fgur 3.4 Thr-phas to two-phas transformaton E = E s snθ + E s cos θ - axs E s θ E s s - axs s - axs θ E = E s cosθ - E s sn θ E s E s s - axs s - axs ω - axs Fgur 3.5 Statonary to rotary rfrnc fram, Park s transformaton 41

58 Th orthogonal axs an ar rotatng at an angular sp of ω. Th θ s th angular splacmnt such that, θ ω = (3.9) t Th nw varabls n - rfrnc fram ar, E E cosθ = snθ snθe cosθ E s s (3.10) Th Park s transformaton matrx s rfrr to as C, cosθ snθ 1 cosθ snθ C = ; C = snθ cosθ (3.11) snθ cosθ Not that, both th matrcs C 1 an C ar orthogonal matrcs such that, C T 1 C 1 = C 1 C T 1 = I an C T C = C C T = I (3.1) whr I rprsnts an ntty matrx. 3.4 Dynamc - Mol Fgur 3.6 shows sourc voltags E 1, E, E 3 as ln-to-nutral voltags for ach of th thr phass. Th phas voltags an ln currnts 1,, an 3 ar gvn by, E1 = Em snωt ; 1 = m sn( ω t + ϕ) E = Em sn( ω t 10) ; = m sn( ω t 10 + ) (3.13) ϕ E = Em sn( ω t 40) ; = sn( ω t 40 + ) 3 3 m ϕ Th currnts la th sourc voltags by anglϕ. E m s th maxmum ln-tonutral voltag, whl m s th pak ln currnt. 4

59 Sourc Voltags Srs Impanc PWM Voltags E 1 R 1 L V 1 E R L V E 3 R L V 3 3 Fgur 3.6 Crcut rprsntaton of systm mathmatcal mol Drvng th - Mol Th ynamc uatons for ach phas can b wrttn as, 1 E 1 = L + R 1 + t E + t V ao = L + R V bo (3.14) 3 E 3 = L + R 3 + t V co In matrx form, Euaton 3.14 can b wrttn as, E E E 1 3 = L t R 1 3 V + V V ao bo co (3.15) 43

60 44 Usng transformaton matrx C 1, w can wrt, = C s s s, an = E E E C E E E s s s, an = co bo ao s s s V V V C V V V 1 0 (3.16) Pr-multplyng Euaton 3.15 by C 1, + + = co bo ao V V V C RC C t L E E E C ) (, Snc C 1 s a constant, t can b takn ns th rvatv trm. + + = s s s s s s s s V V R t L E E (3.17) Euaton 3.17 rprsnts ynamc mol n statonary rfrnc fram. Usng scon transformaton matrx, C, w can wrt, = s s C, an = s s C 1 (3.18) Pr-multplyng Euaton 3.17 by C an usng Euaton 3.18, + + = s s s s s s V V C RC C t LC E E C 1 ) ( = s s V V R t C LC C t LC E E 1 1 ) ( Puttng th valu of C, an ffrntatng wth rspct to tm, = V V R t I L t L E E θ θ θ θ θ θ θ θ cos sn sn cos cos sn sn cos

61 E E cosθ = L snθ snθ ω snθ cosθ ω cosθ ω cosθ ω snθ + L t + R V + V E E 0 1 V = ω L + L + R + (3.19) 1 0 t V whr ω = θ /t. Expanng Euaton 3.19, E = L + ω L + R + V (3.0) t = ω L R V (3.1) t E L + + Euatons 3.0 an 3.1 rprsnt th ynamc - mol of an actv front n nvrtr n a rfrnc fram rotatng at an angular sp ofω. In ths molω,, E, an E ar stat varabls whl V an V ar th nputs. Not that although th an componnts of ln currnts ar orthogonal to ach othr, thy ar not prfctly coupl. Th ynamcs of an ntrfr wth ach othr. Bas on ths ynamc mol an ffctv mtho of control, on n whch th two currnt componnts ar coupl s propos n Chaptr Slctng th Rotatng Coornat Systm A bttr nsght nto th ynamc bhavor of th systm s obtan by choosng a rotatng systm of coornats, whr th stay stat oscllatons sappar. For th ynamc mol scrb n Euatons 3.0 an 3.1, th puls-wth-moulat rctfr voltags srv as actuatng voltags, whl th ln voltags assum th rol smlar to that of rotor nuc voltags n nucton motor [13]. Th PWM voltags control th ln 45

62 currnt so that sr powr factor wth rspct to th ln voltags can b achv. A sutabl choc of coornat systm n ths cas s th on fn by th ln voltags. A movng coornat fram form by th snusoal ln voltags s shown n Fgur 3.7. Th two-phas voltags ar rprsnt by, E = E s cosθ E s snθ E = E s sn θ + E s cosθ rspctvly. E an E ar th projctons of th E s an E s componnts on an axs Th angular sp of rotaton of th movng coornats, ω, s gvn by, θ ω = t As llustrat n Fgur 3.7, slct θ such that, E = 0. Th E s an E s componnts of sourc voltag thus form a rght angl trangl so as to gv, E s tan θ. = E s Ths choc hlps to track θ by xprssng θ n trms of E s an E s as blow, cosθ = E E s s + E s, an snθ = E E s s + E s snθ an θ cos ar us to rotat paramtrs at an angular sp of θ ω =. t Snc θ s th angular splacmnt of th sourc voltags, th abov approach nsurs corrct trackng of supply fruncy vn f t s varyng an not constant. 46

63 E s Cosθ E s E s Snθ s θ E s s Es E + E s E E s s Fgur 3.7 Trackng θ 3.5 Powr Dfntons n - Coornat Systm Usng th systm ynamc mol stablsh n prvous sctons, th control of ln currnts s carr out n a movng rfrnc fram so that th fback sgnals ar c uantts. Ths suggsts that th currnt an/or powr rfrnc commans also n to b fn n a rotatng rfrnc fram. For ths purpos th nstantanous actv an ractv powr n movng coornat fram ar fn blow. Rfrng to th gnralz nstantanous powr thory [10], th nstantanous actv powr P n thr-phas coornats s fn by, P = E E E33 47

64 48 whr E 1, E, E 3 ar th sourc phas-to-nutral voltags, an 1,, 3 ar th ln currnts. In matrx form w can wrt, [ ] = E E E P Convrtng th paramtrs to two-phas movng coornats usng transformaton matrcs C 1 an C, = T C C E E C C P = T T T C C C C E E P ) ( ) ( Snc C 1 an C ar orthogonal, (C 1-1 ) T C 1-1 = I an (C -1 ) T C -1 = I [ ] E E E E P + = = As xplan n prvous scton, E s mantan ual to 0 at all th tms, rsultng n, E P = (3.) In th sam mannr, accorng to th gnralz nstantanous powr thory [11], th ractv powr n thr-phas coornats s gvn by,

65 Q = E Q = Q Q 1 3 E E3 = 3 E1 1 E 3 3 E 1 1 E s 1 s 1 s s Q = ( C E ) ( C ) = C ( E ) Q s = ( E ) = E s s s s E s s Ths s an xprsson for ractv powr n two-phas statonary fram for a balanc thr phas systm. In - movng coornats, th xprsson s gvn by, Q = E E Rcall that E s always mantan to zro valu. Q = E (3.3) Euaton 3.3 shows that for a postv, Q s ngatv, mplyng that th actv rctfr s fng th ractv powr back to th sourc. Altrnatvly for a ngatv, th Q s postv, rsultng n nt nflow of ractv powr from sourc to th loa. 3.6 Actv Rctfr Powr Loss Molng Th control schm bas on th ynamc mol prsnt n th prvous scton s us to trmn th currnt an voltag ratngs of an actv rctfr for a gvn motor loa an compnsaton rurmnts. Furthr, to analyz th systm prformanc an 49

66 ffctv loss mol of an actv rctfr s ncssary. Th loss mol wll hlp stmat powr loss, valuat th ffcncy, an o thrmal analyss. Th hat gnrat as a rsult of powr loss must b conuct away from th powr chps an nto th nvronmnt usng a hatsnk. If an approprat thrmal managmnt systm s not us, th powr vcs wll ovrhat whch coul rsult n falur [14]. Th loss mol can also b us for comparng th powr loss vs-à-vs phas-controll rctfr Estmatng Powr Loss Th frst stp n thrmal sgn s th stmaton of total powr loss. In an actv rctfr usng IGBTs, th two most mportant sourcs of powr sspaton ar conucton losss an swtchng losss. Conucton losss ar th losss that occur whl th IGBT s on an conuctng currnt. Th total powr sspaton urng conucton s comput by multplyng th on-stat saturaton voltag by th on-stat currnt. In PWM applcatons, th conucton loss shoul b multpl by th uty factor to obtan th avrag powr sspat. Th swtchng loss s th powr sspat urng th turn-on an turn-off swtchng transtons. Th most accurat mtho of trmnng swtchng losss s to plot th I c an V c wavforms urng th swtchng transton. Multply th wavforms pont by pont an gt nstantanous powr wavform. Th ara unr th powr wavform s th swtchng nrgy xprss n watt-scons/puls. In aton to th IGBT losss, th fback o conucton an swtchng losss also ns to b consr. 50

67 3.6. Conucton Loss Mol Th swtchs us n smulaton ar al swtchs wth no forwar voltag rop an so no powr loss s assocat wth thm. But, th swtchs stll carry th rat currnt. To stmat conucton losss n an IGBT, th vc on-stat saturaton voltag s rur along wth th on-stat currnt. Onc th IGBT s slct bas on voltag an currnt ratngs, th corrsponng collctor-mttr saturaton voltag charactrstcs ar us to calculat th conucton losss. Fgur 3.8 shows collctor-mttr saturaton voltag vrsus collctor currnt curv for a 100 V, 100 A IGBT manufactur by POWEREX Inc. Ths curv s mol n MATLAB usng a n orr curv fttng tchnu. Gvn a currnt, th ral tm saturaton voltag can b obtan from th curv. Thus accurat stmaton of th conucton loss s possbl [15]. Th conucton losss n fast rcovry o ar stmat n a smlar mannr by frst fnalzng th o ratngs. Th o forwar charactrstcs shown n Fgur 3.9 ar thn mol n MATLAB. Th o currnt s masur an voltag rop across th o for a gvn varabl currnt can b stmat from th vc forwar charactrstcs. Th conucton loss s obtan by multplyng currnt wth th rsultng voltag, an thn avrag wthn on cycl. Th total conucton loss s gvn by, P C = P P (3.4) con _ o + con _ IGBT whr P con _ o an con IGBT P _ ar avrag conucton losss for fast rcovry o an IGBT rspctvly. 51

68 Fgur 3.8 Saturaton voltag charactrstcs for a 100 V, 100 A IGBT Fgur 3.9 Forwar voltag charactrstcs for a 100 V, 100 A o 5

69 3.6.3 Swtchng Loss Mol To stmat th total swtchng loss, IGBT swtch-on an swtch-off losss as wll as o rvrs rcovry losss ar consr. Howvr, as th swtchs us n th smulaton ar al, th turn-on an turn-off tms ar almost nstantanous. In ths cas, swtchng losss ar calculat bas on th amount of currnt to b turn on an off. To calculat swtchng losss n an IGBT, th vc swtchng loss vrsus collctor currnt charactrstcs shown n Fgur 3.10 ar us. Ths curv s mol n MTALAB usng a n orr curv fttng tchnu. Furthr, th rvrs rcovry loss n a o for a gvn collctor currnt s calculat by [14], P RR =.5 I RR t RR VCE ( pk ) 0 f (3.5) sw whr I RR s o pak rcovry currnt, t RR s rvrs rcovry tm; V CE(pk) s th pak voltag across o at th rcovry; an f sw s th swtchng fruncy. Th valus for I RR an t RR can b obtan from th rvrs rcovry curvs shown n Fgur Th total swtchng losss ar assocat wth crcut opratng contons. So, w cannot smply a th IGBT swtchng losss an o rcovry loss to gt th total swtchng loss n th crcut. Consr that th IGBT s turn-on whn th collctor currnt s ngatv. Ths mans th o s frwhlng. Thr s no swtchng loss bcaus th vc s at zro potntal. Now consr th swtch-off opraton. If th collctor currnt s postv, thr wll b crtan swtchng-off loss assocat wth th IGBT. Howvr, f th collctor currnt s ngatv, thn ant-paralll o s carryng th loa currnt an not IGBT [15]. In ths cas th swtchng loss s bascally th o rvrs rcovry loss comput usng Euaton

70 Fgur 3.10 Swtchng nrgy charactrstcs for a 100 V, 100 A IGBT Fgur 3.11 Rvrs rcovry charactrstcs for a 100 V, 100 A o 54

71 Bas on ths scusson th swtchng loss stmaton algorthm s programm n SIMULINK. Usng swtchng loss algorthm along wth th swtchng nrgy an rvrs rcovry plots mnton arlr, th total swtchng loss can b calculat as, P SW = P P (3.6) SWon _ IGBT + PSWoff _ IGBT + RR _ o whr P SWon _ IGBT an P SWoff _ IGBT ar th IGBT swtchng on an off losss. An P RR _ o s th rvrs rcovry loss for antparalll o. Fnally th total hat sspaton assocat wth ach half lg of an actv rctfr s calculat as blow, P = P + P ) + ( P + P + P ) (3.7) L ( con _ o con _ IGBT SWon _ IGBT SWoff _ IGBT RR _ o 3.7 Chaptr Summary In ths chaptr, svral topcs wr scuss. Th systm confguraton for usng an actv motor rv as a shunt compnsator was ntrouc. Th varous faturs of actv rv usful for compnsaton objctv wr lst. Furthr lmtatons of stay stat control to prouc bttr transnt prformanc wr scuss. Ths unrln th n for usng couplng control bas on - thory. Th tals of - thory wr thn ntrouc. Th systm ynamc mol was obtan usng - thory. Th ffrnt transformaton matrcs us to transform thrphas coornats to two-phas statonary an movng fram wr ntrouc. Snc th control wll b carr out n movng - coornats th powr fntons n - coornats ar rur, whch wr ntrouc nxt. Fnally, for valuatng th systm ffcncy an comparng t vs-à-vs o rctfr front n, th powr loss mol was 55

72 prsnt. Th loss mol was bas on vc charactrstcs curvs prov n th vc atasht an also crcut opratng conton. Th ynamc mol prsnt n ths chaptr provs th bulng block for trmnng sutabl control stratgs to achv bttr transnt prformanc of th actv front n nucton motor rv. Th control schm s ntrouc n Chaptr 5. 56

73 4 Actv Front-En Motor Drv Control 4.1 Chaptr Ovrvw In th prvous chaptr, th mathmatcal mol of an actv rctfr scrbng th ynamc bhavor of th actv rctfr was prsnt. Atonally a powr loss mol to stmat th hat sspaton n a rctfr moul was also scuss. Th purpos of ths chaptr s to prsnt a sutabl approach for controllng th rctfr ynamcs. Apart from th front-n rctfr, th loa-s nvrtr an nucton motor ar also part of th systm confguraton. Th scon half of th chaptr s vot to scussons on th mathmatcal mol an fl ornt control of nucton motor. In Scton 4. th ac s pr-phas uvalnt crcut an c s uvalnt crcut of th ln-s convrtr wll b scuss. Th uvalnt crcuts ar bas on th systm ffrntal uatons. In Scton 4.3 a hgh gan fback controllr for controllng ln currnts wll b ntrouc. A schm for stmatng angular fruncy of sourc voltags n ral tm wll also b scuss n ths scton. In Scton 4.4 an nput-output lnarzaton controllr to countract th c-lnk varatons wll b prsnt. For achvng bttr transnt prformanc a f-forwar controllr wll b prsnt n Scton 4.5. In Scton 4.6, th complt control schm an paramtr masurmnts wll b scuss. In Scton 4.7 a mathmatcal mol of an nucton machn wll b ntrouc. Furthr, a classcal fl-ornt controll for nucton motor wll b scuss. 57

74 4. Dynamc Euatons for an Actv Front-En Convrtr For th purpos of fast rspons, th control s carr out n th - rfrnc fram. Ths typ of control s rfrr to as fl-ornt control. Th startng pont of th control s th systm of non-lnar ffrntal uatons whch charactrzs ts bhavor. As rv prvously, th ynamcs of an actv front-n convrtr ar gvn by a systm of ffrntal uatons stat blow, L t L t = E ω L R V (4.1) = E + ω L R V (4.) Th ffrntal uaton govrnng c-lnk voltag also ns to b a to th abov st of systm uatons to compltly fn systm ynamcs. V C t c = (4.3) c M whr, c s th total c-lnk currnt suppl by th rctfr, whl M s th loa-s c currnt whch s th rsult of nucton motor opraton. Th c an M currnts ar shown n Fgur 4.1. Fgur 4. an 4.3 show ac an c s uvalnt crcuts rspctvly. Th c currnt, M, can b vw as a nos n c-lnk voltag V c [13]. A postv M (motorng-mo) wll scharg th c-lnk, whl a ngatv M (rgnraton-mo) wll charg th c-lnk to a hghr potntal. If th c-lnk currnt c suppl by th lns convrtr uals to M, thn w hav, Vc C = 0. t In othr wors, c-lnk voltag rmans constant. 58

75 E 1 R 1 L V 1 c V c M E R L V C c E 3 R L V 3 Motor Loa Sourc 3 Ln-s Convrtr Loa-s Convrtr Fgur 4.1 DC-lnk ynamcs controll by ln-s convrtr Srs Impanc R L E = E + je = + j + _ PWM voltags V = K m V c V = V + jv Fgur 4. AC-s pr-phas uvalnt crcut c Vc M c = K K + K 3 3 C c Invrtr + Motor Loa Fgur 4.3 DC-s uvalnt crcut of an actv rv 59

76 In Euaton 4.1, th trms E an E ar comput from sourc voltags, E 1, E, an E 3. Snc ln voltags ar known, th angular fruncy, ω, can b asly stmat. Th PWM voltags V an V ar th two nputs to th systm whch ar gnrat usng th sn-trangl PWM controllr. L S an R rprsnt srs mpanc. Fgur 4. llustrats ac-s pr-phas uvalnt crcut rprsntaton of Euaton 4.1. V appars as a controll voltag-sourc whch s a functon of a moulaton nx an c-lnk voltag V c. On th othr han, Fgur 4.3 shows c-s uvalnt crcut rprsntaton of Euaton 4.. Th c-lnk currnt, c, appars as a currnt sourc, whch controls th capactor voltag whl supplyng th currnt rur by th motor loa [16]. 4.3 Control of Actv Drv Th abov scusson sts up th non-lnar control problm. Th systm to b controll s bascally multpl-nput-multpl-output (MIMO) typ systm. Th PWM voltag commans, V an V, ar th two nputs to th systm. Th rsultant, an currnts ar th output of th systm. Ths two output currnts ar utlz for two ffrnt purposs. Th componnt s assgn to prouc th sr ractv powr ( Q = E ). Thus, s consr as a ractv compnsaton comman. Furthr, th ral componnt of ln currnts s rur to mantan constant voltag across c-lnk capactor, an also to rv a physcal loa connct to th motor. Thus, s assgn to supply th sr ral powr ( P = E ) to th systm. 60

77 Th control problm s to choos V an V n such a way as to forc an to track th rspctv ractv an ral powr rfrnc trajctors F-Back Control Th sutabl control stratgy for th abov mnton non-lnar systm s th on whch ffctvly lmnats th couplng btwn th two currnt componnts. Ths s on by forcng th systm nto currnt-comman mo usng hgh gan fback. Frstly, th currnt rfrnc commans n to b gnrat. To nsur constant c-lnk voltag, th PI control loop s appl to th c-lnk voltag rror, rsultng n th currnt rfrnc comman, *. Th c currnt, M, f to th loa through an nvrtr s a to * to form a nw currnt rfrnc comman as, * ' ' = K ( V ) + I c _ rf Vc ) t + K P ( Vc _ rf Vc M (4.4) Sconly, th ractv powr compnsaton algorthm wll gnrat a scon currnt rfrnc comman *. Th PI controllrs shown n Fgur 4.4 ar thn appl rctly to th rror btwn currnt rfrnc an actual valus, as shown blow. V V * * * = K ( ) t + K ( ) (4.5) I P * * * = K ( ) t + K ( ) (4.6) I P By appropratly choosng th gans of th PI controllrs, an can b ma to track * an * rspctvly. Consuntly th nw rfrncs, V * an V * for th PWM controllr ar gnrat. Th PWM controllr, f not saturat, wll prouc a swtchng pattrn such that sr actv an ractv powr can b prov. 61

78 1 * V c_rf + - PI Controllr + + * V c M * Compnsaton Comman * + - V * - PI Controllr + - V * - PI Controllr PWM C o n t r o l l r Fgur 4.4 Hgh-gan fback controllr for ln-s convrtr 4.3. Estmatng Angular Fruncy of Sourc Voltags A sutabl choc of coornat systm, fn by th sourc voltags, s ma n Chaptr 3 to achv bttr transnt prformanc. Th thr-phas sourc voltags, sparat by 10 lctrcal grs, rotat at an angular sp of ω raans pr scon. Snc th control s carr out n movng coornats, all th varabls must b convrt to th movng coornat systm, rotatng at an xact sam angular sp of ω ra/ sc. Th sourc voltag fruncy usually rmans unchang urng normal opraton of th powr systm. Howvr, vn a small varaton n ω wll caus rror n all th paramtrs that ar transform nto th rotatng coornat systm. Ths wll rsult n 6

79 rronous fback an consuntly affct th prformanc of th systm. For ths rason, th supply fruncy ns to b track an contnuously stmat n ral tm. Rcall, for a gvn supply fruncy, w choos - axs such that E componnt always rmans zro. Now f th supply fruncy changs, E wll no longr b zro. Th rror n E can b mnmz by a PI controllr to track ω n ral-tm as, ω = K I ( 0 ) P E t + K (0 E ) (4.7) Th nw angular splacmnt θ, s thn gvn by, θ = ω t (4.8) By choosng approprat gans for th PI controllr th varatons n supply fruncy can b track accuratly. Ths s llustrat n Fg 4.5 E s Parks E PI Controllr Intgrator θ = wt Transformaton E s E w = angular fruncy Fgur 4.5 Supply voltag fruncy stmaton 63

80 4.4 Input-Output Lnarzaton Control For a rlatvly constant V c, th fl ornt hgh-gan fback control schm, xplan n th prvous scton, rmovs th couplng ffct. In othr wors, th currnt uatons ar coupl, an th uatons ar lnar as long as c-lnk voltag s constant. Rcall th systm ynamc uatons, L t = E ω L R V L t = E + ω L R V (4.9) V C t c = c M Th PWM voltags V an V can b rprsnt n trms of moulaton nx an c-lnk voltag as, V = G M V (4.10) c V = G M V (4.11) c Whr G s th PWM controllr gan an M an M ar moulatng vctors n - coornats. For larg varatons n c-lnk voltag; howvr, th uatons ar no longr lnar. Ths stuaton arss whn th motor loa changs sunly or urng hgh acclraton an clratons (rgnraton) of motor shaft. Durng c-lnk varatons, th currnt rfrnc vars as a functon of V c. Th ynamcs of thn ntrfr wth th ynamcs of, rsultng nto unsatsfactory prformanc. Ths couplng of currnts can b ffctvly lmnat by consrng an nput-output lnarzaton controllr. 64

81 In ynamc uatons (4.9), V an V ar th nputs, controll n such a way as to gnrat sr currnts. Now fn nw varabls ' ' V an V such that, V V ' = V E + ωl + ' = V E ωl + R R (4.1) (4.13) So that th nw systm ynamc uatons bcom, L t L t ' = V (4.14) ' = V (4.15) In uatons , th ynamcs of an ar coupl. Th hgh gan fback controllr s thn appl to ths currnts to gnrat nw voltag commans. Th fnal voltag commans howvr, shoul account for th substtuton ma n uatons 4.1 an Thus nw voltag rfrncs ar gvn by [1], [17]: V * '* = V + E ωl R (4.16) V * '* = V + E + ωl R (4.17) 4.5 F-Forwar Compnsaton Th lnarzaton controllr xplan n th prvous scton coupls th two currnt controllrs ffctvly, an allows th systm opraton urng varabl c-lnk. Howvr, th systm stll suffrs from slow rspons. 65

82 Rfr to th Fgur 4.1 agan, an consr followng sunc of vnts. If th motor loa changs sunly, c currnt M wll rs sharply, rsultng n a p n c-lnk voltag. Th lnarzaton controllr now trs to rstor th c-lnk voltag back to ts rfrnc valu. If th rat of rs of c currnt M s fastr than rat of rstoraton of clnk voltag, th V c wll contnu to cras untl t rachs zro potntal. Altrnatvly, th rat of rs of M can b rstrct to avo consrabl cras n clnk voltag. In othr wors th systm tm rspons woul b slow. A bttr ynamc rspons s achv by mployng f-forwar compnsaton [18]. Th powr rur to gnrat th sr lctromagntc toru s masur n th c-lnk usng c voltag an currnt snsors. Ths powr ns to b suppl from th sourc. Thus, th f-forwar compnsaton currnt _f can b obtan from [17], K V c c _ f = 1 (4.18) E whr, E s sourc voltag an K 1 s proportonal gan n f-forwar loop. K 1 s allow to vary to mantan th stablty n th currnt loop, an t s also pnnt on ln voltag fluctuatons. Fgur 4.6 llustrats f-forwar compnsaton wth nput-output lnarzaton controllr. 4.6 Complt Control Schm for Actv Front-En Convrtr Bas on abov scussons th complt control schm for control of actv front-n convrtr s mplmnt usng two ac voltag snsors, thr ln currnt snsors, on c currnt snsor, an on c voltag snsor 66

83 c F-forwar Compnsaton K 1 E V c 1/U * + - V * - PI Controllr R V * P W M E Compnsaton Comman * Input-Output Lnarzaton Control + - V * - PI Controllr ω L V * C o n t r o l l r R Fgur 4.6 F-forwar compnsaton for nput-output lnarzaton controllr Fgur 4.7 llustrats th control of front-n convrtr. Th two ac voltag snsors ar connct to th sourc voltag. From ths ln snsors, th thr sourc voltags (phas-nutral) ar avalabl for us. Ths voltags ar furthr transform nto uvalnt two-phas movng coornats E an E. Th - axs ar algn such that th E componnt of th sourc voltags always rmans at zro valu. Th nxt stp s to gnrat currnt rfrncs. Th rfrnc s form as a functon of c-lnk voltag varatons an f-forwar compnsaton. Th c currnt M, s masur by th c currnt snsor plac on loa-s of th capactor. Th rfrnc currnt s gnrat from th ractv powr compnsaton comman. In currnt-comman control mo, th actual currnts an ar forc to follow th rfrnc commans usng hgh-gan fback an nput-output lnarzaton controllr. 67

84 E s E w = angular fruncy θ = wt 3-ph to -ph Transformaton E s Parks Transformaton PI Controllr Intgrator E c 1/L 1/L F-forwar Compnsaton R R L - - V V V - * * Parks Transformaton V s V s Compnsaton Comman Swtchng Functon S1 S S3 V c K 1 V c E 1/U E + V c_rf - V c V c - PI Controllr 1 * V * + * M - PI Controllr R V * P W M Compnsaton Comman * + - V * - PI Controllr ω L V * C o n t r o l l r R Input-Output Lnarzaton Control Fgur 4.7 Complt control schm for front-n convrtr 68

85 Th nw nput for th systm, V an V, ar f to PWM controllr to prov rur swtchng pulss usng thr sn-trangl or spac-vctor PWM algorthm. Th nstantanous valus of currnts an, can b masur usng thr currnt snsors. Altrnatvly, thy ar stmat usng th systm ynamc mol shown n Euaton 4.9. In th mol, L, ω, E an E ar all known; V an V ar unknown. Th nstantanous valus of PWM voltags ar stmat from th swtchng sgnals to IGBT vcs, an th c-lnk voltag as shown blow, V s Vc = (S1 S S3 ) (4.19) 4 An V s Vc = 3 ( S S 3 ) (4.0) 4 whr S 1, S, S 3 ar ntgr varabls whch cannot assum any valus othr than +1 an - 1. Whn th IGBT n th uppr half of th frst lg of th rctfr-brg s swtch on, + V c s connct to th phas-1 of th supply. Thus, S 1 assums valu ual to 1. Whn ths IGBT s swtch off, - V c s connct to th phas-1 of th supply. Thus, S 1 assums valu ual to -1. In th sam mannr S an S 3 assum valu ual to thr 1 or -1. Ths approach masurs nstantanous valus of PWM voltags wthout nng to mploy thr currnt snsors. 69

86 4.7 Inucton Motor Control Th fl of nucton motor control s wll stablsh toay. Th major challngs n controllng nucton motors ar: non-lnar systm ynamcs, nablty to masur control varabls such as rotor flux an rotor currnt physcally, an th motor paramtrs varatons wth hatng such as varatons n rotor rsstanc valu. Takng ths challngs nto account, th unvrsally accpt approach for controllng an nucton motor s th fl-ornt approach also rfrr to as vctor control [19]. Th fl-ornt control als wth rwrtng th systm ynamc uatons n a movng coornat systm that s rotatng wth th rotor flux vctor. In ths nw coornat systm, th ynamcs n motor toru an sp bcoms lnar, prov th rotor flux magntu s kpt constant. For a varabl rotor flux, an nput-output lnarzaton controllr s us that coupls th sp an rotor flux magntu Inucton Motor Dynamc Mol For fl ornt control, th nw coornat systm rotats wth th rotor flux. Snc rotor flux or rotor currnts ar not avalabl for masurmnts, th rotor flux s stmat usng a flux obsrvr. Th rotor flux lnkags n a two-phas statonary rfrnc fram ar xprss as [19], ψ t Ra R n R = ψ Ra pωψ Rb LR R + L R R M Sa (4.1) ψ t Rb R n R = ψ Rb + pωψ Ra LR R + L R R M Sb (4.) 70

87 whr, ψ Ra an ψ Rb ar rotor flux lnkags, n p s numbr of pol-pars of nucton motor, M s coffcnt of mutual nuctanc btwn stator an rotor wnngs, R R an L R ar rotor rsstanc an lakag ractanc rspctvly. ω s th sp of rotaton of rotor. Sa an Sb ar th ln currnts n statonary two-phas coornats. Th motor currnts can b masur usng currnt snsors, whch ar thn transform to uvalnt two-phas valus Sa an Sb. A smpl way to stmat rotor flux lnkags s thn to solv Euatons 4.1 an 4.. Onc rotor flux lnkags ar known, th angular poston n th movng coornat systm can b fn as, ψ tan 1 Rb ρ = ( ) (4.3) ψ Ra Ra Rb ψ = ψ + ψ (4.4) whr ψ s call th magntu of rotor flux lnkag an ρ s th angl of rotor fl flux. Th motor currnts an voltags ar thn rwrttn n th movng coornat systm as, cos ρ = sn ρ sn ρ cos ρ Sa Sb V cos ρ sn ρ V Sa ; = V sn ρ cos ρv Sb (4.5) whr V Sa an V Sb ar motor trmnal voltags n an uvalnt two-phas statonary rfrnc fram., an V, V ar th motor currnts an trmnal voltags n th movng rfrnc fram, along an axs rspctvly. Usng th abov mnton coornat transformaton, a mathmatcal mol of an nucton motor wth stat varabls xprss n movng coornats s gvn by, [19] 71

88 7 θ = ω t (4.6) J T J D t L = ω µψ ω ) ( (4.7) R R R R M L R L R t + = ψ ψ (4.8) S R R p S R R R L V M L R n L L M L R t = σ ψ ω ψ σ γ ) ( (4.9) S R R p p S R L V M L R n n L L M t + = σ ψ ω ψ ω σ γ ) ( (4.30) whr ω s th angular vlocty of th rotor, t ω s angular acclraton, J s momnt of nrta of th rotor, T L s loa toru, an D s coffcnt of frcton. Th lctromagntc toru vlop s thus gvn by, J T µψ =. R S an L S ar stator rsstanc an lakag ractanc rspctvly, whl th motor constants ar fn as, S S S R R L R L L R M + = σ σ γ ) ( an ) ( R p JL M n = µ. (4.31) Ths mol s thn us to vlop an ffctv mtho of control F-Back Control Th ffct of non-lnar trms apparng n th ynamc mol s lmnat usng th hgh-gan fback. For ths, th frst stp s to fn th currnt rfrncs. Dsr rotor acclraton an loa toru wll c how much lctromagntc toru ns to prouc. Th currnt rfrnc * can b assgn to gnrat rur lctromagntc

89 toru. Sconly, as xplan bfor, for th toru an sp ynamcs to rman lnar, ψ shoul b kpt constant. Th scon currnt comman, *, can b assgn th job of kpng ψ constant. Th two currnt rfrncs ar thn gvn by, * D = K 0 ( ωrf ω). t + K1( ωrf ω) + ω / µψ 0 (4.3) J * = Kψ ( ψ ψ + (4.33) I 0 ψ ). t + KψP ( ψ 0 ) 0 Ths nw nputs * an * ar thn gvn PI controllrs to prouc rur motor trmnal voltag rfrncs as blow, * * * V = K ( ) t + K ( ) (4.34) I P * * * V = K ( ) t + K ( ) (4.35) I P By propr choc of proporton an ntgral gans, an can b forc to track thr corrsponng rfrncs. Th rsultant V * an V * commans ar gvn to th nvrtr PWM controllr, to prouc rur swtchng pulss for th IGBTs. Th nw motor trmnal voltags, thus gnrat, wll prouc th lctromagntc toru, ssntal to rv th loa at sr acclraton. At th sam tm th motor trmnal voltags ar such that th rotor flux magntu s mantan constant. Th complt motor control schm s llustrat n Fgur Chaptr Summary In ths chaptr, th control mthos for a front-n convrtr an an nucton motor wr xamn. Th systm ynamcs on ac s an c-s wr scuss wth th hlp of uvalnt crcut rprsntatons. 73

90 s ρ ρ s θ Flux Obsrvr ψ V * V * IDQ V 1 V V 3 Inucton Motor s s θ ω DQ V * * * V = KI ( ) t + K P * ( ) V * * * V = KI ( ) t + K P * ( ) * * ω θ * * * D = K0 ( ωrf ω). t + K1( ωrf ω) + ω / µψ J * = K ( ψ ψ ). t + K ( ψ ψ + ψi 0 ψp 0 ) 0 0 ψ ω rf ψ rf rf Fgur 4.8 Block agram of motor controllr 74

91 Th fback control stratgy for th front-n convrtr was ntrouc nxt. Trackng th angular fruncy of supply voltags was also scuss. Furthr, nputoutput lnarzaton controllr was ntrouc to obtan satsfactory systm prformanc unr varyng c-lnk voltag. For bttr transnt prformanc a f-forwar compnsaton loop was a to th lnarzaton controllr. Th avantags of fforwar compnsaton wr scuss. A block agram of th complt control schm was prsnt, an varous nputs an outputs to th systm wr scuss. Furthr, th nucton motor ynamc mol was analyz. Th fl-ornt control of nucton motor wth hgh-gan fback was scuss. Th control stratgs to achv bttr transnt prformanc scuss n ths chaptr ar us n nxt chaptr to smulat varous scnaros. 75

92 5 Smulaton Rsults 5.1 Chaptr Ovrvw Th prvous two chaptrs ntrouc th thory bhn th rsarch prsnt n ths thss. In ths chaptr, th smulaton rsults wll b prsnt. In Scton 5., a mthoology us n th rsarch wll b prsnt. Th stps prform n smulatng th varous mos of opraton an n valuatng th systm prformanc wll b lst. In Scton 5.3 th smulaton st-up an th softwar confguraton wll b scuss. In Scton 5.4, th actv rv opraton wth an wthout motor loa wll b smulat. Th ffrnt faturs of an actv rv, such as varabl powr factor an bttr control ovr c-lnk voltag wll b vrf. In Scton 5.5, th rv prformanc wll b analyz n tal. Th smulaton ata wll b us to arss sgn ssus, such as vc ratng, powr loss, powr ualty, an thrmal managmnt systm. Furthr, th rv wll b smulat to fn lmts on th amount of ractv powr that can b compnsat. 5. Mthoology us n Rsarch To valuat th prformanc of actv front-n rv by accurat smulatons an to stablsh th lmts on amount of ractv powr that can b compnsat was th man objctv bhn ths work. Th applcaton targt was a 50 hp nucton motor rvng a convyor loa an supplyng maxmum possbl VARs to th utlty. Th broa task was organz nto thr major tasks: 76

93 Prsnt thortcal molng an ffctv control stratgy. Accuratly smulat systm mos of opraton. Analyz systm prformanc from pont of vw of vc ratngs, powr losss, an powr ualty. Th frst stp alt wth rvng th mathmatcal mol of front-n convrtr connct to th utlty. Th - thory prsnt n Chaptr 3 was us to rv th systm mol. Furthr, th ffrnt control prncpls sutabl for npnntly controllng ral an ractv powr suppl to or consum by th rv wr prsnt n Chaptr 4. Bas on ths scussons a comprhnsv control schm was vlop. Th rmanng two tasks, outln abov, ar laborat n ths chaptr Stps Prform n Smulatng Systm Mos of Opraton Th smulatons to monstrat ffrnt mos of opraton wr v n two stags. Durng th frst stag, th loa-s nvrtr an th nucton motor was sconnct from th rst of th systm. Th front-n convrtr was thn controll to prov unty, lang, an laggng powr factor to th utlty, whl c-lnk varatons wr montor. Th magntu of c-lnk rppls an th stp rspons to th ractv powr comman wr us to gaug th ffctvnss of th control schm. Onc th stablty of th controllrs an satsfactory systm rspons was ascrtan, th loa-s nvrtr an motor loa wr connct to th c-lnk. In th scon stag, ffrnt opratng scnaros wr smulat. Ths nclu unty powr factor opraton an ractv compnsaton urng motor acclraton an clraton. 77

94 5.. Stps Prform n Analyzng Systm Prformanc Th task hr was to us th molng an smulatons to analyz th rv prformanc for a gvn applcaton. Th applcaton unr consraton was: actv front-n nucton motor rv provng ractv powr compnsaton to th utlty. Th analyss was carr out wth rgar to: 1. Dtrmnng vc voltag an currnt ratngs.. Amount of ractv compnsaton possbl unr ffrnt loa contons. 3. Dvc powr losss an thrmal sgn consratons. 4. Powr ualty ssus such as total harmonc storton (THD), urng VAR compnsaton. Frst, th applcaton spcfcatons such as motor powr ratng an ln-s powr spcfcaton wr trmn. Approprat c-lnk voltag, capactor an ln-s nuctanc wr chosn. Th lctrcal paramtrs of th nucton motor wr ntf. Accorngly, th motor fl-ornt controllr was carfully tun to prov satsfactory varabl sp opraton. Th nucton motor was acclrat to th full loa, whl ln-s powr factor was mantan at unty. Th currnts carr by th vcs an th voltag wavforms across th vcs wr analyz to trmn th ratngs of IGBTs an ant-paralll os. Onc th swtchs wr slct, th charactrstc curvs of th rspctv swtchs wr mol to stmat th total powr loss. Th ln-s powr factor was mantan at unty an th motor loa was var n stps. Th total harmonc storton of ln currnts an powr losss n actv front-n convrtr wr plott. 78

95 Furthr, th ractv compnsaton comman an th motor loa wr ncras n stps n such a way that pak ln currnt rman blow th rat valu. Th maxmum VAR compnsat at ach stp thus fn th lmt on amount of ractv powr that can b compnsat to th sourc. Ths lmts ar val for a gvn rato of c-lnk voltag to th ln voltag pak, an th currnt ratng of th actv swtchs. To ascrtan th powr ualty at th ln-s, total harmonc storton of ln currnts was calculat n ach stp. 5.3 Smulaton St-up Two thr-phas, two-lvl convrtrs wr n to mplmnt th actv rv confguraton. On of th convrtrs was connct to th thr-phas, wy-connct sourc whl, othr was oprat as a loa-s nvrtr. Th powr lctroncs swtchs mploy n th smulatons wr al IGBTs, wth no forwar voltag rop an almost nstantanous swtchng tms. Th PSIM softwar packag from Powrsm Inc. was us to mplmnt th actv rv confguraton wth motor loa. Fgur 5.1 shows th complt crcut schmatc. Th complt harwar an snsors wr mplmnt n PSIM. Sconly, Smulnk, an xtnson to MATLAB, was us to mplmnt th control functons. Th Smcouplr moul, prov by PSIM was us to ntrfac control an powr sgnals btwn PSIM an Smulnk. Thus harwar confguraton was sparat from th systm control functons. Th smulaton stp-sz n Smulnk an PSIM was chosn to b 1 µs for bttr rsults. All th rfrnc commans for sr opraton an varous control functons wr gnrat n Smulnk. Fgur 5. llustrats th Smulnk mol. 79

96 Fgur 5.1 Th harwar confguraton 80

97 Fgur 5. SIMULINK mol for actv front-n rv control 81

98 5.4 Dmonstratng Systm Mos of Opraton As mnton bfor, two scnaros wr consr to smulat ffrnt mos of opraton. In th frst cas, thr was no motor loa connct to th c-lnk whl n th scon cas, th motor was opratng at full loa. Th front-n convrtr was connct to th thr-phas, wy-connct, 110 V (ln-to-ln), 60 Hz supply. Th srs nuctanc was chosn to b 10 mh. Th c-lnk voltag was mantan constant at 500 V to prov suffcnt margn for currnt control. Th c capactor was 700 µf Wthout Motor Loa In - coornats th ractv powr s gvn by, Q = E (5.1) Snc th sgn of E s chosn to b ngatv, a postv valu rsults n lang ln currnts whl, a ngatv valu causs laggng ln currnts. Fgur 5.3 shows th componnt of ln currnt followng th stp chang n rfrnc comman. Accorngly, th ln-s powr factor changs from unty to lang an thn laggng. Ths s shown n Fgur 5.4. Not th tm rspons to stp chang n compnsaton comman. Th transton from lang to laggng ractv currnt took only a fw mllscons. Fgur 5.5 shows th ffct of compnsaton on c-lnk voltag. Th maxmum rppl magntu was foun to b 5 V, whch s 1% of total c-lnk voltag (500 V). Th currnt rfrnc changs accorng to th c-lnk voltag varatons so that th c-lnk voltag rppl can b kpt to th mnmum valu. Fgur 5.6 shows th componnt of ln currnt trackng th rfrnc. 8

99 Fgur 5.3 componnt of ln currnt trackng th compnsaton comman Fgur 5.4 Rvrsal of ln currnt 83

100 Fgur 5.5 DC-lnk varatons urng compnsaton Fgur 5.6 trackng th rfrnc to mantan constant V c 84

101 On mportant fatur of an actv-front n rctfr s th bttr control ovr clnk voltag. Th stp rspons of th c-lnk controllr to th stp-chang n c-lnk voltag rfrnc, shown n Fgur 5.7, monstrats ths fatur. As can b sn, t took a lttl mor than on cycl (0 ms) for th V c to rach to th nw rfrnc valu. Th chang n c-lnk rfrnc rsult n brf actv currnt componnt for chargng th c-lnk capactor, whl th ractv currnt componnt rman narly unsturb. Fgur 5.8 shows actv an ractv currnt componnts. As can b sn, th couplng control was clarly ffctv. Th ablty of th actv front-n convrtr to smoothly control th c-lnk voltag can b us n mprovng ffcncy of larg powr motor rvs. Tratonally th varabl output powr from motor rv s achv by varyng th moulaton nx an kpng th c-lnk voltag constant. As pont out n [0], th ampltu of moulaton nx affcts th amount of currnt that flows through actv vcs n twolvl PWM nvrtr. Consuntly, at low moulaton ncs th powr loss n th nvrtr s consrably hgh whn compar to output powr rsultng n low ffcncy. Th actv rctfr, on th othr han, can prov varabl output powr by controllng th c-lnk voltag to kp th moulaton nx clos to on. Furthr, th prcntag cor losss n an nucton motor ar mnmz whn th nvrtr s opratng at moulaton nx clos to on [1]. In ths cas an actv frontn convrtr can mprov th ovrall ffcncy of th motor by varyng th c-lnk voltag an allowng th loa-s nvrtr to b oprat at hghr moulaton ncs. Th choc of varabl c-lnk opraton s not avalabl for th rctfr wth phascontroll thyrstors, u to th complxty of control an slow ynamc rspons [1]. 85

102 Fg 5.7 Stp rspons of c-lnk voltag controllr Fg 5.8 Dcoupl control of actv an ractv currnt componnts 86

103 5.4. Wth Motor Loa Th ffctvnss of couplng control also ns to b provn whn opratng unr full motor loa. Ths was on by connctng th loa-s nvrtr to a 110 V, 3 hp, 6-pol nucton motor. Th motor f a convyor typ loa. Th toru for th convyor loa vars lnarly wth angular sp of rotaton. Snc th motor wll b us for a varabl sp opraton, th sp rfrnc, ω, was st as an nput to th motor controllr. For th rctfr controllr, rfrnc was st to prov sr ractv compnsaton urng motor acclraton, clraton, an constant sp opraton. Th motor loa was 40 Nm. Fgur 5.9 shows th sp comman for motor controllr an th ractv compnsaton rfrnc for th rctfr controllr. Th motor was frst acclrat to a sp of 10 rpm (rvolutons pr mnut) n 0.5 scons. Th compnsaton start urng constant sp opraton at tm, t = 0.6 scons. At tm, t = 0.7 scons, th motor bgan clratng. Fgur 5.10 llustrats ln currnt at unty powr factor an latr at lang powr factor wth rspct to th ln voltag. As can b sn n Fgur 5.11, th componnt of ln currnt follow th ractv compnsaton rfrnc whl, componnt prov ral powr rur for acclraton an clraton. Th two currnt componnts rman unaffct by ach othr, thrby llustratng npnnt control ovr ral an ractv powr. Th actual currnts rawn by th motor ar shown n Fgur 5.1 mphaszng halthy opraton of motor. 87

104 Fgur 5.9 Ractv compnsaton an Motor Sp commans Fgur 5.10 Unty an lang powr factor at th sourc 88

105 Fgur 5.11 Dcoupl control urng motorng opraton Fgur 5.1 Motor currnts urng th motor acclraton an clraton 89

106 5.5 Actv Front-En Invrtr Systm Dsgn an Analyss Issus A 50 hp nucton motor was consr to analyz prformanc of an actv front-n rv an to scuss th sgn ssus. Frst stp was to slct systm paramtrs such as convrtr powr ratng, c-lnk voltag, c capactanc, ractanc of ln-s nuctor. Furthr, nucton motor paramtrs n to b ntf to achv satsfactory prformanc from th fl-ornt controllr Systm Spcfcatons Th nucton motor spcfcatons wr: 50 hp, 480 V, 60 Hz, 6-pol, wth bas sp of 100 rpm. Th mchancal loa connct to th motor was convyor typ loa. Th toru for th convyor loa, T L s fn by, T L = K ω Nm (5.) whr, K s a toru constant an ω s motor sp n raans pr scon. Th toru constant s chosn to b ual to.8 so that th mchancal toru at 1100 rpm woul b, π T L = = 3.53 Nm (5.3) 60 Th stay stat motor output powr woul b, P = π mch = kw (5.4) 60 Furthr, th paramtrs for an uvalnt crcut mol of th nucton motor us n th smulatons wr: Stator rsstanc, R s = 0.94 Ω; 90

107 Stator Ractanc, L s = 1.39 mh; Rotor rsstanc, R r = Ω; Rotor Ractanc, L r = 0.74 mh; Magntzng Ractanc, L m = 41 mh; Th motor paramtrs wr assum to b known. In practc howvr, th uvalnt-crcut paramtrs can b stmat usng laboratory tsts []. Th tsts gnrally prform ar a c tst, no-loa tst, an a block rotor tst. Stator rsstanc can b foun by a c tst. Th rmanng paramtrs can b trmn by prformng th no-loa tst an block-rotor tst. Th supply s ha a thr-phas, wy-connct, 480 V (ln-to-ln), 60 Hz sourc. Th c-lnk voltag ns to b chosn as shown n Euaton 5.4, so that th front-n rctfr can gnrat snusoal PWM voltags [1]. Ell V c (5.5) 3 whr E 11 s ln-to-ln supply voltag an V c s c-lnk voltag. A hghr V c s sr, bcaus th voltag rato btwn th E 11 an V c mposs a lmt on amount of ractv powr that can b compnsat [11]. Howvr, hghr V c mans th actv vcs hav a hghr voltag ratng. Th c-lnk voltag s slct to b ual to 1000 V as a tra off btwn ractv compnsaton capablts an th vc voltag ratng. Ths choc obvously satsfs th conton la own by Euaton 5.5. Th ln-s rsstanc, R, was ual to 1 Ω whl, th ln ractanc, L, was chosn as 10 mh. Th c-lnk capactor was slct to b ual to 1000 µf so that c-lnk voltag rppls coul b kpt to th mnmum lvl. 91

108 5.5. Dvc Powr Ratng Consratons To fn vc voltag an currnt ratngs, th nucton motor n to b rvn at full loa. As xplan n Chaptr 4, th K P an K I gans for th fl-ornt controllr wr proprly chosn bas upon th nucton motor paramtrs. Th motor was acclrat to 1100 rpm. Th ln currnt was mantan at unty powr factor wth rspct to supply voltag. Th maxmum voltag that th IGBT an ant-paralll o hav to block s V c (1000 V). As a rsult, th voltag ratng of swtchs n both th front-n convrtr an ln-s nvrtr was slct to b 0% mor than th c-lnk voltag V. It was latr shown that whn th motor loa was var n stps an ractv compnsaton lmt st at ffrnt lvls, th maxmum fluctuatons n c-lnk voltag rman lss than 3% (30 V). Thus, th 0% margn n vc voltag ratng was consr to b suffcnt. For any c-lnk voltag swngs, gratr than 15% (150 V) th convrtr opraton woul b halt. Th pak currnt that flows through th swtchs n front-n convrtr s th pak ln currnt. Fgur 5.13 shows that th pak currnt of 100 A was carr by IGBT an fback o at full loa. Consuntly, th currnt ratng for th swtchs was slct to b 150 A, wth 50% ovrcurrnt margn. Smlarly as sn n Fgur 5.14, for a 480 V motor, th pak currnt to rv a 50 hp loa was 85 A. Ths suggsts th sam vcs us for front-n convrtr can b us for loa-s nvrtr as wll. As a rsult thr s an opportunty for a moular sgn wth smplf assmbly an rpar. 9

109 Fgur 5.13 Currnt flowng through IGBT an ant-paralll o at full motor loa Fgur 5.14 Motor currnts for 3 Nm loa at 1100 rpm (50 hp) 93

110 Furthr, to nsur corrctnss of smulat valus of currnts an voltags, a powr balanc at th sourc an loa s ns to b vrf. Accorngly, powr at th nput an output trmnals of motor s gvn by, N P n = 3 V I cosφ An Pout = π TL (5.6) 60 whr, th motor powr factor s 0.86 an th loa toru, T L = 3.54 Nm. Thus, th ral powr at th nput an output of th motor s, 85 P n = = 4973 W (5.7) 1100 P out = π 3.54 = W (5.8) 60 Th motor coppr losss, cor losss an frcton losss account for th rmanng (P n - P out ) 580 watts. Fgur 5.15 shows ral an ractv currnts. Fgur 5.15 Ral an ractv currnt componnts 94

111 Smlarly powr on th supply s can b calculat. Fgur 5.15 shows th ral componnt of ln currnt to b ual to 119 A, whl th ractv currnt componnt s zro. Rcall that ral an ractv powr n - coornats ar gvn by, P = 3 E I cosϕ = E (5.9) ll Q = 3 E I snϕ = E (5.10) ll From Euaton 5.9 an 5.10, w can wrt, cosϕ = (5.11) + Furthr, th ln-to-ln supply voltag, E ll, s gvn by, ll E = E + E (5.1) Snc, E = 0, th E componnt woul b 480 V. Thus, th ral powr suppl by th convrtr was, P = = 5710 W. (5.13) From Fgur 5.13, th pak ln currnt was foun to b 98 A. So, for th ln s rsstanc of 1 Ω, th powr at th nput of th rctfr, P rct, was, P rct = P 3 I R = = 4714 W (5.14) Bcaus th swtchs us n th smulaton wr all al vcs, thr was no powr loss n th rctfr, c-lnk, or nvrtr. Thus th powr at th nput of rctfr shoul b ual to th powr at th nput of th motor. From Euaton 5.6 an 5.7 w hav P P ( ). Ths llustrats powr balanc btwn sourc an a rct n loa. Th small ffrnc n P rct an P n s an rror n an ln currnt masurmnts. 95

112 5.5.3 Thrmal Managmnt Systm Issus Bas on th voltag an currnt rurmnts for th front-n convrtr, th swtchng vc rcommn was: 100 V, 150 A, IGBT moul (Moul No: CM150DY-4NF) wth bult n fr-whlng o, suppl by POWEREX Inc. Th thrmal loss mol scuss n Chaptr 3 was us to stmat powr losss. Dpnng upon how much hat ns to b sspat, a sutabl thrmal managmnt systm wll b rcommn. Frst, th charactrstc plots for th slct vc wr mol n MATLAB. Fgur 5.16 shows IGBT collctor-mttr saturaton voltag charactrstcs prov n vc atasht whl, Fgur 5.17 shows th actual charactrstcs mol n MATLAB usng curv-fttng tchnus. In a smlar way, IGBT swtchng loss charactrstcs, fr-whlng o forwar, an rvrs rcovry charactrstcs wr also plott. Th swtchng loss curvs prov n th vc ata-sht assum a common clnk voltag of 600 V. Morovr, th swtchng nrgy s xprss n unts of mj/puls. Th trm, Puls, consttuts on pro of a swtchng cycl. So th actual swtchng losss for a 1000 V c-lnk voltag an a swtchng fruncy of 4 khz wr calculat as [15], 1000 E sw _ on = Esw _ onrat f sw W (5.15) E sw _ off = Esw _ offrat f sw W (5.16) 600 whr, E sw_onrat an E sw_offrat ar swtch-on an swtch-off nrgy losss n mj pr puls at 600 V. 96

113 Fgur 5.16 IGBT collctor-mttr charactrstcs prov by th vc ata-sht Fgur 5.17 IGBT collctor-mttr curv mol n MATLAB 97

114 To stmat th maxmum hat sspaton, th front-n convrtr was oprat to th full capacty at unty powr factor. Th conucton an swtchng losss for on IGBT moul at th pak ln currnt of 98 A ar shown n Fgur Th conucton an rvrs rcovry losss n th fr-whlng o ar shown n Fgur Th avrag total powr loss pr swtchng vc (IGBT + o) s gvn by, P L = ( PCon _ o + PCon _ IGBT) + ( PSWon _ IGBT + PSWoff _ IGBT + PRR _ o) (5.17) From Fgur 5.18 an 5.19, th avrag powr loss pr vc, P L, was: P L = = 94 W (5.18) Th amount of hat that can b takn away from th vc juncton to ambnt s gvn by [3], P L T T = (5.19) R R j a θ jc + Rθ cs + θsa whr, R θjc s th vc juncton-to-cas thrmal rsstanc, R jcs s th cas-to-hat snk thrmal rsstanc, an R θsa s th hat snk-to-ar thrmal rsstanc. Th thrmal rsstanc s xprss as C/W. From th vc ata-sht, R θjc s 0.5 C/W an R jcs s C/W. Th maxmum juncton tmpratur rcommn s 15 C. Consrng th worst cas ambnt tmpratur of 50 C, w can calculat R θsa as, = ; Thus, R θ sa = C/W (5.0) R θsa It s not possbl to gt an approprat sz hat snk wth natural convcton whch provs R θsa as low as 0.45 C/W [3]. Thus for ths applcaton, a hat snk wth forc ar coolng s rcommn. 98

115 Fgur 5.18 IGBT powr losss at pak loa Fgur 5.19 Fr whlng o powr losss at pak loa 99