Comparative Analysis of Stator Resistance Estimators in DTC-CSI Fed IM Drive

Transcription

1 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// Comarativ Analyi of Stator Ritanc Etimator in DTC-CSI Fd IM Driv M.Sivakumar 1, T.Thanakodi 2, N.Pannr Slvam 3 1,2 Valivam Dikar Polytchnic Collg, Nagaattinam, Tamilnadu , India. 3 M..A.M.Polytchnic Collg, Trichiraalli, Tamilnadu , India. Abtract Stator ritanc i th mot imortanc to timat torqu, flux in dirct torqu controlld norl d controlld induction motor driv. During low d oration tator ritanc invitably vari du to tmratur and low frquncy. For tabl and accurat oration at low d rquir an aroriat on-lin idntification algorithm for th tator ritanc. Thi ar rood to analyz tator ritanc timation by uing roortional intgral (PI) and MRAS chm in CSI fd Induction motor driv with dirct torqu control during low d oration. Th rformanc of th two control chm ar valuatd in trm of torqu, Sd and flux. Th analyi ha bn carrid out on th bai of th rult obtaind by MATLAB/imulink and hardwar imlmntation. Kyword: Currnt ourc Invrtr, Dirct torqu control, Snorl Sd, Stator ritanc timation, Digital ignal rocing. INTRODUCTION HIGH-POWER mdium-voltag driv alication [1], th currnt-ourc invrtr (CSI) fd driv ar ud incraingly. Th currnt ourc invrtr having iml convrtr toology, inhrnt four-quadrant oration, rliabl fu l hort circuit rotction, and motor frindly wavform (with low dv/dt). Furthr imrov th ytm rformanc, rarch ffort on CSI fd driv hav bn rcntly ut on nw currnt-ourc driv toology, advancd modulation chm dvlomnt [2] [7], control rformanc [8] [11], and fficincy [12], [13], tc. DTC i rcntly dvlod in indutrial driv du to gnrating fat torqu ron. In DTC, th tator ritanc i ud to timat th tator flux [14], [15]. Th tator ritanc i varying du to chang in tmratur and low frquncy; mak th ytm bcom untabl at low d. An accurat valu of th tator ritanc i of crucial imortanc for corrct oration of a norl driv in th low d rgion, inc any mimatch btwn th actual valu and timatd valu may lad not only to a ubtantial d timation rror but to intability a wll [16]. A a conqunc, numrou on-lin chm for tator ritanc timation hav bn rood in rcnt at [16-27]. In thi ar th PI and MRAS bad comnation of tator ritanc ar analyzd for DTC-CSI fd induction motor during low d oration and it rformanc rult ar vrifid by oftwar and hardwar. SYSTEM CONFIGURATION AND CONTROL Figur 1 how th main circuit of th DTC-CSI-fd induction motor driv. L L and C L ar th inductanc and caacitanc of th lin filtr and C M i th filtr caacitanc in motor id. L d i a moothing inductor which i to minimiz th currnt baring roblm of th motor driv [28]. Both th rctifir and th invrtr ar controlld with PWM and dirct torqu controllr (DTC) rctivly. Th lin id rctifir, lft art in Figur 1 ha to control th dc link currnt via th lin id dc link voltag. Diturbanc valu i th machin id dc link voltag, roducd by th induction machin via th invrtr, right art in Figur 1. Th control rformanc i baically influncd by th dc link inductanc. Th machin id invrtr ha to control th currnt in th motor to adjut th motor torqu to th rfrnc valu. Thi i mainly a ha control, a th currnt amlitud in th machin i givn according to th amlitud of th dc link currnt controlld by th rctifir. Figur 1. Currnt ourc convrtr induction machin driv 12364

2 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// Flux, Torqu timation Th functional block diagram of th Snorl vctor controlld driv i hown in Figur 2. It hown that th vctor control algorithm rquir rotor flux oition θ f, which can b timatd from th tator flux ac vctor, i timatd uing V Ri dt (1) Whr V and i ar th tator voltag and currnt ac vctor. Surcrit indicat that th variabl ar rfrrd to tator axi. Th rotor flux vctor, λr i obtaind by ubtracting th lakag flux from th tator flux vctor a in L (2) m r V R L Lr Whr 1 L 2 m L L r i σ L L Lakag factor Stator lf Inductanc Rotor lf Inductanc and L m - magntizing inductanc, Th rotor flux, rotor oition angl, Torqu i timatd from th tator voltag and currnt. 1 d f tan (3) q 3 T i 2 d q i q d Th availabl tator ritanc on-lin idntification chm can b claifid into a coul of ditinct catgori. In gnral, all th mthod rly on tator currnt maurmnt and rdominantly rquir information rgarding tator voltag a wll. A illutratd in Figur 2 th outut of th flux and d controllr ar th ynchronou fram d-axi tator currnt Rfrnc (I* d ) and th rfrnc torqu (T * ), rctivly, whr th torqu ubquntly gnrat th q- axi tator currnt rfrnc (I* q ). Aftr th motor-id caacitor currnt comnation, th command invrtr currnt in th ynchronou d q fram (I dw, I qw) ar obtaind, which i gnrat th dird dc-link currnt (i* dc ) and th invrtr witching angl (θ f). Th CSI outut currnt magnitud i rgulatd by controlling th dc-link currnt through th CSR, whil th CSI orat with DTC witching tabl. Th torqu rror and an adjutabl ha angl θ inv ar th inut of witching tabl. (4) Figur 2. Functional block diagram of vctor control CSI driv bad for rood configuration. Sd Etimation Th motor d timatd from th following (5) r Whr l ω = Stator frquncy in rad/c ω l = li frquncy in rad/c Th motor aramtr mloyd in th control ytm may dviat from th ral on. CSI-fd motor driv hav filtr caacitor connctd at th outut of th invrtr. Thi man that a ortion of th invrtr currnt go through th caacitor. Th influnc of th filtr caacitor on th ytm control i invtigatd in thi ction. Th invrtr rfrnc currnt can b xrd a follow [29]: * dw i * qw i i cd cq i * d * q i i (6) whr i cd and i cq ar th timatd caacitor d, q-axi currnt. To rduc th nitivity and noi caud by th drivativ trm, th timatd caacitor currnt ar uually imlifid a follow: i V cd cq d q C f f i V C (7) Whr C f, ω, v d, and v q ar th invrtr-id filtr caacitanc, motor lctrical angular frquncy, and tator d- axi and q-axi voltag, rctivly

3 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// DIRECT TORQUE CONTROLLER PRINCIPLE Th baic rincil of DTC i to lct tator currnt vctor according to th diffrnc btwn th rfrnc and actual torqu and flux linkag. Stator flux and rotor flux ar timatd from th Equation (8) (9), and (10) taking th intgral of diffrnc btwn th inut voltag and th voltag dro acro th tator ritanc a, d Vd Rˆ iddt (8) q Vq Rˆ iqdt (9) L m r V R L Lr Whr - d-axi flux linkag. d - q-axi flux linkag. q Rˆ P i ˆ (10) - timatd tator ritanc. - numbr of ol air and thn calculat th flux amlitud and find th ctor of 60 dgr in α-β lan whr flux vctor rid, according to th artition hown in Figur 3. In that ca ix intrval of 60 dgr can b dfind in which th currnt and th voltag chang it valu. In vry intrval th currnt from DC link flow through two invrtr lg and two motor ha winding. Figur 3. Sctor in lan whr rotor flux rid From th tator outut currnt and voltag, ur intgrator in (1) and (2) yild flux vctor. Th trajctory of flux i xactly circular, it i imortant to not that th dynamic of tator flux timation do not dnd on th ron of th offt timator. any chang in tator ritanc giv wrong timation of tator flux and conquntly of th lctric torqu and th tator flux oition. An rror in tator flux oition i mor imortant a it can cau th controllr to lct a wrong witching tat which can rult in failur of th controllr. At high d, th tator ritanc dro I*R i mall and can b nglctd. If incra tator ritanc th tator currnt, flux and torqu ar ocillatd. So a mimatch btwn th t valu and actual valu can crat intability. So th aramtr mimatch btwn th controllr and motor mak th driv ytm untabl. So th tator ritanc comnation i ntial to ovrcom intability in DTC controlld IM driv ytm. Stator Ritanc Comnation An obrvr ha bn dignd to timat th chang in th actual tator ritanc during oration of th machin. Th timator obrv if any chang i dtctd, a corronding chang in th tator ritanc i mad. Th availabl tator ritanc on-lin comnation chm can b claifid into a coul of ditinct catgori. Th tator ritanc on-lin comnation mthod i by far th mot frquntly mt and it includ all th timator whr an udatd tator ritanc valu i obtaind through an adativ mchanim. Proortional intgral (PI) or intgral (I) controllr ar ud for thi uro. In MRAS bad ytm th rotor flux timatd from th rfrnc modl and adativ modl which i ud to timat th tator ritanc. Thi ar analy th tator ritanc on-lin comnation on PI control and MRAS control chm, a dicud blow. PI Stator Ritanc Etimator Th block diagram of PI tator ritanc comnator i hown in Figur 4. Th rror in th tator flux i ud a an inut to th PI timator. Th tchniqu i bad on th rincil that th chang in tator ritanc will cau a chang in tator currnt and tator flux linkag λs. Th rror btwn th tator flux linkag λs and it rfrnc * S i roortional to th tator ritanc chang. Th quation for PI ritanc timator i givn by R K K I 1 (11) Whr, K P and K I ar th roortional gain and intgral gain of th PI timator. EFFECT OF STATOR RESISTANCE VARIATION In DTC, th tator flux and rotor flux ar timatd uing th Equation (1) and (2) rctivly. Th variation of R may influnc th calculation of tator flux ignificantly and thrby th ovrall rformanc of th DTC ytm. At low d, th back EMF trm i mall, and th ritiv dro R S*I S i comarabl with th uly voltag magnitud V S. Thrfor Figur 4. Block Diagram for PI Stator ritanc comnation

4 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// Th rror btwn th timatd tator flux and it rfrnc S* i ad through a low a filtr with a vry low cutoff frquncy in ordr to attnuat high frquncy comonnt containd in th timatd tator flux. Thi filtr tim contant hould b mall comard to th tator ritanc timator tim contant to ovrcom it ffct on th tator ritanc adatation. Thn th ignal i ad through a PI timator. Th outut of th PI timator i th rquird chang of ritanc R S du to chang in tmratur or frquncy. Th chang of tator ritanc R S i continuouly addd to th rviouly timatd tator ritanc R S(K-1) Th final timatd tator ritanc R ˆS i again ad through a low a filtr to hav a mooth variation of tator ritanc valu. Thi udatd tator ritanc can b ud dirctly in th controllr. MRAS Bad Control Th rotor d and tator ritanc timation chm i dignd bad on th conct of hyr tability [30] in ordr to mak th ytm aymtotically tabl. For th uro of driving an adatation mchanim it i valid to initially trat rotor d a a contant aramtr, inc it chang lowly comard to th chang in rotor flux. Th tator ritanc of th motor vari with tmratur, but variation ar low o that it can b tratd a a contant aramtr, too. Th configuration of th rood aralll rotor d and tator ritanc i hown in Fig. 5 and i dicud in dtail nxt. In thi ar to analyz th d timator i originally rood in [41] and illutratd in Figur 5, whr th two lfthand id block rform intgration of Equation (7) and (8). Th rfrnc (voltag) modl and adjutabl (currnt) modl ar drivd by th tator voltag and currnt. Th timator orat in th tationary rfrnc fram (α) and it i dcribd with th following quation [41]: L i ˆ m rv V Rˆ L (12) Lr ˆ L 1 m i j ˆ T ˆ r T (13) r K I ˆ K (14) rv ˆ ˆ ˆ ˆ ˆ ˆ (15) rv rv A ymbol ^ dnot in (12) - (15) timatd quantiti, ymbol tand for d/dt, T r i th rotor tim contant and 2 1 Lm / L Lr. All th aramtr in th motor and th timator ar aumd to b of th am valu, xct for th tator ritanc (hnc a hat abov th ymbol in (12)). Undrlind variabl ar ac vctor, and ub-crit V and I tand for th outut of th voltag (rfrnc) and currnt (adjutabl) modl, rctivly. Voltag, currnt and flux ar dnotd with v, i and λ, rctivly, and ubcrit and r tand for tator and rotor, rctivly. Figur 5. Structur of th MRAS ytm for aralll rotor d and tator ritanc timation. A i vidnt from (12)-(15) and Figur 5, th adativ mchanim (PI controllr) rli on an rror quantity that rrnt th diffrnc btwn th intantanou oition of th two rotor flux timat. Th cond dgr of frdom, th diffrnc in amlitud of th two rotor flux timat, i not utilizd. Th aralll rotor d and tator ritanc MRAS timation chm, which will b dvlod, will mak u of thi cond dgr of frdom to achiv imultanou timation of th two quantiti. Th rol of th rfrnc and th adjutabl modl will b intrchangd for thi uro, inc th rotor flux timat of (13) i indndnt of tator ritanc. Lt R S and r dnot th tru valu of th tator ritanc in th motor and rotor d, rctivly. Th ar in gnral diffrnt from th timatd valu. Conquntly, a mimatch btwn th timatd and tru rotor flux ac vctor aar a wll. Th rror quation for th voltag and th currnt modl outut can thn b writtn a; Lr V R Rˆ i (16) Lm V rv rv V j V ˆ (17) I I 1 j I j ˆ ˆ T (18) r I j I ˆ (19) Symbol rv, ˆrV in (17),, ˆ in (19) tand for tru valu of th two rotor flux ac vctor which i obtaind from rfrnc modl (V S-I S) and adativ modl (ω-i S) rctivly. From quation (14) and (15) Th adativ mchanim for ω i obtaind and for R S timation K ˆ IR K R (20) R R R i ˆ ˆ i (21) rv rv ar rood by Poov hyr tability thory

5 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// RESULTS Simulation Rult A aml of imulation rult ar rntd hr. Simulation rult for a DTC ytm with ritanc timator wr obtaind uing a 50-h four-ol, induction machin. Th machin aramtr ar hown in Andix 1. Th rntd imulation rult wr mad uing MATLAB / Simulink oftwar ackag. Th nor l DTC- CSI fd induction motor driv i oratd with low d with fat load chang i hown in Figur (6), i influnc of inaccurat valu of tator ritanc. Th timation rror i high and untabl in tady tat and bcom highr at oint of load chang. Th imulation rult of th rntd control ytm with PI and MRAS timatd tator ritanc tuning i hown in Figur (7) and (8) rctivly. Th actual and rfrnc d, torqu, tator currnt and rotor flux ar rntd in Figur (7) and (8). Th timation rror i vry mall and tabl in tady tat and bcom lowr comard with tator ritanc timator i turnd off at oint of load chang (d) Figur 6. Without R Etimator Rotor Flux Stator Currnt Rotor Sd (d) Torqu From th rformanc of th two timator, it i obviou that th MRAS-bad ritanc timator giv bttr tracking than th PI-bad ritanc timator. Figur 9 how th actual and timatd tator ritanc of th machin with PI and MRAS timator mthod. In both mthod, th timatd tator ritanc follow vry cloly to th actual tator ritanc of th machin. Th MRAS timator i abl to timat th ritanc chang bttr than th PI timator. Exrimntal Rult Figur.10 how a low-owr rototy ytm i contructd for xrimntal vrification with ky aramtr litd in Andix 2. Although th rating of th laboratory rototy i lowr than th ractical high-owr driv, thir ky aramtr ar imilar. All maurd and controllr intrnal variabl ar accibl through th rial link to th PC

6 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// (d) Figur 7. With PI Etimator Rotor Flux Stator Currnt Rotor Sd (d) Torqu A dc motor i could to th haft of th induction machin. It i ulid by a dc driv to gnrat th t load torqu. Th dirct torqu controllr and ritanc timator wr imlmntd with a ingl board comutr that u a 16-b TM320C14 digital ignal rocor (DSP). A 3-h 420-V induction machin wa ud in th xrimnt. Th tator ritanc of th machin, calculatd from tt on th machin, wa found to b 0.435Ω. Th machin currnt and th dc bu voltag wr intrfacd into th controllr through an analog-to-digital convrtr (A/D) built into th DSP board. Th A/D and th multilxr availabl wr vry low. Th command torqu and command tator flux ud ar 11 Nm and 0.4 wb, rctivly. Th tator currnt vctor at th valu of command torqu and command flux wa found to b 10.4 A. Th dirct torqu controllr and th ritanc timator wr rogrammd in ambly languag. In actual orating condition, th rat of chang of tmratur i vry low and o th tator ritanc chang. Practically tator ritanc chang in a nonlinar mannr. (d) Figur 8. With MRAS Etimator Rotor Flux Stator Currnt Rotor Sd (d) Torqu Figur 9. R Etimation A linarly incraing ritanc i imulatd and Figur 13. Figur 11 and 12 how that th tator currnt, Sd and Torqu ron of CSI fd Induction motor driv with a tator ritanc comnatd by PI and MRAS rctivly

7 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// Figur 10. Exrimntal tu Figur 12. Exrimntal rult with MRAS Etimator Stator Currnt Rotor Sd (200rm-10rm) Torqu Figur 11. Exrimntal rult with PI Etimator Stator Currnt Rotor Sd (200rm-10rm) Torqu Figur 13. R timation with PI and MRAS Control whn incra linarly

8 Intrnational Journal of Alid Enginring Rarch ISSN Volum 13, Numbr 15 (2018) Rarch India Publication. htt:// CONCLUSION Th tator ritanc ha bn timatd by uing PI controllr and MRAS controllr and rformanc of controllr analyzd during low d oration of CSI fd driv. Th imulation and xrimntal rult how that both timator ar abl to comnat for th chang in tator ritanc. Th MRAS ritanc timator howd a bttr rformanc than th PI timator. Alo, robutn and ability to orat th controllr with MRAS ritanc timator at vry low d ha alo bn hown xrimntally. APPENDIX 1 INDUCTION MOTOR PARAMETERS Ratd Powr Ratd Voltag :50 h : 460 V Stator Ritanc : Ω Stator Inductanc : 35.5 mh Rotor Ritanc : Ω Rotor Inductanc : 35.5 mh Mutual Inductanc : 34.7 mh Momnt of inrtia : kg.m 2 Friction co fficint Numbr of ol : 4 : 0.1 N.m./rad APPENDIX 2 KEY PARAMETERS OF THE EXPERIMENT SETUP Ratd Powr Ratd Voltag REFERENCES :3 h :208 V Stator Ritanc :0.435 Ω Rotor Ritanc :0.816 Ω Stator Inductanc :71.31 mh Rotor Inductanc :71.31 mh Mutual Inductanc :69.31 mh Momnt of inrtia :0.089 kg.m 2 Friction co fficint Numbr of ol :4 :0.005.m./rad [1] Johi, R.R., Guta, R.A & Wadhwani A.K.,2007, Exrimntal Invtigation on Rid through Caability of Clod Loo Controlld Matrix Convrtr Fd Cag Driv, IETE Tchnical RviwVolum 24, Iu 2. [2] Big, R and Ranganathan, V T., 2002 A novl CSIfd induction motor driv, IEEE Tran. Powr Elctron., vol. 21, no. 4, , [3] Ojo,,O and Vanaarthy, S,2004., Carrir-bad dicontinuou PWM modulation for currnt ourc convrtr, in Conf. Rc. IEEE IAS Annu. Mt. 2004, Oct. 3 7, vol. 4, [4] Halkoaari, T and Tuua, H., 2002 Otimal vctormodulation of a PWM currnt ourc convrtr according to minimal witching lo, in Proc. IEEE PESC, [5] Wichmann, E. P., Burgo, R. P., and Holtz J.,2003., Activ front-nd convrtr for mdium-voltag currnt ourc driv uing quntial-amling ynchronou ac-vctor modulation, IEEE Tran. Ind. Elctron., vol. 50, no. 6, , Dc [6] Holtz J and Oikonomou N.,2007., Synchronou otimal ul width modulation and tator flux trajctory control for mdium-voltag driv, IEEETran.Ind.Al.,vol.43,no.2, ,Mar./Ar [7] Li, Y. W., Wu, B., Xu D., and Zargari N.,2008 Sac vctor qunc invtigation and ynchronization mthod for activ front-nd rctifir in high-owr currnt-ourc driv, IEEE Tran. Ind. Elctron., vol. 55, no. 3, , [8] Rodr ıguz, J., Mor an, L., Pontt, J., Oorio, R., and Kouro, S.,2003, Modling and analyi of commonmod voltag gnratd in mdium voltag PWM CSI driv, IEEETran. PowrElctron.,vol.18,no.3, [9] Nikolic and Jfinic B.,2004, Sd norl dirct torqu control imlmntation in a currnt ourc invrtr fd induction motor driv, in Proc. IEEE PESC, vol. 4, [10] R, S. and Ammann U.,2004., Nw tator voltag controllr for high d inductionmachin fd by currnt-ourc invrtr, in Proc. IEEE PESC, Jun , vol. 1, [11] Pankaj Swarnkar, Shailndra Kumar Jain and Nma, R.K.,2014 Adativ Control Schm for Imroving th Control Sytm Dynamic: A Rviw, IETE Tchnical Rviw, Volum 31, Iu 1, [12] Suh Y., Stink J., and P. Stimr, 2006, A tudy on fficincy of voltag ourc and currnt ourc convrtr ytm for larg motor driv, in Proc. 37 th IEEE Powr Elctron. Sc. Conf., [13] Wichmann E. P., Aquvnqu P., Burgo R., and Rodriguz J.,2008, On th fficincy of voltag ourc and currnt ourc invrtr for highowrdriv, IEEETran.Ind.Elctron.,vol.55,no.4, [14] Habtlr, T. and Divan, D.,1991, Control tratgi for dirct torqu control of induction machin uing dicrt ul modulation, IEEE Tran. Ind. Alicat., [15] Rajahkara K., Kawamura A., and Matu K.,1996 (ditor), Snorl control of AC motor driv, IEEE Pr. [16] Pannr Slvam N., and Rajakaran V, 2014 High Prfomanc oration of DTC-CSI fd IM Driv at low d with On Lin Stator ritanc 12371

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